ICEF9- 2004 International Conference Engineering and Food

DRYING OF YEAST IN SPOUTED BED: FLUID DYNAMIC STUDIES

Alsina, O L.S(4), Rocha, A. P. T. (1), Silva, V.S. (2),Silva, F.L.H.(3),

(1) Sc Dr student. Federal University of Campina Grande, PB, Brazil
anatrindader@uol.com.br
(2) Sc Dr student. Federal University of Campina Grande PB, Brazil
vimario@uol.com.br
(3) Federal University of Campina Grande PB, Brazil
flhs@deq.ufcg.edu.br
(4) Federal University of Campina Grande PB, Brazil
odelsia@deq.ufcg.edu.br

ABSTRACT

A study related to the drying of yeast in spouted bed of inert particles was carried out. It was
observed that the presence of yeast affects the fluid dynamic parameters: the maximum pressure drop
and the minimum spouting pressure drop were lower than in the situation with inert particles only.
Regarding to the minimum spout velocity, no significant variation was observed when the proportion of
yeast to the mass of polystyrene particles was increased.

Key words: drying, yeast, fluid dynamics, spouted.

INTRODUCTION

The yeast is obtained as a byproduct of fermentation in the sugar cane and alcohol industry.
Brazil is the biggest worldwide producer of sugarcane alcohol, with a production estimated at 12
billions of liters per year [1]. Getting this position Brazil became a privileged country regarding to the
utilization of the byproducts obtained in the sugar cane processing, just like the yeast. Yeast, among
other uses, may be an ingredient of animal food as a protein source. It is also reach in vitamins,
especially complex B, useful for palatability.
In order to be used as a food additive, yeast must accomplish some specifications such as
protein and moisture content, granulometry and color. The yeast from distilleries must be processed
before use, to eliminate impurities but especially to reduce their water content to get the commercial
specifications. Some works have been developed in the last years about the drying of yeast.
Grabowski et al [2] studied in experimental laboratory scale the drying of yeast in fluidized and
spouted bed. Based on the characterization results the authors suggested a process starting with
fluidized bed and then, followed by spouted bed drying . Morris and Freire [3] developed a spouted
bed with inert particles equipment to study the drying of bakery yeast past. Operational problems due

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ICEF9- 2004 International Conference Engineering and Food

to the particles agglomeration were found for high feeding rates. Changes in the physical properties of
the yeast were assumed as responsible for this behavior.
This work deals with the influence of the yeast on the fluid dynamic variables in a spouted bed
dryer, specifically the minimum spout velocity, which was considered essential in the initial phase,
because through this results it was defined the air flow rate range to be used in the yeast drying
experiments.
To design a spouted bed it is necessary the previous knowledge of the maximum spoutable
depth on the bed and the fluid dynamics parameters: maximum pressure drop, minimum spouting
pressure drop, minimum spout velocity and the characterization of the particle system.
The transition mechanism of the fixed bed to the conventional spouting was described by
Mathur and Epstein [4], through the characteristic pressure drop curve as a function of the gas
velocity. The maximum pressure drop (∆PM) is a parameter of fundamental importance in the spout
bed industrial units projects, because based on it we can specify the blower power needed to break
out the surface of the bed. The minimum spouting pressure drop (∆PSM) is the pressure drop in the
developed and constant stable spout. This parameter provides the energy used during the spout
operation. The minimum spouting velocity (UjM) was defined by Mathur and Epstein [4] as the lowest
velocity for the spout to exist. This parameter depends on the particles and solid physical properties
and on the bed geometry as well.

EXPERIMENTAL
The raw-material used in the dryer feeding was the pressed commercial Saccharomyces
cerevisiae yeast. With 70% ( wet basis) moisture content and sieved to a particle diameter of 0.833
mm. As inert material, it was used polystyrene particles, whose characterization and some properties
are listed in the Table 1.
Table 1 – Polystyrene Physical Properties
Dv 0.3260 cm
ρ1 0.6511 g/cm3
ρs 1.0450 g/cm3
εl 0.411
φ 0.8673
Ap 2101.6 m-1

source: ALSINA et alli (1996)

The spouted bed dryer, shown in Figure 1, is constituted by an acrylic conical base, with a 60
0
C internal angle, fixed to a cylindrical column also made of acrylic, with a 10.3 cm internal diameter
and a 25.3 cm height.
At the top of the column above the bed a deflective screen impede the gross particles
entrainment allowing the yeast fines passage to be collected at the lateral cyclone. Thermocouples
and pressure probes were at the bottom and top of the bed for measuring the pressure drop and air

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ICEF9- 2004 International Conference Engineering and Food

temperature during the experimental runs. The feeding of yeast was made by gravity at the top of the
column.

Figure 1 – Experimental equipment: Spouted bed dryer

The characteristic curve of the spouted bed refers to the pressure drop measured as a
function of the air velocity. The determination of the characteristic curves was carried out with the inert
particles mass fixed in 250g, which corresponds to 8 cm in the height of the drying column. The yeast
fed mass proportion varied in 2%, 4% and 6% of the inert particle mass. Once the spouting was
established, the bed was fed with yeast by gravity at the top of the column. Immediately after the
feeding, the dryer was turned off and the valve that controlled the air input in the bed was closed. The
air velocity was continuously increasing and the corresponding pressure drop registered. This
procedure was performed to a total valve opening. The registered ∆PSM corresponded to the onset of
stable spouting. The opposite procedure started varying the air flow rate very carefully to obtain the
returning curve. During the process of obtaining the pressure drop characteristic curves, the
temperature was maintained around 45 ºC. The pressure drop at the distributor was subtracted from
the total drop to just obtain the bed pressure drop. The same procedure was used to obtain the
characteristic curves for the spouted bed without yeast.

RESULTS AND DISCUSSION

In the Figure 2 the pressure drop curve as a function of the air increasing velocity is presented
for a fixed bed height of 8 cm and variable yeast to inert particles ratio. By comparing in the figure the
characteristic curves for quantities of fed yeast 0, 2, 4 and 6% it is observed that the presence of yeast
decreases in a large extent the maximum pressure drop. For a ratio of inert/yeast 2, 4 and 6% it was
observed a maximum pressure drop of a half, in relation with the bed of inert particles without yeast.

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ICEF9- 2004 International Conference Engineering and Food

1800
ML/MI = 0%
1600
ML/MI = 2%
ML/MI = 4%
1400 ML/MI = 6%

1200 Drying time:0 min

Pressure Drop (N/m )

2
1000

800

600

400

200

0
0,00 0,05 0,10 0,15 0,20 0,25
air velocity (m/s)

Figure 2 – Pressure drop as a function air velocity (increasing)

However, with the presence of yeat, in spite of a decreasing maximum pressure drop with the
yeast concentration, the variation is not so significant as in the former case (with and without yeast). It
is also observed in the Figure 2 that the maximum in pressure drop occurs at greater air velocities
than in the case without yeast. This fact would be related to a better solids circulation, that would
facilitate the gas flow, reducing the resistance and occurring in this way, a smaller pressure drop. This
behavior is different from that observed with fruit pulp, where the addition of pulp was accompanied by
instabilities in the fountain associated with higher pressure drop at the pick. Lima[5] observed that,
with the increasing percentage of West Indian cherry pulp fed in the spout bed dryer, the maximum
pressure drop increased showing a behavior opposite to the yeast’s. Silva [6] found similar results to
those obtained in this work, in spouted beds formed by a mixture of particles: gross, with spoutable
characteristics, and the fines, floated and entrained across the bed. For the characteristic curves in
function of the air decreasing velocity, show in the Figure 3, it was verified that the determination of
the Ujm from these curves is submitted to uncertainties due to the difficulty in observing the region
where the collapse of the spout happens. However, it was observed in the Figure 3 that there wasn’t a
significant variation of the UjM with the presence of yeast and even with the yeast proportion
increasing. A similar result was found by Silva[6] working with a bed made by polystyrene particles
and maize flour. In all the conditions studied by the author, there wasn’t variation of the UjM.

600
ML/MI = 0%
550
ML/MI = 2%
500 ML/MI = 4%
ML/MI = 6%
450 Drying time: 0 min
400
Pressure drop (N/m )
2

350
300
250
200
150
100
50
0
0,00 0,05 0,10 0,15 0,20 0,25
air velocity (m/s)

Figure 3 – Pressure drop as a function of the air velocity (decreasing)

It is known that the UjM is affected directly by the particles bed height. Analyzing the bed height
formed by the mixture of particles in this work it was observed that this is predominantly formed by

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ICEF9- 2004 International Conference Engineering and Food

particles of greater diameter, i.e., the fine particles quantity (yeast) present in the mixture doesn’t
affect significantly the bed geometry, justifying the Ujm practically independence with the yeast
weighed fractions. However, a week increasing tendency can be observed in Table 2, with the
presence of a maximum at 4 % of yeast. This maximum corresponds clearly to a minimum in the
minimal spouting pressure drop. This behavior can be associated to the influence of two opposite
effects: on one side, the presence of yeast in moderate quantities, facilitates the solids circulation,
acting as a “ lubricant” in the interstices of the gross polystyrene particles; otherwise, higher fines
quantities may obstruct the air flow, decreasing the bed porosity and compensating the “lubricant”
effect. This behavior was already observed by Silva[6] and Alsina et al.[7] . The “lubricant” effect was
also used to explain [8], observations in the fluid dynamics of a spouted bed of inert particles with
“umbu” pulp
This difference regarding to the fruit pulp and similar to the particles mixture is because, in the
case of fruits, the fed pulp adheres to the inert particles. According to what Medeiros [9] observed,
there is the formation of solid bridges that would be the main responsible by the effects observed
about the fluid dynamics. In the case of yeast, however, there was no adherence and/or formation of a
film on the inert particles, what would justify the behavior exactly like the one observed by Alsina et
al.[10] with mixture of no sticky particles.
TABLE 2 – Fluid dynamic parameters as a function of the yeast proportion
MY/M ∆PM ∆PSM USM
%i (N/m2) (N/m2) (m/s)
0 1649.5 399.1 0.170
2 610.3 210.4 0.185
4 531.7 169.3 0.192
6 524.7 190.0 0.178

CONCLUSIONS

The presence of yeast modifies the fluid dynamic parameters on the spouted bed. The
maximum pressure drop (∆PM) decreases with the increasing of the MY/MI, proportion. The same
tendency was found for the ∆PSM , but a minimum was observed. Regarding to the USM there wasn’t
significant variation with the proportion of yeast increasing, but a feeble increasing tendency can be
noticed, with the presence of a maximum at the level of 4% of yeast, corresponding to the minimum in
∆PSM .
REFERENCES

[1] GHIRALDINI, J.A., FILHO, D.L. and ROSSEL, C.E.V. Estudos de otimização da
recuperação de biomassa de levedura em destilarias, In: ITAL Instituto Tecnológico de
Alimentos. Produção de Biomassa de levedura: Utilização em Alimentação Animal.
Workshop, Campinas – SP, p 59-63 , 1996

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ICEF9- 2004 International Conference Engineering and Food

[2] GRABOWSKI, S.; MUJUMDAR, A.s.; RAMASWAMY, H.S. and STRUMILLO, C.

Evaluation of fluidized versus spouted bed drying of backer’s yeast. In: Drying
Tecnology, p. 625-634, 1997.
[3] MORRIS, J. A. &FREIRE, J.T. Drying of yeast paste in a spouted bed dryer. 7Th.
International Drying Symposium. Czechoslovakia, 1990.
[4] MATHUR, K. B. and EPSTEIN, N., Spouted Beds. Academic Press, New York, 1974.
[5] LIMA, L. M. R. Estudos das variáveis fluidodinâmicas na secagem de polpa de
acerola em leito de jorro convencional. Dissertação (Mestrado em Engenharia Química),
Campina Grande – PB, UFPB, 1996.
[6] SILVA, O. S. Comportamento fluidodinâmico em leito de jorro constituído por
mistura de partículas. Dissertação (Mestrado em Engenharia Química), UFPB. Campina
Grande –PB, 1996.
[7] Alsina, O.L. S.; Almeida, M.M. and Silva, O.S. Efeito da presença de pó no composto
de urucu em leito de jorro . Revista Brasileira de Corantes Naturais v2(1) p 115-128, 1996 [
[[8] Lima, M.F.M, Almeida, M.M, Vasconcelos, L.G.S. and Alsina, O.L.S. Drying of “umbu”
pulp in spouted bed, Characteristic curves. Drying’ 92 , ed by A.S. Mujumdar. p1508-
1513, Elsevier Sc. Publishers,1992.
[9] Medeiros, M.F.D. , Influência da composição química dos materiais do desempenho
do processo de secagem de polpas de frutas em leito de jorro. Tese de doutorado,
Unicamp, Campinas – SP, 2001
[10] ALSINA, O. L. S.; MORAIS, V. L. M.; LIMA, L. M. R. & SOARES, F. H. L., Studies on the
Performance of the Spouted Bed dryer for west Indian cherry pulp. X International Drying
Symposium (IDS”96). Kraków, Poland, Vol. B, pp. 865 -872, 1996.

6
 ICEF9

One–equation model for two dimensional turbulent flow and heat transfer
throughout food macroporous media.

Graciela ALVAREZ 1*, Jean. MOUREH*, Onrawee.LAGUERRE, **, Denis FLICK**

Key words : Numerical simulation, air velocity fields, heat transfer heterogeinity macroporous media
**

UMR Génie Industriel Alimentaire Cemagref-ENSIA-INAPG-INRA

1
corresponding author graciela.alvarez@cemagref.fr
* Cemagref Unité Génie des procédés frigorifiques BP 44, 92160 Antony
** Institut National Agronomique Département OMIP 75231 Paris Cedex 05
ABSTRACTS

In food industry, cooling process by forced convection is frequently applied to stacks of food products. Airflow
velocities could be typically between 0,5 to 3 m/s, the characteristic dimension of the products is few centimetres and
airflow is turbulent inside porous media. A one–equation model for two dimensional turbulent flow and heat transfer
throughout porous medium was established allowing to predict airflow velocity and turbulence fields inside the stack of
products considered as macro porous medium. Local heat transfer coefficient was related to local air velocity and local
turbulence using an empirical correlation. The model was validated in a two dimensional air flow configuration
generated by two baffles located at the inlet and at the outlet of the stack of the products that forced the airflow to follow
a “S” shape pathway. Experimental measurements of local heat transfer coefficients are in good agreement with
simulated results.

NOMENCLATURE

a,b,c thermal model parameters Greek Symbols

d,e flow model parameters , (m-1)
D spheres diameter, (m) εk dissipation rate of turbulent kinetic energy
h heat transfer coefficient, (W.m-2.K-1) (m2.s-3)
k turbulent kinetic energy, (m2.s-2) λ thermal conductivity, (W.m-1.K-1)
Nu Nusselt number (hD/λ) ρ density, (kg.m-3)
p pressure, (Pa ) ϕ porosity (void fraction)
Pk production of turbulent kinetic
energy, (m2.s-3) Subscripts
Pr Prandtl number (0.71 for air)
Re Reynolds number (ρvD/µ(1-ϕ)) ∞ referred to equilibrium value
Tu turbulence intensity ((2k)1/2/v) ave average
v superficial velocity, (m.s-1)

1
1. INTRODUCTION

Cooling stacks of food products by forced air convection induces major heterogeneities in their treatment. This is the
case, for example with fruits or vegetables cooled and stored in cold chambers. Products located behind blind walls may
not be sufficiently cooled. This can lead to microbial proliferation and consequent rotting. Furthermore, products
exposed to high velocities may be desiccated. Poor management of temperature can lead to important quality losses of
the product (Alvarez and Trystram 1995).

Heterogeneity of treatment is due to the heating of the air when it passes through the stack of products, but also to
local variations in heat transfer coefficient between the air and the surface of the products (Alvarez and Flick 1999)
because airflow throughout stacks of products is non uniform, the velocity modulus varies locally. Its values are highest
in preferential pathways (for example between the product and internal walls) and the smallest values of velocity
modulus are located at the recirculating zones (for exemple behind blind walls) which affects heat transfer intensity. To
take into account this effect, classical empirical correlation between Nusselt number and Reynolds number are used.

Nevertheless, free stream turbulence is known to have a major influence on heat transfer phenomena. To take into
account the effect of the turbulence on heat transfer intensity, currently a multiplicative factor is applied on the Nusselt
number obtained for very low turbulence intensity (typically Tu <2%). Several studies (Morgan 1975) established
experimental correlations between Nusselt number, modified Reynolds number (to take into account hydraulic diameter,
void fraction and average interstitial velocity) and intensity of the turbulence inside the stack of following form:

Nu = aRe b Pr 1 / 3 (1 + c.Tu ) (1)

where a,b and c : are constants related to the shape of the products, porosity, and stack characteristic (random,
in-line, staggered).

The main problem of this approach is the fact that measurements and interpretation of the velocity field and velocity
fluctuations inside the porous media are delicate. We propose in this paper a model to predict non-uniform turbulent
airflow throughout a stack of products allowing to calculate velocity and turbulence fields inside the stack considered as
porous media. Our approach is semi-empirical because the model can be reduced to its main terms and it requires few
parameters to be experimentally identified. The model can be used, after identification procedure, for other shape of
products. For the purpose of this paper, the model was validated for a “model of stack of spheres” with a void fraction of
0.34.

2. MODELLING
We consider the stack of products as a porous medium. To calculate velocity and pressure fields we use
Forchheimer-extended Darcy’s law for incompressible flow. The first term on the right-hand side (Darcy’s term)
accounts for microscopic viscous drag, which is negligible in our case (high Reynolds number) while the second term
accounts for the form drag, which is due to inertial effects (direction changes). The equations are reduced to:

ρ ρ
The mass conservation equation : ∇ ⋅ v = 0 (2)
ρ ρρ
The momentum conservation equation : ∇p = −d ρ v v (3)

2
 where d is a constant which is a function of : the shape of the products, the void fraction and products arrangement.

Air velocity used in equation 3 is the both temporally and spatially averaged air velocity. Air velocity temporally
fluctuations could be characterizeded in particular by the turbulent kinetic energy (k) defined as the root mean square
(variance) of the fluctuations of the velocity modulus divided by two (Nakayama and Kuwahara 1999).
We propose here a simple one-equation transport simple model to calculate turbulent kinetic energy. As Nakayama
and Kuwahara (1999) have done, we assumed that the production of turbulent kinetic energy Pk is proportional to the
cube of the velocity. The latter term can be interpreted as the transformation of part of the kinetic energy of the mean
flow into fluctuation energy due to drag. The production of turbulent kinetic energy is assumed equal to the scalar
multiplication of drag forces by the velocity:

ρ ρρ ρ3
Pk = d v v.v = d v (4)

Dissipation of turbulent kinetic energy is assumed to be of first order. Thus the dissipation term is assumed to be
proportional to k and it is also proportional to the norm of the velocity to respect dimensional criteria:
ρ
εk = e k v where e is an experimental identified parameter (5)

Finally diffusion term of turbulent kinetic energy is neglected compared to convection term (high Reynolds number).
We can write then:
ρ ρ ρ3 ρ
The conservation of turbulent kinetic energy : ∇ ⋅ kv = d v − e k v (6)

Set of equations (2), (3) et (6), allows to calculate pressure, velocity and turbulent kinetic energy fields inside porous
medium and requires only two parameter which are experimentally identified (d and e).

Nusselt number (or heat transfer coefficient) for each product in the stack can be calculated from local modified
Reynolds number and local intensity of turbulence (mean value of the zone occupied by the object). For this we use
equation (1) with three parameters (a, b and c)
ρ
ρvD 2k
Re = Tu = ρ (7)
µ( 1 − ϕ ) v

For one-directional fully developed flow (far enough from the inlet), there is an equilibrium between production and
dissipation of turbulent kinetic energy:

d ρ2 2d
Pk = ε k → k = k ∞ = v → Tu = Tu ∞ = (4)
e e

The values of a,b,c,d and e, parameters were experimentally identified by measuring of pressure drop throughout the
stack (macro porous medium) and heat transfer coefficient in one-directional flow (Flick, Leslous, Alvarez 2003).

3. RESULTS AND EXPERIMENTAL VALIDATION

The experimental device used is an air blast tunnel consisting of a rectangular section followed by a converging
channel connected to an air extraction duct. The porous medium, shown in Figures 1 and 2, consists of 75 mm diameter
PVC spheres. It is used for the experimental validation in two directional flow. Average void fraction was 0.34. Airflow
rate was imposed to obtain a superficial air velocity of 2.3 m/s. It is based on the total cross section surface (inlet +
baffle sections). For modelling purpose we assume that the pressure is uniform over total cross sections at the inlet and

3
at the outlet and we adjust pressure drop in order to obtain the experimental superficial air velocity (2,3 m/s). Pressure
gradient normal to the wall is equal to zero. This means that near the wall air velocity is parallel to the concerned wall.

Figure 1 . Two dimensional air flow (baffle Figure 2. Experimental porous medium.
configuration). Experimental positions of
heat transfer coefficient measurement.

Diameter of spheres
= 75 mm

thermocouple
electrical heater

Figure 3. Aluminium spheres used for heat transfer

coefficient measurements
To measure local heat transfer coefficient we use aluminium spheres equipped with an electrical heater placed at
their centre, allowing a constant flux (1415 W/m²) to be delivered. They were placed among spheres in PVC. A Copper-
Constantan thermocouple was inserted in the sphere (Figure 3). In the case of aluminium sphere the Biot number is
under 0.1 (h<200 W/m²/K, D=0.075m, λalu >200 W/m/K). We use stationary method to measure local heat transfer
coefficient. Conduction between spheres could be neglected, as the aluminium spheres were in contact with empty PVC
spheres.

Figure 4 shows the heterogeneity of heat transfer coefficients estimated by the model. The average heat transfer
coefficient of all the studied positions was have= 127 W.m-2.K-1. Local heat transfer intensity inside the porous media
varies up to more or less 20% from average value. Lower values are observed at the corners (re-circulating zones) and
highest values are observed at the inlet and outlet zones (preferential pathway). In Figure 4 we can notice that for the

4
symmetrical positions the values are higher at the outlet than at the inlet.

Figure 5 shows the heterogeneity of the measured heat transfer coefficients. We observe a good agreement between
predicted values and experimental results. We found the same predicted tendencies above described. Experimental
values of heat transfer coefficient obtained in previous work, (Flick, Leslous, Alvarez 2003), under one-directional flow
conditions.

0.77 1.17 1.01 1.00

0.79 1.01 1.17 1.06 0.98
0.93
0.86 0.96 1.05 1.07 1.06 hpredicted hmesured
0.94 0.98 1,00 1.00 0.99 have .predicted
1.13
have .predicted
0.99
1.04 1.05 1.01 0.93 0.89
1.24 0.91
1.13 1.18 1.17 0.92 0.75

Figure 5. Measured local heat transfer

Figure 4. Predicted local heat transfer
coefficient divided by the
coefficient divided by the
average predicted value
average predicted value

Figure 6 shows the heterogeneity of velocity field. Superficial air velocity values at the corners are 35% lower than
the average value, that explains the lowest heat transfer coefficient value at this position. At the opposite, near inlet and
outlet sections superficial air velocity value is up to 60% higher than the average one. This allows to justify the highest
values of heat transfer coefficient. On the other hand calculated velocity field is symmetrical, because if we change the
sign of the velocity and pressure, the equations (2) and (3) remain verified. Thus the velocity field does not allow to
explain alone the dissymmetry for the measured heat transfer coefficient.

This asymmetry is clearly explained by the intensity of the turbulence, which is low at the inlet (< 5%), it increases
when the air passes through porous medium because turbulence is generated by the vortices in the wake of the spheres.
So turbulence intensity increases with the rows up to an equilibrium value reached when production is equal to
dissipation.

Velocity fluctuations are similar in magnitude to interstitial average velocity (v/ϕ), this justifies that the calculated
intensity of the turbulence could increase up to 300%. In our case the equilibrium between production and dissipation is
reached after one or two spheres rows. If the void fraction of porous media is higher (more space between the spheres),
the equilibrium value will be reached after several spheres rows.

Figure 7 illustrates the ratio between calculated local intensity of the turbulence and equilibrium value. This ratio can
be higher than 1 because a large amount of turbulent kinetic energy is produced at the high velocity zones and it can be
transported to the low velocity zones. The lowest values observed at the inlet give an explanation to the observed
asymmetry with regard to heat transfer coefficients: the first row is exposed to quiet ambient air and turbulence intensity
is very low so that heat transfer coefficient is lower compared to the last row which is exposed to an airflow where
intensity of the turbulence is very high.

5
 2.3m/s

1.35 1.15 0.95 0.75 0.75

0.66 1.04 1.56 1.60 1.49

ρ 1.02 1.11 1.07 1.00 0.98

Tu predicted
0.89 1.00 1.18 1.28 1.29
v predicted 0.95 1.02 1.05 1.07 1.08
1.08 1.09 1.10 1.09 1.08
Tu ∞
v ave 0.94 0.95 0.97 1.05 1.12

1.29 1.28 1.18 1.00 0.89

0.96 0.92 0.92 0.92 1.19

1.49 1.60 1.56 1.04 0.66

Figure 6. Predicted local velocities Figure 7. Predicted local turbulence

divided by the average divided by the equilibrium
value. value.
4. CONCLUSION

A model was established to predict turbulent flow and heat transfer inside a stack of products considered as a porous
medium. The model requires only 5 parameters to be experimentally identified, they depend on the shape of the objects,
void fraction and kind of stack arrangement. The model allows to take into account the influence, at the same time, of
the local velocity (recirculations/ preferential pathways of the air) and of the production of the turbulent kinetic energy
inside the porous medium that enhances heat transfer.

5. REFERENCES

[1] G. Alvarez, G. Trystram (1995), Design of a new strategy for the control of the refrigeration process : fruit and
vegetables conditioned in a pallet, Food Control 6 (6) 345-347.

[2] G.Alvarez, D. Flick, (1999) Analysis of heterogeneous cooling of agricultural products inside bins. Part II :
thermal study. J.Food Engineering, 39 239-245.

[3] V. Morgan, (1975) The overall convection heat transfer from smooth circular cylinders, Advances in heat
Transfer, 11 1999-225.

[4] N. Nakayama, F. Kuwahara, (1999) A macroscopic turbulence model for flow in a porous medium. J. Fluids
Engineering 121 427-433.

6
[5] D. Flick, A. Leslous, G.Alvarez, (2003) Modélisation semi-empirique des écoulements et des transferts dans un
milieu poreux en écoulement turbulent. International Journal of Refrigeration. 26(3) 349-359.

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ICEF9 2004
International Conference Engineering and Food

Air impingement freezing and thawing of foods

Anderson, Brent A. (1), Sarkar, Arnab (2), R. Paul Singh (3)

(1) Biological & Agricultural Engineering, University of California, Davis,

One Shields Avenue, Davis, CA 95616
banderson@ucdavis.edu
(2) Biological & Agricultural Engineering, University of California, Davis,
One Shields Avenue, Davis, CA 95616
asarkar@ucdavis.edu
(3) Biological & Agricultural Engineering, University of California, Davis,
One Shields Avenue, Davis, CA 95616
rpsingh@ucdavis.edu

Abstract:
In freeze preservation of foods, freezing and thawing times are critical factors influencing
product quality. In the present work, the application of air impingement technology to speed the
freezing and thawing of foods was investigated. Air impingement processing is the utilization of high
velocity jets of air directed at the product surface, which results in increased convective heat transfer.
Visualization techniques and the use of computational fluid dynamics (CFD) were used to visualize
and quantify fluid flow in these systems. Convective heat transfer coefficients during air impingement
were measured. Air impingement also increases mass transfer rates; therefore, various coverings
were used to reduce moisture loss during thawing. Numerical models were developed to predict heat
and mass transfer during impingement freezing and thawing, and results agreed well with
experiments.

Keywords: impingement, freezing, thawing, CFD, heat transfer

Introduction:
In the food industry, there is always interest in obtaining shorter processing times. Shorter
processing times allow increased throughput, lower cost per unit, and in many cases, improved
product quality. One of the more recent developments in the food industry is the application of air
impingement technology. Air impingement processing is the utilization of high velocity jets of air
directed at the product’s surface. Typical jet velocities at the nozzle exit range from 20 to 80 m/s. The
high velocity and turbulence caused by this action can greatly increase the rate of convective heat
transfer at the surface. In traditional heating methods, using still air or slowly stirred air, a thermal
boundary layer develops around the product, which slows the rates of heat transfer. With air
impingement processing, the size of these boundary layers can be greatly reduced. Air impingement
systems have been used in various industrial operations involving heat and mass transfer such as
textile and paper drying, electronic cooling and glass quenching. More recently, air impingement
systems have been applied to industrial food processing operations such as drying, baking, toasting,
and freezing (1-6) with significant reductions in process times (7).
With the growing use of frozen foods both in retail and in food service, there is a need to
develop improved methods for freezing and thawing. Most traditional methods are either undesirably
slow (still or stirred air) or are quite expensive (cryogenic freezing and microwave thawing). The
application of air impingement technology to freezing and thawing applications may give improved
benefits.

Objectives:
The goal of this research was to study the application of air impingement technology to the
freezing and thawing of food products. To accomplish this goal, several objectives were set:
• To use visualization techniques to study special flow features of impingement systems
• To apply computational fluid dynamics (CFD) to simulate fluid flow and heat transfer in these
systems
• To measure heat transfer coefficients for air impingement under freezing-thawing conditions
• To study various surface coverings in an attempt to minimize moisture loss during
impingement thawing
• To develop simulation models to predict freezing and thawing times during impingement
processing.
ICEF9 2004
International Conference Engineering and Food

Materials and Methods:

Flow visualization experiments were conducted using helium filled bubbles and a planar flow
visualization technique. A helium bubble-generating device (Sage Action Inc., Ithaca, New York) was
used to produce neutrally buoyant tracer (seeding) particles that were visualized. A calomel lighting
source was used as the lighting system. A cylindrical lens arrangement was used to focus the light
source into a plane sheet of light (0.5 cm thickness. A Kodak DCS 200 digital CCD camera with a
Nikon N8008s lens was used for taking images, and analysis was done with image processing toolbox
in Matlab version 6.0, release 12.

Plenum

Camer
Light

Impingement
Lens
Figure 1: Experimental setup for flow visualization experiments

The complete Navier-Stokes’ equations with turbulence for external flow as a steady state
case using Fluent 6.0 CFD solver with Gambit 3.0 mesh generating software. The turbulent
dissipation terms were estimated using 2-equation turbulence models (κ−ε model).
Heat transfer coefficients under air impingement jets were measured using two different
methods. Since heat transfer coefficients in impingement systems vary both with position and with
time, a single, simple lumped capacitance measurement would not be accurate. One method used
involved building a plate with micro-calorimeters. This technique is an extension of the lumped
capacitance technique. Small transducers with thermocouples attached to them (micro-calorimeters)
were used at various spatial locations instead of using a single transducer. The setup consisted of thin
copper disks (0.08 cm thickness) that acted as micro-calorimeters flush mounted on polyurethane
foam insulation at various spatial locations. The circumference of the micro-calorimeter was insulated
and the exposed surface of the insulation was covered with a copper plate that had holes punched to
accommodate the calorimetric disks (Figure 2). Heat transfer coefficients were determined by
analyzing the transient heat transfer curve assuming that the disks behaved as lumped capacitances
(8). In the second method, thermocouples were inserted near the surface a nylon disk at various
radial positions. The disk was treated under impingement conditions, and temperature versus time
data was evaluated using a 1-D sequential-regularization method for Inverse Heat Conduction (9-10).
This resulted in heat transfer coefficients at various radial positions that also varied with time.

Impingement
Plate

Heat transfer
sensor disk

Figure 2: Micro-calorimeter plate for heat transfer coefficient measurements (adapted from 11)
ICEF9 2004
International Conference Engineering and Food

Since the increased convection caused by air impingement processing also causes increased
mass transfer, various coverings were evaluated in an attempt to minimize moisture loss. Experiments
were carried out using Tylose, a meat analog. A mold was constructed for the Tylose, with
thermocouples located at various radial positions. Experiments were conducted using thawing Tylose
in the mold with the following conditions: uncovered, aluminum foil, plastic wrap, olive oil spray, and
paraffin wax. Mass loss following thawing was measured.

Figure 3: Product mold for freezing/thawing of Tylose

In order to predict freezing and thawing times under impingement conditions, explicit finite
difference models were programmed in Matlab v. 6.1. The Enthalpy Method was used to account for
the phase change in the material (12), and temperature dependent thermal properties of Tylose were
used from Succar (13). Simulations were used to model freezing and thawing times with a convective
boundary on one surface and insulated on the opposite surface. Results were compared to those
experimentally determined using the Tylose mold.

Results and Discussion:

Some of the flow dependent features that are important for impingement systems were
observed using the visualization experiments. These features include transition to turbulence and
recirculation (Figure 4), and the effect of different nozzle length-to-diameter ratios (Figure 5).

Figure 4: (a) Transition to turbulence along the product surface, (b) recirculation of the air flow.
ICEF9 2004
International Conference Engineering and Food

(a) (b)
Figure 5: Effect of nozzle length-to-diameter ratio on the spread (a) L/D = 8, (b) L/D = 0.5

Simulation modeling using CFD showed that commercial solvers can be used to solve
impingement flow and heat transfer in simple cases such as heating or cooling as an unsteady state
problem. An example is shown in Figure 6. However, even though the flow is essentially steady, the
heat transfer is unsteady, which makes the simulations very time consuming. In addition, most
commercial CFD solvers cannot easily solve phase change problems, such as freezing and thawing.

Figure 6: Results from an unsteady state impingement heat transfer simulation from a CFD solver

Average heat transfer coefficients during impingement processing at freezing/thawing

temperatures were found to range from 30 to 180 W/m2K. Faster air velocities measured at the nozzle
exit were found to cause higher heat transfer coefficients at the product surface. From the
measurements done using the plate with micro-calorimeters, it was found that heat transfer
coefficients were highest at stagnation and decreased at increasing radial distances. Results for
various velocities from a single, round nozzle, 1.9 cm in diameter and 7.6 cm from product surface are
shown in Figure 7.
Use of the nylon disk for heat transfer coefficient measurements allowed the determination of
heat transfer coefficient with time. Results for an experiment with a jet at 39 m/s from a 1.9 cm
diameter nozzle, 14 cm from product surface are shown in Figure 8. Heat transfer coefficients were
found to increase as thawing progressed, possibly due to the frost formation and subsequent
evaporation. In addition a secondary maxima was found at an r/D of approximately one, as was found
by Jambunathan et al (14). This was not found in the experiments using the micro-calorimeters,
possibly because the first calorimeter away from stagnation was at an r/D of approximately 2.5.
ICEF9 2004
International Conference Engineering and Food

150

Velocity (m/s)
Effective heat transfer coefficient (W/m²K)
130
29
24
110 21
19
15.7
90

70

50

30
0 1 2 3 4 5 6 7 8
radial position / nozzle diameter ratio

Figure 7: Heat transfer coefficients measured using micro-calorimeter plate

r/D = 0
r/D = 0.5
r/D = 0.8
r/D = 1.0
r/D = 1.6
r/D = 1.8
r/D = 2.3
r/D = 2.9

Figure 8: Heat transfer coefficients measured using a nylon disk with air velocity of 39 m/s

Various coverings were found to be successful in minimizing moisture loss during thawing.
Product was thawed using the same impingement setup with air at approximately 50% relative
humidity. Results can be found in Table 1. Aluminum foil and plastic wrap essentially eliminated all
moisture loss, while olive oil and paraffin wax were slightly less effective. Another potential method to
reduce moisture loss is to utilize air with higher humidity.

Table 1: Percent mass and moisture loss following Impingement thawing using air at 50% RH
Mass loss Moisture loss
Plastic wrap 0.0% 0.0%
Aluminum Foil -0.1% -0.1%
Paraffin -0.4% -0.6%
Olive oil -1.6% -2.0%
Uncovered -3.5% -4.6%
ICEF9 2004
International Conference Engineering and Food

Programs written to predict freezing and thawing times from air impingement systems showed
good agreement with experimental results. Freezing times were found to be 3 to 4 times faster in
impingement systems than when freezing in a cold room at the same temperature, though actual
improvement in freezing times depends strongly on the thickness of the product. Thawing times using
impingement systems were found to be 6 to 10 times faster than thawing in a refrigerator. Predicted
freezing and thawing times were found to be within 5 to 20% of the experimentally measured times.

Conclusions:
In this work, studies of the application of impingement systems to freezing and thawing
processes were carried out. Understanding the application of this technology to these processes
requires studying the fluid flow on the product, determining surface boundary conditions, and
accounting for any moisture loss that may occur. Impingement technology has the potential to reduce
freezing and thawing times which may be a benefit to the industry.

References:
1. Li A., Walker C.E. Cake baking in conventional, impingement and hybrid ovens. Journal of Food
Science. 61(1): 188-191, 1996.
2. LujanAcosta J., Moreira R.G., SeyedYagoobi J. Air-impingement drying of tortilla chips. Drying
Technology. 15(3-4): 881-897, 1997.
3. Midden T.M. Impingement air baking for snack foods. Cereal Foods World 40(8): 532-535, 1995.
4. Moreira R.G. Impingement drying of foods using hot air and superheated steam. Journal of Food
Engineering. 49(4): 291-295, 2001.
5. Nitin N., Karwe M.V. Heat transfer coefficient for cookie shaped objects in a hot air jet impingement
oven. Journal of Food Process Engineering. 24(1): 51-69, 2001.
6. Ovadia D.Z., Walker C.E. Impingement in food processing. Food Technology. 52 (4): 46-50, 1998.
7. Wahlby U., Skjoldebrand C., Junker E. Impact of impingement on cooking time and food quality.
Journal of Food Engineering. 43(3): 179-187, 2000.
8. Sarkar A, Singh R.P. Spatial variation of heat transfer coefficient in air impingement applications.
Journal of Food Science. 68(3):910-916, 2003.
9. Beck J.V., Blackwell B., St. Clair C.R. Jr. Inverse heat conduction: Ill-posed problems, Wiley-
Interscience, New York, 1985.
10. Scott E.P., Beck, J.V., Heldman, D.R. Estimation of time variable heat transfer coefficients in
frozen foods during storage. Journal of Food Engineering, 15: 99-121, 1992
11. Sarkar A.
12. Mannapperuma J.D., Singh, R.P. Prediction of freezing and thawing times of foods using a
numerical method based on enthalpy formulation, Journal of Food Science, 53(2): 626-630, 1988.
13. Succar, J. Heat transfer during freezing and thawing of foods, in Developments in Food
Preservation – 5, S.Thorne, ed., Elsevier Applied Science, New York, 253-304, 1989.
14. Jambunathan K., Lai E., Moss M.A., Button B.L. A review of heat transfer data for single circular
jet impingement, International Journal of Heat and Fluid Flow, 13(2): 106-115, 1992.
 ICEF-2004
International Conference Engineering and Food

NUMERICAL SIMULATION AND EXPERIMENT IN DOMESTIC REFRIGERATORS

Sami BEN AMARA(1),Denis FLICK(2), Jean Moureh(3), Graciela ALVAREZ(4), Onrawee LAGUERRE(5)
UMR Genie Industriel Alimentaire (Cemagref / ENSIA / INA-PG / INRA)
(1) UR GPAN Cemagref, BP 44, 92163 Antony Cedex, sami.benamara@cemagref.fr
(2) INAPG, 16 rue Claude Bernard, 75231 Paris Cedex 05, flick@inapg.inra.fr
(3) UR GPAN Cemagref, BP 44, 92163 Antony Cedex, jean.moureh@cemagref.fr
(4) UR GPAN Cemagref, BP 44, 92163 Antony Cedex, graciela.alvarez@cemagref.fr
(5) UR GPAN Cemagref, BP 44, 92163 Antony Cedex, onrawee.laguerre@cemagref.fr

ABSTRACT

This work was carried out in order to study the heat transfer and air flow by natural convection in a
domestic refrigerator (without ventilation). Three configurations were investigated: empty refrigerator
with and without shelves and loaded refrigerator. Both experimental and numerical approaches were
used. Simulations using a CFD software was undertaken supposing a constant evaporator
temperature and laminar 3D-flow. Air temperature and velocity fields were shown. It was found, for all
cases studied, that the warm zone is located at the top of the refrigerator and the cold zone at the
bottom. The air temperature obtained from simulations was compared with the experimental values.
Good agreement was obtained particularly at the bottom part of the refrigerator. However, in the cases
of empty refrigerator (with and without shelves), the model over predicted the air temperature at the
top part. This may relate to the fact that radiation was not taken into account in the model.

KEY WORDS: natural convection, simulation, heat transfer, flow, domestic refrigerator.

INTRODUCTION

In unventilated domestic refrigerators, where heat transfer occurs by natural convection, temperature
heterogeneity is often observed and some indications show that food is often stored at too high
temperatures. Surveys on the air temperature inside domestic refrigerator in real use condition have
been carried out in different countries: North Ireland (Flynn et al., 1992), U.K. (James and Evans,
1992), Netherlands (Lezenne Coulander ,1994), New Zealand (O’Brien, 1997) and Greece (Sergelidis
et al.,1997). These surveys show that the average air temperature inside refrigerators is around 6°C
(min~0°C and max~12°C), while the values required by standard is 4 or 5°C depending on the
country.
A recent survey in France (Laguerre et al., 2002) shows that 25% of the refrigerators have an average
temperature over 8°C. Moreover, due to very low air circulation, strong temperature heterogeneity is
often observed, with warm zones (sanitary risk) and cold zone (freezing risk).
Some studies have investigated heat transfer and airflow in empty refrigerators. Pereira and Nieckele
(1997) studied heat exchange by natural convection between air and the evaporator. Silva and Melo
(1998) experimentally characterized an unventilated refrigerator by temperature cartography and local
flux on walls and the evaporator. Deschamps et al. (1999) carried out a numerical study to predict air
velocity and temperature distribution.
A new generation of refrigerators is equipped by glass shelves. This is related to commercial reasons
(easy cleaning, design etc.). This type of shelves present obstacle to airflow compared to the grid
shelves. Therefore, it is interesting to study the effect of glass shelves and the presence of product on
the heat transfer and airflow in refrigerators.
This work was carried out in order to gain a better insight into heat transfer by natural convection
inside a refrigerator. Three configurations were studied: empty refrigerator with and without shelves
and refrigerator loaded by product. The objective was to quantify and compare the temperature and
velocity distribution for these three cases. Both experimental and numerical (CFD software)
approaches were used.

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1 LABORATORY INVESTIGATION OF A DOMESTIC REFRIGERATOR

A static cold refrigerator (without ventilation) was used in this work. A schematic representation of this
refrigerator and the general dimensions are shown in figure 1. Three cases were studied:
- Empty refrigerator, without shelves (figure 1-a),
- Empty refrigerator equipped with glass shelves (figure 1-b),
- Refrigerator loaded by test product (methyl cellulose packages) (figure 1-c).

Plan of symmetry
1.2 cm
44 cm 52 cm

23 cm
Evaporator 0.4 cm

20 cm

136 cm 90 cm
26 cm
Thermocouples

20 cm
Shelves
21 cm 48 cm 24 cm

18 cm
23 cm

Central axis Plan situated at 8 cm

fromThe side wall
(a) (b)

2.7 cm 10 cm
30 cm
2 cm

15 cm

10 cm

Product
s
4 cm
(c)

Figure 1 : Domestic refrigerator geometry (a)- empty refrigerator (b)-refrigerator with glass shelves (c)
refrigerator loaded by test product.

All experiments were carried out at 20 ± 0.2°C controlled room temperature. As shown in figure (1),
the evaporator is located on the upper part of the cabinet. The indentation observed on the bottom
right of the figures represents compressor placement.
Air temperature were measured experimentally using calibrated thermocouple (type-T) placed in
different positions of the symmetry plan of the refrigerator and on the plan situated at 8 cm from
sidewall (figure 1).

2 MODELLING AND MESH STRUCTURE

The simulations were performed using a CFD software. Structured mesh was used to describe the
geometry of the refrigerator. The number of cells used in each case is shown in table 1 and mesh
structures are shown in figure 2. Only the half of the refrigerator has to be meshed because of a
symmetry plan. Finer meshes were used near walls and shelves.

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Table 1: Number of cells used for the simulations

Height Width (half) Depth Total

Dimension [cm] 136 26 44 -
Empty refrigerator [mesh] 138 28 66 255 024
Refrigerator with shelves [mesh] 222 28 66 410 256
Refrigerator loaded by test product [mesh] 240 62 74 1 101 120

(a) (b) (c)

Figure 2 : Mesh structure (a)- empty refrigerator (b)-refrigerator with glass shelves (c)-refrigerator
loaded by test product

The air motion inside the cabinet is produced by buoyancy forces acting on a fluid of non-uniform
temperature field. The governing dimensionless number is the Rayleigh, eq.(1).
g β ΔT L3 (1)
Ra =
αν
Where g is the gravitational acceleration, β is the coefficient of volume expansion, L is the
characteristic length scale, α is the thermal diffusivity, ν is the cinematic viscosity, and ΔT is the
characteristic temperature difference.
The Rayleigh (Ra) number determine the flow regime: laminar or turbulent. It is generally considered
9 8
that the flow is laminar when Ra ≤ 10 . In the present study, it’s value was 6.4 10 (estimation based
on the height of the evaporator cold-wall and the temperature difference between the cabinet air and
the cold-wall surface). Several studies showed that turbulence does not change the observed air
temperature pattern (Deschamps and Parta., 1999, Kingston et al., 1994). Thus laminar flow
assumption was made for the flow regime.
The heat transfer by radiation between the internal surfaces of the cabinet was not taken in account.
The thermal boundary conditions were based on experimental data. Uniform global heat transfer
-2 -1
coefficient between external air and internal wall (0.34 Wm K ), constant external air temperature
(20°C) and constant evaporator temperature (- 0.5 °C) which was the average value during ‘on’ and
-1 -1
‘off’ running cycles of compressor. The thermal conductivity of glass shelves was 0.75 Wm K .

3 RESULTS AND DISCUSSIONS

3.1. Numerical results

The air temperature fields obtained from simulations for the three cases are presented in figures 3. In
the case of empty refrigerator (Figures 3-a), temperature stratification is observed: temperature
increases from the bottom to the top but it is almost homogeneous at a given height. The thermal
boundary layer thickness is small at the top of the evaporator and it increases until the bottom, the
average value is about 1.5 cm. The air temperature varies form 1 to 8°C for 80% of the total volume.
The average air temperature in the vegetable box is 9°C. Near the side wall the temperature field has

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a similar pattern as that in the symmetry plan but the temperature is slightly higher because of the
heat penetration trough this side wall.
In the case of refrigerator with glass shelves (Figures 3-b), the temperature stratification is similar to
that of empty refrigerator. Almost the same thermal boundary layer (1.5 cm average thickness) is
observed along the evaporator. The air temperature is relatively homogeneous between two shelves.
However, in spite that the air temperature at the top half of the refrigerator is close in the two cases,
the air located between bottom-half (for the 3 lower shelves) is colder than that without shelves. Near
the side wall, the temperature is higher than that in the symmetry plan especially at the upper zone
between two shelves.
In the case of refrigerator loaded by test product, (Figures 3-c), the temperature stratification is roughly
similar to the first two cases (empty with and without shelves): warm zone at the top and cold zone at
the bottom. But, at the same height level, the air temperature is slightly heterogeneous excepted at the
top shelve where the temperature is relatively constant at the same height.
The simulation results show that, the heat transfer between evaporator and air increases with the
presence of obstacles (shelves and product). This may due to the fact that the obstacles enhance the
air circulation near to the evaporator.
It is to be reminded that for loaded refrigerator, the symmetry plan is located between 2 piles of test
product. That is the reason why the product packages are not shown in the figure.

(a) (b) ( c)
Figure 3 : Predicted temperature fields in the symmetry plan [°C] (a)- empty refrigerator (b)-refrigerator
with glass shelves (c)-refrigerator loaded by test product

The air velocity fields obtained from simulations for the three cases are presented in figures 4. In the
case of empty refrigerator (Figures 4-a), cold air flows downward along the evaporator wall with an
increasing velocity. This velocity reaches the maximum value (0.21 m/s) when approaching the bottom
of the evaporator. Then, air flows upward along the door with a decreasing velocity while the
temperature increases (cf. Figures 3-a) due to the heat penetration through the door. The air is nearly
immobile at the top of the refrigerator; this explains the high temperature observed in this location. Air
flows also horizontally from left to right to supply the downward flow near the evaporator. A big re-
circulation zone is observed at the bottom. Small air re-circulations are also observed particularly in
the vegetable box.

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(a) (b) ( c)
-1
Figure 4 : Path line (from grey to dark vs velocity magnitude) in the symmetry plan [m s ] (a)- empty
refrigerator (b)-refrigerator with glass shelves (c)-loaded refrigerator

In the case of refrigerator equipped with glass shelves (Figures 4-b) and refrigerator loaded by product
(Figures 4-c), in addition to that airflow along the evaporator wall and the door, which are similar to
that of empty refrigerator, there are also air re-circulations in the space between two shelves or
between shelve and product. This re-circulation is more obvious at the bottom while the others are
more chaotic. The maximum air velocity is 0.2 m/s. Near the side wall, a complex 3D flow pattern is
observed between the shelves because air tends to flow downwards near the evaporator and upwards
near the side wall.

3.2 Comparison of numerical and experimental results

A comparison of the predicted and measured air temperature at various heights is shown in figure 5.
This comparison was performed by using the dimensionless temperature. The numerical results tend
to over predict temperature especially at the top of the refrigerator with and without shelves. The
difference between the two values can reach 7°C at the top in the case of refrigerator without shelves.
This may be due to radiation, which is not taken into account in the simulations. In fact, there is
radiation notably between the upper wall and the evaporator and the corresponding heat exchange
would lower the upper wall temperature and consequently lower the air temperature in this zone. It is
therefore necessary to take into account this fact in our next study. The numerical results in the case
of refrigerator loaded by product are closer to the experimental values probably because the product
acts as shield for radiation.

CONCLUSION

Simulations of heat transfer and airflow in a refrigerator were carried out using a CFD software in 3
dimensional geometry. The following conditions were supposed: laminar flow and constant evaporator
temperature.
The air temperature obtained from simulations was compared with the experimental value for the three
cases: empty refrigerator with and without shelves and loaded refrigerator. The temperature at the top
is always higher than that at the bottom. Relatively good agreement between predicted and measured
temperature was observed from the bottom until the mid-height of the refrigerator. Then, in the cases
of empty refrigerator (with and without shelves) the air temperature was over predicted from the mid-
height until the top of the refrigerator. This difference can be explained by the radiation, which was not
taken into account in the model. It was observed that the presence of shelves and product in the
refrigerator contributes to a change of air velocity and temperature fields. It seems that the presence
of obstacles (shelves and product) enhances the heat transfer between the evaporator and air.
The results analysis (position of the cold and warm zones) could lead to some technical
recommendations for the constructors and practical advice for the consumers.

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1,4 1,4 1,4

1,2 1,2 1,2

Y position [m]
1 1

Y position [m]
Y position [m]

0,8 0,8 0,8

0,6 0,6 0,6

0,4 0,4 0,4

0,2 0,2 0,2

0 0,2 0,4 0,6 0,8 0 0,2 0,4 0,6 0,8 0 0,2 0,4 0,6 0,8
(T-Tevp) / (Tamb-Tevp) (T-Tevp) / (Tamb-Tevp) (T-tevp) / (Tamb-Tevp)

(a) (b) ( c)

Figure 5 : Predicted ( ) and measured ( ) temperature in the central axis of the plan of symmetry
(a)- empty refrigerator (b)-refrigerator with shelves (c)- loaded refrigerator.

NOMENCLATURE
-2
g Gravitational acceleration (m s ) ΔT Characteristic temperature difference (K)
2 -1
L Characteristic length scale (m) α Thermal diffusivity (m s )
-1
T Temperature (K) β Coefficient of volume expansion (K )
2 -1
Tevp Evaporator Temperature (K) ν Cinematic viscosity (m s )
Tamb Ambient temperature (K)

REFERENCES
th
1. Deschamps, C.J., Prata, A.T, Heat and fluid flow inside a household refrigerator cabinet, 20
International Congress of Refrigeration, IIR/IIF, Sydney , 1999.
2. Flynn, O.M., Blair, I., McDowell, D., The efficiency and consumer operation of domestic
refrigerators, Int. J. Refrig., vol 15, no 5, p. 307-312., 1992.
3. James, S.J., Evans, J., The temperature performances of domestic refrigerators, Int. J. Refrig., vol
15, p. 313-319., 1992.
4. Kingston, P.,Woolley, N., Tridimas, Y., Fluid flow and heat transfer calculations in a domestic
refrigerator, FIDAP UK User meeting, Fluent France S A, p. 1-11, 1994.
5. Laguerre, O., Derens, E., Palagos, B., Study of domestic refrigerator temperature and analysis of
factors affecting temperature: a French survey, Int. J. Refrig., vol 25, p. 653-659, 2002.
6. Lezenne Coulander de P.A., Koelkast temperature thuis, Report of the regional Inspectorate for
Health Protection. Leeuwarden. The Netherlands, 1994.
7. O’Brien G.D., Domestic refrigerator air temperatures and the public’s awareness of refrigerator
use, International Journal of Environmental Health Research, vol 7, p. 141-148, 1997.
8. Pereira, R.H., Nieckele, A.O., Natural convection in the evaporator region of household
refrigerators, Proc. Brazilian Congress Mechanical Eng., Bauru, CD rom, paper COB1236, 1997.
9. Sergelidis, D., Abrahim, A., Sarimvei, A., Panoulis, C., Karaioannoglou, P., Genigeorgis, C.,
Temperature distribution and prevalence of Listeria spp. in domestic, retail and industrial
refrigerators in Greece, International Journal of Food Microbiology, vol 34, p. 171-177, 1997.
10. Silva, L.W., Melo C., Heat transfer characterization in roll-bond evaporators, MSC. Dissertation,
Federal University of Santa Catarina, Brazil, 1998.

6
Dynamic gauging for measuring the thickness and mechanical properties of soft solid deposits

Chew J.Y.M.(1), Höfling V.(2), Augustin W.(3), Paterson W.R.(4) and Wilson D.I.(5)

Department of Chemical Engineering, Pembroke Street, Cambridge, CB2 3RA, UK

(1) ymjc2@cam.ac.uk, (4) bill_paterson@cheng.cam.ac.uk, (5) ian_wilson@cheng.cam.ac.uk
Institute of Thermal & Chemical Process Engineering, TU Braunschweig, D-38106, Germany
(2) v.hoefling@tu-bs.de, (3) w.augustin@tu-bs.de

ABSTRACT
Fluid dynamic gauging is a technique for tracking the thickness of developing (or receding)
macro-layers of soft materials on solid surfaces immersed in a liquid environment, in situ and in real
time. The technique has been extended using computational fluid dynamics to quantify the stresses
required to remove a model soil (dried tomato paste) from stainless steel discs, and the associated
deformation behaviour. Ageing via baking resulted in clear increases in soil strength.

Keywords: computational fluid dynamics, dynamic gauging, paste, fouling, strength

INTRODUCTION
Fouling and cleaning are critically important in food processing in terms of their influence on
food safety and hygiene as well as on plant operability and product quality. Selection of an appropriate
cleaning technology is determined by the properties and behaviour of the soil, amongst other factors,
and can be problematic when this information is lacking. This is particularly true of many food
deposits and biofilms which, being foams, gels or high voidage structures, are readily compressed and
may be difficult to study outside their native environment due to shrinkage or slump.
The strength of a fouling deposit, which is one of the key parameters in cleaning and removal,
changes over time and is difficult to quantify. Furthermore, the deposit strength is usually a function of
the degree of ageing in the layer: Müller-Steinhagen1 described ageing as the most poorly understood
aspect of fouling. Quantitative links to cleaning performance parameters such as shear strength are
rarely reported in the literature. Ageing usually results in stronger deposits as a result of extended
reaction, reduction in deposit voidage or generation of adhesive extracellular material. Knowledge of
the shear strength of deposits might allow equipment designers to select flow conditions which would
mitigate fouling by erosion of growing deposits. The mechanical behaviour of soft fouling layers is
often overlooked owing to the difficulty in quantifying it reliably, or is determined indirectly. Fryer &
Slater2 expressed the adhesive strength of milk foulants in terms of surface shear stress values
estimated from pressure drop measurements. Devices such as radial flow cells are also used,
although the stress distribution in these geometries is not simple. Zhang and co-workers have
recently developed a direct, micro-mechanical determination of deposit strength by micro-
manipulation. This technique uses small blades which are pulled through a fouling deposit; the force
recorded is expressed as an apparent adhesive strength of the fouling layer. Liu et al.3 reported the
effect of drying time, hydration and metal surface roughness on the adhesive characteristics of a
model food soil, namely tomato paste.
An alternative approach is to employ the shearing action of a fluid jet impinging on a surface to
characterise the shear response of the surface material. For example, Vaishnav et al.4 studied the
deformation of canine endothelium tissue using laminar impinging jets and related the response to the
stress field predicted from the solutions to the governing fluid dynamics equations. This paper
describes results from a similar approach applied to the recently developed technique of fluid dynamic
gauging (FDG). Tuladhar et al.5 developed this technique for measuring the thickness of soft deposits
in a liquid environment in situ using a convergent-divergent jet. Figure 1(a) illustrates the principle. A
pressure difference is set up between the fluid near the deposit surface and the discharge end of the
gauge, so that fluid tends to flow into the nozzle. When the distance between the surface and the
nozzle, h, is small, such that h/dt < c. 0.25, the mass flow rate through the nozzle, m, is very sensitive
to the value of h and measurement of m may therefore be used to locate the position of the surface in
space. The technique was successfully used to study the swelling and removal of soft layers of
denatured whey protein gels from steel surfaces exposed to solutions of aqueous sodium hydroxide,
simulating CIP of dairy soils. Observations during that work suggested that the stresses imposed by
the gauging flow on the weakest deposit layers could cause significant deformation of the surface.
This is undesirable for gauging, but the onset of deformation – which could be recorded by gauging –
is related to the strength required to deform the deposit. Knowledge of the stresses imposed by the
ICEF9 – 2003
International Conference Engineering and Food

gauging flows on the surface would therefore afford a method for measuring the shearing yield
strength of the deposit, as well as the deposit thickness, in situ and in real time.
(a) (b)
2

nozzle

dt 45o
stainless
steel deposit
1
h Fluid
inlet

Figure 1(a): Principle of dynamic gauging. Figure 1(b): Streamlines for gauging flow at
Ret = 120 and h/dt = 0.20.

This paper describes briefly the application of computational fluid dynamics (CFD) to calculate
the velocity field and thereby the shear stress acting on deposit layers being studied by FDG. The
governing Navier-Stokes (N-S) and continuity equations for these steady, laminar, Newtonian,
incompressible and axisymmetric flows are solved numerically and the simulations compared with
experimental data sets. The enhanced FDG technique is then used to investigate the deformation
characteristics of a tomato model food paste. Results from independent laboratory studies
demonstrate the repeatability of the procedures and suggest that enhanced FDG represents an
affordable and reliable method to study soil cleaning characteristics.

CFD SIMULATIONS
FDG under quasi-stagnant conditions, i.e. when the motion of the fluid is due only to the slow
flow into the gauge, represents a case of a steady, laminar, incompressible and axisymmetric flow of a
Newtonian fluid which is governed by the N-S and continuity equations. Although in the laboratory the
pressure difference driving the flow is generated by a gravitational head, for CFD simulations, it is
often more convenient to ignore gravity and simply impose a chosen pressure difference to drive the
flow (Tritton6). The non-dimensional N-S and continuity equations are:
1 2
Navier-Stokes: V ⋅ ∇ V = −∇P + ∇ V (1)
Re
Continuity: div V = ∇ ⋅ V = 0 (2)

where V is the dimensionless velocity vector and P is the dimensionless pressure, with
1
V= v (3)
2vc
p
P= (4)
4ρ v c
2

2 ρ vc l c
Re = (5)
µ
∇ = lc ∇ * (6).
The subscript c implies a characteristic value and the superscript ‘*’ on ∇ implies that the operator is
dimensional. These equations were solved using the Augmented Lagrangian Method implemented by
the partial differential solver, FastfloTM. Spatial discretization was performed using the finite element
method, with finer grids/elements assigned in the nozzle-clearance region. A detailed description of
ICEF9 – 2003
International Conference Engineering and Food

the simulations is given in 7. Figure 1(b) shows the streamlines predicted for Ret = 120 and h/dt = 0.20.
The velocity gradients are largest in the clearance region between the nozzle and the surface, so that
localized regions of higher shear stress are predicted there. The associated stress field was calculated
once the velocity field simulations had converged.

EXPERIMENTAL
The gauging nozzle used in this study was constructed from Perspex with dt = 20 mm and
d = 5 mm, and mounted in a large tank. During an experiment, process fluid is sucked from the quasi-
stagnant surroundings (1) into the nozzle (2) and then to a flow-rate measuring device. The suction
pressure is maintained constant by fixing the hydrostatic head, H. The discharge flow rate, m, is
measured gravimetrically and the errors in all measured parameters were small.
Model tomato food pastes were generated using the method reported by Liu et al.3. Tomato
paste with the composition (wt%): 4.7 protein, 14.9 carbohydrate, 14.4 sugar, 0.4 fat, 2.0 fibre and
63.6 water, was obtained from a supermarket. The paste was spread evenly (thickness ~ 2.0 mm)
onto stainless steel discs of 316 to give soil patches of diameter ~ 30 mm. The samples were then
heated/dried in a vacuum oven (Gallenkamp) at 100oC over times ranging from 0.5 to 4.0 h. The
structures of the dried soils were characterized by scanning electron microscopy (SEM, Philips XL 30
Series FEG) after gold/palladium sputtering. The 0.5 h samples were freeze-dried prior to imaging to
reduce their moisture content to a level acceptable for SEM analysis (< 10% moisture). The dried
samples were hydrated in reverse osmosis water at 18oC for more than 1.0 h prior to any gauging flow
experiments. This period was selected because Liu et al. reported negligible effects of hydration time
on the adhesive strength of their dried tomato paste soils after one hour.
For each sample, the initial thickness of the tomato paste, δo, was determined using the
protocol outlined in Tuladhar et al.5 using low values of H (typically < 20 mm) in order to
minimize/eliminate any deformation. The vertical movement of the gauge towards the surface was
operated in advancing mode i.e. starting from h/dt > 1.0. The discharge flow rates were recorded as
the gauge was moved gradually towards the sample, with H kept constant. The time required for the
deposit to reach its equilibrium thickness, δ, at each value of h/dt was less than 120 s. After δ was
measured, the gauge was advanced further towards the surface. The behaviour of the sample could
also be observed through a magnifying glass; photographs of the deposits before and after
deformation were also recorded.

RESULTS AND DISCUSSION

Figure 2(a) shows the simulated normal stress distributions on the gauged surface plotted
alongside experimental data obtained with sucrose solution (35 wt%, viscosity = 3.7 mPa s) at H = 55
mm. The normal stress imposed on the surface was measured via a 0.5 mm diameter pressure
tapping located in a horizontal plate across which the gauging nozzle could be traversed via a vernier
scale (details are given in 8). The plots show good agreement. Separate simulations indicated that the
presence of the tapping on the gauged surface does not interfere with the flow in the gauge. The CFD
predictions show that the sharp peaks of the suction pressure occur within the inside radius of the
nozzle, i.e. for R < 0.25. The experimental measurements show flatter peaks in the higher pressure
region, which is partly due to the pressure tapping giving an average value of the stress over the
exposed surface (port diameter is 0.5 mm, giving a ratio of port diameter to nozzle diameter of 0.1).
The corresponding distributions of shear stress on the gauged surface are plotted in Figure
2(b). The shear stress increases from zero at the symmetry point on the centreline (R = 0), peaks at
the radial position of the inner rim of the nozzle (R ~ 0.25), and then approaches zero asymptotically
for large R. The shoulder located outside the nozzle outer radius (R ~ 0.62) arises from the inertial
effects in the flow which disappear at low Ret. For all cases considered, the peak shear stress values
was located at R ~ 0.25, i.e. close to the inner radius of the rim of the nozzle.
Figures 3(b,d) shows that the gauging flow generated a small crater located below the
gauging axis. Visual monitoring indicated that the material failed by breakage away from the stainless
steel surface, with visible lumps of material being detached by the gauging flow. This observation
suggests that dynamic gauging will measure the adhesive interaction between the soil and the
substrate, rather than cohesive forces within the layer. Furthermore, it was noted that the deposits
generated by extended drying detached in larger pieces, whereas the most moist sample – being
softest – eroded away smoothly. This difference in brittleness is consistent with the microstructures
indicated by the SEM images in Figure 3(a,c).
ICEF9 – 2003
International Conference Engineering and Food

700
(a)
600
C

500

B
- Pwall [Pa]
400 Inner radius of the nozzle rim, R i = 0.25
Outer radius of the nozzle rim, R o = 0.50
300
A
200

100

0
0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00

30
(b)
C
25

B
20
τwall [Pa]

A Inner radius of the nozzle rim, R i = 0.25

15
Outer radius of the nozzle rim, R o = 0.50

10

0
0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00

Figure 2: Stress distribution on the gauged surface for 35 wt% sucrose solution with H = 55 mm.
(a) Normal stress. Line – CFD predictions; symbols – experimental measurements.
A, circles – h/dt = 0.20; B, squares – h/dt = 0.14; C, triangles – h/dt = 0.10.
(b) Shear stress predictions, symbols as above.

(a) (b) (c) (d)

Figure 3: Samples before [SEM (a), (c)] and after [(b), (d)] FDG deformation.
Samples dried for (a,b) 0.5 h and (c,d) 2.0 h.

The response of the layers to imposed shear stress is expressed in terms of the degree of
deformation, δ*, a normalized deposit thickness, given by
ICEF9 – 2003
International Conference Engineering and Food

δ
δ* = (7)
δo
where δ is the deposit thickness measured at the shear stress calculated for a given geometry and
flow. Figure 4 presents the deformation characteristics of the hydrated, baked tomato paste in terms of
the maximum shear stress imposed on the surface. The results denote average values for four
samples at each test condition. Each data set in the Figure shows small deformation at low shear
stresses and a transition to complete removal (δ*= 0) over a narrow range of shear stress values,
indicative of yield stress or fracture behaviour. The transition is sensitive to the extent of drying – and
hence to ageing and structure development. The difference in the deformation profile between the
moist sample (0.5 h drying) and others is noteworthy, as the former exhibits a gradual response
whereas the latter sets exhibit brittle breakage at some critical value (denoted by filled symbols). This
difference in behaviour is also consistent with the removal patterns observed in Figures 3(b) and (d). It
should be noted that the data in the Figure were generated at two laboratories, in Cambridge and in
Braunschweig, using similar apparatus and materials. The good agreement between the results
indicates that the technique and procedure is reproducible and readily implemented and suggests that
enhanced FDG represents a reliable method to study soil cleaning characteristics.

1.00
Sample drying time

0.5 h
0.80
1.0 h
2.0 h
0.60 3.0 h
4.0 h
δ*

0.40

0.20

0.00
0 2 4 6 8 10 12 14 16

Maximum shear stress, τmax [Pa]

Figure 4: Deformation behavior in response to maximum shear stress imposed by gauging flow.

1.00

0.80

Sandpaper grades
0.60
Normal
δ*

80
0.40 180
240
0.20

0.00
2 3 4 5 6 7 8 9 10

Maximum shear stress, τ m ax [Pa]

Figure 5: Deformation of tomato paste dried for 1.0 h for stainless steel surfaces of different roughness

The role of suction, namely removal by the normal stress difference, was investigated by
preparing soil samples on stainless steel discs with different surface characteristics. This parameter
ICEF9 – 2003
International Conference Engineering and Food

should affect adhesive interactions, with a small affect on soil cohesion. The surfaces were roughened
using graded sandpapers (80, 180 and 240) and the roughness was measured using a Mahr
Perthometer PGK. The arithmetic mean of the absolute departure of the roughness profile from the
mean line, Rz, for the stainless steel surfaces treated with sandpaper 80, 180 and 240 were 4.4 µm,
3.1 µm and 2.7 µm respectively (stainless steel with normal surface finish had a Rz value of 2.4 µm).
The pastes in this case were dried for 1.0 h and the averages from repeated tests are plotted in
Figure 5. The strength of the deposit clearly increased with surface roughness and indicates that the
critical parameter being measured for the brittle soils in these studies is the adhesive interaction
between the samples and the steel surface. It is also noteworthy that the largest critical shear strength
value for this series of samples (~ 9.2 Pa) is lower than that for samples dried for 2.0 h (~12 Pa) on
plates with a normal finish. FDG thus offers an affordable and simple method for testing adhesion of
hydrated macro-layers to surfaces, as would arise in cleaning-in-place operations.

CONCLUSIONS
The FDG technique has been extended by CFD to afford measurements of the strength of soft
deposits in a Newtonian fluid environment. This application has been demonstrated by a study of the
removal behaviour of a model food soil, namely dried tomato paste, from stainless steel surfaces. The
shearing yield strength of the tomato paste was found to be strongly dependent on the extent of
baking (ageing), approaching an asymptote as the material was transformed from a soft, malleable
paste into a brittle semi-solid. The effect of surface roughness was evident and also indicated that
aged deposits were being removed by breakdown of adhesive interactions.

ACKNOWLEDGEMENTS
JYMC wishes to acknowledge support from the Cambridge Commonwealth Trust. We thank
Dr. S.S.S. Cardoso for assistance with the CFD calculations, Tony Burgess (Department of Anatomy,
Cambridge, U.K.) for aid with electron microscopy, Sabine Knoblauch (ICTV, Braunschweig) for
assistance in surface roughness measurements. The collaboration with TU-Braunschweig was
sponsored by the British Council/FDG under ARC Project 1197.

NOMENCLATURE
d gauging tube diameter, m Re Reynolds number
dt gauging nozzle diameter, m vc characteristic velocity, m/s
h clearance, m V velocity vector, m/s
H hydrostatic head, m δo initial deposit thickness, m
lc characteristic length, m δ∗ normalized deposit thickness
m discharge flow rate, kg/s µ viscosity, Pa s
P pressure, Pa ρ density, kg/m3
Pwall wall pressure, Pa τmax maximum shear stress, Pa
RZ surface roughness value, m τwall wall shear stress, Pa

REFERENCES
1. Müller-Steinhagen H. “Heat Exchanger Fouling – Mitigation and Cleaning Technologies.”
IChemE, Essen, Germany, 25p, 2000.
2. Fryer P.J., Slater. N.K.H. A novel fouling monitor. Chemical Engineering Communications, 57,
39-152, 1987.
3. Liu W., Christian G.K., Zhang Z., Fryer P.J. Development and use of a micromanipulation
technique for measuring the force required to disrupt and remove fouling deposits. Trans
IChemE, 80 Part C, 286-291, 2002.
4. Vaishnav R.N., Patel D.J., Atabek H.B., Deshpande M.D., Plowman F., Vossoughi J.
Determination of the local erosion stress of the canine endothelium using a jet impingement
method. Journal Biomechanical Engineering, 105, 77-83, 1983.
5. Tuladhar T.R., Paterson W.R., MacLeod N., Wilson D.I. Investigation of alkaline cleaning-in-place
of whey protein deposits using dynamic gauging. Trans IChemE, 80 Part C, 199-213, 2002.
6. Tritton D.J. (1988). Physical Fluid Dynamics (2nd ed.). Oxford University Press, Oxford, U.K., 58-
59p, 1988.
7. Chew J.Y.M., Cardoso S.S.S., Paterson W.R., Wilson, D.I. CFD studies of dynamic gauging.
Chemical Engineering Science, 2003, in press.
8. Chew J.Y.M., Paterson W.R., Wilson, D.I. Fluid dynamic gauging for measuring the strength of
soft deposits. Submitted to Journal of Food Engineering, 2003.
ICEF9 – 2004
International Conference Engineering and Food

The modelling of the flow of smoke in an electrostatic smoking process

Havet M. (1), Pierrat D. (2), Delanoue N. (1), Pottier L. (1), Baron R. (3)
(1) ENITIAA, Laboratoire GEPEA UMR CNRS 6144, Rue de la Géraudière, BP82225,
44322 NANTES Cedex 03 France,
havet@enitiaa-nantes.fr
(2) CETIM, 74 route de la Jonelière, 44000 NANTES France
daniel.pierrat@cetim.fr
(3) IFREMER, Laboratoire de Génie Alimentaire, Rue de l’île d’Yeu, BP 21105,
44311 NANTES Cedex 03 France
rbaron@ifremer.fr

Abstract
As the traditional process of food smoking is very slow, the electrostatic smoking
process is promising. It consists in applying an electric force to particles of smoke in
order they precipitate. To design this process, we determined the characteristics of
the smoke using a laser light scattering. These measurements permitted to choose
an algebraic slip model in order to study the turbulent two-phase flow of smoke. First
results are obtained in a standard geometry of an electrostatic precipitator.

Key words: smoke, laser light scattering, turbulence, modeling, CFD.

Introduction
The traditional process of food smoking constitutes one of the oldest known methods
of conservation of meat products, associated with drying and salting. More than one
means of conservation, the smoking process is especially used today at organoleptic
goals. There are two main smoking processes which are the hot smoking, leading to
smoked and cooked products, and the cold smoking, more used for the fish smoking.
After being slightly salted, then dried, the fish are subjected to the action of smoke
coming from the incomplete combustion of sawdust or shavings. During this phase,
which can last a few hours, the fish continues to be dehydrated and impregnates
volatile compounds present in smoke. For smoked salmon, the temperature is
maintained between 20 and 25°C and it does not exceed 30°C, to avoid a surface
dehydration that could limit the smoke penetration.
As the traditional smoking process is very slow, and imposes rather long former
handling, manufacturers are forced towards productivity gains in respect of the
organoleptic and hygienic quality of the products. For theses reasons, the
electrostatic smoking process is very promising. It consists in conveying fish in a
tunnel through an electrostatic field which permits to smoke in few minutes. This
continuous process has been developed by IFREMER and CIRAD which jointly
register a patent [1]. Figure 1 represents a sketch of this process associated with the
salting and drying phases.
ICEF9 – 2004
International Conference Engineering and Food

Figure 1: Sketch of the continuous salting – drying –smoking process

This promising technology needs to be improved in order to maintain an industrial

rate in good conditions. At the moment, the Electrostatic Smoking Process leads to a
too important smoke deposit on the walls of the tunnel. Moreover, the smoke deposit
on the fish is not homogeneous: it varies with time and space. The improvement of
the process needs to carry out experiments and to understand very well the
fundamental physics.

The electrostatic precipitation

The electrostatic smoking process of food is in keeping with the more general scope
of electrostatic precipitation [2, 3]. The principle is that when a particle with an electric
charge is placed in an electric field, it is subjected to a force parallel to the electric
field. This elementary principle makes it possible to apply a force to particles so that
they are driven in an area and precipitate preferentially on a given surface.

To obtain the effect of precipitation, the particles must first acquire an electric charge,
and secondly these particles must be inside an electric field of sufficient intensity so
that they are directed towards the wished path under the influence of this electric
field. The electric discharges form the basis of the electrostatic precipitation since
they generate the ions which will come to be fixed on the particles to collect. These
discharges are obtained by applying a high voltage to a conductor of low dimensions
(called the discharge electrode), typically an arrangement of successive wires, facing
to a large-sized electrode, typically a plate connected to the ground.

At the vicinity of the discharge electrode, a non-uniform and very intense electric field
is generated. For a local electric field from approximately 3 MV/m (this critical value is
called “disruptive field”), a discharge takes place in the air in the neighbourhood of
the electrode and generates the ions which are at the origin of the charge acquired
by the particles [4]. This phenomenon is called “corona effect”. In addition to the
electrode geometry, the corona effect is influenced by the polarity of the discharge
electrode and by the gas properties.

All the concerned phenomena are complex and at the present time only partially
formalized [5]. Figure 2 represents a sketch of the coupling effects between the
particulate phase (smoke), the gas phase (air) and the electrical Corona [2].
ICEF9 – 2004
International Conference Engineering and Food

Particulate Fluid-Particles Gas

Dynamics
Phase Phase
Particle
Charging Charge
Electric Advection
Body
Field
Force
Distortion

Electrical
Corona
Figure 2: Coupling between components of the model

The transported particles (particulate phase) undergo the combined action of the
electric forces and the turbulent flow of the carrying phase (gas phase). With the
turbulent flow of the carrying phase is added an electro-hydrodynamic current
produced by the effect of corona discharge, there is a generation of a "ionic wind" in
the inter-electrodes space in the presence of an electric field of strong intensity.
The particles trajectories depends on the gravity force, the viscous drag force of
particles in the phase carrying and a Coulomb force determined by the product of the
particle charge and the local electric field. Before modeling this rather complex
process we need to get a better knowledge on the smoke properties.

The smoke properties

Wood smoke is composed of two phases, namely a particulate or dispersed phase
and a gaseous or dispersing phase. The dispersed phase is the visible portion of
smoke and the particles are usually in the form of liquid droplets that formed by
condensation. Literature is neither abundant nor consensual on particle distribution.
According to Maga [6], the particles from all smoke sources have an average
diameter between 0.196 and 0.346 µm. However, Kleeman et al. [7] measured
particle distribution between 0.02 and 0.250 µm and Bonneto [8] measured volume
distributions with a peak at approximately 0.7 µm diameter. According to Sainclivier
[9], in a "young" smoke produced by an auto-combustion generator, droplets are very
small (approximately 0.1 µm) but their size change as a function of time. Droplets
collide with one another due to Brownian motion and adhere to form larger particles.
There is an increase in particle size coupled with a decrease in number
concentration. This phenomenon of coagulation depends on the initial number
concentration and size particles. Sainclivier calculated that for a concentration of 1
mg of particles per litre of smoke and for initial particles diameter of 0.10 µm, 10 s is
required for the number concentration to decrease to one-half of its initial value.
From these considerations, we carried out experiments in order to measure the
distribution of smoke particles emitted from a friction generator (MUVERO FOOD,
model Technic FR1002). In this generator, an intact wood block is pressed against a
rapidly rotating metal friction wheel. Heat obtained by friction is sufficient to cause
wood pyrolysis and to produce instantaneous and dense smoke. Phases of friction
(constant time of 12 s.) are followed by phases of rest (variable time) to avoid an
overheating being able to cause departures of fire.
Particle size determination was run at least in duplicate using a Malvern Master Sizer
S (Malvern Instruments, Ltd) laser diffraction analyzer with a 300 mm Fourier cell.
The smoke produced by friction was introduced into a box plug during a variable time
(from 50 s. to 30 min.) to point out coagulation effects. The smoke was then fed to
the measuring cell thanks to a sucking up system placed downstream the analyzer.
ICEF9 – 2004
International Conference Engineering and Food

In this work, we assumed spherical particles and the median diameter, D[v,0.5], the
size at which 50% of particles by volume are smaller and 50% are larger, was
chosen to allow comparisons with literature data. The refractive indices of particles
and gas phases were 1.45 and 1.00 respectively.

Results on the physical properties of smoke

Figure 3 presents two experimental distributions obtained for a smoke having a lag
time of fifteen minutes in the box plug. This distribution, which can be suitably
modelled by a law log – normal, is characterised by a median diameter equal to
1.31µm. This value is greater than those issued from the literature but it is mainly due
to coagulation effects. Indeed, this distribution is greatly dependent on the lag time in
the box plug. All our experiments showed an increase of the median diameter and of
the span with this lag time (Figure 4).

15 1,80
#1 Experiments
%

Median diameter (µm)

#2 Coagulation law
10 1,40

5 1,00

0
0,60
0,1 1 10 100 0 500 1000 1500 2000
diam eter (µm )
Time (s)

Figure 3: Granulometric distribution of smoke of Figure 4: Evolution of the median diameter with time
beech after 900 s

The increase of the median diameter can be modelled according to the coagulation
by Brownian diffusion for a monodisperse distribution [10]:

d p(t)=d p0(1+ N0 Kt) 3 with N(t)= N 0

1+ N 0 Kt and dp : diameter, dp0 : initial diameter, N0 :
initial numeric particles concentration and K the coagulation coefficient. It appears
that the growth of the particle diameter follows perfectly this law (figure 4). In our
case, adjustment of the various coefficients provided the following values: dp0 = 0.60
µm, K = 3.57.10-16 and N0 = 1.4.1013 particles/m3. It is noticeable that the coagulation
phenomenon is well predicted and permits to deduce the initial diameter and
concentration of particles. These results permit to calculate the volume fraction of
smoke particles (1.6.10-6 m3/m3) and to consider that the smoke is very diluted.

Model of the electrostatic process

To model the flow of a dispersed phase (smoke particles) in a continuous phase (air)
the Lagrangian and Eulerian approaches are the most popular. The Lagrangian
technique permits to follow each particle by calculation of all trajectories using
balance equations. It presents some drawbacks because a great number of
trajectories should be calculated and it requires very short time steps and great
computational ressources. The Eulerian technique considers two phases with an
interface and requires the calculation of momentum equations for each phase. As the
smoke is diluted and the relaxation time of particles is low, we choose an alternative
ICEF9 – 2004
International Conference Engineering and Food

approach: the Algebraic Slip Model (ASM). We consider a mixture which is a

continuous medium in which there is a dispersed phase. This approach, where the
continuous and dispersed phase behave as a single fluid (velocity u), is valid for
particles whose diameter is less than 5µm. A classical Reynolds Average Navier-
Stokes equations is used to model the turbulence and the ionic wind is considered as
a source term in the momentum equation of the continuous phase (Eq. 2). For the
particle phase of smoke, we consider from our experiments a transport equation for
only one class of particle with a volume fraction rp (Eq. 3). The slip velocity (relative to
the air velocity uc) depends on the electric charge of the particles (qp) and the Electric
field solved from Eq. 5. A Poisson equation permits to calculate the electric potential
taking into account the ionic charge (Eq. 4).
∂ρ ∂ ρU j
+ =0 (1)
∂t ∂ xj
∂ρ U i ∂ρ U j U i ∂P ∂   ∂ U i ∂ U j 
  + ρ ion Ei
+ =− +  µ eff∂x
+

(2)
∂t ∂ xj ∂ xi ∂ x j   j ∂ x i 

∂   qp E  
max
∂ρ rp r − D ∂rp  = − De
+ ρ Uc + (3)
∂ x j   3πµd p  ∂ xj 
p p
∂t
 
∂ V
2
ρ
= − ion (4)
∂ xj
2
ε0
∂V
Ej =− (5)
∂ xj
The CFD Code CFX4.4 (AEA Technology) was customized in order to solve these
equations which are fully coupled. We tested our model in a simple configuration:
three wires between an insulated and a collecting plate. We considered in this first
approach that the electric field is not dependent on the ionic charge and that the
contribution of the ionic wind is negligible. Moreover, the deposal term is not taken
into account (De=0). Figure 5 presents the electric potential between the wires
(40kV) and a collecting plate (0 V). We observed, close to the wires, a high electric
field which permits to precipitate particle towards the collecting plate. Figure 6
confirms that the concentration of particles is greater close to this electrode.

Figure 5: Evolution of the electric potential

ICEF9 – 2004
International Conference Engineering and Food

Figure 6: Evolution of the smoke concentration (kg/m3)

These results confirm that our model is able to predict the physical phenomena
encountered in an electrostatic precipitator under restricted assumptions, we will
perform more computational efforts in order to improve the model.

Conclusion
The electrostatic smoking process is a promising technology which should be
investigated before expand to the industry. This study permits to obtain a better
understanding of the physical phenomena and on the smoke characteristics. We show
that the median diameter of smoke particles is close to 0.7 µm and that coagulation
effects appear. These experimental results lead us to choose the ASM model in order
to numerically predict the flow of smoke under electrostatic conditions. The electro-
hydrodynamic model was solved to predict the physical phenomena encountered in an
electrostatic precipitator. The results are satisfying but further investigations should be
carried out in order to improve the model and to validate it using experimental data.

References:
1. Collignan A., Knockaert C., Raoult-Wack A.L., Vallet J.L. “ Procédé et dispositif de salage, séchage
et de fumage à froid de produits alimentaires carnés.“ Brevet Ifremer/Cirad n° 92/08 958 – 1992 (*)
2. Choï B.S., Fletcher C.A.J. “Turbulent particle dispersion in an electrostatic precipitator.“ Applied
Mathematical Modelling, 1998, 22:1009-1021
3. Park S.J., Kim S.S. “Effects of particle space-charge and turbulent diffusion on performance of plate-
plate electrostatic precipitators.“ Journal of Electrostatics, 1998, 45:121-137
4. Chen J., Davidson J.H. “Electron density and energy distributions in the positive DC corona :
Interpretation for corona-enhanced chemical reactions.” Plasma chemistry and plasma processing, Vol.
22, N°2,199-222, 2002.
5. Tochon P. “Etude numérique et expérimentale d’électrofiltres industriels.“ Thèse de l’université
Joseph Fourier, Grenoble I, 1997
6. Maga J., 1988. Smoke in food processing. , Boca Raton, Florida.
7. Kleeman M.J., Schauer J.J. and Cass G.R., 1999. “Size and composition distribution of particulate
matter emitted from wod burning, meat charbroiling, and Cigarettes.” Environmental Science and
Technology, 33(22), 3516-3523.
8. Bonneto A. “Caractérisation de la fumée de fumage.” DESS Physique des Aérosols PARIS XII, 1994
9. Sainclivier M. “L'industrie alimentaire halieutique. Chapitre V : Le fumage. “ Bulletin scientifique et
technique de l'école nationale supérieure agronomique et du centre de recherches de Rennes, 1985
10. Hinds W. “ Aerosol Technology – Properties, behavior and measurement of airbone particles“ –
John Wiley and Sons Inc., 1999.
ICEF9 – 2004
International Conference Engineering and Food

Airflow and heat transfer in packed bed of agricultural produce (potatoes, broccoli):
comparison of different predictive approaches
1 2 2
Jacobsson Annelie , Sarkar Arnab and Singh R. Paul
1
SIK, The Swedish Institute for Food and Biotechnology, Ideon, SE-223 70 Lund, Sweden.
E-mail: aj@sik.se
2
Department of Biological and Agricultural Engineering, UC Davis, One Shields Ave, CA 95616, USA.
E-mail: asarkar@ucdavis.edu
E-mail: rpsingh@ucdavis.edu

Abstract
Computational fluid dynamics, CFD, with the porous media assumption was used to simulate the
airflow and cooling of potatoes and broccoli. The porous media approach for flow could be extended to
irregularly shaped produce; 3.5 % deviation. For heat transfer, the transient assumption gave the most
satisfactory results. However, for irregularly shaped products the lumped approach was more suitable.

Keywords: CFD, porous media, airflow, heat transfer, geometry

Introduction
Forced-air cooling is one important method for cooling agricultural products. Here the agricultural
commodities are stored in bins, or boxes stacked on pallets, in cold storage rooms. The geometrical
design of the boxes or bins, the air flow rates, and the cooling air, are important factors affecting
cooling and evaporative water loss (1-2). Flow through packed beds of regular shapes i.e. oranges
and potatoes, using the porous media assumption with a Darcy-Forchheimer-Brinkman (DFB) type
model has been modelled (3-4), and heat transfer inside packed beds of agricultural commodities has
been the subject of intense research. Two ways of modelling packed beds has been described (5); the
two-phase model (air phase and solid product phase) for heat transfer and the equivalent conductivity
model. The two-phase model has been applied assuming lumped heat transfer inside the solid (6-7)
and assuming transient conductive heat transfer inside the solid (8-9).

The objectives in this study were to extend the DFB model for flow in porous media to irregularly
shaped produce, i.e. broccoli, and to investigate the applicability of the various approaches for
modelling heat transfer in packed beds of regularly and irregularly shaped produce, i.e. potatoes and
broccoli. Experiments of flow and forced air cooling were conducted in order to validate the modelling.

Experimental approach
The apparatus used for the airflow and cooling experiments is shown in figure 1. The pressure across
the plate was measured using a digital manometer, series 475-000 MARK III (Dwyer Instruments Inc.,
Michigan City, USA). Local air velocities were measured using a Thermo-Anemometer model 8500D-II
(Alnor Instrument Co., Skokie, USA).

Orifice plate Tubes for measuring pressure

Air flow
Suction fan

Tunnel filled with produce

Figure 1. Schematic figure of the setup, simulating forced-air cooling used for airflow and cooling
experiments.
ICEF9 – 2004
International Conference Engineering and Food

Airflow measurements
The pressure drop in the packed bed was measured at eight points along the length of the tunnel for
five different airflow rates in the range of 0.38-0.70 m/s for the potatoes, and 0.15-0.26 m/s for the
broccoli, with three replicates for each flow rate.

Forced-air cooling
The temperature was monitored at three different points on an individual piece of produce, and at
eight different points in the tunnel during cooling from 19 °C to 6 respectively 4 °C. The air
temperature was monitored at the same eight points. Thermocouples (T type, 24 gauge, Omega
Engineering Inc., Stamford, USA), and a 21X data acquisition system (Campbell Scientific Inc., Logan,
USA) were used to collect the data. Before and after cooling, the weight of the product was measured,
and after cooling the exact location of the thermocouples inside the product was determined. The
average air temperature was 3.5 °C, the relative humidity of the room was 90 %, and the airflow rate
3
was 0.001 m /s/kg.

Determination of the characteristic dimensions

The dimensions were determined from 75 respectively 60 randomly selected potatoes and broccoli.
The particle density (ρparticle) of the potatoes was determined using the volume of an ellipsoid of
equivalent dimensions, while the ρparticle of the broccoli was assumed to be that reported in literature
(10). The bulk density (ρbulk) was determined by the weight of the produce in the tunnel, and the tunnel
volume. Using the data relating to the dimensions and the densities, the porosity and the effective
diameter were calculated (Eq. 1 and 2). The effective diameter of the broccoli was calculated as a
combination of a cylinder and half a sphere using the weighted average surface-to-volume ratio
method (11).

6V ρbulk
d eff = ; ε = 1− [1, 2]
A ρ particle

Modelling approach
The Ergun constants, (K1 and K2) respectively for the potato and the broccoli were determined by
fitting the pressure drop per unit length versus the velocity data. The constants were then calculated
with Eq. (4) and (5) using the calculated deff and ε. A review of the theory can be found in (12).

∆p (1 − ε ) 2 µ u (1 − ε ) ρ u 2
Ergun equation; = K1 + K [3]
l ε 3 deff2 2
ε 3 deff

1 (1 − ε )2 (1 − ε )
Where = K1 ; β = K2 [4, 5]
κ d eff ε
2 3
d eff ε 3

Airflow simulation
The DFB model was solved in two dimensions using the FLUENT 6.0.20 CFD solver on the Windows
NT platform (FLUENT Inc. Lebanon, USA). Meshing was done using Gambit 2.0.4 (FLUENT Inc.). The
grid was made denser at the walls of the tunnel to accommodate wall effects. The boundary conditions
were specified, the pressure at the inlet was defined as the total pressure difference across the tunnel
and the pressure outlet as zero with wall effects as the other boundaries. The inlet air turbulence
intensity was assumed as 10 % and turbulence modelling was carried out using a k-ε type turbulence
model. To validate the model the simulation was conducted for a given pressure drop across the
packed bed and the flow rate predicted by the model was compared against experimental results.

Heat transfer simulation

The different approaches for the solution of heat transfer in a porous media were applied using a CFD
segregated unsteady solver (FLUENT 6.0.20), using mesh generated for the flow simulation.

1. Composite media assumption. The input variables required were the thermal properties of the
product and the air, inlet and boundary conditions for the energy. The thermal properties were
assumed constant and are shown in Table 1. The initial conditions for the porous media was assumed
as constant and the inlet temperature were that of a constant average temperature of the cold storage,
ICEF9 – 2004
International Conference Engineering and Food

3.5 °C. The walls were assumed to be zero flux boundaries. When the product and air is considered
as a composite media, the energy equation for the porous media can be described as equation 6.

∂
∂t
{ερ a caTa + (1 − ε ) ρ p c pTs } + ∇ {u ( ρ a caTa )} = ∇ ( keff ∇Tc ) + S
v
[6]

Where keff = ε k f + (1 − ε ) k s and Tc is the temperature of the composite media (Tc= Ta = Ts) and S is
the enthalpy source in the media, assumed to be zero (12).

2. Lumped heat transfer in solid phase. The average velocity predicted by the modelled airflow was
used to determine the convective heat transfer coefficient (h) using empirical correlations (13).
Equation 6 for the air phase can be simplified to Eq. 7, assuming that the product did not conduct or
store any heat, that the conductive heat transfer through the air phase was small, and that the source
of heat into the airflow is a result of convection from the surface of the product. This approach was
used to modify the porous media heat transfer model in order to solve the air phase of a two-phase
model. The solid phase was solved as a user-defined function (UDF) of a lumped model for heat
transfer in the solid phase Eq. 8. The boundary conditions are similar to those of the composite media
approach. In the case of broccoli, the surface evaporation effect was taken into account in the
simulation, since the moisture loss was considerable when cooling the broccoli.

 ∂Ta v 
ρ a ca  + ∇ ( uTa )  = − hA (Ta − Tp ) [7]
 ∂t 
∂Tp
= hA (Ta − Tp ) + q
.
ρ pcp [8]
∂t
3. Transient heat transfer in solid phase. The solution of the air phase equation was similar to that
carried out during the lumped approach. Instead of solving the lumped model, a transient conduction
equation was solved using an iterative numerical scheme. For potatoes, the transient conduction
equation was assumed to be that of a sphere, Eq. 9, and it was solved in conjunction with the flow
equation using a finite difference scheme.

1 1  2 ∂Tp  ∂Tp
 kr  = ρcp [9]
r ∂r 
2
∂r  ∂t

In the case of broccoli, using the transient approach was not possible in this study, and should be
considered as a topic for further research.

Results and discussion

Experimental results
A summary of the characteristic parameters of the potato and the broccoli is shown in Table 1.

Airflow measurements. An increased airflow rate resulted in an increased pressure drop per unit
length. The K1 and K2 for potato (K1 = 737, K2 = 1.3) and broccoli (K1 = 12226, K2 = 20.1) were in
accordance with previous studies (1, 4, 14) except for the K1 for potato which was higher than the data
published by van der Smam (K1 = 180).

Forced-air cooling. The cooling rate varied along the tunnel, the objects placed close to the air inlet
cooled faster than the ones placed at the end of the tunnel. Monitoring the air temperature confirmed
the slower fall in temperature at the end of the tunnel. The time needed to cool potatoes from 19 °C to
6 °C was 93 minutes, while to cool broccoli from 19 °C to 4 °C was 60 minutes. Forced-air cooling
resulted in a weight loss of 1.8 % in the broccoli, while for the potato no weight loss could be detected.

Model output and validation

Flow simulation using DFB model. In order to validate the model it was run for a specific pressure
drop, and the predicted superficial velocity was compared to the experimental velocity under the same
conditions. The results showed that it is possible to use the Ergun equation and the porous media
ICEF9 – 2004
International Conference Engineering and Food

assumption for non-spherical products as long as the characteristics of the product are well known.
The model proved to give good correlations with the experiments; the deviation being 7.2 % in the
potato and 3.5 % in the broccoli. Among other factors, this deviation from the experimental results
might be a result of channelling the airflow along the walls. The parameters needed for flow
simulations are shown in Table 1.

The influence of the product characteristics, i.e. the effective diameter, density, and porosity, were
investigated and found to have a significant impact on the sensitivity of the model. As an example,
decreasing the density of the potato by 10 % from the correct value resulted in a 21 % deviation of the
model, when compared with the experimental data, instead of 7 %.

Table 1. Parameters used for modelling of potato and broccoli.

Parameters Potato Broccoli

Diameter, d (mm) ellipsoid; 48; 57; 99.6 stem/head; 40.8/101

Effective diameter, deff (mm) 40.5 54.9
3
Particle density, ρparticle (kg/m ) 1172 272
3
Bulk density, ρbulk (kg/m ) 547 860
Porosity, ε 0.545 0.687
Specific heat capacity, Cp (kJ/kg/K) 3.48 3.84
Thermal conductivity, k (W/m/K) 0.528 0.596
Weight, m (kg) 27 12
Pressure inlet, p (Pa) 17 16
Ergun coefficients: K1 737 12226
K2 1.3 20.1
Superficial velocity, predicted by
FLUENT, upred (m/s) 0.44 0.22
Superficial velocity, measured, um (m/s) 0.408 0.212
Reynolds number, Re 402 >500
Colburn factor, jH 0.052 0.040
2
Heat transfer coefficient, h (W/m /K) 64 20-29

Heat transfer modelling

The advantages and disadvantages of applying the various solution strategies to heat transfer in the
case of regularly and irregularly shaped agricultural commodities is summarized in Table 2.

Table 2. Comparison of the various heat transfer simulation procedures for packed beds.
Simulation approach Characteristics of the solution

Composite media - Short simulation time*; 20 minutes for 2 hr flow time

- Only average temperatures are useful for design or analysis
- Significant variations from experiments
Two-phase modelling - Intermediate simulation time*; 6 hrs for 2 hr flow time
- lumped assumption in - Predicted curve follows general trend but has significant errors for
solid phase high Biot numbers
Two-phase modelling - Long simulation time*; 12 to 24 hrs for 2 hr flow time depending on
- transient assumption in number of nodes in solid phase
solid phase - Excellent agreement with experimental results for shapes that can
be modelled as cases of one dimensional heat transfer
- For irregular shaped produce such as broccoli it is difficult to apply
in a CFD simulation

* Simulation times are a factor of mesh density, time step size and computing power of machine

1. Composite thermal properties. The composite media approach only provides an average
temperature profile of the entire package. Hence, outputs of the average of the air and solid in the
package were compared to the simulation results. The simulation time was brief, however, the
predictions were unsatisfactory with significant errors when compared to the experimental results for
potatoes. Similar differences were noted in simulations using broccoli.
ICEF9 – 2004
International Conference Engineering and Food

2. Two-phase modelling using lumped capacitance. The lumped approach, when applied to potatoes,
gave satisfactory results. It overestimates the air temperature and underestimates the lumped-solid
temperature. This error may be attributed to the validity of the lumped approach, since the Biot
number (NBi = hD/k) for the given case is in the order of 2. Applying the lumped approach on broccoli
showed that although the air phase simulation is reasonably satisfactory (within 2 °C) the solid phase
simulation varies considerably from the experimental results. The errors are more significant in
broccoli where NBi is higher since broccoli has a larger characteristic dimension. Thus, the lumped
approach may be applicable only for lower flow rates in smaller products where NBi values are less
than 0.1.

3. Two-phase modelling using transient conduction in the product phase. The results for the potato
(regular shape) fitted well with the experimentally-determined temperature profiles. The errors were
within 1 °C, which is well within the limits of experimental uncertainty. Fig. 2 shows similarly simulated
curves vs. experimentally determined curves for the air phase. The variations between the simulated
and experimentally determined temperatures are larger, especially near the outlet. This may be due to
errors in estimating the turbulence at the exit. In the case of broccoli (irregular shape), assuming the
stem as the critical mass for cooling ignores the heat generated by the crown. On the other hand,
simulating heat transfer from the entire broccoli would require two or three dimensional modelling. This
will increase the simulation time significantly and is consequently impractical.

20

18

16 Outlet of tunnel

14 Middle of tunnel
Temperature (°C)

12 Simulated-outlet

10 Simulated-middle

0
0 20 40 60 80 100 120 140 160 180
Time (min)

Figure 2. Experimental and simulated temperature profiles for air in a packed bed of potatoes, using
two-phase heat transfer with transient conduction.

Conclusions
The DFB simulation approach for flow in packed agricultural commodities can be extended to
irregularly shaped produce such as broccoli. The simulation of heat transfer using the composite
media approach is the simplest, but was found to not be applicable for agricultural commodities.
Among two-phase modelling approaches, the lumped approach is simple to apply. However, its use is
restricted due to internal temperature considerations. The application of the lumped approach to cases
where the Biot number is significantly > 0.1 is not accurate. The approach of solving the transient
equation for heat transfer inside a food product is ideal and provides the most satisfactory results.
However, its application to CFD simulations is limited to regularly shaped geometries. Thus, for
irregular shapes, the lumped approach may be a reasonable alternative with engineering accuracy.
For regular shapes which can be approximated as spheres, infinite cylinders or slabs, the transient
approach is more appropriate.

Acknowledgement
This work was financially supported by LiFT-Future Technologies for Food Production and ESN; The
European Sensory Network.
ICEF9 – 2004
International Conference Engineering and Food

Nomenclature
2 -1
A surface area, m u airflow velocity, m s
-1 -1 3
Cp specific heat capacity, kJ kg K V volume, m
-1 -1 -1
c specific heat, kJ kg K ∆p/l pressure drop per unit length, Pa m
D product diameter, m NBi Biot number
d product diameter, m β Forchheimer constant
deff effective diameter of the product, m ε The porosity of the medium
H enthalpy of vaporisation, J/kg κ permeability of the porous media
-2 -1 -1
h heat transfer coefficient, W m K µ dynamic viscosity of air, Pa s
jH Colburn factor µeff the effective dynamic viscosity in the
-1
K1 Ergun constant boundary layer of the wall, Pa s
-3
K2 Ergun constant ρ density of air, kg m
-1 -1 -3
k thermal conductivity, W m K ρbulk bulk density, kg m
-1 -3
keff effective thermal conductivity, W m ρparticle particle density, kg m
-1
K
m weight, kg Subscripts
. a air
q evaporative cooling effect, J/s c composite medium
p pressure, Pa f fluid
Re Reynolds number m measured
r radius, m p product
S enthalpy source in the media, kJ pred predicted
T temperature, K s solid
t time, s

References
1. Chau K.V., Gaffney J.J., Baird C.D., Church G.A. Resistance to air flow of oranges in bulk and in
cartons. ASAE paper, 83-6007, 1983.
2. Gilles S.L., Toivonen P.M.A. Cooling method influences the postharvest quality of broccoli.
HortScience, 30, 313-315, 1995.
3. van der Sman R.G.M. Solving the vent hole design problem for seed potato packages with the
Lattice Boltzmann scheme. International Journal of Comparative Fluid Dynamics, 11, 237-248,1999.
4. van der Smam R.G.M. Prediction of airflow through a vented box by the Darcy-Forchheimer
equation. Journal of Food Engineering, 55, 49-57, 2002.
5. Jefferson C.P. Prediction of breakthrough curves in packed beds. AICHE Journal, 18, 409-420,
1972.
6. Bakker-Arkema F.W., Bickert W.G. A deep-bed computational cooling procedure for biological
products. Transactions of the ASAE, 9, 834-836, 845, 1966.
7. van Beek G., Meffert H.F.T. Cooling of horticultural produce with heat and mass transfer by
diffusion. Developments in food preservation-1. Ed, Thorne, Applied Science publishers ltd, London.
pp. 39-92p, 1981.
8. Hughes P.J., Klein S.A., Close D.J. Packed bed thermal storage models for solar heating and
cooling systems. Journal of Heat Transfer-Transactions of the ASME, 98, 336-338, 1976.
9. Baird C.D., Gaffney J.J. A numerical procedure for calculating heat transfer in bulk loads of fruits or
vegetables. ASHRAE transactions, 82, 525-540, 1976.
10. Sprenger Instituut. Produktgegevens groente en fruit. Mededeling Nr. 30:2. Wageningen, the
Netherlands, 1982.
11. Macdonald I.F., El-Sayed M.S., Mow K., Dullien F.A.L. Flow through porous media- the Ergun
equation revisited. Industrial Engineering Chemistry and Fundamentals, 18, 199-208, 1979.
12. Jacobsson A., Sarkar A., Singh R.P. Airflow and heat transfer in packed bed of agricultural
produce (potatoes,broccoli): Comparison of different predictive approaches. Submitted to Journal of
Food Engineering, 2003. (ref number 03/2027.)
13. Bird R.B., Stewart W.E., Lightfoot E.N. Transport phenomena. John Wiley & Sons, New York, 407-
412p, 1960.
14. Mackinnon, I.R. Heat and mass transfer of fresh broccoli, leaf lettuce, mushrooms and sweet corn
during forced-air cooling. Thesis, University of Guelph, Canada, 1993.
ICEF9-2004
International Conference on Engineering and Food

A Sensivitity Analysis of a Continuous Ohmic Heating Process for Hydrocolloid Solutions

Marcotte M. (1), Chen C.R. (1), Ramaswamy H.S. (2)

(1) Agriculture and Agri-Food Canada’s Food Research and Development Centre, 3600 Casavant
Blvd West, St. Hyacinthe, QC, J2S 8E3, Canada.
marcottem@agr.gc.ca
chencu@agr.gc.ca

(2) Department of Food Science and Agricultural Chemistry, Macdonald Campus of McGill University,
21,111 Lakeshore, Ste-Anne-de-Bellevue, QC, H9X 3V9, Canada.
ramaswamy@macdonald.mcgill.ca

Abstract: A sensitivity analysis of process parameters was performed for a continuous ohmic heating
of hydrocolloid solutions It included: 1) the effect of individual factors and their interactions, 2) the
development of regression models. Simulations were carried out using a CFD model. Out of many
process parameters, specific heat (Cp), electrical voltage (V), volume fluid flow rate (Vm), electrical
conductivities (ke, ce) were the most sensitive with respect to their effect on temperature distributions.

Keywords: ohmic heating, sensitivity analysis, CFD, modeling, hydrocolloid solutions, electrical
heating

Introduction: Ohmic heating as a promising emerging technology has been greatly recognized
because of its wide adaptability to different food types such as liquid, solid and liquid mixing with
particulates. Available literature on the theoretical and experimental work on ohmic heating is
abundant. Modeling of ohmic heating system has been one of the popular subjects. Most published
models have tried to describe the thermal behavior of particles in a still liquid and they were validated
experimentally for a single particle in a static heater (1-2). For multiple particle systems in static ohmic
heaters, simplified models were presented for a limited number of particles (3-5). Few papers dealt
with the operability of a continuous ohmic heating process for liquids. (6) reported on the behavior of
non-Newtonian liquids in a continuous ohmic heater. Temperature dependency on thermophysical
properties was considered. (7) studied the thermohydraulic behaviour of a liquid flowing into a vertical
continuous ohmic heating column. (8) developed a computer simulation model of a continuous ohmic
heating system for viscous non-Newtonian liquid foods, in which effects of electrodes and surface heat
transfer were first considered. It was found that the temperature distribution at the exit of ohmic
heating system was different than the one observed for tubular flow (6-7). Results showed that the
highest temperature was not on the wall because of losses to the surroundings and the lowest
temperature was not at the center. It was difficult to obtain a good agreement between experimental
and theoretical results. Systematic research on complex processes can be carried out by use of CFD
model, which might be impossible or very difficult and time-consuming for experimental studies.

The objective of this study was to perform a sensitivity analysis of main processing conditions to the
temperature distribution characteristics at the exit of the ohmic heating unit using a theoretical model
solved by the FIDAP (Fluent Inc.), a computational fluid dynamics (CFD) software. Independent
variable parameters included specific heat (Cp), electricity voltage (V), volume fluid flow rate (Vm),
fluid density (ρ), temperature dependent electric and thermal conductivities (ke, ce, k and c),
temperature dependent rheological properties (m and n). Dependent variables were temperature
distributions: center temperature (Tc), wall temperature (Tw), minimum and maximum temperatures
(Tmin and Tmax) and their differences. Specifically, the objectives were: 1) to determine individual
effects of processing conditions; 2) to investigate comprehensive effects of main processing conditions
and their interactions; 3) to develop comprehensive regression models to predict the relationships
between main processing conditions and characteristic parameters of the exit temperature distribution.

Ohmic heating unit: As presented in Figure 1, the continuous ohmic heating unit is a collinear heater.
The electric field distribution is parallel to the flow of product. The unit comprised three titanium
electrodes and two spacer tubes or heating sections. All internal surfaces in contact with the food are
constructed from insulating glass material except for the electrodes. The internal diameter of the glass
tube is 5.08 cm. The length of the heating sections i.e. the space between the two first electrodes is
56.2 cm. For the other heating section, the length was 56.7 cm. A power unit (Hammond
manufacturing, S87853, Guelph, ON, Canada and Bectrol Technologies Inc., St. Hyacinthe, QC,
ICEF9-2004
International Conference on Engineering and Food

Canada) was used to generate the necessary electrical field at the three electrodes. It includes: a
variable transformer, an isolation transformer, a voltage transducer, a current transducer, power relays
and fuses. Physical limits of the power unit were 900 V for the voltage and 10 A for the current. A
positive displacement pump (ALBIN Pump SLP-220, Atlanta, GA) was used to flow the product
vertically from the bottom to the top between the electrodes from an inlet tank to an outlet plastic tank.
First, the fluid was pumped horizontally in a 3-m length. Then, the fluid was passing through the two
vertical ohmic heating sections (2 m). On the last part of the horizontal cylinder at the exit of the pipe,
the length of the pipe was 55.8 cm. It was followed by a vertical pipe of 68.5 cm that fed the outlet
plastic tank. A constant voltage was applied to the three titanium electrodes. Six Teflon coated type T
thermocouples (Omega Engineering, Stamford, CT) were installed to measure the temperature of the
carrier fluid at the center of the cylinder (T1, T2, T4, T6, T8, T10 and T12). As well, six Teflon coated
type T thermocouples were also used to determine the temperature of the fluid close to the wall (T3,
T5, T7, T9 and T11). Time, temperature, current and voltage were monitored and recorded at 10 s
intervals using a data logger (Model Hydra 2225, John Fluke MFG Co. Inc., Everett, WA).

CFD Modeling: The continuous flow ohmic heating operated at steady-state. Partial differential
equations governing flow and heat transfer in a cylinder coordinate system were given by:

Continuity Equation:
1 ∂ ∂
(rρv) + ( ρu ) = 0
r ∂r ∂z
Energy Equation:
∂T ∂T k 1 ∂ ∂T ∂ 2T  ⋅
v + u =  (r ) +  + Q
∂r ∂z ρc p  r ∂r ∂r ∂z 2 
Momentum equation in both vertical and radial directions:

∂u ∂u ∂p ∂ ∂u ∂2 
ρv + ρu = − +  (ηr ) + 2 (ηu ) + ρg
∂r ∂z ∂z  ∂r ∂r ∂z 

∂v ∂v ∂ ∂v ∂2 
ρv + ρu =  (ηr ) + 2 (ηv)
∂r ∂z  ∂r ∂r ∂z 

Electrical potential and heat generation:

1 ∂ ∂V ∂2
(ke r ) + 2 keV = 0
r ∂r ∂r ∂z

⋅  ∂V  2  ∂V  
2

Q = ke   +   
 ∂r   ∂z  

where v is the velocity component in the r axial direction, u is the velocity component in the z axial
direction, ρ is the density of fluid; T is the temperature of fluid; η is the apparent viscosity; V is the
⋅
voltage; Q is the heat generation.

Initial and boundary conditions:

∂T
At the wall: (r=R)= v=0, u=0 and k = h(Tr − T )
∂r
ICEF9-2004
International Conference on Engineering and Food

∂T
At the axi-symmetry: v = 0, = 0
∂r
At the inlet:
T = T0
 n +1

 3n + 1   r n 
v = vm  1−  
 n + 1  R 
 
At electrode 1 and 3: V=0, v=u=0
At electrode 2: V=600, v=u=0

Selection of sensitive inputs and target outputs: Several factors were chosen: 1) specific heat
(Cp); 2) electricity voltage (V); 3) volume fluid flow rate (Vm); 4) fluid density (ρ); 5) temperature
dependent electric and thermal conductivities (ke, ce, k and c); 6) temperature dependent rheological
properties (m, n and temperature dependent coefficients, A1 and A2), 7) surface heat transfer (h).
Values of these parameters are shown in Table 1. Processing conditions with 0 code level (Table 1)
were defined as the base condition (X0), generated experimentally and used to validate the CFD
model. Processing conditions at other code levels (-1, -2, 1 and 2) were Xi=X0(1+i*10%) where X was
one of the processing parameter, i was the number of the code level. Target outputs were the
temperature distribution at the exit of the continuous ohmic heating system, which is shown in Figure
2. The main characteristic parameters included the center temperature (Tc), the wall temperature
(Tw), the minimum temperature (Tmin) and the maximum temperature (Tmax), and their differences
such as: DT1= Tc–Tmin , DT2= Tmax –Tmin, DT3= Tmax–Tw, DT4=Tw–Tc.
Outlet
150

T12

Electrode 3
V=0 V
T11

T10
567

T9 Tmax
DT3

T8

Tw
T7

Electrode 2
DT4

V=600 V
T6
DT2

T5
Tc
Tmin
562

T4
DT1

T3

T2

Electrode 1
V=0 V
150

T1

50.8 Inlet

Figure 1 Figure 2

Modeling performance: The modeling performance of the developed CFD model was evaluated by
two statistical values: correlation coefficient, R2 and average relative error, Er.
Experimental design: Two types of experimental design were used in this study: a single factor
factorial (individual effects of various parameters) and a second central composite design (CCD)
(combined effects of important parameters). For all of single factor experimental design, except for one
parameter variable to be investigated, other parameters were kept the 0 code level as shown in Table
1. A standardized CCD was used as an experimental plan.
ICEF9-2004
International Conference on Engineering and Food

Table 1. Code Numbers and Levels of Input Variables

Code Cp Vm V h ρ ke ce k c m n A1 A2
-2 4894 3.00 720 48 1201 1.248 0.051 0.408 0.072 5.653 0.685 0.0221 0.0140
-1 4486 2.75 660 44 1101 1.144 0.047 0.374 0.066 4.153 0.587 0.0203 0.0129
0 4078 2.50 600 40 1001 1.04 0.043 0.340 0.060 2.884 0.489 0.0184 0.0117
1 3670 2.25 540 36 901 0.936 0.038 0.306 0.054 1.846 0.391 0.0166 0.0105
2 3262 2.00 480 32 801 0.832 0.034 0.272 0.048 1.038 0.294 0.0148 0.0094

2 3 2
Cp: J/kgK; Vm: L/min; V:V; h: W/m K; r: kg/m ; ke: S/m; ce: S/mK; k: W/mK; c: W/mK ; m: Pa.s

Regression modeling: A second order multiple regression model was used for describing both
temperature distribution characteristics including four points temperatures and four temperature
differences, which is given by: Y=b0+Σbi Xi + Σbij XiXj + Σbii X2ii for (i <> j, i=1…n, j=1… n) where Y
was the response variable (center temperature, Tc; wall temperature, Tw; minimum temperature,
Tmin, maximum temperature, Tmax; or one of temperature differences DT1, DT2 , DT3 and DT4). X
was the independent variable, which can be one of processing parameters: specific heat, Cp, volume
velocity, Vm, Voltage, V, and electric conductivity, ke and ce. bo, bi, bij and bii were the regression
coefficients of intercept, first order, interaction, and second order, respectively. The significant level of
sensitivity analysis was represented by signs: *, **, ***, which meant p <0.05, 0.01, 0.001, respectively.

Results and Discussion:

Performance of the CFD Model: Before performing any sensitivity analysis, it was important to
ensure that the developed CFD model was matching the experimental data for same processing
conditions. More details on CFD modeling performance was already described in another paper (9).
Figure 3ab shows experimental data at different locations of both wall and center (along the z-axis)
temperatures. There is a rapid increase of temperature at the beginning of the process (unsteady
state) until temperatures reached a plateau (steady state). Constant values are maintained. The time
to reach the steady state was around 100s for center temperatures and 200s for wall temperatures.
From Figures 3cd, it can be shown that predicted temperatures match very well those obtained
experimentally. Statistical results (R2>0.96 and Er < 5.4%) confirmed that there was an agreement.
Therefore, the CFD model could be used for this particular sensitivity analysis.

(a) Centre (b) Wall

55 80
T12
50 70 T11
45 T10
60 T9
Temperatrue (C)

Temperatrue (C)

T8 (a) (b)
40 T7 80 15
50
35 Tc DT1
T6 40 T5 70
30 DT2
Delta T (C)

T4 T3 Tmin 10
25 30 60 DT3
T (C)

T2 Tmax
20 T1 DT4
20 T1 50 Tw
15 10 5
10 40
0
0 100 200 300 400 0 100 200 300 400 30 0
Time (s) Time (s) 3000 3500 4000 4500 5000 3000 3500 4000 4500 5000
Cp (J/kgC) Cp (J/kgC)

(a) Wall Temperature (b) Center Temperature (c) (d)

80 60 100 25
90 Tc
R2 = 0.9606 20 DT1
R2 = 0.9856 80 Tmin
Delta T (C)

70 Er=5.4% DT2
Er=4.7% 70 15
T (C)

50 Tmax
DT3
60 60 Tw
10 DT4
Predicted

50
Predicted

50 40 40 5
30 0
40 450 500 550 600 650 700 750 450 500 550 600 650 700 750
30 V V
30

20 20
20 30 40 50 60 70 80 20 30 40 50 60
Experimental Experimental

Figure 3 Figure 4

Individual Effects: Figure 4 shows examples of individual effects of various processing parameters.
An increase of Cp resulted in a decrease of the temperature at specific locations. It can also be found
ICEF9-2004
International Conference on Engineering and Food

that DT1 increased with Cp increase. DT4 decreased with Cp. DT2 and DT3 remained the same. It
indicated that Cp influenced the temperature difference at the center of the ohmic heating unit only.
The effects of Vm and ρ on temperature locations and differences were similar to those of Cp (results
not shown). The effect of V was the inverse. DT1 and DT2 were not influenced by V. But V did not
affect DT1 and DT3 but influenced greatly DT2 and DT4. It means that increasing the voltage resulted
in larger temperature differences between the wall and the center of the pipe. Temperature (Tw and
Tmax) were slightly affected by h and DT2 and DT4 were slightly affected by h (results not shown).

Figure 5 shows the effect of ke and k on the temperatures at various locations and temperature
differences. With an increase of ke, temperatures at all points increased since the heat generated by
electricity increases with the increase of electrical conductivity. Temperature difference DT2 and DT4
also increased with an increase of ke. This is normally not expected in traditional sterilization. The
effect on DT1 and DT3 was very small meaning that temperature differences at the center and the wall
were not influenced by ke. A similar trend was observed for ce. Within the studied ranges, the effect of
k on temperature distributions was very small while c was influencing the temperature distribution at
the exit (results not shown).

Figure 5 Figure 6
(a) (b) (a) (b)
70 16 70 18
14 16
Tc DT1
60 12 DT1 60 14
Tmin Tc
12

Delta T (C)
Delta T (C)

10 DT2
DT2 Tmin
Tmax 10
T (C)

T (C)
50 8 50 DT3
DT3 Tmax 8
Tw 6 DT4
DT4 6
Tw
40 4 40 4
2 2
0 30 0
30
0,8 0,9 1 1,1 1,2 1,3 0,150 0,350 0,550 0,750 0,150 0,350 0,550 0,750
0,8 0,9 1 1,1 1,2 1,3
ke ke n n

(c) (d) (c) (d)

70 16 70 16
14 14
Tc Tc
60 12 DT1 60 12 DT1
Tmin Tmin

Delta T (C)
Delta T (C)

10 10 DT2
Tmax DT2
T (C)

Tmax 8
T(C)

50 8 50 DT3
Tw DT3 Tw 6
6 DT4
DT4 40 4
40 4
2
2 0
30
30 0 1,00 2,00 3,00 4,00 5,00 6,00
1,00 2,00 3,00 4,00 5,00 6,00
0,25 0,3 0,35 0,4 0,25 0,3 0,35 0,4 0 0 0 0 0 0 0 0 0 0 0 0
k k m m

Figure 6 show the effect of rheological properties (m and n). The consistency index (m) did not affect
both temperatures and temperature differences but the flow index (n) has a major impact. Similarly,
temperatures and temperature differences were not influenced by A1 and A2.

Regression Models and Response Surfaces: Regression models were developed using a CCD with
the 5 following parameters (Cp, Vm, V, ke and ce). Very high values of R2 were obtained (greater than
0.96) (results not shown). These models were used to plot various 3D graphs. As an example, Figure
7 represents Tc and various processing parameters.

Figure 7
(a) Cp vs V m (b) Cp vs V

24,830
30,891
36,953
46,633 43,014
50,596 49,075
54,558 55,137
58,520 61,198
62,482 67,259
66,445 73,321
70,407 79,382
74,369 above
78,331
82,294
above

(c) Cp vs ke (d) Cp vs ce

44,031
42,479 47,278
45,251 50,526
48,024 53,773
50,797 57,021
53,570 60,268
56,342 63,516
59,115 66,763
61,888 70,011
64,661 73,258
67,433 above
above
ICEF9-2004
International Conference on Engineering and Food

It can be shown that Tc decreased with an increase in Cp but the decreasing rate varied with Vm.
There was an interaction between Cp and Vm. Similar graphs were plotted for Tw, DT1, DT2, DT3 and
DT4 (results not shown).

Conclusions: A sensitivity analysis of a continuous ohmic heating system was carried out using a
CFD computer simulation model that was validated experimentally. Within the range, Cp, Vm, V and
ke were the most sensitive to influence the temperatures at various locations and the temperature
differences. Most relationships were found to be non-linear. Multiple regression models were
developed and used to represent in 3D the individual effect and their interactions.

References:
1. de Alwis A.A.P., Fryer P.J. A finite-element analysis of heat generation and transfer during ohmic
heating of food. Chemical Engineering Science, 45(6), 1547-1559. 1990.
2. Fryer P.J., de Alwis A.A.P., Koury E., Stapley A.G.F., Zhang, L. Ohmic Processing of Solid-Liquid
Mixtures: Heat Generation and Convection Effects. Journal of Food Engineering, 18, 102-125.
1993.
3. Zaror C.A., Pyle D.L., Molnar G. Mathematical modelling of an ohmic heating steriliser. Journal of
Food Engineering, 19, 33-53. 1993.
4. Sastry S.K., Palaniappan S. Mathematical modeling and experimental studies on ohmic heating of
liquid-particle mixtures in a static heater. Journal of Food Process Engineering, 15, 241-261. 1992.
5. Zhang L., Fryer P.J. Models for the electrical heating of solid-liquid food mixtures. Chemical
Engineering Science, 48(4), 633-642. 1993.
6. Muller F.L., Pain J.P., Villon P. On the Behaviour of Non-Newtonian Liquids in Collinear Ohmic
Heaters. In Proceedings of the Tenth International Heat Transfer Conference Freezing, melting,
internal forced convection and heat exchangers (Volume 4. pp. 285-290). Brighton, UK. 1994.
7. Quarini G.L. Thermalhydraulic Aspects of the Ohmic Heating Process. Journal of Food
Engineering, 24, 561-574. 1995.
8. Marcotte M. Ohmic heating of viscous liquids. Ph. D. Thesis. McGill University, Montreal, Quebec,
Canada. 1999.
9. Marcotte M., Trigui M., Chen C., Ramaswamy H.S. Modelling of continuous ohmic heating for
hydrocolloid solutions using computational fluid dynamics (CFD). J. Food Eng. 2002. (In review)
 ICEF9 - 2004
International Conference Engineering and Food

Airflow modelling by computational fluid dynamics

in an industrial plant filled with food products

Mirade Pierre-Sylvain (1), Agabriel Etienne (2), Brunet Yves (3), Boulard Thierry (4)

(1) (2) INRA – Theix, Equipe Génie des Procédés, Laboratoire Station de
Recherches sur la Viande, Département Transformation des Produits Animaux,
63122 St-Genès-Champanelle, France.
e-mail: mirade@clermont.inra.fr
(3) INRA – Bordeaux, Equipe Processus de Transfert, Unité de Bioclimatologie,
Département Environnement et Agronomie, Domaine de la Grande Ferrade, BP 81,
33883 Villenave-d’Ornon cedex, France.
e-mail: Yves.Brunet@bordeaux.inra.fr
(4) INRA – Avignon, Equipe Systèmes de Cultures Maraîchers Sous Abris, Unité
Plantes et Systèmes de culture Horticoles, Département Environnement et
Agronomie, Domaine St Paul, Site Agroparc, 84914 Avignon cedex 9, France.
e-mail: boulard@avignon.inra.fr

Abstract

The ability of a porous medium model coupled to the Darcy-Forchheimer equation to

predict air velocity within a stack of cheeses was assessed. The results show that
only the Forchheimer coefficient need be taken into account, and that this coefficient
can be determined either from experiments in wind tunnels or from computational
fluid dynamics (CFD) calculations. The accuracy of the prediction of the air velocity
within the stack with the porous medium approach was evaluated at 19%.
(Keywords: Porous medium; CFD; Darcy-Forchheimer; air velocity; cheese)

1. Introduction

Computational fluid dynamics (CFD) can solve fluid flow problems coupled
with heat transfer and turbulence phenomena using a computational grid, where the
Navier-Stokes equations are solved across each grid cell by means of an iterative
procedure requiring specific algorithms. With the development of cheaper, powerful
computers and commercial packages, CFD has for many years been increasingly
applied in the food industry to assess the performance of industrial food processing
plants and to analyse the effects of modifying operating conditions or design
parameters [1], [2]. Given the specific features of industrial food plants, which are
often filled with a large number of products (for example, several thousand pieces in
cheese ripening rooms or sausage dryers), attempting a complete representation of
the plant with its contents in three dimensions (3D) is unreasonable, and anyway out
of the range of the computers currently used. On the other hand, a more
macroscopic modelling is conceivable, based on reference volumes including several
elements coupled with sink or source terms. In this macroscopic approach the filling
of the plant with food products is modelled as a mega-porous medium. We consider
mega-porous media and not simply porous media because the products occupy only
a small part of the whole volume in comparison with air.
 ICEF9 - 2004
International Conference Engineering and Food

The purpose of this work was to apply to a food industry situation the
methodology developed in bioclimatology to assess airflows in greenhouses or wind
circulation in forests [3], and based on the Darcy-Forchheimer approach. From
experimental measurements and CFD calculations performed with the code Fluent
6.1 [4], we tested the ability of this methodology to model the airflow within stacks of
cheeses.

2. Materials and method

2.1. The Darcy-Forchheimer and porous medium approach

The porous medium model can be used for a wide variety of problems
including flows through packed beds, perforated plates or, in our case, through
stacks of food products. Porous media are modelled by the addition of a momentum
source term to the standard fluid flow equations. This term is composed of two parts:
a viscous loss term (Darcy - the first term on the right-hand side of Equation (1)), and
an inertial loss term (Forchheimer - the second term on the right-hand side of
Equation (1)). In the case of a homogeneous porous medium, the momentum source
term S i is written as:
µ 1 
Si = −  vi + ρ C2 vi vi  (1)
α 2 
where µ is the dynamic viscosity of the fluid, α is the medium permeability, ρ is the
fluid density, C 2 is the inertial resistance factor and vi is the fluid velocity.
The momentum sink Si contributes to the pressure gradient in the porous
zone, creating a pressure drop proportional to the fluid velocity or to the velocity
squared.

2.2. The experiments performed

To experimentally determine the Darcy and Forchheimer coefficients

corresponding to the airflow through stacks of cheeses, we built the cubic stack of
cans depicted in Figure 1. As we were only interested in the effects on the
momentum equation, we replaced the cheeses by cans with the same dimensions,
i.e. diameter 10 cm and height 4.4 cm.

800
mm

Figure 1. View of the cubic stack

of cans, modelling a stack of
cheeses, used in the wind tunnel
of the laboratory to determine the
100 mm Darcy and Forchheimer
coefficients.
 ICEF9 - 2004
International Conference Engineering and Food

The experiments consisted in installing this stack in a laboratory wind tunnel in

which the air velocity could be varied from 0.1 to 5 m.s-1, measuring the mean air
velocity around the can located in the middle of the stack, together with the mean
static pressure gradient in the horizontal direction. Two series of experiments were
performed to determine the coefficients in the three space directions; they
corresponded to the following two configurations: airflow parallel to the surface of the
cans and airflow perpendicular to the surface of the cans.
The mean air velocity around the can was calculated from measurements
made at five points around the can located in the middle of the stack using a hot-film
type anemometer (model 8465, TSI, St Paul, USA). The mean pressure gradient in
the horizontal direction was determined from five measurements of static pressure
drop between one point around the can and one point below the stack, and from the
distance below the two measurement points. To achieve this, we used an electronic
pressure gauge (model 8705, TSI, St Paul, USA).

2.3. The CFD calculations performed

Using the code Fluent 6.1 [4], we performed two series of 3D CFD
calculations: the first one was to determine the Darcy and Forchheimer coefficients
numerically to compare them with the measured values, and the second one was to
verify the ability of the porous medium including the coefficients determined
previously to model the airflow within the stack of cans.
In the first 3D numerical model, only a part of the stack in Figure 1 was
represented and meshed with tetrahedral cells, because of obvious symmetries. The
CFD results allowed the mean air velocity around each can and the mean pressure
gradient to be easily determined in the two configurations in which the stack was
positioned in the main airflow direction.
In the second 3D numerical model, the stack of cans located in the wind tunnel
was not really represented; it was taken into account as porous medium, that is by a
fluid volume meshed using large hexahedral cells and in which the
Darcy-Forchheimer theory was applied. On the other hand, as the code Fluent [4]
assumes that the cells meshing the porous medium zone are “100% open”, the
coefficients we determined in our case from the variation of the pressure drop with
the velocity through the actual set-up in Figure 1, which was partially open to flow but
not 100% open, had consequently to be modified. For this reason, the determined
and “Fluent” inertial resistance factors were linked by the following relationship:
2
C2 Fluent = C 2 Det (2)
ρ γ l pm
where:
C2 Fluent is the inertial resistance factor we set in the porous medium defined in the
CFD model
C2 Det is the inertial resistance factor we determined from the results obtained, either
experimentally or numerically.
γ and lpm are the porosity and thickness of the porous medium, respectively.

In the two numerical models, the airflow was considered as steady,

incompressible and isothermal. The main flow turbulence was taken into account
using the standard k-ε model far from cans assumed to be smooth and where the
 ICEF9 - 2004
International Conference Engineering and Food

standard wall function was applied. The first-order upwind differencing scheme and
the Simple algorithm were chosen. In the inlet area, the magnitudes of the air velocity
and turbulence parameters were specified. Calculations were made on a PC Athlon
1900 XP+.

3. Results and discussion

3.1. Determination of the Darcy and Forchheimer coefficients

For the stack of cans placed perpendicular to the main airflow direction,
Figure 2 shows the mean static pressure gradient as a function of the mean air
velocity squared, obtained from measurements made in the wind tunnel and from
CFD calculations. The linear relation means that the Darcy term, which is
proportional to the velocity, is negligible, even for very low air velocities.
Consequently, the slope of the straight lines obtained by linear regression
corresponds to the Forchheimer term, i.e . to the term ½.ρ.C2 of Equation (1).

200
from CFD calculations
y = 5.46x
2
)

R = 1.00
-1

160
Mean pressure gradient (Pa.m

y = 5.04x
2
R = 0.99
120

from measurements
Figure 2. Mean
in the wind tunnel
80
pressure gradient as a
function of the mean
air velocity squared
measured in the wind
40 tunnel or computed,
for a stack of cans
placed perpendicular
0 to the main airflow
0 10 20 30 40 direction.
2 -2
Mean air velocity squared (m .s )

Comparison of the Forchheimer terms determined experimentally and by CFD

calculations showed good agreement between the two. Thus this parameter can
probably be assessed by a numerical approach, which is easier than the
experimental one.

Figure 3 gives the results for the case where the stack of cans is placed
parallel to the main airflow direction. Values of pressure gradient were lower than
before, showing that the air flows more easily inside the stack in this second
configuration. The Darcy coefficient is still negligible.
On the other hand, Figure 3 shows a marked discrepancy in the prediction of
the values of the Forchheimer coefficients between the experimental and numerical
approaches. Because of technical problems, not all the measurement points of static
pressure and air velocity could be made, particularly in the free space between the
can chosen for the study and the others around it, which certainly led to an
 ICEF9 - 2004
International Conference Engineering and Food

overestimation of the mean air velocity. However, assuming a nil value for the air
velocity in the volume in question, which is certainly close to reality, gives a slope of
the straight line of 1.7 instead of 0.51 as given by Figure 3, close to the computed
value (1.86). Consequently the real value of the Forchheimer term for this second
configuration is taken as equal to 1.86.

50
)
-1

40
Mean pressure gradient (Pa.m

y = 1.86x from CFD calculations y = 0.51x

2 2
R = 1.00 R = 0.99
30 Figure 3. Mean
from measurements pressure gradient
in the wind tunnel as a function of
20 the mean air
velocity squared
measured in the
10
wind tunnel or
computed, for a
stack of cans
placed parallel to
0
the main airflow
0 10 20 30 40 50 60 70 80 90
2 -2
direction.
Mean air velocity squared (m .s )

3.2. Validity of a porous medium for modelling the airflow within the stack of
cans

In the second CFD model built, the stack of cans located in the wind tunnel
was modelled as a porous medium with large hexahedral cells, making the problem
easier to mesh than the actual geometry of the stack. From the coefficients
determined above and Equation (2), we calculated the coefficients to be set in the
Fluent porous medium model, taking a value of porosity equal to 0.46 in the direction
where the cans are perpendicular to the airflow and to 0.55, in the two other space
directions.
Figure 4 shows a comparison in the calculation of the mean air velocity within
the stack from the two numerical approaches used, i.e. from a full representation of
the actual geometry of the stack and from the porous medium model.
6
y = 1.85x
2
R =1
Mean air velocity in the pile or in the porous

From the porous medium

y = 1.56x
2
R =1
4
medium (m.s )
-1

From the actual geometry

of the stack of cans

2 Figure 4. Calculation of the

mean air velocity within the
stack of cans, from the actual
geometry of the stack and from
0
the porous medium model.
0 1 2 3 4
-1
Mean air velocity before the pile or the porous medium (m.s )
 ICEF9 - 2004
International Conference Engineering and Food

Although there is a difference of 19% between the two predictions of the air
velocity within the stack (Figure 4), using a porous medium seems to be a good way
to model the airflow patterns within stacks of cheeses, particularly as the magnitudes
of the air velocity in cheese ripening situations rarely exceed 0.5 m.s-1. As meshing
porous medium volumes needs very fe w cells and is easier to build than meshing the
actual geometry of a stack filled with cans (or cheeses), this approach should be
suitable for assessing airflow in large food plants filled with several hundreds or
thousands of products.

4. Conclusion

In this paper we have discussed the ability of a porous medium approach

coupled to the Darcy-Forchheimer equation to model the airflow within a stack of
cheeses, without representing the complete actual geometry. The results show that
only the Forchheimer coefficient need be considered, even for very low air velocities,
and that this coefficient can be determined not only experimentally in wind tunnels,
which is time-consuming and sometimes very difficult, but just as well numerically
from the study of the airflow within a part of the stack.
The validation of this approach to model the airflow in a real 3D industrial
ripening room is in progress in our laboratory, together with a sensitive study to
evaluate how the values of the Darcy and Forchheimer coefficients vary with the
geometry of the stack of cheeses, i.e. with the filling rate of a stack and with the size
of the cheeses. In the future, to fully model what exactly occurs within a stack of
cheeses being ripened, a methodology taking into account heat and mass exchanges
must be developed and coupled to the Darcy-Forchheimer approach.

5. References

1. Scott G., Richardson P. The application of computational fluid dynamics in the food industry. Trends
in Food Science and Technology, 8, 119-124, 1997.
2. Xia B., Sun D.W. Applications of computational fluid dynamics (CFD) in the food industry: a review.
Computers and Electronics in Agriculture, 34, 1-3, 2002.
3. Bartzanas T., Boulard T., Kittas C. Numerical simulation of the airflow and temperature distribution
in a tunnel greenhouse equipped with insect-proof screen in the openings. Computers and Electronics
in Agriculture, 34, 207-221, 2002.
4. Fluent 6: user’s guide. Lebanon: Fluent Inc., 2001
 ICEF9 – 2003
International Conference Engineering and Food

Analysis of the airflow patterns inside a French cheese ripening room –

influence of the design of the blowing duct on ventilation homogeneity

Mirade Pierre-Sylvain (1), Carles Aminata (2), Rougier Tania (3)

(1) (2) (3) INRA – Theix, Equipe Génie des Procédés, Laboratoire Station de Recherches sur la
Viande, Département Transformation des Produits Animaux, 63122 St-Genès-Champanelle, France.
e-mail: mirade@clermont.inra.fr

Abstract

We studied, experimentally and numerically, the influence of the design of blower ducts made of textile
material on ventilation homogeneity in a pilot cheese ripening room. We tested three blowing ducts
with holes of different diameters: 3, 6 and 20 mm, at constant total airflow rate blown in the room. The
results showed different ventilation levels and ranging heterogeneity around the cheeses. The smaller
the hole diameter, the more homogeneous was the ventilation.
(Keywords: air velocity; cheese; ripening; blowing duct)

1. Introduction

Blowing ducts made of textile material are currently used for ventilating industrial food plants in
which low air velocities are needed to ensure correct treatment of products, such as in cheese
ripening rooms, or to provide adequate comfort for people working, for example, in meat carcass
cutting workshops. Different types of blowing ducts made of textile material exist: some are porous,
others are fitted with holes or slits.
We studied, experimentally and numerically by means of computational fluid dynamics (CFD),
the influence of the design of the blowing duct on ventilation homogeneity and level around cheeses
stacked in a pilot ripening room. For this purpose, we tested three blowing ducts with holes of different
diameters: 3 mm, 6 mm and 20 mm. The total airflow rate blown in the room and the air velocity at the
output from the holes were the same in all three configurations.

2. Materials and method

2.1. The pilot ripening room

The pilot ripening room was 5.8 m long, 4.8 m wide and 2.9 m high, making a volume of
3
81 m . Inside this room, 6 rows of 7 stacks of 16 racks of 21 cans (i.e. in all 14 112 cans) were
installed to obtain a filling pattern representing current industrial practice (Figure 1). As our interest in
this study was how the air flowed inside the room, we replaced cheeses by cans with the same
dimensions, namely diameter 10 cm and length 4.4 cm.
An air conditioning system (two fans and two batteries) installed in a space located above the
ceiling of the pilot ripening room controlled the temperature and flow rate of the air blown into the
room.
Inside the pilot ripening room, the ventilation system was composed of a blowing duct made of
textile material and a suction duct, respectively 340 mm and 315 mm in diameter (Figure 1). The
blowing duct, running along the ceiling at half-width in the room, was fitted on each side with 3 rows of
holes 3 mm or 6 mm in diameter or one row of holes 20 mm in diameter. After being blown into the
room, the air was extracted 35 cm from the ground by means of a suction duct placed against a
vertical wall at half-width in the room (Figure 1). The suction duct was connected to the space located
above the ceiling of the pilot ripening room where the fans were installed. The whole airflow rate blown
3 -1
in the room was 1600 m .h , i.e. an air change rate of 20 volumes per hour, which corresponds to
normal industrial practice.
 ICEF9 – 2003
International Conference Engineering and Food

Blowing
Gaine duct
de
fitted withàholes Rangées
Rows of de piles
stacks
soufflage trous

System for
Système de
automatically
déplacement
moving the Débit = 1600
Airflow : 3/h
rate m
motorisé
sensors 1600 m 3 .h -1

Vue deview
Top dessus
Centrale
Data logger
d’acquisition

Stacksde
Piles ofclaies
‘cheese’
de
racks Soufflage
‘fromages’ Blowing duct
Aspiration
Extraction duct
Gaine
Extraction
Figure 1. Views of the
d’aspiration
duct
pilot cheese ripening
room built for this work
X

2.2. Measuring the air velocity

The difficulties met in the measurement of air velocity in food plants are due to (i) the presence
of blowers and obstacles that causes the air direction and velocity to vary rapidly with time, and (ii)
large and rapid variations in space of the mean airflow direction and magnitude, making the use of
anemometers that are airflow direction-independent absolutely necessary. Tests in several industrial
food plants have revealed that measurements performed with a hot-film type anemometer at an
acquisition frequency of 1 Hz must be averaged over at least several minutes to obtain a constant
value of the mean air velocity (we call this method the ‘standard average procedure’).
As this last procedure is tedious and time-consuming, a fast, powerful and accurate method
for measuring the air velocity by means of a hot-film type anemometer in an industrial flow has been
developed [1]. This method allows the average values of air velocity to be calculated at up to several
thousand points by the following procedure: (i) probes are moved slowly and continuously, and
measurements are recorded at regular intervals, and (ii) a signal processing technique (development
in Fourier’s series and low-pass filtering) is applied to the data to eliminate time variations due to
airflow unsteadiness as fully as possible, and thus obtain mean air velocity values versus spatial
co-ordinates.
In the free spaces in the pilot ripening room, i.e. between the rows of stacked racks and above
the stacks, to use the fast method set up at the laboratory, a specific system (Figure 1) was built to
support and automatically move the measurement devices with a slow and fairly constant velocity: the
multidirectional hot-film type anemometers used (model 8465, TSI, St Paul, USA) were connected to a
-1
data logger (model DT600, DataTaker, Rowville, Australia). A travel velocity of about 1.5 cm s was
chosen for these experiments.
Within the stacks of ‘cheeses’, only the standard average procedure was suitable; we built a
telescopic antenna to move the sensors (model 8475, TSI, St Paul, USA) into the free space between
two racks of cans. Preliminary tests showed that 40 s was needed to obtain a constant value of mean
velocity, for an acquisition frequency of 0.2 Hz. To easily connect the measurements performed with
the two methods, we chose a regular experimental mesh in the three space directions, with one
measurement point every 19 cm in width, 21 cm in length and 20 cm in height. The results of the air
velocity measurements come out as coloured graphs where each colour corresponds to a velocity
level. Analysing several coloured graphs of this type allows the airflow patterns in the room to be
assessed.
 ICEF9 – 2003
International Conference Engineering and Food

2.3. CFD calculations performed

With the development of cheaper, powerful computers and commercial packages, CFD has for
many years been increasingly applied in the food industry to assess the performance of industrial food
processing plants and to analyse the effects of modifying operating conditions or design parameters
[2], [3].
From the geometrical configuration presented in Figure 1, we used the code Fluent 6.0 [4] to
build a numerical model based on an unstructured three-dimensional (3D) mesh of about 1.2 million
cells. From the previous mesh, three variants of the numerical model were built, corresponding to the
three different blowing ducts studied in this work. To make it possible to link the very fine mesh of the
holes of the blowing duct and the coarser mesh built in the other parts of the duct, ‘boundary-layer’
type cells that were hexahedral in shape were needed in the vicinity of the holes.
During the numerical calculation, the airflow was considered as steady, incompressible,
isothermal and turbulent. The main flow turbulence was taken into account using the standard k-ε
model far from walls assumed to be smooth and where the standard wall function was applied. The
first-order upwind differencing scheme and the Simple algorithm were chosen. In the inlet area
-1
corresponding to the holes, an air velocity of 11 m.s and a turbulence rate of 10% were specified. A
classical outflow-type boundary condition was applied at the bottom of the extraction duct. n I the
model, the filling of the pilot ripening room was taken into account as a porous medium (that is as a
fluid volume in the Fluent approach) coupled with Ergun’s equation, in which two parameters must be
adjusted according to three space directions: (i) a characteristic length of the elements filling the
volume considered as a porous medium, that is the diameter or the height of a can, and (ii) a void
fraction, adjusted by comparing the calculated air velocity fields with the measured ones (hence void
fractions of 40% and 90% were determined according to vertical and lateral directions, respectively,
for the blowing duct with holes 6 mm in diameter). Calculations were performed on a PC Athlon 1900
XP+ with 1.5 Go of RAM, and took about 28 h.

3. Results and discussion

3.1. Air velocity fields measured in the pilot ripening room

According to a vertical section, Figure 2 depicts the air velocity fields measured at half-length
in the pilot ripening room, for the three different blowing ducts. Although the three experiments were
performed with the same whole airflow rate blown into the room and with the same air velocity at the
output of the holes of the blowing ducts, analysis of this figure reveals different ventilation levels and
ranging heterogeneity around the cans. The air blown through the holes flows along the ceiling and
the wall, before being separated into two parts when it reaches the top of the side stack: from here,
the first part of the air still flows down along the wall before entering the stack, and the second part of
the airflow travels towards the blowing duct, giving rise to a large swirl above the side stack with quite
high air velocities (Figure 2).
Inside the side stack of cans, a marked gradient of air velocity distribution appeared according
the height as the air velocities peaked in the low part of the stack while the upper part of the stack was
clearly poorly ventilated, whatever the blowing duct considered. On the other hand, the gradient of air
velocities varied with the diameter of the holes in the blowing duct: the smaller the holes, the lower the
air velocities and the heterogeneity around the cans. With a diameter of 3mm, the air velocities
-1 -1
ranged from less than 0.1 m.s to 0.3 m.s (Figure 2a), whereas with a hole diameter of 6 mm, they
-1 -1
ranged from less than 0.1 m.s to 0.45 m.s (Figure 2b), and for a hole diameter of 20 mm, the peak
-1
air velocity reached 0.6 m.s (Figure 2c).
Poor ventilation was visible within the stack located in the middle of the room, whatever the
-1
blowing duct considered, although some velocities exceeded 0.1 m.s when the hole diameter was
20 mm (Figure 2c). Careful analysis of the air velocities measured in this stack reveals that half the
-1
measurements recorded were below 0.05 m.s .

In view of these results, careful attention must be paid to the choice of a blowing duct in food
plants, because the heat and mass exchanges between the surface of a product and the air are
directly related to the air velocity around the product. For example, an experimental study has shown
that the water exchanges at the surface of a cheese 10 cm in diameter and 4 cm in height can triple
-1 -1
when the air velocity around the cheese is increased from 0.1 m.s to 0.45 m.s [5].
 ICEF9 – 2003
International Conference Engineering and Food

1.4-1.5
1.3-1.4 284
1.2-1.3
249
1.1-1.2

Height in the room (cm)

1-1.1
209
0.9-1
0.8-0.9
169
0.7-0.8
0.6-0.7
129
0.5-0.6
0.4-0.5
89
0.3-0.4
0.2-0.3 49
0.1-0.2
0-0.1 9
Air velocity (m/s) 262 205 148 91 34
(a)
Width in the room (cm)

Figure 2. Air velocity fields 1.4-1.5 289

measured at half-length in the 1.3-1.4
pilot ripening room, for (a) a 1.2-1.3 249
blowing duct with holes 3 mm in 1.1-1.2

Height in the room (cm)

diameter, (b) a blowing duct with 1-1.1 209
holes 6 mm in diameter and (c) a 0.9-1
blowing duct with holes 20 mm in 0.8-0.9 169
diameter (in the figures, the circle 0.7-0.8
indicates the location of the 0.6-0.7 129
blowing duct and the white 0.5-0.6
0.4-0.5
rectangles represent the outline of 89
0.3-0.4
the stacks of cans. Owing to
0.2-0.3
symmetry, only the half-width of 49
0.1-0.2
the room is shown).
0-0.1
9 (b)
262 205 148 91 34
Width in the room (cm)

289

1.4-1.5
1.3-1.4
249
1.2-1.3
Height in the room (cm)

1.1-1.2 209
1-1.1
0.9-1 169
0.8-0.9
0.7-0.8 129
0.6-0.7
0.5-0.6 89
0.4-0.5
0.3-0.4 49
0.2-0.3
0.1-0.2
9
0-0.1 262 205 148 91 34
(c)
Width in the room (cm)
 ICEF9 – 2003
International Conference Engineering and Food

3.2. Air velocity fields calculated

Figure 3 gives the air velocity field calculated from a Fluent simulation at half-length in the
ripening room, for the blowing duct with holes 6 mm in diameter.

Figure 3. Air velocity fields calculated

at half-length in the pilot ripening
room, for a blowing duct with holes
6 mm in diameter (in the figure, the
circle indicates the location of the
blowing duct and the white
rectangles represent the outline of
the stacks of cans).

This figure confirms the findings resulting from the measurements, i.e. higher air velocities
along the ceiling and the side walls, marked gradient in air velocity distribution in the side stacks and
poor ventilation in the stack located in the middle of the room. According to this figure, the CFD model
correctly predicts the airflow patterns inside the room and the stacks of cans, with, nevertheless, some
discrepancies in the prediction of the magnitudes. The numerical model seems to underestimate the
air ventilation level, presumably owing to the use of the first-order upwind differencing scheme, which
is known to reduce strong gradients and give rise to numerical diffusion.
Figure 4 confirms that increasing the hole diameter of the blowing duct leads to an increase in
ventilation level and the air velocity gradient in the side stacks, as indicated by measurements
(Figure 2c). The CFD results (not presented in this paper) obtained when the hole diameter of the
blowing duct is reduced to 3 mm closely agree with those of Figure 2a.

284

249

Figure 4. Air velocity fields calculated

Height in the room (cm)

209
at half-length in the pilot ripening
room, for a blowing duct with holes
169 20 mm in diameter (in the figure, the
circle indicates the location of the
129 blowing duct and the white
rectangles represent the outline of
the stacks of cans. Owing to
89
symmetry, only the half-width of the
room is shown).
49

9
262 205 148 91 34
Width in the room (cm) (b)
 ICEF9 – 2003
International Conference Engineering and Food

4. Conclusion

This study shows that careful attention must be paid to the choice and use of blowing ducts
made of textile material for ventilating food plants. Although no variation occurred in the total airflow
rate and velocities at the output from the holes, changing the diameter of the holes in the blowing
ducts led to differences in ventilation level in the room and around the cheeses, thereby modifying the
mass exchanges between the cheeses and the air.

5. Acknowledgements

The authors thank the French ministries of research and agriculture, ‘Arilait Recherches’ for
their financial support, and ATT for correcting the English version of this paper. This work is a part of a
research project involving the LGMPA laboratory of the INRA centre of Thiverval-Grignon and three
industrial firms: Safrair, Ysebaert and l’Ermitage.

6. References

1. Mirade P.S., Daudin J.D. A new experimental method for measuring and visualising air flow in large
food plants. Journal of Food Engineering, 36, 31-49, 1998.
2. Scott G., Richardson P. The application of computational fluid dynamics in the food industry. Trends
in Food Science and Technology, 8, 119-124, 1997.
3. Xia B., Sun D.W. Applications of computational fluid dynamics (CFD) in the food industry: a review.
Computers and Electronics in Agriculture, 34, 1-3, 2002.
4. Fluent 6: user’s guide. Lebanon: Fluent Inc., 2001
5. Rougier T. Caractérisation expérimentale de l’aéraulique d’un hâloir de fromagerie pilote : mesures
de vitesses d’air et de coefficients de transferts chaleur/matière. Mémoire de DEA Sciences des
Aliments et Nutrition, Université Blaise Pascal de Clermont-Ferrand, 26 p., 2002.
ICEF9 – 2004
International Conference on Engineering and Food

CFD simulation of airflow in a full scale flatbed dryer in the Mekong delta, Vietnam

Nguyen Thuan Nhi (1), Verboven Pieter (2), Baelmans Martine (3), De Baerdemaeker Josse (4),
Nicolaï Bart M. (2)

(1) College of Technology, Cantho University, Vietnam

nhi.nguyenthuan@student.kuleuven.ac.be
(2) Laboratory of Postharvest Technology, K.U.Leuven, Belgium
pieter.verboven@agr.kuleuven.ac.be, bart.nicolai@agr.kuleuven.ac.be
(3) Department of Mechanical Engineering, K.U.Leuven, Belgium
martine.baelmans@mech.kuleuven.ac.be
(4) Laboratory of Agricultural Machinery and Processing, K.U.Leuven, Belgium
josse.debaerdemaeker@agr.kuleuven.ac.be

Abstract
In order to improve flatbed rice dryers, which have been used in Mekong delta (MD), Vietnam, the
airflow in a flatbed dryer in MD was investigated. A mathematical model was developed to compute
the local airflow at different positions in the flatbed dryer and investigate the effect of dryer geometry,
with a k-ε model for turbulence and separate models to account for fan pressure and rotation, and for
resistance of screens. Measured and simulated velocity profiles agreed. High velocities were found
near the side walls of the drying bin, and low velocities in the center near the distribution channel.

Key words: airflow, CFD, drying, modelling, rice.

Introduction
The Mekong Delta (MD) is an important rice-producing region with a production of more than 50% of
the total rice output of Vietnam. With only 21% of the total population, MD accounted for more than
90% of Vietnam’s rice export in the past 10 years. MD encounters a high level of post harvest losses
due to poor drying practice. The only practical means of preventing rice quality deterioration is
immediate drying the fresh harvested paddy.
Traditional sun drying is still the most widely used method of drying high moisture grain whenever the
sun shines. Sun drying requires little capital cost (hard surface and rakes), but a high labour cost for
turning the grain regularly and protecting it from the wet weather. Dry season losses may also occur
through livestock, rodents, birds, insects, spillage, but the wet season losses are far greater. One main
crop in MD is harvested during the raining season, the initial grain moisture content of this crop is high,
but the available drying time is limited. Consequently, the postharvest losses due to drying delays are
very high, in some cases as high as 25%. Because of the long process times, the deterioration of
quality due to several aforementioned factors, the sun drying method has no future for complete drying
in humid tropical regions as MD.
The commercial grain dryer in Vietnam functions by forcing heated air though a bed of grain. The air is
the convective medium that supplies heat for evaporating moisture form the rice and then carries the
water vapour out of the grain mass. Basically, dryers are either batch type with shallow or deep beds,
either static or recirculated for mixing purposes, or they may be large, expensive, and sophisticated
continuous-flow devices intended for multi-stage drying. Systems based on continuous-flow drying
should incorporate a tempering bin.
With the current economic and social conditions in MD, flatbed drying can be implemented. It has the
advantages of simple structure and low drying cost. The head yield and seed viability of drying rice by
the flat bed dryer is higher than sun drying. MD promotes the manufacturers to increase to number
flatbed dryers for reducing the current post harvest losses. The need for research to modify the flatbed
to reduce investment costs and improving dryer performance is consequently great.
For designing an appropriate flatbed dryer, the air and heat distribution inside the dryer have to be
studied. The airflow distribution depends on the product properties, the geometry and characteristic of
the dryer. The air movement can be determined based on the conservation differential equations for
mass, and momentum. An analytical solution can be found only in simple cases. The variables can be
examined experimentally, but this is a tedious, costly, time-consuming method, moreover this method
cannot be used to optimise the structure of the dryer in the early phase of design. Alternative
numerical methods can be used. Mathioulaskis et al [1] applied the PHOENICS code to simulate the
ICEF9 – 2004
International Conference on Engineering and Food

air movement in a tray dryer for fruits by computational fluid dynamics (CFD). The pressure profiles
and the air velocities in the drying chamber above the product were determined by CFD and a lack of
spatial homogeneity of the air velocities above the product was found. There was a variation in the
degree of the dryness in several trays and the non-uniformity was traced into certain areas of the
chamber. The results showed that CFD could be a reliable tool for the analysis of flow fields developed
inside the drying chamber.
Southwell et al. [2] used computational fluid dynamics techniques to assess design alternatives for the
plenum chamber of a small spray dryer. The inlet region of a pilot-scale, co-current spray drier was
simulated using the proprietary CFD codes, CFX4 and CFX5. Several design alternatives were
considered for correcting uneven inlet air distribution, which is known to influence spray drier
performance and airflow patterns. The simulations were used to assess each alternative prior to
construction, assuming isothermal and incompressible flow conditions. The CFD simulations proved
useful in predicting the trends in flow distributions in each of the designs.
Nguyen Thuan et al [3] used the CFX5 to analyse the distribution of airflow in a limted scale empty
dryer model. The model predictions were validated based on experimental data. The airflow patterns in
the scale model at different fan speeds were given the average calculated error ranges from 33.2 to
42.6 %, with a good agreement of velcoity profiles. In this study, The CFD model is used to calculate
the steady, isothermal 3D forced airflow in a full scale empty flatbed dryer which is popular in MD. The
CFX 4.4 (Ansys Inc., Canonsburg, USA) code was applied.

Methodology
The governing equations based on the conservation of mass and momentum of a Newtonian fluid flow,
as applied to an infinitesimal small control volume d x 1 d x 2 d x 3 , in a Cartesian co-ordinate system xi
(i =1,2,3), are :

∂ρu i
= 0 (1)
∂xi
∂ρu j u i ∂  ∂u ∂u j  ∂  2 ∂u j 
= µ i + − p + µ  + Si (2)
∂xi ∂ x j  ∂ x j ∂ x i  ∂ x i  3 ∂ x j 

In these formulae, U(u1,u2,u3) (m/s) is the velocity vector; p is the pressure (Pa), T is temperature (°C),
the density ρ (kg/m³) and the viscosity µ.(kg/m.s). The term Si represents sources of momentum
(external forces) per unit volume.
The k-ε models are the most widely validated turbulence models in literature and are the standard
models to use in the commercial codes. However, they have limitations, which necessitates the
validation of the CFD results. The k-ε model uses an eddy-viscosity hypothesis for the turbulence,
expressing the turbulent stresses as an additional viscous stress term. In the k-ε model, the turbulent
viscosity is expressed in terms of two variables: the turbulence kinetic energy k and its dissipation rate
ε. Recognising that turbulence acts similarly to an increase of viscosity, the following approach is
usually followed on a time-averaged scale [4]:
µ eff = µ + µT (4)
2
k (5)
µ T = C µ ρ
ε
∂ ρk µ
+ div ( ρ U k ) − div (( µ + T ) gradk ) = P − ρ ε (6)
∂t σk
∂ ρε µT ε ε2
+ div ( ρ U ε ) − div (( µ + ) grad ε ) = C1 P − C2ρ (7)
∂t σε k k

where P is a term containing the shear production, and:

C µ = 0 . 09 ; σ k = 1 .0 ; σ ε = 1 . 3 ; C 1 = 1 . 44 ; C 2 = 1 . 92 (8)

The dependent variables in equations (1) and (2) are then replaced by their time-averaged
equivalents, and µ in equation (2) is substituted by the effective viscosity µeff. Near walls, the equations

2
ICEF9 – 2004
International Conference on Engineering and Food

do not hold and standard logarithmic wall profiles are implemented. This way the need to integrate the
model equations up to the wall is avoided.
The selected dryer for study was the model SHG-8, which is a flat-bed dryer with a maximum capacity
of 8 tons per batch. The dryer was designed by the University of Agriculture and Forestry, Hochiminh
City (UAF). The dryer used for validation was located in Song Hau state farm, Cantho, Vietnam.
The grain is held stationary in a rectangular bin through out the drying process. The dimension of the
bin is 10m x 5m. The grain depth is normally in the range of 20 to 40 cm. Air is forced into the plenum
chamber below the false floor by two axial fans powered by a engine of 22-25 HP. Heat derived from
burning rice husk is supplied to the air before it goes through the fans. The drying air temperature is
kept below 43°C to prevent the cracking of the paddy. It takes about 8 hours to dry wet paddy from
initial moisture content of 26% to the a safe storage level of 13-14%.
In order to achieve a more uniform air distribution in the grain bin, the plenum has a complex design
(figure 1). The air is forced by the fans through 2 inlets of 0.75 m in diameter. Then it goes through a
distribution chamber and enters the main plenum through 10 openings. The main plenum is divided
into 5 smaller compartments. Each plenum chamber has two openings to the distribution chamber.

Rice supporting screen

4 brick walls

Plenum chamber

1m

6 8m

10m
Distribution chamber

10 openings

Figure 1 Drawing of the SHG-8 flat-bed dryer

The perforated screen, which the rice rests, is supported by a wooden frame. It consists of a coarse
metal screen, and a fine plastic screen on the upper part. The plastic screen was fixed at its position
by the cross bars made of wood. Because of the complicated geometry, the false floor is treated and
the pressure drop is calculated by the following equation [5] in terms of the superficial velocity through
the screen:

∆pfloor= 1.07( U/Of)2 (9)

where ∆pfloor is the pressure drop across the floor (Pa/m), U is air flow rate (m3/m2.s). In this
assumption, U is the air velocity through the floor (m/s), Of is the percentage open area in floor.
The axial fans of the set-up were made by UAF and are 0.75 m in diameter and 0.42 m in fan hub
diameter. Characteristic curves of the fan was obtained by testing at the College of Technology,
Cantho University, Vietnam. The fan testing applied the Japanese Industrial Standard testing method

3
ICEF9 – 2004
International Conference on Engineering and Food

for fans and blowers (JIS B 8330-1962). The swirl effect of the axial fans is considered based on the
study of Temmerman et al. [6]. The mean tangential velocity of the actual fan is calculated by:

∆pt (10)
C mfan =
ρη t π D m n

where ∆pt is total fan pressure (Pa) , ηt is the theoretical fan efficiency and n is the rotational speed.
Let Dext be the diameter of the fan (blade circle) (m), Dint the diameter of the fan hub (m), then:

3
2 D ext − D int
3
(11)
Dm =
3 D ext − D int2
2

The CFX 4.4 software package was used for solving the model. This was run on a PC with an Intel
Pentium II 450 MHz processor, 512 KB cache, SDRAM 1024 MB. The popular finite volume method of
discretisation was used in this study. All the equations were integrated over each small control volume
around discrete points in the flow domain. A body-fitted structured grid covers the geometry. Three
different grid resolutions had been studied: 71280 control volumes for the coarse grid, 228960 control
volumes for the intermediate grid and 565920 elements for the fine grid. One-way bias seeds were
used in the width of the dryer, the grid was refined at the edge between the distribution chamber and
the plenum. The refinement was gradual to avoid large errors. After integration, the resulting terms are
discretised with finite difference approximations. The resulting system of non-linear equations was
solved by means of an iterative solution algorithm provided by the computer code CFX 4.4. Hybrid
differencing was applied since it exploited the favourable properties of the upwind and central
differencing schemes.

Hot film velocity meters (TSI 8475 and TSI 8465, St. Paul, MN, USA) were used. The calibrated
accuracy was 3% of the reading or 1% of full scale of the selected range. The transducers were
connected to a PC with a data logger (HP 34070A, USA). The HP BenchLink data logger software was
used to interface with the data acquisition. The differences between the measurement and the model
were expressed as:

U CFD − U exp
E=∑ * 100 (12)
U exp

Results and discussions

The general flow patterns were obtained. The air flow predicted by the CFX model of the intermediate
grid is presented in the upper picture of figure2 at the surface y= 0.54m above the plenum floor. The
measured airflow rate at the surface y = 0.54 m is shown in the lower picture in figure2. The air was
forced by the fans into the distribution chamber and spread out through the openings of the plenum.
The last openings received more air and created a high velocity zone in the end corner of the bin. This
was seen in both experiments and calculations (figure 2). The middle zone, near the air inlets has a
low air velocity magnitude. There is a zone next to the distribution chamber which has a negative
airflow direction, caused by a negative relative pressure at this location, entraining air from outside .
The validation of the calculated flow pattern was assessed by comparing the calculated and the
measured velocities. The zones with non-uniform velocities distribution which are important for drying
process can be predicted, especially for the very high and very low velocity zones.
An average error of 40.9 % was achieved by applying the intermediate grid. Grid independence was
not reached. The coarse grid and fine grid had an average error of 43.7 % and 42.2%, respectively.

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ICEF9 – 2004
International Conference on Engineering and Food

Measured Airflow rate (m/s) 0.875-1

0.75-0.875

9 0.625-0.75

7
Locations at Z 0.5-0.625

5 axis
0.375-0.5
3
0.25-0.375
1
19

17

15

13

11

0.125-0.25
Locations at X axis

0-0.125
Figure 2 The predicted airflow rate (m/s) at the surface y=0.54 m (upper) in comparing with the
measured airflow rate (lower).

The histogram of Yplus is plotted for three mesh sizes in figure 3. For the coarse grid the value of
Yplus is too large, about 83% of Yplus is larger than 100, so that the wall profile is insufficiently
resolved. The intermediate grid have a small improving, around 67% of yplus is larger than 100, this
develops the overall accuracy a little bit. In case of the fine grid, 58% of yplus is larger than 100,
although the percentage is down, but still a too big value to reduce the error from the intermediate grid.
More effort is needed to optimise the grid structure.

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ICEF9 – 2004
International Conference on Engineering and Food

Histogram of YPlus for different mesh grids

60
P robability density (% )

50
40 coarse grid
30 intermediate grid
20 fine grid
10
0 0

0
40

80

12

16

YPlus value 20

Figure 3 Histogram of yplus for three difference mesh grids

Conclusions
A CFD model of the 3D airflow in an empty full scale dryer in MD was discussed. The general flow
patterns were obtained. The model predictions were validated based on experimental data with an
average calculated error of 40.9 %. The grid refinement was not always effective. It needs to consider
a carefully refinement at specific local areas. The accuracy for the velocity was limited due to the k-ε
turbulence model as well as measurement errors due to many disturbing factors from outside.
This result is an essential device for a designer to develop the rice dryer, as well as improving the
performance of the existing dryer by finding out the deficiencies of air flow patterns.
The research will be continued to study the air and heat distribution in a loaded flat bed dryer.
Acknowledgements
The author wishes to thank the VLIR-CTU Institutional University Co-operation of the Flemish
Interuniversity Council for financial support. Pieter Verboven is postdoctoral researcher of the Flemish
Fund for Scientific Research (F.W.O.-Vlaanderen).
References
1. Mathioulaskis E., Krarathanos V. T. and Belessiotis V. G. Simulation of air movement in a dryer by
computational fluid dynamics: Application for drying of fruits. J. Food Eng. 36, 183-200, 1998.
2. Southwell, D. B., Langrish T. A. G., Fletcher D. F., and Tambunan A. H. Use of computational fluid
dynamics techniques to assess design alternatives for the plenum chamber of a small spray dryer.
First Asia-Australia Drying Conference, Bali, Indonesia, October 1999.
3. Nguyen Thuan, N., Verboven P., Baelmans M., De Baerdemaker J., and Nicolai B. M., Simulation of
Airflow in a Flatbed Dryer by Computational Fluid Dynamics: Application for the Drying of Rice in
Mekong Delta, Vietnam. ASAE international meeting, Las Vegas, Nevada, USA, July 2003.
4. Launder B.E. and Spalding D.B. The numerical computation of turbulent flow. Computational
Methods In Applied Mechanical Engineering, 3, 269-289, 1974.
5. Brooker, D. B., Bakker-Arkema F. W., and Hall C. W. Drying and Storage of Grains and Oilseeds.
Van Nostrand Reinhold, New York, 1992.
6. Temmerman, W., Christiaens F., and Baelmans M. Application of Fan Models for Thermal
Simulation. ISPS 1997 Proceedings: 81-86, 1997.

6
ICEF9 - 2003
International Conference Engineering and Food

Prediction and optimization of asymmetric mixing patterns in tanks

Tress A.J.G. (1), Stubbe P. (2), Jensen B.B.B. (3), Friis A. (4)
(1) Food Process Engineering Group, BioCentrum-DTU, Lyngby, DK-2800
ajgt@biocentrum.dtu.dk
(2) Food Process Engineering Group, BioCentrum-DTU, Lyngby, DK-2800
ps@biocentrum.dtu.dk
(3) Food Process Engineering Group, BioCentrum-DTU, Lyngby, DK-2800
bbb@biocentrum.dtu.dk
(4) Food Process Engineering Group, BioCentrum-DTU, Lyngby, DK-2800
af@biocentrum.dtu.dk

Abstract

The CFD model developed in this work predicts mixing patterns in silo-tanks. It provides
information about the behavior of two-phase flows stirred with two pitched blade
turbines placed parallel to the tank wall and at an angle of 45°. The results from the
studies are applied to reduce the energy requirements for mixing and optimize mixing
efficiency.

Introduction

In the food and chemical industry, agitating and mixing equipments are utilized for many
different purposes. The designs of such stirring devices have to a very high degree
been performed based on rules of thumb, traditions and by a scale-up of small
experiments. The final large-scale design often does not achieve the mixing goals,
because the dimensionless parameters, used for scaling up, can never take into
account all the details of geometry and flow. This is especially devastating for
equipment with large amounts of power input.

The efficiency of mixing operations often has a big impact on production costs and
product quality. The issue is to design an agitator that will provide the required level of
mixing in the shortest possibel time. Computational Fluid Dynamics models are now
regularly used to calculate the flow patterns in stirred vessels. It was slow to take root in
this area because of the difficulty of modeling the complex flow created by the impellers.
However, the latest software provides an accuracy, that can easily compete with that of
experimental methods. It is therefore possible to calculate the flow around a rotating
impeller inside a stirred tanks.
ICEF9 - 2003
International Conference Engineering and Food

Tank configuration

The stirred tanks studied in this work were cylindrical, flat-bottomed vessels with a
diameter of 0.64m, the liquid column height is 2.5m. The tank has two 45° pitched blade
impellers with a diameter of 0.13m. The blades have a length, width, and thickness of
0.06m, 0.028m, and 0.007m respectively. The impellers are located 0.106m from the
side of the vessel at 0.37 m and 150 m over the bottom. (Fig.1.)

The difference between the two tanks studied is the impellers’ orientation. One has the
impellers tilted 45°, while in the other tank, the impellers are parallel to the tank wall.

Fig. 1. Silo tank with two pitched blade impellers.

Computational Method

The tank and the impellers were modeled in three dimensions in Gambit 2.0.4. In order
to use the sliding mesh method to model the rotation of the impellers, each impeller has
to sit inside a rotationally symmetric grid of it's own. The grid in the tank need to provide
holes to fit the impellers' grids into. The computational grid for the impellers is a T/Grid
unstructured mesh of spacing 1 with 4780 cells, while the tank is also a T/Grid
unstructured mesh but with a spacing of 2 and 753398 cells. The total number of cells is
762728.
ICEF9 - 2003
International Conference Engineering and Food

With the Multiple Reference Frame model the tank is divided in three regions that are
treated separately: the impeller close to the bottom, the impeller higher in the tank, and
the tank region that include the bulk of the liquid, the tank walls, and the tank bottom.

The fluid mixture model is designed for two or more fluid phases. The phases are
treated as interpenetrating continua. The mixture model is solved for the mixture
momentum equation and prescribed relative velocities to describe the dispersed
phases.
The two fluid phases simulated in this work were water with a density of 998kg/m3 and
cream with 20% fat, that has a density of 1010kg/m3 at 3°C [1]. The tank was filled with
0.643m3 of water and 0.160 m3 of cream. The patch volume fraction was set for the
cream phase with a value of 1. [2]

The impeller rotational speed was 190rpm, both impellers rotated in the same direction
pushing the flow away from the closest tank wall. The impeller Reynolds number (Re=
ρND2/μ) was 37000, so turbulence was modeled using the standard k-ε model.

To simulate the unsteady flow in the tank the governing equations of mass, momentum,
turbulent kinetic energy, turbulent dissipation rate and slip velocity were solved using
Fluent 6.0. All simulations were initiated from a zero-velocity flow field and a volume
fraction of 0.5. The initial time step of 0.001s was increased every time the convergence
was reached in less than 9 iterations.

Results

The local velocity magnitude in the middle plane of the tank through the impellers shows
that the highest velocities are found near the impeller blade tips. The velocities
decrease while the fluid moves away from the impellers.

The flow patterns in the two tanks can be seen in fig. 2 after 8 seconds mixing. The tank
with the tilted impellers is shown to the right. In the tank with tilted impellers it can be
seen how the jet from the impellers reach all the way to the opposing wall. On the other
hand, there is hardly any movement away from the impellers in the tank with parallel
impellers. Probably this is because the impellers are placed too close to the wall to allow
for the water to flow in behind the impellers as fast as they can pump it away. This has
to be investigated in a further work.
ICEF9 - 2003
International Conference Engineering and Food

Fig. 2. Velocity vectors in the two tanks after 8s.

The mixing pattern in the tanks can be seen in fig. 3. The tank with the tilted impellers is
to the right again. The cream is in the top and water in the bottom. Between cream and
water there is a zone with a mixture of cream and water. In the tank with parallel
impellers the cream seems to fall towards the bottom due to gravity. When the cream
passes the top most impeller a jet of cream is shot away from the impeller.

The cream in the tank with tilted impellers is sucked into the upper impeller and shot
down towards the bottom. The pure cream reaches all the way down to the impeller
leaving less cream at the top than in the tank with parallel impellers.

It must be anticipated that given longer time, the tilted impellers will pump the cream
down to the bottom faster than the parallel impellers.
ICEF9 - 2003
International Conference Engineering and Food

Fig. 3. Mixing pattern in the two tanks after 8s.

Conclusions

The flow occurring in both stirred vessels is three dimensional, extremely complex, and
highly non-uniform, and therefore hard to treat analytically. However, a numerical
approach can handle the complex flows, and gives more detailed data, than could be
achieved by experimental means.

Comparing the two tanks shows that the tank with the inclined impellers has much more
movement than the other. This seems to be due to the impellers parallel to the wall
being too close to the wall, and therefore restricted in the amount of water flowing
towards the "inlet" side of the impellers.

Overall the mixing seems to proceed faster in the tank with the tilted impellers. Further
investigations will tell if the impellers parallel to the tank wall will improve by being
moved a longer into the tank.
ICEF9 - 2003
International Conference Engineering and Food

Reference

1.Fellows P. J. “Food processing technology. Principles and practice.” Ed. Woodhead

Publishing Limited, England, 37p, 1997.

2. Fluent incorporated. “Fluent 5 user’s Guide Volume 3”.Ed Fluent incorporated, USA.
15-36, 16-24p, 1998.

3.Bakker A., LaRoche R., Wang M. Calabrese R. Sliding Mesh Simulation of Laminar
Flow in stirred reactors. Publish in “The online CFM book” at http://www.bakker.org/cfm.
2000.
 ICEF9 – 2004 International Conference on Engineering and Food

Design changes to shell flows in tubular heat exchangers to effect heat recovery

Tucker, G.S. (1), Shaw, G.H. (1), Cronje, M.C. (1), Jones, T.E.R. (2), James, P.W. (2)
and Hughes, J.P. (2)

(1) Campden & Chorleywood Food Research Association, Chipping Campden, Glos, GL55 6LD, UK
g.tucker@campden.co.uk (2) University of Plymouth, Plymouth, PL4 8AA, UK

The objective was to design and demonstrate the use of an innovative tubular heat exchanger to
recover heat from shear-sensitive, medium viscosity foods with minimal quality damage. The major
technical challenge was to modify the shell-side flow around the tubes in order to enhance heat
transfer efficiency and reduce pressure drop. CFD simulations supported the temperature and
pressure measurements on a modified shell pass and showed good agreement between measured
and predicted wall shear rates.

Keywords: tubular heat exchanger, pressure drop, CFD, viscous foods

Introduction

Heat recovery using tubular heat exchangers, or regeneration, is used in the food industry for heating
1
and cooling of low viscosity food products such as milk, fruit juices and beverages (see footnote ). In
such systems, the hot processed food product is cooled down in the tube inserts by the cold
unprocessed food product that, in turn, is heated in the surrounding shell. The processed food product
passes through the tube inserts in a direction counter current to the cold food product in the shell (see
figure 1). An alternative is to pass the cold food product through the tubes and the hot processed food
product in the shell, which is more effective thermally, but in this case it is of paramount importance
that the shell-side flows are designed hygienically.

Figure 1: Illustration of the counter current flows in a conventional heat recovery (regeneration) THE
for low viscosity liquids

1
‘Low viscosity’ products refers to those whose viscosity varies with temperature, or possibly with
shear rate, but viscosities are never larger than ~0.1 Pa.s. ‘Medium viscosity’ products refers to those
whose viscosity varies with both temperature and shear rate, with viscosities that are typically orders of
magnitude larger than the ‘low viscosity’ products. These products may also exhibit elastic effects.

1
 ICEF9 – 2004 International Conference on Engineering and Food

A range of tubular exchangers are available to the food industry that are suitable for processing food
products from low viscosity milk to medium viscosity fruit purees and pastes, with or without
particulates. There is an interest in applying the regenerative technology to medium viscosity food
products in order to save energy costs. This process has not yet been attempted because of the
technical barriers relating to the heat transfer and pressure drop conditions likely to be experienced
with these food products.

Several types of tube insert can be used within the heat exchanger shells, with the choice dependent
on the rheology of the food product and the heat duty application. Tube bundles of, for example, 19 or
37 tubes with individual tube diameters less than 16 mm are not suitable, because they are likely to
incur high pressure drops and mal-distribution of flow within the bundle. The potential tube insert
range for medium viscosity food products includes:

i. Multi-tubes, in bundles of 7 or 12 tubes, for food products with pulp or particulates up to 5

mm.
ii. Fibre-tubes in bundles of 4 for food products with long fibres or pulp

Food Product Rheology

Food products with a viscosity greater than that of milk, juices and beverages, are likely to contain
thickening agents that have complex molecular structures [3] (e.g. pectins, starches, gums). Some
thickeners are naturally occurring in the food, while others are added in combinations to obtain a
desired ‘texture’ or ‘consistency’. For most heat exchanger design purposes, it is industry practice to
describe the viscous behaviour using simple rheological models such as the power law model.
However, the flows may be such that elastic, as well as viscous, effects are important, particularly in
regions where the flow expands or contracts, such as in the entry and exit manifolds. Under these
circumstances it may be necessary to characterise the elastic properties for full definition of the shell-
side flows, where stagnation zones need to be predicted and avoided.

Heat Recovery in the Non-Food Industries

Research work on laminar flow of medium viscosity food products in counter-current heat exchange [4]
is sparse and few publications can be found in the literature for the oil and chemical industries. There
is a 1977 Russian paper [5] that studied heat exchange in transverse flow of viscous oils round a
cylinder, at low Reynolds numbers (19.4 to 483). A 1976 German paper [6] reported a continuous
pasteurised sludge system that incorporated a ‘regenerative spiral heat exchanger’ to treat dairy
effluents. However, for these fluids, there was no need to protect the delicate molecular structure or to
maintain hygienic processing conditions. Both of these factors are essential for food industry
applications.

Heat Recovery in the Food Industry

Apart from the heat recovery systems used for milk, fruit juices and beverages, little work has been
published on foods of a higher viscosity. There is one report on ghee production [7] that describes
heat recovery, but at the pasteurisation temperatures (85-100 °C) the ghee viscosity was much
reduced, to the extent that flow conditions were close to the laminar-turbulent transitional region or
even fully turbulent. Ghee is also similar to the oils and sludges in that it is a Newtonian liquid with a
simple molecular structure that does not require such a careful treatment as the food materials studied
here.

The lack of published information on heat recovery for medium viscosity materials in heat exchangers
has arisen in part because, until recently, the computational methods could not model the flow fields
for viscous and elastic materials in such complex geometries. For food materials, the technical issues
are not energy savings alone, but the need to avoid damage to the delicate macromolecular structures
that give rise to the ‘consistency’ of finished food products.

2
 ICEF9 – 2004 International Conference on Engineering and Food

The principles of using heat recovery with medium viscosity food products were addressed within an
ETSU-funded project [8] that has proven the potential for making substantial energy savings. For
example, the energy transferred during heat recovery was approximately 20 % of the total, for
n
pasteurised starch solutions up to 5.0 wt% (Colflo 67, National Starch; n=0.29 k= 8.71 Pa.s ) using 16
mm diameter multi-tubes. The ETSU project was concerned solely with proving the principles and did
not consider in detail the hygienic design of manifolds, tube supports and shell-flows, nor did it
investigate novel shell designs for enhancing heat transfer in the thermal boundary layers. Its intention
was to utilise existing equipment with a limited range of starch solutions.

The objectives of the work reported here were to quantify velocities and temperatures within the shell
of a commercial 7x16 Tetra Spiraflo (Tetra Pak), so that a computational fluid dynamics (CFD) model
could be developed and validated. This model was intended to be used to estimate the potential heat
transfer gains that could be achieved by re-designing the outer shell and any components that
contributed to sub-optimal heat transfer.

Methods

Theoretical

An important feature of the project was the numerical simulation of the flow and heat transfer in the
shell-side of a 7x16 multi-tube exchanger. This was accomplished using the ANSYS CFX code for
inelastic viscous fluids, and the Fluent POLYFLOW code for elastic fluids. Recent experimental and
numerical work [9,10] demonstrated the feasibility of modelling the geometry of a shell and tube heat
exchanger using the CFX code. Figure 2 illustrates a longitudinal cross-section through the shell
showing the velocity vectors as the fluid enters from the manifold and goes through a 90° turn. One of
the tube inserts is shown in the cross-section as a blank area where flow cannot occur.

n
Figure 2. Predicted flow velocities of a 3.0 wt% Cerestar C*Tex starch solution (n=0.8 k=0.0423 Pa.s )
-1
at 30 L.min at the inlet manifold of the shell.

One of the key physical properties that required accurate measurement were the rheological
characteristics under the flow conditions experienced. To achieve this, a wide gap double concentric
cylinder cell was manufactured, instrumented, calibrated and analysed. The cell design allowed for the
presence of particulates (up to 3 mm) within the gap, improved temperature uniformity of the sample,
and prevented surface drying at elevated temperatures.

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 ICEF9 – 2004 International Conference on Engineering and Food

Experimental

A range of methods was used to generate data to validate prediction from the CFD models. This was
necessary to confirm the correct initial development of the CFD models before moving on to
predictions of new design configurations. In one validation method, a transparent model heat
exchanger was constructed with solid tubes and a square cross-section shell. This allowed shear
stress probes to be mounted along the shell to generate measurements for comparison with
predictions from the CFD. Data gathered with this system was isothermal.

Work also focussed on the acquisition of non-isothermal data on the full scale Tetra Spiraflo system.
One 70 mm diameter shell pass of a Tetra Spiraflo system was modified to allow temperature and
pressure measurements to be taken on the shell side of the exchanger. The tubes used were 7x16
multitubes (MT). Temperature measurements were taken along the length of the outside of the shell
with surface probes at locations that corresponded with the smallest gaps between the tube inserts
and the shell. Thin wire type T thermocouples were taped in place at these locations and
measurements taken with a datalogger (Grant Squirrel) at five second intervals. A range of starch
solutions were passed through the shell at several different flow rates, whilst heated water in the tubes
flowed counter current to the starch. Data was analysed under steady state conditions allowing
average data values to be taken for each measurement point.

Further temperature measurements were taken within the shell itself using type T thermocouples
passed through compression fittings to an immersion depth of 5.0 mm. The fittings were located in
rings of five sensors at six positions along half the shell. The sets were positioned closer together
around the manifold as the flow of the product into or out of the shell at this point would encounter the
most disruption due to the positioning of the tubes at 90° to the flow path. As with the external
temperature measurements, a range of starch solutions were used for the trials along with commercial
food products in the medium viscosity range.

The same Tetra Spiraflo 7x16 MT was fitted with a series of manometers to measure the pressure
drop along the length of the shell. 5.0 mm internal diameter tubing was attached to fittings, which were
positioned at seven points along the top of the shell pass. This enabled the pressure drop to be
determined along the shell at ambient temperature for a range of flow rates and solutions. Data was
used to provide further evidence that the CFD simulations were correct.

The final experimental set-up consisted of the construction of a transparent shell for a 7x16 MT so that
flow visualisation experiments could be conducted. To simplify construction of the shell, a standard
n
steel manifold was used for the product inlet. A 1.0 wt% CMC solution (n=0.63 k=1.6 Pa.s ) was used
as the product. A range of methods was used to investigate the shell side flow patterns. CMC mixed
with dye was injected into various points of the inlet flow, and also through holes drilled in the shell
itself. This latter method allowed variation in product flow around the tube supports to be investigated.
The behaviour of the dye was analysed by calculating the rates of dye dispersion along the length and
by video analysis.

For all the data acquisition trials, data analysis was only carried out once the experimental rigs had
reached steady state conditions. The approach to steady state from start-up was not of concern at this
stage of the work. This was of critical importance for allowing an accurate comparison to be made
between the actual experimental values and those predicted within the CFD models.

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 ICEF9 – 2004 International Conference on Engineering and Food

RESULTS AND DISCUSSION

Pressure Drop
-1
For a 3.0 wt% Cerestar C*Tex starch solution at a flow rate of 15 L.min , experimental data indicated
a linear pressure drop along the length of shell pass from 10,000 Pa at the inlet down to around 6,500
Pa at the outlet. This correlated closely with the CFD predictions (see figure 3)

11000
Experiment
10000 Prediction
Pressure (Pa.)

9000

8000

7000

6000
0 1 2 3 4 5 6
z (m)

Figure 3. Graph showing experimental and predicted values of pressure on the shell side of a 7x16
MT, as a function of the distance along the shell (z)

Temperature Measurements

For a 3.0 wt% Cerestar C*Tex starch solution in the shell side flowing counter current to water at 71.0
°C in the tubes, variation in temperatures was measured along the length of the shell. The initial set of
readings were for sensors located in the dead zone behind the inlet manifold, which were higher than
the product inlet temperature of 39.3°C. After this, a steady increase in average temperature was
measured along the length of the shell. However, the temperatures measured in the sensor rings were
not uniform, with the top temperatures higher than those towards the bottom. This was thought to have
been caused by natural convection effects.

Flow Visualisation

The main output of the trials on the transparent shell pass was the acquisition of shell side product
flow velocities. These were obtained at a range of positions on the shell and with the injection of the
dye being carried out at different depths into the product flow. Correlation of experimental velocities
with predicted velocities from the CFD model were sufficiently close to conclude that the CFD model
was giving correct predictions.

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 ICEF9 – 2004 International Conference on Engineering and Food

DISCUSSION AND CONCLUSIONS

The work is currently at an advanced stage, with all the necessary tools for understanding the
behaviour of medium viscosity liquids on the shell side of a tubular heat exchanger now developed.
The next stage is to identify design problems resulting from the current design when used with medium
viscosity liquids flowing in the shell. The first of these are the manifolds that act as inlets and outlets to
the shell. The current design of manifold shows dead zones with poor product flow and heat transfer
for the more viscous products looked at (figure 2). Another aspect of the current design that affects the
product flow is the tube supports that maintain the correct spacing between the tubes. These require
either redesigning or removing completely with alternative methods being developed for ensuring the
correct orientation of the tubes. The spacing of the tubes themselves could be optimised in order to
generate more uniformity in velocity and shear rate around the tube bundle.

With the identification of these and other potential design improvements, changes can be evaluated
within the CFD models without recourse to expensive experimental tests. Once these changes have
been proven computationally, a prototype tubular heat exchanger to recover heat from shear-sensitive,
medium viscosity foods can be constructed.

Acknowledgement

This project is funded through the DEFRA Advanced and Hygienic Food Manufacturing LINK scheme,
in collaboration with the University of Plymouth, Tetra Pak UK Ltd, HJ Heinz Co. Ltd, New Covent
Garden Food Company, Centura Foods, GlaxoSmithKline, Fluent Europe, ANSYS CFX, TA
Instruments. (July 2001 – December 2004). The financial support of the Department for Environment,
Food & Rural Affairs is gratefully acknowledged.

References

1. Tucker, G.S. and Bolmstedt, U. Liquid Foods International, March. (1999).

2. Anon Tetra Bridge, September 4. (1998).
3. Bolmstedt, U. MAFF/BBSRC Food LINK Programmes Dissemination Meeting, SCI, 14/15
Belgrave Square, London. 13 January 1998. (1998).
4. Ho, C-D. Int. J. Heat & Mass Trans, 43, pp3263-3274, 2000. (2000).
5. Smolyak, A.A. Vesti Akademii Navuk BSSR, No.4, pp99-104. (1977).
6. Anon Deutsche-Milchwirtschaft, 27 (34), 1055-1057. (1976).
7. Abichandani, H., Sarma, S.C. and Bector, B.S. Indian Food Industry, 10 (4), pp35-36. (1991).
8. Tucker, G. S., Shaw, G. H. Heat Recovery in Tubular Heat Exchangers for Medium Viscosity
Products. CCFRA R&D Report 140. (2001).
9. Jones, T.E.R., Hughes, J.P. and James, P.W. Experimental and numerical simulation of the flow
nd
of Newtonian and non-Newtonian fluids in rotating cans. 2 Int. Conf. on Food Structure and
Rheology, Zurich, March, 2000. (2000).
10. Hamid, R. Q. and Roetzel. W. “Experimental determination of flow and temperature fields in a shell
rd
and tube heat exchanger”, pp 355-364, 3 Int. Conf. on Advances in Fluid Mechanics, Montreal,
May, 2000. (2000).

6
ICEF9 – 2004
International Conference on Engineering and Food

Combined Discrete Elements and CFD modelling of air flow through randomly filled boxes with
spherical food products
P. Verboven(1); E. Tijskens(2), Q.T. Ho(1), H. Ramon(2); B.M. Nicolaï(1)
(1) Flemish Centre/Laboratory of Postharvest Technology, K.U.Leuven, W. de Croylaan 42, B-3001,
Leuven, Belgium
email: pieter.verboven@agr.kuleuven.ac.be
(2) Laboratory of Agricultural Machinery and Processing, K.U.Leuven, Kasteelpark Arenberg 30, B-
3001, Leuven, Belgium
email: engelbert.tijskens@agr.kuleuven.ac.be

Abstract
Air flow in European Pool System (EPS) boxes (30×40×16cm) was studied. Spherical particles
mimicking horticultural products like apples, oranges or tomatoes were considered. Discrete element
modelling was applied to simulate the filling of a box with spheres with a uniformly distributed diameter
(65-75mm). The air flow (300/900 m3 h-1 m-2) in the voids between the particles was solved by means
of a non-structured finite volume CFD code. The results were compared to measurements. An
important effect of stacking in small boxes is air flow channeling.

Keywords: CFD, DE, air flow, cooling, postharvest storage

Introduction
Knowledge of air flow in bulks of agricultural and horticultural products is important for proper cooling
and control of optimal storage conditions. Traditionally, air flow analysis in bulks is performed by
means of empirical relationships of the bulk-average properties, meaning the mean flow rate through
and pressure drop across the bulk. This results in Darcy-Forchheimer models [1,2,3]. The well-known
Ergun equation [4] is an example of this approach. Being originally developed for a large bulk of
randomly stacked spheres of uniform diameter, the Ergun equation may not hold for small bulks,
confined by walls [5]. Instead of relating bulk flow rate and pressure drop, an explicit model of the bulk
geometry can provide understanding of flow patterns and consequences for cooling. The objectives of
this work were to explore and demonstrate the possibilities of combining the techniques of Discrete
Elements and Computational Fluid Dynamics to solve the airflow in the voids between stacked
spheres in a box with ventilation slots, based on the fundamental equations of aerodynamics, and
incorporating randomness of particle size and position in the box.

Materials and methods

EPS Box and tomatoes

EPS (Euro Pool System, Leidschendam, The Netherlands) boxes of dimensions 30×40×16cm were
used in this study (Figure 1). The standard size and physical strength of the boxes renders them very
popular for fruit and vegetables handling and distribution in Europe. The boxes were filled with 6kg of
tomatoes (cultivar Tradiro, VMV Auction, Mechelen, Belgium) of size class 70 to 75 mm diameter
(Figure 1).

Figure 1. EPS box with 6 kg of tomatoes (30×40×16cm)

Velocity measurement
Measurement of air flow in EPS boxes was performed in a small wind tunnel (Figure 2). Velocity
profiles were measured by means of a omni-directional hot film sensor (TSI 8475, ST. Paul, MN,
USA). Upstream velocity ( to determine flow rate) and inlet velocities at the opening and slots were
measured (Table 1), as well the vertical air velocity profile in between the spherical particles at 9

1
ICEF9 – 2004
International Conference on Engineering and Food
positions throughout the box (Figure 2). The 9 positions were chosen at 3 different vertical planes
perpendicular to the air flow, respectively at 1, 18.5 and 30.5 cm from the inlet side of the box. The
measurements were fully described by Ho (2003).
Fan Stack of boxes Perforated screen

Air flow
Air flow Velocity
Air flow cm
40 sensor
Cylinder
frame

40cm Experimental
200cm Exp. box box
(a) (b) (c)
Figure 2. Experimental set-up: (a) wind tunnel, (b) stack of boxes with central experimental box, (c)
velocity sensor positioning

Discrete elements model (DE model)

In order to generate a realistic computer model of a stacking of tomatoes a chosen number of spheres
with random diameter were placed in random positions above the bottom of the box. In this initial
configuration the spheres do not touch each other, or the walls of the box (see figure 3.a). Then the
spheres were allowed to settle under the influence of gravity until an equilibrium position was reached
(see figure 3.b). In this equilibrium situation the spheres are in contact with the walls and neighbouring
spheres with a finite contact area as a consequence of the forces acting on them. The motion of the
particles to their equilibrium position was modelled by a Discrete Elements model (DE model). This is
a numerical technique for solving the equations of motion of an assembly of interacting grains. Each
grain has 6 degrees of freedom (3 translational and 3 rotational) governed by the basic laws of
mechanics expressing conservation of momentum and angular momentum:

x = ∑ Fext , Iω
m&& & = ∑ r × Fext . [1]

Here, m and I , are the sphere’s mass and inertia tensor, x and ω its position and angular velocity.
The dots denote differentiation with respect to time. Fext is an externally force applied to the sphere
and r its point of application. Forces accounted for are the gravity and contact forces due to collision
with other spheres or walls. Contact forces are described by a contact force model. They have a
normal component describing the relation between force and deformation normal to the contact
surface and a tangential component describing the relation between force and deformation tangential
to the contact surface. Both have an elastic and a damping contribution. In addition the tangential
component includes dry friction. A description of the contact force models applied here and their
experimental deformation can be found in [8,9]. A detailed account of DEM for agricultural products is
given in [7]. An important aspect of the physical model applied here is that particles in contact have a
finite overlap which mimics the finite area of the contact. The size of the overlap and of the contact
area is related to the contact force through the contact force model. This restricts in a physically
realistic way the volume where the air can circulate and the tomato-air interfacial area where the
tomatoes can exchange heat with the air.

Computational Fluid Dynamics model (CFD model)

GEOMETRY CREATION
The output of the DE model (position and radius of spheres) was directly imported into a geometry
modelling program. For this purpose, ANSYS 5.7 (Ansys Inc., Canonsburg, PA) was used. ANSYS
allows to easily create the spherical solid volumes, remove the overlap between touching particles and
generate the resulting trimmed surfaces. Additional box surfaces, inlet and outlet openings and
ventilation slots, as well as the intersections of these with sphere surfaces were created in the
geometry modeller of ANSYS (Figure 4). The surface geometry was then read into CFX5 (Ansys Inc.,
Canonsburg, PA) in Initial Graphics Exchange Specifications (IGES) file format, an ANSI Standard
formatted file to exchange geometry data among CAD systems.

2
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International Conference on Engineering and Food

(a) random initial position (b) final configuration in a 30×40×16cm EPS box

Figure 3. Calculated drop of spheres in the EPS box with the DE model (35 spheres 65-75mm random
diameter, and random initial position)
Based on the bounding surface topology, the closed pore volume geometry was created by means of
a single B-rep solid (Figure 5). A B-rep solid is only defined by its shell of surfaces and is not
parameterized. Therefore, the limitation of a maximum number of 6 faces of normal parameterised
solids (e.g., a brick) vanishes and any number of congruent surfaces can define a B-rep solid.

middle plane
y
(distance from x (air flow direction)
middle plane)

Figure 4. Geometrical outline of the DE-CFD Figure 5. DE-CFD solid model (half of geometry)
model

MESH CREATION
CFX5 (Ansys Inc., Canonsburg, PA) was employed to create the computational mesh on the
geometry. First, a triangular surface mesh was created on the geometry faces using Delaunay
triangulation, defining a maximum edge length of 0.02 m. The tetrahedral volume mesh was created
from the surface mesh, using the maximum edge length, and accounting for small spaces between
surfaces, which should be bridged by at least 3 elements. Furthermore, edge proximity is used to
smooth the mesh at the edge of a surfaces with large elements and a surface with small elements. If
these parameters were insufficient to produce elements without small angles, a mesh control was
used on the curved areas of the concerned spheres to reduce the error between the straight edge of
the element and the curved face to less than 1/1000 of the sphere radius . With this procedure, a
mesh of 700,000 to 1,000,000 volume elements over the box was created (Figure 6). Due to
restrictions of computational resources, the full box could not be meshed. Therefore, only one half of
the box was meshed, with the rough approximation of symmetry along the central streamwise axis of
the box.
AIR FLOW MODEL
Air flow was solved by means of the laminar steady incompressible Navier-Stokes equations:
∇•u=0 [2]

∂
∇ • ( ρu u i ) = − p + ∇ • (µ ∇u i ) [3]
∂xi

3
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International Conference on Engineering and Food

(a) (b)
Figure 6. Details of unstructured surface (a) and volume (b) mesh of the DE-CFD model
Turbulence will be taken into account at a later stage. Equation [2] is the incompressible continuity
equation and equation [3] states the conservation of momentum (ρui) in direction i (i = 1,2,3 for
Cartesian coordinates x, y and z). The velocity vector u [m s-1] consists of components ui, each of
which is the solution of a separate equation. In the above equations, p [Pa] is pressure, ρ [kg m-3] is
density and µ [kg m-1 s-1] the dynamic viscosity of air. The above equations [1-2] were subject to the
following boundary conditions. At the inlet opening and slots a constant normal velocity was defined.
At walls, a no-slip condition (zero tangential velocity) was implemented, at symmetry planes a zero
normal velocity was set and at the outlet plane and slots, the relative pressure was defined 0. Table 1
lists the values of the inlet boundary conditions, which were measured in an experimental study by Ho
(2003) and air properties.

Table 1: Inlet boundary conditions* and air properties

Inlet opening velocity [m s-1] 0.4/1.2° Air viscosity [kg m-1 s-1] 1.79×10-5
-1
Inlet slot velocity [m s ] 0.18/0.54° Air density [kg m-3] 1.29
(*) Based on the experiments of Ho (2003). Velocities at inlet openings and slots were uniform across all areas for all measured
flow rates.
3 -1 -2
(°) Two levels of air flow rate were investigated: 300/900 m h m . The study of Ho (2003) showed that the proportion of the
velocity at the opening to the velocity at the slots was always around 2.8, regardless of the supplied flow rate.

SOLUTION PROCEDURE
The equations [2-3] were solved on the geometry mesh by means of the solver CFX5.6 (Ansys Inc.,
Canonsburg, PA), using the finite volume method combined with a high resolution advection scheme
which balances second order accuracy with boundedness of the solution. CFX 5.6 uses a coupled
solver methodology to simultaneously solve for pressure and velocity, therefore removing the need for
a pressure-velocity coupling iteration, requiring only iterations for linearisation of the coefficients in the
discretised equations. The resulting set of linear equations was solved by an Algebraic Multigrid
method. The solution was monitored by means of the root mean square of the residuals, normalised
with respect to the average flux through the domain. Iterations were performed until the normalised
residuals were below 10-7, corresponding to machine accuracy in single precision. The CFD models
were run on a PC workstation with 2 PIII 933 MHz processors and 2Gb RAM memory. On a single
processor CPU time was 15 hours for a mesh size of 733,000 volume elements A speed-up of 1.5 was
achieved by using the two processors in parallel.

Results and discussions

Air flow pattern of the DE-CFD model

Flow fields are given in Figure 7. Figure 7 displays 2 simulations that demonstrate the effect of
different random stackings in the box. A high through-put of air is found in the head space of the box,
where there are no obstacles to the flow. More importantly, details of the flow, at low velocity, in the
vicinity of the products in the box can be calculated. As such, these simulations can be a basis for
heat and mass transfer calculations to individual particles in the box, requiring no further
approximations and empirical correlations as are required in continuum models for bulks [3]. Next,
stochastic Monte Carlo simulations are possible to account for the effects of variations in particle
dimension and stacking of particles to provide statistically meaningful predictions of temperature
profiles and cooling times.

4
ICEF9 – 2004
International Conference on Engineering and Food

y=
0 cm

y=
5 cm

y=
9 cm

y=
13.5 cm

DE simulation 1 DE simulation 2
Figure 7. Calculated velocity vector patterns [0 to 0.7 m s-1] in the EPS box with 35 spheres (65-75
mm diameter), in vertical cross sections aligned with the flow direction at different distances from the
middle plane of the box. On the figures, air flow is from left to right. The left and right figures are
respectively for different geometries resulting from the DE model random simulation. Flow rate = 300
m3 h-1m-2.

Comparison to measurement
It was seen in the measurements (Ho, 2003) as well as in the DE-CFD simulation that the velocity
profiles in the bulk do not change with flow rate for a particular configuration of the spheres. In Figure
8, the velocity profiles are given for a flow rate of 900 m3 h-1m-2 and for the sphere stacking on the right
hand side of Figure 7. Both in the measurement and the DE-CFD simulation it is difficult to recognise a
pattern in the velocity field inside the bulk, due to the complex flow field displayed in Figure 7. In
general, the velocity increases with height with maxima in the head space, and decreases with
distance from the middle plane of the box. The difference in the maximum magnitude of the velocity (in
the head space) between experiment and model is considerable, but is attributed to sharp gradients at
the interface of bulk and head space (and therefore difficult to capture exactly), in addition to the
uncertainty on the measured flow rate (+/- 30%) and differences in head space volume between
experiments and this particular random DE-CFD model. Furthermore, the velocity profiles for the left
hand side configuration in Figure 7 obviously differ considerable from the right hand side stacking
pattern. This illustrates the need for stochastic simulation of these kind of models, in order to obtain
statistically meaningful results. The same can be concluded for the experimental approach.

Conclusion
The combination of Discrete Elements and CFD provides a powerful tool to investigate flow patterns in
random bulks of particles. Meshing and convergence could be achieved for complex configurations.

5
ICEF9 – 2004
International Conference on Engineering and Food

Exp

DE-CFD

x = 1 cm x = 18.5 cm x = 30.5 cm

Figure 8. Comparison of measured and calculated velocity in the EPS box with 30-35 spheres (65-75
mm diameter), in different cross sections perpendicular to the flow direction, measured by x from the
inlet. The different vertical profiles in each plot are for different distances form the middle plane of the
box (indicated by y). The DE-CFD calculations are for the geometry in the right hand side of Figure 7.
The models will be used to improve the understanding of flow, heat and mass transfer in bulks of food
products in randomly filled containers. Stochastic simulation then becomes a necessity. Furthermore,
the following issues need to be addressed: mesh size sensitivity, buoyancy, turbulence modelling and
irregular food shapes. The former three aspects require larger computational resources, while the
latter requires a modification of the DE model for irregular shapes.

Acknowledgements
Pieter Verboven is Postdoctoral Researcher of the Flemish Fund for Scientific Research (F.W.O.-
Vlaanderen). The Research Council of the Catholic University of Leuven (project IDO 00/008) is
acknowledged for financial support. Acknowledgement is also extended to the Flemish Minister of
Small Enterprises, Traders and Agriculture for research project support.

References
1. van der Sman R. G. M. Prediction of air flow through a vented box by the Darcy-Forchheimer
equation, Journal of Food Engineering, 55, 49-57, 2002.
2. Alvarez G., Bournet P.-E., Flick D. Two-dimensional simulation of turbulent flow and transfer
through stacked spheres. International Journal of Heat and Mass Transfer, 46(13), 2459-2469, 2003.
3. Hoang M.L., Verboven P., Baelmans M., Nicolaï B.M. A continuum model for air flow, heat and
mass transfer in bulk of chicory roots, accepted in Transactions of the ASAE, 2003.
4. Ergun S. Fluid flow through packed columns, Chemical Engineering Progress, 48(2), 89, 1952.
5. Eisfeld B., Schnitzlein K. The influence of confining walls on the pressure drop in packed beds.
Chemical Engineering Science, 56, 4321-4329, 2001.
6. Ho Q.T. “Analysis of heat transfer during cooling of horticultural products in EPS boxes.” Master’s
Thesis, Faculty of Agricultural and Applied Biological Sciences, K.U.Leuven, Leuven, Belgium, 90p,
2003.
7. Tijskens E., Ramon H., De Baerdemaeker J. Discrete element modelling for process simulation in
agriculture, Journal of Sound and Vibration 266:493-514, 2003.
8. Van Zeebroeck, M.; Tijskens E.; Van Liedekerke, P.; Deli, V.; De Baerdemaeker J., Ramon H.
Determination of Dynamical Behaviour of Biological Materials during impact using a Pendulum Device.
Journal of Sound and Vibration 266:465-480, 2003.
9. Van Zeebroeck, M., Tijskens, E., Dintwa, E., Deli V., Loodts, J., De Baerdemaeker, J., Ramon, H.:
"Determination of the parameters of a tangential contact force model for viscoelastic materials (i.e.
fruits) using a rheometer device". Postharvest Biology and Technology, 2003 (In review).

6
ICEF9-2004
International Conference Engineering and Food

Measurement of velocity distributions of viscous fluids

using Positron Emission Particle Tracking

Bakalis Serafim*1, Cox P.W2. and Fryer P.J.2

1
School of Chemical Engineering, National Technical University of Athens, Greece.
Email: sbakalis@chemeng.ntua.gr
2 3
, Centre for Formulation Engineering, School of Engineering University of Birmingham,
E-mail: p.j.fryer@bham.ac.uk, p.w.cox@bham.ac.uk.

ABSTRACT
Positron Emission Particle Tracking (PEPT) is a novel technique that can be used to trace the path of a
radioactive particle within opaque fluids in pilot scale equipment. A barrel moving extruder was been
designed and manufactured to be used for PEPT measurements. Velocity distributions were estimated
from the measured tracer locations. Experimentally measured velocity distributions compared favourably
with velocities obtained from a three dimensional numerical simulation.

Keywords: velocity measurement, heat exchanger, PEPT.

INTRODUCTION
The growing number of industrial applications of twin-screw extrusion technology over the last decades
has led to an increasing interest in mathematical description of the extrusion process. Substantial effort
has been devoted to take the empirical knowledge of twin-extrusion process to deterministic quantitative
understanding through a combination of analytical and numerical techniques.

For simple situations of flow of Newtonian fluid under isothermal conditions in a wide and shallow screw
channel, the velocity profile and extruder characteristics can be obtained analytically (Harper, 1981). For
realistic materials and screw geometries the numerical solution of the governing mathematical equations
is usually obtained by discritization methods such as finite difference (Chiruvella et al., 1996), finite
element (Dhanasekharan and Kokini, 2003) or flow analysis network (Sebastian and Rakos 1992). Due to
the complicated geometry and complex material behaviour, the numerical procedures employed to
simulate a three-dimensional flow in the screw channels of a twin-screw extruder are computationally time
intensive. A few researchers have reported velocity measurements in extruders. Bakalis and Karwe
(2002) measured velocity distributions in the nip and translational regions of a twin screw extruder using
Laser Doppler Anemometry (LDA). Agemura et al., (1995) investigated the flow in a specially designed
model single screw extruder using Magnetic Resonance Imaging (MRI). LDA requires optical access to
the flow, limiting the possible applications to transparent materials. Although, using MRI, velocity
measurements can be performed in opaque materials, due to the nature of the tomographic techniques,
the experimental equipment can not contain metal. Bakalis and Fryer (2001) have used Positron Emission
Particle Tracking (PEPT) to measure velocity distributions and Bakalis et al., (2004) have detailed how the
method can be used. Although the method is cumbersome, because of the need to have the vessels
under study within the camera, it can be used to obtain velocity distributions in realistic heat transfer
conditions, i.e. for opaque fluids in metal equipment.

The objective of this study was to measure velocity distributions in a specially designed and manufactured
single screw extruder using PEPT. The experimentally measured velocity distributions will be used to
evaluate a numerical simulation.

MATERIALS AND METHODS

Positron Emission Particle Tracking
The School of Physics at Birmingham has developed a unique way of following flows in opaque fluids,
using Positron Emission Particle Tracking (PEPT). In this technique a tracer particle (600 µm in diameter

*
To whom all correspondence should be addressed
ICEF9-2004
International Conference Engineering and Food

or less) is passed through a system. The tracer has been treated so that it is radioactive, emitting
positrons which then generate a pair of back-to-back gamma rays on collision with an electron. A tracer
can be followed by detecting the gamma rays and triangulating their position. The radioisotope used (19F)
is chosen to have a half life of 2 hours, so that residual radioactivity is negligible after a few hours. The
technique can be used in pilot scale equipment as the gamma rays can penetrate reasonable thicknesses
of metal (up to 10 cm).

Experimental equipment
A schematic representation of the channel is shown in Fig. 1. The geometry consists of a stationary
square channel and a rotating barrel. The aspect ratio W/H, where W is the width and H the height of the
channel, is 10:1, while the width of the channel is 100 mm. The aspect ratio of the channel was such that
the end effects from the screw flights would not be significant. Fluid could be circulated on the outer
surface to provide the means for heat transfer. The geometry described in Fig. 1 is similar to an unravelled
channel in the barrel moving formulation that is quite often used in simplifying extrusion processes. This
channel was built in a cylinder having a diameter D of 0.2 m. The diameter of the cylinder was selected to
ensure that the geometry of the channel would remain square.

The aim of the experiment was to study well developed flows and thus had to be such to allow a
reasonable residence time. The ratio of the axial length L of the equipment, to the diameter of the screw
was selected to be 10, resulting in a 2 m long heat exchanger. Although several values of the screw pitch
were considered, a straight channel (pitch equal to zero) was manufactured. The mechanism of transport
is different compared to an extruder. In the screw channels of an extruder pressure is generated as a
result of the pitch angle. In the current design, there is a pressure drop rather than a pressure rise inside
the equipment. Therefore, a gear pump had to be used to provide the necessary pressure for the material
to flow. In a latter stage screws varying in their pitch angle will be manufactured.

Channel
Output
Circulating flu id Input
Moving
V
barrel 0.220mm GAP

10 mm
Stationary
screw 100 mm
Stationary
rotor

Fig. 1 schem atic representation of the channel Fig. 2 Final design of the equipment
The design required some ingenuity in order to measure temperature and pressure. In typical extruders,
where the barrel is stationary, temperature and pressure measurements can be done through the barrel.
In this case though temperature and pressure devices had to be installed in the screw, which is stationary.
In Fig. 2 a schematic representation of the pilot scale heat exchanger is shown. The screw (stator) was
held constant while a motor was used to rotate the barrel (rotor). A series of bearings were used to allow
the relative motion of the rotor to the stator. Gaskets were used to prevent leakage of the fluid from the rig.
Heating medium can be circulated outside the barrel. Fins were added to the, rotating, barrel allowing
circulation of the heating medium to provide a uniform temperature along the barrel. Another issue was
selection of the material for construction. Although stainless steel would be the first material of choice, the
estimated final weight of the equipment obliged us to use aluminium. Furthermore, aluminium has a lower
density than stainless steel, less obstructive to the passage of gamma rays, resulting in the measurement
of more accurate velocity distributions. Although in this work the heat exchanger was used for isothermal
flows of Newtonian fluids, in the future flows involving heat transfer will be considered. Thus, a motor
having 100 hp that would provide the necessary torque in non-isothermal flows was selected. A frame was
designed to allow PEPT measurements and easy transport and set up of the equipment was designed
and manufactured.
ICEF9-2003
International Conference Engineering and Food

Positron Emission Particle Tracking

Radionuclides which decay by the emission of a positron (a positive electron) make useful tracers since
the positron rapidly annihilates with an electron, producing a pair of 511 keV γ-rays which are emitted
almost exactly 'back-to-back'. Coincident detection of these two γ-rays by a pair of detectors defines a
line passing close to the point of emission; detection of a number of events makes it possible to identify
the point of origin of the signal. This is the basis of the imaging technique of Positron Emission Particle
Tracking (PEPT). Details of the method can be found in Parker et al., 1999.

Experimental set-up
Since the radioactive particle has to remain in the system in order to measure the velocity distributions, a
simple closed loop system had to be used. The schematic representation of the experimental set up is
shown in Figure 3 (a). In fig. 3 (b) a picture of the experimental set up is shown.

A gear pump that minimized damage of the particles was used. The volume of the fluid was relatively high
when compared to the flow rate, resulting in a circulation time for the particle of approximately 3 min. To
decrease the time of the experiment up to 12 particles were introduced to the system so that one was
always in the field of the camera.

y
PEPT camera
z x Reservoir
Pump y
z
x

(a)
(b)
Fig. 3 Experimental set up
Materials
A shear thinning fluid with well defined rheological properties was used. More specifically a 1% aqueous
CMC solution. k = 8.5, n = 0.55 was selected. The rheological properties of the solution were measured
using a cone and plate geometry in a Bohlin rheometer.

Results and Discussion

Particle paths
In Fig. 4 (a) typical particle
paths for two tracers for a
rotating channel are shown. The
colour represents the time at
which tracer locations were
obtained. Thus, different colours
correspond to different tracer
passes. As i expected the
rotation of the barrel resulted in
a circular motion of the tracer.
While tracer travels along the
axial, z, direction the x position
changes dramatically. In fig 4
(b) the motion of the same
tracers is shown in three
Fig. 4 Typical particle paths dimensions. One can see that
ICEF9-2004
International Conference Engineering and Food

the motion of the tracers is three dimensional. Velocity distributions were estimated from the tracer
locations as described in Bakalis and Fryer (2001). The velocity values were constant along the axial
direction indicating that the flow field was fully developed. In Fig 5 typical velocity profiles are shown for
different levels of flow rate. In Fig. 5 (a) the Ux velocity distribution is shown along the height of the
channel. One has to keep in mind that the only non zero velocity component of the barrel is Ux. For the
experiments shown in Fig 5 the barrel resulted in a Ux = 0.1 m/s. Close to the barrel, i.e. at y = 0.01 m, the
experimentally measured velocity distribution is within 2% from the velocity distribution of the barrel.
Velocity distributions close to barrel appeared to be quite scattered when compared to the remaining data.
A possible explanation of this phenomena is scattering of gamma rays in the rotating barrel. As it was
expected the velocity values close to the stationary screw root, i.e. at y = -0.004 m, is zero. There is no net
H
flow of material across the y axis. Therefore integral given the flowrate across the y axis ∫ Uxdy should be
0
equal to zero. The estimated value of the previous integral (8.5E-6) can be considered to be equal to zero.
In Fig 5 (b) the Uz velocity distribution is shown across the y axis. As it was expected higher flow rate
result in higher Uz values. The flow rate Q is equal to the integral of Uz across the cross section of the

∫
channel, Q = UzdA . Due to the relatively high aspect ratio of the channel the end effect of the flights
A
can be neglected. Thus an estimation of the flowrate can be obtained from the following equation:
H
Q = W ∫ Uzdy . The previous relation results for both cases in an error of 5%, which is smaller than the
0
error associated with the measurement of flow rate. In Fig 5 (c) Uy velocity component is shown along the
x axis. Although close to the stationary channel the velocity values should be equal to zero, it was not
possible to obtain velocity values close to the boundaries. Bakalis and Fryer (2001) reported that it was
not possible to measure velocity distributions close to stationary boundaries. Thus, this represents a
limitation of the method.

0.008
0.008

0.004
y (m)

0.004
y (m)

0.000 0.000
7E-5 m3/s 3
7E-5 m /s
3.47E-5 m3/s 3.47E-5 m3/s
-0.004 -0.004
-0.04 0.00 0.04 0.08 0.12 0.00 0.04 0.08 0.12
Ux (m/s) Uy (m/s)

(a) (b)
0.015 y
0.010
7E-5 m3/s
3.47E-5 m3/s
y
x
0.005
z
Uy (m/s)

0.000
z
-0.005 x
-0.010

-0.015
-0.08 -0.04 0.00 0.04 0.08
x (m)

(c)

Fig 5 velocity profiles for a 1% cmc solution (shear thinning) for two
level s of flowrate
ICEF9-2004
International Conference Engineering and Food

A commercial fluid dynamics software (FEMLAB) was used to simulate the flow field. In Fig 6 a
comparison between experimentally measured and numerically predicted velocity distributions is shown.
One can see that numerically predicted velocity distributions compare favourably with the experimentally
measured values.

0.012 0.012

0.008 0.008

y (m)
y (m)

0.004 0.004

experimental
0.000 0.000
simulation
y experimental
simulation

-0.04 0.00 0.04 0.08 0.12 0.00 0.04 0.08 0.12

Ux (m/s) Uz (m/s)
z
x

Fig. 6 Compari son of experimentally predicted and numerically

obtained velocity di stributions.
CONCLUSIONS
A specially designed and manufactured heat exchanger was used to measure velocity distributions
using PEPT. The heat exchanger is similar to a singe screw extruder and will be used to measure
velocities in complicated flow situations. Experimentally obtained velocity distributions appeared to agree
with boundary conditions. Velocity distributions obtained from a numerical simulation simulation agreed
favourably with the experimentally measured values.

ACKNOWLEDGEMENTS
This research was funded by Unilever Research Colworth.

REFERENCES

1. Agemura, C.K., Kauten, R.J. and McCarthy K.L. “Flow fields in straight and tapered screw
extrudes using Magnetic Resonance Imaging.” Journal of Food Engineering, 25, 55-72, 1995.

2. Bakalis S, Parker DJ and Fryer P.J. “Measuring velocity distributions of viscous fluids using
PEPT.” AIChEJ, In print.

3. Bakalis S, Fryer P.J. “Measurement of velocity distributions of viscous fluids using Positron
Emitting Particle Tracking.” 6th Congress of Chemical Engineering, Melbourne, 2001.

4. Bakalis S. and Karwe M.V. “Velocity distributions and volume flow rates in the nip and
translational regions of a co-rotating, self-wiping, twin-screw extruder” Journal of Food
Engineering, 5, 4, 273-282, 2002.

5. Chiruvella, R.V., Jaluria Y., Karwe M.V. and Sernas, V. ”Transport in a twin-screw extruder for the
processing of polymers.” Polymer Engineer Science, 36: 1531-1540, 1996.
ICEF9-2004
International Conference Engineering and Food

6. Dhanasekharan K.M. and Kokini J.L. “Design and scaling of wheat dough extrusion by numerical
simulation of flow and heat transfer.” Journal of Food Engineering, 60,4 421-430.
7. Harper J.M. “Extrusion of foods.” Ed. CRC Press, Boca Raton Fla, 180p, 1981.

8. Sebastian, D.H. and R. Rakos, "Simulation of Transport phenomena for kneading elements in
twin-screw extruders," In: Food Extrusion Science and Technology by J.L. Kokini, C.-T. Ho & M.V.
Karwe (Eds), Marcel Dekker, New York, 105p, 1992.
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International Conference Engineering and Food

PREDICTION OF OPTIMAL HEAT TRANSFER FROM SLOT AIR JETS IMPINGING ON

CYLINDRICAL FOOD PRODUCTS USING CFD.

Olsson E.E.M.1, Ahrné L.M.2, Trägårdh A.C.3

1
SIK – The Swedish Institute for Food and Biotechnology, P.O. Box 5401,
SE-402 29 Göteborg, Sweden, eva.olsson@sik.se
2
SIK – The Swedish Institute for Food and Biotechnology, P.O. Box 5401,
SE-402 29 Göteborg, Sweden, lilia.ahrne@sik.se
3
Dept. of Food Technology, Engineering and Nutrition, Lund University,
P.O. Box 124, SE-221 00 Lund, Sweden, christian.tragardh@livstek.lth.se

Abstract

The distribution of heat transfer around cylindrical food products placed on different surfaces using
impinging slot air jets (Re=23,000-100,000) has been determined using CFD. A single jet, multiple jets
and double impingement (jets from both above and below) are considered. The objective was to find
the optimal jet configuration for maximum heat transfer using the same mass flow per cylinder. Two
jets from above, impinging on a cylinder placed on a solid surface, gave the highest rate of heat
transfer.

Keywords

Heat transfer, Impingement, Cylinder, CFD, SST

Introduction

Impinging jets are widely used to increase mass and heat transfer in different applications. In the food
industry, impingement can be used for heating, baking, drying, cooling and freezing. Ovadia and
Walker (1) have reviewed the use of impingement in food applications.

Numerous numerical and experimental studies of impinging jets are found in the literature. Reviews
have been made by Jambunathan et al. (2) and Downs and James (3), among others. The use of
computational fluid dynamics (CFD) increases and is often used as a tool to predict flow and heat
transfer. Scott and Richardson (4) and Xia and Sun (5) have reviewed the use of CFD in the food
area.

The objectives of this study are: (1) to determine the heat transfer distribution around cylinders under
different jet configurations and (2) optimise the number of jets that creates the highest heat transfer
rate, using the same total mass flow per cylinder. A single jet, multiple jets and double impingement
(jets from both above and below) are considered. In the case of single and multiple jets the cylinders
are placed on a solid (non-perforated) surface, while in the case of double impingement, different
kinds of surfaces are investigated (none, two rectangular bars or a frame of several rectangular bars).

Numerical method

Steady state simulations in two dimensions of slot air jets impinging on a cylindrical food product in a
semi-confined domain have been performed using the k-ω based SST model in CFX 5.5. The
distribution of heat transfer (local Nusselt numbers) around the cylinders has been determined for
various numbers of jets, for a Reynolds number based on the jet width (d) in the range of 23,000-
100,000.
 ICEF9 – 2003
International Conference Engineering and Food

The computational domain is different depending on the jet

configuration, but the basic design and boundary conditions Wall
O/d
are seen in Fig. 1. The walls are assumed to be adiabatic, the
L/d
pressure in the domain is 0.1 MPa, the temperature of the d/2 d
Inlets
inflow is 2°C and the surface temperature of the food product

Symmetry plane
Opening
is 35°C. The diameter of the cylinder is 35 mm, the width of
H/d
the jets is 30 mm and the jet-to-cylinder distance (H/d) is 4.

In double impingement, a jet from above and a jet from below

Solid foods Solid surface or
impinge on a cylinder. For comparison reasons, the same total D
rectangular bars
amount of mass flow per cylinder is used. The rate of mass
flow is only dependent on the velocity (the jet width is
constant). In case of double impingement, two jets are
impinging on one cylinder, meaning that each jet has half the
velocity as one jet impinging on one cylinder has. The total
amount of air flow is then kept constant. (The Reynolds
number for the jets is halved.)

In the case of double impingement the cylinder is placed on

either two rectangular bars (3x3 mm) parallel to the cylinder or
on a frame of several rectangular bars and this is compared to
no surface. For a frame of several bars different mass flow Fig. 1. The computational
distributions are simulated. These are: 50% from both above domain(s).
and below, 60% from above, 40% from below and 70% and
30% from above and below respectively.

The mesh consists of tetrahedral control volumes with 25 layers of cumulative prisms near the cylinder
surface. The simulations have been made on a Compaq Pentium III 800 MHz with 384 MB RAM and a
Sun Ultra 10 workstation with 512 MB RAM.

The governing equations

Equations that describe the airflow and the heat transfer from the impinging jets to the cylindrical food
products are the continuity equation, the Navier-Stokes equations and a temperature equation, all
averaged and the turbulent quantities are solved using Boussinesq assumption and a two-equation
approach:

∂U j
=0 (1)
∂x j
∂( U iU j )  ∂U ∂U j 
ρ
∂U i
∂t
+ρ
∂x j
=−
∂P
+
∂xi ∂x j
∂
( )
τ ij + τ ijturb ; τ ij = µ  i +
 ∂x ∂ x
; τ ijturb = − ρ u i′u ′j

(2)
 j i 
∂( U j T ) µ
ρc p
∂T
∂t
+ ρc p
∂x j
=
∂
∂x j
(
q j + q turb
j )
; qj =
c p ∂
Pr ∂x j
T
; q turb
j = − ρc p u ′j T ′ (3)

The SST turbulence model

The shear stress transport (SST) model of Menter (6) with a low-Reynolds approach has been used
for all simulations. The SST model is a two-equation model which blends between a k-ω model near
the surface and a k-ε model outside the boundary layer. The definition of eddy viscosity is also
modified to account for the transport of turbulent shear stress.

A comparison of measurement of heat transfer around a cylinder from the literature and simulations
with two-equation models in CFX 5.5 showed that the SST model was the best two-equation model
(Olsson et al. (7)).
 ICEF9 – 2003
International Conference Engineering and Food

Fig. 2. Streamlines of the velocity, Re=50000. a) A single jet and a single cylinder. b) Two jets and two
cylinders (L/d=2). c) Three jets and three cylinders (L/d=2). Adapted from Olsson et al. (7,8).

Results and discussion

Flow characteristics

The airflow from one, two and three jets impinging on the same number of cylinders can be seen in
Fig. 2. The computational domain has a symmetry plane in the centre of the jet. The airflow from a
single jet is described in Olsson et al. (7) and two and three jets in Olsson et al. (8). The flow pattern
for double impingement (two jets, one cylinder) can be seen in Fig. 3. In Fig. 3a the mass flow rate is
50% (of the total mass flow) from above and 50% from below and in Fig. 3b the mass flow is 60% and
40% respectively.

The rectangular bars, which the cylinder

is placed on, do not interfere much with
the large flow pattern. The flow is
disturbed only on a local scale close to
the bars. With the same mass flow from
above as from below, the jets impinge on
the top and bottom respectively of the
cylinder. Most of the flow becomes a jet,
parallel to the bars, which merge with the
flow from the other jet and exits the
domain in the centre of the opening.
When the same amount of air flow is
used in both directions, the flow from the
jets is balanced. The separation occurs at
a smaller angle (θ=50-60°) as compared
to a single jet impinging on a cylinder
placed on a solid surface.

When larger amount of air from above

than from below is used, the recirculation
zones in the upper and lower part of the
domain are both moved downwards, the
upper one slightly to the left, and the
lower one to the right due to change of
airflow. The separation point on the upper
part occurs at a larger angle than before
and less amount of air strike the lower
part of cylinder. Fig. 3. Streamlines of the velocity. a) Airflow 50% from
both above and below. b) Airflow 60% from above and
40% from below.
 ICEF9 – 2003
International Conference Engineering and Food

350 350
1jet
1 jet
2 jets 300 300 2 jets
centre jet (o f 3 jets)
3 jets, cyl 1
o uter jets (o f 3 jets) 250 250 3 jets, cyl 2
do uble imp. (50:50) double imp.
200 200
Nu

Num
150 150

100 100

50 50

0 0
-180 -135 -90 -45 0 45 90 135 180 0 20000 40000 60000 80000 100000
θ Re
Fig. 4. Local heat transfer around the cylinder for Fig. 5. Comparison of average Nusselt
a single jet, two jets (L/d=2) and three jets (L/d=2), numbers on the cylinders for a single jet,
Re=50,000. Partly adapted from Olsson et al. (7,8). two and three jets and double impinge-
ment. Partly adapted from Olsson et al. (8).

Heat transfer

Single and multiple jets on solid surface

The distribution of heat transfer around a cylinder under a single impinging jet has been investigated in
Olsson et al. (7). It was found that the average Nusselt number and stagnation point Nusselt number
increases with higher Reynolds numbers and surface curvature (d/D), but have a low dependency on
the jet-to-cylinder distance (H/d). Reynolds numbers in the range of 23,000-100,000, d/D of 0.29-1.14
and H/d of 2-8 were investigated.

The interaction of two and three jets impinging on circular cylinders with the same total mass flow per
cylinder as for a single jet has been studied in Olsson et al. (8). The heat transfer for two jets and the
outer cylinders in three jets was highest for a distance of two jet widths (L/d=2) between the jets (lower
heat transfer was found for smaller and larger distances), but for the centre jet of the three jets, the
heat transfer was increased with larger distances. It was concluded that the heat transfer distribution
and the average heat transfer are dependent on the jet configuration. In Fig. 4 the distribution of heat
transfer around cylinders impinged by one, two and three jets are compared (for two and three jets
L/d=2). The interaction between two jets is most beneficial. The average heat transfer is higher than
for a single jet. For three jets the centre cylinder has about the same heat transfer as a single jet
(increased in the stagnation point), but on the outer cylinders the heat transfer is lower and the
distribution around the cylinders is different. This is further discussed in Olsson et al. (8). The average
heat transfer of the different jet configurations is shown in Fig. 5.

Double impingement

In double jet impingement one jet from above and one jet from below impinge on a cylinder. For
comparison, the same total mass flow of air per cylinder is used, i.e. the velocity is halved. To support
the cylinder, two different cases were considered; two rectangular bars or a frame of several
rectangular bars, parallel to the cylinder. These cases were compared to a cylinder without any
support (floating in the air). The result for Re=23,000 is seen in Fig. 6. If no plate is used the heat
transfer on upper and lower part of the cylinder is symmetric. The heat transfer is high in the
stagnation point, decreasing to the separation point (θ=50-60°) and increasing to θ ≈90° where the jet
from above and below is met, see Fig. 6. When the cylinder is placed on two bars the heat transfer is
very low next to the supporting bars and the distribution of heat transfer is adjusted. For a cylinder
placed on the frame of several bars, the other bars in the domain (that don’t support the cylinder), do
not influence the heat transfer on the cylinder to a great extent. The streamlines in Fig. 3 show that the
flow field in the domain is only slightly disturbed by the bars.
 ICEF9 – 2003
International Conference Engineering and Food

350 350
tw o bars Re=23000
300 300
no surface Re=50000
250 frame of several bars 250

200 200
Nu

Nu
150 150

100 100

50 50

0 0
0 45 90 135 180 0 45 90 135 180
θ θ

Fig. 6. Heat transfer distribution around the Fig. 7. Local heat transfer around the cylinder
cylinder placed on different surfaces in double placed on a net of rectangular bars in double
impingement. Note: Re=23,000. impingement for two Reynolds numbers
(23,000 and 50,000).

The heat transfer increases with higher Reynolds numbers. Results from two Reynolds numbers
(23,000 and 50,000) can be seen in Fig. 7. The separation point on the upper part of the cylinder
occurs at a smaller angle as compared to a single jet with flow from only above, because of the jet
from below. The bars supporting the cylinder disturb the local heat transfer and decrease the average
heat transfer, see Table 1.

The distribution of mass flow from the jets was further investigated. The original situation with 50% of
the mass flow from above and 50% from below was compared to 60/40% and 70/30%. The resulting
heat transfer distribution is seen in Fig. 8. More airflow from above impinging on top of the cylinder
results in higher local Nusselt numbers on the upper part of the cylinder and the opposite for the lower
part of the cylinder. The result is verified by the streamlines of the velocity shown before.

The Nusselt number distribution on the cylinder and the average Nusselt number of the double
impingement situation of a cylinder placed on a frame of several bars and 50/50% situation is
compared to one, two and three jets in Fig. 4 and 5 respectively, where it is shown that the double
impingement situation has the lowest rate of heat transfer. The average Nusselt numbers of the other
cases can be seen in Table 1. The average heat transfer for the different cylinder support situations is

350
50:50
300
60:40
250 Re Nu (average)
70:30 No plate 23000 67.4
200 Two bars ‘’ 59.1
Net ‘’ 58.9
Nu

150
Re Nu (average)
100
50:50 50000 98.8
50 60:40 ‘’ 98.3
70:30 ‘’ 104.8
0
0 45 90 135 180
θ

Fig. 8. Local heat transfer around the cylinder Table 1. Average Nusselt numbers of the
placed on a frame of several rectangular bars different jet configurations.
and different velocity configuration (in double
impingement), Re=50,000.
 ICEF9 – 2003
International Conference Engineering and Food

the same. The average Nusselt number for Re=50,000 and 50/50% mass flow is the same as for
60/40% situation, while the average Nusselt number is slightly higher for the 70/30% situation and the
heat transfer is more evenly distributed. The effect of uneven heat transfer was also discussed in
Olsson et al. (8).

Conclusions

An air jet impinging on a cylinder creates high but unevenly distributed heat transfer around the
cylinder. Different configurations of multiple jets, using the same total mass flow, result in different
collaboration between the jets. In Olsson et al. (8), it was found that the distance and opening between
the jets where of great significance and that two jets impinging on two cylinders results in highest heat
transfer rates.

In this study it was concluded that the rectangular bars supporting the cylinder in double impingement
affect and reduce the local heat transfer on the cylinder. For maximum heat transfer to the cylinder,
these bars should be placed where it is already low heat transfer, i.e. in the separation point on the
lower part of the cylinder (θ ≈125-130°). A frame of several parallel rectangular bars does not
significantly affect the heat transfer as compared to only two bars. Different mass flow from above and
below, changes the local heat transfer on the cylinder, higher rates are found on the top of the cylinder
and lower on the bottom, creating slightly increased average heat transfer.

In comparison to single and multiple jets impinging on a cylinder placed on a solid non-perforated
surface, the double impingement situation is not successful. The highest heat transfer is still found for
the case with two jets a distance of two jet widths apart. The advantage with double impingement is
however that the power required to create high velocity could be reduced since the mass flow is
divided in above and below. In conclusion, the number and interaction of the jets involved, strongly
influence the amount and distribution of heat transfer around the cylinders and should be considered
when predicting optimal heat transfer to the food product.

Acknowledgements

This project was financed by the Swedish Knowledge Foundation (KK-stiftelsen) and Ircon AB in
Vänersborg, Sweden.

References

1. Ovadia, D.Z., Walker, C.E. (1998). Impingement in food processing. Food Technology, 52(4), 46-
50.

2. Jambunathan, K., Lai, E., Moss, M.A., Button, B.L. (1992). A review of heat transfer data for single
circular jet impingement. International Journal of Heat and Fluid Flow, 13(2), 106-115.

3. Downs, S.J., James, E.H. (1987). Jet impingement heat transfer - a literature survey. American
Society of Mechanical Engineers (Paper), 87-HT-35, 1-11.

4. Scott, G., Richardson, P. (1997). The application of computational fluid dynamics in the food
industry. Trends in Food Science and Technology, April (vol 8), 119-124.

5. Xia, B., Sun, D.-W. (2002). Applications of computational fluid dynamics (CFD) in the food industry:
A review. Computers and Electronics in Agriculture, 34, 5-24.

6. Menter, F.R. (1994). Two-equation eddy-viscosity turbulence models for engineering applications.
AIAA Journal, 32(8), 1598-1604

7. Olsson E.E.M., Ahrné L.M., Trägårdh A.C. Heat transfer from a slot jet impinging on a circular
cylinder. Accepted for publication in Journal of Food Engineering

8. Olsson E.E.M., Ahrné L.M., Trägårdh A.C. Flow and heat transfer from multiple slot jets impinging
on circular cylinders. Submitted for publication.
ICEF9 – 2004
International Conference Engineering and Food

Numerical studies of heat transfer with shear thinning fluids in scraped-surface heat exchangers

D. L. Pyle (1), K.-H. Sun (2), N. Hall-Taylor (3), A. D. Fitt (4), C. P. Please (5), M. J. Baines (6)

(1) School of Food Biosciences, University of Reading, RG6 6AP, UK

d.l.pyle@reading.ac.uk
(2) School of Food Biosciences, University of Reading, RG6 6AP, UK
k.sun@reading.ac.uk
(3) Chemtech International Ltd, Reading, RG2 0LP, UK
nick@chemtechinternational.com
(4) School of Mathematics, University of Southampton, SO17 1BJ, UK
adf@maths.soton.ac.uk
(5) School of Mathematics, University of Southampton, SO17 1BJ, UK
cpp@maths.soton.ac.uk
(6) Department of Mathematics, University of Reading, RG6 6AP, UK
m.j.baines@reading.ac.uk
_______________________________
Abstract
Heat transfer in scraped-surface heat exchangers (SSHEs) is studied using Finite Element numerical
methods for a hydrodynamic fully developed flow. The fluid is assumed to be non-Newtonian,
specifically shear thinning. The results show the shear thinning index and thermal boundary conditions
affect the axial local and overall heat transfer. Matters concerning scale-up problems and ideas for
improving overall heat transfer performance are also discussed.
Key-words: CFD, Heat Transfer, Power Law, Viscous Dissipation.

Introduction
Scraped-surface heat exchangers (SSHEs) are a type of multifunctional food processing component.
They are widely used for continuously sterilizing, cooling and texturing of highly viscous food materials
such as margarine, peanut butter, salad dressing, jam, thick soups and ice-cream. Most such
foodstuffs are non-Newtonian and their viscosity is highly temperature dependent. In a typical SSHE,
the outer cylinder is jacketed (for heating or cooling) and blades are attached to the rotating shaft
(inner cylinder). As the food material is pumped through the annular gap, the blades (scrapers)
periodically remove material from the heat transfer surface to prevent fouling and increase mixing.
SSHEs can therefore be used to provide the controlled (high-temperature-short-time) heat transfer
that is routinely required for structuring delicate materials. A detailed understanding of SSHE operation
is crucial as both the nutritional content and textural attractiveness of the final products depend
critically on the mechanical and thermal histories of the material during processing. The food industry
is therefore extremely interested in improving understanding of SSHEs to maximise productivity,
improve product quality, whilst minimising energy consumption and improving food product novelty.

Owing to the complex geometry and typical internal environment in an SSHE, experimental studies
have mainly been limited to quantifying global effects or integral values, such as energy input,
residence time distribution and overall heat transfer performance [1]. Since an appreciation of the local
flow behaviour is crucial for understanding the combined mechanical and thermal properties of an
SSHE, extensive experimental efforts have been undertaken to study flow in model SSHE systems in
the absence of heat transfer [2, 3, 4]. Numerical and analytical studies have also been carried out with
non-Newtonian fluids for isothermal problems relevant to SSHEs [5, 6]. A 3D non-isothermal numerical
study [7] determined the flow of a Newtonian fluid in an SSHE, predicting the velocity, temperature
distribution and Nusselt number. Numerical studies of flow and heat transfer problems have also been
studied [8, 9, 10] for a range of 2D and quasi-3D sub-problems in simplified SSHE geometries with
power law fluids. A valuable modelling approach has been to develop models of sub- or paradigm
problems of direct relevance to SSHE design and operation. The results demonstrate how the blade
mounting sites and the blade hole details affect the flow, mixing and local stagnation zones. The
results also show the effects of fluid shear- and heat-thinning on the size of the local viscous
dissipation. In particular, it is clear that in high shear regions the local viscous heating is much smaller
and heat thinning effects are thus reduced for shear thinning fluids compared to Newtonian fluids.

In this study, we examine the effects of axial flow on the flow and heat transfer for a fully developed
(large Prandtl number) power law fluid hydrodynamic flow. The results show the effects of the shear

1
ICEF9 – 2004
International Conference Engineering and Food

thinning index and thermal boundary conditions on both local axial and overall heat transfer. Scale-up
problems and possibilities for improving overall heat transfer performance are also discussed.

Differential equations and numerical procedure

In a typical SSHE, the outer cylinder of radius R, say, is stationary. The blades are attached to an
inner cylinder (radius L) that rotates at a constant speed U. We consider SSHE flow in a rectangular
coordinate system with the frame of reference fixed in the inner cylinder i.e. rotating at constant
angular velocity ω=U/L. The x- and y-axes are in the plane of the tangential flow and the z-axis is in
the direction of the axial flow. A schematic view of a cross section at an x-y plane, the blade mounting
positions and the coordinate system is given in Fig. 1, which shows the outer cylinder rotating in a
clockwise direction. In the configuration considered here, the radius ratio is RR=1.5 and four blades
(without leakage) are evenly spaced around the cylinder circumference and mounted tangentially to
the inner cylinder.

If the physical properties of the fluids (density, viscosity, specific heat, thermal conductivity etc.) are
assumed independent of temperature and there is no phase change during device operation, then the
velocity de-couples from the temperature. Owing to the high viscosity of typical SSHE fluids the
Prandtl number is very large (>1000). Thermal boundary layers are therefore much thinner than
velocity boundary layers. We assume that the velocity profile is fully developed before the fluid enters
the heating zone. Thus the velocity does not change with either axial location or the thermal boundary
conditions and may be determined first. The temperature is then determined separately using the
known velocity field.

Flow equations and boundary conditions

We consider isothermal, laminar, steady flow of an incompressible viscous fluid. It is reasonable to
assume that all the velocity components are functions of x and y only, and, from the w momentum
equation, the axial pressure gradient is therefore also independent of z. The flow field is the same at
any cross section in x-y plane. The velocity scales are the inner cylinder velocity U for the tangential
velocity components u and v, and the average axial velocity W for the axial velocity component w. The
scales for length and pressure are the inner cylinder radius L and µ F U L , respectively. The

( )
1
characteristic viscosity µ F is the viscosity given at a shear rate γ& = (U / L ) + (W / L ) 2 . Neglecting
2 2

Coriolis forces, at any cross section in the x-y plane the non-dimensional governing equations are

∂u * ∂v *
+ =0 (1)
∂x * ∂y *
 ∂u * ∂u *  ∂p * ∂ µ ∂u * ∂ µ ∂u *
ReU  u * * + v * *  = − * + * ( ) + ( ) (2)
 ∂x ∂y  ∂x ∂x µ F ∂x * ∂y * µ F ∂y *
 * ∂v * * ∂v 
*
∂p * ∂ µ ∂v * ∂ µ ∂v *
Re U  u +v =− * + *( )+ * ( ) (3)
 ∂x
*
∂y *  ∂y ∂x µ F ∂x * ∂y µ F ∂y *
 ∂w * ∂w *  ∂ µ ∂w * ∂ µ ∂w *
ReU  u * * + v * *  = fReW + * ( ) + ( ) (4)
 ∂x ∂y  ∂x µ F ∂x * ∂y * µ F ∂y *

where * denotes a non-dimensional variable, Re U = ρUL / µ F is the tangential Reynolds number,

ρWL is the axial flow Reynolds number, or a non-dimensional axial volume flux, and − pz L
ReW = f =
µF ρW 2
is the non-dimensional axial pressure gradient or friction factor. The frictional pressure gradient is
− p z L ρWL − p Z L2
defined as f ⋅ ReW = . = .
ρW 2 µ F µ FW

2
ICEF9 – 2004
International Conference Engineering and Food

W ReW
The velocity ratio or Reynolds number ratio is α= = . Since during industrial SSHE
U ReU
applications the tangential flow dominates, values of the velocity ratio are selected to be less than 0.2.

The boundary conditions in the plane of the tangential flow are

(At the outer cylinder) u = RR cos θ , v = RR sin θ , w = 0 .
* * *
(5)
(At the inner cylinder and blades) u = v = w = 0.
* * *
(6)

A generalized shear thinning power law viscosity µ = c m I 2 ( m −1) / 2 is used. Here cm is the consistency
index (Pa-sm), which varies with the material. The shear-thinning index m also varies with the material.
A typical value of m for food materials such as fruit jam, peanut butter etc. is 0.33. Newtonian fluids
are also considered in this text for completeness. I2 is the second invariant of the shear rate tensor.
( m −1) / 2
 2 2

Non-dimensionalized by the characteristic viscosity µ F = c m   U  +  W   the final form of the
 L   L  
 
viscosity is
( m −1) / 2
µ  I 2 
*

= + c  + c2
µ F  (1 + α 2 )
(7)
1 

 ∂u * 2 ∂v * 2 ∂u * ∂v * 2 2 ∂w
*
2 ∂w
*

=  2( * ) + 2( * ) + ( * + * ) + α ( * ) + α ( * ) 2  .
* 2
where I2
 ∂x ∂y ∂y ∂x ∂x ∂y 
The constants c1 and c2 are included to ensure that the viscosity has a nonzero finite value in the
whole domain. Values of c1=0.000001 and c2=0.0001 were selected; numerical experiments show that
this modification has an insignificant effect on the bulk viscosity whist giving physically reasonable
viscosity values.

Energy equation and thermal boundary conditions

We assume that the entering stream has a uniform temperature Tin and the temperature of the outer
cylinder is maintained at a constant temperature Tw, the other walls are adiabatic and the axial
(T − Tin )
conduction term may be neglected. The non-dimensional temperature is T
*
= where the
∆T
temperature difference is defined as ∆T = Tin − Tw . (The absolute value is used so that the
Brinkman number is positive for both cooling and heating.) The energy equation is
∂T * * ∂T
*
* ∂T
*
∂ 2T * ∂ 2T * µ
PeU (u *
+v ) + PeW w = + + Br ( ) I 2* (8)
∂x *
∂y *
∂z *
∂x * 2
∂y * 2
µF
where PeU=Pr*ReU and PeW=Pr*ReW are the Peclet numbers corresponding to the tangential and axial
cpµF µ FU 2
flows, respectively. The Prandtl number is Pr = and the Brinkman number is Br = .
k k∆T
The thermal boundary conditions in the plane of the tangential flow are
*
(At the outer cylinder): Isothermal, Tw = ±1, heating / cooling . (9)
dT *
(At the inner cylinder and the blades): Adiabatic, = 0. (10)
dn *
*
The initial temperature at the inlet z*=0 is assumed to be Tin = 0 . (11)

At a given axial location, the heat transfer between the outer cylinder and the fluid is characterised by
the wall heat flux and bulk-mean temperature. The axial local wall heat flux at a location z is defined

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ICEF9 – 2004
International Conference Engineering and Food

∂T
as q = − k . The fluid bulk-mean temperature is an axial/longitudinal flow-weighted average of
∂n R,z

the local fluid temperature Tm =

∫ wTdA .
A
In this text the term “wall heat flux” refers to the
∫ wdA
A
dimensionless circumferentially-averaged axial local wall heat flux given by
qL 1 ∂T *
Nu = q * =
k∆ T
=−
2πRR ∫ ∂n
RR
*
which will be positive for cooling and negative for heating
z*
conditions.

The non-dimensional partial differential equations above were solved using with the commercial finite
element partial differential equation solver FastfloTM [11]. This is not a “black box” CFD package.
Selected numerical methods have to be implemented through user programming. To solve for the flow
field, the augmented Lagrangian method and Newton-Raphson method were used. Knowing the
velocity, the energy equation may be solved by a marching scheme in the axial direction. The basic
computer code implemented here is the same as that used for previous cases ([8, 9, 10]) where a
detailed discussion of the mesh, numerical formulation for the velocity and temperature fields may be
found.

Results and discussions

For power law fluids, the non-dimensional parameters are interdependent. For instance, if the cylinder
rotation velocity changes then the Reynolds number, Peclet number and Brinkman number will also
change. Therefore parametric studies need to be carried out in two different ways. One is to change
individual non-dimensional parameters. For scale-up purposes, individual physical parameters are
changed. For the computations recorded here, the values L=0.05m and W=0.1m/s were used. The
dimensionless pressure, tangential flow quasi-streamlines and axial velocity at a cross section of a
SSHE for m=0.33, ReU =3.17 (U=0.5m/s) are shown in Fig. 1. The corresponding dimensionless
temperature fields for cooling with Pew=2000, Br=0.164 at z=0.1, 0.2, 1.0 and 1.8m are shown in Fig.
2. On the temperature contour plots, lower contour values are represented by a darker colour. Near
the entrance the temperature is uniform (z=0.1m), and further down the channel the cooling effect can
be seen.

Fig. 3 shows the axial local averaged heat flux and bulk-mean temperature for heating and cooling at
Br=0.41667, ReU=10, Pew=500, m=0.33 (U=1m/s). Note that the Reynolds number does not vary
linearly with U because of the change in characteristic viscosity. Due to viscous dissipation, extra heat
needs to be removed from the wall for cooling of the fluid material while less heat is required for
heating for the same change in bulk temperature. Eventually the wall heat flux reaches the same value
in a thermally fully developed region. The effects of shear thinning index on the wall heat flux and fluid
bulk-mean temperature for cooling at Br=0.41667, ReU =10, Pew=500 (U=1m/s) are shown in Fig. 4. It
is seen that the bulk-mean temperature is lower for m=0.33 than m=1.0. Apart from close to the
entrance, the same trend is found in Nu. The reason is that the viscous dissipation is determined by
local velocity gradients and the local effective viscosity. In SSHEs, close to the singularity corners the
velocity gradients are very high. Therefore, the viscous dissipation is very high for constant viscosity
Newtonian fluids. However, for shear thinning fluids the viscosity is reduced in high shear regions and
the combined effects of high shear and low viscosity result in lower viscous dissipation. This is
consistent with our 2D heat transfer results [8]. Harrod [1] also indicated that the measured heat
transfer was different for heating and cooling conditions and that the largest differences were found
when the materials were Newtonian. It is not surprising that similar results were found in a single
screw extruder by Karwe and Jaluria [12], where the geometry is similar.

Fig. 5a shows the effect of the parameter PeW on the wall heat flux for cooling conditions at ReU=10,
Br=0.41667, m= 0.33. It is seen that in SSHEs with axial flow, the wall heat flux changes with Peclet
number in both the thermal entrance and thermally developed regions. This contrasts with the 2D
results where there is no net contribution to the average wall flux from the convection term [8]. The
effect of cylinder rotation velocity U on heat transfer for m=0.33 is shown in Fig. 5b. For U=1.0m/s the
values of the dimensionless parameters were Re=10, Pew=2000, Br=0.41667.

4
ICEF9 – 2004
International Conference Engineering and Food

Conclusions
Finite element methods have been used successfully to study heat transfer in hydrodynamically fully
developed flows of power law fluids in SSHEs with axial through-flow. The results show that for power
low fluids the viscous dissipation is lower than for Newtonian fluids. For the same set of non-
dimensional parameters, the bulk-mean temperature and wall heat flux is lower for power law fluids
than for Newtonian fluids. This is consistent with our 2D SSHE results.

In SSHEs with fully developed hydrodynamic flow, the axial local averaged heat flux in the thermal
entrance region and in the fully developed thermal region depends on the Peclet number.

It is seen that the wall heat flux is gradually reduced down the channel. The heat transfer could thus
be improved by avoiding thermally developed regions, reducing the section length for isothermal wall
temperature or by using staggered short blades.

Acknowledgements
The second author acknowledges financial support from The University of Reading.

References
1. Harrod, M. Scraped surface heat exchangers-A literature survey of flow patterns mixing effects,
residence time distribution, heat transfer and power requirements. J. Food Proc. Eng., 9, 1-62,
1986.
2. Wang, W., Walton, J.H., McCarthy, K.L. Flow profiles of power law fluids in scraped surface heat
exchanger geometry using MRI. J. Food Proc. Eng., 22, 11-27, 1999.
3. Dumont, E., Fayolle, F. and Legrand, J. Flow regimes and wall shear rates determination within a
scraped surface heat exchanger. J. Food Eng., 45, 195-207, 2000.
4. Rodruiguez, S. Flow measurements in scraped surface heat exchangers, PhD, Birmingham
University, 2000.
5. Stranzinger M. Feigl K. and Windhab E. Non-Newtonian flow behaviour in narrow annular gap
reactors. Chem. Eng. Sci., 56, 3347-3363, 2001.
6. Fitt A.D. and Please C.P. Asymptotic analysis of the flow of shear-thinning food stuffs in annular
scraped heat exchangers. J. Eng. Math., 39, 345-366, 2001.
7. Baccar, M. and Abid, M.S. Numerical analysis of three-dimensional flow and thermal behaviour in
a scraped surface heat exchanger. Rev. Gen. Therm. Fr., 36, 782-790, 1997.
8. Sun, K.-H., Pyle, D.L., Fitt, A.D., Please, C.P., Baines, M.J. and Hall-Taylor, N. Numerical Study of
2D Heat Transfer in a Scraped Surface Heat Exchanger. Int. J. Computers and Fluids. 2003
(Accepted for publication).
9. Sun, K.-H., Pyle, D.L., Hall-Taylor, N., Baines, M.J. and Fitt, A.D. Velocity profiles and frictional
pressure drop for shear thinning materials in lid driven cavities with fully developed axial flow.
Submitted to Chem. Eng. Sci., 2003.
10. Sun, K.-H., Pyle, D.L., Fitt, A.D., Please, C.P., Hall-Taylor, N. and Baines, M.J. Heat transfer and
thermal entrance length with shear thinning materials in lid driven cavities with fully developed
axial flow. 2003 (Submitted to Int. J. Heat and Mass Transfer).
11. Fastflo Tutorial Guide V3, Oxford, Numerical Algorithms Group, 2000.
12. Karwe M.V. and Jaluria Y. Numerical simulation of fluid flow and heat transfer in a single screw
extruder for non-Newtonian fluids. Numerical heat transfer A, 17, 167-190, 1990.

5
ICEF9 – 2004
International Conference Engineering and Food

Fig.1. Schematic view of a cross section at x-y plane, pressure, quasi-streamline and axial velocity
distribution for m=0.33, ReU =3.17.

Fig. 2. Temperature distributions. Cooling for m=0.33, ReU =3.17, Pew=2000, Br=0.164.

40 1.5
Bulk mean temperature

30 1
Wall Heat Flux

20
10 0.5
Cooling Cooling
0 0
Heating Heating
-10 -0.5
-20
-30 -1
-40 -1.5
0.0001 0.001 0.01 0.1 1 0.0001 0.001 0.01 0.1 1
(z/L)/Pew (z/L)/Pew

Fig. 3. Wall heat flux and fluid bulk-mean temperature for heating and cooling.
m=0.33, ReU =10, Pew=500, Br=0.41667.
80 0
Bulk mean temperature

70 -0.1
m=1.0
Wall Heat Flux

60 -0.2
50 -0.3 m=0.33
m=1.0
40 -0.4
m=0.33
30 -0.5
20 -0.6
10 -0.7
0 -0.8
0 6 12 18 24 30 36 0 6 12 18 24 30 36
z/L z/L

Fig. 4. Effect of m on wall heat flux and fluid bulk-mean temperature.

Cooling for ReU =10, Pew=2000, Br=0.41667.
100 80
70
Wall Heat Flux

Wall Heat Flux

60
Pew=200 50 U=0.5m/s
10 Pew=2000 40 U=1.0m/s
Pew=20000 30 U=1.5m/s
20
10
1 0
0.001 0.01 0.1 1 0 6 12 18 24 30 36
(z/L)/Pew z/L

(a) (b)
Fig. 5. a. Effect of Peclet number on heat transfer for m=0.33, ReU=10, Br=0.41667
b. Effect of rotation velocity on heat transfer for m=0.33.

6
ICEF9 2003
International Conference on Engineering and Food

The use of Computational Fluid Dynamics for predicting the microbiological safety of foods.
.(1) (1) (2) (1)
Asteriadou K , Hasting A.P.M . Bird M.R . and Melrose J .
(1)
Unilever R&D, Colworth House, UK.
(2)
University of Bath, Department of Chemical Engineering.
Konstantia.Asteriadou@unilever.com

Abstract
FLUENT, a commercial CFD (Computational Fluid Dynamics) code, has been used to predict product
flow and temperature profiles within process equipment and comparing these predictions with
experimental results. Initial predictions of velocity and temperature profiles for low viscosity fluids in
typical equipment geometries have been obtained. Applications of this approach will enable the
interaction between food products and equipment geometries to be predicted as well as assessing the
implications for food safety or spoilage. Future work will also include the modelling of more complex
fluids and fouling and cleaning kinetics.

Key words: modelling, CFD, hygienic design, microbial kinetics, food processing, food safety.

INTRODUCTION

The growth or inactivation of micro-organisms is dependent on the temperature profile and the
[1]
residence time of the product within the system. The temperature and residence time, in their turn,
depend on the fluid velocity. For these reasons it is important to have correct estimations of the velocity
and temperature so that the microbial kinetics can be predicted as accurate as possible and hence the
implications for food safety.
Thermal processes are commonly encountered in the food industry. Products pass through heated
equipment for sterilisation or pasteurisation. Pasteurisation is designed to kill pathogens that are of
high risk for health. Sterilisation involves higher thermal processes that aim to get rid of the rest of
vegetative spores and bacteria. Major inconveniences during these processes are often caused by
[2]
biological fouling: the deposits or accumulations of microorganisms found upon various surfaces .
Also some stagnant areas, where the product has a prolonged residence time, may be sources of
spoilage that could end up in the bulk flow.
Cleaning in place (CIP) processes are used in the food industry in order to remove fouling deposits.
CIP is a means of cleaning equipment without dismantling it by circulating detergent solutions through
it. The flow velocities are critical for effective cleaning. CIP cleans and in some cases can sterilise the
product contact surfaces at the same time and can also be automated. It reduces the cleaning
shutdown periods of a plant, so it is a considerable way of cost saving. The efficiency of cleaning can
[3]
be improved by the right combination of temperature, concentration of cleaning solution and flow .
The science of CIP is based on applying the required amount of energy to the equipment to ensure
that it is cleaned. The energy is basically provided by the temperature of the solution (thermal energy),
the detergent or the solvent (chemical energy) and the application of suitable pipeline velocities or
pressure (kinetic energy). The shear stress developed on the walls of the equipment can be critical for
[4]
the rate of fouling removal as can the thickness of the boundary layer. For this reason, turbulent
flows are essential since they have a strong interaction with boundary layers. However, laminar flow is
often found when processing products under many processing conditions.
In both CIP and process lines there are equipment geometries that may be unhygienic because the
heat and mass exchange in their domain is low and/or accumulation of product might occur. Such
[5]
geometries can be dead-ends, T-junctions, down-stands, up-stands, expansions etc. . It may not
always be convenient or practical to remove these parts.
It was therefore considered important to model different flows in domains that comprise these kind of
geometries in order to see how useful the CFD modelling can be for predicting thermal variations etc.
For CIP processes turbulent flows are of interest, whilst for thermal processes laminar flows are more
often encountered. FLUENT was chosen because it applies the finite volume method and is
considered to cope very well with 3D and turbulent flows.

CFD
The aim of this work is the development of a modelling approach to predict the implications of
processing on microbiological growth and hence the safety of food products. The tool selected for this
purpose is FLUENT, a commercial CFD (Computational Fluid Dynamics) code. CFD is widely applied
in industry, although there has not been so far any reported use of it in combining engineering unit
ICEF9 2003
International Conference on Engineering and Food

operations such as fluid flow and heat transfer with biological systems such as microbiological growth
and inactivation.
CFD is the analysis of systems involving fluid flow, heat transfer and associated phenomena such as
chemical reactions by means of computer-based simulations. The code used, FLUENT, is based on
the finite volume method. The design of the geometry is done in GAMBIT, which is an integrated
processor for CFD analysis. The standard FLUENT interface cannot be programmed to anticipate
every user's needs. For this reason the User Defined Functions (UDFs) are commonly used. A user-
defined function, is a function programmed by a user that can be dynamically linked with the FLUENT
solver to enhance the standard features of the code. User-defined functions are written in the C
programming language.
The temperature in FLUENT was modelled using a UDF to describe the natural convection heat
transfer coefficient set as boundary condition at the walls of the T-area. The above coefficient was
given by the equation:
n
hl æ βg∆Tl 3 ρ 2 C p µ ö
= C çç
′ ÷÷ (1)
k è µ 2
k ø
where C’ and n are constants determined for various geometries and g is the gravitational acceleration.
The physical properties of air: density ρ, specific heat Cp, viscosity µ and thermal conductivity k are
calculated at the average temperature of the wall surface and the environmental temperature. The
coefficient of cubical expansion, β, is taken as 1/T, where T is the absolute temperature and l is the
length of the vertical pipe. FLUENT uses the temperature at the wall (Twall) every time it solves the heat
transfer equation between the wall and the environmental air (Tenv):
∆Τ = Twall − Tenv .

For all the models the flow and the temperature profiles were solved. For the laminar flows the one
available solver for laminar flow was applied, for the turbulent flows of 500 lt/hr and 600 lt/hr the SST k-
[6]
ω and for the higher ones the RNG k-ε . For the wall boundary condition on the dead-leg, was used a
UDF to describe the natural convection heat transfer coefficient for the heat flux between the wall and
the environmental air.

Experiments
The study here is of a flow past a T-junction in which the vertical arm is blocked, Fig 1, thus creating a
potentially dead space where stagnant product may remain for extended periods of time. The pipes are
of 0.023m diameter and before and after the T-piece are 1.5 metres and 0.5 metres lengths of
horizontal pipework. The length of the dead-leg is 0.2325m, measured from the centre of the horizontal
tube.

T-junction

0.5m 1.5m
outlet inlet
Dead end

0.023m
Figure 1: Schematic of the pipework geometry studied.

The horizontal pipe was insulated, so that constant temperatures can be maintained along the
length. However, the vertical pipe is not lagged so there are heat losses to the air via natural
convection around the T-piece. In the experimental setup, 6 thermocouples type k 0.5mm are located
down the centre of the vertical pipe. The temperature profiles from the thermocouples, in steady state,
were compared with the prediction of the simulation.
The flows varied between 150lt/hr (~0.08m/s) and 1333lt/hr (~0.71m/s), corresponding to a
Reynold’s number of between 1000 and 16000 when using water and hence both laminar and turbulent
flow regimes were achieved. The temperature at the inlet of the horizontal part of the pipework was
o
maintained at around 50 C. To provide a significant temperature difference from ambient conditions
ICEF9 2003
International Conference on Engineering and Food

and hence create a temperature gradient down the unlagged pipe. The simulations were compared
against our own experiments at steady state for different water flowrates.

Results and discussion

The steady state experiments were carried out for different flows between laminar and turbulence. The
importance of the kind of flow lies on the fact that there are areas formed in the T-piece where the fluid
is stagnant and stays at the bottom or is forming eddies that recirculate without interacting with the bulk
flow and some others do. This can be visualised by comparing the velocity vectors and magnitudes for
different flows (Fig. 2 (a), (b)). For the lowest flow, the velocity is almost zero after the first 7cm down
the vertical pipe. For the highest flow the velocity is negligible after around 15cm down the pipe. By
further observation and animation of the path lines (Fig. 3 (a), (b)) along the t-piece, for the lowest flow
(150 lt/hr) there are vortices formed between the first 5.5 and 6.5cm that travel all the way up to the top
ending in the bulk flow (Fig. 3(a)). The effect is more pronounced at higher flows (1333lt/hr, Fig (b))
where the interaction between the dead-leg and the bulk flow occurs in the space 5.5-13.5 cm in the
vertical pipe of the T-area.

0.15m
0.07 m

(a) (b)

Figure 2(a), (b): Velocity vectors at the dead-leg area for flows: 150, 1333 lt/hr.

Figure 3 (a), (b): Pathlines of massless particles that follow the flow in the T-piece, coloured by velocity
magnitude for (a) 150 lt/hr and (b) 1333 lt/hr.

The reason for using a UDF instead of a single heat transfer coefficient is the fact that there is a
significant temperature gradient across the dead end. Figures 4, 5 show the comparison of the
temperature distribution along the centre of the T-piece for laminar (150 lt/hr) and turbulent flow (1333
ICEF9 2003
International Conference on Engineering and Food

lt/hr) between the experimental measurements and the models run using single value of heat transfer
coefficient (Fig.4(a),5(a)) and UDF described coefficient (Fig.4(b),5(b)). For the laminar flow the
maximum temperature difference was approximately five degrees noticed at the positions where the
last three thermocouples are placed (Fig 4(a)). By using a temperature dependent coefficient the
agreement between prediction and experiment is much better (Fig.4(b)).
The difference is more significant in the turbulent flow (Fig.5), where, using a single heat transfer
coefficient for the natural convection can result in differences of temperature of approximately 15
degrees towards the bottom of the T-piece (Fig5(a)). Figure 5(b) shows that the application of the UDF
gives a much more accurate match between the experimental data and the model.

Modelled Temperature Experimental measurements (K) Modelled Temperature Experimental measurements

330

325
325

Temperature (K)
Temperature (K)

320
320

315 315

310
310

305
305

300 300
0.225 0.175 0.125 0.075 0.025 -0.025 0.225 0.175 0.125 0.075 0.025 -0.025
Distance (m) Distance (m)
(a) (b)
Figure 4: Comparison of T along the centre of the dead leg between the models and the experiments
for laminar flow using (a) single heat transfer coefficient and (b) wall temperature dependent UDF.

Modelled Temperature Experimental Measurements Modelled Temperature Experimental measurement

330 330
325 325
Temperature (K)
Temperature (K)

320 320
315 315
310 310
305 305
300 300
0.225 0.175 0.125 0.075 0.025 -0.025 0.225 0.175 0.125 0.075 0.025 -0.025
Distance (m) Distance (m)

(a) (b)
Figure 5: Comparison of T along the centre of the dead leg between the models and the experiments
for turbulent flow using (a) single heat transfer coefficient and (b) wall temperature dependent UDF.

Increasing the flow we can see the influence on the temperature distribution down the geometry of
interest. This can be visualised by comparing the contours of temperature on a surface chosen along
the centre of the vertical area (Fig.6). The temperature remains higher further down the geometry.
ICEF9 2003
International Conference on Engineering and Food

150lt/hr 600lt/hr 1000lt/hr 1333lt/hr

Figure 6: Contours of temperature along the dead leg for various flows.

We can also have a general idea of the velocity distribution down the vertical pipe at various flows by
looking at figure 7. There we can notice how the velocity drops further down along the centre of tube as
the flow increases. For the same flows and areas we take the results of the temperature distribution
(Fig. 8), where we can see the increasing length

1 5 0 lt/hr 6 0 0 lt/hr 1 0 0 0 lt/hr 1 3 3 3 lt/hr

0.2
0 .1 8
0 .1 6
Velocity (m/s)

0 .1 4
0 .1 2
0.1
0 .0 8
0 .0 6
0 .0 4
0 .0 2
0
0 .2 32 0 .21 2 0.19 2 0 .1 7 2 0.15 2 0 .1 32 0 .11 2 0 .0 92 0 .0 7 2 0.05 2 0 .0 32 0 .0 1 2
D is tan c e (m )

Figure 7: Velocity distribution along the centre of the T area for different flows

150 lt/hr 600 lt/hr 1000 lt/hr 1333 lt/hr

3 29

3 24
Temperature (K)

3 19

3 14

3 09

3 04
0 .2 2 5 0 .1 75 0 .12 5 0 .0 75 0.02 5
D is ta n c e (m )

Figure 8: Temperature distribution along the centre of the T area for different flows.
ICEF9 2003
International Conference on Engineering and Food

Future work
The encouraging results of the above work, suggest that a general rule correlating depth down the T-
piece and velocity or temperature drop can be deduced. Hence, this can be expanded and applied for
different geometries as well, such as up-stands, pipe couplings etc. In addition to different geometries,
a wider range of food products with a range of rheologies will be studied.
Also, biofouling is a common problem in the food industry and is a process that can be controlled with
difficulty. However, this work is intended to explore into modelling that kind of surface reactions and
see how deposits are attached to the surfaces and how they can be detached under adequate shear
stresses and temperature conditions.
Most of these processes of surface reactions are transitional and un-steady solutions are necessary to
be obtained using FLUENT, which will give us a monitored in-line view of the formation of the biofilm.
By managing to control and model temperature and residence times and also predict the biofouling
rates, we have a reliable method of assessing a food production line. Then, it is possible to judge
which areas are risky and which equipment geometries are unhygienic and need to be treated under
different conditions to avoid spoilage and contamination of the product.

Conclusions
The validation of the temperature distribution for the particular geometry shows that FLUENT is an
appropriate method for the prediction of temperature and residence time profiles. Without a realistic
prediction of temperature and residence time distribution, prediction of microbial kinetics cannot be
applied with any confidence. The post processing of the above models shows that there is interaction
between the bulk flow and the dead-leg at various lengths that increases when the flow increases. This
means that with higher velocities there are less stagnant areas and a CIP cleaning, for instance, is
more effective. However, for the specific geometry, the flows applied were not high enough, since there
is always accumulation of product at the bottom of the T piece. So, with the existing conditions, the T-
junction modelled would undoubtedly be considered unhygienic.
The use of the code demands a good knowledge of the engineering aspects. Application of a more
accurate natural convection wall boundary condition had a significant impact on the results and makes
the code an even safer tool to use, since there is good agreement with the experimental
measurements. Moreover, knowing that the temperature is closely coupled with the velocity profile, we
can visualise in FLUENT the recirculation areas and also the parts of the dead-leg that are going to
interact with the bulk flow. In that way it can be predicted whether product will accumulate and cleaning
may be ineffective, and where, if the temperatures and residence times will allow growth of bacteria
and create potential safety problems.

References
1. Zwietering M. H. and Hasting A. P. M., Modelling the Hygienic Processing of Foods-Influence of
Individual Process stages, Food and Bioproducts Processing, vol. 75, no. C3, pp. 168-173.
2. Verran Joanna, When a biofilm not a biofilm-and does it really matter?. Proceedings of the Fouling,
Cleaning and Disinfection in Food Processing held at Jesus College, Cambridge, 3-5 April 2002,
pp. 49-54, Department of Chemical Engineering, University of Cambridge, UK.
3. van Asselt AJ, van Houwelingen G, Giffel MCT, Monitoring system for improving cleaning
efficiency of cleaning-in-place processes in dairy environments, Food and Bioproducts Processing,
80 (C4): 276-280 DEC 2002
4. Lelievre C, Antonini G, Faille C, Benezech T, Cleaning-in-place - Modelling of cleaning kinetics of
pipes soiled by Bacillus spores assuming a process combining removal and deposition, Food and
Bioproducts Processing, 80 (C4): 305-311 DEC 2002
5. Friis A, Jensen BBB, Prediction of hygiene in food processing equipment using flow modelling,
Food and Bioproducts Processing, vol. 80 (C4): 281-285 DEC 2002
6. FLUENT Inc 2001, FLUENT 6 User’s guide Volume 2, pp. 10-8/10-43.
 STUDY OF THE FLOW AND HEAT TRANSFERS IN A WALL JET
CARRYING DROPLETS –
Mist-flow in refrigerated display cabinets.
M. DARBOURET1, J. MOUREH 1*, G. LETANG1, H. BOISSON2, G. ALVAREZ1
1 Cemagref Antony Unité de Recherche en Génie des Procédés Frigorifiques Parc de Tourvoi BP 44 92163 Antony CEDEX
2 IMFT Institut de Mecanique des Fluides de Toulouse
* corresponding author jean.moureh@cemagref.fr

Abstract
From production to consumption, throughout the so-called “cold chain”, food requires strict temperature control.
Display cabinets play an essential role in food conservation as they are considered as one of the weakest links of this
chain. Most of the refrigerated cabinets are forced-air open display cabinets. An air curtain separates frozen-food from
the ambient air. Nevertheless, changes of the ambient conditions can cause dramatic differences on the temperature of
the load. The temperature of the warmest products can be higher than the maximal authorised temperature by European
standard.
This study takes part of a project concerning the use of mist injection to improve performances of refrigerated display
cabinets. In a first step, flow simulations give a global view of the flow inside the cabinet. Then, temperatures that can
be reached in the products without injection of mist, are calculated solving the energy equation. The introduction of a
discrete phase model enables the prediction of the droplets deposition rate along the products surface. Three different
approaches are considered in order to take into account the heat transfer due to droplets evaporation on this surface.
Mesures realized on a cabinet permit, on the one hand, to draw a velocity map of the air curtain, and, on the other hand,
to estimate the heat transfer coefficient evolution along the products surface.

Keywords : cold chain, refrigerated display cabinet, air curtains, computational fluid dynamics (CFD), multiple jets,
heat transfers, convection, radiation, evaporation, wall jet, mist, two-phase flow. Nomenclature
NOMENCLATURE
Cp Constant pression specific heat(J/kgK)
D Molecular diffusivity (m²/s)
Greek letters:
hc ,h heat transfer coefficient (W/m²K)
hm mass transfer coefficient (m/s)
H enthalpy (J) α Thermal diffusivity (m²/s)
∆Hv latent vaporisation heat of water (J/kg) ρ density (kg/m3)
m mass flow rate (kg/s) σ Stefan-Boltzmann
P pressure (Pa) constant(W/m2K4)
S Exchange surface (m²) εrad radiative emissivity
T Temperature (K) λ thermal conductivity (W/mK)
U velocity (m/s) ν kinematic viscosity (m²/s)
Φ Thermal flux (W/m²)
Steam mass fraction(kg /dry air kg)
1- Introduction
Our eating habits in France lead to a great consumption of refrigerated and frozen food. Indeed, more than 45% of the
global amount of consumed products are concerned by the so-called “cold chain”. Therefore, this “cold chain”
represents not only a sanitary issue, but also an enormous economic issue. Concerning hygiene, despite the significant
improvements that have been made since 1992, some risks of poisoning with salmonella or listeria still remain. These
health hazards can be reduced by cleaner production sites on the one hand and by the control of the temperature of the
products from production to consumption , or cold chain, on the other hand.
Among the different steps of the cold chain, refrigerated display cabinets are considered as one of the weakest link.
Indeed, they have to meet two antagonist requirements: to show the products and to keep them refrigerated. The first
goal implies an intensive lighting to catch the consumer attention. This lighting is responsible for an important thermal
radiation which tends to warm the products surfaces and the cold air curtain is not sufficient to maintain temperature
below +6°C.
Several studies have already been carried out about this kind of cabinets. The first ones are based on global energy
balances between the refrigerated display cabinet and its environment. Rigot et al ([1],[2]), for instance studied the
influence of the atmosphere on the refrigerated cabinets performances. Numerous measurements in supermarkets have
evidenced the relative poor performances of such cabinets in case of variable ambient conditions. The latest studies
have recourse to Computational Fluid Dynamics (CFD) and calculate the velocity and temperature fields in every point
of a meshed domain. Numerical simulations are a very interesting tool in that field as they lead to good predictions of
the temperatures that can be reached locally in the refrigerated cabinets depending on the air curtain temperature, the air
flow rate, and thermal radiation of lights, etc... Solving the equations of conservation of mass, momentum and energy,
they represent a promising way of optimising the design step of such appliances. 2D simulations have been made by
Bobbo et al [3] with the finite elements method, by Van Oort et al [4] with CFD PHOENICS software, or by Baléo et al
[5] with FLUENT® software. As for 3D simulations, some have been achieved by Lan et al [6] with CFD-FLOW3D.
Both Lan et al and Baléo et al, chose a k-ε turbulence of model Cortella [7]for example published a numerical study
based on a large eddy simulation of the air curtains flow. All of these studies have shown the numerical and
experimental results are in quite good agreement.
Regarding the difficulties encountered to keep food at the required temperature in such refrigerated display cabinet, the
solution that we consider here is to use of mist injection in the air curtain. The point is that the injection of fine droplets
should improve the thermal performances of such appliances. Indeed, these droplets, carried by the air curtain, are to
settle on the warm surface the products, and to evaporate there. Their evaporation should absorb the thermal energy
excess and lead to a decrease of the products temperature. The mist injection could then be a way of respecting the
European standard concerning safety temperatures.
We present here a CFD analysis of refrigerated display cabinets with or without mist injection and a comparison with
experimental data obtained on a real display cabinet.

2- Devices and Methods

Numerical and experimental studies have been carried out in parallel in order to compare numerical predictions with
experimental results. We propose now a description of the numerical approach and of the experimental set-up.

Numerical simulations
2D simulations were followed by 3D simulations in order to have an idea of the influence of the 3D geometry on the
flow calculation inside the cabinet. Figure 1 shows the geometry of the cabinet and the boundary conditions used for the
calculations.
G
Geomet Tamb = 298 K Tamb = 298 K
Pamb = 1 bar Pamb = 1 bar
ry
Protecting Glass

Uin Heat
Tin= 272 K source

Loading
platfor FOOD

Uout
Evaporator Isolated wall
T2= 268K T1 = 275K
h2= 7 W/m²K h 1=2 W/m²K
Figure1: Geometry and boundary conditions used for numerical simulations.

The considered cabinet is developed by the BONNET-NÉVÉ company. It is a caterer’s cabinet designed to keep cheese
or meat refrigerated. Below the loading platform, two fans blow the air through an evaporator where it is cooled down.
Then this cold air enters the cabinet trough a perforated plate with 2 mm diameter holes.
We consider here this cabinet full of products. These products are assumed to form a step as it is usually the case during
trials of such appliances in cold room. Moreover, the grid is slightly above the higher surface of the products, just like
in case of maximum filling conditions. Not only the cabinet itself is meshed, but also a part of the room around in order
to estimate the influence of the cabinet on its environment.
Mesh

Products
surface Inlet
grid
 Figure 2: Views of created Mesh
Figure 2 presents different views of the meshes created for the
numerical study. This is a non-structured mesh achieved with
GAMBIT® software. The thinner cells are located in the high velocity gradients zones, i.e. in the air curtain and
particularly near the inlet jets. For radiation calculation purpose, 1mm high cells were created at the surface of the
products.
Boundary conditions
We consider a steady-state flow. Turbulent motion is solved with a k-ε model and the inlet turbulence intensity is
supposed to be 5%. The characteristic length of the turbulence is taken equal to diameter of the inlet holes, i.e. 2mm.
The boundary conditions, shown in Figure 1, are the following:
- The velocity is Uin = 2 m.s-1 , in each hole at the inlet; and Uout = 1.3 m s-1 at the outlet so that the mass flow rate is
conserved.
- The air blows in the cabinet at the temperature Tin = 272 K, and the ambient air is supposed to be at rest with
homogeneous pressure and temperature: (Tamb = 298 K, Pamb= 1 bar).
- Heat transfers due to forced convection between food and the cold air below the loading platform are taken into
account setting heat transfer coefficients h as represented on Figure 1. Bobbo et al [3], published some reasonable
values of the heat transfer coefficients. For instance, in the vicinity of the evaporator, the heat transfer coefficient is
more important than elsewhere as it includes both conduction and convection heat transfers. The temperature of the
air circulating below the platform is also a parameter of the calculations. It is set regarding what is actually
obtained in reality.
- Surface radiation is replaced by an equivalent volume heat source in the upper surface of the products. Under the
hypothesis that food behaves as a grey body, the radiation heat flux is:
(
Φ rad = εσ Tamb − TS
4 4
)
Introducing a radiation coefficient in order to compare the contributions of each kind of transfer:
( )
Φ rad = hrad (Tamb − Ts ) with hrad =ε radσ Tamb +Ts (Tamb +Ts ) .
2 2

A user-defined function calculates the radiation source in each point of the mesh taking into account the temperature
difference (Tamb − Ts ) between the surface of the products and the room walls.
In the case of 3D geometry, calculations are made in a slice of the cabinet so that periodicity boundary conditions can
be imposed on each cutting surface.

Discrete phase
Concerning the discrete phase introduced by the droplets injection in the air curtains, the working hypothesis are that:
- droplets are injected on the whole surface of the holes,
- all the droplets have the same diameter,
- droplets do not evaporate along their trajectory before impacting the products,
- droplets impacting the products settle there and disappear of the computed domain.
This last hypothesis enables us to have an idea of the total amount of droplets hitting each point of the surface.

Mist Cooling
Two different ways of calculating the effect of mist on temperature profiles have been considered.
‰ The first method envisaged was to replace the dry cold air by wet cold air. In that case the mist is seen as a single phase
which physical properties slightly differ from those of dry air.
Indeed, supposing the air curtain is saturated air, its specific heat can be calculated taking into account the latent heat of
the water:
H sat = H water + H dry −air = H sat
0
+ Cp dry −air T (1 − ω sat (T )) + ω sat (T )∆H v
∂H sat  ∂ω 
Cp sat =  = Cp dry − air + ∆H v sat 
∂T  P ∂T  p
For the range of temperature considered, one can assume that Cpsat ≈2013 J / kgK . Moreover, the mist density is
evaluated from the injected water mass, ρ≈ 1.35 kg.m-3.

‰ The second method was the introduction of user-defined functions in FLUENT® in order to take into account the
evaporation of droplets impacting the products. This calculation is based on an energy balance considering the heat
transfers by conduction inside the products, convection at the interface, and radiation. The energy conservation equation
can be written:
 ρ prod Vcell Cp prod ∆T = S (Φ conv + Φ cond + Φ rad + Φ evap )
In this case, two different regimes can be observed and are to be taken into account for the calculation of the
evaporation heat flux Φ evap :
- The non-wetting regime, is obtained when the local energy of the products is high enough to evaporate of the total
amount of droplets impacting (mimpact):
SΦevap = mevap ∆Hv = mimpact ∆Hv
- The wetting regime is reached when the amount of water received on the surface is bigger than the amount that can
be evaporated. In this case, water evaporation is mass diffusion controlled.
SΦ evap = hm ρ eau (ω sat (TS ) − ωcell (Tcell ))∆H v
The mass transfer coefficient hm introduced here is linked to the heat transfer coefficient hc through the Chilton-Colburn
D
analogy. hm = hc . As for the coefficient hc, it is estimated from the surface flux Φs as follows:
λ
Tcell
ΦS
hc = .
(TS − Tcell )
Ts
Experimental set-up
Some experimental measurements have been performed on a cabinet specially supplied by the BONNET-NÉVÉ
company. For a better agreement between computations and experimental data, planks were installed in the cabinet to
reproduce the step arrangement of the products. We also had some thermocouples, a hot wire anemometer and a heat
transfer coefficient sensor at our disposal. The latter is the homemade sensor. Its composition is presented in Figure 3.
Its working principle is based on the measurement of a flux trough a warmed plate. Indeed, a resistor heats the metal
plate. The flux-meter measures the global heat transfer Q through its surface S. This global flux includes a radiation
and a convection contribution and is proportional to the temperature difference between the air and the hot surface.
Q
(hconv + hrad ) =
S (Thot−surface − Tair )

Flux-meter
Metal plate
Cylindrical
Heating resistor

Insulating

Figure 3: Structure of the homemade heat transfer coefficient sensor.

This sensor is set on such a way that its upper surface is perfectly at the same level as the planks in order to avoid a flow
disturbance. Assuming that the temperature on the products surface is uniform, the radiation effect can be considered as
uniform, and hrad as constant. Although this device does not allows us to estimate real values of heat transfer coefficient,
it is a good way of evaluating its behaviour along the products surface from the inlet until the outlet. hrad can be
estimated at hrad ≈ 4,8W / m ² K .

3- Results and Discussion

Air Flow
Figure 4 presents a comparison of the velocity maps computed by FLUENT® (4-a) and measured with the hot wire
anemometer (4-b). It highlights the good agreement between computed and experimental results as far as global
behaviour of the curtain is concerned. Indeed, on both map one can find two dead zones with very small air velocity
magnitudes. They are located just below the inlet grid and downstream the step. The falling distances of the air curtain
on the food surface are also similar.
Moreover, the velocity profiles in different sections also tally. Nevertheless, the velocity magnitudes differ in some
points. These differences can be explained on the one hand by the non-unidirectional property of the flow measured by
the hot wire, and, on the other hand by the slightly inclination of the real cabinet inlet grid.
Figure 4: Comparison of computed and measured velocity maps (m.s-1).

Air curtain falls on food Air curtain falls on

x ≈ 0,18 m. food x ≈ 0,15 m.
a- Computed velocity map b- Measured velocity map

Figure 5 presents the evolution of computed and measured relative heat transfer coefficients along the products surface.
The general behaviours of these coefficients are the same in both cases. The maximum of these curves do not coincide
as the air curtain does not fall on the products exactly at the same abscissa. One can check on these curves that the
higher velocity magnitudes are, the higher heat transfer coefficients are, and vice versa. Therefore, this figure is another
validation of the flow calculation and the k-ε model seems to be appropriated for that configuration.

1 0,40%
Droplets
0,9 h*calculated
calculé impacting (%) 0,35%
0,8 h*measured
mesuré 0,30%
0,7
0,25%
h*=h/hmax

0,6 5,2% of
0,20% injected
0,5 droplets
0,4 0,15%
19% of
0,3 0,10% injected
0,2 0,05% droplets
0,1 0,00% 0 0,2 0,4 x(m) 0,6 0,8
0
0 0,2 x*=x/xmax
0,4 0,6 0,8 1 Figure 5 : Comparison between simulated and measured
heat transfer coefficients (W.m-²K-1) along the products
surface.
Figure 6: Droplets deposition rate along the products su rface.
Consequently, the air flow computation seems to be validated by the experimental data. This validation enables us to
feel confident about the results we obtain in the out of reach flow zones for experimental measurements.

Two-phase Flow
Figure 6 presents the results of the calculation with droplets injection in the air curtain. The droplets deposition rate
along the surface is calculated so that one can located the regions where the mist injection should have the most
important effect. Only 20% the total amount of injected droplets settle on the food surface. Among these impacting
droplets, 80% fall on the products upstream the step, and 20% downstream. Nevertheless, the products temperatures
commonly increase from the air inlet to the outlet as the temperature of the air curtain increases. This result points out
the fact that the droplets injection process has to be adapted in order to target and reach the hottest zones of the cabinet.

4- Conclusion
The quite good agreement between computed and measured results reveals FLUENT® as a promising tool to study air
flow in refrigerated cabinets. The results of the two-phase flow highlight the technical difficulties of the mist injection
process. The amount of water injected should be enough to significantly decrease the products temperature, but the
products should not be wetted. Indeed, a water excess could lead to bacteria proliferations..

5- Acknowledgements
This study could not have been achieved without the participation of our partner BONNET-NEVE.
 6- References

[1] RIGOT G. Modélisation et simulation des meubles frigorifiques de vente fonctionnant dans des conditions
variables,20th International Congress of refrigeration, IIR/IIF, Sydney, 1999.
[2] RIGOT G. Interaction environnement et meubles de vente, RPF n°835 (1996) 53-56.
[3] BOBBO S., CORTELLA G., MANZAN M. The temperature of frozen foods in open display cabinets: simulation
and testing, 19th International Congress of Refrigeration, Proceedings vol II (1995) 697 –704.
[4] VAN OORT H., VAN GERWEN R.J.M., Air flow optimisation in refrigerated cabinets,19th International
Congress of refrigeration, Proceedings vol. II, (1998) 446-453.
[5] BALÉO J.N., GUYONNAUD L., SOLLIEC C., Numerical simulation of air flow distribution in a refrigerated
display case air curtain, 19th International Congress of Refrigeration, Proceedings Vol. II (1995) 681-688.
[6] LAN T.H., GOTHAM D.H.T., COLLINS M.W., A numerical simulation of the air flow and heat transfer in a
refrigerated food display cabinet, 2nd European Thermal-Sciences and 14th UIT National Heat Transfer Conference,
(1996) 1139-1146.
[7] CORTELLA G., CFD-aided retail cabinets design, Computers and electronics in agriculture. (2002)
[8] DARBOURET M., Etude aéraulique et thermique d’un jet pariétal chargé de gouttelettes- Brumisation dans les
meubles frigorifiques de vente, Master report, Cemagref - Antony, 2002.
ICEF9-2004 International Conference Engineering and Food Article No. 554

Effect of liquid flowrate and flow geometry on the breakage of

whey protein precipitate particles

(1) Sinead P. Heffernan, (2) Edmond P. Byrne, (3) Gregory M. Cartland Glover, (4) Nicolas Peron,
(5) John J. Fitzpatrick

(1) Department of Process Engineering, University College Cork, Cork, Ireland

s.p.heffernan@mars.ucc.ie
(2) Department of Process Engineering, University College Cork, Cork, Ireland
e.byrne@ucc.ie
(3)Department of Process Engineering, University College Cork, Cork, Ireland
g.cartlandglover@ucc.ie
(4) Department of Process Engineering, University College Cork, Cork, Ireland
n.peron@ucc.ie
(5) Department of Process Engineering, University College Cork, Cork, Ireland
j.fitzpatrick@ucc.ie

Abstract

The transport of food protein precipitates may alter the precipitate particle properties, which may
affect how they behave in subsequent processes. For example, the transport of precipitate solution
through pumps, pipes and valves and into a centrifugal separator may cause changes in particle size
and density, which may affect the performance of the separator. This work investigates the effect of
flow velocity and geometry on the breakage of whey protein precipitates by passing a precipitate
solution through defined geometries including pipes, valves, elbows and tee-junctions. Experimental
data is presented on particle breakage for flow through each geometry.

Keywords: protein precipitates, particle breakage, separation

1. Introduction

Milk contains two major protein groups, the caseins and whey proteins. Caseins account for ~ 80% of
the total protein in bovine milk. The whey proteins account for about 20% of total bovine milk proteins,
and represent an excellent source of both functional and nutritional proteins. The main whey proteins
are β-lactoglobulin and α-lactalbumin, two small globular proteins that account for 80% of total whey
proteins [1].
Precipitation of casein, through acid addition or by rennet addition leaves a residual liquid known as
whey. Whey protein concentrate (WPC) can then be produced using various membrane technologies
to remove the excess water from the whey, in addition to the lactose, salts and minerals [2].
There are a number of methods for WPC fractionation. Isoelectric precipitation is a common such
method and is based on a combination of temperature and pH adjustment in an agitated vessel. It
results in the formation of α-la rich precipitate phase and β-lg rich supernatant phase [3].
Precipitation occurs in four distinct stages: nucleation, growth of nuclei, aggregation of nuclei and
conditioning of the aggregates [4]. The physical properties of the aggregates depend on several
factors including precipitation reactor variables.
The complete design of the precipitation stage requires an understanding of the interaction with the
subsequent separation operation, for example centrifugation, as protein precipitates are biologically
fragile and are subjected to shear induced break-up during subsequent processing.
Protein precipitates are fractal in nature, which implies that their local densities decrease with
increasing radial distance from the centre [5]. Size, compactness, density and strength are important
factors in determining the efficiency of a centrifugal separation stage [6]. Shear history is found to
affect the formation of whey protein precipitates in terms of size, strength [7] and fractal dimension [8].
By employing low impeller shear rates during formation, larger aggregates resulted compared to those
formed under higher impeller shear rates. However these larger aggregates are weak and fragile and
are extremely susceptible to shear induced breakage during subsequent highly turbulent processing. It
ICEF9-2004 International Conference Engineering and Food Article No. 554

is desirable to produce aggregates that are compact and strong, and are less susceptible to the
breakage during the recovery stage.
Precipitate particles may suffer significant breakage in high-shear processing environments such as
pumps and centrifuge feed zones, in complex piping systems and valves and as they pass through
other items of process equipment that are involved in transfer from the precipitation/ageing vessel to
the separator [9]. For example, high flow stresses generated by extremely rapid acceleration of
material upon entrance into the centrifuge leads to aggregate breakage and hence lower recoveries
[10].
The objective of this work was to investigate how the flowrates and flow geometries that particles
experience during processing (post formation and vessel ageing) affect their size and other separation
characteristics. The overall objective was to investigate how this know-how can be applied in
processing, for example in the design of certain geometries to minimize breakage.

2. Material and Methods

2.1 Protein precipitation and fractionation

α-Lactalbumin rich precipitates were batch produced in an agitated vessel. Precipitation of a 10%
WPC preparation was effected by adjusting temperature and pH to the appropriate values (60°C and
pH between 4.1-4.2) at an impeller speed of 750rpm, corresponding to an average spatial shear rate
of 1118s-1 in the vessel. This speed, which determines the shear rate at which precipitates are
exposed to during their formative stages during acid addition, is critical in determining the properties of
the aggregates being formed [7].
2M HCl was added at a constant rate as a precipitation agent. Once the acid had been added to the
solution and the pH had fallen to the isoelectric pH, the impeller speed was adjusted to 200rpm for
ageing and aggregates were aged at this impeller speed for 50 min. Table 1 details the composition of
the WPC feed powder used in this study (provided by Dairygold, Mitchelstown, Co. Cork, Ireland).

Table 1 Composition of WPC35

WPC component % Composition (w/w)
Lactose 51.07
Protein 35.5
Fat 3.13
Moisture 4.00
Ash 6.3

2.2 Sampling
A small sample was taken immediately after acid addition (aging time = 0 sec). This sample was
immediately added to a beaker of chilled water (4˚C) at a sample to water ratio 1:2, and placed in a
fridge at 4˚C to prevent further particle growth before being sized. Following the ageing period,
samples were taken and diluted in cold distilled water to create 1% dispersions (this was carried out in
order to neglect particle-particle interaction during subsequent processing.

2.3 Processing of Particles

Particles were held in a cylindrical reservoir before being pumped through a shearing rig using
compressed air, with pressures in the range of 1-7 bar, (Fig. 1).

Fig. 1 Cylindrical chamber

ICEF9-2004 International Conference Engineering and Food Article No. 554

The shearing rig comprised of a small length of pipe of diameter 2.362mm attached to the base of the
cylindrical reservoir by a threaded fitting, this was followed by an on/off ball valve, onto which the
various geometrical configuration could be attached (Fig. 2).
Particles were pumped through the various geometries attached to the on/off valves (Figs. 3-7) at
flowrates in the range of 1-6gs-1. This flowrate range was necessary in order to allow comparison of
the amount of particle break-up that was occurring in geometries at similar flowrates. Particles were
first processed through the entrance region without any attached fittings to investigate any reduction
occurring upon exiting the chamber.

Geometries
attached onto
on/off ball valve

Fig. 2 Entrance section of shearing rig

Prepared WPC precipitate dispersions were passed through each geometry at four different flowrates
This was achieved by modifying the compressed air pressure. Reynolds number for the flowrates were
in the range of 1,721-10,323 i.e. moderate to high levels of turbulence. Experiments were carried out
in triplicate for each geometry.

Fig. 3 Straight 20mm pipe (transition) Fig. 4 Straight 60mm pipe

Fig. 5 60mm pipe + 45° Bend Fig. 6 60mm pipe + 180° Bend

Fig. 7 60mm pipe + 40° partially open ball valve

ICEF9-2004 International Conference Engineering and Food Article No. 554

2.4 Particle characterization

Particle size distribution was measured by laser diffraction using a Malvern Mastersizer S particle
sizer to ascertain the effects of high shear exposure through the different geometries on aggregates
particle size distribution and compactness. Particle sizing was carried out in duplicate for samples; pre
ageing, post ageing and four samples for each geometry
Particle size is the most important factor determining the separation efficiency of precipitates (by
gravitational or accelerated (centrifugal) settling). This is demonstrated by Stokes’ law which predicts
particle sedimentation rates for a single spherical particle (rate is proportional to diameter squared).
Stokes’ Law also suggests that that particle density is an important factor determining the settling rate.
Protein precipitates cannot be readily characterised by a single value for density as they comprise a
dense inner core surrounded by progressively looser, less strongly bound outer layers, i.e. density
decreases with radial distance from the centre. Such particles can be described as having fractal
characteristics. An aggregate in three-dimensional space may be considered to be fractal if its density
decreases with radial distance, r from the origin such that ρ(r) ∝ rDf-3 where Df is known as the fractal
dimension. An aggregate with a fractal dimension of three in 3 dimensional space will have a
completely solid compact structure and its density will correspond to the density of the primary
particles from which it is composed. Whereas, an aggregate with a fractal dimension less than three
will exhibit a porous structure. The fractal dimension of the particles can be estimated from the laser
light scattering data.

3. Results and Discussion

3.1 Effect of flowrate on particle size distribution (PSD) profile of whey protein precipitates
Increasing flowrate of the dispersion through the rig has a destructive impact on the PSD profile of
whey protein precipitates. Take for example particles subject to processing through a 100mm straight
pipe (Fig. 4 with 60mm replaced by 100mm) at different flowrates (Fig. 8).

%
20 100

90

80

70

60

10
Re = 9635 Re =3441
50

40

30

20

10
0 0
0.1 1.0 10.0 100.0
Particle Diameter (µm.)
Fig. 8 PSD profile of whey protein precipitates after experiencing rig flow at Re of 3,341 and
9,635

Prior to processing the majority of particles lie within the range 2µm-30µm, but after being subject to
a flow of 2gs-1 the majority lie within the range 2µm-25µm, while if this flowrate is increased to 5.6gs-1
the level of turbulence increases dramatically from an Re of around 3,441 to almost 9,635 and there is
a huge shift in the PSD profile as the majority of particles now lie within the range 1µm-13µm. In
addition to this an appreciable increase in the volume and number of primary (sub-micron) particles is
observed as can be seen from Fig. 8.

3.2 Effect of process rig flowrate on size and fractal dimension of whey protein
precipitates.
The effect of rig processing flowrate on median diameter, d50 and fractal dimension, Df, of whey
protein precipitates is illustrated in Fig. 9. Here again, particles have been processed through a
100mm pipe at flowrates ranging from 2gs-1 to 5.6gs-1, with corresponding Re in the range 3,441 to
ICEF9-2004 International Conference Engineering and Food Article No. 554

9,635. Prior to processing, the particle median diameter is 8.12 ± 0.08µm. The median diameter
decreases with increasing flowrate through the rig. It appears that at higher flowrates, the rate of
breakage is accelerated. This may suggest that breakage is occurring as a result of fracture of the
precipitates into a number of smaller particles, so great is the reduction in diameter experienced (the
reduction in volume experienced is even greater), whereas at lower flowrate, it is more likely that size
reduction is cased by erosion of the looser outer layers. This hypothesis is reinforced by the values for
the fractal dimensions displayed - from a rather porous 2.6 for the larger particles higher more
compact levels after high shear processing.
The fractal dimension of the whey protein precipitates are about 2.61 following vessel formation and
ageing. Fractal dimension of the precipitates is seen to escalate with increasing flowrate through the
100mm pipe, more gradually at first and increasingly as the level of turbulence, and hence rate of
shear increases. This relationship is primarily related to median size of the precipitates; below a size of
around 5.5 µm, the rate of increase in Df is greater, compared to a markedly slower increase in Df
above this size.

2.90 9

2.85 8
Particle fractal dimension

Median diameter ( µm)

2.80 d50
7
2.75
6
2.70
5
2.65
Df
2.60 4

2.55 3
0 1 2 3 4 5 6 7
Mass flowrate through rig (g/s)

Fig. 9 Effect of flow flowrate through rig with a 100mm (0.74mm φ) pipe, on fractal dimension
(Df) and median diameter (d50) of whey protein precipitates.

3.3 Effect of flow geometry on the break-up of whey protein precipitates.

Increasing flowrate results in smaller particles sizes, as can be seen in flow along a straight pipe
configuration (Fig. 9). In addition, flow geometry also has an influence on particle break-up. As the flow
geometry becomes more complex more particle break-up occurs as can be seen in Fig. 10. The
geometry with the sharp transition in diameter is seen to have the most critical effect on shattering the
precipitates (Fig. 3 above), whereby particles are forced to pass through a transition from 2.286mm to
0.74mm in diameter, a huge acceleration in velocity is experienced by the particles, resulting in
significant particle break-up, especially as the flowrate is increased. All other geometries demonstrarte
the effect on particle size after particles have passed through this transition so as expected there is a
reduced level of further breakage through each of the subsequent geometries. Nevertheless,
subsequent breakage is significant as evidence by a further reduction in median particle size for all
geometries employed. Particle size reduction increased with geometric complexity and increased from
the straight pipe (Fig. 4) to the 45˚ bend (Fig. 5) and in turn to the 180˚ bend (Fig. 6). A partially open
ball valve (40˚ open) had an even greater effect (Fig. 7) causing a significant amount of shattering
among the aggregates, as particles are forced to flow through a very narrow and complex constriction.
Indeed the level of turbulence is so great at this geometry that the effect on particle size is similar to
that which is observed when processing at pilot scale upon entering the feed zone in a centrifuge inlet
(8).
ICEF9-2004 International Conference Engineering and Food Article No. 554

8
Median diameter (µm)

3
0 1 2 3 4 5 6 7
Mass flowrate through rig (g/s)

Fig. 10 Median Diameter versus mass flowrate for particles subject to flow through the
following geometries; (a) entrance zone, ( ), (b) straight 20mm pipe, ( ), (c) straight 60mm
pipe, ( ), (d) 60mm pipe including a 45° turn, ( ), (e) 60mm pipe including a 180° turn, ( ) and (f)
60mm pipe including a 40° open ball valve, ( ).

5. Conclusion
Exposing protein particles to high velocity regimes, leads to substantial breakage as high shear rates
are encountered. Particle breakage could be reduced by redesigning area of high turbulence. For
example, sudden transition or constriction in flow, where the majority of particle break-up is observed
to occur. Such turbulence may exist at the inlet zone in a centrifuge. Breakage of precipitate particle
suspensions is most likely to occur as the precipitate suspension leaves the centrifuge feed pipe and
passes into the rotor, where it is rapidly accelerated and thus subjected to high shear forces [10].
Disruption produces smaller particles, which are more difficult to recover in the disc stack of the
centrifuge. Thus by redesign of these zones, of rapid acceleration and high turbulence, for example
replacing sudden transition, by more gradual changing geometries, and reducing acceleration, particle
break-up can be notably reduced and thus increasing yields and efficiency of a centrifuge. Finally,
computational fluid dynamics (CFD) can be applied to model the flow dynamics through each
geometry for estimating the shear-rates and turbulent dissipation rates that are responsible for particle
breakage. Furthermore, population balance modeling can be applied for predicting the change in the
distribution of particle size caused by particle breakage.

References
1. Maubois, J.L., Ollivier, G., Extraction of milk proteins, In: Food proteins and their applications, 579-
595, Damodaran, S., Paraf, A., (Eds), Marcel Sekker, New York, USA, 1997.

2. Fox, P.F., Mulvihill, D.M., Developments in milk protein processing, Food Science and Technology
Today, 7, 152, 1993.

3. Pearce, R.J., Thermal Separation of β-lactoglobulin and α-lactalbumin in bovine cheddar cheese
whey, The Australian Journal of Dairy technology, 38, 144-149, 1983.

4. Nelson, C.D., Glatz, C.E., Primary particle formation in protein precipitation, Biotechnology and
Bioengineering, 27, 1435-1443, 1985.

5. Ayazi Shamlou, P., Stavrinides, S., Titchener-Hooker, N., Hoare, M., Growth independent breakage
frequency of protein precipitates in turbulently agitated bioreactors, Chemical Engineering Science, 49,
2647-2656, 1994.
ICEF9-2004 International Conference Engineering and Food Article No. 554

6. Devereux, N., Hoare, M., Dunhill, P., The development of improved methods for the industrial
recovery of protein methods, Solid-Liquid Separation-11, Gregory, J., (Ed), Ellis-Horwood Ltd,
Chichester, England, 1984.

7. Byrne, E.P., Fitzpatrick, J.J., Investigation of how agitation during precipitation and subsequent
processing affects the particle size distribution and separation of α-lactalbumin enriched whey protein
precipitates, Biochemical Engineering Journal, 10, 17-25, 2002.

8. Byrne, E.P., Fitzpatrick, J.J., Pampel, L.W. and Titchener-Hooker, N.J., Influence of shear on
particle size and fractal dimension of whey protein precipitates: implications for scale-up and
centrifugal clarification efficiency, Chemical Engineering Science, 57, 3767-3779, 2002.

9. Ayazi Shamlou, P., Stavrinides, S., Titchener-Hooker, N., Hoare, M., Turbulent breakage of protein
precipitates in mechanically stirred bioreactors, Bioprocess Engineering, 14, 237-243, 1996.

10. Mannweiler, K., Hoare, M., The scale down of an industrial disc stack centrifuge, Bioprocess
Engineering, 8, 19-25, 1992.
ICEF9 – 2004

International Conference Engineering and Food

A Numerical Method for Virtual Cleaning Testing

Jensen B.B.B. (1) and Friis A. (2)

(1) Food Process Engineering Group, BioCentrum-DTU, Soltofts Plads, build 221,
2800 Lyngby, Denmark
bbb@biocentrum.dtu.dk
(2) Food Process Engineering Group, BioCentrum-DTU, Soltofts Plads, build. 221,
2800 Lyngby, Denmark
af@biocentrum.dtu.dk

Abstract
A numerical method based on Computational Fluid Dynamics was developed for
optimisation of the hygienic state of food processing equipment. The numerical
method allows equipment manufacturer to predict cleanability as an integrated part of
the design phase. Cleanability was predicted across different flows utilising fluid
exchange, wall shear stress, dynamics of flow patterns and turbulence parameters.

Keywords: CFD, Hygienic design, RFC, EHEDG, Food Processing

Introduction
The existence of a tool for visual prediction of difficult to clean areas in a piece of
closed processing equipment is almost a reality as will be shown in this paper. Such
a tool can assist:
• design engineers in prediction of areas that are a potential hazard. This is now
possible in the entire design process.
• sales and marketing people for convincing costumers that their product has a
superb hygienic design and show why it is so.
• in setting up cleaning-in-place programs, and to identify what equipment to
dismantle and give a manual cleaning.
• authors of guidelines to get increased understanding of why certain flow
features are advantageous with respect to cleaning and why others are not
• in evaluation of CIP procedures as areas for sampling can be found using this
tool
• hygienic design course and in-house teachers for teaching operators, cleaning
staff and maintainers. The tools allows for visualising why certain designs are
problematic
• etc.

With the recent research (1, 2, 3 and 4), a tool for predicting cleanability is no longer
a phantom. The conclusion of the work presented in this paper is that potentially
difficult to clean areas can, in fact, be predicted from a critical wall shear stress for a
particular cleaning situation (soil, surface and CIP) and by combining knowledge of
the wall shear stress and fluid exchange in a component (as illustrated in Table 1).
This paper gives an example of predicted cleanability.
ICEF9 – 2004

International Conference Engineering and Food

Table 1: Proposed combinations of wall shear stress and fluid exchange that is needed in order to
remove a certain type of soil by a certain CIP procedure from a certain surface.

High exchange Normal exchange Low exchange

High force Cleaned Cleaned Both

Critical force Cleaned Both Uncleaned

Low force Both Uncleaned Uncleaned

Description of the ”Virtual Cleaning Test”

The virtual cleaning test described in this paper assumes the existents of a critical
wall shear stress when the fluid exchange is independent of the wall shear stress
magnitude.

The first action to take in the virtual cleaning test outlined in Figure 1, was to find a
critical wall shear stress for the cleaning test investigated, in this case the European
Hygienic and Engineering Design Group (EHEDG) test. The critical wall shear stress
was found from cleaning experiments in a radial flowcell (RFC) as described in (1).
The wall shear stress generated from the flow through the RFC was predicted from
Computational Fluid Dynamics (CFD) simulations. In theory the critical wall shear
stress is universal for the CIP procedure investigated.

Prediction of areas difficult to clean was done from a transient CFD simulation of the
flow in the component investigated. The obvious approach was to identify areas with
wall shear stress below the critical wall shear stress. However, investigations showed
that satisfactory predictions were unreachable (2, 3 and 4). This can be explained by

Figure 1: The procedure and steps of the virtual cleaning test on a mixproof valve. The component
tested could be any piece of closed processing equipment.
ICEF9 – 2004

International Conference Engineering and Food

the fact that inside geometries, that are different from a straight pipe or a duct, the
fluid exchange depends on the flow patterns. Including qualitative information on fluid
exchange from the transient CFD simulation proves to give good predictions of
cleanability. A method involving the quantitative fluid exchange is investigated.

Incitement
An essential, but often overseen, part of food processing is the cleaning of closed
processing equipment. Most manufacturers producing food are aware of the fact that
cleaning is required to avoid microorganism caused spoilage and, in the worst-case,
food related diseases, with following death. Frequent cleaning-in-place (CIP) along
with occasionally dismantling of equipment is performed to prevent contamination of
the product. The cleaning of closed processing equipment is linked to the CIP
procedure through contact time, temperature, chemicals and mechanical force on
the surface. The magnitude of time, temperature and chemicals all has an impact on
the expenses of the cleaning procedure. Time with respect to money and
wastewater; temperature with respect to money and indirect pollution as the energy
to raise the temperature most often comes from combustion of fossil fuels; and
finally chemicals are expensive and wastewater treatment is required in order to
decrease environmental stresses. The mechanical action on the other hand, and
closely linked here to also the mechanisms of distributing CIP liquid, is possible to
increase/change by altering the design of a process line or a specific component. To
do such changes knowledge of the influence of different flow patterns on the
cleaning effect is very important.

In Europe normative document (e.g. EN1672-2) and voluntary guidelines exists (the
EHEDG guidelines). The normative documents give the basic rules to be respected
for processing equipment and layout of processing plants. The guidelines offer a
more elaborate introduction into the basic rules, tips and hints of good hygienic
design for both closed and open processing equipment. The guidelines of EHEDG
also present an actual cleaning test for closed processing equipment (5). The
cleaning test is based on the philosophy that each single component of a processing
plant has to be just as, or more cleanable than, a straight piece of stainless steel
pipe with a pre-defined surface roughness and with a dimension of the same size as
the dimension of the inlet pipe of the equipment to be tested. If a component passes
the test and also respects the basic design criteria’s, a certificate is given for good
hygienic design.

The incitement for the work presented in this paper is two sided. Firstly, it would be
of great benefit to manufacturers of food processing equipment to be able to predict
the outcome of the EHEDG cleaning test. Hence, cleaning test can be done virtually
by simulations, which allows comparing of many different design changes with
respect to cleaning. Secondly, making a virtual cleaning test that show the effect of
fluid flow on cleaning in processing equipment increases the understanding of why
some flow phenomenons increases the cleaning effect and why some do not (see
(6)). This could set new standards for equipment design.

Experimental Method
Two series of cleaning trails was performed; one series of experiments in a Radial
Flowcell (RFC) (1) and one series in a mixproof valve with spherical shaped valve
ICEF9 – 2004

International Conference Engineering and Food

houses (4). All cleaning trails were based on the EHEDG cleaning trail (5) with a few
modifications for the purpose of this work. The cleaning method and changes are
thoroughly described in (4) for the mixproof valve and for the radial flowcell the
experiments and results are thoroughly described in (1).

The most important points to make on the EHEDG cleaning method is that the CIP
procedure is a very mild one to ensure uncleaned areas in the reference pipe and
the component. Otherwise a comparison is difficult to do. The results from the
cleaning test are given as discoloured agar in the areas not properly cleaned.

The cleaning trails on the mixproof valve were performed in steady-state mode in
order not to influence the flow from movements of the stem and seat. During CIP a
mixproof valve spends most time having flow going straight through each valve
house.

Numerical Method
The numerical method used here was the finite volume method based on
discretisation of the Navier-Stokes equations:

∂ (ρφ )  ∂u ′φ ′ ∂ vuφ ′ ∂ w′φ ′ 

+ div( ρφU ) = div(Γφ gradφ ) + − − −  + Sφ
∂t  ∂ x ∂y ∂z 

Discretisation of the Navier-Stokes equations was done by a 2nd order self-filtered

central difference scheme and the pressure was couple to the mass flow by the
SIMPLE algorithm. Transport of turbulent kinetic energy and its dissipation was done
using the RNG k-ε model. Technical information on the models can be found in e.g.
(7). Transient simulations were performed in order to predict the fluid exchange. For
wall shear stress predictions a steady state simulation is sufficient. The flow domain
of the mixproof valve was divided into approximately 160,000 hexahedral shaped
cells. Thorough information of the mesh and validation of the simulation by
comparison to laser sheet visualisation and laser Doppler anemometry
measurements are presented in (8). The most important point to make on the mesh
generation is the treatment of the near-wall region. As near-wall features (wall shear
stress and fluid exchange in the near-wall region) is important to the cleaning effect
special attention was given to the mesh in the near-wall region. The two-layer
approach of Norris and Reynolds (9) was implemented in order to resolve the flow in
the boundary layer region close to the wall. Hence, the non-dimensional distance
(y+) between the wall and the first grid point was below 3 everywhere in the valve
house. The high importance of near-wall treatment and resolution in the near-wall
region on the magnitude of wall shear stress and positions of local extremes are
shown in (10).

Results and Discussion

It was shown that the result of the cleaning test on four different components could
be roughly predicted by comparing the critical wall shear stress (3.5 Pa for the
EHEDG test) found in (1) with the wall shear stresses in the component found by
CFD simulations (4 and 8). The four components were; a mixproof valve with
spherical valve houses, a simplified “mixproof valve” with square houses, a short
ICEF9 – 2004

International Conference Engineering and Food

upstand and a filler valve. To improve the predictions it was found that a qualitative
comparison of the fluid exchange in the near–wall zone of a component could
explain why some areas with wall shear stress as low as 1/10th of the critical wall
shear stress was, in fact, cleaned and why areas exposed to wall shear stresses
much higher than the critical wall shear stress could not be cleaned (10)! An
example on predicted cleanability is show in Figure 2.

A B

C
Figure 2: An example of the match between results from two experiments (C), that predicted using the
critical wall shear stress (A) and as an extra aid the fluid exchange predicted by CFD in a square
valve house (flow from left to right). Picture (C) show the experimental results on the two sides of the
square valve house (dark grey is experiment one, and light grey is experiment two). In picture (A) the
dark areas are exposed to wall shear stress below 3.5 Pa and the white area above 3.5 Pa (the
critical wall shear stress found in (1). In picture (B), dark colour represents the new fluid, while the
brighter colours represent mixtures of new and old fluid. That is areas of slow fluid exchange. For
results from the valve with spherical shaped valve houses reference is given to (4).

Figure 2 shows that almost the entire of the valve house sidewalls was predicted
uncleaned because of low wall shear stress. Only small areas near the top, bottom
and outlet had wall shear stress above 3.5 Pa. Comparing that to the results from
the cleaning test showed that areas of very low wall shear stress actually was
cleaned and the part close to the outlet was not cleaned, even though large wall
shear stresses were present in this region. The fluid exchange explains this. Fluid
exchange was relatively slow in the uncleaned area close to the outlet. Areas of low
wall shear stress that was found cleaned is shown to have a fluid exchange that was
larger than the areas of same wall shear stress that was not cleaned.

Conclusion
The basis for a tool for evaluating the cleanability of a closed processing component
has been presented. The results are very promising on four different geometries.
However, work is still required on the subject of quantifying the combination of wall
shear stress level and fluid exchange, as illustrated in Table 1, that are required to
remove the EHEDG soil during an EHEDG test.

As transient simulations of fluid flow is very time consuming a method using only
steady state simulations is also being investigated. Based in the work of Lelièvre et
al. (3), a model trying to predict the relative magnitude of the fluctuating part of the
wall shear stress using steady state simulations is under development. This shortens
the simulation time dramatically and a faster design process is possible.
ICEF9 – 2004

International Conference Engineering and Food

Acknowledgement

The study was supported by a grant from The Danish Agency for Trading and
Industry of the Danish Ministry of Commerce. The authors also express their
gratitude to Jens Folkmar Andersen and Preben Esbensen, Alfa Laval LKM A/S,
Kolding, Denmark; Erik-Ole Jensen, Arla Foods amba, Viby, Denmark; Kersti
Haugan, Novadan, Kolding, Denmark; Michael Dahl, Biotechnological Institute,
Kolding, Denmark; Professor Jens-Adler Nissen and Food technician Helle V.
Mathiasen both BioCentrum, DTU for their dedicated work and fruitful discussions.

Reference list
1
Jensen, B.B.B., Friis, A. Critical Wall Shear Stress for the EHEDG Test Method.
Chemical Engineering and Processing. In Press, 2003.
2
Jensen, B.B.B., Adler-Nissen, J., Andersen, J.F., Friis, A. Prediction of cleanability
in food processing equipment using CFD. Proceedings of the Eighth International
Congress on Engineering and Food (ICEF8), Welti-Chanes, J., Barbosa-Canvas,
G.V. and Aguilera, J.M. (eds.), Technomic Publishing Co., Lancaster Pennsylvania,
Volume II, Chapter XIII.3: 1859-1863, 2000.
3
Lelièvre, C., Legentilhomme, P., Gaucher, C., Legrand, J., Faille, C., Bénézech, T.
Cleaning in place: effect of local wall shear stress variation on bacterial removal from
stainless steel equipment. Chemical Engineering Science, 57, 1287-1297. 2002.
4
Jensen, B.B.B., Friis, A. Predicting the Cleanability of Mix-proof Valves by use of
Wall Shear Stress. Journal of Food Process Engineering. Submitted. 2003.
5
Timperley, A.W., Bourion, F., Bénézech, T., Carpentier, B., Curiel, G.J., Haugan, K.,
Hofman, J., Kastelein, J., Ronner, U., Tragardh, C., Wirtanen G. “A Method for the
Assessment of In-Place Cleanability of Food Processing Equipment”. EHEDG, 2nd
ed., 1-14, 2000.
6
Friis, A., Jensen, B.B.B. Prediction of Hygiene in Food Processing Equipment using
Flow Modelling. Trans IchemE, Part C: Food and Bioproducts Processing. Vol
80,281-285. 2002.
7
Versteeg, H.K., Malalasekera, W. “An Introduction to Computational Fluid Dynamics
- The finite Volume Method (1 ed.)”. Longman Scientific and Technical, Essex,
England. 1995.
8
Jensen, B.B.B., Friis, A. Prediction of Flow in Mix-Proof Valve by use of CFD –
Validation by LDA. Journal of Food Process Engineering. Submitted. 2003.
9
Norris, L. H., Reynolds, W. C. “Turbulent Channel Flow with a Moving Wavy
Boundary”. FM-10, Stanford University, USA. 1975.
10
Jensen, B.B.B. “Hygienic Design of Food Processing Equipment by use of
Computational Fluid Dynamics”. BioCentrum-DTU, Technical University of Denmark,
Lyngby, Denmark, 2003.
 ICEF9-2004 1

DIFFUSION OF SUBSTRATES AND METABOLITES WITHIN SOLID MEDIUM IN RELATION WITH

THE GROWTH OF Penicillium camembertii
ALDARF Mazen, AZIZA Majda, FOURCADE Florence, AMRANE Abdeltif

Laboratoire des Procédés de Séparation, Université de Rennes 1, U.C. INRA, 263 Avenue du
Général Leclerc, CS 74205, 35042 Rennes Cedex, France
abdeltif.amrane@univ-rennes1.fr

ABSTRACT
A diffusion/reaction model predicting the evolution of the gradient concentrations of substrates
consumed and metabolites released within solid model media has been developed and found to
match experimental gradient concentrations until the end of growth. All the parameters can be
experimentally determined and have a clear biological meaning. The model provides an insight into
the possible limitations in solid model media.

Key words: Penicillium camembertii, Solid-state fermentation, growth, diffusion,

Modelization.

INTRODUCTION
Camembert is one of the most famous cheese in France. Thanks to its gustative quality, it has become
a mass market product.
The ripening process plays an essential role in soft camembert cheese manufacture because curd
texturization and organoleptic characteristics responsible for the gustative properties of the final
product appear during this phase.
For many years, it has been known that the texturization results from the neutralization of the curd
during ripening[1-4], which is a consequence of the growth of Geotrichum candidum and Penicillium
camembertii on the surface of the cheese[5, 6]. Indeed both fungi assimilate lactic acid present in the
curd as a carbon and energy source[1, 3], and the peptides as nitrogen source resulting in the release
of ammonia[6, 7].
The consumption of lactic acid by the microorganisms induces a diffusion of this specie from the core
to the rind resulting in a concentration gradient. In a similar way, ammonium release at the surface of
the curd induces a diffusion of this component from the rind to the core. These diffusional mechanisms
appear therefore as one of the main factors in soft cheese manufacturing.
To our knowledge, no work concerning the diffusional mechanisms, resulting from the concentration
gradients of mineral elements, substrates or metabolites, induced by fungal growth are available in the
literature. Only few studies concerning the mineral migration of calcium and phosphorus[5] and some
salts[8, 9], all under pH control, can be found. These authors have examined the mineral distribution
between the rind, the under-rind and the center of cheeses or model cheeses.
The main purpose of this paper is to study the diffusional mechanisms and to propose a theoretical
approach which can be subsequently applied to curd during ripening for its monitoring and control. In
this aim, a diffusion / reaction model has been developed: the diffusion of lactate from the bottom of
the gel to the upper surface or that of ammonium from top to bottom induced by their respective
 ICEF9-2004 2

consumption and production at the surface of the gel due to fungal growth. Pure cultures of Penicillium
camembertii have been chosen as an example to validate the model.
Obviously, a soft cheese during ripening is a rather complex system[9]. Moreover, there is no simple
way to determine the biomass concentration at the surface of the cheese[10]. For a better
understanding of the fundamental phenomena, it appears therefore more suitable, in a first approach,
to mimic the real system (lactic curd during ripening) by cultures of P. camembertii at the surface of
synthetic solid medium. A gelified medium containing, among other things, tryptic casein peptone and
lactate to simulate the aqueous phase of Camembert cheese[11], have been chosen.

MATERIAL AND METHODS

Microorganisms
Freeze-dried spores of the commercial strain Penicillium camembertii LV2 (Rhodia Food, Dangé St
Romain, France) were stored at +7°C. They were rehydrated for 1 h in sterile medium at 25 °C.

Media and Cultures

Cultures were carried out in Petri dishes of 18 cm (internal diameter), at 12 °C and 98 % relative
hygrometry, to simulate the operating conditions in a salting room during the ripening of Camembert
cheese, in a cooling incubator Friocell MMM 111 l (Bioblock, Illkirch, France). The presence of a
saturated solution of K2SO4 in the cooling incubator allowed maintaining the relative hygrometry at
-1
98 %. The composition of the peptone based and lactate medium was (g.L ): agarose, 20 (Biokar
Diagnostics, Beauvais, France), and tryptic casein peptone, 10. Sodium L(+)-lactate (Prolabo, Paris,
France), 10. Both media were supplemented with the following solutions:
-1
- 50 mL.L of EDTA chelated trace elements (TE) [12], the final trace elements concentrations were
-1
(mg.L ): Mg, 25; Fe, 20; Ca, 18; Zn, 4.5; Mo, 2; Cu, 1.3.
-1
- 500 mL.L of inorganic phosphates (Pi), derived from the phosphate solution of Trinci[12], containing
-1
(g.L ): KH2PO4, 3.4; Na2HPO4, 3.55.
The pH of both media was then adjusted to 4.5 with HCl 1M.
500 mL of medium were sterilized (121°C, 20 min) and then poured into the Petri dish. After gelling,
the surface of the medium was inoculated with 10 mL of the suspension of rehydrated spores.

Analysis
During the fermentation, cores were sampled by stamping out the culture with a sterile hollow punch.
By means of tweezers, the thin layers of biomass on the top of the cores were peeled off, dried and
weighted; the total biomass concentration was expressed in gram of dry weight per liter of gel.
The remainder of the solid samples was set in a microtome; slices of approximately 3 mm were then
cut with a razor and weighted. Every slice was put down into an Eppendorf tube and the pH was
measured by sticking a 5 mm diameter combination pH electrode (Mettler Toledo, Viroflay, France)
into the solid sample after homogenization. For lactate and ammonium analysis, every slice was
dissolved by heating in 10 mL distilled water; L(+)-lactate was then determined enzymatically (Sigma
Diagnostics, St Quentin Fallavier, France) and ammonium by the Nessler method[13].
 ICEF9-2004 3

Total nitrogen was determined on a core by the Nessler method [13], after mineralization of the
sample. The subtraction of ammonium concentration in the core from the total nitrogen led to the
peptone concentration at each time.

RESULTS AND DISCUSSION

Mycelial growth can be described using the widespread logistic or Verlhust relation[14-17] (Fig 1):

e µm * t
x = x0 * xm * (1)
x m − x 0 + x 0 * e µm * t
-1
where x and x0, xm are the biomass concentrations (g.L ) at a given time t and its initial and maximal
-1
value respectively, µm is the maximal specific growth rate (day ).

5 a 9 10 b
0.12

4 8 8
0.10

3 7 6 0.08
x (g.L-1)

s, z (g.L-1)

m (g.L-1)
pH

0.06
2 6 4
b
0.04

1 5 2
0.02

0 4 0 0.00
0 3 6 9 12 15 0 3 6 9 12 15

Fig 1. Time-courses of growth (o), alkalinization (•) (a), peptone (•) and lactate (∇) consumptions,
and ammonium release (•) for P. camembertii growing at the surface of the solid medium. Continuous
line: growth modelization using the Verlhust model (Eq. 1).

As previously shown [18], lactate consumption is assumed to be involved in cellular biosynthesis as a

carbon source and in energy supply for growth and cellular maintenance. From this, its consumption
would appear as partially linked to growth and in order to take into account the substrate limitation at
 s 
the end culture, an additional term 1 − res  has been added:
 s 

ds dx s
− = A* + B * x * ( 1 − res ) (2)
dt dt s
With sres being the residual lactate concentration.
The additional term in the above equation (2) has been previously introduced to account for cessation
of lactate production due to substrate limitation [19].
Amino acids contain excess nitrogen in relation to their carbon content [20]. The excess nitrogen is
released as ammonium, after amino acid deamination [21, 22]. As for substrate consumption,
 ICEF9-2004 4

ammonium production resulted from both biosynthesis and viable cell maintenance, and appears
therefore partially linked to growth:

dm dx z
= A* + B * x * ( 1 − res ) (3)
dt dt z
Where m corresponded to the metabolite (ammonium) concentration, zres, the residual peptone
concentration.
z
The additional term ( 1 − res ) in the above equation (3) has been added to account for cessation of
z
ammonium production due to nitrogen substrate limitation (peptones).
A and B, the coefficients for substrate consumption or metabolite production resulting from cellular
biosynthesis and maintenance, associated and non-growth associated respectively
They were determined from the experimental data of lactate and peptones consumption and
ammonium production (Fig 1) and optimized using the EXCEL solver system.

Initially, lactate and peptones were uniformly distributed in the gel at a concentration s0 and z0
respectively. From the initial time t = 0, the biomass grew uniformly at the surface of the gel (y = 0)
following Eq. (1); at the upper surface of the gel (low y), the lactate concentration decreased and the
ammonium concentration increased but remained constant in a cross section of the gel (plane one-
dimensional diffusion). Since the lactate consumption and ammonium production are given by Eqs. (2)
2
and (3), their flux across a section of 1 cm of gel (at y = 0) is given by the following relation:

ds dm
Flux = L * (4) or Flux = L * (5)
dt dt
The flux was nil on all the other limits of the gel: the under side of the Petri dish was impermeable
(y = L) and there was no concentration gradient through the side faces.
Therefore the following partial derivative equation had to be solved (second Fick relation with constant
coefficient diffusion D):

∂ 2s ∂s
D* − =0 (6)
∂y 2 ∂t

With the following initial conditions:

For lactate: t = 0, s(y, 0) = s0, 0 ≤ y ≤ L,
For ammonium: t = 0, m(y, 0) = 0, 0 ≤ y ≤ L

The following limit conditions:

 dx  s 
For lactate: y = 0, Flux = −L *  A * + B * x * 1 − res   (7)
 dt  s 

 dx  z 
For ammonium: y = 0, Flux = L *  A * + B * x * 1 − res   (8)
 dt  z 
And a nil flux on the other sides of the gel.
 ICEF9-2004 5

The numerical resolution of the above systems was carried out using the Galerkin Finite Element
Method (PDease software) to give the concentration profiles s(y) of lactate and ammonium at different
times (Fig 2a and b, respectively).

Lactate (s) consumption started simultaneously with growth. Consumption rate increased until
-1 -1
reaching a value of 0.8 g.L .day after 5 days of culture, followed by a decrease of the rate until
lactate exhaustion at the surface of the medium (Fig 2a).
Resolution of equations (6) and (7) by considering the optimized values of the parameters: A = 1.15, B
-1 2 -1
= 0.185 day , as well as the diffusion coefficient of lactate into the gel D = 0.4 cm .day , gave the
theoretical concentration gradients. As observed, the calculated gradients matched the experimental
gradients from the beginning to the end of growth, namely 9 days of culture.

s (g.L-1) m (g.l-1)
a 0.20 b
days
8
2
3 0.16 days
4
15
6 5
0.12
6
11
4 7
0.08 10
8
8
9
2 7
10 0.04
6

4
0 0.00
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6
y (cm) y (cm)

Fig 2. Concentration gradients of lactate (a) and ammonium (b) induced by their respective
consumption and production by P. camembertii growing at the surface of the solid medium. Symbols:
experimental data points; continuous lines: recalculated diffusion gradients (Eq. 6).

High ammonium concentration (m) gradients were observed from 6 to 8 days of culture (Fig 2b). This
has to be related to the high rate of ammonium production during this part of growth (Fig 1). Indeed,
ammonium production resulted from the deamination of carbon and nitrogen source amino acids [18]
and the carbon requirement for cellular biosynthesis and for cell respiration was high during this part of
growth (Fig 1). During maintenance phase, the production rate decreased and entailed weak
concentration gradients. Resolution of equations (6) and (8) with the optimal values of the parameters:
-1 2 -1
A = 0.008, B = 0.004 day and D = 0.8 cm .day , gave the theoretical concentration gradients of
ammonium, which matched the experimental gradients excepted in the beginning of growth.
 ICEF9-2004 6

In conclusion, the reaction/diffusion model introduced in this work described rather well the
consumption of substrate or the production of metabolite in relation to growth. The validation of the
model on synthetic solid medium can be considered as a preliminary step, which has to be followed by
a similar work on the real medium, lactic curd, in view of the comprehension of the mechanism of curd
neutralization, responsible for texturization development.

1. Lenoir, J., The surface flora and its role in the ripening of cheese. Int. Dairy Fed. Bull., 1984.
171: p. 3-20.
2. Vassal, L. and J.C. Gripon, Bitterness of cheeses on the camembert type: role of rennet and
Penicillium caseicolum, means of its control. Le Lait, 1984. 643-644: p. 397-417.
3. Fox, P.F., J.A. Lucey, and T.M. Cogan, Glycolysis and related reactions during cheese
manufacture and ripening. Crit. Rev. Food Sci. Nutr., 1990. 29: p. 237-253.
4. Molimard, P., et al., Bitterness and nitrogen fractions of mold ripened cheese of Camembert
type: impact of the association of Geotrichum candidum and Penicillium camembertii. Le Lait,
1994. 74: p. 361-374.
5. Le Gräet, Y., et al., Mineral migration in soft cheese during ripening. Le Lait, 1983. 629-630: p.
317-332.
6. Karahadian, C. and R.C. Lindsay, Integrated roles of lactate, ammonia, and calcium in texture
development of mold surface-ripened cheese. J. Dairy Sci., 1987. 70(2): p. 909-918.
7. Lucey, J.A. and P.F. Fox, Importance of calcium and phosphate in cheese manufacture, a
review. J. Dairy Sci., 1993. 76(2): p. 1714-1724.
8. Le Gräet, Y. and G. Brulé, Macro and trace elements migration in Camembert soft cheese
during ripening. Le Lait, 1988. 68: p. 219-234.
9. Gaucheron, F., et al., Evolution of various salt concentrations in the moisture and in the outer
layer and centre of a model cheese during its brining and storage in an ammoniacal
atmosphere. Le Lait, 1999. 79: p. 553-566.
10. Molimard, P., et al., Growth of Penicillium camemberti and Geotrichum candidum in pure and
mixed cultures on experimental mold ripened cheese of Camembert-type. Le Lait, 1995. 75: p.
3-16.
11. Boutrou, R., et al., Changes in the composition of juice expressed from Camembert cheese
during ripening. Le lait, 1999. 79: p. 503-513.
12. Trinci, A.P.J., A kinetic study of the growth of Aspergillus nidulans and other fungi. J. Gen.
Microbiol., 1969. 57: p. 11-24.
13. Rodier, J., Ammoniacal nitrogen analysis., in Water analysis. 1975, Dunod: Paris. p. 116-120.
14. Moraine, R.A. and P. Rogovin, Kinetics of polysaccharide B-1459 fermentation. Biotechnol.
Bioeng., 1966. 8: p. 511-524.
15. Norton, S., C. Lacroix, and J.C. Vuillemard, Kinetic study of continuous whey permeate
fermentation by immobilised Lactobacillus helveticus for lactic acid production. Enzyme
Microb. Technol., 1994. 6: p. 457-466.
16. Diaz, C., et al., On-line analysis and modelling microbial growth using a hybrid system
approach. Process Biochem., 1999. 34: p. 39-47.
17. Pandey, A., C.R. Soccol, and D. Mitchell, New developments in solid state fermentation: I -
bioprocesses and products. Process Biochem., 2000. 35: p. 1153-1169.
18. Aldarf, M., A. Amrane, and Y. Prigent, Reconstruction of the biomass history from carbon and
nitrogen substrate consumption, ammonia release and proton transfer during solid cultures of
Geotrichum candidum and Penicillium camembertii. Appl. Microbiol. Biotechnol., 2002b. 58: p.
823-829.
19. Amrane, A., Batch cultures of supplemented whey permeate using Lactobacillus helveticus:
unstructured model for biomass formation, substrate consumption and lactic acid production.
Enzyme Microb. Technol., 2001. 28: p. 827-834.
20. Deacon, J.W., Modern Mycology. 1997, Oxford, United Kingdom: Blackwell Science Ltd. 303.
21. Hemme, D., M. Ferchichi, and M.J. Desmazeaud, L'avenir des levains lactiques et des levains
non lactiques. I.A.A., 1986: p. 318-324.
22. Cerning, J., et al., Biochemical activities of Penicillium used in cheese making. Le Lait, 1987.
67: p. 3-39.
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n. 922-wine ferment.pdf

WINE FERMENTATION: A DETERMINISTIC MODEL TO STUDY THE YEAST GROWTH CYCLE,

MONITORING SPECIFIC ANALYTES
Altieri C*(1)., Del Nobile M.A. (2), D’Amato D. (3), Corbo M.R. (4), Centonze D. (5), Sinigaglia M. (6)
(1) *corresponding author, - Department of Food Science, University of Foggia, Via Napoli, 25 – 71100 -
Foggia, Italy , c.altieri@unifg.it
(2) Department of Food Science, University of Foggia, Via Napoli, 25 – 71100 - Foggia, Italy,
m.delnobile@unifg.it
(3) Department of Food Science, University of Foggia, Via Napoli, 25 – 71100 - Foggia, Italy,
d.damato@unifg.it
(4) Department of Food Science, University of Foggia, Via Napoli, 25 – 71100 - Foggia, Italy,
m.corbo@unifg.it
(5) Department of Food Science, University of Foggia, Via Napoli, 25 – 71100 - Foggia, Italy,
d.centonze@unifg.it
(6) - Department of Food Science, University of Foggia, Via Napoli, 25 – 71100 - Foggia, Italy,
m.sinigaglia@unifg.it
1. ABSTRACT
The modeling of microbial growth behavior is of great relevance regarding the control of many industrial
process. In this work a deterministic model to predict the growth curve of microorganisms, from inoculation to
death, is presented. To validate the model a Saccharomyces cervisiae strain has been used. Cell, nitrogen,
ethanol and sugar concentration were monitored. The proposed model was successfully fitted to the four
sets of available data. It was possible to quantitatively describe all aspects of the wine fermentation.

KEYWORDS: Predictive microbiology, Modeling, Wine fermentation process, Yeast Growth-Cycle.

2. INTRODUCTION
Fermentation predictability and wine quality is principally dependent on wine yeast attributes even if a
wide range of factors affect the fermentation performances of yeasts. In particular, the ability to adapt to
nutritional deficiency and to cope with the presence of inhibitory substances is of vital importance to
fermentation performance.
Successful yeast adaptation to changes in extracellular parameters during wine fermentation requires
the timely perception (sensing) of chemical or physical environmental parameters followed by transmission of
the information to the relevant cell compartments. Chemical signals include the concentrations of some
nutrients, such as fermentable sugars, assimilable nitrogen, oxygen, vitamins, ergosterol, etc., and the
presence of inhibitory substances such as ethanol, agrochemical residues, killer toxins, etc.. Such complexity
accounts for the difficulty to predict the kinetic behaviour of the fermentation process. In fact, slow and
incomplete alcoholic fermentation are a chronic problem for the wine industry and factors leading to sluggish
and stuck fermentations have been extensively studied and reviewed (Bisson 1999). However, early
diagnosis of the causes of fermentation arrest is critical and currently an incomplete fermentation is not
recognizable until the rate of sugar consumption has been observed to decrease.
A number of models have been developed to predict microbial growth in foods (Baranyi and Roberts
1995, Pruitt and Kamau 1993, Skinner and others 1994, Marin 1999). Many of these models may be
classified as empirical (Mckellar 1997, McKellar and Knight 2000) describing sigmoidal functions that
approximate bacterial growth curves (cell concentration versus time). While empirical model are useful for
correlating a wide range of batch growth data and have predictive value, they fail to provide any real insight
into the underlying mechanisms controlling cell growth. On the contrary, mechanistic models, which are more
complex from a mathematical point of view, give a detailed description of all phenomena involved during cell
growth (Whiting and Cygnarowicz-Provost 1992, Baranyi 1998), providing valuable quantitative information
that can be advantageously used to control (either promoting or inhibiting) microorganism growth.
In the present paper a mechanistic model is developed describing the phenomena behind the dynamic
changes observed in all phases of the investigated experimental system. A deterministic approach was used
to describe the entire wine fermentation process. To evaluate the effect of initial nitrogen concentration, the
proposed model was validated in model systems at two different values of nitrogen content. The ability to
resolve the entire wine fermentation process into the three basic phenomena involved, namely, cell growth,
cell death, cell nutrient consumption and toxic metabolites production, is the main distinguishing feature of
the proposed model in respect to those reported in the literature (Baranyi and others 1993a, 1993b).
3. MATERIALS AND METHODS
3.1 Medium
Fermentations were conducted using 800 ml total volume in 1000 ml Erlenmeyer flasks. The chemically

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defined medium used in this work was similar to that used by Delfini and Costa (1993). The composition of
-1 -1 -1
the standard medium was the following: glucose 200 g · l ; tartaric acid 3 g · l ; L(+)malic acid 2 g · l ;
-1 -1 -1 -1 -1
KH2PO4 1 g · l ; MgSO4 · 7H2O 0.5 g · l ; NaCl 0.1 g · l ; CaCl2 0.1 g · l ; inositol 0.25 g · l ; H3BO3,
-1
ZnSO4, MnCl2, FeCl2, CuSO4, KI, thiamin, calcium pantothenate, pyridoxin, nicotinic acid 100 µg · l ; and
-1
biotin 25 µg · l . In order to evaluate the effect of ammonium the concentrations of (NH4)2HPO4 and
-1 -1
(NH4)2SO4 were 0.225 g·l in the test A and 0.45 g·l in the test B. Initial pH was adjusted to 3.15 with KOH.
It is worth noting that the synthetic medium used in this investigation has been used as wine model system in
fermentation studies by several authors (Delfini and Costa 1993, Garcia and others 1994) because of its
good correspondence with grape juice. Moreover, the musts belonging to different vineyards, and obtained
with different technologies, show variable composition that can influence the yeast metabolism. Therefore,
must is generally not suited either to investigate the underling mechanisms controlling wine fermentation or
to validate a mechanist model.
3.2 Yeast strain
Superlievito DC Saccharomyces cerevisiae (DAL CIN s.p.a., Milano) was used. The inoculum was
5
about 1·10 cfu/ml. Although a typical wine making process is conducted in non-sterile environment involving
more than just one microorganism, a single strain of yeast was used in this study. In fact, fermentation
predictability and wine quality is directly dependent on wine yeast attributes that consist in a rapid
establishment of numerical and metabolic dominance in the early phase of wine fermentation.
3.3 Monitoring and control of the fermentations
Samples were taken each 12 hours, during the period of rapid cell growth, later the samples were taken
every day. The viable cell number was determined by counting the colony forming units (cfu) on Sabouraud
Dextrose Agar (Oxoid, Italy). The plates were incubated at 25°C for 48 hours. The ammonium, glucose and
ethanol concentrations were measured using enzymatic tests kits (La Roche Ltd., Basel Switzerland). In
addition ammonium concentrations were measured using an enzymatic assay (Sigma Chemical Co., Milan
Italy). Fermentations were carried out at 25°C in tri plicate.
3.4 Fitting procedures
To fit the experimental data with the proposed model the Robust method was adopted (Press and
others 1989). There is a double reason for using the Robust method: firstly, the model is not a simple
expression, but it consists of a set of ordinary differential equations that must be numerically solved;
secondly, to proper validate the proposed model the four set available of data (i.e., the concentration of
microorganism, nitrogen, sugar, and ethanol versus time) must be simultaneously fitted.
The criterion used to evaluate goodness of fit was the relative percent difference between experimental
and predicted values or mean relative deviation modulus (Boquet et al. 1978)
The set of differential equations was solved by using a fourth-order Runge-Kutta formula (Press and
others 1989).
4. MODELING
When microorganisms are inoculated into a new extracellular environment, they first try to adapt
themselves to the new media (lag phase). While adapting to the new extracellular environment, both their
proliferation and death rate can be considered negligible (Baranyi and others 1993a, 1993b). Once adapted,
the microorganisms follow their cycle life: they proliferate and die (Baranyi and others 1993a, 1993b). The
proliferation and death rates depend on various factors, such as the state of the extracellular environment
and the state of the cell population. Right after the cells are adapted to the new environment, there are
favorable environmental conditions, such as high nutrient concentration and low concentration of toxic
metabolites. Therefore, the proliferation rate is much higher than the death rate, leading to an increase of the
total microbial population (exponential growth phase). While growing, the living cells gradually change the
state of the extracellular environment (either by reducing the nutrient concentration or by increasing the
concentration of toxic metabolites) from a favorable environment to a continuously less favorable one. As a
consequence, the proliferation rate decreases while the death rate increases, leading to a gradual decrease
of the growth rate (i.e., the difference between the proliferation rate and the death rate) until it falls down to
zero (stationary phase). Later, due to the continuous change of the extracellular environment, the
proliferation rate becomes lower than the death rate, leading to a decrease of the cell concentration (death
phase). Given the above description of the change over time of microbial population in wine fermentation, it
follows that to develop a model able to predict the entire growth curve it is necessary to describe: the rate at
which the cells adapt themselves to the new extracellular media, the proliferation rate, the death rate, and
the rate at which the extracellular environment changes over time, due to the presence of living cells. Even
though the adaptation phase is of crucial importance in determining the efficiency of S. cerevisiae in wine
fermentation, it is generally very fast. Therefore, from the point of view of a kinetic description of the
phenomena involved during fermentation, it is reasonable to neglect the lag phase. In the following the
quantitative description of the above is provided along with the hypothesis used to derive the model.
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The proposed model is based on the assumption that: a) the nitrogen concentration is considered to be
the only factor influencing cell proliferation rate (Bailey and Ollis 1986a); b) the amount of nutrient released
by the dead cells, which contribute to the increase in the overall nutrient concentration, is neglected (Bailey
and Ollis 1986b); c) ethanol concentration is considered the only factor influencing cell death rate ( Ansanay-
Galeote and others 2001).
The proliferation rate of adapted microorganisms depends on both cell concentration and the
physicochemical state of the extracellular environment. As reported above the latter depends only on the
nitrogen concentration. To describe the proliferation rate (R1(t)) of adapted microorganisms a first order
kinetic was used:
{{ } }
R1(t) = µ0 ⋅ exp [N(t)] c − 1 ⋅ P(t )
n
(1)

{ {
The term µ ⋅ exp [N( t)]n c
0 }− 1}is similar to the “inhibition function” introduced by Baranyi and Roberts
(1994), which accounts for the dependence of the proliferation rate on the nitrogen concentration. The
parameter µ0 is the kinetic constant of the cell proliferation phenomenon; for a given value of concentration of
both proliferating cells and nitrogen, the higher is µ0 the higher is the rate of cell proliferation.
As reported in literature the rate at which the proliferating cells die generally follows a first order kinetic
(Baranyi and others 1996):

{[ ]
R 2 (t ) = k 0d ⋅ exp E(t ) d − E T ⋅ P(t)
n
} (2)
Where R2(t) is the death rate (cfu/(hg)) at time t.
0
d {[
The term k ⋅ exp E (t) d − E ]
n
T } accounts for the dependence of R2(t) on ethanol concentration.
The parameter ET is related to the threshold value for ethanol concentration over which R2(t) becomes
0
increasingly large, leading to a decrease of cell population. The parameter k is the kinetic constant of the
d
0
cell dying phenomenon; for a given concentration of both proliferating cells and ethanol, the higher is k the
d
higher is the cell death rate.
To evaluate the change in the extracellular environment over time, it was assumed that the rate of
nitrogen consumption is proportional to the proliferation rate as shown in equation (3):

dN (t )
= −
0 {{ } }
µ ⋅ exp [N( t)]n c − 1 ⋅ P(t )
(3)
dt YX / N
The parameter YX/N is a yield coefficient of biomass on nitrogen. The ethanol production has been supposed
to be as a completely non-growth-associated stoichiometric bioconversion of sugar to ethanol (Luedeking
and Piret 1959):
dE(t )
dt
[ ]
= β0 ⋅S( t) ⋅ P(t ) (4) dS( t)
dt
= −
[ ]
β0 ⋅ S(t) ⋅ P(t)
YE / S
(5)

YE/S is the stoichiometric coefficient describing the formation of ethanol from sugar.
According to the above description of the phenomena taking place during wine fermentation, the
concentration of microorganisms is given by the following expression: dP (t ) = R (t ) − R (t) (6)
dt1 2
Equations (3), (4), (5) and (6) form a set of 4 ordinary differential equations, whose unknown are P(t), N(t),
E(t) and S(t), the concentration of microrganisms at timt t (cfu/g), the nitrogen concentration (g/l), the ethanol
concentration in the extracellular environment at time t (g/l) and the sugar concentration in the extracellular
environment (g/l) at time t, respectively. The above system was numerically solved with the following initial
conditions: P(0) = P0, N(0) = N0, E(0) = 0, S(0) = S0, and fitted to the experimental data.
5. RESULTS AND DISCUSSION
To validate the proposed model the yeast growth-cycle in a model wine system was monitored at 25 °C
and at two different values of the initial nitrogen concentration. The concentrations of cells, nitrogen, sugar
and ethanol were monitored during the entire fermentation process. Figures 1-4 show the time course during
fermentation of P(t), N(t), E(t) and S(t). The curves shown in figures 1-4 are the best fit of the proposed
model to the experimental data (the results of the fitting are listed in table 1). It is worth noting that the
proposed model was simultaneously fitted to the four sets of data available (i.e., P(t), N(t), E(t) and S(t)). The

3
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values obtained in the present investigation for E% (the relative percent difference between experimental
and predicted values) in the case of Test A were 14%, 17%, 16% and 27% for P(t), N(t), E(t) and S(t)
respectively, while for Test B the values of E% obtained were 21%, 9.0%, 13% and 20% for P(t), N(t), E(t)
and S(t) respectively. Considering the model was simultaneously fitted to the four sets of data available, the
data shown in figures 1-4, and that reported above for E% are satisfying, thus corroborating the validity of
the approach and the hypothesis used to derive it.
As also reported in the literature (Skinner and others 1994) the strength of a mechanistic model, such
as that proposed in this work, besides its ability to fit the experimental data, is to provide valuable information
on the phenomena involved during the cell growth-cycle. In the following the proposed model is used to
quantitatively describe the evolution of R1(t), R2(t), dE(t)/dt, dN(t)/dt and dS(t)/dt during wine fermentation. All
the curves shown in the figures 5-8 were predicted by means of the proposed model using the data listed in
0
table 1. It is worth noting that with the exception of two parameters (i.e., µ0 and k , where there is a slight
d
superposition of the confidence intervals) the confidence intervals don’t superimpose each other. Therefore,
it is reasonable to assume that the differences between the curves predicted by the model are significant.
Figure 5 shows the time course during fermentation of R1(t) in the case of Test A and Test B. As one
would expect, both curves are bell shaped. In particular, the peak of the curve relative Test A is higher than
that of the curve relative to Test B, and takes place at about the same time. Figure 6 shows R2(t) plotted as a
function of time. As reported in the above figure, the peak relative to Test B is higher than that relative to
Test A and takes place at shorter time. The differences between the two sets of data shown in Figure 1 are a
direct consequence of what reported in figures 5 and 6. In fact, the viable cells grow faster and die slower in
the case of Test A than in the case of Test B. Figure 7 shows the opposite of the rate of nitrogen
consumption plotted as a function of time. In this case the peak of the curve for Test A is lower than that of
the curve for Test B. This is due to the fact that the value of YX/N for Test A is higher than that for Test B.
Figure 8 shows the opposite of the sugar consumption rate plotted as a function of time. As one would
expect, both curves are bell shaped. Contrarily to what shown in figure 5, the peak of the curve relative Test
B is higher than that of the curve relative to Test A. Figure 9 show the ethanol production rate plotted as a
function of time. In this case a behavior similar to that shown in Figure 8 is observed.

1.2

2 0.8

0 0.4

-2 0.0
0 400 800 1200 0 100 200
Time [h] Time [h]
Figure 1 Figure 2

1.2

80 0.8

40
0.4

0
0.0
0 400 800 1200 0 400 800 1200
Time [h] Time [h]
Figure 3 Figure 4

4
 ICEF9-2004
5

2.105
8.105

1.105
4.105

0 0
0 50 100 150 0 400 800 1200
Time [h] Time [h]

Figure 5 Figure 6

2.0

6.10-3

4.10-3 1.0

2.10-3

0 0.0
0 50 100 150 0 200 400 600 800 1000
Time [h] Time [h]

Figure7 Figure8

0.8

0.4

0.0
0 200 400 600 800 1000
Time [h]

Figure 9

6. CONCLUSIONS
A deterministic model to predict the growth curve of microorganisms, from inoculation to death, is
presented. To validate the model a S. cerevisiae strain has been used to conduct wine fermentation tests at
25 °C. Cell, nitrogen, ethanol and sugar concentratio ns were monitored during fermentation. The proposed
model was simultaneously fitted to the four sets of available data. The results obtained are satisfying,
corroborating the validity of the approach and the hypothesis used to derive it. The above results point out
that the large amount of information that can be obtained by fitting the proposed model to the experimental
data far overweight the mathematical complexity characterizing the proposed model.

5
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Table 1 The data reported in the square brackets are the upper and lower limits of the confidence
interval (95%) calculated on the base of 100 converging
*
interactions.
Model Test A Test B
parameters

REFERENCES
1. Bisson L.F. Stuck and sluggish fermentation. µ0 [1/h] 1.32 1.51
American Journal of Enology and Viticulture * *
[1.15, 1.48] [1.42, 1.59]
50,107-119. 1999.
2. Baranyi J., Roberts T.A. Mathematics of predictive nc 0.775 1.31
food microbiology. International Journal of Food
* *
Microbiology 26,199-218. 1995. [0.731, 0.814] [1.29, 1.34]
3. Pruitt K.M., Kamau D.N. Mathematical models of
bacterial growth, inhibition and death under k0 [1/h] 1.85 8.34
d
combined stress conditions. Journal of Industrial [0.365, 8.21]
*
[7.78, 8.62]
*

Microbiology 12,221-231. 1993.

4. Skinner G.E., Larkin J.W., Rhodehamel E.J. nd 1.10 1.25
Mathematical modeling of microbial growth: a * *
review. Journal of Food Safety 14,175-217. 1994. [1.08, 1.11] [1.24, 1.26]
5. Marin R. Alcoholic Fermentation Modeling: Current E  n  l 128 222
T  g d
and Perspectives. American Journal of Enology and   
 l  
Viticolture 50(2),166-178. 1999. [123, 136]
*
[213, 229]
*

6. McKellar R.C., Knight K. A combined discrete-

8 7
continuous model describing the lag phase of YX/N 1.50·10 9.51·10
Listeria monocytogenes. International Journal of 8 8 * 7
[1.46·10 , 1.52·10 ] [9.18·10 ,
Food Microbiology 54,171-180. 2000. 7 *
9.75·10 ]
7. Whiting R.C., Cygnarowicz-Provost M. A
quantitative model for bacterial growth and decline. YE/S 0.411 0.382
Food Microbiology 9,269-277. 1992. * *
[0.401, 0.422] [0.371, 0.394]
8. Baranyi J. Comparison of stochastic and
deterministic concepts of bacterial lag. Journal of
Theoretical Biology 192,403-408. 1998. µ0  g  1.96·10
-10
3.11·10
-10

9. Hajmeer M.N., Basheer I.A., Fung D.Y.C. Marsden  

 h ⋅ cfu  -10 - -10
J.L. A nonlinear response surface model based on [1.90·10 , 2.03·10 [3.00·10 ,
10 * -10 *
] 3.23·10 ]
artificial neural networks for growth of
Saccharomyces cervisiae. Journal of Rapid Methods and Automation 6,103-118. 1998.
10. Baranyi J., Roberts T.A., McClure P. Some properties of a nonautonomous deterministic growth
model describing the adjustment of the bacterial population to a new environment. IMA Journal of
Mathematics Applied in Medicine & Biology 10,293-299. 1993a.
11. Baranyi J., Roberts T.A., McClure P. A non-autonomous differential equation to model bacterial
growth. Food Microbiology 10,43-59. 1993b.
12. Delfini C., Costa A. Effects of the grape must lees and insoluble materials on the alcoholic
fermentation rate and the production of acetic acid, pyruvic acid, and acetaldehyde. American
Journal of Enology and Viticulture 44,86-92. 1993.
13. Garcia M.J., Casp A., Aleixandre J.L. Influenza del ceppo di lievito e della temperatura di
fermentazione sulla concentrazione di alcuni composti volatili. Rivista di Viticoltura ed Enologia
4,29-37. 1994.
14. Press W.H., Flannery B.P., Teukolsky S.A., Vetterling W.T. Numerical Recipes in Pascal.
Cambridge:University Press. p 602-607. 1989.
15. Boquet R., Chirifie J., Iglesias H.A. Equations for Fitting Water Sorption Isotherms of Foods. II.
Evaluation of various Two-Parameters Models. Journal of Food Technology 13,19-327. 1978.
nd
16. Bailey J.E., Ollis D.F. Biochemical Engineering Fundamentals. 2 ed. New York:McGrow-Hill Higher
Education. 375 p. 1986a.
nd
17. Bailey J.E., Ollis D.F. Biochemical Engineering Fundamentals. 2 ed. New York:McGrow-Hill Higher
Education. 397 p. 1986b.
18. Ansanay-Galeote V., Blondin B., Dequin S., Sablayrolles J.M. Stress effect of ethanol on
fermentation kinetics by stationary-phase cells of Saccharomyces cerevisiae. Biotechnology Letters
23,677-681. 2001.
19. Luedecking R., Piret E.L. Kinetic of the lactic acid fermentation. Batch process at controlled pH.
Journal of Biochemistry, Microbiology Technology and Engineering 1,393-412. 1959.

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ICEF9-2003
International Conference Engineering and Food

MODELING OF PARTITION COEFFICIENT IN FOOD/PACKAGING SYSTEM

ARAB TEHRANY. Elmira (1), DESOBRY (2)

(1) Institut National Polytechnique de Lorraine (INPL). Laboratoire de Physicochimie & Génie
Alimentaires. ENSAIA-2.av.de la Forêt de Haye. Boîte postale 172-54505. VANDOEUVRE les Nancy
Cedex (France).
Elmira.Arab-Therany@ensaia.inpl-nancy.fr
(2) Institut National Polytechnique de Lorraine (INPL). Laboratoire de Physicochimie & Génie
Alimentaires. ENSAIA-2.av.de la Forêt de Haye. Boîte postale 172-54505. VANDOEUVRE les Nancy
Cedex (France).
Stephane.Desobry@ensaia.inpl-nancy.fr

ABSTRACT
Partition coefficient of solvents (different chemical structure) determined in past/polymer systems with
CPG-ET (¨Perkin-Elmer) at 25°C. All programs and calculations were carried out with Matlab 6.5 (The
MathWorks Inc) software. Partition coefficient in octanol/water system is linked to various descriptors,
and different physicochemical properties. Partitioning of organic compounds to food or reference
system (octanol/water) depends on the chemical and physical structure of solvent, polymer and food.

KEYWORDS : Food safety, Aromas, Migration modeling, QSPR.

INTODUCTION
Food contamination can result from various interactions between food and packaging materials.
Migration of volatiles, additives, monomers and oligomers from packaging materials into food or
adsorption of volatiles compounds from the food by the polymer have a negative impacts on the
quality of food and many imply a risk to human health. Partition coefficient is important for defined as
the ratio of migrant equilibrium concentration in the polymeric material to its equilibrium concentration,
in the food phase.
The molecular partition coefficient (log P) in octanol/water (reference system) is the physical chemistry
property chosen here to study a wide variety of organic molecules (1). It is a simple measure of the
hydrophobic/hydrophilic character of a given substance.
Structure/property relations (QSPR), widely reported in recent years. They are unquestionably of great
importance in modern chemistry, biochemistry, physical chemistry properties, medicinal chemistry
biological activities and for food safety. A major goal of quantitative structure-property relationship
studies is to find a mathematical relationship between the property under investigation (e.g. Pka,
partition coefficient, etc), and one or more descriptive parameters (descriptors) related to molecule
structure (2, 3, 4).
The value of partition coefficient is dependent on the relative solubility of the material in two very
different polarity solvents that have been correlated to toxicity, carcinogenocity and several molecular
properties. This parameter is available from experimental determinations for extensive series of
molecules, but there are cases where such values are still unknown as, for example, when molecules
are completely new or/and when experimental determination is rather difficult or subject to large
uncertainties (5).

METHOD
The partition coefficient of a solute may be approximated by its relative solubility in two solvents.
There are three major forces that affect the solubility of a molecule in a solvent: hydrophobic,
dispersive, and electrostatic interactions. Log Pow is to correlate with fundamental physicochemical
properties. Log P values have been calculated from constitutional and Quantum-chemical descriptors.
Constitutional descriptors depend fundamentally on the composition of the molecule. The counts of
atoms of different elements and the molecular weight reflect the composition. In addition, quantum-
chemical calculations can provide varied information about chemical structure including geometric and
electrostatic data. They have clarified of the detailed intra- and intermolecular interaction mechanisms
determining include the energies (total energy and binding energy), dipole moments, polarity indices,
molecular polarizability, orbital electron densities, HOMO and LUMO energies etc.
Octanol-water partition coefficients at 25°C for a diverse set of 42 organic compounds were compiled
from the literature and these are listed in table 1 as log Pow. This heterogeneous set of compounds
includes aromatic and nonaromatic hydrocarbons, alcohols, carboxylic acids, aldehydes, amines,
ketones, and esters.

1
ICEF9-2003
International Conference Engineering and Food

Table 1. Experimental and calculated log P values

Name Molecular Hansen Total Boiling Binding Percent Percent log P exp log P
Weights Polarity* Energy* Point* Energy* oxygen H (6.7.8)
cal
methanol 32.04 12.28 -28.56 54.02 -1.76 49.93 12.58 -0.77 -0.46
ethanol 46.06 8.80 -37.25 78.89 -3.01 34.74 13.12 -0.31 -0.23
1-propanol 60.09 6.87 -45.94 97.12 -4.26 26.62 13.41 0.25 0.22
1-butanol 74.12 5.65 -54.63 116.92 -5.50 21.58 13.59 0.88 0.72
1-pentanol 88.114 4.49 -63.32 138.63 -6.75 18.15 13.72 1.56 1.31
1-hexanol 102.17 3.91 -72.01 160.64 -8.00 15.65 13.81 2.03 1.88
1-heptanol 116.2 3.59 -80.70 182.29 -9.24 13.76 13.87 2.38 2.45
1-octanol 130.23 3.23 -89.39 160.64 -10.49 12.28 13.93 2.88 3.39
2-methyl3-pentanol 102.17 6.05 -72.00 135.83 -7.99 13.81 70.53 2.03 1.82
methane 16.04 0.00 -10.11 -164.00 -1.39 0.00 25.13 1.09 0.67
ethane 30.06 0.00 -18.80 -88.60 -2.64 0.00 20.11 1.81 1.81
propane 44.09 0.00 -27.49 -44.69 -3.89 0.00 18.28 2.36 2.44
butane 58.12 0.00 -36.18 -0.70 -5.14 0.00 17.34 2.89 2.87
pentane 72.15 0.00 -44.87 35.52 -6.38 0.00 16.76 3.39 3.25
hexane 86.17 0.00 -53.56 68.13 -7.63 0.00 16.37 3.90 3.64
heptane 100.2 0.00 -62.25 97.89 -8.88 0.00 16.09 4.66 4.04
octane 114.23 0.00 -70.94 125.30 -10.12 0.00 15.88 5.18 4.42
methanal 30.02 18.76 -26.83 -19.50 -1.30 53.28 6.71 0.35 0.28
propanal 58.08 6.34 -44.22 47.43 -3.81 27.54 10.41 0.59 0.75
butanal 72.10 5.27 -52.91 77.41 -5.06 22.18 11.18 0.88 1.01
pentanal 86.13 4.45 -61.60 103.06 -6.31 18.57 11.70 1.31 1.42
hexanal 100.16 3.86 -70.29 128.00 -7.55 15.97 12.07 1.78 1.87
heptanal 114.18 3.40 -78.98 151.93 -8.80 12.47 12.35 2.42 2.38
acetone 58.08 10.39 -44.24 56.21 -3.83 27.54 10.41 -0.24 0.29
2-butanone 72.10 9.01 -52.93 73.11 -5.08 22.18 11.18 0.29 0.69
2-pentanone 86.13 7.73 -61.62 102.72 -6.32 18.57 11.70 0.91 1.09
2-hexanone 100.16 6.77 -70.31 128.08 -7.57 15.97 12.07 1.38 1.60
2-heptanone 114.18 5.96 -78.99 152.43 -8.81 14.01 12.35 1.98 2.13
2-octanone 128.21 5.33 -87.68 175.67 -10.06 12.47 12.57 2.37 2.71
acetic acid 60.05 7.91 -54.01 104.90 -2.96 53.28 6.71 -0.17 -0.79
methyl acetate 74.07 7.24 -62.68 35.82 -4.19 43.19 8.16 0.18 0.02
ethyl acetate 88.10 5.35 -71.38 55.97 -5.44 31.33 9.15 0.73 0.59
Isopropyl acetate 102.13 4.65 -80.07 73.18 -6.69 36.31 9.86 1.21 1.20
decanoic acid 172.26 5.25 -123.52 261.16 -12.93 18.57 11.70 3.91 4.04
methyl cinnamate 162.18 9.12 -115.32 222.63 -11.12 19.72 6.21 2.79 2.26
p-cymene 134.22 0.72 -81.86 177.68 -11.27 0.00 10.51 4.10 4.63
methylamine 31.05 8.05 -22.56 -6.79 -2.12 0.00 16.22 -0.57 -0.58
ethylamine 45.08 6.02 -31.25 16.61 -3.37 0.00 15.64 -0.13 0.20
propylamine 59.11 4.93 -39.94 47.73 -4.62 0.00 15.34 0.48 0.78
limonene 136.23 0.97 -83.47 181.85 -11.60 37.46 11.83 4.20 4.67
butyrolactone 86.09 16.59 -69.94 204.56 -5.29 37.16 7.02 -0.64 -1.26
isoamyl alcohol 88.14 4.55 -63.31 135.38 -6.74 18.15 13.72 1.42 1.30
benzoate methyl 136.15 9.77 -99.68 176.04 -9.08 23.50 5.92 2.10 1.54
isoamyl acetat 130.18 3.27 -97.44 130.08 -9.18 24.57 10.83 2.13 2.49
acetaldehyde 44.05 8.00 -35.53 19.66 -2.57 36.31 9.15 0.43 0.68
2-methyl propanal 72.10 5.28 -52.91 62.81 -5.06 22.18 11.18 1.48 1.12
diacetyle 86.09 13.42 -69.66 141.74 -5.00 37.16 7.02 -1.50 -1.05
butyl acetate 116.15 3.63 -88.76 110.33 -7.94 27.54 10.41 1.00 1.79
vanillin 152.14 9.90 -118.12 230.80 -9.44 31.54 5.29 1.23 1.52

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furaldehyde 96.08 14.86 -75.18 48.99 -5.64 0.00 4.19 0.41 0.17
Ethyl benzoate 150.17 8.60 -108.37 190.96 -10.33 21.30 6.71 1.84 2.29
*Hansen polarity:delta/sqr(Mpa),Total Energ and Binding Energy: Atomic units, Boiling point: (degrees C)
In the present article, there is a correlation between the observed partition coefficient of the molecules
and some structural descriptors that make up a molecule. The molecular descriptors for each
compound were calculated from knowledge of the Molecular Modeling Pro, version 5 (Chemsw
Software Inc). All programs and calculations were carried out with MATLAB 6.5 (The MathWorks Inc)
software. A program then identifies the parameters of a classical 2nd order polynomial model. The
general form of the equation was as follows:
N N −1 N N
log P = a0 + ∑xi
i ai + ∑ ∑ xi x j bij + ∑ xi2 ci (1)
i =1 j =i +1 i =1
where a0, ai, bij, ci are constant, xi is the ith structural descriptor considered in this model. In the first
time, we used a 10 parameters model: polarity, total energy, boiling point, binding energy, solubility,
mass percent of carbon, hydrogen, oxygen, nitrogen, and molecular weight. Results show that some
parameters are correlated and thus some results pointed out some structural descriptors which seems
to have not influence on the accuracy/quantify of the model. They have thus been discarded. In
simplification reason, interactions have also been neglected. We decreased the number of factors
down to 7.

RESULTS AND DISCUSSION

We generated our model for log P calculation by analyzing 42 compounds of diverse structures.
Our model was based on the 7 molecular descriptors.

log P=4.945 - 0.106P + 0.252E - 7× 10-3B – 2.159Be - 0.237H + 0.039O - 6×10-4M2 +10-3E2 (2)

where P is the polarity, E is the total energy, B is the boiling point, Be is the binding energy, H, O are
the mass percent for hydrogen, oxygen, respectively and M is the molecular weight.
We validated our model with 9 different molecules (ethanol, hexanol, butanal, 2-hexanone,
methylamine, limonene, isoamyl alcohol, vanillin and ethyl benzoate) which were not taken into
account in the identification step.
Values for r2 of 0.941 and 0.983 were found for equation (2) and model validation, respectively. The
experimental and calculated log P values for the different series of molecules are presented in table 1,
where one can verify the good agreement between both results. Student analysis presented the
validation of the coefficient for our model in table 2. It shows that all of the coefficients are significant.
A is the coefficient of model, ∆A is the variation.
Table 2. Statistical analyze

A A- ∆A A + ∆A
4.5637 4.9455 5.3273
-0.1151 -0.1069 -0.0986
0.2408 0.2528 0.2648
-0.0081 -0.0075 -0.0070
-2.2442 -2.1595 -2.0748
-0.2522 -0.2370 -0.2219
0.0371 0.0399 0.0427
-0.0007 -0.0006 -0.0006
0.0015 0.0017 0.0018

The relation of log P values calculated using equation 2 and the corresponding experimental values
showed in Figures 1 and 2.

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Figure 1. Correlation between experimental log P and Figure 2. Correlation between experimental log P and Calculated
Calculated log P from equation 2 for 42 compounds log P from equation 2 from validation model for 9 molecules

The goal of these studies is to find both the best regression model for the prediction of log P, and also
to determine which types of descriptors are the most sensitive to log P. Importance of each descriptors
showed in table 3.

Table 3. Molecular Descriptors

Descriptors Depends on
Molecular weight Characteristic of the atomic composition of a molecule
Mass percent of an Number of atoms of that type per molecule
atom
polarity Measure of polarity of the molecules (molecules with localized
positive and negative regions are said to be polar)

Boiling point Molecular dipole moment, H-bonding, presence or absence of

heteroatoms, dimer formation, presence of multiple functional groups
in the molecule, and association forces such as van der waals forces
Total energy (CNDO) Depend on electrostatic, polarization, dispersion and repulsion
Energy terms respectively
Binding energy Is the difference between the total energy of the equilibrium
molecular geometry and the sum of the atomic energies of the
constituent atoms

Although, combination of two types descriptors (Constitutional and Quantum-chemical descriptors)

gave a good result. Molecular weight can be important because the size of the molecule had a great
impact on amounts absorbed, larger molecules being absorbed to a larger extent than the smaller
ones and highly branched molecules were absorbed to a greater extent than linear molecule.
Compounds with higher molecular weights have lower aqueous solubilities. They also tend to be less
volatile. More polar organic compounds tend to have higher water solubilities. Less polar organic
compounds are less soluble. In particular, compounds containing oxygen and nitrogen tend to be
more water-soluble. Number of atoms show the percent of polar and nonpolar atom such as O, H.
Intermolecular hydrogen bonding is expected to increase the hydrophobicity, and although it is
observed in many aromatic systems, it may not be true for aliphatic systems. The boiling point of the
compound is predetermined by the interactions in the liquid. Therefore, it is expected to be related
directly to the chemical structure of the molecule. Also boiling point depends on different descriptors
like Electrostatic, Topological and Quantum-chemical descriptors. They are interesting on energy
binding, hydrophobicity, and transfer of energy. A semiempirical quantum chemistry program (CNDO)
that we have used in our model to calculate the total energy and binding energy of a molecule. CNDO
stands for ‘Complete neglect of differential overlap’. The total energy is the sum of the total one-center
and two-center terms. The one-center energy terms include electron-electron repulsion and electron-

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nuclear attraction. The two-center energy terms include resonance energy, exchange energy,
electron-electron repulsion, electron-nuclear attraction, and nuclear-nuclear repulsion.

PARTITION COEFFICIENT IN FOOD/PACKAGING SYSTEM

MATERIALS AND METHODS

Polyamide (PA) film, thickness 15 µm was manufactured at Danisco Flexible (Barbezieux, France).
The solvents, ethyl acetate (99.7% purity) and acetone (99.5% purity) were purchased from MERCK,
acetaldehyde (99% purity) from LABISI and acetonitrile (99.9% purity) CARLO ERBA.. The solubility in
water at 25 °C 9.1, 10.13, 9.6, 11.7 and their hydrophobocity (Log P) is 0.73, 0.43, -0.24, and -0.33,
respectively. Log P represents the hydrophobocity : the higher Log P, the more hydrophobic a
compound.
Raw paste was supplied in our laboratory at 25°C on 6 types with different percentage of ingredient.
The ingredients were starch, water and butter.

Table 4. showed 6 types of paste

N° of experience Starch (%) Butter (%) Water (%)
1 70 5 25
2 65 10 25
3 60 15 25
4 60 5 35
5 55 10 35
6 50 15 35

APPARATUS
Analyses were carried out on a Perkin-Elmer 8500 Gas Chromatograph with flame ionisation detector
and a 30 m × 0.25 mm fused silica capillary column (Varian, Canada). Operating conditions were:
Azote carrier gas at 2 ml/min and temperature at injector port (250 °C), column (140 °C) and detector
(250 °C). A Perkin-Elmer GP-100 graphics printer was used.

DETERMINATION OF PARTITION COEFFICIENT (KP)

Partitioning of organic compounds between the paste and air was quantified by the method described
previously. 1 gr paste weighted to the nearest mg and sealed in a 9 ml glass vial with a butyl rubber
septum and aluminum crimp cap. Then the vials were injected with 2 µl of solvent. Strips of PA (2×2
cm) was cut in small piece on placed into a 9 ml vial. Then the vials were injected with 2 µl of solvent.
Equilibrium days varied from 1 to 2 days according to solvent and sample. After equilibrium time, 200
µl sample of headspace was injected into the GC by gas tight syringe at 35 °C. Then, we transferred
the paste in the other vial for determination of the amount of solvent in paste.

RESULTS AND DISCUSSION

Part of our research was to determine the relative effects of changes in % fat and % water content on
Kp of the paste. Partition coefficient (Kp) for the compounds between the paste and air showed in
table 5.

Table 5. Partition coefficient of 4 solvents between 6 types of paste and air

Paste 1 113±12 210±7 280±36 697±4
Paste 2 142±36 253±42 320±48 670±67
Paste 3 253±23 314±4 435±5 626±10
Paste 4 112±2 239±26 331±37 681±71
Paste 5 146±28 311±35 350±66 694±71
Paste 6 160±28 327±48 356±42 591±29

For Max % of water (35%), we fined 3 paste in our table : paste 4, 5, 6 with 5, 10, and 15 % of butter
respectively.
The affinity order of the four solvents in the various paste was not always the same. Kp of AE, AA, and
AO increase with % of fat. On the other hand, Kp of AN decrease with increasing of butter from 5% to
15%. We examined the utility of comparing differences in Log P, solubility parameter and the other

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properties to explain these affinity orders. Among solvents, the non-polar Kp’s were mostly affected by
ingredient fat content, while the polar solvents were affected mostly by changes in water content.
According to Log P, AN and AO were more hydrophile than the AA and AE. This property influence on
partition coefficient of each solvent.
Reduced water content affected the partitioning behavior of the solvent. With decreasing of water
content, linear plot of partitioning ratios vs. % of fat for AE, AA, and AO was higher than 35 % water.
The partitioning coefficient of the 4 solvents between polyamide and air during 1 and 2 days of storage
at 20°C are summarized in figure 3.

350

300
partition coefficient

250

200

150

100

50

0
AE AO AA AN

Figure 3: Partition coefficient of 4 solvents between polyamide and air.

Polyamide showed a higher affinity for the polar compound such as acetonitrile. In case of
acetaldehyde, this affinity is higher than ethyl acetate, acetone and acetonitrile. The smaller the
difference between the δ values of two substances the greater the solubility. Other factors important in
prediction of solubility include polarity and hydrogen-bonding character of the substances.
PA, has a solubility parameter near to the δ value of the AA. For this reason, they were absorbed to a
greater extent into this polymer. In addition Kp value of AA which is involved in hydrogen bonding with
PA is higher than AE and AO.

CONCLUSION
Partition coefficient in octanol-water system is linked to various descriptors, and different
physicochemical properties. In this work, we found the most important descriptors to define of physical
meaning and particular property studies.
We demonstrated that the molecular descriptors derived from the constitutional and Quantum-
chemically calculated have wide applicability for determination of log P. The present model get better
results than these obtained with classical octanol-water log P values.
Partitioning of organic compounds to food depends on the chemical and physical structure of
solvent, polymer and food. Some properties of molecule such as the Log P and solubility parameter
influence on partition coefficient. Fat and water content of ingredients are major factors of control.

REFERENCES
(1) Leo, A. J. Calculating log Poct from structures. Chemical Reviews, 93, 1281-1305,1993.
(2) Murugan,R.,Grendze,M.P.,Toomey,J.E.,Katritzky,A.R.,Karelson,M.,Lobanov,V.,Rachwal,P.
Predicting physical properties from molecular structure.CHEMTECH, 17-23,1994.
(3) Katritzky,A.R., Lobanov, V.S., Karelson, M. QSPR : The correlation and quantitative prediction of
chemical and physical properties from structure. Chemical Society Reviews, 279-287,1995.
(4) Katritzky, A. R., Karelson, M., Lobanov, V. S. QSPR as a means of predicting and understanding
chemical and physical properties in terms of structure. Pure and Applied Chemistry, 69, 245-248,
1997.
(5) Dochowicz, P., Castro, E.A. A rather simple method to calculate log P values in QSAR/QSPR
studies. Acta Chimica Slovenica, 47, 281-292, 2000.
(6) Rekker, R. F. The hydrophobic fragmental constant. Ed. Elsevier, New York, 1977.
(7) Hansch, C., Leo, A. Substituent constants for correlation analysis in chemistry and biology. Ed.
Wiley, New York,1979.
(8) Klopman, G., Iroff, L. D. Calculation of partition coefficients by the charge density method. Journal
of Computational Chemistry, 2, 152-160,1981.

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Turbidimetric kinematics of milk during rennet coagulation and relation with composition
(1) (2) (3)
Bornaz S. , Sammari J. et Sahli A.

(1) Ecole Supérieure des Industries Alimentaires de Tunisie – Cité Elkhadra – Tunis (Tunisie)
b_salwa@yahoo.fr
(2) Centre Professionnel en Agro-alimentaire – Cité Elkhadra – Tunis (Tunisie)
(3) Institut National Agronomique de Tunisie - 43, Avenue Charles Nicolle 1082 Tunis (Tunisie)
sahli_inat_tn@yahoo.fr

ABSTRACT
Based on the turbidimetric method, a follow-up of enzymatic coagulation was realised on 18 milk
samples. An empirical model was established based on the general shape of the turbidimetric signal
versus coagulation time. Very good prediction of the experimental data using this model was
obtained. Relationships between characteristic points of the turbidimetric profile were obtained.
Significant correlation between these points, visual time, and milk composition were studied.

Keywords: milk, enzymatic coagulation, composition, turbidimetry, modelling

1. INTRODUCTION
The coagulation of milk, obtained from the physical and chemical modification of native casein
under the action of rennet and/or lactic acid, is the initial and most important phase of cheese making.
It corresponds to an irreversible change of a physical stage, where a milk, initially at a liquid state,
changes to a solid state called gel or coagulum (1). Rennet gel, when observed by an electronic
microscope, appears as a tridimentionnal network of chains and casein micelles enclosing the
aqueous phase (2).
The reticulation of rennet gel is influenced by several factors. Some are linked to the condition of
coagulation. Others depend on the physical and chemical characteristics and technological
treatments of milk (1,3,4). There are several methods to measure the evolution of milk during the
enzymatic coagulation: visual methods, chemical methods, rheological methods, optical methods,
ultrasonic methods, particle canting methods and thermal methods.
In this work, evolution of the enzymatic coagulation of milk through the turbidimetric method was
studied. For a more precise analysis of the experimental curves and a better characterisation of their
singular points related to the aptitude for coagulation of the milk samples, a numerical treatment was
realised. For this purpose, a theoretical model, which has been shown to better describe turbidimetric
kinetics, was used. The objectives are: (1) Outline characteristic relations between coagulation
parameters and (2) Study the influence of milk composition on these parameters.
2. MATERIALS AND METHODS
Eighteen different samples of milk, coming from six selected farms in Tunisia, were collected. In
order to prevent any microbial development, potassium bicarbonate, at 0.06% concentration, was
added to the milk just after collection. Then, the samples were skimmed at 40°C. The following
physical and chemical analysis were run: pH is measured with a pH meter type HANNA. Acidity is
measured according to the norm NT14-32 (5). The density is measured according to the norm NT14-
29 (6). The amount of total nitrogen is evaluated by spectrophotometry with a Milkoscan 4000 (7).
The methods used to determine the calcium and phosphorus levels were, respectively, described by
the Tunisian norms NT 14-52 and NT 14-53 (8,9). Each analysis was run three times.
Gelification tests were done in three stages. The first step was concerned curd preparation at
laboratory scale according to the following procedure: renneting of 1 litre of skimmed milk at its initial
pH with 0.1 ml of a liquid rennet solution (520 mg/l of chymosin, from Rhodia, France). Milk
temperature was maintained at 35 °C. A visual evaluation of the time from the beginning milk fluidity
change "tv" was noticed. Finally, a follow up of milk turbitity during gelification was effected using
turbidimeter HACH model 2100AN. This test was realised under the same renneting conditions as
those used for micro making of curd. All these tests were done threefold.
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3. RESULTS AND DISCUSSIONS

3.1. Physical and chemical characterisation of the raw material
Results concerning physical and chemical characteristics of the 18 samples of skimmed milk are
summarised in table 1. These results are compared to those mentioned in the literature (10).
Table 1. Physical and chemical characteristics of skimmed milk samples
Parameters MIN MAX MEAN CV (%)
pH 6.6 7.0 6.8 2.0
Acidity (°Dornic) 15.0 17.0 16.3 4.5
Total solid fat free (%) 7.3 9.2 8.4 6.6
Density 1.029 1.037 1.033 0.2
Total nitrogen (g/l) 22.5 39.1 32.2 16.4
Phosphorus (g/l) 0.15 1.69 0.63 84.6
Calcium (g/l) 0.67 1.09 0.93 13.8

However, one of these samples showed a very low protein content. This is also the case of
phosphorus content for some samples. At the same time, the interval of variation is particularly large
concerning this element.
3.2. The follow up of coagulation by turbidimetric and visual methods
3.2.1. General description of coagulation kinetics
Figure 1 represents an example of turbidimetric signals evolution during rennet coagulation,
obtained from one of the studied samples. The curve represented in figure 1a gives the variation of
milk turbidity in function of time. Figure 1b represents the evolution of speed coagulation as a
function of time. In a first approach, the kinetics of rennet coagulation of milk shows a sigmoïdal
profile. In accordance with subsequent works (11,12), three stages emerge: stage one of latency
through which a law variation of turbidity is observed. This stage corresponds to a stage of enzymatic
hydrolysis. It is situated between "t0" and "t100", "t100" being the time corresponding to turbidity
variation of 100 NTU. The second stage corresponds to a high increase of turbidity. It is characterised
by the presence of an inflexion point of the turbidimetric signal (ti, Ti), materialised by a peak in speed
curve. This stage is situated between "t100" and "tg". The gelification point (tg, Tg) is represented in the
derivation curve, either by a change in the slope, or by the presence of a second peak.

8500 50 Inf lexion point

)
-1

Coagulation point
Turbidimetric speed (NTU min

40
Tc 8000
Turbidity (NTU)

Tg Gelif ication point

30
7500
Ti
Gelification point 20
Coagulation point
Tmilk-100
Tmilk 7000 10
Inf lexion point

6500 0
0 30 60 90 120 0 30 60 90 120
t0 t100 ti t g tc
Tim e (m inute) Tim e (m inute)

(a) (b)
Figure 1. Turbidimetric kinematics of the milk during rennet coagulation. (a) Turbidimetric signal and
(b) turbidimetric speed
During the second stage, size increase, aggregation of particles and coagulation proper of the milk
are observed (11,12). In a third stage, starting at time "tg", a constant level is reached when the gel is
made. It is a gel restucturation stage.
3.2.2. Experimental results
The extremes and means experimental values of characteristics points of turbidimetric curves
obtained from the 18 milk samples are summarised in table 2.
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Table 2. Characteristic parameters of turbidimetric curves and visual time of

gelification
MIN MAX MEAN CV(%)
Tmilk (NTU) 6980 7970 7504 4%
Ti (NTU) 7410 9250 8122 7%
Tc (NTU) 7980 9910 8943 7%
t100 (minutes) 6 30 16 41%
ti (minutes) 12 84 29 60%
tc (minutes) 64 152 103 26%
tv (minutes) 12 48 21 42%

From these registrations, we can see that, during coagulation, milk goes from an initial turbidity of
7500 NTU to a final turbidity of the coagulum of about 9000 NTU. On another hand, gaps between
samples are relatively low (less than 7%). Concerning the duration of the different stages, these
results show that the hydrolysis stage, identified by the time "t100", last about 16 minutes, but
important gaps have been observed between samples (CV=41%). This high variability in the
behaviour of selected milks has been observed in the registrations of the occurrence time of the
inflexion point "ti" (CV=60%). Also, heterogeneity was seen concerning the time of coagulation "tc"
where extreme times of 64 and 152 minutes have been registered. Comparing these times with time
of the beginning of gelification "tv" observed visually (table 2), it appears that "tv" is situated between
t100 and ti and is characterised by a high variability (CV=42%). This variability between milks for the
characteristic points of the turbidimetric kinetics during coagulation led us to search a theoretical
approach able to describe this kinetic.
3.3. Modeling of the turbidimetry time curve
3.3.1. Theoretical model
The theoretical model chosen, that give the best fit of the experimental kinetics data is:
b
T( t ) = a + [1]
(1 + (c × t ) )
d e

Where, T : Turbidity (NTU) ; t : time ; a, b, c, d and e : model parameters where a : final turbidity of
coagulum Tc (NTU) ; b : variation (Tmilk-Tc) of the initial turbidity of milk and final turbidity of coagulum
-1
(NTU) ; c : the inverse of the characteristic time of coagulation (min ).
Coagulation speed has been estimated by the derivative of the chosen function [1] (T'(t)). Also, the
inflexion point (ti,Ti), corresponding to the maximum of speed curve, has been identified by the zero
"
of the second-order derivative function (T (t)=0). The gelification point (tg,Tg), corresponding to the
change of slope of the speed curve, has been identified by the root of the third-order derivative
function (T'"(t)=0).
3.3.2. Performance studies
Table 3 resumes extremes and means values of model parameters identified for all milk samples.
Identification of these five parameters has been mode using the Marquardt-Levenberg, non-linear
optimization method using the computer program "Curve expert 3.1".
Table 3. Characteristic parameters of the turbidimetric kinetic model and
comparison with experimental results
Parameters MIN MAX MEAN CV (%)
a (NTU) 8070 9880 9038 7%
b (NTU) -1895 -876 -1504 -22%
c (min-1) 0.002 0.281 0.059 114%
d 1.660 30.400 6.564 99%
e 0.018 327.00 32.142 269%
Comparison of experimental and theoretical profiles
Cd* 0.981 0.999 0.996 0.4%
Cd : coefficient of determination
The calculation of the coefficient of determination Cd between experimental and theoretical
turbidities, shows a good precision of the model to describe evolution of milk turbidity during the
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2
coagulation process (R > 0.98). Figure 2 illustrates an example of comparison between experimental
and theoretical kinetics.
The analysis of characteristic points calculated 8500
Ex periment
60

by the theoretical model shows that they are Model

T ur b idim e tric s p e e d (NTU m in -1 )

50
comparatively close to those determined
8000
experimentally. In fact, we have noted a high

Tu r bid ity (NTU)

40
concordance between theoretical and
experimental times, for the inflexion point "ti" 7500 Tu rd idim e tric s ig na l 30
2
(n=18, R =0.98) and coagulation point "tc" (n=18,
2
R =0.84) and between theoretical and 20
experimental turbidities for the inflexion point "Ti" 7000
2 Spe ed s ig na l
(n=18, R =0.88) and coagulation point "Tc" (n=18, 10
2
R =1.00). The relatively less good concordance
between theoretical and experimental turbidities 6500 0
at the inflexion point may be due to the 0 30 60 90 120
Tim e (m inu te )
incremental time of experimental acquisition
(∆t=4 minutes) which make the exact Figure 2. Comparison between experimental
determination of the turbidity at this point very and theoretical kinetics
difficult. It's due to the extreme rapid evolution of
turbidity at this part of the curve (figure 1). In fact, this particularity proper to the inflexion point is due
to the complexity of phase II, which correspond to the stage of micelles aggregation. It is a physical
state of milk that can be judged as intermediate and very rapid passage from renneted milk at an
initial liquid state to a state of final gel. Therefor an incremental time of acquisition relatively low is
advised for the follow up and the characterisation of this stage of coagulation.
3.4. Predictive relations
3.4.1. Characteristics relations between parameters of coagulation
As shown in figure 3, it appears that turbidity 10000
data are related to the initial milk turbitity for the R2 = 0.96
Infle xion T i or Ge lification T g or

inflexion, gelification and coagulation points.

Coagulation T c tu r bidity (NTU)

9500 R2 = 0.92
Hence, turbidimetric signal depends on the initial
state of milk which demonstrate the utility of the 9000
use of this technique for the characterisation of
R2 = 0.95
the kinetics of enzymatic coagulation. 8500
Through this study, it appears also that the
knowledge of the time at inflexion point "ti" allows 8000
to predict the time at gelification point "tg" (n=18; Inf lex ion point
2
R =0.97) which mean the time of change from 7500 Gelif ic ation point
milk solution to the state of gel, i.e. the end of the
Coagulation point
second phase of coagulation (figure 4a). Also, a 7000
correlation at level of 5% is noted between the 6500 7000 7500 8000 8500
relative turbidity τg (τg=Tg-Tmilk) and τi (τi=Ti-Tmilk) Initial m ilk tur bidity T milk (NTU)
of these two points (figure 4b). These correlations
argue that the transition sol-gel is a quasi linear Figure 3. Relations between initial turbidity of
process. However, we have not found significant milk and these observed at inflexion,
relations between times of coagulation and those gelification and coagulation points
2 2
of inflexion ([n=18; R =0.10]; figure 4a) and/or gelification (n=18; R =0.08). Also, low correlation is
found between relative turbidity at point of coagulation τc (τc=Tc-Tmilk) and those at point of inflexion τi
2 2
([n=18; R =0.66]; figure 4b) or gelification (n=18; R =0.71). This is attributed to the nature of the
process. In fact, the second stage, characterised by "ti" and "tg" is a stage of gelification, whether the
third stage, characterised by the time of coagulation "tc" is a stage of reorganisation of coagulum.
These two stages don't seem to be controlled by the same laws, neither influenced by the same
factors.
Concerning the relations between the characteristics times of the turbidimetric signal during the
milk coagulation and the time of the beginning of visible gelification "tv", a correlation between the
2
time for the hydrolysis stage "t100" and the visual time "tv" (n=18; R =0.66) is noticed. Also, significant
2
correlation at level 5% between the visual time and times of inflexion "ti" (n=18; R =0.80) and of
2
gelification "tg" (n=18; R =0.73) are obtained. The existence of important links between this visual
ICEF9 - 2003
International Conference Engineering and Food

time and times "ti" and "tg" shows that it is possible to predict from "tv" the different times of passage
of the milk from a state of solution to a state of gel.

240 2000

c
Gelification tg or Coagulation t c

1800

Gelification g or Coagulation
1600

relative turbidity ( NTU)

180
1400
tim e (m inutes)

R2 = 0.10
1200
120 1000
800 R2 = 0.66
R2 = 0.97 600
60
Gelif ication point 400 Gelification point
Coagulation point 200 2
R = 0.98 Coagulation point
0 0
0 10 20 30 40 50 60 70 80 90 0 200 400 600 800 1000
Inflexion time ti (m inutes) Inflexion relative turbidity τ i (∆ NTU)

(a) (b)
Figure 4. Relations between inflexion point and gelification and coagulation points
(a) time relations and (b) turbidity relations
3.4.2. Characteristic relations with milk composition
In order to study the quantitative influence of the quality of milk on the three stages of enzymatic
coagulation, the possible relations between the different results registered from turbidimetric profiles
and some parameters of the composition of milk (P, Ca, N and Ca/N) were scanned.
Concerning the effect of composition on turbidities (Tmilk, Ti, Tg and Tc), the results obtained show
that phosphorus has no influence on turbidity whereas calcium richness of milk tends to reduce the
turbidity and that of nitrogen tends to increase it (table 4). These facts seem to be true all along the
coagulation process as suggested by good correlations founded with relative turbidities at those points
(τi=Ti-Tmilk, τg=Tg-Tmilk, and τc=Tc-Tmilk,).
Table 4. Relations between some milk compo- Table 5. Relations between some milk compo-
nents and characteristic turbidities nents and characteristic times
Skim milk Skim milk
P Ca N Ca/N P Ca N Ca/N
Tmilk ns XXX (-) XXX (+) XXX (-) t100 ns ns ns ns
Ti ns XXX (-) XX (+) XXX (-) ti ns ns ns ns
Tg ns XXX (-) XX (+) XXX (-) tg ns ns ns ns
Tc ns XX (-) XX (+) XXX (-) tc ns ns ns ns
Ti-Tmilk ns XX (-) X (+) XXX (-) ti-t100 ns X (-) ns XX (-)
Tg-Tmilk ns XX (-) X (+) XXX (-) tg-t100 ns X (-) ns XX (-)
Tc-Tmilk ns XX (-) XX (+) XXX (-) tc-t100 ns ns ns ns
Tc-Tg ns ns ns ns tc-tg ns ns ns ns
(XXX, XX and X significant correlation's at 1%, (XXX, XX and X significant correlation's at 1%,
5% and 10% levels, respectively) 5% and 10% levels, respectively)
Concerning the effect of milk composition on the characteristic times of turbidimetric kinetics
(table 5), results show that the composition of milk has no influence on the duration of hydrolysis
stage "t100". This is in concordance with various studies concerning the absence of nitrogen, calcium
and phosphorus effects in the action process of the enzyme at the start (13,14).
The second evidence is the importance of milk calcium during the stage of gelification (stage II). In
fact, we noted that an increase in calcium concentration led to a reduction in time of gelification (tg-
t100) as it is showed by Cayot and Lorient (15). However, we have not found a significant effect of
phosphorus on characteristic times. Phosphorus has rather an effect on firmness of gel and curd
drainage aptitude through its role in the inter micellar relations (14,16). Concerning nitrogen, the result
ICEF9 - 2003
International Conference Engineering and Food

obtained in this study corresponds to that of Fox and Mulvihill (17) were no effect of protein level on
the coagulation time is founded.
On another hand, the similarity of correlations found with calcium concentration and those with
Ca/N ratio put in evidence the important role of calcium in the forming of calcium bonds between
casein micelles during stage II of aggregation (3). It has been reported that Ca/N ratio of milk is in
relation with their cheese aptitude (18).
4. CONCLUSION
This work allowed, from different samples of milk, with different physical and chemical
characteristics, to examine the aptitude of turbidimetric method to analyse the kinetic of enzymatic
coagulation. Using the mathematical relationships developed in this study, the dynamic parameters
for the three stages of the rennet coagulation process can be determined. Moreover, some
correlations between the parameters of coagulation were highlighted. Among the most interesting
correlations, we will cite links existing between initial turbidity of milk with gelification turbidity or
coagulation turbidity and links between times of inflexion and gelification and with time of visual
observation. Also, correlations found between characteristic points of the turbidimetric signal and
some variables of milk composition suggest that it would be possible to predict the kinetic of
enzymatic coagulation by the simple knowledge of some constituents of milk.

REFERENCES
1. Eck A., Gillis J.C. Le fromage, Tec & Doc, Paris, 513p, 1997
2. Tarodo de la Fuente B., Lablee J., Cuq J.L. Le lait - Coagulation et synérèse. Industries
Alimentaires et Agricoles, 116, 19-26, 1999
3. Mathieu J. Initiation à la technologie fromagère. Tec & Doc, Paris, 220p, 2000.
4. Daviau C., Famelart M.H., Pierre A., Goudédranche H., Jacob D., Maubois J.L., Rennet
coagulation of skim milk and curd drainage : effect of pH, casein concentration, ionic strength and
heat treatment. Le lait, 80, 397-415, 2000.
5. INORP. NT14-29. Détermination de la densité du lait. INORPI, 1983.
6. INORP. NT14-28. Détermination de l’acidité du lait. INORPI, 1983.
7. Leray O, Influence de l’origine géographique du lait sur la précision des dosages de matière
grasse et des protéines par spectroscopie dans le moyen infrarouge. Le lait, 69, 547-560, 1989.
8. INORP. NT14-52. Détermination de la teneur en en calcium du lait. INORPI, 1983.
9. INORP. NT14-53. Détermination de la teneur phosphore du lait. INORPI, 1983.
10. Alais C. Science du lait. Principes et techniques laitières. Société d’Edition et de Promotion Agro-
Alimentaires, Industrielles et Commerciales, Paris, 390p, 1984.
11. Hardy J., Sher J. Mesure en continu de la coagulation du lait par une méthode optiqur. In :
Automatic control and optimisation of food process symp. Applied Science Publishers, London,
357-369, 1986.
12. Sher J., Hardy J. Utilisation d’une méthode turbidimètrique pour étudier l’effet des différentes
étapes de préparation des laits sur leur coagulabilité. Science des Aliments, 7, 159-165, 1987.
13. Noël Y. Comparaison des cinétiques de coagulation enzymatique et mixte du lait. Influence du
calcium. Le lait, 69, 479-490, 1989.
14. Remeuf F., Lenoir J., Duby C. Etude des relations entre les caractéristiques physico-chimiques
des laits de chèvre et leur aptitude à la coagulation par la présure. Le lait, 69, 499-518, 1989.
15. Cayot P., Lorient D. Structures et technofonctions des protéines du lait. Tec & Doc, Paris, 15-286,
1998.
16. Remeuf F., Cossin V., Dervin C., Lenoir J., Tomassone R. Relations entre les caractères physico-
chimiques des laits et leur aptitude fromagère. Le lait, 71, 397-421, 1991.
17. Fox P.F., Mulvihill D.M. Casein. in : Food gels. Elsevier Science Publishing, New York, 121-173,
1990.
18. Lenoir J., Veisseyre R. Coagulation du lait par la présure et correction des laits de fromagerie. In :
Le lait matière première de l’industrie laitière, INRA-CEPIL, Paris, 329-340, 1987.
ICEF9 2003
International Conference Engineering and Food

Mathematical modelling of microwave heating process

Campañone, L.A. (1) and Zaritzky N.E. (1,2)
(1) Dpto Ing. Qca., Fac .de Ingeniería, Universidad Nacional de La Plata, Argentina. lacampa@ing.
unlp. edu.ar.
(2) Centro de Investigación y Desarrollo en Criotecnología de Alimentos, Argentina.UNLP-CONICET
Calle 47 y 116 La Plata ( 1900) Argentina

Abstract

A mathematical method was developed to simulate microwave heating solving the unsteady heat
transfer differential equation with a non-linear heat generation term, obtained from Lambert´s law. An
implicit finite difference method in one-dimensional system and an alterning direction method in two
and three-dimensional heat transfer conditions were applied. The model was validated with
experimental data of potato, mashed potato and meat products.
Keywords: microwave, mathematical modelling, temperature.

Introduction

Microwave heating was developed 30 years ago and its use has been expanded with the constantly
increasing market of microwable packaged products (1). Modifications of the way of life and consumer
trends need ready to eat food or at least food that can be cooked rapidly before eating. Microwaves
offer rapid temperature increase, due to its capacity of generating energy inside the product. However,
problems associated to temperature distribution inside the product are important. One of these
problems is the presence of hot points in different zones, depending on product geometry. Many
authors have studied this phenomenon by several years, because its relevance on industrial
applications (1, 2, 3). To characterize temperature distribution in different products several authors
have faced microwave heating and cooking with mathematical studies. Finite differences and finite
elements are the preferred numerical methods used to solve microwave process equations. Ohlsson
and Bengston (3) analyzed one-dimensional microwave heating, using finite differences; they solved
heat transfer equations on an infinite slab and calculated internal temperatures in a meat piece.
Swami (4) developed a finite differences method to describe heating of gels with high water content
and NaCl using cylindrical and orthogonal geometries.
Maxwell equations can be applied to describe microwave heating regardless the numerical method
used (finite differences or finite elements). Maxwell equations describe propagation of radiation in a
dielectric medium. However, due to this complex formulation, a simplification considering an
exponential decay of microwave absorption inside the product by applying Lambert’s law, is usually
adopted.
The objectives of the present work were:
1) To analyze microwave heating of large sized food products (meat pieces, trays of mashed potato,
etc).
2) To develop a mathematical model to predict temperature profiles in foods heated by microwaves,
solving numerically the unsteady heat transfer differential equation. The internal generation term due
to electromagnetic energy absorption will be described by Lambert’s law approximation.
3) To validate numerical predictions with experimental data obtained in our laboratory and
experimental data from literature.

Mathematical model

To formulate the mathematical model the following assumptions were made:

1-Uniform initial temperature of products.
2-Temperature dependent thermal and dielectric properties.
3-Volume changes during heating were not considered.
4-Convective boundary conditions.
5-Electric field incidence was normal to the product surface.
Heat transfer was described by the following microscopic energy balance:

∂T
ρC p = ∇ ( k∇ T ) + Q (1)
∂t

where Q is term of volumetric heat generation. In terms of power, equation (1) can be rewritten as:
ICEF9 2003
International Conference Engineering and Food

∂T
V ρ Cp = V (∇ k ∇ T ) + P (2)
∂t

where V is the volume of the product and P is the power generated by microwave absorption. Under
the particular case of one dimensional geometry, equation (2) can be expressed in terms of a generic
index GI which considers the different product shapes: 0 for slab, 1 for infinite cylinder and 2 for spheres:

∂T ∂ k ∂T ∂ 2T k ∂T
V ρ Cp =V + Vk + VGI +P (3)
∂t ∂x ∂ x ∂x 2
x∂x

Equation (3) is valid for the whole product (0 ≤ x ≤ L), where x is the axial or radial coordinate and L is
the half-thickness or radius.
Initial and boundary conditions used are:

t=0 T = Tini 0≤ x≤L (4)

∂T
x =0 −k =0 t>0 (5)
∂x
∂T
x=L −k = h(T − Ta ) t >0 (6)
∂x
Under bi and three-dimensional cases these initial and boundary conditions are valid for all the spatial
components considered.
The term Q represents the power absorbed by the material during microwave heating.
Heat generation is a function of temperature at a fixed position, in this work Lambert’s law was applied
(4):
P = Po e ( −2 αd ) (7)
where Po is the power at the surface and α is an attenuation factor, which is depends on the dielectric
constant ε´ and the loss factor ε´´ as follows:

α=
[
2π ε´ (1 + tan 2 δ) 1 / 2 − 1 ] (8)
λ 2
ε´´
δ = tan −1   (9)
ε
Numerical solution

Under one-dimensional case (slab, infinite cylinder and sphere) equation (3) was solved with the
corresponding initial and boundary conditions. Energy balance is a non-linear differential equation,
without analytical solution; thus, numerical solution was carried out using the Implicit Finite Differences
Method of Crank-Nicolson (5).
Through this procedure the following general equation to calculate temperatures was obtained:

 V k n V (k n − k n ) V GI k in  n +1  Vi ρi Cpi
n n
Vi k in 
Ti n+1+1  − i i 2 − i i +1 2 i −1 − i  + T  + +
 2∆x 8∆x 4(i − 1) ∆x 2   ∆t ∆x 2 
i

 − V k n V (k n − k n ) V GI k in  n  Vi k i
n
Vi (k in+1 − kin−1 ) Vi GI k in 
+ Ti n−1+1  i 2i + i i +1 2 i −1 + i  = T  + +  + (10)
4(i − 1) ∆x 2 
i +1 
 2∆x 8∆x  2∆x
2
8∆x 2 4(i − 1)∆x 2 
 V ρn Cpn V k n   V k n V ( k n − k n ) V GI k in 
+ Ti n  i i i − i i2  + Ti −n1  i i 2 − i i +1 2 i −1 − i  + Pi
 ∆t ∆x   2∆x 8∆x 4(i − 1)∆x 2 

where i corresponds to the node position, n is the time interval, ∆x is the spatial increment and ∆t is the
time increment, such as x = i ∆x y t = n ∆t, with i = 0 (center), b (border).
ICEF9 2003
International Conference Engineering and Food

This equation is valid for 0 < i < b; Vi is the volume of the element between nodes (i+1/2) and (i-1/2), and
Pi is the power calculated between the same nodes. For the central and border nodes Vi and Pi were
calculated between nodes (i+1/2) and (i-1/2), respectively.
Microscopic energy balance has a discontinuity at the center for spheres and infinite cylinders. This
problem can be solved by applying L´Hôpital rule. Finite differences were replaced in the modified
microscopic energy balance to obtain the equation that calculates temperature at the center. Resulting
expression showed two points (i-1,n) and (i-1,n+1) that are outside the domain (fictitious points). To
evaluate them boundary condition ( 5) was discretized for times n and (n+1) ∆t.
On food surface (i = b) equation (10) shows two fictitious points (i+1,n) and (i+1,n+1), to evaluate them
discretized boundary condition (6) was used.
The equations system with an associated tridiagonal matrix was solved using Thomas’ Algorithm. The
code was programmed in Fortran 90.
In the case of finite cylinders, an alternating solution scheme was used (6). Firstly, energy balance
was solved for the axial direction, considering GI=0. Obtained temperatures were intermediate values
with no physical meaning. Then, microscopic energy balance was solved for radial direction,
considering GI=1 in the equation system. Intermediate values of temperature were fed to the system
n
as T values. At this stage actual temperature values in the cylinder were calculated.
Similarly, when the product is a brick, an alternating solution scheme for this three-dimensional
geometry was used (6).

Materials and methods

Food products were heated in a microwave oven. Samples of ground beef and mashed potato were
moulded under different geometries: cubes (6 cm side), cylinders of two different dimensions (8 cm in
diameter x 6 cm high and 8 cm in diameter x 4 cm high) and spheres (7 cm in diameter). Acrylic
containers were used for cylinders and spheres and glass containers for cube samples; both materials
are transparent to radiation.
A domestic microwave oven (BGH), with a maximum power of 1000 W, and a frequency of 2450 MHz
was utilized to simulate heating of food under common conditions. Samples were held in the center of
the oven cavity on an acrylic support placed on a turn table. The rotation of the sample makes more
uniform the electric field . Turning speed was 1 turn each 12 seconds.
Sample temperatures were measured before and after heating with T type thermocouples and
recorded by a datalogger Keithley DAS-TC/B, conected to a PC. Software allowed measuring and
logging data of 16 thermocuples simultaneously, with a sampling interval of 1 second.
The time elapsed between removal of samples from the oven and temperature measurement was
measured and minimized.
The power absorbed by each sample geometry was determined. In the case of cubes and cylinders
power was measured by a calorimetric method (1). Absorbed power was calculated by heating
different volumes of water under the same operating conditions as the assayed products (position,
power and container shape). A non-linear model was proposed to estimate the relationship between
power and water content. A statistical program (SYSTAT 10) was used to estimate model parameters
and standard deviations by non–linear regression. The following relationships were obtained:

Cylinder shape:

1246.5 W
Po = 2
, 50≤W(g) ≤400, r =0.997
1.45W + 79.53

Brick shape:

Po = 18.164W − 0.172 W 2 + 0.0007 W 3 − 910 −7 W 4 , 50≤W(g) ≤200, r2 = 0.989

where W is the weight of water.

In the case of spheres it was difficult to apply the former methodology to calculate absorbed power.
Thus, it was calculated fitting predicted temperature data to experimental ones, for a selected
operating condition. Table 1 summarizes thermal and electromagnetic properties of the assayed
products used in the simulation. Domain was discretized selecting 15 points and a time interval of 1
second for all numerical runs.
ICEF9 2003
International Conference Engineering and Food

Table 1: Thermal and electromagnetic properties of foods used to simulate microwave heating.

Property Beef Mashed Potato Potato

3
Density (kg/m ) 1053 (7) 1056 (9) 1067 (1)
-4
Conductivity 0.0866+0.501 YO+ +5.052 10 0.5608+0.002005 T 0.648 (1)
-5 2
(W/(m°C)) YO T (7) -0.802 10 T (9)

Specific heat 1448 (1-Y O)+4187 YO 4207-1.405 3630 (1)

2
(J/(kg ºC)) (7) T+0.01506 T (9)
2 2
Atenuation Factor 50.516-0.1521 T +0.0025 T + 50.069-0.42653T (10) 64.56-1.366 T+0.0252 T
-1 -7 3 3
(m ) +6 10 T (8) -0.0001113 T (1)

Results and discussion

Mathematical model was validated with temperature data measured in our laboratory for beef and
mashed potato and with experimental data of potatoes obtained by Zhou et. al. (1).
The model under one-dimensional transfer was validated with ground beef spheres. Figures 1 (a) and
(b) show predicted results for the numerical model and experimental data obtained in our laboratory.
The energy of the microwaves has a focus in the center of the sphere, generating hot points or
maximum temperature values. These results agreed with those reported by other authors (2,3).
Numerical results showed a satisfactory agreement with experimental data .
The model under bi-dimensional geometry was validated with data obtained in our laboratory using
mashed potato cylinders. Figures 2 (a) and (b) show experimental data and numerical simulation. In
both cases, microwaves had a focus in the center of the cylinders, showing hot points and leading to a
non-uniform radial distribution. Numerical results followed experimental data trend. Deviations can be
attributed to different sources: error in thermocouple locations and a non-uniform distribution of the
electromagnetic field around the cylinders that cannot be avoided exclusively by the rotation of the
samples. Nevertheless, the model satisfactory predicts the temperature at the center, which is the hot
point for cylinder heating.
Finally, three-dimensional transfer was validated using experimental data obtained from literature (1).
Figures 3 (a) and (b) show experimental thermal histories of the center and border of the potato
rectangular blocks. Experimental data showed that microwave energy is focussed at the product
corners, giving hot points and generating a non-uniform increase of temperature. Figure 3 shows
predicted values by our model and by a finite element method developed by Zhou et al. (1). Estimation
of numerical data obtained with our model has a similar deviation to that obtained by Zhou et al. (1).
Thus, both methods finite differences (applied in the present work) and finite elements had equivalent
estimation errors for these geometries. The highest deviations appeared at the end of the heating
process because the product reaches temperatures close to the water boiling point and in these cases
evaporation has to be considered.

Conclusions

Microscopic energy balance was solved considering a non-linear generation term given by Lambert’s
Law, to consider the system under microwave heating.
Mathematical model was satisfactory solved using finite differences method for one, two and three
o
dimensions. It was also validated (below 100 C) against experimental temperature data both from
literature and from our laboratory. The model can be applied to common practices of microwave
heating. Numerical software is an appropriate tool to select operative conditions necessary to optimize
technological processes to get high quality products.
ICEF9 2003
International Conference Engineering and Food

90 80

80 (a)
70 (b)
70
60
60
50
50
T (ºC)

T (ºC)
40
40
30
30
20
20

10 10

0 0
-4 -3 -2 -1 0 1 2 3 4 -4 -3 -2 -1 0 1 2 3 4
x(cm) x(cm)

Figure 1: Experimental results (symbols) and numerical model predictions (continuous line) for
spheres of beef (7cm in diameter) after different heating times: (a) 48 seconds; (b) 60 seconds.

30 60
(a)
(b)
25 50

20 40
T (ºC)

T (ºC)

15 30

10 20

5 10

0 0
-4 -3 -2 -1 0 1 2 3 4 -4 -3 -2 -1 0 1 2 3 4
x (cm)
x(cm)

Figure 2: Experimental radial temperature profiles (symbols) and numerical predictions (continuous
line) in cylinders of mashed potatoes ( central cross section) for different heating times (a) 20 seconds
(diameter=8 cm, height= 6 cm); (b) 30 seconds (diameter=8cm, height = 4 cm) .
ICEF9 2003
International Conference Engineering and Food

70 120

(a) (b)
60
100

50
80

40
T (ºC)

T (ºC)
60
30

40
20

20
10

0 0
0 10 20 30 40 50 60 70 80 0 20 40 60 80 100
t (seg) t (seg)

Figure 3: Comparison between the results predicted by the finite difference method developed in the
present work (continuous line), and published results (1): experimental data ( n ), results predicted by
the finite elements (l) in a rectangular block of potato (64x48x30 mm): (a) center, (b) corner.

References

1. Zhou L., Puri V.M., Anantheswaran R.C. and Yeh G. Finite element modelling of heat and mass
transfer in food materials during microwave heating-model, development and validation. Journal of
Food Engineering, 25, 509-529, 1995.
2. Sale A.J.H. A review of microwave for food processing. Journal Food Technology, 11, 319-329,
1976.
3. Ohlsson T. and Bengtsson N. Microwave heating profile in foods-a comparison between heating
and computer simulation. Microwave Energy Applied Newsletter, 6, 3-8, 1971.
4. Swami S. Microwave heating characteristics of simulated high moisture foods. MS thesis, University
of Massachusetts, Amherts, MA, USA, 1982.
5. Forsythe G.E. and Wasow W.R. Finite difference methods for partial differential equations. John
Wiley and Sons, New York, 1960.
6. Cleland D.J. and Cleland A.C. An alterning direction, implicit finite difference scheme for heat
conduction with phase change in finite cylinders. XVIII International Congress of Refrigeration,
Montreal, 356, 1991.
7. Mascheroni, R.H. and Calvelo, A. Modelo de descenso crioscópico en tejidos cárneos. La
Alimentación Latinoamericana, 12, 34 – 42, 1978.
8. Gunasekaran N. Effect of fat content and food type on heat transfer during microwave heating. MS
thesis, Virginia Polytechnic Institute and State University, Virginia, 2002.
9. Fraile P. And Burg P. Reheating of a chilled dish of mashed potatoes in a superheated steam oven.
Journal of Food Engineering, 33, 57-80, 1997.
10. Regier M., Housova J. and Hoke K. Dielectric properties of mashed potatoes. International Journal
of Food Properties, 4(3), 431-439, 2001.
ICEF9 - 2004
International Congress of Engineering and Food

Some Limitations of Finite Difference Methods when Used to Calculate the Effective Thermal
Conductivity of a Random Resistor Network
1 1 1 2 3
J. K. Carson , M. F. North , S. J. Lovatt , D. J. Tanner , A. C. Cleland

1 AgResearch Ltd, Private Bag 3123, Hamilton, New Zealand,

james.carson@agreserach.co.nz, mike.north@agresearch.co.nz, simon.lovatt@agresearch.co.nz
2 Food Science Australia, PO Box 52, North Ryde, NSW 1670, Australia,
David.Tanner@foodscience.afisc.csiro.au
3. IPENZ, PO Box 12241, Wellington, New Zealand,
acleland@ipenz.org.nz

Abstract
Effective thermal conductivity studies often make use of random resistor networks to model
heterogeneous materials such as foods. The regular arrangement of these networks makes them
appear well suited to solution by simple finite difference methods. This paper shows that using finite
difference methods to model random resistor networks is not as straight-forward an exercise as it
might seem, since a very fine grid is required due to discontinuities in the thermal conductivity
distribution.

Keywords: Effective Thermal Conductivity, Finite Difference Methods

1 Introduction

The prediction of the thermal or electrical conductivity of heterogeneous materials has received
attention over many years, in particular for those situations where one of the components has a
conductivity that is much greater or smaller than the conductivities of the other components, as is the
case with porous foods. Both analytical [1-3] and numerical methods [4-6] have been employed to
study the problem with the aim of deriving predictive effective conductivity models.

A numerical approach that has been used on a number of occasions (including [4-6]) is to model a
material as a network of resistors. Each individual resistor in the network is randomly assigned the
conductivity of one of the components of the material. In this way, a conceptual material can be made
up from a random distribution of its components. If the number of resistors in the network is sufficiently
large that each resistor represents only a small fraction of the overall network and if the components
are distributed randomly then, by a statistical argument, the overall conductivity of the material will be
approximately uniform and hence may be represented by a single conductivity known as the effective
conductivity.

Finite difference methods have often been used to solve the steady-state heat transfer problems
associated with random resistor networks. A feature of some of these studies is that only one
temperature node was used for each resistor in the network. The implicit assumption is that the
temperature gradients across the resistors are flat enough that one finite temperature step in each
direction sufficiently models the temperature profile over that resistor. The aim of the work reported
here was to discover the sensitivity of the results obtained from these types of resistor network
analyses to the fineness of the nodal grid.

2 Method

Numerical models were constructed to simulate a guarded hot-plate apparatus from which the
effective thermal conductivity (ke) of theoretical materials could be calculated, as described by Carson
et al. [7]. The hot-plate was divided into individual conductivity regions (i.e. resistors) that could have
either of two thermal conductivity values k1 or k2, representing the two different components (Fig. 1).
Each thermal conductivity region was assigned a random number (Na) between 0 and 1. The thermal
conductivity of the region was determined by whether Na was greater than the desired volume fraction
for component 2 (v2), i.e.: if Na > v2 then thermal conductivity of that region was equal to k1 otherwise it
was equal to k2. Once the steady-state temperature distribution of the theoretical material had been
determined, the effective thermal conductivity of the material could be calculated from a heat balance
over the grid [7].
ICEF9 - 2004
International Congress of Engineering and Food

= k1
= k2

Figure 1: Theoretical test material comprised of randomly distributed regions of components 1 and 2

The finite difference method that was used was similar to that described by Phelan and Niemann [5].
Laplace’s equation in two dimensions was rearranged so that it could be expressed in the form shown
in Eq. (1):

Ti − T j
∑j Rij
=0 (1)

where Ti was the temperature at node i and Tj referred to the temperature at any node j adjacent to
node i. The Rij term was the resistance to heat flow between nodes i and j. Temperature nodes were
positioned in a square arrangement with each temperature node a unit spacing apart from the
adjacent nodes along the coordinate axes. The Rij terms that were used were the same as those
found in Table 3-4 of Holman [8] with the exception of the internal nodes. The equations in Holman [8]
assume uniform thermal conductivity and so it was necessary to derive an appropriate term for the
internal nodes that allowed for variable conductivity as follows:

0.5 0.5
Rij = + (2)
ki kj

where ki and kj referred to the conductivities at the nodes Ti and Tj. Hence, for each temperature node
there was a corresponding thermal conductivity node. When the nodes were within the same thermal
conductivity region:

ki = k j (3)

and Eq. (2) was reduced to:

ICEF9 - 2004
International Congress of Engineering and Food

1 1
Rij = = (4)
ki k j

which was the same as the term found in Table 3-4 of Holman [8].

The calculations were performed using Microsoft Excel 2000 (Microsoft Corporation, Redmond,
WA). Equation (1) was rearranged to be explicit for each Ti:

∑T j / Rij
Ti =
j
(5)
∑1 / R
j
ij

and then solved iteratively using Excel’s iteration function. Iterations were continued until the
-5
maximum change in a nodal temperature was less than 10 % and the discrepancy between the heat
balance performed at the hot and cold ends of the finite difference model was less than 0.5% [7].

Some previous workers who have used finite difference methods to solve random resistor network
problems used only one node per resistor (i.e. conductivity region). In this study, the number of nodes
per conductivity region (nN/nR) was varied in order to determine the significance to the results of the
fineness of the grid of nodes. Simulations were performed over a range of volume fractions of
components 1 and 2. All models contained 625 (25 x 25) conductivity regions. The first set of
simulations was run with a model having one temperature node per thermal conductivity region (i.e.
nN/nR = 1) and therefore was made up of a 25 x 25 grid of nodes. In the second and third sets of
simulations, nN/nR was increased to 16 and 100 respectively, and hence the second model had 100 x
100 nodes, and the third model had 250 x 250 nodes.

3 Results and Discussion

Since the ke measurements were performed over a range of volume fractions it was useful to display
the results as plots of relative effective thermal conductivity (ke/k1) against the volume fraction of one
-1 -1
of the components (v2). In all the simulations, the value of k1 was 0.5 W m K and the value of k2 was
-1 -1
0.03 W m K , which, respectively, corresponded to the thermal conductivities of the condensed
phase and gaseous phase of a porous food.

Figure 2 shows a graph of the simulation results from the models with different nN/nR values. There
were clear discrepancies between the results from each model, as much as 26% between the results
from the model with 1 node per conductivity region and the model with 100 nodes per conductivity
region, even though all three models were simulating identical thermal conductivity distributions.
Figure 3 shows a plot of the ke/k1 results as a function of the nN/nR for a v2 value of 0.5, including
points from models with nN/nR values of 4, 9, 25 and 36. Since the value of ke/k1 appears to converge
as nN/nR increases, it suggests that the discrepancy between the results from the different models is
due to the relative fineness of the grid of nodes used in the different models.

Figures 4 to 6 show the temperature profiles calculated with nN/nR values of 1, 16 and 100 for the nine
adjacent conductivity regions highlighted in Fig. 1. The difference between the temperature surfaces
shown in Figs. 4 and 6 highlights the effect of approximating a smooth curve with a finite number of
straight lines, especially for the low thermal conductivity regions where the temperature gradients are
steep.

The fineness of the nodal grid affects two important sources of error inherent with finite difference
simulations: truncation error and discretization error [9,10]. In general, both sources of error are
reduced as the fineness of the grid is increased (i.e. nN/nR is increased). These results suggest that
random resistor network models with nN/nR = 1 may have unacceptable levels of truncation and/or
discretization error.
ICEF9 - 2004
International Congress of Engineering and Food

Although the regular geometric arrangement of resistor network models means that they appear well
suited to being solved by simple finite difference methods the results obtained in this work have shown
that models with nN/nR = 1 may not always be accurate, although they may provide useful insights
when used to study relative phenomena.

n N /n R==11
nN/nR
0.8 n N /n R==16
nN/nR 16
n N /n R==100
nN/nR 100

0.6
k e/k 1

0.4

0.2

0
0 0.2 0.4 0.6 0.8 1
v2

Figure 2: Effective thermal conductivity values calculated from finite difference simulations for a range
of volume fractions.

0.25

0.23

0.21
k e/k 1

0.19

0.17

0.15
0 20 40 60 80 100
n N /n R

Figure 3: Dependence of effective thermal conductivity calculated from finite difference simulations on
the number of nodes per thermal conductivity region (nN/nR).
ICEF9 - 2004
International Congress of Engineering and Food

10.5
10
9.5
Temperature (°C)

9
8.5
8
7.5
S3
7
6.5 S2
6
S1
1
2
3

Figure 4: Nodal temperatures for the selected portion of the (nN/nR) = 1 model.

11
10.5
10
Temperature (°C)

9.5
9
8.5
8
7.5
7 S9
6.5
S5
6
1 S1
5
9

Figure 5: Nodal temperatures for the selected portion of the (nN/nR) = 16 model.
ICEF9 - 2004
International Congress of Engineering and Food

11
10.5
10

Temperature (°C)
9.5
9
8.5
8
7.5
7 S21
6.5
6
S11
1 11 S1
21

Figure 6: Nodal temperatures for the selected portion of the (nN/nR ) = 100 model.

4 Conclusion

Although random resistor networks appear to be ideally suited to finite difference modelling, the
simulations performed in this study have shown a clear dependence of the calculated effective thermal
conductivity on the number of temperature nodes per conductivity region. This dependence suggests
that the discretization of the temperature profile by one temperature step per conductivity region may
not be sufficient to give accurate results. Results from random resistor network studies should be
viewed with caution if it is unclear how the finite difference calculations were performed.

References:
rd
1. Maxwell, J. C. A Treatise on Electricity and Magnetism. Dover Publications Inc, New York, 3
Ed, 1904 (reprinted in 1954)
2. Landauer, R. The Electrical Resistance of Binary Metallic Mixtures. Journal of Applied
Physics, 23 p779-784,1952
3. Krischer, O. Die wissenschaftlichen Grundlagen der Trocknungstechnik (The Scientific
fundamentals of Drying Technology) cited in English in Chapter 7 of Keey, R. B. Drying of
Loose and Particulate Materials, Hemisphere Pub. Corp., New York, 1992
4. Kirkpatrick, S. Percolation and Conduction. Reviews of Modern Physics, 45, p574-588, 1973
5. Phelan, P. E., Niemann, R. C. Effective Thermal Conductivity of a Thin Randomly Oriented
Composite Material. ASME Journal of Heat Transfer, 120, p971-976, 1998
6. Davies, L. J., Fryer, P. J. Effective Electrical Conductivity of Foods. Proceedings of the Eighth
International Congress on Engineering and Food, p146-150, 2001
7. Carson, J. K., Lovatt, S. J., Tanner, D. J., Cleland, A. C. An analysis of the influence of
material structure on the effective thermal conductivity of porous materials using finite element
simulations. International Journal of Refrigeration, 26, 8, p873-880, 2003
th
8. Holman, J. P. Heat Transfer 7 Edition, McGraw-Hill Book Company, Singapore, 1992
nd
9. Crank, J. The Mathematics of Diffusion 2 Edition, Oxford University Press, Oxford, 1973
10. Smith, G. D. Numerical Solution of Partial Differential Equations: Finite Difference Methods,
rd
3 Edition, Oxford University Press, Oxford, 1986
ICEF9 – 2004
International Conference Engineering and Food

3K\VLFDO5HILQLQJRI&RFRQXW2LO%DWFKDQG&RQWLQXRXV6LPXODWLRQ

Roberta Ceriani (1), Antonio J.A. Meirelles (2)

LASEFI (Physical Separation Laboratory), Food Engineering Department, State University of

Campinas (UNICAMP), P.O. Box 6121, Zip Code 13083-970, Campinas, São Paulo, Brazil
(1) berta@fea.unicamp.br, (2) tomze@fea.unicamp.br
$EVWUDFW
Neutral oil losses were quantified for batch and continuous physical refining of coconut oil. All
the oil complexity was considered using group contribution equations within the simulation programs.
The batch deodorizer was modeled as a differential distillation and the continuous deodorizer as a
stripping column. In a case study (208 °C and 1 mmHg), the neutral oil losses for the continuous and
batch processes where respectively, 2.43 and 2.06% for a final acidity of 0.0216%.

.H\ZRUGV
Physical refining, simulation, batch, continuous, coconut oil and neutral oil loss.
,QWURGXFWLRQ
Physical refining and deodorization are processes of the oil industry that intend to strip off
odoriferous compounds and fatty acids. They are based on the large difference in the volatility
between the oil and the majority of its unwanted substances. However the high temperatures and low
pressures applied also generate the vaporization of an acylglycerol part from the oil, known as neutral
oil loss (1-3). One of the reasons for the occurrence of neutral oil loss is the similarity between the
volatilities of long-chain fatty acids and short-chain monoacylglycerols (2).
This work presents a comparison between batch and continuous physical refining simulations
using a group contribution approach for all the physical property calculations. Coconut oil was selected
because of its high level of short-chain and saturated fatty acids (4) and its high free fatty acid (FFA)
content (between 1 and 6%) denote the presence of short-chain mono- and diacylglycerols (2) in a
considerable amount.
The batch deodorizer modeling was based in a differential distillation with stripping steam
injection after the heating period (5). The continuous deodorizer was considered as a stripping
column. The vapor-liquid equilibria of these fatty systems are described by group contribution
equations for vapor pressures (5) and activity coefficients (5, 6) published elsewhere. Well-known
group contribution estimation methods can be used (7) for other physical properties. All the oil
complexity, expressed by its whole composition in tri-, di-, and monoacylglycerols and free fatty acids,
is considered within the simulation, to quantify and qualify neutral oil losses during physical refining.
In previous works (5, 8) the VLE and the batch deodorizer modeling have been extensively
discussed. For this reason, we present a brief explanation on these two topics in association with the
continuous deodorizer modeling.
0RGHOLQJDEDWFKDQGDFRQWLQXRXVGHRGRUL]HU
Physical refining is essentially a mass transfer process and therefore its vapor-liquid equilibria
(VLE) have to be described. In this work, the vapor pressure equation and the thermodynamic
approach suggested by Ceriani and Meirelles (5) were applied. The VLE model is described below (5)
φ VDW  9 / ⋅ (3 − 3L YS ) [1]
\ L ⋅ 3 = γ L ⋅ [L ⋅ 3L YS ⋅ ℑL where ℑL = L ⋅ exp L 
φL  5 ⋅7 
where ℑL is the non-ideality factor of the vapor phase, [L and \L are the molar fractions of
component L in the liquid and vapor phases, respectively, 3 is the total pressure, 5 is the gas constant,
7 is the system temperature, 3L YS and φ LVDW are, respectively, the vapor pressure and the fugacity
coefficient of the pure component, γ L is the activity coefficient φ L is the fugacity coefficient and 9L / is
the liquid molar volume of component L Deodorizing units operate at low pressures and high
temperatures. As a consequence, the vapor pressures of some components, as water and short-chain
fatty acids (C6:0 to C12:0) are sufficiently high to produce φ LVDW values markedly different from unity.
This is the reason to describe rigorously the VLE observed in this kind of process (5).
ICEF9 – 2004
International Conference Engineering and Food

A batch deodorization is similar to a multicomponent differential distillation, for which the total
and component balances are given by (8, 9):
d6 and d6 ⋅ [ L  [2]
= −9 = −9 ⋅ \ L
dW dW
where 6 is the total moles of liquid in the still, 9 is the molar vaporization rate in moles/time and [Land
\Lare the liquid and vapor mole fractions of component L in the liquid and vapor phases, respectively.
Assuming that the liquid and vapor phases are in equilibrium at each instant, i.e., that the still acts as a
theoretical stage, the equilibrium relationship can be stated as Equation 1.
For the receiver distillate tank, the total and component balances are (8, 9):
d' and d'L [3]
=9 =9 ⋅\ L
dW dW
where ' is the total moles of distillate and 'L is moles of component L in the tank.
Combining Equations 2 and 3 together with the equilibrium relationship (Eq.1) we have a system that
is easily solvable by direct numerical integration (10)
In this work, we have simulated a batch deodorization in a way similar to the operation of an
industrial batch deodorizer (8). According to Anderson (11), a batch of incoming fresh oil is usually
slowly heated under vacuum conditions to the deodorizing temperature, at which time sparging steam
is introduced and the process is performed until the required oil acidity is obtained. The process
simulation was divided in two parts (8): (1) KHDWLQJ (in absence of water) and (2) VWULSSLQJ with sparge
steam at constant temperature, which was allowed by the presence of water in the liquid phase. The
simulation of the first part (KHDWLQJ) was conducted in order to obtain the boiling temperature at each
time by equaling the sum of the partial pressures of the fatty compounds to the system total pressure.
When the deodorizing temperature was achieved (the start of VWULSSLQJ), water was included as the
(Q+1) th component in the liquid phase. Equation 4 (8) below was then solved to determine the water
concentration in the liquid at the chosen temperature and pressure conditions.
[ ]
Q +1
I = 3 − ∑ γ L ⋅ [ L ⋅ 3L YS ⋅ ℑ L [4]
L =1
All the models depicted above use an iterative procedure for convergence, as Newton-
Raphson (10). 3L YS , γ L and ℑL are calculated for each component, including water, in each and every
iteration.
The continuous physical refiner performs the same basic functions as the batch equipment but
is designed for a larger operation. In this equipment, the oil is refined by flowing over a series of trays
countercurrent to the flow of stripping steam, injected on each tray. The refined oil is collected at the
bottom (first stage) of the equipment. As indicated by Stage (12), a physical refiner requires four to five
trays. Within the simulation, an important aspect to consider is that the first stage is not under the top
pressure but under a pressure, which is increased by the pressure drop of each tray, 1 mmHg approx.
(13).
The multicomponent column modeling was based in the method described by Naphtali and
Sandholm (14). The general equations, which include material- and energy balances and Murphree
efficiencies coupled with vapor-liquid equilibrium relationships, are fully described by Naphtali and
Sandholm (14) and Fredenslund HW DO (6). This method also uses Newton-Raphson as the iterative
procedure for convergence. In our simulations, the Murphree efficiencies were taken as unity, i.e.,
each tray was considered as an ideal equilibrium stage.
The simulation programs discussed above were elaborated and performed in MatLab®.
(VWLPDWLRQRIRLOFRPSRVLWLRQDQGSK\VLFDOSURSHUWLHV
Crude vegetable oils are formed by tri-, di- and monoacylglycerols in addition with a variety of
other compounds, including flavors and pigments. The total concentration of these minor compounds
normally ranges between 0.02 and 0.2% (15). Because in this work, we are concerned about neutral
oil losses, we have considered acylglycerols and fatty acids as components of the oil in our
simulations.
From the fatty acid composition (16) of coconut oil (0, molecular weight of 587.86 g/gmol and
5.45 of iodine value) shown in Table 1, its composition in triacylglycerols (TAG) was estimated using
the procedure of Antoniosi Filho HW DO (17), considering 84% of TAG as trisaturated ones (18). We
have already used this procedure in previous works (5, 8) with success. The estimated TAG
composition is shown in Table 2. The partial acylglycerol composition was obtained intuitively from the
estimated TAG composition (see Table 2). As a whole, the estimated coconut oil was divided into 67
components, i.e., 11 fatty acids (Table 1), 30 triacylglycerols (Table 2) and 26 partial acylglycerols
(Table 2). The monoacylglycerols (MAGs) and diacylglycerols (DAGs) considered are brought in Table
ICEF9 – 2004
International Conference Engineering and Food

2. The concentration given in Tables 1 and 2 add to 100% within each fatty compound class. The
crude coconut oil had 3% mass concentration of diacylglycerols (DAG), 1% of monoacylglycerols
(MAG) (19) and 3% of acidity, expressed as percentage of oleic acid. Note that the oil acidity was
composed by all fatty acids shown in Table 1.

Table 1-Fatty Acid Composition of Coconut Oil

Fatty Trivial name Mass Mole
acid (abbreviation) (%) (%)
C6:0 Caproic (Co) 0.60 1.05
C8:0 Caprilic (Cp) 9.40 13.21
C10:0 Capric (C) 7.80 9.18
C12:0 Lauric (L) 48.20 48.76
C14:0 Miristic (M) 16.80 14.91
C16:0 Palmitic (P) 7.70 6.08
C18:0 Stearic (S) 2.30 1.64
C18:1 Oleic (O) 5.60 4.02
C18:2 Linoleic (Li) 1.50 1.08
C18:3 Linolenic (Ln) 0.05 0.04
C20:1 Gadoleic (G) 0.05 0.03

Table 2-Estimated Composition of Coconut Oil

Triacylglycerols Diacylglycerol
D
E Major 0  Mass Mole acylglycerol 0D Mass Mole
Group
Triacylglycerol (g/gmol) (%) (%) compound (g/gmol) (%) (%)
22:0 CoCpCp 442 0.04 0.06 CoCp 316 0.05 0.07
24:0 CpCpCp 470 0.23 0.32 CpCp 344 2.59 3.33
26:0 CpCpC 498 0.70 0.90 CpC 372 3.67 4.37
28:0 CpCpL 526 2.65 3.25 CpL 400 19.77 21.86
30:0 CpCL 554 4.48 5.21 CL 428 18.14 18.74
32:0 CpLL 582 11.16 12.38 LL 456 34.52 33.48
34:0 CLL 610 12.55 13.28 LM 484 2.06 1.88
36:0 LLL 638 18.71 18.92 LP 512 7.20 6.22
38:0 LLM 666 14.54 14.09 LS 540 0.96 0.79
40:0 LLP 694 9.40 8.74 MS 568 0.23 0.18
42:0 LMP 722 4.93 4.40 CpO 482 0.54 0.50
44:0 LMS 750 1.98 1.70 CO 510 1.40 1.21
46:0 LPS 778 0.68 0.57 LO 538 5.97 4.91
48:0 MPS 806 0.19 0.15 MO 566 0.51 0.40
34:1 CpOCp 608 0.26 0.28 CpLi 452 0.49 0.48
36:1 CpOC 636 0.49 0.49 CLi 508 0.37 0.32
38:1 CpOL 664 2.06 2.01 LLi 536 1.53 1.26
40:1 COL 692 2.01 1.87 Monoacylglycerol
42:1 LOL 720 4.50 4.03 Co 190 0.03 0.04
44:1 LOM 748 2.70 2.32 Cp 218 13.84 16.97
46:1 LOP 776 1.47 1.22 C 246 11.34 12.32
48:1 MOP 804 0.62 0.50 L 274 62.87 61.31
50:1 MOS 832 0.16 0.13 M 302 1.39 1.23
34:2 CpCpLi 606 0.07 0.07 P 330 3.84 3.11
36:2 CpCLi 634 0.13 0.13 S 358 0.64 0.48
38:2 CpLiL 662 0.55 0.54 O 356 4.68 3.51
40:2 CLiL 690 0.53 0.50 Li 354 1.37 1.03
42:2 LLiL 718 1.20 1.08
44:2 LLiM 746 0.66 0.57
46:2 LLiP 774 0.35 0.29
D
0, molecular weight (g/gmol). For other abbreviations see Table 1.
E
Isomer set including different triacylglycerols, but all with the same number of fatty acid
carbons and double bounds. For example, Group 34:1 means the isomer set of
triacylglycerols with 34 fatty acid carbons and 1 double bound.
ICEF9 – 2004
International Conference Engineering and Food

To design multicomponent distillation columns, physical property estimations are required.

Because of the high number and diversity of compounds in the vegetable oil, we have selected group
contribution methods to such predictions.
For fugacity coefficients, a virial equation truncated at the second term in combination with
mixing rules was used. Critical properties and acentric factors of the pure components are needed to
calculate second virial coefficients. Well-known estimation methods as Joback’s technique for critical
volumes and pressures, and Fedor’s group contributions for critical temperatures can be used (7). The
9L / values for all components can be obtained with the modified Rackett technique (7).
For the energy balances, vapor and liquid heat capacities, and enthalpies of vaporization are
needed. We have selected Joback’s technique for ideal vapor heat capacities, Rowlinson-Bondi’s
method for liquid heat capacities (7) and the method of Tu and Liu (20) for estimation of the enthalpy
of vaporization of each compound involved.
5HVXOWVDQGGLVFXVVLRQ
To compare the batch and the continuous physical refiners, it was first necessary to establish
a base for this comparison. For our simulations, we have considered that both the batch and the
continuous plant give the same hour production of the final product (refined oil). Taking a batch size of
10,000 kg (15), and a complete corresponding operating cycle of 8 h (15), the mass flow rate for the
continuous plant was set as 1,250 kg/h. The operating conditions selected are shown in Table 3.

Table 3-Operating conditions for the batch and the continuous

physical refiner simulations
Parameter Batch Continuous
Oil load 10,000 kg 1,250 kg/h
% sparge (stripping) steam 1.4 % 2%
Temperature (°C) 207.93 207.93
Pressure (mmHg) 1 1
Pressure drop (mmHg) --- 1 per tray
Number of trays --- 5
Volatile flow rate a 100 kg/h ---
Initial acidity (% of oleic acid) 3.00 3.00
Final acidity (% of oleic acid) 0.02 0.02
Entrainment None None
a
Volatile flow rate refers to the mass of volatile compounds
that is stripped of the oil per time for the batch simulation.

For the batch process simulation it is necessary to set a value for the volatile flow rate (see
Table 3). This parameter corresponds to the mass of volatile compounds that is stripped of the oil per
time. It was set by dividing the mass of FFA and MAG in the crude coconut oil (400 kg) in 4 h, which is
the effective deodorizing time (15). For the batch refiner, the % of stripping steam (see Table 3) is a
result of the simulation. In a real situation, this value is probably higher, since in the simulation we
have considered that the vapor is perfectly mixed within the oil, i.e., the water concentration is kept at
its saturation value for the temperature and pressure conditions.
The temperature values referred at Table 3 correspond to the deodorizing temperature of the
batch process (after the heating period) and to the converged temperature of the fifth stage of the
continuous column (given as a result of the program). In both simulations (batch and continuous), the
loss by entrainment was not considered. The entrainment occurs when droplets of oil are thrown
upward into the vapor outlet, and carried out of the deodorizer, increasing neutral oil loss significantly.
Figure 1 shows the profile per time of the boiling temperatures and the molar water
concentrations in the liquid phase for the batch simulation. As can be seen, the deodorizing
temperature (207.93°C was reached after 93 minutes of process (KHDWLQJ SHULRG) when started the
injection of stripping steam. At this time, water was included as a component of the liquid phase. The
calculated water molar fraction in the oil was very low along the VWULSSLQJSHULRG, but the presence of
water in the liquid phase allows the occurrence of the deodorization process without further
temperature increase.
Free fatty acids are among the most easily evaporated materials in vegetable oil, and are the
main fraction of the distillate (Figure 2). The acylglycerols are much less volatile, but some evaporation
is evident. Our results show that most of the neutral oil loss is from mono- and diacylglycerols, since
they have a lower molecular weight than the triacylglycerols. At the end of the batch process, the
neutral oil loss was 2.06%, formed by 22.9% of TAGs, 30.5% of DAGs and 46.6% of MAGs.
ICEF9 – 2004
International Conference Engineering and Food

To reach the final acidity of 0.02%, it was necessary 253 min of processing (4 h and 13 min),
with 2h and 40 min of steam injection. The remaining time for completing 8h is necessary to load the
deodorizer, withdraw the refined oil and prepare the equipment for a new crude oil load.

)LJXUH Variation of the boiling temperatures )LJXUHAcidity and acylglycerols in the

and water molar fraction in the liquid phase distillate for the batch physical refining of
with time for the batch physical refining of coconut oil.
coconut oil.

 
)LJXUHComposition of initial and final )LJXUHMass fractions of free fatty acids
products of the continuous physical refining and acylglycerols per stage within the
equipment

Using the parameters shown in Table 3, the simulation of the continuous physical refining was
performed. In comparison with the batch process, neutral oil loss was higher (2.43%), but distributed
differently for each class of acylglycerols (27.4% TAGs, 32.7% DAGs and 39.9% MAGs). From the
8.49 kg/h of TAGs lost in the distillate for the continuous process, 97.4% were formed by short-chain
TAGs (0<694 g/gmol). Similar results are found for the classes of DAGs and MAGs. In general, the
continuous simulation has given higher losses in comparison with the batch process, excluding MAGs.
As shown in Figure 3, FFAs is the main fraction of the distillate, followed by MAGs, DAGs and TAGs.
The refined oil is almost absent of FFAs and MAGs, since these classes of compounds add 0.06% of
the final product.
Figure 4 shows the profile of the mass fraction of FFA and acylglycerol curves in the liquid and
vapor phases within the column. As expected, the FFA concentration in the oil diminishes as it flows
down into the column (from stage 5 to 1) while the vapor phase becomes richer of it.
&RQFOXVLRQ
The results reported in this present work have indicated that the methodology suggested by
Ceriani and Meirelles (5) in combination with the batch (8) and the continuous physical refining
modeling is a valuable tool to deeply investigate common processes of the vegetable oil industry. As
ICEF9 – 2004
International Conference Engineering and Food

already discussed by Petrauskaitè et al (2), neutral oil loss are direct related to the profitability of a
vegetable oil plant.
5HIHUHQFHV
1. Verleyen T., Verhe R., Garcia L., Dewettinck K., Huyghebaert A., De Greyt W. Gas
Chromatographic Characterization of Vegetable Oil Deodorization Distillate, Journal of
Chromatography A, 921, 277-285, 2001.
2. Petrauskaité V., De Greyt W.F., Kellens M.J. Physical Refining of Coconut Oil: Effect of Crude Oil
Quality and Deodorization Conditions on Neutral Oil Loss, Journal of the American Oil Chemists
Society, 77, 581-586, 2000.
3. Ruiz-Mendez M.V., Marquez-Ruiz G., Dobarganes M.C., Quantitative Determination of Major
Components of Vegetable Oil Deodorization Distillates. Grasas y aceites, 40, 22-25, 1995.
4. Canapi E.C., Agustin Y.T.V., Moro E.A., Pedrosa E., Luz J.M., Bendano J. Coconut Oil, “Bailey´s
Industrial Oil and Fat Products”, vol.2, 97-124, Wiley-Interscience, New York, 1996.
5. Ceriani R., Meirelles A.J.A. Predicting Vapor-Liquid Equilibria of Fatty Systems. Fluid Phase
Equilibria, “in press”.
6. Fredenslund A., Gmehling J., Rasmussen P. “Vapor-liquid equilibria using UNIFAC”, Elsevier,
Amsterdan, 380p, 1977.
7. Reid R. C., Prausnitz J.M., Poling B.E. “The Properties of Gases and Liquids”, McGraw-Hill, New
York, 741p, 1987.
8. Ceriani, R., Meirelles A.J.A. Simulation of Batch Physical Refining and Deodorization Processes.
Journal of the American Oil Chemists Society, (submitted)
9. Ingham, J., Dunn I.J., Heinzle E., Prenosil J.E. “Chemical Engineering Dynamic: Modeling with PC
Simulation”, VCH Publishers, Weihneim, 589-593, 1995.
10. Ramirez, W.F. “Computational Methods for Process Simulation”, Butterworth-Heinemann, Oxford,
82-83, 1997.
11. Anderson, D., A Primer on Oils Processing Technology, “Bailey’s Industrial Oil and Fat Products”,
vol. 4, 1-60, Wiley-Interscience, New York, 1996.
12. Stage, H. The Physical Refining Process. Journal of the American Oil Chemists Society, 62, 2,
299-308, 1985.
13. White, F.B. Deodorization. Journal of the American Oil Chemists Society, 29, 11, 515-526, 1953.
14. Naphtali, L.M., Sandholm, D.P. Multicomponent separation calculations by linearization. AIChe
Journal, 17, 1, 148-153, 1971.
15. Carlson K.F. A Primer on Oils Processing Technology, “Bailey’s Industrial Oil and Fat Products”,
vol. 4, 339-391 Wiley-Interscience, New York, 1996.
16. Firestone D. “Physical and Chemical Characteristics of Oils, Fats and Waxes”, AOCS Press,
Champaign, 152p, 1999.
17. N.R. Antoniosi Filho, O.L. Mendes and F.M. Lanças, Journal of Chromatography, 40, 557-562,
1995.
18. Theme, J.G. “Coconut Oil Processing” FAO, Rome, 251p, 1968.
19. Loncin, M. “L’Hydrolyze Spontanée des Huiles Glycéridiques et en Particulier de l’Huile de Palme“.
Maison D’Editon, Couillet, 62 p, 1962.
20. Tu, C.H., Liu C.P. “Group-Contribution Estimation of the Enthalpy of Vaporization of Organic
Compounds“. Fluid Phase Equilibria, 121, 45-65, 1996.
$FNQRZOHGJHPHQWV
FAPESP (03/04949-3 and 01/06798-7), CNPq (521011/95-7), FINEP and CAPES for the financial
support.


   

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 ICEF9 – 2003
International Conference Engineering and Food

SIMULATION OF THE BEHAVIOUR OF VOLATILE COMPONENTS IN CONTINUOUS DISTILLATION OF

FERMENTED JUICE TO PRODUCE RUM
Coustel J.(1,2), Ariouat N.(1), Decloux M.(1),

1. UMR GENIAL - GIA department. ENSIA. 1, av des Olympiades. 91744 Massy. France. decloux@ensia.fr
2. Distillerie Rivière du Mât - Chemin Manioc, Beaufonds 97470 Saint-Benoît. France.

ABSTRACT
The aim of this work was to use the ProSimPlus simulation program to study the behaviour of certain volatile
components (ethyl acetate, methanol, propanol, isobutanol, amyl alcohol) named "congeners", that are
vaporised with ethanol during rum distillation. Due to the composition of alcohol solutions, it was necessary to
choose a thermodynamic model based on interaction coefficients to assess the equilibrium data. The NRTL
and UNIFAC models were tested. Most of the three parameters in the NRTL model were obtained from the
Chemistry Data Series. Simulations of the distillation of simple ethanol-water solutions were used to highlight
the precautions necessary when interpreting the results obtained with the ProSimPlus program. In spite of
certain limitations, it was possible to justify the need, firstly, to use two columns in series to remove methanol
and ethyl acetate from rum, and secondly, to extract small flows at different plates in the first column to
remove heavy congeners (propanol, isobutanol, amyl alcohol).

Key words: distillation, ethanol, ethanol congeners, simulation, brandy, rum, ProSimPlus

INTRODUCTION
Rum is the third mostly widely consumed type of brandy in the world, after whiskies and Cognac. To achieve
quality control, it is important to determine the behaviour of other volatile components (congeners) that are
vaporised with ethanol. Some of these participate positively in brandy quality, and others not. It is therefore
necessary to remove them, in varying proportions. Congeners behaviour depend on their volatility relative to
ethanol. At the end of the 19 th century, the relative volatility coefficients of the principal components were
determined separately at levels lower than 2%(w/w) in the entire range of water-ethanol concentrations by
Sorel(1). Until now, these values have been used to explain congener behaviour in the distillation columns(2).
However, since that time, numerous studies have been carried out on thermodynamic models, and
simulation programs have been developed for petroleum distillation, which include the ProSimPlus program.
The aim of the present work was to test the ability of this simulation program to reflect the behaviour of
congeners. A rum distillation process was used to check the reliability of the results. Because of limitations
on the length, this paper is focused on the results obtained.

DESCRIPTION OF THE RUM DISTILLERY

The rum distillery under study uses cane molasses as its feed material. The alcohol concentration in the beer
(fermented broth) ranges from 8 to 10%alc/vol (alcohol by volume). This beer also contains congeners, that
are either "head congeners" (ethyl acetate and methanol) or "heavy" congeners (propanol, isobutanol and
amyl alcohol). The composition of the beer used for the simulation is shown in Table 1.

Table 1 : composition of beer used for the simulation (HPA : Hectolitre of Pure Alcohol)
Congener usual names In beer MW Chemical formula ProSimPlus In beer
type g/HPA g/mole number mole/mole
water 18 water 1921 up to 1
ethanol 46 ethanol 1102 0.03
head ethyl acetate 12 88 ethyl acetate 1313 2.1 10-6
methanol 15 32 methanol 1101 7.2 10-6
propanol 100 60 1-propanol 1103 26.0 10-6
heavy isobutanol 50 60 2-methyl-1-propanol 1106 13.0 10-6
amyl alcohol 140 88 3-methyl-1-butanol 1123 26.0 10-6

Distillation plant has two plate columns in series (Figure 1): the first one, "rectifying column" fed by the beer
contains 20 plates in the stripping section (below the feed) and 46 plates in the rectifying section (above the
feed). Several series of draw-offs take place from plates 1-3-5, 7-9 and 11-13. The distillate is collected as
"intermediate rum" few plates from the top (plates 46 to 41) with an alcohol concentration of about
96.1%alc/vol (0.86 mole/mole). A small percentage of "heads" is drawn off from the condenser to the "poor
quality alcohol tank”. The intermediate rum feeds a second column "demethylising columm" containing
50 plates at the plate 35. The rum is run off from the bottom of the column, and “heads” are collected at the
outlet of the condensers and sent into the poor quality alcohol tank. The productivity of this distillery is
400 HPA/d (hectolitre of pure alcohol per day).

1
 ICEF9 – 2003
International Conference Engineering and Food

Beer
9.4 %alc/vol vent vent
30°C
111 2 3

46 50
heads to storage Heads to storage
96.4 %alc/vol 96.7 %alc/vol

42 intermediate rum
35
96.1 %alc/vol
Rectifying Demethy-
section
92/93 lising
column

13-15 propanol draw

92 %alc/vol
isobutanol draw boiler
7-9-11
86 %alc/vol

1-3-5 fusel oil draw final light rum

55 %alc/vol 96.0 %alc/vol
78 °C
stripping
section

20 plates

boiler
Figure 1: Rum distillery plant
stillage

GENERAL INFORMATION ON THE PROSIMPLUS SIMULATION PROGRAM

ProSimPlus is a simulation program for continuous processes (distillation, mixing, etc.), developed in 1975
by Professor Koehret at ENSIACET. It is now marketed by PROSIM S.A.. Components are chosen in the
Component Plus file linked with the ProsimPlus program which contains standard data on 1508 products.
Several criteria can help to find a component (usual name, chemical formula, Dechema number). The choice
of the right thermodynamic model is crucial to obtaining reliable results. When components in a mixture
interact strongly in the liquid phase (which is the case for alcohol solutions), it is necessary to use an activity
coefficient-based model to evaluate equilibrium data: P ⋅ y i = γ i ⋅ x i ⋅ Pi° , where P, is the entire pressure, and
for component i : yi the molar fraction of the vapour phase, γi the activity coefficient, xi the molar fraction in
the liquid phase and Pi° the saturated pressure at equilibrium temperature. Several models have been
developed to assess the activity coefficient γi. We tested the NRTL (Non-Random Two Liquids) and UNIFAC
(UNIversal quasi-chemical Functional group Activity Coefficients) models.
- The NRTL model is based on knowledge of the activity coefficient for each couple of components
considered separately. For each binary couple, two interaction coefficients (γ1, γ2) are assessed using the
NRTL equation based on three adjustable parameters. It is then necessary to obtain these parameters.
Regarding the 7 components under consideration, the parameters for only 9 out of the 21 combinations
were included in the ProSimPlus program. It was then necessary to search in the Chemistry Data
Series(3) for the other combinations. The parameters applied are shown in Table 2.
- To overcome the problems in determining these parameters, methods based on group predictions were
developed. In this respect, the UNIFAC model considers the activity coefficients of functional groups of
molecules rather than the molecules themselves, for example: CH3, OH, CH2, CH, CH3COO, CH3OH,
H2O. Then, based on the few functional groups with known thermodynamic proprieties, it is possible to
rebuild a system and determine both its thermodynamic characteristics and equilibrium data. The
UNIFAC model can be used for solutions containing no polymers or salts.

2
 ICEF9 – 2003
International Conference Engineering and Food

Table 2: Parameters applied to assess the interaction coefficients of the NRTL model
i j C ij C ji αij
water ethanol 1616.810 -635.560 0.1448
water ethyl acetate 731.931 1009.970 0.2890
water methanol 845.206 -253.880 0.2994
water 1-propanol 1898.140 2238.480 0.2870
water 2-methyl-1-propanol 2122.561 189.814 0.3291
water 3-methyl-1-butanol 3633.530 -494.839 0.2816
ethanol ethyl acetate 457.666 144.813 0.2984
ethanol methanol 12.734 -25.997 0.3356
ethanol 1-propanol 347.000 -297.249 0.2980
ethanol 2-methyl-1-propanol 592.689 6365.943 0.2806
ethanol 3-methyl-1-butanol 51.171 -42.861 0.3009
ethyl acetate methanol 420.736 345.542 0.2962
ethyl acetate 1-propanol 410.697 37.222 0.3030
ethyl acetate 2-methyl-1-propanol 410.647 37.222 0.3033
ethyl acetate 3-methyl-1-butanol 410.697 37.222 0.3030
methanol 1-propanol 24.90 9.5349 0.3011
methanol 2-methyl-1-propanol -242.128 180.103 0.3041
methanol 3-methyl-1-butanol 156.224 5.0455 0.3025
1-propanol 2-methyl-1-propanol -419.061 775.664 0.3165
1-propanol 3-methyl-1-butanol 12.221 -31.830 0.3033
2-methyl-1-propanol 3-methyl-1-butanol 741.463 -545.94 0.3040

Our attention focused on continuous distillation with the full condensation of vapour at the top of the column
and heating with a boiler fed by steam. To simulate distillation, the mathematical model used in the
ProSimPlus program is based on the theoretical stage concept, with an option of introducing a plate
efficiency coefficient. It is necessary to fix the number of theoretical plates, the position of feeds as well as
characteristics of the feed (composition, flow, temperature). To achieve convergence, it is necessary to
choose both:
1. one option of the following:
1.1 distillate flow and reflux ratio
1.2 distillate flow and quantity of heat transferred to the boiler
1.3 reflux ratio and quantity of heat transferred to the boiler.
2. one or more specifications fixing the adjustable parameters as a function of the number of extractions
and the type of action required on each (e.g. ethanol yield recovery in the distillate through action on the
distillate flow).

SIMULATION OF WATER-ETHANOL MIXING IN THE RECTIFYING COLUMN

A first column containing 66 plates (46 in the rectifying section with 70% efficiency and 20 in the stripping
section with 60% efficiency) was considered. The feed was a pure water-ethanol mixture at 9.4%alc/vol
(0.03mole/mole), a temperature of 78°C and a flow rate of 961 100 mole/h (17.8 m3/h of beer and 400 HPA/d
of productivity). Extractions were removed in liquid form at their boiling point. The aim was to determine how
such a column could produce a distillate purity of 96.4%alc/vol (0.87 mole/mole).

After numerous test runs not described here, the convergence system chosen was option 1.1 (distillate flow
and reflux ratio). Depending on the operating conditions (productivity, alcohol concentration of feed and
number of plates in the column), a reflux ratio of 3.8 was fixed and a distillate flow of 33 000 mole/h was
used to initiate calculations. Only one specification was necessary. The one chosen was ethanol recovery in
the distillate of 99.2%, with action on the distillate flow. It can be seen (Figure 2a) that the ethanol
concentration profile in the stripping section was abnormal, as if there had been an accumulation of ethanol
in some plates. Indeed, it was possible to increase the ethanol recovery specification in the distillate and to
obtain convergence of up to a 99.99%. The ethanol profile was then much more realistic (Figure 2b). The
distillate purity was too low (0.8632 rather than the 0.87 required). In order to attain a distillate purity of 0.87,
the reflux ratio and ethanol recovery were increased step by step. It was necessary to impose a reflux ratio
of 5.2. (Figure 2c) and to increase the ethanol recovery up to 99.9988%. This result demonstrates the
difficulty in increasing purity to a level near the azeotrope limit (0.8943) and that the stripping zone is not the
limiting parameter. The UNIFAC model was then tested, retaining the previous parameters. The program did
not converge and it was necessary to reduce the reflux ratio to 4.2 and increase ethanol recovery up to

3
 ICEF9 – 2003
International Conference Engineering and Food

99.999% to achieve convergence (Figure 2d). The distillate purity thus obtained was 0.8703. According to
our knowledge on the distillery plant results, the UNIFAC method would appear to be less reliable.

44 44 44 44
40 40 40 40
36 36 36 36
32 32 32 32
28 28 28 28
24 24 24 24
20 20 20 20
16 16 16 16
12 12 12 12
8 8 8 8
4 4 4 4
0 0 0 0
-4 -4 -4 -4
-8 -8 -8 -8
-12 -12 -12 -12
-16 -16 2b -16 2c -16 2d
2a
-20 -20 -20 -20
0.0 0.4 0.8 0.0 0.4 0.8 0.0 0.4 0.8 0.0 0.4 0.8

Figure 2: Simulation of the distillation of an ethanol-water solution

SIMULATION OF THE MIXING SOLUTION

The different congeners (Table 1) were added step by step. The NRTL model was selected first.

Simulation in the presence of "head congeners"

The reflux ratio of 5.2 and ethanol yield of 99.9988%, as used previously, were retained. Figure 3a shows
the methanol and ethyl acetate concentration profiles.

44 ethanol 44
40 16 16
40
36 36 12 12
32 32 8 8
28 28 methanol 4 4
24 24 0 0 methanol
20 20 -4 -4 ethyl acetate
ethyl
16 16 -8 -8
acetate
12 12 -12 -12
8 8 -16 -16
4 4 -20 -20
0 0
-4 -24 -24
-4 -28
-8 -28
-8
-12 -32 -32
-12
-16 -36 -36
-16
-20 -20 0.86 0.87 0.88 0 5.E-03 1.E-02
0.0 0.2 0.4 0.6 0.8 0 1.E-04 2.E-04 3.E-04
3a-first column 3b- demethyliser column
Figure 3: Simulation of the distillation of an ethanol-water-ethyl acetate-methanol solution in 2 columns

Ethyl acetate was concentrated in the head, unlike methanol that was partially spread throughout the entire
column. This latter result could be explained by the fact that methanol is less volatile than ethanol in low
ethanol concentration solutions, but slightly more volatile than ethanol in concentrated solutions.
Nonetheless, 99.52% of the methanol and 100% of the ethyl acetate were drawn with the distillate. As in final
rum, the methanol and ethyl acetate levels needed to be decreased, a second column (50 plates) with a feed
at plate 35 was added, as is the case in the distillery plant. Convergence option 1.1 (distillate flow and reflux
ratio) was chosen as previously. Because the objective of this column was to concentrate head congeners at

4
 ICEF9 – 2003
International Conference Engineering and Food

the top so as to be able to draw them using the lowest possible flow rate, a high flux ratio of 100 and an
initial distillate flow of 500 mole/h were chosen. The aim was to attain a methanol concentration lower than
4.10-5 mole/mole (10 g/HPA) in the rum extraction at the bottom. The specification was ethanol recovery of
98% at the bottom with the distillate flow as variable. After convergence, the methanol concentration profile
was observed and ethanol recovery in the rum was modified to obtain the specified methanol concentration.
The optimum value was ethanol recovery in rum of 98.3%. Under such conditions (Figure 3b) the distillate
had ethanol concentration of 0.869 and methanol concentration of 0.0113 which lead to an alcohol
concentration of 0.88 mole/mole (96.7%alc/vol). The distillate contained 84.48% of the methanol and 100%
of the ethyl acetate
To reduce the levels of other volatile components such as sulphides, aldehydes, CO2 and noxious gases, it
is usual, in the rectifying column, to draw off a small flow at the outflow of the last condenser and to extract
the distillate few plates below the top of the column. This design was tested by simulation: intermediate rum
was extracted from plate 41 (5 from the top) and a small flow was extracted from the condenser. Option 1.2
(distillate flow and quantity of heat transferred to the boiler) was chosen, taking the heat value obtained
previously to initiate calculations. As specifications, 1.2% of ethanol loss from the condenser draw-off and
recovery of 98.7% of ethanol in "intermediate rum" were selected. Convergence was never achieved, and
option 1.1 (distillate flow and reflux ratio) was repeated. The reflux ratio that would permit convergence was
determined step by step. The range of reflux ratio values within which convergence was achieved was very
narrow. It was then decided to resume the work without taking account of this head extraction.

Simulation in the presence of “heavy congeners”

With respect to heavy congeners (higher alcohol), the results concerning propanol are shown. The same
parameters as previously were applied. The propanol concentration in the feed was 26.10-6 mole/mole. It can
be seen from Figure 4a that propanol accumulated on intermediate plates (around number 12). Its presence
induced a significant change to the ethanol concentration profile, and its concentration in the distillate fell
sharply (from 0.87 to 0.844). Propanol was totally drawn with the distillate. In the demethylising column
(Figure 4b), all propanol was extracted with the rum from the bottom. It was therefore essential to perform a
further extraction from the first column, and plate 13 was chosen to fix conditions near the distillery plant.
After several tests, it was decided to fix a 4% loss of ethanol for that extraction, which is a standard value
applied in distillery plants. After numerous tests, convergence was achieved with ethanol recovery in the
distillate of 95.995%. It can be seen from Figure 4c that the maximum concentration of propanol fell from
0.085 to 0.021. Most of the propanol (99.73%) was drawn from the column by the extraction at the 13th plate.
The ethanol concentration in the distillate reached 0.868.
44 44 16 44 44
40 40 12 40 40
36 36 8 36
4 36
32 32 32 32
0
28 28 28 28
-4
24 24 -8 24 24
20 20 -12 20 20
16 16 -16 16 16
12 12 -20 12 12
8 8 -24 8 8
4 4 -28 4 4
0 0 -32 0 0
-4 -4 -36 -4 -4
-8 -8 0.E+00 5.E-04 1.E-03 -8 -8
-12 -12 4b-propanol in -12 -12
-16 -16 demethylyser -16 -16
-20 -20 -20 -20
column
0.0 0.4 0.8 0.00 0.04 0.08 0.0 0.4 0.8 0.00 0.04 0.08
4a-first column 4c-first column with an extraction plate 13
Figure 4: Simulation of the distillation of an ethanol-water-propanol solution

Simulation with all components

The composition of the feed was as shown in Table 1. Both columns had the same structure and reflux ratio
as previously (5.2 and 100). Three intermediate outflows were considered in the rectifying section at plates
1, 7 and 13, in order to remove amyl alcohol, isobutanol and propanol respectively. Several extraction flows
were tested. Figure 5 shows the ethanol and high alcohol profiles in the first column, for two distributions of
ethanol loss in the different draw-offs. The ethanol profiles were the same and only one of them is presented.
These results were in accordance with the concentration profiles observed in the distillery plant.

5
 ICEF9 – 2003
International Conference Engineering and Food

44 44 44
ethanol
40 40 40
propanol propanol
36 36 36
32 32 amyl 32 amyl
28 28 alcohol 28 alcohol
24 24 isobutanol 24 isobutanol
20 20 20
16 16 16
pL13-4% pL13-5%
12 12 12
8 8 8
pL7-1% pL7-2%
4 4 4
0 0 pL1-4% 0 pL1-2%
-4 -4 -4
-8 -8 -8
-12 -12 -12
-16 -16 5a -16 5b
-20 -20 -20
0.0 0.2 0.4 0.6 0.8 0.00 0.01 0.02 0.00 0.01 0.02
Figure 5: Concentration profiles of ethanol and high alcohol components in the first column

44 44
UNIFAC model was tested with the same initial ethanol
40 40
data. Convergence was achieved with a reflux propanol
36 36
ratio of 3.8 (rather than 5.2 with the NRTL model). 32
32 amyl
It can be seen from Figure 6 that the high alcohol
28 28 alcohol
concentration profiles differed markedly from
24 24 isobutanol
previously. All peak concentrations were obtained
at nearly the same plate. Once again, it appears 20 20
that the UNIFAC model does not provide a true 16 16
12 pL13-5%
representation of the thermodynamic data. 12
8 8 pL7-2%
4 4
0 0 pL1-2%
-4 -4
-8 -8
-12 -12
-16 -16
-20 -20
0.0 0.2 0.4 0.6 0.8 0.00 0.01 0.02
Figure 6: Concentration profiles using the UNIFAC model

CONCLUSION
The aim of this work was to test the possibility of using the ProSimPlus program to simulate the behaviour of
volatile congeners during the distillation of alcohol solutions in continuous distillation columns. The first
results obtained here justified the need to use two columns in series to remove methanol and ethyl acetate
from the rum, and secondly, to extract small flows at different plates in the rectifying section of the first
column in order to remove heavy congeners (propanol, isobutanol, amyl alcohol). However, the application
of ProSimPlus program is not without problems. Firstly, the availability of a good thermodynamic model is
important to assess equilibrium data. The NRTL model appeared to be more reliable in this respect than
UNIFAC, but few parameters of the NRTL model have been published. Secondly, the program does not
converge easily because it is necessary to fix the variable values. It should be more convenient to have the
possibility to fix limits as being “higher than” or “lower than”, which is closer to the conditions prevailing in
distillation columns. Further studies are required to clarify these problems.

BIBLIOGRAPHY
1. Mariller C. La distillation fractionnée et la rectification. Dunod et Pinat, Paris, 1917.
2. Jacques K.A., LyonsT.P., Kelsall, D.R. The alcohol textbook. University press, Nottingham, pp. 350, 1999.
3. Gmehling et al. Vapor-liquid equilibrium data collection, Chemistry Data Series, Dechema, Francfurt, 1977-1988.

6
ICEF9 – 2004
International Conference Engineering and Food

Analysis of heat loads and optimisation of refrigeration systems for wineries

T. R. Delves (1), M. Weedon (2), J. P. Louis (3)

(1) National Wine and Grape Industry Centre. Charles Sturt University, Wagga
Wagga, 2678, Australia. tdelves@csu.edu.au

(2) National Wine and Grape Industry Centre. Charles Sturt University, Wagga
Wagga, 2678, Australia. mweedon@csu.edu.au

(3) National Wine and Grape Industry Centre. Charles Sturt University, Wagga
Wagga, 2678, Australia. jlouis@csu.edu.au

Abstract:

Refrigeration is important in winemaking and may account for up to 70% of the total
energy use within a winery. This paper examines the major heat loads which occur
during winemaking, including heat of fermentation and solar heat gain to outside
tanks. The elements of a mathematical model are proposed with an aim of providing
a tool to assist in improving the efficiency of a winery refrigeration system.

Keywords: energy, modelling, optimisation, refrigeration, wine.

1.0 Introduction

Due to the high ambient temperatures (300C – 350C) experience during the harvest
period in many regions of Australia, refrigeration is a particularly important
component of winemaking. Refrigeration is used for chilling grape must prior to
pressing, chilling grape juice, fermentation control, chilling finished wines and cooling
barrel storage areas. Refrigeration, however, comes at a significant cost to the
winemaker, and may account for 60% - 70% of the total energy used in a winery 1.

Refrigeration systems in wineries almost universally rely on the use of a secondary

refrigerant, which is usually an ethanol/water mixture. The secondary refrigerant,
often referred to as ‘brine’, is pumped into either separate heat exchangers or ‘dimple
plate’ heat exchangers attached to the tank wall.

This study examines the major heat loads which occur in the wine making process,
and suggests ways in which the heat loads may be incorporated into a model of the
total refrigeration system. With this model, it is proposed that certain parameters
such as brine storage volume, brine temperature, brine flow rate and the utilisation of
‘off peak power’ will be optimised, leading to reduced energy use in wineries.

2.0 Heat Loads

The various heat loads acting on a typical winery refrigeration system will be
discussed. These loads include must chilling, juice/wine cooling, fermentation loads
and solar heat load to outside tanks. During the busy vintage period (between
ICEF9 – 2004
International Conference Engineering and Food
February and April in Australia) many of these loads will overlap, an important
consideration for the initial sizing of the refrigeration plant.

2.1 Must chilling loads

Must is the grape product after crushing, consisting of juice, skins and seeds. For the
making of white table wines, grape must is usually chilled after crushing to 100C – 18
0
C in order to minimise oxidations and to help preserve the delicate aromas and
flavours in the juice. Must chilling represents a high refrigeration load for a
refrigeration system and occurs at regular intervals during each day of vintage. A
secondary refrigeration system utilising storage of chilled brine is quite appropriate
for meeting this type of fluctuating load.

The actual rate of heat removal from the must can easily be calculated using:

q = m Cp ∆T (1)

where: q = rate of heat removal (kW)

m = mass flow rate (kg/s)
Cp = specific heat of must (kJ/kg 0C)
∆T = temperature change of must (0C)

The pumping of chilled must poses certain problems in a winery due to the high
viscosity, resulting from the combined effect of a high solids content and reduced
temperature of the product. A typical viscosity of 15 mPas for must at 100C has been
proposed 2, while for comparison, water at the same temperature has a viscosity of
only 1.3 mPas. As a consequence, heat exchangers used for must chilling need to be
of generous dimensions and should contain no obvious flow constrictions.

2.2 Juice / wine cooling loads

Juice for the making of white table wines may be settled at reduced temperatures in
tanks prior to fermentation. The rate of heat removal from the juice is given by:

q = M Cp ∆T/t (2)

where: q = rate of heat removal (kW)

M = mass of juice (kg)
Cp= specific heat of juice (kJ/kg 0C)
∆T/t = rate of temperature drop (0C/s)

This relationship is also valid for the chilling of wine, providing appropriate values for
the mass and Cp are used.

2.3 Fermentation loads

During the process of fermentation, where grape sugars (glucose and fructose) are
converted to alcohol, heat is produced at the rate of 545 kJ/kg of sugar 3. This heat
ICEF9 – 2004
International Conference Engineering and Food
will rapidly raise the temperature of the fermenting juice, ultimately killing the yeast
cells responsible for fermentation. Hence, heat needs to be removed from the
fermentation vessel. This is usually accomplished by circulating brine in jacketed
tanks. White wine ferments are generally maintained at 12 0C to 16 0C while red wine
ferments are kept between 18 0C and 24 0C.

The fermentation load from red wine is of particular importance in refrigeration load
calculations, due to the higher fermentation rate compared with white wines. Red
wine fermentation vessels are generally uninsulated to aid heat dissipation, as
ferment temperatures exceed ambient temperatures for most of the day. To enable
additional cooling, fermentation vessels usually have a jacket (dimple plate) heat
exchanger welded into the vessel wall. Since the rate of fermentation is temperature
dependent, the winemaker has good control of the fermentation rate simply by
adjusting the amount of cooling applied to a fermentation vessel.

2.4 Fermentation trials

The fluid flow patterns and temperature distribution inside a red wine fermentation
vessel are quite complex. To measure this internal temperature distribution, a
temperature sensing array, consisting of three stainless steel tubes each containing
15 Dallas Semiconductor 18B20 temperature sensors, was placed in a stainless steel
red wine fermentation vessel, as illustrated in figure 1. As each sensor has a unique
electronic serial number, multiple devices can be wired in parallel on three wires;
power, signal and ground.

The Array
• Legs are 50mm stainless steel tubing
• 15 sensors per leg
• 45 sensors in the array
Additional sensors on:
• Ambient air
• Brine in
3m • Upper brine out
• Lower brine out

1.2m

Figure 1 Wine fermentation vessel showing temperature sensing array

and cooling jackets.

Temperatures were recorded every 2.5 minutes during the fermentation period and
for several days post fermentation. The average tank and ambient air temperatures
recorded are shown in figure 2. The graph shows that during fermentation, when tank
cooling was applied to the tank jacket, fermentation temperatures were maintained at
a constant 220C. When the fermentation was complete, and the cooling turned off,
the tank temperature reduced in a cyclic nature, following the diurnal variations in
the ambient temperatures.
ICEF9 – 2004
International Conference Engineering and Food
Considerably higher temperatures of 250C - 33 0C were recorded in the cap (mass of
floating skins on top of the fermenting juice) of the fermenting juice. Cap
temperatures, however, reduced rapidly when the cap was irrigated with juice drawn
from the bottom of the fermentation vessel.

30

25

20
Temperature (C)

15
ambient air
temperature
tank temperature

10

Refrigerated tem perature control

5

0
16-Apr-02 20-Apr-02 24-Apr-02 28-Apr-02 2-May-02

Figure 2 Temperature profile of fermenting juice

2.5 Solar load predictions

Many medium and large scale wineries (over 500 tonne crush) have outside stainless
steel tanks for wine storage. Such tanks are often insulated with polystyrene (75mm)
clad with aluminium (0.8 mm). Tanks which are uninsulated, however, are subject to
considerable heat gain from solar radiation.

A mathematical model has been developed to determine the amount of heat received
by an outside tank due to solar radiation. By monitoring the temperature profile of a
tank during the night period, a relationship was developed to link rate of heat loss
(kW) to ambient overnight temperature conditions. This relationship was also applied
during daylight hours to calculate tank heating due to ambient temperature conditions
(ambient heating). Subsequent temperature monitoring of the tank in daylight hours
provided an indication of the rate of heat gain from both ambient temperature and
direct solar contributions. Hence, the solar component of heating could be isolated,
using the simple relationship:

qs = qT – qA (3)

where qS = rate of heat gain due to solar radiation (kW)

qT = total rate of heat gain (kW)
qA = rate of heat gain from ambient conditions (kW)
ICEF9 – 2004
International Conference Engineering and Food

The effect of solar radiation on the second tank in a line of tanks, running from North
to South, is shown in figure 3.
800

600

400

200
Heating

0
tota l hea ting
0 6 12 18 24
M od eled hea ting
-200

S olar he atin g
-400

-600

-800

Hour of day

Figure 3 Typical daily cycle of solar heating, modelled (ambient)

heating, and total heating.

The graph indicates that there are two peaks of solar heating, at approximately 9:00
am and 3:00 pm. The likely explanation for this is that the sun contributes most direct
radiative heating when it is at low inclination, when shining directly onto the Eastern
and Western sides of the tank. The model also reveals that there is a reduction in
solar gain to the tank at mid-day. This is primarily due to shading caused by the
adjacent tank to the North. Furthermore, the sun, being at a high altitude angle, is
radiating its energy onto the lid of the tank, which is smaller in area than the tank
sides and also not in direct contact with the tank contents, due to the ullage (air
space) in the tank.

Using methods cited by Duffie and Beckman4, the intensity of the diffuse and direct
beam solar radiation was calculated. As the tank being studied was shaded for part
of the day, a simple shading algorithm using solar azimuth was applied to the direct
beam component of the sunlight. Figure 4 shows a comparison between the solar
heating from figure 3 in Watts and predicts solar heating in Watts per square metre.

To extend this direct solar heating study, an array of 200L stainless steel tanks filled
with water has been set up in an open area to monitor the effects of solar heat gains
and tank shading from adjacent tanks. Shading effects will also be compared in tanks
positioned in rows having North-South and East-West orientation. This trial is
presently in progress and data will be available in December 2003.
ICEF9 – 2004
International Conference Engineering and Food
800

600

400

Solar heating
Heating

Predicted Shadowed
Predicted UnShadowed

200

0
0 6 12 18 24

-200
Hour of day

Figure 4 Solar and predicted heating of a shadowed tank, compared with the
predicted heating of an unshadowed tank

3.0 Conclusions

The research to date has concentrated on monitoring fermentation temperatures and

the modelling of solar heat loads to wine tanks. The trials currently in progress will
quantify the heat load received by outdoor tanks and also investigate the effects of
shading from adjacent tanks in lines of tanks with different orientations.

Future work will include modelling of the heat loads and creating an overall heat load
/ refrigeration model. It is envisaged that this model will enable certain parameters of
the refrigeration system to be optimised, resulting in reduced energy costs for
wineries.

4.0 Acknowledgments

The authors wish to acknowledge the assistance of the Rutherglen Estates winery,
Gordon Brothers Refrigeration and Professor Geoff Scollary, Professor of Oenology,
Charles Sturt University.

5.0 References

1. Broadbridge W. Energy management for quality and value. The Australian

grapegrower & winemaker. pp 24-25, May 1994.

2. White R., Adamson B.,Rankine B. Refrigeration for winemakers. Winetitles,

Adelaide. pp 23, 1989.

3. White R., Adamson B.,Rankine B. Refrigeration for winemakers. Winetitles,

Adelaide. pp 11, 1989.

4. Duffie J. A., Beckman W. A. Solar engineering of thermal processes, 2nd ed,

Wiley, New York, pp 15, 73,75, 1991.
 ICEF9 – 2004 International Conference Engineering and Food

Two-dimensional thermal expansion of a foamed food product :

modelling and simulation

Doursat Christophe (1), Flick Denis (2)

UMR Génie Industriel Alimentaire, Cemagref – ENSIA – INA P-G - INRA

Institut National Agronomique Paris-Grignon, 16 rue Claude Bernard, 75231 Paris Cedex 05.
(1) doursat@inapg.fr
(2) flick@inapg.fr

Abstract :
A model is proposed to forecast the expansion during baking of sponge batter taking into account
conductive heat transfers, water sorption equilibrium, thermal dilatation, bubbles pressure and batter
elasticity. Equations discretisation are based on control volumes with elastic properties, which distort
with batter. Bidimensional numerical simulations are consistent with physical observations made by
several authors.

Key words : modelling, foamed product, elasticity, thermal expansion.

Nomenclature
Cp specific heat capacity. Subscript : s for dry m mass. Subscript : s for dry matter, v for
matter, w for water, g for uncondensable vapour, w for water (liquid and vapour) and g
gas and v for vapour (J.kg-1.K-1) for uncondensable gas (kg)
P external pressure (Pa)
∆H v water vaporisation enthalpy (J.kg-1)
p, pv, pg, pvsat total gas phase pressure, partial water
ε porosity of material vapour and uncondensable gas pressures,
ε strain tensor saturated vapour pressure in the bubbles (Pa)
H specific enthalpy (J.kg-1) p’ relative total gas phase pressure in the
bubbles (Pa)
I identity matrix σ stress tensor (Pa)
k spring’s stiffness (per unit length in the ρ
third direction) (N.m-1.m-1) x = ( x, y ) position (m)
ρ
l spring’s length (m) X = ( X ,Y ) displacement (external pressure refe-
λ, µ Lame’s constants. Subscript : e for rence 0) (m)
equivalent porous media and m for non ρ
X ' = ( X ' ,Y ' ) displacement (external pressure refe-
porous media (N.m-2)
λth thermal conductivity. Subscript : b for rence P) (m)
batter and e for equivalent material (batter Xw kg of water by kg of dry matter
and gas bubbles) (W.m-1.K-1)

1. Introduction
Many food products are foamed before they are submitted to a thermal treatment. This is the case, for
example, with a sponge cake which is basically composed of a gas phase (air and water vapour)
dispersed in a continuous batter of complex rheological (liquid-solid) behaviour. During baking, the
bubbles expand under thermal dilatation and water evaporation. At the same time, batter elastic
and/or viscous strains limits the expansion. It’s important to master the strains of the product and the
stresses for example, to avoid fractures in it or to control its final shape.

A model is proposed to forecast the expansion of such a product taking into account conductive heat
transfers (depending on porosity), water sorption equilibrium, thermal gas dilatation, bubbles pressure
and batter elasticity. These are the main occurring phenomena at the beginning of the baking, but
some others will have later to be considered (vapo-condensation, water and vapour transfer…). The
aim of this work is to obtain a model :
ƒ easy to manipulate,
ƒ easy to generalise to viscoelastic behaviour,
ƒ compatible with simple numerical solving of heat and mass transfer by finite volume approach on
control volumes with elastic properties, which distort with batter.
2. Modelling of mechanical structure

2.1. Non porous elastic media

The aim of this paragraph is to show that the equations of isothermal isotropic linear elasticity can be
approached, for particular values of the Poisson's ratio, by springs network equilibrium equations.

2.1.1. Navier equation

Considering an elastic solid, the strain tensor is defined by:

ρρ ρρ
1
(
ε = 2 ∇X + ∇ X t ) (1)
and the stress tensor is provided by Hooke’s law :
ρ ρ ρρ ρρ
(. )
σ = λ ∇ X I + µ ∇X + ∇X t ( ) (2)
The equations of static equilibrium are obtained from the divergence of the stress tensor and are
called the Navier equations :
ρ ρ ρρ ρρ ρ ρ
ρ
. (. ) (
∇  λ ∇ X I + µ ∇X + ∇X t  + ρ g = 0
 
) (3)

2.1.2. Two-dimensional deformation

In two particular cases, deformation can be considered bidimensional. The Navier equations (3) for
ρ
X ( x, y ) becomes then :
ρ ρ ρρ ρρ ρ ρ
ρ
. (. ) (
∇  λ' ∇ X I + µ' ∇X + ∇X t  + ρ g = 0
 
) (4)

• for plane deformations ( ε xz = ε yz = ε zz = 0 ) λ' = λ , and µ' = µ . This is approximately the case
during the cooking of a batter for which one dimension is large compared to the others.
2µ
• for plane stresses ( σ xz = σ yz = σ zz = 0 ) λ' = λ λ +2µ , and µ' = µ . This approximation could be
used for the cooking of a low-thickness biscuit on a plate.

2.1.3. Springs network

ρ
(. )
A particular discretisation (refer to [1]) of the stress balance ∇ σ in Navier equations (4), based on a
small displacements hypothesis, can be interpreted as the forces balance for the springs network
shown bellow :
• horizontal and vertical springs stiffness : k ' = (λ'+3µ') / 2 (for unit length in the third direction)
• diagonal springs stiffness : k = (λ'+µ') / 2
• torsion springs stiffness : C = (µ'−λ' )∆y / 2 .

The considered springs are Hookean. Each spring is defined by its stiffness k, original length l*, and
ρ ρ ρ ρ ρ
its extremities positions x i and x j ( ∆x = x j − x i ). The force exerted on extremity i is defined by :
ρ  ρ ρ
ρ * ∆x 
f i , j (∆x ) = k ∆x − l
 ρ (5)
 ∆x 

In order to simplify the model, we assume that the Lame’s constants agree λ' = µ' . That is equivalent
λ 1
to impose a Poisson's ratio ν = 2( λ + µ )
of the 3d material equal to 4
in the case of a plane strain field
1
and to 3
in the case of a plane stress field, which is consistent with the values of many materials.
The model is then reduced to six springs for each cell (figure on the right) of
same stiffness ( k = λ' ). Four springs define the perimeter of the cell and the
two others are carried by the diagonals.

The forces balance at each node of the grid is :

ρ ρ ρ
∑ fk + m g = 0 (6)

2.2. Elastic porous media

Many works predict composite or porous media properties using homogenisation methods. In the case
of dilute spherical pores (small values of porosity ε) inside an elastic material, the Lame’s constant λe
and µe of the porous medium without, external or internal, gas pressure are given by [2] :

λ e = λ m −
(
(λ m + 2µm ) λ2m + 2λ mµm − µ 2m ε )
 µm (λ m + µm )
 (7)
 µ = µ 1 − 2 m m + 2µm ) ε 
 µ (λ
m  
 e  λ m + µm 
where λm and µm are the non porous medium properties. In the particular case where λ m = µ m the
equations (7) are simplified : λ e = µe = λ m (1 − 3ε ) .
The introduction of bubbles into the material can thus be modelled by establishing a relation between
the springs stiffness and the porosity as follows : k (ε ) = λ m (1 − 3ε ) . To adapt this to the case of higher
porosity and to ensure that k (1) = 0 , we propose :
k (ε ) = λ m (1 − ε )
3
(8)

2.3. Elastic porous media with differential gas pressure

We will now describe how the behaviour of a material is modified by the presence of a gas, with a
pressure p inside the pores (refer to the figure bellow). Firstly we remind that, if an elastic body of
initial surface S0 is subjected to a uniform pressure P, the variation of the surface checks
S −S0 P
θ= S0
= − K , where K is the bulk modulus of material.

Configuration a) can be obtained by superposition of the states b) and c). In state b), the body is
P −p
subjected to an external pressure P-p and θ b = − Ke
with Ke the bulk modulus of porous material with

empty pores ( K e = λ e + µ e in two-dimensional case). In state c), the external and internal pressures
are both equal to p. Since the fluid phase and the solid phase are submitted to the same pressure, the
pore can be neglected and the bulk modulus of the elastic solid without pores Km can be used so that
p P*
θ c = − K . The superposition of the states b) and c) can be written θ = θ a + θ b = − K where
m e

P * = P − α p is called effective pressure, with:

Ke
α = 1− (9)
Km
Hooke’s law (2) is given for a reference configuration (null
strains) without atmospheric pressure. When the external and
internal pressures are both equal to the atmospheric pressure
ρ
P, the porous material is submitted to the displacement X *
which defines a new reference configuration.
The stress tensor for the porous media with a relative overpressure (p-P) in the bubbles can finally be
written as the sum of two contributions : an elastic tensile stress for the batter and an isotropic
pressure stress for the bubbles :
ρ ρ ρρ ρρ
ρ ρ ρ*
(. ) ( )
σ ' = λ e ∇ X ' I + µ e ∇X '+∇X ' t + α( p − P ) I (10)
where X ' = X − X is the displacement from the new reference configuration (where p=P).

Basically the proposed mechanical model is a network of springs which stiffness depends on the
porosity (8). The effects of pore pressure are taken into account by adding pressure forces, which
depend on α p' = α( p − P ) . At each node, the forces equilibrium is :
ρ ρ ρ ρ
∑ fkρ(ε)ρ+ m g + ρ∑ fα(ε )p' = 0 (11)
This forms a non-linear set of equations, F ( X , ε, p ) = 0 , to be solved by Newton-Raphson.

3. Modelling of internal heat transfer

Our aim is to propose a description of some basic physics at the beginning of baking process by
taking into account two elementary processes : heat transfer by conduction from the surface to the
core, and batter expansion due to the internal gas over-pressure.

3.1. Hypothesis

A sponge cake is basically composed of a gas phase (air or other uncondensable gas and water
vapour) dispersed in a continuous batter composed of dry matter and water. As we consider the
beginning of the baking, the bubbles can be considered as closed. We take account of conductive
heat transfer and of water evaporation (contained in the batter) but not of gas generation and mass
transfer (water) or vapo-condensation phenomena.
The aim of the model is to predict the time and space profiles for four state variables ; liquid water
content Xw, temperature T, total pressure p in the bubbles and porosity of the material ε.

3.2. Conservation equations

We use a finite volume approach in which the cells can be distorted, the nodes being attached to the
dry matter. This approach allows to write simple conservation laws since there is no convection
through cell faces.
In each cell, temperature, bubble pressure, mass of water, mass of
dry matter and porosity are defined.
At the beginning, the batter is divided into square cells, and during
baking, the bubbles expand under thermal dilatation and water
evaporation deforming the mesh.

3.2.1. Mass conservation

It is to notice that the dry matter mass by cell (ms) is constant as the cell faces are bounded to dry
matter. Also the total mass of water (vapour and liquid) is constant :
mw = mv + X w m s (12)
The cell volume is the sum of the bubble volume (εV), the dry matter volume and the liquid water
volume :
m m
V = εV + s + X w s (13)
ρs ρw
3.2.2. State equations

We suppose that a local thermodynamic equilibrium exists. To express the model equations with the
selected variables, it is necessary to introduce the state thermodynamic equations :
ƒ the sorption equilibrium relationship :
pv = aw ( X w ) pvsat (T ) (14)
where the selected model for desorption isotherm of the batter, according to [3], is
 
aw ( X w ) = exp −B  with B=2.95 and C=0.78 in SI units.
 (100 X )C 
 w 
ƒ the perfect gas law for the gas phase (water vapour and uncondensable gas) :
m mg
pv εV = v RT pg εV = RT (15)
Mv Mg
where the vapour mass mv can be expressed in terms of X w (12) and the uncondensable gas mass
mg is constant as the bubbles are closed.
With (13), (14) and (15) we obtain a relation between X w , T and ε in each cell : f(Xw,T, ε)=0 and the
total pressure p=pv+pg can also be expressed versus X w , T and ε.

[ ( ]
The enthalpy corresponding to one cell, can be expressed as follows :
)
H = m s C p s + X w C p w + m g C p g + mv C p v T + mv ∆H (16)
in which we can substitute mv expressed in terms of X w and finally obtain a relation g ( X w ,T , H ) = 0 .

3.2.3. Thermodynamical equilibrium

A set of equations is obtained :

 f ( X w ,T , ε ) = 0

g ( X w ,T , H ) = 0
which can be solved, for given porosity (ε) and enthalpy (H) by Newton-Raphson method. The results
are the temperature, the batter water content and finally the total bubble pressure.
ρ ρ ρ
Combined with the mechanical model, F ( X , ε, p ) = 0 (11) these equations describe the mechanical
and thermodynamical equilibrium of the set of cells at each time for given enthalpies in each cell.

3.3. Heat transfer

We only consider the heat transfer which results from the conduction from the surface to the core. The
Crank-Nicholson scheme is used for time derivative and, in each cell, an energy balance is calculated
ρ ρ
taking into account the thermal conduction, according to Fourier’s law q = −λ th.e ∇T . Heterogeneous
and polyphasic material is assimilated to a continuous medium of equivalent thermal conductivity
(Maxwell’s upper bound model) :
  λ  
 3ε 1 − λ th.b  
λ th.e λ  th.g 
= th.b 1 +  (17)
λ th.g λ th.g  (1 − ε ) + λ th.b (2 + ε ) 
 λ th.g 
 
Xw
with batter’s thermal conductivity λ th.b = a + b according to [3].
1+ Xw
4. Numerical simulation
The beginning of baking of a cake batter in a mould, in a batch oven, has been simulated. The initial
geometry is a square domain of 4cm height. The initial properties of the batter were ; ε0 = 0.3, T0 =
20°C and Xw0 = 0.5. The heat transfer coefficient on the surface of batter is 10 W.m-2.K-1 and oven
temperature is 120°C. The mechanical boundary conditions are free slippage on the mould, and free
surface at the contact with air. Because of the symmetry, simulation has been performed only on the
half-domain with null flux on the symmetry plan.

Parameter Value Units Parameter Value Units

Cpg 1012 J.kg-1.K-1 a 0.645 W.m-1.K-1
Cps 1952 J.kg-1.K-1 b 0.134 W.m-1.K-1
C pv 2027 J.kg-1.K-1 λth.g 0.025 W.m-1.K-1
Cpw 4217 J.kg-1.K-1 ∆H 2258 kJ.kg-1
 t=0s t = 1000 s Here are presented the simulated deformation
and temperature field after 1000s.
Below are figured the temperature and pressure
evolutions :
ƒ solid line : centre of cell 1
ƒ dashed line : centre of cell 2
ƒ dotted line : centre of cell 3
ƒ total pressure p : without symbol
ƒ gas pressure pg : with star
ƒ vapour pressure pv : with circle.

The deformation is consistent with the one

experienced during a real baking particularly at
the top of the mould.
The pressures evolutions evidence that the main
factor of expansion is not the thermal dilatation of
the uncondensable gas (which partial pressure
decreases) but evaporation of water.

5. Perspectives
We remain far from a complete model of baking of a biscuit. However, the developed model can be
easily improved by adding mass transfers (water and gas) for the baking modelling part. For the
mechanical part, we could consider that the length of the springs, as far as their stiffness, depend of
moisture, of temperature and of the thermal and hydrous history. That would be equivalent to use a
model of non-linear thermo-hygroelasticity. It would be also possible to take into account a viscoelastic
behaviour by combining springs and Newtonian dashpots. A starting point could be the existing work
[4] on the evolution of the viscoelastic parameters of batter during baking, from which the
corresponding evolutions of the springs and dashpots parameters can be easily deduced. Lastly, a
tridimensional approach is possible by considering cubes whose faces are constituted by springs.

6. References

1. Doursat C., Flick D., Un modèle simple à manipuler pour décrire la déformation de produits
alimentaires solides lors de traitements thermiques, Congrès français de Thermique, 499-504,
Vittel 2002.
2. Thorpe M. F., Sen P. N., Elastic moduli of two-dimensional composite continua with elliptical
inclusions, Journal of Acoustical Society of America, 77 (5), 1674-1680, 1985.
3. Lostie M., Peczalski R., Andrieu J., Laurent M., Study of sponge cake batter baking process. II.
Modeling and parameter estimation, Journal of Food Engineering,, 55 (4) 349-357, 2002.
4. Yasukawa T., Mizukoshi M., Aigami K., Dynamic viscoelastic properties of cake batter expansion
and heat setting, Proc. of symp. “Fundamentals of dough rheology”, Ed H. Faridi and J. M.
Faubion, 63, AACC 1986.
ICEF9 - 2004
International Conference Engineering and Food

MODELLING THE QUALITY ATTRIBUTES OF YOGHURT: TEXTURE DEVELOPMENT

Alix Dubert (1), Alistair Grandison (2), Keshavan Niranjan (3)

(1) School of Food Bisciences, The University of Reading, PO Box 226, Whiteknights, RG6 6AP,
Reading, UK – a.s.dubert@reading.ac.uk
(2) Same address as (1) – a.s.grandison@reading.ac.uk
(3) Same address as (1) –afsniran@reading.ac.uk

Abstract – Set and stirred yoghurts with total protein content ranging from 4 to 6% were produced
using different ratio of caseins to whey proteins. The texture of yoghurt was studied using a texture
analyser. Although the Texture Analyser indicated the gel strength of set yoghurt, it could not
distinguish between samples which had the same level of protein but different ratios of casein to whey
proteins. This problem was overcome in the case of stirred yoghurt by using a reverse flow
viscometer. Viscosity data clearly showed that, for a given protein concentration, higher casein to
whey protein ratio resulted in a stirred yoghurt having a higher consistency.
Key words – yoghurt, texture analyser, caseins, whey proteins, reverse flow viscometer

1. Introduction

The origin of fermented milk products can be traced back to at least ten thousands years. There is
evidence to show that the first civilisations to produce fermented milks were populations of
Mesopotamia, North East Africa and Indians in Asia. Milk collected from sheep, goats or cows was left
in a warm place in animal skins to ferment until it solidified (1). Yoghurt is one of the best selling
fermented milk products today. It is manufactured by fermenting milk with starter-culture bacteria
which transforms lactose to lactic acid forming a protein gel.

In addition to fermentation, two other methods are available to acidify milk: i) direct addition of an acid
such as hydrochloric acid (HCl), and ii) addition of GDL (Glucono-Delta-Lactone) – widely used in food
processing as an acidulent - whose gradual hydrolysis to gluconic acid results in pH drop and gel
formation (2,3). This acidulent, known more formally by the name D-gluconic acid delta lactone, has
the empirical formula: C6H10O6. It is available as a fine, white, and nearly odourless crystalline powder
with a sweet taste and an acid after-taste (4). GDL has been used as a model acidulant to investigate
mechanisms leading to the formation of yoghurt (5). From an experimental point of view, it is very
convenient because acidification of milk occurs more rapidly than under fermentation conditions (2 - 3
hours instead of 4 - 5 hours). Further, the final pH of GDL-induced gels is strongly dependent on its
starting concentration in milk. When added to an aqueous system, GDL readily forms an equilibrium
mixture of lactone and gluconic acid, which are intermediates in the oxidation of glucose through the
pentose phosphate cycle (Fig. 1). Gel formation occurs when casein micelles, destabilised either by
the action of chymosin or by souring (6), coagulate to form a firm gel composed of strands of casein
micelles which to form a matrix of proteins. The whey protein is entrapped inside a matrix of strands.
In general, the higher the level of proteins in the milk base, the stronger is the resultant gel (7).

The aim of this study was to investigate the effects of: 1. the total protein concentration and 2. the ratio
of caseins to whey proteins on texture development, when model milk solutions composed of proteins
and skim milk ultrafiltrate, were acidulated with GDL.

1
ICEF9 - 2004
International Conference Engineering and Food

HO OH HO OH
+
H

HO HO
O O OH+ O

Glucono-delta-lactone
OH 2

OH OH OH 2+

+ O
-H
OH OH OH OH OH

OH OH

Gluconic acid

Figure 1: GDL acidic hydrolysis when added to an aqueous solution

2. Materials and methods

2.1 Materials
Model milk: pasteurised skim milk from Express Dairies (Ruislip, Middlesex) was ultrafiltrated using a
ES625 membrane (25,000 MW cut-off). Proteins were added to this UF skim milk. The casein and
whey protein content were adjusted using calcium caseinate (Lactoprodan DI-8905, Arla Foods
Ingredients, Denmark) and defatted whey protein concentrate (Volactive 80, Volac International Ltd,
Royston, Herts). The total protein concentrations were adjusted to: 4, 5 and 6% of the solution. The
ratio between caseins and whey proteins was maintained at the following values: 90-10%, 80-20%,
70-30% and 60-40%. The GDL used was 99% pure (ADM Ringaskiddy, ADM Ingredients Ltd, Widnes,
Cheshire). The amount added was estimated to give a final pH of 4.4 (± 0.12) in 3 hours, using the
following equation:
GDL amount (%) = 0.280 + 0.1865 * caseins (%) + 0.1879 * whey proteins (%)
The above formula was determined empirically by tracing pH as a function of time in solutions having
different levels of proteins, caseins and added GDL.

2.2 Acidulation procedure

The procedure is schematically illustrated in Fig 2. All experiments were conducted in triplicate.

2.3 Texture measurement:

The texture of set and stirred yoghurt was characterised at 4°C, using Texture Analyser TA.XT2 with a
cylindrical probe of 50 mm diameter. In addition, the stirred yoghurts were also characterised by timing
their flow in U-tube viscometers (sizes D and E) at 4°C.

2
ICEF9 - 2004
International Conference Engineering and Food

Sodium caseinate + Defatted whey protein + Skim milk ultrafiltrate

(approximately 1.8L total
volume)

Mixed for 2 min - 4500 RPM

(Silverson)

Storage at 4°C for overnight

hydration

pH adjustment to 6.8 with 0.1M

NaOH

Heated to 40°C with stirring

Divided into 200 ml portions

and transferred to lidded
yoghurt pots containing GDL

Acidification at 40°C - 3 hours

Cooling in ice to approximately

20°C - 20 min

For testing set yoghurt For testing stirred yoghurt

Pots further cooled to 4°C (3 hrs) Pots stirred using Silverson for 30 s

Texture Analysis Pots further cooled to 4°C (3 hrs)

Texture Analysis or U-tube

Gentle stir and measure pH
viscometer

Figure 2: protocol followed for making up set and stirred yoghurt

.

3. Results and discussion

3.1 Texture characterisation using the Texture Analyser

3.1.1 Set yoghurts

3
ICEF9 - 2004
International Conference Engineering and Food

Force in compression measured by the texture analyser for the set

yoghurts at different protein concentrations

3,50

3,00

2,50
Peak force (N)

60% Casein - 40% Whey

2,00 70% Casein - 30% Whey

1,50 80% Casein - 20% Whey

90% Casein - 10% Whey
1,00

0,50

0,00
Set yoghurt (4%) Set yoghurt (5%) Set yoghurt (6%)
Total protein concentration

Figure 3: Peak force measured by Texture Analyser on set yoghurt, as a function of protein
concentration (4, 5, 6%) and ratio of casein to protein

From Fig 3, it is possible to see that the gel strength increases with total protein content; this is
consistent with earlier work (8). The effect of the ratio of caseins to whey proteins is not categorically
clear from the data. It appears that the gels generally become marginally stronger with a higher
proportion of casein.

3.1.2 Stirred yoghurts

Force in compression measured by the texture analyser for the stirred

yoghurts

0,80
0,70
Peak force (N)

0,60 60% Casein - 40% Whey

0,50
70% Casein - 30% Whey
0,40
80% Casein - 20% Whey
0,30
0,20 90% Casein - 10% Whey
0,10
0,00
s

s
)

ur

ur

ur
4%

%
(5

(6

ho

ho

ho
t(

rt

rt

4
ur

hu

hu

r2

r2
gh

r
g

fte

fte

fte
yo

yo

yo

)a

)a

)a
ed

ed

ed

4%

5%

6%
irr

irr

irr
St

St

St

t(

t(

t(
ur

ur

ur
gh

gh

gh
yo

yo

yo
ed

ed

ed
irr

irr

irr
St

St

St

Total protein concentration and types of

yoghurts

Figure 4: Peak force measured by the Texture Analyser on the stirred yoghurts on the day of
production and after 24 hours at different protein levels

4
ICEF9 - 2004
International Conference Engineering and Food

The trends observed in the case of stirred yoghurt are similar to those observed with set yoghurt. From
Fig 4 it is possible to see that the gel strength increases with the total protein content. However, it is
not possible to draw specific conclusions about the effects of caseins to whey proteins ratio on the
texture, as the difference between the peak forces is not significant. This is probably due to the lack of
sensitivity of the Texture Analyser probe. It is also important to note that storage for 24 hours does not
affect the texture significantly.

3.2 Texture characterisation of stirred yoghurt using U-tube viscometer

Viscosity of the different stirred yoghurts measured with U-tube

viscometer

70
60
Viscosity (cps)

50 60% Casein - 40% Whey

40 70% Casein - 30% Whey
30 80% Casein - 20% Whey
20 90% Casein - 10% Whey
10
0
4% 5% 6%
Total protein concentration

Figure 5: Viscosity measurements for the stirred yoghurts at different total protein concentrations and
ratio of caseins to whey proteins

Since the Texture Analyser was not sufficiently sensitive to differentiate between different stirred
yoghurts, it was decided to use flow characteristics in a U-tube viscometer.
Effects of caseins and whey protein on stirred yoghurt texture can be clearly distinguished from
viscosity measurements. For example, if we consider the effect of casein to whey protein ratio at 5%
total protein concentration, 60-40% mixture gives a viscosity of 14.7 mPas whereas 90-10% mixture
gives a distinctly higher viscosity of 29.7 mPas. Viscosity measurements on stirred yoghurts confirm
that higher casein content relative to whey protein yields a higher consistency.

4. Conclusions and future work

This set of experiments has shown that even though Texture Analyser gives a rapid measure of
texture, it is not sensitive enough to differentiate between samples having the same total protein
concentration, but different casein to whey protein ratio. This problem can be surmounted in the case
of stirred yoghurt by using a U-tube viscometer. It would be interesting to understand the response of
set yoghurt to shear.

5. References

(1) Hartley DL and Denariaz G (1993) The role of lactic acid bacteria in yoghurt fermentation,
International Journal of Immunotherapy, IX (1), 3-17

(2) Lucey JA and Singh H (1998) Formation and physical properties of acid milk gels: a review, Food
Research International, 30 (7), 529-542

(3) Trop M and Kushelevsky A (1985) The reaction of Glucono-Delta-Lactone with proteins, Journal of
Dairy Science, 68, 2534-2535

(4) FAO Nutrition Meetings, Reports Series No. 40 A, B, C, WHO/Food Add./67.29,

http://www.inchem.org/documents/jecfa/jecmono/40abcj42.htm

5
ICEF9 - 2004
International Conference Engineering and Food

(5) JA Lucey, M Tamehana, H Singh and P Munro (2000) Rheological properties of milk gels bormed
by a combination of rennet and glucono-delta-lactone, Journal of Dairy Research, 67, 415-427

(6) Tamine AY and Robinson RK (1999) Yoghurt: Science and Technology, Woodhead publishing Ltd,
Cambridge

(7) Tamine AY, Robinson RK and Latrille E (2001) Yoghurt and other fermented milks, Chapter 6 in
Mechanisation and automation in dairy technology, edited by Tamine AY and Law BA, Sheffield
Academic Press Ltd, England

(9) Tamine AY and Marshall VME (1997) Microbiology and biochemistry of cheese and fermented
milk, 2nd edition, edited by Law BA, Blackie Academic & Professional, London, 57-152

6
 ICEF9 – 2004
International Conference Engineering and Food

Effective Use of Analytical Solutions of Regular Geometries to

Experimentally Determine Heat and Mass Transfer Parameters

Erdoğdu, Ferruh

Address:
University of Mersin, Department of Food Engineering, 33343 Çiftlikköy-Mersin, Turkey

e-mail:
ferruherdogdu@mersin.edu.tr

Abstract
Analytical solutions for regular geometries (slab, cylinder and sphere) have a broad use to experimentally
determine the heat and mass transfer parameters. They, with the use of experimental data, would give a
greater advantage over the use of other methods. Effective use of further numerical optimization
techniques with them would enable the simultaneous determination of the related parameters with the
experimental data.

Key words: Analytical solutions, heat and mass transfer parameters.

Introduction
In heat and mass transfer problems, the knowledge of heat (heat transfer coefficient and thermal
diffusivity) and mass (diffusion coefficient and mass transfer coefficient) transfer parameters are required
to define and model the related process. Analytical solutions for regular shaped geometries (infinite
cylinder, finite cylinder, infinite slab, finite slab and sphere) with different initial and boundary conditions
have an extensive use to simplify the heat and mass transfer problems and to experimentally determine
the related parameters. In addition to the mathematical formulations with the explicitly defined boundary
conditions, the experimental data is also needed with the proper use of these solutions. Then, use of
these solutions alone or together with some numerical optimization techniques may also enable the
determination of these parameters. These solutions, with the use of experimental data would give a
greater advantage over the use of other methods; for example use of lumped system approach with high
thermal conductivity materials to determine the convective heat transfer coefficient or assumption of an
infinite heat or mass transfer coefficient to determine thermal diffusivity or diffusion coefficient. There are
certain issues about the use of these assumptions. For example, sometimes it is even suggested the
temperature readings should be taken at the geometric center of the product, or that location should be
known to determine the heat transfer parameters. Actually, it is not required, and any temperature data
may be used to determine the heat transfer coefficient with known thermal diffusivity value or vice versa.
Therefore, the objective of this work was to explain the use of analytical solutions of regular geometries to
determine the heat and mass transfer parameters from the experimental data.
 ICEF9 – 2004
International Conference Engineering and Food

Methods
Governing differential equation and solutions for an infinite cylinder, infinite slab and a sphere are
given as follows with the defined initial and boundary conditions:
The governing differential equation:

1 ∂  n ∂φ  1 ∂φ
⋅ x ⋅ = ⋅ (1)
x n ∂x  ∂x  Ω ∂t
where φ is temperature or mass concentration; x is location in geometry to characterize heat or mass
transfer(m); n is characteristic number (n=0 for infinite slab, n=1 for infinite cylinder, and n=2 for sphere);
and Ω is thermal or mass diffusivity (m²/s).
Solutions for eq. 1, for initial condition of constant uniform temperature or mass distribution and
boundary conditions of central symmetry and convective boundary at the surface, are given for these
geometries as follows.
Infinite slab:

φ − φ∞ ∞
 2 ⋅ sin λn  x 
ψ= = ∑ ⋅ cos  λn ⋅  ⋅ exp ( −λn2 ⋅ Fo ) (2)
φi − φ ∞ n = 1  λn + sin λn ⋅ cos λn  L 
Infinite cylinder:

φ − φ∞ ∞ 
J (λ )  x 
⋅ J 0  λn ⋅  ⋅ exp ( −λn2 ⋅ Fo )
2
ψ= = ∑ ⋅ 2 1 n 2 (3)
φi − φ ∞  λn J 0 ( λn ) + J1 ( λn )
n = 1  L 
Sphere:

  r 
φ − φ∞ ∞  2 ⋅ (sin λ − λ ⋅ cos λ ) cos  λn ⋅ R  
ψ=
φi − φ ∞
= ∑ n n

λn − sin λn ⋅ cos λn
n
⋅ 
( n )
 ⋅ exp −λ 2 ⋅ Fo  (4)
n = 1 
r
λn ⋅
 R 

where Fo is Fourier number and the λn ’s are given as follows for infinite slab, infinite cylinder and sphere,
respectively:
Bi = λ ⋅ tan λ (5)

J1 (λ )
Bi = λ ⋅ (6)
J 0 (λ )
λ
Bi = 1 − (7)
tan λ
th st
where Bi is Biot number, and J0 and J1 are the first kind 0 and 1 order Bessel functions.
These equations may easily be used to determine the heat and/or mass transfer parameters:
When the convective heat or mass transfer coefficient (therefore the Biot number is known), thermal
diffusivity or diffusion coefficient value may easily be determined from an experimental data. Let us
 ICEF9 – 2004
International Conference Engineering and Food

assume that the temperature change at a certain location of a spherical object in a highly agitated medium
is recorded to determine thermal diffusivity. Due to the agitation, convective heat transfer coefficient may
be assumed to be infinite, and eqs. 4 and 7 with Fourier (Fo) and Biot (Bi) number definitions are used to
accomplish this objective. First of all, since the heat transfer coefficient and therefore the Bi is assumed to
be infinite, and roots of eq. 7 are determined to be ( π , 2π ,3π ,... and so on). Due to the fact that the

 φ − φ∞ 
temperature ratio ( ln   ) becomes linear after a certain time ( Fo ≥ 0.2 ), the first term of eq. 7 is
 φi − φ ∞ 
then used to characterize the linear change in this region. When the natural logarithm of both sides of eq.
7 is taken with the first term approximation (n=1), the following equation is obtained:

 φ − φ∞  2 α ⋅t
ln   = A1 − λ1 ⋅ 2 (8)
 φi − φ∞  R
where

 r
cos  λ1 ⋅ 
2 ⋅ (sin λ1 − λ1 ⋅ cos λ1 )  R
A1 = ⋅ (9)
λ1 − sin λ1 ⋅ cos λ1 λ1 ⋅
r
R
α
As seen in eq. 8, slope of the temperature ratio versus time is equal to −λ1 ⋅
2
. Then, with the known
R2
slope and radius of the spherical material, the thermal diffusivity value may be determined. As one
realizes, this method does not mention at which point in the material where the experimental data is
recorded since, regardless of the location, temperature ratio curves have the same slope after the
linearization starts. The eq. 8 also shows that the slope is independent of the location. Fig. 1 shows the
r r r
change in experimental temperature ratios taken in different locations ( = 0, = 0.5, and = 0.98 ) of
R R R
r r
an apple cooked in boiling water. = 0 is center while = 0.98 is the location just underneath the
R R
surface.
 ICEF9 – 2004
International Conference Engineering and Food

-1

-2

-3 r/R=0
ln(T.R.)

-4 r/R=0.5
-5 r/R=0.97

-6
-7

-8
0 1000 2000 3000 4000
Time (s)

Figure 1. Change of temperature ratio (ln(T.R.) at different locations in an apple cooked in boiling water.

As seen in Fig. 1, the temperature ratios become linear after a certain time (e.g. t<1000
seconds), and slopes seem to be equal. When a linear regression is applied to this data after the
-1
linearization starts, the slopes are found to be -0.0013 s . Then the thermal diffusivity value is calculated
-7
as 1.18x10 m²/s following the above described method. Convective heat transfer coefficient may also be
determined using the same method when a thermal diffusivity-know material is used. In this case, using

the slope, λ1 is determined, and it is used to calculate the Bi and therefore the convective heat transfer
coefficient. Of course, in addition to the thermal diffusivity, thermal conductivity of the experimental
material must be known in this case.
This method may also be applied for mass transfer calculations. In this case, since the mass
change in a product is generally recorded throughout the whole volume, eqs. 2 to 4 are integrated through
the whole volume resulting in:
Infinite slab:
∞  
φ − φ∞ 2 ⋅ sin 2 λn
ψ= = ∑ ⋅ exp ( −λn2 ⋅ Fo ) (10)
φi − φ ∞ n = 1  λn ⋅ ( λn + sin λn ⋅ cos λn ) 
Infinite cylinder:

∞  
φ − φ∞ 4 ⋅ J 1 ( λn )
2

ψ= = ∑  ⋅ exp ( −λn ⋅ Fo )
2
(11)
φi − φ ∞

2 2
(
n = 1 λn ⋅ J 0 ( λn ) + J 1 ( λn )
 2
) 

 ICEF9 – 2004
International Conference Engineering and Food

Sphere:
∞ 
6 ⋅ (sin λn − λn ⋅ cos λn ) 
2
φ − φ∞
ψ= = ∑ 3 ⋅ exp ( −λn2 ⋅ Fo ) (12)
φi − φ ∞ n = 1  λn ⋅ ( λn − sin λn ⋅ cos λn )
 
Then, the above described method to determine the thermal diffusivity may be easily applied now to
determine the diffusion coefficient. In mass transfer case, the mass transfer coefficient may not be easy to
determine. Therefore, a general approach in the literature is to assume it as infinite one and then continue
with the calculations. However, knowing of heat transfer coefficient may enable to determine mass
transfer coefficient through the so-called analogy of Chilton-Colburn:
2
h  Pr  3
kc = ⋅  (13)
ρ ⋅ cp  Sc 
where kc is mass transfer coefficient (m/s), h is convective heat transfer coefficient (W/m²-K), ρ (kg/m³)
and c p (J/kg-K) are density and heat capacity of the heating medium, respectively, Pr is Prandtl number,
and Sc is Schmidt number. Basically, knowing mass transfer coefficient with experimental data to
determine the diffusion coefficient results in a eq. 8, formed through combination of eqs. 5 to 8. Then,
solving this leads to the determination of diffusion coefficient.
kc ⋅ L
λ ⋅ tan λ =
( )
(14)
− slope
λ2
where L is the characteristic dimension. The same method also holds for the heat transfer case when the
heat transfer coefficient of the medium is known.

Conclusions
These solutions, with experimental data would give a greater advantage over the use of other
existing methods; for example, use of lumped system approach with high thermal conductivity materials to
determine the convective heat transfer coefficient. In addition to this, effective use of further explicit and
implicit numerical models with optimization techniques would increase the benefits of these solutions, and
several of the required parameters may be determined simultaneously with the use of a single set of
experimental data.

References
1. Carslaw, H. S., & Jaeger, J. C. Conduction of Heat in Solids. New York, 1986.
2. Crank, J. The Mathematics of Diffusion. New York, 1970.
 ICEF9 – 2004
International Conference Engineering and Food

Infinite Geometry Approximations and Errors in

Heat and Mass Transfer Problems

Turhan, Mahir, (1) and Erdoğdu, F. (2)

Address:
Department of Food Engineering, University of Mersin 33343 Ciftlikkoy-Mersin, Turkey

e-mail:
(1) mturhan@mersin.edu.tr
(2) ferruherdogdu@mersin.edu.tr

Abstract
Multi-dimensional shape of foods is one reason making the solutions to transient heat and mass
transfer problems difficult and forcing the infinite geometry approximations. Resulting errors of these
assumptions were determined as a function of Fourier (1 to 6000) and Biot (0.01 to 10000) numbers for
different slab and rod geometries, categorized with respect to the different locations and to the average
temperature or mass change of each geometrical shape and then evaluated using analytical solutions.
Key words: Error, transient transfer, infinite geometry approximation.

Introduction
Irregular shapes and complex structure of biological materials make the transient heat and mass
transfer problems complicated. In addition to this, temperature dependent thermal and physical properties
and non-isotropic properties bring extra difficulties to the solution of these problems. Therefore, numerical
finite difference or finite element solutions are mostly required and/or preferred over analytical solutions.
Sometimes, the approximation of an irregular geometry by a regular one (a slab, a cylinder or a sphere) is
applied to enable the use of an easy analytical solution with certain initial and boundary conditions. This
approximation practically relies on comparing surface areas of regular objects subjected to transient heat
or mass transfer. Depending on the larger area, the object may be approximated with a certain infinite
geometry. For example, If a cylinder has larger base area compared to its lateral area like a very thin
burger patty, it may be assumed as an infinite slab. These assumptions basically reduce the
multidimensional unsteady state solutions to one-dimension and make the model simpler. Of course, all
these assumptions bring certain errors with them. Therefore, the objective of this study was to quantify
and characterize these errors based on average and location changes with respect to different Biot (Bi)
and Fourier (Fo) numbers.

Materials and Methods

Mathematical Background:
The governing equations for transient heat/mass transfer in slab and cylinder shaped objects are
given as follows [1, 2]:
 ICEF9 – 2004
International Conference Engineering and Food

Slab (in cartesian coordinates):

∂ 2φ ∂ 2φ ∂ 2φ 1 ∂φ
+ + = (1)
∂x 2
∂y 2
∂z 2
Ω ∂t
Cylinder (in cylindrical coordinates):

1 ∂  ∂φ  1 ∂ 2 φ ∂ 2 φ 1 ∂φ
 r  + 2 + = (2)
r ∂ r  ∂ r  r ∂θ 2 ∂ z 2 Ω ∂ t
Solutions for these equations in three-dimension are complicated. However, transient transfer in a
slab (as a three-dimensional problem) and cylinder (as a two- or three-dimensional problem) may be
approached as combination of one-dimensional problems in different directions leading to simplification for
the complex problem. Then, solutions for cylinder and slab may be derived using super-imposition
techniques. Eq. (3) and Eq. (5) are the analytical solutions for constant-isotropic properties subjected to
symmetry along the center and convective boundary conditions (Eq. 6 to 8) with an initial condition of
constant temperature/mass distribution (5) of infinite slab and infinite cylinder, respectively [1,2]:
Infinite slab:

φ −φ ∞  2 sin λ n 
cos  λ n  exp ( − λ n2 Fo )
∞
 x
ψ = =∑  (3)
φ i − φ ∞ n = 1  λ n + sin λ n cos λ n  L 

where λ is given by:

Bi = λ tan λ (4)

Infinite cylinder:

φ −φ ∞  2 J 1 (λ n ) 
( )
∞
 r 
ψ = =∑   λ  − λ 2

 λ n J 0 (λ n ) + J 1 (λ n )
J exp Fo (5)
φi − φ ∞ n = 1
0 n n
 R
2 2

where λ is given by:
J 1 (λ )
Bi = λ (6)
J 0 (λ )

∂ φ (δ , t )
−κ = η [φ ( δ , t ) − φ ∞ ] δ = L or R (7)
∂x
∂φ ( 0,t )
=0 (8)
∂x
φ ( x , 0 ) = φ0 (9)
 ICEF9 – 2004
International Conference Engineering and Food

The volume average temperature or mass concentration for these geometries is obtained
integrating Eqs. (6) and (8) throughout the whole volume. The following equations are derived to calculate
the volume average temperature/mass concentration change after integration.

For infinite plate:

φa − φ ∞  2 sin 2 λ n 
( )
∞
ψa = = ∑  exp − λ 2
Fo  (10)
φ i −φ  λ n ( λ n + sin λ n cos λ n )
n
∞ n =1 
For infinite cylinder:

φ a−φ ∞  4 J 2 (λ ) 
exp ( − λ n2 Fo )
∞
ψa = =∑  2 2 1 n 2
[
φ i − φ ∞ n = 1  λ n J 0 (λ n ) + J 1 (λ n )  ] (11)

Using the super imposition technique, the solutions for a three dimensional finite slab and a two
dimensional finite cylinder can be given as:

 φ−φ ∞   φ−φ ∞   φ−φ∞   φ − φ∞ 

  =      (12)
φ i − φ ∞  φ i − φ ∞  φ i − φ ∞  φ i − φ ∞ 
finite inf inite inf inite inf inite
plate plate , depth plate , width plate , height

 φ −φ∞   φ − φ∞   φ−φ ∞ 
  =    (13)
φ i − φ ∞   φ i − φ ∞   φ i − φ ∞ 
finite inf inite inf inite
cylinder cylinder plate

Methods:
Slab (circular and squared slab with a reference of infinite slab) and rod geometries (cylindrical
and square rods with a reference of infinite cylinder) with a constant principle dimension (PD where the
heat or mass transfer is dominant) and a variable dimension (VD where the heat or mass transfer is
negligible) were used. A corresponding infinite geometry with the same PD was assigned as a reference
for each geometry, e.g. infinite slab for the circular slab, and Ψ and Ψa values at certain locations between
the symmetry center and the transfer surface values were determined. Then, these changes were also
determined for the corresponding finite geometry with the same Bi and PD where the VD changed from 1
to infinity. Using these data, two types of errors were determined for the given process time: i) at different
locations between the center of symmetry and transfer surface (location error, εL), and ii) with respect to
average temperature or mass change (average error, εa) of a given geometry. Error curves giving the
variation of εL or εa with Fo (1 to 6000) were obtained at Bi of 0.01 to infinity. The process time was
chosen for the Ψref value to be 0.90 at the center of the given finite geometry due to the significance of the
center point changes. The error (ε) was calculated during the given process time (Table 1) using the
temperature or mass ratio changes with respect to the reference values at time-wise equally spaced 100
points (Eq. 14) [3].
 ICEF9 – 2004
International Conference Engineering and Food

1 n = 100  ψ a − ψ a , ref 
ε=
100
∑
n =1

 ψ a , ref
 100

(14)

All these calculations were accomplished using a computer program written in Microsoft Visual Basic
V.6.0.
Table 1. Times (min) for the temperature or mass ratio to be 0.90 at the center of the different principle
dimensions (PD) of the reference geometries (infinite slab and infinite cylinder) versus Biot number (Bi).

Bi

PD (mm) 0.01 0.1 1 10 100 1000 ∞

Infinite slab
2 35.83 3.71 0.51 0.19 0.163 0.160 0.159

5 223.98 23.22 3.16 1.20 1.019 1.000 0.999

10 895.94 92.86 12.64 4.81 4.076 4.003 3.996

20 3583.78 371.46 50.58 19.25 16.304 16.015 15.986

40 14335.12 1485.82 202.31 76.99 65.215 64.059 63.944

Infinite cylinder

2 71.64 7.40 0.98 0.36 0.303 0.298 0.297

5 447.75 46.22 6.12 2.25 1.896 1.862 1.859

10 1791.0 184.89 24.48 8.98 7.584 7.449 7.436

20 7164.0 739.57 97.93 35.92 30.336 29.797 29.745

40 28656.0 2958.30 391.72 143.69 121.345 119.189 118.981

Results and Discussion

For all the slab and rod geometries, location error (εL) and average error (εa) associated with
assuming a regular finite geometry as a regular infinite one was determined for different Fo (1 to 6000)
and Bi (0.01 to infinity) for the process times given in Table 1. εL and εa were found to be affected by Fo
and Bi while the errors dramatically increased with increasing Fo at any given Bi [3]. At Bi ≥ 100, the
change in the error values did not increase significantly with increasing Bi since the Bi basically reaches to
an infinite value. In all geometries, the PD did not affect the εL and εa, and for a given geometry, εL did not
change with location and Bi. To numerically characterize and determine the changes of the location and
average errors with respect to Fo and Bi to easily use in different studies to approximate the geometries
for easier solutions, the error changes were applied to fit an empirical equation. They were found to be
 ICEF9 – 2004
International Conference Engineering and Food

best fitted by the following cascade type equation Table Curve 2D v.2.03 (Jandel Scientific, San Rafeal,
CA, USA)

 b exp[ − c ( Fo − d ) ] − c exp[ − b ( Fo − d ) ]
ε = a 1 +  (15)
 c − b 
where a, b, c, and d are regression coefficients. These coefficients in Eq. (15) given in Table 2 was also
correlated with respect to the Bi numbers for both location and average errors for the geometries used.

Table 2. The coefficients for equation 15 to estimate the errors based on location and average changes
with respect to Biot numbers (Bi).

Geometry Bi Error based on location Error based on average changes

a B c d a b c d
0.01 94.307 0.0011 0.0071 253.41 94.306 0.0011 0.0068 245.59
0.1 94.289 0.0102 0.0838 30.634 94.354 0.0103 0.0661 25.426
Circular
slab 1 94.121 0.0759 0.7846 5.9389 94.778 0.0795 0.5587 3.4324
10 93.676 0.2111 1.2514 2.4890 95.344 0.2473 4.3174 1.2346
100 93.720 0.2481 1.4456 2.1427 95.113 0.3247 135.32 1.0681
0.01 94.302 0.0011 0.0072 255.60 94.303 0.0011 0.0068 245.56

Squared 0.1 94.220 0.0101 0.0846 31.601 94.324 0.0102 0.0654 25.367
slab 1 93.647 0.0738 0.5602 6.0177 94.616 0.0767 0.5528 3.3907
10 92.725 0.2033 0.8331 2.5202 95.007 0.2316 5.5029 1.2464
100 92.745 0.2387 0.9646 2.1787 94.617 0.3091 11329. 1.0585
0.01 94.503 0.0015 0.0054 484.37 94.498 0.0015 0.0053 479.97

Cylindrical 0.1 94.494 0.0145 0.0599 52.721 94.509 0.0148 0.0513 49.542
rod 1 94.155 0.1087 0.5584 8.1589 94.629 0.1122 0.3945 6.4319
10 93.655 0.2990 1.3524 3.2494 95.408 0.2899 1.8885 2.2579
100 93.598 0.3550 1.5857 2.7516 96.051 0.3260 5.5325 1.8979
0.01 87.883 0.0031 0.0025 475.89 87.886 0.0028 0.0026 471.85

Square rod 0.1 89.059 0.0192 0.0403 52.344 87.947 0.0268 0.0257 49.184
1 85.189 0.2234 0.2090 8.3769 88.371 0.2089 0.1829 6.7071
10 85.892 0.4370 0.7346 3.8454 95.841 1.7399 0.2659 2.7744
100 84.632 0.6313 0.7282 3.1429 99.463 0.2813 7.1021 2.2553

Conclusions

The location and average errors resulted in when a finite regular geometry was approximated with
an infinite one during transient heat and mass transfer processes were determined and found to be
 ICEF9 – 2004
International Conference Engineering and Food

affected by Fo, Bi. While the location did not affect the change in errors at the same Bi and geometry, the
εa values were always greater than εL at the same Fo - Bi and the geometry
References

1. Carslaw, H. S., & Jaeger, J. C. Conduction of Heat in Solids. New York, 1986.
2. Crank, J. The Mathematics of Diffusion. New York, 1970.
3. Turhan, M., and Erdoğdu, F. Error associated with assuming a finite regular geometry as an infinite
one for modeling of transient heat and mass transfer processes. Journal of Food Engineering, 59, 291-
296, 2003.
Notation
Bi : Biot number
Fo : Fourier number
st th st
J0 , J1 : 1 kind, 0 and 1 order of Bessel functions
L : half thickness of an infinite slab (m)

PD : principle dimension

r : distance of a certain location from the center in an infinite cylinder in x-

direction (m)
R : radius (m)
t : time (s)

VD : variable dimension (m)

x : distance of a certain location from the center of symmetry in an infinite plate

in x-direction (m)
ε : error (%)

εa : error with respect to the volume averaged temperature or mass change (%)

εL : error with respect to the temperature or mass change at a certain location (%)

δ : half thickness for an infinite slab, radius for an infinite cylinder, characteristic
dimension for a finite geometry to determine Fo: the ratio of volume / transfer
area (m)
φ, φi, and φ∞ : temperature or mass concentration at t = t, t = 0, and t = ∞, respectively (K or
3
kg/m )
2
η : heat transfer (W/m -K) or mass transfer coefficient (m/s)
2
κ : thermal conductivity (W/m-K) or mass diffusivity (m /s)
λ : root of the characteristic equations for analytical solutions

Ψ : dimensionless temperature or mass concentration ratio

2
Ω : thermal or mass diffusivity (m /s)

Ψa : volume averaged dimensionless temperature or mass concentration ratio

Ψref andΨa, ref : reference for location or average dimensionless temperature or mass
concentration ratio
ICEF9 – 2004 International Conference Engineering and Food

Experimental And Numerical Investigation Of The Wire Cutting Of Cheese

Goh SM (1), Charalambides MN (2), Williams JG (3)

Department of Mechanical Engineering,
Imperial College London,
London SW7 2BX,
United Kingdom
(1) smg2@imperial.ac.uk
(2) m.charalambides@imperial.ac.uk
(3) g.williams@imperial.ac.uk

Abstract
The wire cutting process of cheese was investigated through experiments and finite element
simulations. A non-linear viscoelastic constitutive relationship was used to model the cheese and
Coulomb friction was assumed at the wire-cheese contact interface. Two fracture criteria were
used:critical fracture strain and a cohesive zone model. Predictions of the steady-state cutting force
are demonstrated.

Keywords
Food; Fracture; Viscoelastic; Cutting

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ICEF9 – 2004 International Conference Engineering and Food

1 Introduction
Many food processes, such as shredding and cutting, involve breaking the food into smaller
components. Fracture of food also occurs during mastication when the structure of the food is broken
down and the flavour and aroma are released. In order to understand the way food breaks down, it is
necessary to know the fracture properties. One test that has been proposed for measuring the
fracture properties of foods is wire cutting [1,2]. The test involves pushing wires of various diameters
into a specimen from an initial indentation to a steady-state cutting stage (Figure 1). The objective of
this study was to compute the cutting forces in the wire cutting test using fundamental mechanical
properties. Due to the complicated stress states of the process, numerical models were utilised.

Indentation Steady State

Phase Cutting Phase

2.5

1.5
force (N)

0.5

0
0 2 4 6 8
wire displacement (mm)

Figure 1 Typical force-displacement relationship in wire cutting test.

2 Experiments
The tests were performed on mild Cheddar and Gruyere samples at 21°C. Wire cutting tests were
performed using five diameters, d , of 0.25, 0.5, 0.89, 1.6 and 2mm at 5mm/min. The specimens
were rectangular blocks of length 25mm, height 20mm and width 15mm for the three smaller
diameters. Blocks of length 30mm, height 30mm, and thicknesses 20mm and 30mm were used for
the 1.6mm and 2mm diameters respectively.

The material calibration tests involved monotonic uniaxial compression and compressive stress
relaxation tests. The monotonic compression tests were performed at constant true strain rates of
0.25, 2.5 and 25/min. The relaxation tests were performed at a constant true strain rate of 2.5/min up
to a strain of approximately 0.04 where the crosshead position was held constant thereafter for 20
minutes. Prior to the start of test, the platens were lubricated with Superlube (Loctite Corp.) to
eliminate the friction at the sample-platen interface [3]. The true stress, σ , and true strain, ε , were
calculated by assuming that the material was incompressible [4,5,6].

3 Numerical Simulations
3.1 Mesh Definition
The numerical simulations were performed in the commercial finite element code ABAQUS. Two
separate models were developed, and the geometries are shown in Figure 2. The first model
corresponds to the indentation stage to predict crack initiation. The second model was used to
simulate crack propagation. In all cases, four noded, plane strain elements were used.

2
ICEF9 – 2004 International Conference Engineering and Food

wire wire
cohesive
elements

cheese cheese
y y
x (a) x (b)

Figure 2 Finite element geometry for (a) indentation (b) crack propagation models.

3.2 Material Model

The cheese samples were assumed to be incompressible and homogeneous. A non-linear
viscoelastic model consisting of separable strain and time dependent functions was chosen as the
constitutive model [7]. The strain dependent function was based on rubber elasticity theory. The time
dependent function was defined by the Prony series consisting of five time constants with values of
0.1s, 1s, 10s, 100s and 1000s. The material parameters were calibrated using the procedure as
described in [8].

3.3 Fracture Criteria

In the indentation model, a simple fracture criterion based on a critical strain was used to predict crack
initiation. The critical strain, ε crit , was assumed to be equal to the fracture strain as measured in the
uniaxial compression test. The maximum tensile strain, ε xx,max , in the model was monitored such that
when ε crit was reached, the indentation force was assumed to give the steady-state cutting force.

In the crack propagation simulations, the fracture process was modelled by cohesive elements along
the line of symmetry where the fracture path was defined. The cohesive elements [9] were
characterised by a traction-separation curve which is described by a third order polynomial and is
defined by the fracture toughness, Gc , and a peak stress, σˆ (Figure 3). The critical separation, δ crit ,
is given by 16Gc 9σˆ . The attraction of the cohesive elements is that they provide a means of
describing material damage without the need to model individual failure micro-mechanisms within the
zone [10]. Furthermore, the computation of the macroscopic work of fracture is conveniently
separated into a local work of fracture and the energy dissipated through other processes such as
plastic deformation or viscous flow.

140
120 σˆ
100
traction, T

80
60
Gc
40
20
δ crit
0
0 0.1 0.2
δ (mm)

Figure 3 Traction-separation curve for the cohesive elements.

3.4 Surface Friction

The surface friction was assumed to be described by the Coulomb friction relationship. The coefficient
of friction, µ , was taken from previous studies of mild Cheddar and Gruyere [3,6]. In these studies,
cylindrical specimens of various height/diameter ratios were compressed between steel platens under

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ICEF9 – 2004 International Conference Engineering and Food

nonlubricated condition. The stress-strain data were approximated with the solution for the analysis of
compression of a deforming flat circular disk [11] to compute µ . The values of µ were found to be
0.16 and 0.14 for mild Cheddar and Gruyere respectively.

4 Results and Discussions

The stress-strain curves of the cheeses up to the point of failure are shown in Figure 4. The stresses
increased significantly with increasing strain rate, but the fracture strains remained constant at
approximately 0.5 and 0.45 for mild Cheddar and Gruyere respectively.

80 100
.
. 90 ε =25/min
70 ε =25/min
80
60
70 .
ε =2.5/min
stress (kPa)

stress (kPa)
50 .
60
ε =2.5/min
40 50 .
. ε =0.25/min
30 ε =0.25/min 40
30
20
20
10
(a) 10 (b)
0 0
0 0.1 0.2 0.3 0.4 0.5 0.6 0 0.1 0.2 0.3 0.4 0.5 0.6
strain strain

Figure 4 Stress-strain relationships for (a) mild Cheddar (b) Gruyere.

The experimental steady-state wire cutting data are shown in Figure 5. The cutting energy increased
almost linearly with wire diameter for mild Cheddar but the degree of non-linearity was more apparent
for Gruyere. Since the cutting energy consists of the energies for fracture, plastic/viscous dissipation
as well as surface friction dissipation, it is common to assume that the fracture energy is constant for
the different wire diameters and is equal to the fracture toughness. Therefore, by extrapolating the
cutting energies to the theoretical zero wire diameter, the fracture toughness can be obtained since
the cutting energy is then consumed solely for fracture. Following this conventional wisdom, lines
were fitted to the data to obtain Gc from the intercepts. Due to the apparent non-linearity in the data,
two different lines were fitted, depending on whether the data corresponding to the two largest
diameters were included. The values of Gc are found to be between 14.7-15.2J/m2 for mild Cheddar
and 12.5-42.2J/m2 for Gruyere.

The predictions of the steady-state cutting force using the indentation model are in good agreement
with the experimental data as shown in Figure 5. This suggests that the critical strain criterion can be
utilised to predict the cutting force.

200 250
experiment experiment
indentation model indentation model
160 crack propagation model 200 crack propagation model
F /b (J/m )

F /b (J/m )

120 150
2

80 100

40 50
(a) (b)
0 0
0 0.5 1 1.5 2 0 0.5 1 1.5 2
wire diameter (mm) wire diameter (mm)

Figure 5 Wire cutting data for (a) mild Cheddar (b) Gruyere.

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ICEF9 – 2004 International Conference Engineering and Food

In the absence of independent fracture data to calibrate the cohesive elements, the values of Gc and
σ̂ had to be determined by matching the numerical steady-state energies to the experimental data
through a trial and error approach. This was done for d =0.25mm, and the same values of Gc and σ̂
were subsequently applied to the other wire diameters. The ratio of Gc to σ̂ was chosen so that δ crit
was arbitrarily fixed at 0.22mm and smaller than 0.25mm which is the smallest wire diameter used in
the experiments. The value of δ crit has to be smaller than the wire diameter, otherwise complete
decohesion of the cohesive elements does not occur. The values of Gc and σ̂ were found to be
15J/m2 and 120kPa for mild Cheddar and 25J/m2 and 200kPa for Gruyere. The values Gc appear
reasonable and are comparable to those estimated from simple extrapolation of the experimental data
to zero wire diameter as discussed earlier. The values of σ̂ appear relatively high compared to the
stress-strain data (Figure 4). This is due to the highly constrained deformation ahead of the wire
which imposes a high hydrostatic stress. Additional experimental tests (Figure 6) where the length of
the specimen was changed to vary the degree of constraint in the deformation ahead of the wire
suggest that the constraint increases the cutting force.

300

250

200
F /b (J/m )
2

150

100

50
length
0
0 10 20 30 40
length (mm)

Figure 6 Effect of specimen length on wire cutting forces; d =2mm

The steady-state cutting forces obtained from the crack propagation model are shown in Figure 5. It
can be seen that the numerical predictions match the experimental measurements for small wire
diameters, but are increasingly underestimated with increasing wire diameter. A possible reason for
the discrepancy is that the amount of damage caused by the wire increases with increasing wire
diameter, as evidenced by the rougher cut surface (Figure 7). The numerical model, which is based
on a single crack propagation, may be too simplistic to account for the complicated deformation
modes.

0.25mm 0.5mm 0.89mm 1.6mm 2mm

15mm

Figure 7 Fracture surface of wire cutting specimens for mild Cheddar.

5 Conclusions
The prediction of the steady-state wire cutting force was possible through the use of a critical fracture
strain criterion and a consideration of the forces at crack initiation. Larger discrepancies in the

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ICEF9 – 2004 International Conference Engineering and Food

predictions of the steady-state cutting force were observed when the cohesize zone model was used.
This could be due to the rather complicated deformation states that occur during the steady-state
cutting process that are not reproduced with sufficient accuracy in the crack propagation model.
Further investigations are under way to explore the effect of strain rates due to the use of different wire
diameters and different cutting speeds.

References

1. Kamyab I., Chakrabarti S., Williams J.G. Cutting cheese with wire. Journal of Materials Science,
33, 2763-2770, 1998
2. Luyten H. The rheological and fracture properties of Gouda cheese. Ph.D. thesis, Wageningen
Agricultural University, 1988
3. Charalambides M.N., Goh S.M., Lim S.L., Williams J.G. The analysis of the frictional effect on
stress-strain data from uniaxial compression of cheese. Journal of Materials Science, 36, 2313-
2321, 2001
4. Prentice J.H., Langley K.R., Marshall R.J. “Cheese Rheology” in Cheese: Chemistry, Physics and
Microbiology, Volume 1, 2nd ed. P.F. Fox, (Ed.) Chapman and Hall, London, 303-341, 1993
5. Rohm H., Jaros D., deHaan M. A video-based method for determination of average stress-strain
relations in uniaxial compression of selected foods. Journal of Texture Studies, 28, 245-255, 1997
6. Goh S.M. An engineering approach to food texture studies. Ph.D. thesis, Imperial College
London, 2002
7. ABAQUS’s user manual ver 5.8. Hibbitt, Karlsson and Sorensen (UK), Cheshire, 1998
8. Goh S.M., Charalambides M.N., Williams J.G. Large strain time dependent behaviour of cheese.
Journal of Rheology, 47, 701-716, 2003
9. Chen J., Crisfield M., Kinloch A.J., Busso E., Matthews F.L., Qiu Y. Predicting progressive
delamination of composite material specimens via interface elements. Mechanics of Composite
Materials and Structures, 6, 1-17, 1999
10. Pandya K.C., Williams J.G. Cohesive zone modelling of crack growth in polymers - Part 1 -
Experimental measurement of cohesive law. Plastics and Rubber Composites, 29, 439-446, 2000
11. Dieter G.E. Mechanical Metallurgy. SI Metric Ed. McGraw-Hill, Tokyo, 1998

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International Conference Engineering and Food

PREDICTION OF MOISTURE TRANSFER IN COMPOSITE FOODS WITH EDIBLE FILMS

(1), (2) (3) (3) (4) (1)

Guillard Valérie , Broyart Bertrand , Bonazzi Catherine , Guilbert Stéphane , Gontard Nathalie

(1)
UMR IATE (Ingénierie des Agropolymères et des Technologie Emergentes),
Université Montpellier II, cc023, place Eugène Bataillon 34095 Montpellier cedex 5, France
guillard@arpb.univ-montp2.fr, gontard@arpb.univ-montp2.fr
(2)
CTCPA, 11 rue Marcel Lucquet, 32000 Auch
(3)
UMR Génie Industriel Alimentaire, ENSIA-INRA,
1 avenue des olympiades, 91744 Massy cedex, France
broyart@ensia.inra.fr, bonazzi@ensia.inra.fr
(4)
UMR IATE, ENSAM-INRA,
2 place Pierre Viala, 34060 Montpellier cedex 1, France
guilbert@ensam.inra.fr

Abstract. Moisture transfer in composite foods constituted of compartments of various initial aw

(sponge-cake and biscuit as cereal-based compartment, agar gel as fresh filling and edible films as
moisture barrier) has been experimentally and mathematically investigated. Predictive models
appeared to be very helpful for selecting films with required barrier properties or for predicting the
shelf-life of composite foods.

Keywords. Moisture transfer, composite food, edible barrier film, shelf-life prediction, food quality

INTRODUCTION

The increased consumer demand for ready-to-eat foods has initiated the development in the bakery
industry of composite foods constituted of a cereal-based compartment of low or intermediate aw
(biscuit or sponge-cake) in contact with a higher aw filling. Moisture migration is a common problem in
such composite foods where water diffuses from the higher to the lower aw compartment. A small
change in the moisture content of the cereal-based compartment can drastically affect its texture [1].
An effective means to control water movement in composite food is to situate at the interface between
compartments an edible film or coating with good moisture barrier properties [2-4]. Despite the
modelling of moisture transfer through a film in a composite food would be of high interest for
predicting shelf-life and selecting edible films with the required barrier properties, very few studies
dealing with modelling and use of a barrier film in a composite food were reported in literature.
Development of a global study of water transfer in composite foods with a cereal-based food
compartment and edible film at the interface appeared thus as a major scientific challenge.
The objective of this work was to study the moisture transfer in composite foods constituted of dry or
intermediate aw cereal-based food (respectively biscuit and sponge-cake) in direct contact with high aw
filling (agar gel) or separated from the same filling by an edible film. The adequacy of two models [4, 5]

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to predict moisture transfer, and thus, shelf-life of the studied composite foods was verified. Effect of
film composition and temperature on film barrier properties was investigated.

MODEL DEVELOPMENT

General theory. To analyze mass diffusion phenomena in the composite food, the food system is
assumed to be composed of three finite plane sheets placed side by side (Figure 1). The wet
compartment is considered as a non rate-limiting (NRL) compartment for moisture transfer, i.e. the
moisture content for this (NRL) wet compartment is assumed to be uniform in the cylindrical space
domain but variable in time. Film and dry compartments are considered as rate-limiting (RL)
compartments for moisture transfer, i.e., the moisture content in such compartments is assumed to be
variable in the cylindrical space domain and in time.

Wet compartment Film Dry compartment

High aw filling X2, 2, Cereal-based

X1, 1 Deff2 compartment
X3, 3, Deff3(X3)

x
-L1 -L2 0 L3

Figure 1 : Schema of the three-compartments model food system. X is the local moisture content (g/g dry basis), is the density
(kg of dry matter per bulk volume in m3) and Deff is the effective diffusivity of water (m²/s)

At the interfaces between the wet compartment and the film and between the film and the dry
compartment, water activity equilibrium is assumed to be reached instantaneously
a w 1 = a w 2 for x = L 2
(1)
a w 2 = a w 3 for x = 0

As moisture sorption isotherms for the three materials are modelled using the Ferro Fontan equation
[6]
c
a 1
X= ln × (2)
aw b

where a, b and c are unknowns parameters.

which may be rearranged as
1
a w = a exp bX c (3)

Using equation (3) for expressing each water activity equilibrium in equation (1) and expressing
moisture content in edible film (X2) and in dry compartment (X3) respectively as a function of moisture
content in wet compartment (X1) and edible film (X2), equation (1) becomes
c2
1
X 2 = B12 X1 c1 + A 21 for x = L 2 (4)

c3
1
X 3 = B 23 X 2 c2 + A 32 for x = 0 (5)

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b1 1 a b2 1 a
where B12 = , A 21 = Ln 2 and B 23 = , A 32 = Ln 3
b2 b2 a1 b3 b3 a2

For the (NRL) wet compartment,

X1 = (X1)0 for t = 0 (6)

and the variations of uniform moisture content (X1) is given by

dX1 X2
1 L1 = 2 Deff 2 for t > 0 (7)
dt x x= L2

X2
where 2 Deff 2 represents the net water mass flux gained by the film.
x x= L2

Assuming that the value of water diffusivity in the film (Deff 2) is constant, variations of moisture content
within the (RL) film compartment (X2) is given by the one-dimensional mass diffusion equation
2
X2 X2
= Deff 2 for L2 < x < 0 (8)
t x2
with the following initial and boundary conditions :
- Film compartment is initially at a uniform concentration (X2)0
X2 = (X2 )0 for t = 0 and –L2 x 0 (9)

- Water activity equilibrium is assumed to be reached instantaneously at the interface between

wet and film compartments and between film and dry compartments, so equations (4) and (5)
applied
- The flux of moisture out of the film compartment is equal to the flux of moisture into the dry
compartment
X2 X3
Deff 2 ms2 = Deff 3 ms3 for x = 0 (10)
x x
Variations of moisture content within the (RL) dry compartment (X3) is given by the one-dimensional
non linear mass diffusion equation
X3 X3
= Deff 3 for 0 < x < L 3 (11)
t x x

with the following initial and boundary conditions :

- Dry compartment is initially at a uniform concentration (X3)0
X3 = (X3 )0 for t = 0 and 0 x L3 (12)

- No moisture gradient exists at the end of the dry compartment

X3
Deff 3 = 0 for x = L3 (13)
x

Numerical method. The finite-difference method is used to solve numerically the system of equations
governing moisture transfer in the food system and MATLAB software (The Mathworks Inc, Natick,
MA, USA) is used to compute the system of equations and realize simulations. The same hypothesis
on water transport equations and water transfer at the interface between the wet and the dry
compartments were made for the two-compartments system [5].
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Model parameters were for each compartments initial water activity or moisture content, water sorption
isotherm equation, effective diffusivity and density excepted for (NRL) agar gel compartment for which
effective diffusivity was not required. Model parameters are given in previous studies for sponge-cake,
agar gel, edible films [4] and biscuit [7].

EXPERIMENTAL SECTION

A - Experimental and simulated moisture distribution profiles in a composite food.

The drastic moistening of cereal-based food (sponge-cake or biscuit) placed in direct contact with high
aw agar gel was experimentally observed through measurements of mass average moisture content
evolution with time (Figures 2 & 3). Acetylated monoglycerides films placed at the interface between
wet and dry compartments strongly reduced moisture transfer between compartments.

30
70 98 40

content of agar gel (g/100g

65 97

content of biscuit (g/100g

25 35
content of agar gel (g/100g

Mass average moisture

Mass average moisture

content of sponge-cake

60 96
Mass average moisture

Mass average moisture

(g/100g wet basis)

55 95 20 30
wet basis)

50 94 w.b.)

w.b.)
15 25
45 93
40 92 10 20
35 91
30 90 5 15
25 89
0 10
20 88
0 10 20 30
0 10 20 30
Storage tim e (days)
Storage time (days)

Figure 2 : Experimental (symbols) and predicted (black and grey curves Figure 3 : Experimental (symbols) and predicted (black and grey
for sponge-cake and agar gel respectively) mass average moisture curves for sponge-cake and agar gel respectively) mass average
content of a sponge-cake (initial aw = 0.840) in direct contact with an agar moisture content of a biscuit (initial aw = 0.180) in direct contact with
gel (initial aw = 0.999, ) or separated of the same agar gel by a 300 µm an agar gel (initial aw = 0.900, ) or separated of the same agar gel
film of ACETEM 50 ( ) or TSED 619 ( ). Vertical bars are standard by a 316 µm film of TSED 619 ( ). Vertical bars are standard
deviation. Experimental data for agar gel were not represented for more deviation. Experimental data for agar gel were not represented for
legibility. more legibility.

For example, considering a critical aw value of 0.87 for many yeasts growth [8] and the corresponding
moisture content in sponge-cake of 30% w.b., a TSED619 film allowed to increase the shelf-life of the
composite food more than 9 days instead of 6 days for an ACETEM 50 film and only 6 hours without
film (Figure 1). In Figure 2, considering a critical moisture content of 10% w.b. [1] for crispy cereal-
based products, loss of texture within biscuit placed directly in contact with agar gel was reached
rapidly in a few hours. Placing a TSED619 film at the interface between biscuit and agar gel delayed
the loss of crispness of more than 3 days (Figure 2) confirming the potential interest of using
acetylated monoglycerides films to control moisture transfer in composite cereal-based foods.
Experimental data were compared with predicted ones (Figure 1 & 2). The model successfully
predicted the experimental biscuit and sponge-cake moisture contents evolution with time with Root
Mean Square Error (RMSE) value lower than experimental error in each case. The model can be thus

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International Conference Engineering and Food

considered as an adequate tool for predicting moisture transfer between compartments of a composite
food and, thus, for predicting shelf-life or selecting edible film with required barrier properties.

B - Water barrier properties of edible films

Displaying barrier efficiency of various edible films by comparing experimental moisture contents
profiles measured in each food compartment is not easily realized because of unavoidable variability
in film thickness. Mass average moisture content evolution with time of sponge-cake separated from
agar gel by edible films of various compositions was thus simulated using the model and fixed film
thickness (100 µm). Different edible films were chosen : a widely studied hydrophilic material as wheat
gluten, a commonly used commercial barrier film as dark chocolate and four acetylated
monoglycerides films presenting various degree of acetylation and chains length (TSED613,
TSED619, ACETEM50, ACETEM70) for their interesting mechanical and barrier properties [9-11].

70 97
(1)
Mass average moisture content of

(2)
(3)

Mass average moisture content of

(4)
(5,6) 96.5
sponge-cake (g/100g w.b.)

60 (6)

agar gel (g/100g w.b.)

(5) 96
(4)
(3) 95.5
50
(2)
(1) 95

40 94.5

94
30
93.5

20 93
0 5 10 15 20 25 30
Storage tim e (days)

Figure 4 : Predicted mass average moisture content evolution of sponge-cake (continuous lines) separated of agar gel (dotted
lines, initial aw of 0.999) by a film of 100 µm thickness and variable composition : (1) TSED 619, (2) ACETEM 70, (3) ACETEM
50, (4) TSED 613, (5) wheat gluten and (6) dark chocolate films (from [4])

According to the type of edible film used, the evolution of predicted average moisture content of
sponge-cake could be quite different and could allow to classify films barrier efficiency (Figure 4).
Taking into account the RMSE values obtained for model validation (about 3%), the following
classification of the studied edible films for their moisture barrier efficiency could be proposed :
TSED619>ACETEM70>ACETEM50 TSED613>wheat gluten dark chocolate. The unexpected low
barrier properties of dark chocolate in the conditions of the present study could be related to the high
water sorption equilibrium of this material for aw above 0.80 [4]. This observation suggested that dark
chocolate could be used as a good water barrier in composite food provided that aw conditions remain
lower than 0.80.

C - Shelf-life prediction.

The models were then used for predicting temperature disruption during storage of composite foods of
various compositions. Predicted effect of abusive temperature (2 days at 20°C) during storage at 5°C
of a sponge-cake in direct contact with agar gels or separated from agar gel by a 100 µm ACETEM 50
film is presented in Figure 5.

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International Conference Engineering and Food

(1)
50 25

of the cereal-based compartment

Mass average moisture content
45
20

(g/100g wet basis)

Temperature (°C)
40
(2) 15
35
(3)
10
30

5
25

20 0
0 2 4 6
Storage tim e (days)

Figure 5 : Simulated effect of temperature abuse (grey lines) on mass average moisture content evolution with time (black solid
lines) of a sponge-cake placed either in direct contact with an agar gel of initial aw of (1) 0.999 or (2) 0.950 or (3) separated from
the agar gel of 0.999 initial aw by a 100 µm film of ACETEM 50.

For simulation at lower agar gel water activity (0.950 instead of 0.999), the rate of moisture transfer
between agar gel and sponge-cake decreases and, thus, the shelf-life of the composite food increases
of 10 hours to more than 2 days. The use of an acetylated monoglycerides film at the interface
between agar gel (0.999 initial aw) and sponge-cake allowed to increase the composite food shelf-life
of more than 4 days in spite of the activating effect of temperature on diffusion within ACETEM 50 film
(Figure 5). This observation suggested that combining reduce of wet filling aw and use of appropriate
barrier film could allowed to considerably increase the shelf-life of composite foods with sponge-cake
as cereal-based compartment even if they are stored in abusive conditions. Predictive models, thus,
appeared as very helpful tool for creating new composite food products.

REFERENCES

1. Roudaut G., Dacremont C., Le Meste M. Influence of water on the crispness of cereal-based foods : acoustic,
mechanical, and sensory studies. J. Texture Stud., 2, 199-213, 1998
2. Kamper S.L., Fennema O. Use of an Edible Film to Maintain Water-Vapor Gradients in Foods. Journal of Food
Science, 50, 2, 382-384, 1985
3. Guilbert S., Gontard N., Gorris L.G.M. Prolongation of the shelf-life of perishable food products using biodegradable
films and coatings. Food Science and Technology-Lebensmittel-Wissenschaft & Technologie, 29, 1-2, 10-17, 1996
4. Guillard V., Broyart B., Bonazzi C., Guilbert S., Gontard N. Preventing moisture transfer in a composite food using
edible lipid-based film and computer simulations. Journal of Food Science, 68, 7, 2267-2277, 2003
5. Guillard V., Broyart B., Bonazzi C., Guilbert S., Gontard N. Evolution of moisture distribution during storage in a
composite food modelling and simulation. Journal of Food Science, 68, 3, 958-966, 20036.
6. Ferro-Fontan C., Chirife J., Sancho E., Iglesias H.A. Analysis of a model for water sorption phenomena in foods.
Journal of Food Science, 47, 1590-1594, 1982
7. Guillard V., Broyart B., Bonazzi C., Guilbert S., Gontard N. Moisture diffusivity and transfer modelling in dry biscuit.
Journal of Food Engineering, 2003, In press.
8. Fontana A. Water activity's role in food safety and quality. Food Safety Magazine, 19-21, 57, 2001.
9. Lovegreen N.V., Feuge R.O. Permeability of acetostearin products to water vapor. J Agr Food Chem, 2, 558-563,
1954
10. Newman A.A. The aceto-glycerides, a new food ingredient. Food Manufacture, 37, 525-528, 1962
11. Lowe E., Hamilton W. E., Morgan A. I., Watters G. G., Durkee E. L. , Continuous Raisin Coater. Food Technology,
17, 11, 1447, 1963

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ICEF9 – 2004
International Conference on Engineering and Food

HTST Milk Processing: Evaluating the Thermal Lethality

inside Plate Heat Exchangers

Gut J.A.W.1, Fernandes R.1, Tadini C.C.1*, Pinto J.M.1,2

1
Department of Chemical Engineering, University of São Paulo
P.O.Box 61548, São Paulo, SP, 05424-970, BRAZIL
catadini@usp.br
2
Dept. of Chemical and Biological Sciences and Engineering, Polytechnic University
Six Metrotech Center, Brooklyn, NY, 11201, USA
jpinto@poly.edu

Abstract: In the design of HTST processes, the lethality inside the plate heat exchanger and the heat
loss at the holding tube are usually neglected. Thus, the thermal processing becomes more intensive
than required and nutrient and sensorial losses may occur. In this work, the overall thermal lethality in
milk pasteurization is evaluated by taking into account the lethality throughout the exchanger and the
results are compared with the case that considers the lethality for the holding tube only.

Keywords: milk pasteurization, thermal lethality, plate heat exchangers, food process modeling.

1.Introduction
Plate heat exchangers (PHEs) are extensively used in the dairy industry for
HTST (high temperature short time) pasteurization due to their excellent thermal
characteristics, good flow distribution and flexibility for cleaning in place,
disassembling and resizing. Usually the pasteurization process is designed by
assuming that the thermal inactivation occurs exclusively inside the holding tube at
constant pasteurization temperature. By neglecting the thermal inactivation that
occurs inside the PHE and the temperature drop for the holding tube, the length of
the tube may be overestimated and nutrient and sensorial losses may occur in
practice. With the use of PHE simulation it is possible to obtain the temperature
profiles in all of its channels and to further determine the extent of thermal
inactivation throughout the pasteurizer. Moreover, the simulation results can be used
to design more efficiently the pasteurization equipment so to ensure the inactivation
of harmful microorganisms while preserving food nutrients and sensorial
characteristics.
Since consumer demand for food products with lower costs, high quality and
nutritive value is increasing, much research has been carried out to optimize the
quality and safety of many processes, such as UHT (ultra high temperature) and
HTST continuous processing of liquid foods [1]. Jung and Fryer [2] simulated the
sterilization of liquid food products in tubular heat exchangers and concluded that the
common safety margin used in the food industry leads to significant over-processing
and unnecessary losses in product quality. Moreover, Grijspeerdt et al. [3] analyzed
three commercial UHT milk treatment systems and verified through process
simulation that they were over-designed with respect to bacterial inactivation.
In this work, the overall thermal lethality in milk pasteurization processing is
evaluated taking also into account the lethality throughout the PHE and the results
are compared with the lethality for the isothermal holding tube only. A rigorous

*
Corresponding author (e-mail: catadini@usp.br)
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International Conference on Engineering and Food

thermal model of the PHE is applied for obtaining the temperature profiles along its
channels.

2. Mathematical Modeling of the Pasteurization Process

The fundamental structure of the pasteurizer comprises the PHE, which is
divided in three or more heat exchange sections, the heating and cooling circuits and
the holding tube, as shown in the example of Figure 1.

Pasteurized
Product

Holding Tube
cooling regeneration heating

heating
regeneration
Raw cooling
Product
Figure 1: Schematic of the pasteurization unit and of the sections of the PHE.

The PHE model for generalized configurations presented by Gut and Pinto [4] is
used to generate the temperature profiles in all the PHE channels. The model was
developed for a single-section PHE assuming steady-state operation, no heat losses,
constant overall heat transfer coefficient throughout the exchanger, one-dimensional
incompressible plug-flow, no heat transfer in the direction of flow, uniform flow
distribution through the channels of a pass, perfect mixture at the end of a pass and
no phase-changes. Since the pasteurizer contains various sections, the model is first
used to represent each section separately before generating the complete model of
the pasteurizer. A section of the PHE is represented by a sequence of channels,
numbered from 1 to the corresponding number of channels (NC).
Based on the aforementioned assumptions, the energy balance applied to an
arbitrary channel i of a section of the PHE yields eq.(1), where Ti (x) is the
temperature of the fluid inside channel i; x is the coordinate tangential to channel flow
(0 ≤ x ≤ L); si indicates the direction of the flow inside channel i (si = +1 is the flow
follows the x direction and si = –1 otherwise); U is the mean overall heat transfer
coefficient (defined in eq.(2)); w is the channel width; Φ is the plate area enlargement
factor; Wi is the mass flow rate inside channel i (obtained by dividing the flow rate by
the corresponding number of channels per pass, N); and Cpi is the specific heat of
the fluid in channel i.

dTi s i ⋅ U ⋅ w ⋅ Φ
= ⋅ (Ti −1 − 2 ⋅ Ti + Ti +1 ) , 1 ≤ i ≤ NC (1)
dx W i ⋅ Cpi
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International Conference on Engineering and Food

1 1 1 e plate
= + + + R hot + R cold (2)
U hhot hcold λ plate

Heat transfer correlations, such as Nu=a·Reb ·Prc , are required for obtaining the
convective heat transfer coefficients inside the channels (hhot and hcold). Usual values
for the empirical parameters a, b and c are supplied in the works of Shah and Focke
[5] and Saunders [6]. If the fluid has non-Newtonian behavior, Re and Pr should be
calculated using suitable generalized forms, such as the ones suggested by Gut and
Pinto [4] for the power-law rheological model.
Boundary conditions for the temperatures of the channels are required in order
to solve the system of differential equations generated from eq.(1). The boundary
conditions represent the physical connection among the channels and passes. The
three possible forms of boundary conditions are presented in Table 1.

Table 1: Thermal boundary conditions for the PHE modeling

Boundary Condition Equation Form
Fluid inlet: the temperature at the
entrance of the first pass is the same as Ti x =0 or L
= T inlet , i ∈ first pass
the stream inlet temperature.

Change of pass: there is a perfect 1 N

mixture of the fluid leaving the channels of

Ti x =0 or L
=
N
∑T j x =0 or L
, i ∈ current pass
j ∈ previous
a pass, before entering the next one. pass

Fluid outlet: the stream outlet 1 N

temperature results from a perfect mixture

Toutlet =
N
∑T j x =0 or L
j ∈ last
of the fluid leaving the last pass. pass

The mathematical modeling of the pasteurizer consists of the thermal modeling

of the PHE sections, the boundary conditions that represent the connection among
sections, the assumed temperature drop for the holding tube and the specifications
for mass flow rates and inlet temperatures of the product, heating and cooling
streams [7]. The model consists of a system of first order linear ordinary differential
equations and algebraic equations, which can be solved by analytical or numerical
methods, such as the method of finite differences. The main result is the product
temperature profile inside the pasteurizer.
The integrated lethality or F-value, denoted by F in eq.(3), is employed for
evaluating the level of heat treatment of the process [8]. The F-value can be
considered to be the holding time at a given reference temperature Tref (assuming
instant heating and cooling) to which the whole process is equivalent, thus it can be
used to compare different processes [9]. In eq.(3), z is the Z-value for the inactivation
kinetics (defined as the temperature change required to change the D-value by a
factor of 10, where the D-value is the time required to obtain a 90 % inactivation at
constant temperature) and t is the time for a batch process or the residence time for
a continuous process.

t t T (t )−Tref

FTref = ∫ Lt (t ) dt = ∫10 z
dt (3)
0 0
ICEF9 – 2004
International Conference on Engineering and Food

The temperature profiles in the plate heat exchanger channels and in the
holding tube obtained from the pasteurizer model are further used for obtaining the
temperature-time distribution of the product in the pasteurizer, T(t), and the F-value is
then calculated through eq.(3). In this work, plug flow is assumed in the pasteurizer
for the calculations.

Example of Application
The proposed pasteurizer model was applied for the evaluation of a HTST milk
pasteurization process. The number of channels and pass-arrangement of the three
PHE sections, as well as the inlet conditions of the streams are presented in Table 2.
The main dimensions of the PHE are similar those of the exchanger Q030 RKS-10
[10] and the heat transfer and friction factor correlation supplied by Sauders [6] for
chevron plates with corrugation inclination angle of 45° were used. The holding tube
(nominal diameter: 2” sanitary, length: 7.6 m) was sized for a residence time of 16 s
at 72 °C in turbulent flow. A temperature drop of 2 °C is assumed for the holding
tube, as in Landfeld et al. [11].

Table 2: Configuration of the PHE sections and inlet conditions of the streams [7]
Section NC Hot side Cold side Inlet W (kg/h) T (°C)
Regeneration 96 24×2 24×2 Milk (13% t.s.) 3,000 5
Heating 16 4×2 2×4 Hot Water 4,500 80
Cooling 12 3×2 3×2 Cold Water 5,500 2

An appropriate finite difference method was applied for the solution of the
pasteurizer model using the software gPROMS [12]. The obtained temperature
profiles inside the PHE channels were used for generating the milk temperature-time
distribution shown in Figure 2 (the horizontal flow inside the PHE was neglected
because of the small thickness of the plates and channels).

75 1.0

70
0.9
65

60 0.8

55 T (t )
0.7
50

45 0.6
T (°C)

40
Regeneration II
Regeneration I

Holding Tube

0.5
Lt
Heating

Cooling

35

30 0.4

25
0.3
20

15 0.2

10 L t (t )
0.1
5

0 0.0
0 20 40 60 80 100 120 140 160
t (s)
Figure 2: Milk temperature and lethality profiles for the example
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International Conference on Engineering and Food

The process lethality was evaluated considering the thermal inactivation of

Coxiella burnetti with z = 4.4 °C [13] and the obtained lethality profile is presented in
Figure 2, where the temperature at the entrance of the holding tube is considered as
reference, Tref = 74.14 °C. The integrated lethality, obtained numerically, is F72°C =
45.7 s, whereas the lethality for the holding tube only, assuming isothermal
conditions for the outlet temperature of 72.14 °C, is F72°C = 17.2 s (details in Table 3).
For this example, the actual lethality is more than twice the required value for
Coxiella burnetti because the holding tube was sized neglecting the thermal
inactivation inside the PHE and the temperature drop in the holding tube. As a
consequence, unnecessary deterioration of nutrients and sensorial quality occur and
also energy is wasted at the heating and cooling circuits. Moreover, cheese
production yield may be affected. For the given process conditions, one tenth of the
holding tube would be enough to achieve the desired level of heat treatment, F72°C =
16 s.

Table 3: Integrated lethality inside the pasteurizer for the example

Individual
Section Accumulated F72°C (s)
Contribution on F (%)
Regeneration section I 0.07 0.2
Heating section 8.74 19.0
Holding Tube 43.14 75.3
Regeneration section II 45.67 5.5
Cooling Section 45.67 0.0
Total 45.7 100

Conclusions
The mathematical modeling of the a HTST milk pasteurizer, comprising a multi-
section PHE, holding tube and heating and cooling circuits, was presented. The
resulting model consists of a system of first order linear ordinary differential
equations and algebraic equations, which can be solved by analytical or numerical
methods. The simulation results are used for obtaining the temperature-time
distribution of the milk stream, which is applied for evaluating the level of heat
treatment of the process. An example of application is presented and it is verified that
the length of the holding tube is overdesigned because its original design did not
account for the thermal inactivation inside the PHE and the temperature drop in the
holding tube. Process simulation showed to be an important tool for designing more
efficiently the pasteurization equipment so to ensure the inactivation of harmful
microorganisms while preserving food nutrients and sensorial characteristics and
also reducing operational costs.
ICEF9 – 2004
International Conference on Engineering and Food

Nomenclature
2
a model parameter U overall heat transfer coef. (W/m ·°C)
b model parameter v velocity inside the channel (m/s)
Cp specific heat (J/kg·K) W mass flow rate (kg/s)
c model parameter Wi mass flow rate inside channel i (kg/s)
De channel equivalent diameter, 2·d/Φ (m) w channel width (m)
d mean channel gap (m) x plate length coordinate (m)
e thickness (m) z Z-value (°C)
FTref integrated lethality or F-value at Tref (s)
2
h convective heat transfer coef. (W/m ·°C) Greek Symbols
L effective plate length (m) λ thermal conductivity (W/m·°C)
Lt thermal lethality µ viscosity (Pa·s)
3
N number of channels per pass ρ density (kg/m )
NC number of channels Φ plate area enlargement factor
Nu Nusselt number, h·De/k
Pr Prandtl number, Cp·µ/k Subscripts
Q heat load (W) cold cold side of a PHE section
Re Reynolds number, De·v·ρ/µ hot hot side of a PHE section
2
R fouling factor (m ·°C/W) inlet stream inlet
si channel i flow direction parameter outlet stream outlet
T temperature (°C) plate plate
t time (s) ref reference

Acknowledgments
The authors would like to acknowledge financial support from FAPESP (The State of
São Paulo Research Foundation) and from CNPq (National Council for Scientific and
Technological Development).

References
1. Nott K.P., Hall L.D. Advances in Temperature Validation of Foods. Trends in Food Science &
Technology, 10, 11, 366-374, 1999.
2. Jung A., Fryer P.J. Optimising the Quality of Safe Food: Computational Modelling of a Continuous
Sterilisation Process. Chem. Engng Science, 54, 6, 717-730, 1999.
3. Grijspeerdt K., Mortier L., De Block J., van Renterghem R. Applications of Modelling to Optimise
Ultra High Temperature Milk Heat Exchangers with Respect to Fouling. Food Control, in print,
2003.
4. Gut J.A.W., Pinto J.M. Modeling of Plate Heat Exchangers with Generalized Configurations. Int. J.
Heat Mass Transfer, 46, 14, 2571-2585, 2003.
5. Shah R.K., Focke W.W. Plate Heat Exchangers and their Design Theory, in: Shah R.K., Subbarao
E.C., Mashelkar R.A. (eds.) “Heat Transfer Equipment Design.” Hemisphere P.C., New York,
804p, 1988.
6. Saunders E.A.D. “Heat Exchangers: Selection, Design & Construction.” Longman S.&T., Harlow,
568p, 1988.
7. Gut J.A.W., Pinto J.M. Selecting Optimal Configurations for Multi-Section Plate Heat Exchangers
in Pasteurization Processes. Ind. Engng Chem. Research, in press. 2003.
8. Sumbo C.R. “Thermobacteriology in Food Processing.” Academic Press, New York, 329p, 1973.
9. Lewis M., Heppell N. “Continuous Thermal Processing of Foods: Pasteurization and UHT
Sterilization.” Aspen Publishers, Gaithersburg, 447p, 2000.
10. APV. “Data Sheet: Quasar-Plate Heat Exchanger Q030 RKS-10.” Kolding, 4p, 2000.
11. Landfeld A., Zitný R., Houska M., Kýhos K., Novotná P. Residence Time Distribution during Egg
Yolk Pasteurization. Czech J Food Sci, 20, 5, 193-201, 2002.
12. Process Systems Enterprise. “gPROMS Introductory User Guide.” Release 2.1.1, London, 2002.
13. Sung N., Collins M.T. Thermal Tolerance of Mycobacterium paratuberculosis. Applied and
Environmental Microbiology, 64, 3, 999-1005, 1998.
ICEF9 – 2004
International Conference Engineering and Food

A MATHEMATICAL MODEL FOR OHMIC THAWING

ICIER Filiz (1), ILICALI Coskan (2), SASTRY Sudhir K. (3)
(1), (2) Food Engineering Dep., Engineering Fac., Ege University, 35100, Bornova- IZMIR, TURKEY
ficier@food.ege.edu.tr
ilicali@bornova.ege.edu.tr
(3) Dep.of Food,Agricultural and Biological Eng., Ohio State University, 590 Woody Hayes Drive,
Colombus, OH 43210, USA
sastry.2@osu.edu

ABSTRACT
Temperature history of Tylose samples which were ohmically thawed for the voltage gradients of 37.5,
40, 45 and 60 V/cm were plotted. The temperature dependencies of the electrical conductivity of the
Tylose samples were determined. The proposed mathematical model predicted shorter thawing times
than the experimental ones, for all voltage gradients. A system performance coefficient (SPC) was
defined as an indicator of the non-uniformity in the sample.
Keywords: ohmic thawing, electrical conductivity, Tylose

INTRODUCTION
Ohmic heating is based on the passage of electrical current through a food product that serves
as an electrical resistance. Heat is generated instantly inside the food. The temperature distribution
during heating may be calculated by solving the energy balance equation with a heat generation term
and applying the appropriate initial and boundary conditions (1).
Ohmic heating can also be used to thaw frozen food particulates. This method has been
proposed for use in thawing of fish and meat blocks (2). (3) and (4) employed similar methods based
on the electroconductive heating of the frozen meat chunks immersed in a liquid and positioned
between two electrodes having no direct contact with the piece. (5) used manually controlled ohmic
heating to thaw shrimp blocks. (6) reported that frozen shrimp has a two order of magnitude lower
electrical conductivity than thawed shrimp.(7) reported that the time for ohmic thawing is comparable
to water immersion thawing time, without the incidence of hot spots.
Ohmic thawing do not use any water or generate much wastewater, reduces the nutrient quality
of the food samples and is more energy efficient. It can be an alternative method to thaw frozen foods,
but heating must be controlled to prevent non-uniformity resulting in runaway heating, or the formation
of hot spots (7).
Although ohmic thawing has been attempted by several researchers, studies on the modelling
of ohmic thawing are limited. The objectives of this study were to obtain the temperature dependent
electrical conductivity change during ohmic thawing and to model the ohmic thawing process.

MATERIAL AND METHOD

Experimental Set-Up:
Experimental device (Figure 1) consisted of an isolating transformer, a power supply, a variable
transformer, an AC/DC transducer, a data-logger (21 X, Campbell Scientific Inc., Utah), an interface
and a microcomputer.

Isolating AC/DC Data-logger

transformer Transducer
Computer
Thermocouple
Power supply
0-270 V, 60 Hz
Sample Electrodes
Figure 1. Schematic diagram of the ohmic thawing system

Two platinum plated titanium disk electrodes with diameter of 0.0254 m were placed at the circular
ends of the cylindrical test cell. A Teflon coated T-type copper-constantan thermocouple probes
(Omega Eng. Inc., Stanford, CT) with a compression fitting was used to measure the temperature at
the geometric center of the sample. Voltage and current transducers were used to measure the
voltage across and the current through the samples.
ICEF9 – 2004
International Conference Engineering and Food

Methodology:
The test material was “Karlsruhe Test Substance (Tylose)”, a crystallised methyl cellulose gel
(Cole Parmer Inst. Comp, USA) having a moisture content of 77%. The properties of Tylose are given
in Table 1. Cylindrical Tylose samples having the length of 0.02 m and 0.03 m and a diameter of
0.0254 were prepared by covering all exposed surfaces with polyethylene films as mentioned in (8). A
T-type Teflon coated thermocouple was inserted at the geometric center of the sample. They were
frozen in a freezer (-40°C inside temperature) until the center temperature of the sample reached –
10°C. Frozen samples were placed between two electrodes (with slight pressure to insure good
contact without damage). The sample was heated up to 20°C by applying the voltage gradients in the
range of 37.5-60 V/cm at 60Hz a.c. Low voltages were chosen in accordance with the suggestions of
(4). The current, voltage and temperature were recorded by a data-logger every 1 s during the thawing
process and electrical conductivities were determined as (9);
IL
σ= (S/m) (1)
AV
The data were then transferred to a microcomputer. The heating rates and changes in electrical
conductivity were analysed for the temperature range of –8°C and +20 °C. The study was carried out
for triplicate samples.
The time-temperature data were plotted to obtain the thawing curves for the test samples during
ohmic thawing. A uniform temperature distribution was assumed for electrical conductivity
calculations. The electrical conductivities of samples were calculated from voltage and current data
using Eq. (1). The temperature dependencies of electrical conductivity values above and below
freezing point of the samples were predicted by regression analysis (SPSS 10.0 Statistical Package,
1999).
Model:
For a stationary medium with no internal resistance, heat balance on the uniform solid can be
written as follows;
• ∂T
u = ρCp (2)
∂t
•
where u is the temperature dependent volumetric heat generation rate (10).
The volumetric heat generation term can be written as;
,
2
u = ∇V σ (3)
for the case of constant voltage gradient (11). Heating rates can be calculated assuming uniform heat
generation throughout the sample. The entire solid thus heats at the same rate and Eq. (2) becomes;
•
1 dT
∆V 2σ = mCp (4)
Kc dt
where Kc=L/A. Eq. (4) was solved by the forward finite difference method. The time step used in the
computation was 0.01 s. The properties and parameters used in model are given in Table 1. The
specific heat was calculated by the following equation for temperatures below the freezing point (12);
b
Cp = a + (5)
(T fw −T)
n

The energy given to the samples was calculated by using recorded data;
Qgiven = ∑ ∆V I t (6)
The energy needed to thaw the sample fully and to heat it to a prescribed temperature was
calculated as;
Tf

Qneeded = m∆H = m( H fin − H i ) = m(Cpunf (T fin − T f ) + ∫ Cp dT ) (7)

Ti
For the case of no heat loss to the surroundings, Qgiven should be equal to Qneeded for a system
having a uniform temperature. The difference between these two values will be an indication of the
non-uniform heating in the sample. The system performance coefficient (SPC) was defined as the
ratio of Qneeded to Qgiven. SPC values were calculated for the test runs.
ICEF9 – 2004
International Conference Engineering and Food

Table 1. The properties and parameters used in model calculations

Property or parameter Value (dimension)

Freezing point of Tylose * -0.6 (°C)
The voltages applied 75, 90, 120 (V)
Length of the sample 0.02 , 0.03 (m)
Diameter of the sample 0.0254 (m)
Initial temperature -8 (°C)
Final temperature 20 (°C)
Diameter of the electrodes 0.0254 (m)
Specific heat above freezing point* 3660 (J/kgK)
a: empirical constant in Eq 5 associated with specific heat of fully frozen 1417 (J/ kgK)
*
b: empirical constant in Eq 5* 122056 (JK(n-1)/kg)
n: empirical constant appearing in Eq 5* 1.696
Density of Tylose* 1000 kg/m3
• from (12)

RESULTS AND DISCUSSION

Ohmic heating was performed to thaw the Tylose samples (food analog). Two different sample
lengths and three different voltages were used to determine the effect of electrical field strength on
ohmic thawing.
75/2 90/2 120/2 120/3
20
15
temperature (°C)

10
5
0
-5 0 50 100 150 200 250
-10
time (s)

Figure 2. Experimental ohmic thawing curves of the Tylose samples at different voltage gradients
(legend shows the voltage gradients V/cm of the samples with length of 0.02 m (2) and 0.03 m
(3) thawed by 75, 90 and 120 V)

As shown in Figure 2, thawing time decreases as voltage gradient applied increases. The time
required for the thawing the sample from -8°C to 20°C by applying 37.5 V/cm was approximately the
2.5 times of the thawing time by 60 V/cm voltage gradient. This difference was mainly caused by
higher electrical conductivities in higher voltage gradients applied as shown in Figure 3 and higher
internal energy rates at higher voltage gradients.

120/3 75/2
Electrical conductivity (S/m)
Electrical conductivity (S/m)

120/2 1 90/2
1,4
1,2 0,8
1 0,6
0,8
0,6 0,4
0,4 0,2
0,2 0
0
-10 0 10 20 30
-10 0 10 20 30
Temperature (°C)
Temperature (°C)

Figure 3. Electrical conductivity-temperature plots of Tylose samples ohmically thawed

(Legends show the voltage gradients applied V/cm; by the voltages of 75 V, 90 V and
120 V, for sample lengths of 0.02 m shown by 2 and 0.03 m shown by 3)
ICEF9 – 2004
International Conference Engineering and Food

The electrical conductivities of the samples increased as the temperature increased during
thawing (Figure 3). The electrical conductivity –temperature polynomial relationships for four different
voltage gradients were determined by regression, as shown in Table 2. High correlation coefficients
were obtained. The relationships were determined for two regions; below the freezing point (-8 to -
0.6°C) and above the freezing point (-0.6 to 20°C). Although the changes in the electrical conductivity
values by the temperature were small below the freezing point, a sharp increase was obtained above
the freezing point (Figure 3).

Table 2. Electrical conductivity- temperature relations of Tylose samples

Sample Voltage Temperature Electrical conductivity-temperature R2

length applied range
(m) (V)
T<Tf σ= 0.0004 T3 + 0.0088 T2 + 0.0695 T+ 0.2167 0.998
75 T>=Tf σ=-0.00001 T4 + 0.0006 T3-0.0102 T2 + 0.0809 0.998
T + 0.2373
0.02 T<Tf σ= 0.0022 T2 + 0.0406 T + 0.2035 0.997
90 T>=Tf σ= 0.0337 T + 0.2155 0.999
T<Tf σ=0.0018 T2 + 0.032 T + 0.1577 0.998
120 T>=Tf σ=0.0636 T + 0.1783 0.996
0.03 T<Tf σ= 0.0004 T3 + 0.009 T2 + 0.0793 T + 0.2746 0.999
120 T>=Tf σ= -0.0015 T2 + 0.0778 T + 0.2851 0.999

37.5 V/cm-exp 37.5 V/cm-mod

20 45 V/cm-exp 45 V/cm-mod
Temperature (°C)

15
10
5
0
-5 0 50 100 150 200 250 300
-10
Time(s)

40 V/cm-exp 40 V/cm-mod
20 60 V/cm-exp 60 V/cm-mod

15
Temperature (°C)

10

0
0 50 100 150 200 250
-5

-10
Time (s)

Figure 4. Comparison between the model and experimental thawing curves for different voltage
gradients (at legend; mod-model calculations, exp-experimental results)

The obtained temperature dependent electrical conductivity relationships were used in the
model predictions. The present model assumed no heat gain from the surroundings and fully uniform
thawing in the sample. As shown in Figure 4, the mathematical model predicted lower thawing times
than the experimental ones. Below the freezing point, experimental and predicted thawing rates were
similar to each other. However, the calculated temperature values were higher than experimental
values above the freezing point similar to the results of (11), (13), (14), (15) and (16). In this region,
ICEF9 – 2004
International Conference Engineering and Food

the mathematical model predicted 17 % less heating time for 60 V/cm and 31 % for 45 V/cm. As
comparison, the deviation in the results was lower at 0.03 m length of Tylose than 0.02 m length.
It is thought that the probable non-uniformity of temperature distribution was lower at the
longer sample. The non-uniform thawing can be explained partly by the poor contact of the sample
end surfaces with the electrodes during experiments as a result of volumetric shrinkage during
thawing. It might caused electrical conductivity variations in different locations of the solid sample. In
(17) non-uniformity in electric field or/and differences in electrical conductivities were given as the
reason of the variation of the observed temperatures in different locations.
The fully contact is the most important factor for the ohmic thawing of the solid materials. As
mentioned in (4) if a liquid for immersion of the sample is not used, the poor contact between end
surfaces of the product and the electrodes can take place. This also affects the performance of the
system and can cause non-uniform temperature distribution.

Table 3. Comparison of the experimental and predicted results

Sample Applied Voltage Thawing time (s) Qneeded Qgiven SPC

length voltage gradient Predicted Experimental (J) (J)
(m) (V) (V/cm)

0.02 75 37.5 188 232 3443 1612 2.1

0.02 90 45 112 163 4039 1712 2.4
0.02 120 60 78 93 3309 1613 2.1
0.03 120 40 134 185 6159 3722 1.7

To characterize the non-uniformity in the samples, the SPC values were used. The total energy
given experimentally and the total theoretical energy required for complete thawing were compared in
Table 3. The SPC values were in the range of 1.7-2.4. These values showed that the amount of heat
required for complete thawing was greater than the heat given to the sample. This means that while
the center of the sample was thawed, the other portions might be still in the frozen state. So, non-
uniform thawing occurred in the samples. Especially, the higher non-uniform temperature distribution
caused higher deviations at shorter samples. The model also predicted lower thawing times as a result
of assuming fully thawing in the sample. (7) discussed that the more heat was absorbed by the block
from the environment, and the smaller was the fraction of electrical heat in the total heat necessary to
thaw the blocks.
The findings from this study showed that approximately half of the energy required to fully thaw
the sample has been supplied from electrical energy. SPC values between 1.7 and 2.4 have been
attributed primarily to runaway heating.

CONCLUSION
The proposed model predicted shorter thawing times than the experimental results. This may be
due to non-uniform temperature distribution in the sample and the assumptions made in the model
calculations. A model which considers the spatial variation of temperatures and improvement of the
control of the process conditions will be helpful in future modeling studies on ohmic thawing.

NOMENCLATURE
A: Area of cross-section of the electrodes (m2)
Cp: Specific heat (J/kg K)
Kc: Cell constant (1/m)
I: Current (A)
L: The distance between the electrodes (m)
m: Mass of the sample (kg)
Q: The amount of energy (J)
T: Temperature (°C)
t: time (s)
V: Voltage applied (V)
ρ: Density of the sample (kg /m3)
σ: Electrical conductivity (S/m)
Subscripts;
f: the freezing point
i: initial
ICEF9 – 2004
International Conference Engineering and Food

fin: final
fw: freezing point of pure water, 0°C
unf: unfrozen

REFERENCES
1.Salengke M.S. “Electrothermal effects of ohmic heating on biomaterials: Temperature monitoring,
heating of solid-liquid mixtures, and pretreatment effects on drying rate and oil uptake. Ph.D
Thesis, Ohio State University, 2000.
2.Segars R.A. and Kapsalis J.C. The use of joule heating for the rapid heating and thawing of frozen
foods. 1 st International Congress on Engineering and Food, 68. 1976.
3.Naveh D., Kopelman I.J. and Mizrahi S. Electroconductive thawing by liquid contact. Journal of Food
Technology, 18, 171-176, 1983.
4.Yun,C.G., Lee D.H. and Park J. Ohmic thawing of a frozen meat chunk. Korean Journal of Food
Science and Technology, 30, 4, 842-847, 1998.
5.Henderson J.T. “Ohmic thawing of frozen shrimp: Preliminary technical and economic feasibility” Ms.
Thesis, University of Florida, FL., 1993.
6.Luzuriaga D.A., Roberts J.S., Balaban M.O. Electrical conductivity of frozen shrimp and flounder at
different temperatures and voltage levels. Journal Aquatic Food Production and Technology,
3, 5, 41-63, 1996.
7.Roberts J.S. and Balaban M.O., Zimmerman R. and Luzuriaga D. Design and testing of a prototype
ohmic thawing unit. Computers and Electronics in Agriculture, 19, 211-222, 1998.
8.Hayakawa K., Nonino C., Succar J., Comini G. and Giudice S. Two dimensional heat conduction in
food undergoing freezing: Development of computerised model. Journal of Food Science, 48,
1849-1853, 1983.
9.Wang W.C. and Sastry S.K. Salt diffusion into vegetable tissue as a pre-treatment for ohmic heating:
Electrical conductivity profiles and vacuum infusion studies. Journal of Food Engineering, 20,
299-309, 1993.
10.Sastry S.K. and Salengke S. Ohmic heating of solid-liquid mixtures: A comparison of mathematical
models under worst-case heating conditions. Journal of Food Process Engineering, 21, 441-
458, 1998.
11.Sastry S.K. and Palaniappan S. Mathematical modeling and experimental studies on ohmic heating
of liquid-particle mixtures in a static heater. Journal of Food Process Engineering, 15, 241-
261, 1992.
12.Succar J. and Hayakawa K. A response surface method for the estimation of convective and
radiative heat transfer coefficients during freezing and thawing of foods. Journal of Food
Science, 51, 5, 1314-1322, 1986.
13.Fryer P.J., de Alwis A.A.P., Koury E., Stapley A.G.F. and Zhang L. Ohmic processing of solid-liquid
mixtures: Heat generation and convection effects. Journal of Food Engineering, 18, 101-125,
1993.
14.Bouallou C., Buzan G. and Meyrignac R. Steam generation in porous media by volumetric ohmic
heating. International Journal of Heat and Mass Transfer, 40, 17, 4229-4238, 1997.
15.Fu W.R. and Hsieh C.C. Simulation and verification of two-dimensional ohmic heating in static
system. Journal of Food Science, 64, 946-949, 1999.
16.Icier F.“The experimental investigation and mathematical modeling of ohmic heating of foods”
Ph.D. Thesis, Ege University, Turkey, 2003.
17.Ruan R., Chen P., Chang K., Kim H.J. and Taub I.A. Rapid food particle temperature mapping
during ohmic heating using Flash MRI. Journal of Food Science, 64, 6, 1024-1026, 1999.
ICEF9 – 2004
International Conference Engineering and Food

A Study of Designing Techniques to Incorporate Consumers' 'Kansei' into Tea Beverage

Ikeda G(1), Hioki M(1), Nagai H(2) and Sagara Y(1)

(1) Department of Global Agricultural Science, The University of Tokyo

Yayoi 1-1-1, Bunkyo-ku, Tokyo, Japan 113-8657
aa27124@mail.ecc.u-tokyo.ac.jp
(2) New Products Development Division, Suntory Limited
Motoakasaka 1-2-3, Minato-ku, Tokyo, Japan 107-8430
Hajime_Nagai@suntory.co.jp

ABSTRACT
The designing techniques of green tea beverages were devised to incorporate consumers' kansei
into the flavor- and taste-active compounds. Sensory evaluation and instrumental analysis using GC
and HPLC were carried out for green tea samples. Preferable combinations of sensory attributes and
volatile or non-volatile components were predicted through ANN analysis of their correlations. The
preferable combinations were clearly different among consumers having different social positions.

KEYWORDS: kansei engineering, green tea, artificial neural network, sensory evaluation, consumer
preference

INTRODUCTION
Kansei engineering was founded 30 years ago, as an ergonomics and consumer-oriented
technology for a new product development1). Since the Japanese word “kansei” includes various
interpretations, there is no exact equivalent in European languages. Thus it is briefly defined as: 1)
sensing abilities of sensory organs which involve perception in response to external stimuli, 2)
dynamics of emotions elicited by senses and 3) sensory desires that are considered to be controlled by
reason and the mind. Thus kansei can be proposed for adoption into the English language. When
consumers wish to buy something, they will have a kind of feeling and image in their mind. If their
feeling could be implemented in the new product, they would be more satisfied with the product. Kansei
engineering is defined as "translating the customer's kansei into the product design domain". In an
earlier study, its specified paradigm and methodology related to foods has been proposed as “Food
Kansei Engineering” by Sagara2), coauthor of this paper.
Due to large number of organic compounds present in tea, it is difficult to design tea beverages
according to an absolute standard3). The volatile and non-volatile compounds existing in a tea
beverage determine its quality, however, the quality is ensured by a human taste panel. Then the
relationship between the compounds and the quality should be elucidated in order to translate kansei
into tea products. On the other hand, genetic sensitivity to the bitter taste of PROP
(6-n-propylthiouracil) was linked to lower acceptance for Japanese green tea4). Food preference can be
ICEF9 – 2004
International Conference Engineering and Food

highly variable, especially across sexes, ages, and a broad range of dieting habits and ethnic and
cultural backgrounds.
In the present study, volatile and non-volatile components in liquid green tea beverage were
identified using GC and HPLC. Descriptive sensory analysis of the tastes and flavors was carried out,
and the sensory responses for different compounds were analyzed for correlation with an artificial
neural network (ANN). Furthermore, the differences in consumer's kansei were compared among
social positions.

MATERIALS AND METHODS

Experimental Samples
Eight tea samples were prepared as one standard sample, four taste- and three flavor-controlled
samples. These tea test samples have different qualities in their taste and flavors.

Instrumental Analysis
Volatile compounds from standard and flavor-controlled samples were analyzed with a GC (Agilent
6890). The absolute concentrations of the odor-active compounds in green tea were determined by the
ratio of peak area of each compound to the internal standard and the calibration curves of authentic
samples. Gas Chromatography/Olfactometry (GC/O) was also conducted to identify the odor quality.
Non-volatile compounds of eight samples were analyzed by HPLC (Shimadzu LC-10Avp and Waters
AccQTagTM Amino Acid Analysis System 2690xe).

Human Sensory Analysis

Panel. Sensory analysis was performed by a panel of 240 consumers, who were 80 female senior
high school or university students, 80 female office workers in the age range of 20-39 and 80 male
office workers in the age range of 20-59.
Sensory evaluation. The samples were profiled using sensory 7-points descriptive analysis. Both
sniffing and tasting were performed in order to allow evaluation of odors, flavors and tastes. The
samples were described and discriminated by the following 18 sensory attributes: flavor intensity of
green, floral and roast, taste intensity of total, bitter, sweet, aftertastes, smoothness and the other 10
attributes. Preference testing was carried out to obtain an overall impression of each sample. Each of
the 240 consumers performed the evaluation of 4 samples in a fully randomized order.

Statistical Analysis
PCA analysis. A principal component analysis (PCA) was performed on the sensory data to
discriminate the response of sensory evaluation as simple and complex flavors. This analysis was
carried out using the statistical analysis software JMP 5 (SAS Institute Inc).
Liner regression analysis. The correlations between human preference score and sensory attributes
score were evaluated by liner regression analysis. The correlation coefficients were used to investigate
which sensory attributes affected the score of preference.
ICEF9 – 2004
International Conference Engineering and Food

Figure 1. PCA plot of sensory factors for the tea sample data

ANN analysis. An artificial neural network analysis (ANN) was carried out on instrumental and
sensory data. The ANN analyses are performed with the JMP software package. The networks have a
characteristic layered architecture, the so-called multilayer perceptron (MLP) network architecture.
They consist of one hidden layer between the input and output layers, which enables broad flexibility
thus allows solutions with a broad range of problems5). Prediction of concentration ratio of components
was performed to determine the most preferable design of green tea beverage.

RESULTS AND DISCUSSION

Sensory Analysis
The results of PCA, using the normalized sensory data for each attributes, are shown in Figure1. In
this figure, the eight samples are indicated with alphabetical letters. Four principal components were
kept, which accounted for 68.11% of the variance in the dataset, since PC #1, PC #2, PC #3 and PC #4
accounted for 34.44, 22.18, 5.96 and 5.54% of the variance, respectively, where PC #5 accounted for
4.05%. After a rotation of factor loadings using varimax method for clear interpretation of sensory
factors, four qualities appear to be evident, which were smoothness, thickness, fragrance and
sweetness.

Table 1. The values of correlation coefficient R for green tea in different panels

Predicting preference score of tea samples based on sensory factors was conducted on female
students, female and male office workers (Table 1). Liner regression demonstrated the contribution of
smoothness to preference scores (R = 0.59), while also impacting thickness and fragrance (R = 0.40
and 0.38 in Table 1) based on male office worker. Predictive indices for female students demonstrated
ICEF9 – 2004
International Conference Engineering and Food

Figure 2. Non-volatile compounds Figure 3. Volatile compounds of S-V samples

for P-W samples

that thickness and fragrance of green tea were not critical, in contrast with the relative importance of
sweetness (R = 0.03, 0.03, and 0.31, respectively). Results indicated a need to keep smoothness
levels for green tea due to their positive sensory implications in the processed product.

Instrumental Analysis
Figure 2 shows the total catechin and total amino acid for eight samples P-W. It can be seen that
sample P has the highest total amino acid. Sample Q and R exhibited the significant higher levels of
total catechin. Among the 20 GC peaks, 12 were recognized by sniffing in the GC-O analysis. The
distribution of odor-active compounds in flavored samples S-V is shown in Figure 3. The total
concentrations of similar odor descriptions, "flowery", "roast", "green" and "sweety", were determined.
Sample T indicated the highest flowery and green odors, while sample S shows the highest
concentration of roast and sweety odors.

Figure 4. Preferable combination of sensory factors and the analyzed components

Analysis for Correlation between Instrumental and Sensory Analyses

ANN analysis was carried out, and each of the sensory factors was analyzed to correlate with
instrumental analysis data for the distribution of total catechin, total amino acid, flowery, roast and
green odors. Figure 5 shows the preferable combination of sensory factors and compounds of green
tea indicating the best predicted score of preference using ANN for three panels having different social
ICEF9 – 2004
International Conference Engineering and Food

positions. Relatively high levels of flowery and roast flavor concentrations were found to cause the
sensory attributes of higher sweetness that were preferred by female students. Female and male office
workers showed their preference for green tea containing greater amount of total amino acid, which
allowed higher thickness and fragrance.

CONCLUSIONS
The designing techniques of green tea beverages were devised to incorporate consumers' kansei
into the flavor- and taste-active compounds. It was demonstrated that the techniques introduced in this
study were useful for the development of tea beverages.

REFERENCES
1. Nagamachi M. Kansei engineering as a powerful consumer-oriented technology for product
development. Applied Ergonomics, 33, 3, 289-94, 2002

2. Sagara Y. "Kansei" engineering for investigating food preference. Jpn. J. Taste Smell Res. 8, 2,
153-159, 2001

3. Dutta R., Kashwan K.R., Bhuyan M., Hines E.L., Gardner J.W. Electronic nose based tea quality
standardization. Neural Networks, 16, 5-6, 847-853, 2003

4. Drewnowski et al. Genetic taste markers and food preferences. Drug Metabolism And Disposition,
29, 535–538, 2001

5. Wailzer et al. Prediction of the aroma quality and the threshold values of some pyrazines using
artificial neural networks. Journal of Medicinal Chemistry, 44, 17, 2805-2813, 2001
 ICEF9-2004
International Conference Engineering and Food

Temperature and water activity calculations at the surface of unwrapped food

products during decontamination by jets of hot air
Kondjoyan A.*1, Belaubre N.1, Daudin J.D.1, Rouaud O.2, Havet M.2, Foster A.3
and Swain M.3
1
INRA, Station de Recherches sur la Viande, 63122 St Genès Champanelle, France
2
ENITIAA, rue de la Géraudière, BP 82225, 44322 Nantes cedex 3, France
3
FRPERC, University of Bristol, Churchill Building, Langford, N. Somerset, BS40 5DU, UK
*Correspondence: alain.kondjoyan @clermont.inra.fr

Abstract
A numerical thermal model developed previously to take into account heat transfers
by convection, radiation and evaporation during the heating and cooling of a solid
food product by a jet of air is coupled with another model which describes the
transfer of water inside the product. Response of the coupled model to a variation of
numerical parameters is tested. Temperature and water activity calculated at the
surface of an unwrapped product during a decontamination treatment are discussed
in relation to experimental results.

Key words: heat-water transfer, temperature, water activity, hot air, modelling.

Introduction
There is a renewed interest in thermal decontamination of the surface of food
products due to both the demand of consumers for safer products and their dislike
of the use of chemicals and irradiation. Existing scientific papers and prototypes
prove that heat treatments are efficient in decreasing significantly the microbial
contamination at the surface of meat products. However, these treatments are
difficult to apply and the exact amount of bacteria that are killed remains under
debate [1]. A European project (EU QLK1-CT-2001-01415, BUGDEATH coordinated
by the FRPERC, University of Bristol) aims to produce a model that predicts the
effect of thermal treatments, based on hot air or steam, on the surface
decontamination of food products. The final model shall be usable by engineers and
microbiologists and thus it shall be simple and quick to run. Authors of the present
paper are in charge of the thermal modelling and its validation, while other partners
realize microbial inactivation experiments and inactivation modelling [2] and building
of the apparatus. A numerical thermal model has been developed previously to take
into account heat transfers by convection, radiation and evaporation during the
heating and cooling of a solid food product by a jet of air [3, 4]. In this model water
evaporation was calculated assuming that the water activity was constant at the
surface of the food product during the decontamination treatment. This initial thermal
model proved to be accurate to predict surface temperature during the heating and
cooling of non evaporating products by jets of air, in static as well as in very fast
transient conditions. Surface temperature prediction was less good on evaporating
food products due the simple assumption of a constant water activity at the surface of
the product during heat treatment. It was also important to predict the evolution of aw s
during these heat treatments because of its effect on the thermal inactivation of
bacteria. Thus the previous thermal model has been coupled to an adapted
numerical version of the water diffusion model of Baucour et al. [5] to describe the
evolution of a w s during hot air decontamination treatments.
 ICEF9-2004
International Conference Engineering and Food

Model description
Heat and water transfers were considered to be of one dimension (1D), i.e. the product
was assumed to be a flat plate of infinite length and width, with a bottom side lying
down on a support and a top side subjected to the airflow. Product thickness was
0.0178 m
The evolution in time, t, of the temperature, T, inside the product due to conduction was
described by the heat diffusion equation (Fourier’s second law) which is linear and
parabolic in 1D [6]. Two different thermal boundary conditions were applied on each
side of the plate which agreed with the experimental situation used for model validation.
The external fluxes used to describe these thermal boundary conditions on the up and
downside of the product were expressed in the form of the Newton law i.e. the heat flux
was proportional to a transfer coefficient and to the difference in temperature between
the surface of the product and its outside. For product downside the outside
temperature was that of the support and the value of the heat transfer coefficient which
took into account the exchange by conduction between the support and the product
was constant and equal to 5 W.m-2.K-1. A preliminary sensitivity analysis had shown that
an increase of 20 W.m-2.K-1 of this value did not affect the result obtained on the top
side of the product. On the top side of the product the outside temperature chosen by
the model was the greatest of the air temperature or the radiation temperature (Tair in
present experiments ). The transfer coefficient was an effective transfer coefficient
which took into account the exchanges by convection, radiation and evaporation and
which value varies with time.

Air-Flow
RH,Patm
Heat

? ∂T  =heff (Tair − T sup )

 ∂x inf
( )
D(Csup) ∂C =k'(P(Tdew )-aws P(TS ))
∂x sup

Upside
P evaporation
R
O
D
∂ T( x,t )
∂t
= Dt
∂ 2T(x, t )
∂x2 ∂t ∂x
(
∂ C = ∂ D(C)∂C
∂x
)
U
C
T
λ ∂T  = hinf (Tsup port − Tinf )
 ∂x  inf
(∂∂Cx )
inf
=0
Downside
Fig. 1: Physical phenomena and mathematical relations exchang
taken into account in the coupled heat-water model.

Water transfer inside the product was calculated using the model of Baucour et al.
[5] based on the nonlinear Fickian diffusion law which was written as a function of a
dry abscissa to take into account product shrinkage. No evaporation occurred on the
downside of the product which made contact with the support. On the top side the
evaporated flux of water was the product of the mass transfer coefficient by the
saturated water vapour pressure at the dew point temperature minus the saturated
 ICEF9-2004
International Conference Engineering and Food

water vapour pressure at the surface temperature. The mass transfer coefficient was
calculated from the heat transfer coefficient using the Lewis relation. Ample
validations of this relation have been performed previously by the authors for
samples of different shapes subjected to various turbulent air flow conditions [7].
Previous equations were discretised by a finite difference method using the second
order numerical scheme of Crank-Nicolson which has the advantage of being
numerically stable and accurate [6]. In the heat transfer model the effective convective
transfer coefficient value was recalculated at the end of each time step using the
actualised values of the temperature and water activity coming from the previous time
step. In the non linear water diffusion equation water diffusivity and water activity were
also lagged by one time step [6]. Local water diffusivity and water activity were
determined from the function of diffusivity and sorption curve using the local water
concentration determined at the previous time step. The initial water content of the
product was assumed to be 3 kg of water by kg of dry matter and its water activity equal
to 1.

Results
Calculations were performed on an unwrapped piece of lean beef meat 0.0178 m
thick subjected, during 5 or 10 minutes, to a jet of air of velocity 17-20 m/s, of
temperature 103.5°C and of dew point temperature 4°C.
Water activity was calculated from the concentration of water in the first mesh at the
top surface of the product using sorption curves. Sorption curves depend on product
temperature and are usually not very well known in the high humidity range. Different
sorption curves were considered, those of Baucour on Gelatine at 3.5°C, on lean
beef meat and on pork at 20°C, which gave accurate results in the high humidity
range [8], those of Comaposada i Beringues on ham not salted at 5°C, 13°C and
26°C [9] and those coming from the review of Motarjemi on
Raw minced beef at 70°C [10]. All these results were coherent and for surface
temperature in between those corresponding to the previous curves water activity
was obtained by interpolation.
Diffusivity of water at 20°C as a function of water concentration on lean beef meat
was given by the experiments of Ruiz-Cabrera [11]. The effect of product
temperature on water diffusivity was calculated using an Arrhenius relation. Energy of
activation used in this relation varies from 15 kJ to 35 kJ depending on the author [9,
10]. An average value of 25 kJ was chosen in present calculations.
Choice of time step and mesh are very important for numerical calculations. The
speed-up procedure used previously in the thermal model to optimise time steps led
to numerical instabilities for the coupled model. Thus it was left aside and the larger
time step value (0.02 s) which avoided instabilities was chosen. When the thermal
model was used alone, only 50 meshes were required to calculate the evolution of
the surface temperature with an accuracy of 0.1°C. The effect of an increase to 600
meshes on the results of the coupled model was tested. Results showed that the
thinnest meshing was require to capture accurately the moment when aw s began to
decrease below 1. Requirements of a very short time step and of a great number of
meshes led to very long calculation times. Six hours were needed (on a PC
2GHz/512Mb) by the coupled model
to calculate temperature kinetics for a 10 minute treatment compared to only a few
tens of seconds with the initial thermal model
 ICEF9-2004
International Conference Engineering and Food

Surface Inside

Water concentration (kg water/kg dry matter)

3.0
10 min.
2.5
6.5min.

2.0
3.5min.

1.5 1.5min.

1.0

0.5
Thickness (m)
0.0
0.0E+00 5.0E-04 1.0E-03 1.5E-03

Fig. 2: Calculations by the coupled heat-water model of the variation in

the water profiles inside the lean beef meat sample subjected to the jet of
hot air at 103.5°C.

Profiles of water concentration obtained inside the product at different times are
given in figure 2. The variation of surface location with time (increase of the first X
value) indicates product shrinkage. Profiles remains very sharp even for long
calculations times. The Water content varies from almost 0 kgw/kgdm to 1.5 kgw /kgdm
in less than 0.1mm. This shows that the drying phenomena occurs almost totally in a
very thin part of the product.

The surface temperature and water concentration calculated by the coupled heat-
water model are given in figure 3 a-b. Water activity evolution calculated by the
coupled model confirms that the surface of food products dries very quickly (Fig.3b).
This intense drying has to be taken into account when describing the thermal
inactivation of bacteria. The coupled model improves the prediction of the increase of
surface temperature compare to results obtained by the initial thermal model
assuming a constant value of aw s. Agreement between the coupled model and
measurements is very good in the first seconds of the treatment. However afterwards
the increase of surface temperature calculated by the coupled model is much less
than measurements. This proves that the product dries even quicker than what is
predicted by the coupled model.
 ICEF9-2004
International Conference Engineering and Food

(a)
100 Surface temperature (°C)
90 No evaporation

80
70 Experiment

60
coupled model
50
40

30
Fully wetted
20

10
Time (s)
0
0 100 200 300 400 500 600

(b)
aws
1.0

0.8

0.6

0.4

0.2

0.0
Time (s)
0 100 200 300

Fig. 3: (a) Calculations of the surface temperature by

the coupled heat-water model, comparison with
measurements and with previous calculated results
assuming no evaporation or on the contrary an always
fully-wetted product; (b) calculations by the coupled
heat-water model of the decrease in aws.

To refine this analyse the sensitivity of calculated results to the uncertainties on the
effect of temperature on the sorption curves and on the water diffusivity relation has
to be made. A complete validation of the calculations would required to be able to
measure: (1) the water content at different locations inside the very thin layer of
product which dries and (2) the evolution of the water activity at the surface of this
thin layer. New techniques, which would avoid bias such as product re-wetting, are
needed.
 ICEF9-2004
International Conference Engineering and Food

Conclusion
A coupled heat-water one-dimensional model was developed to calculate the
temperature and water concentration at the surface and inside an unwrapped meat
product subjected to a jet of hot air. Even in a one-dimensional case calculations are
long, due to the short time step and great number of meshes needed to capture
physical phenomena. Results show that only a very thin part of the product located
just under the surface is drying. It seems that this drying is underestimated by the
model. However present analysis has to be completed by sensitivity tests on the
effect of temperature on the sorption curves and water diffusivity relations. Moreover
new experimental techniques are needed to validate the calculations on the evolution
of a w s and of the profile of water concentration .

References:
[1] James, C James, S. Meat Decontamination the state of the art. Bristol, UK: MAFF Advanced
Fellowship in Food Process Engineering, 140 p, 1997.
[2] Valdramidis V.P., Geeraerd A.H., Bernaerts K., Kondjoyan A. and Van Impe J.F. Realistic dynamic
temperature profiles as a key ingredient for microbial inactivation modelling: backstage microbiological
considerations.4th International Conference on Predictive Modelling in Foods, June 15-19 June 2003,
Quimper (France), 253-255, 2003.
[3] Kondjoyan, A., Havet, M. Modelling heat transfer in a jet of hot air to decontaminate meat products.
Science des Aliments, 23, 157-161, 2003.
[4] Belaubre, N., Kondjoyan, A., Foster, A., Swain, M., Zuniga, R., Havet, M. Surface temperature
predictions during hot dry air decontamination – First validations of the model inside a
th
decontamination rig. 4 Int. Conf. On Predictive modelling in foods, 15-19 June 2003, Quimper
(France), 250-252, 2003.
[5] Baucour, P., Ruiz-Cabrera, M. A. & Daudin, J. D. Food surface water activity prediction in water
transfer processes : incidence of sorption isotherm in the high humidity range. Pp C10.7-1,
Vol.Pres.Orale in proceedings of II European Congress of Chemical Engineering , Montpellier, France,
1999.
[6] Özisik, M.N. “Finite Difference Methods in Heat Transfer”, CRC Press, 412p, 1994.
[7] Kondjoyan, A., Daudin, J.D. Determination of transfer coefficients by psychrometry. International
Journal of Heat Mass Transfer, 36, 7,1807-1818, 1993.
[8] Baucour. Mesure des isothermes de sorption dans les hautes humidités. Modélisation du couplage
transfert d’eau et croissance bactérienne en surface des viandes, Thèse de Doctorat de l’Université
Blaise Pascal Clermont-Fd (France), 130p, 2000.
[9] Comaposada i Beringues, J. Sorption isotherms and water diffusivity in muscles of pork ham at
different NaCl contents, PhD Politecnica de Catalunya Barcelona (Spain), 192p, 1999.
[10] Motarjemi, Y. A study of some physical properties of water in foodstuffs, PhD Lund University
(Sweden), 204p,1988.
[11] Ruiz Cabrera, M.-A. Détermination de la relation entre la diffusivité de l’eau et la teneur en eau
dans les matériaux déformables à partir d’images RMN - Elaboration de la méthode avec des gels de
gélatine et transposition à la viande, Thèse de Doctorat de l’Université Blaise Pascal Clermont-Fd
(France), 122p, 1999.
ICEF9 - 2004
International Conference Engineering and Food

Diffusion coefficients of Algerian rosemary oleoresin during solvent extraction under

different operating conditions

S. Krim(1), C. Boutekedjiret(2), F. Bentahar(1).

(1) Laboratoire des Phénomènes de Transfert, Département de Génie chimique et Cryogénie,
Faculté de Génie Mécanique et Génie des Procédés, Université des Sciences et de la
Technologie Houari Boumediène (USTHB). B.P. 32 El Alia 16111 Bab-Ezzouar, ALGER,
Tél./Fax : (213) 21 24 71 69.
e-mail : Sch_Krim@yahoo.fr
e-mail : fatihabentahar@yahoo.fr
(2) Département de Génie Chimique, Ecole Nationale Polytechnique. 10 Avenue Hacène Badi.
B.P. 182 El-Harrach 16200 ALGER, Tél./Fax : (213) 21 52 29 73.
e-mail : c_boutekedjiret@yahoo.fr

ABSTRACT

The present paper deals with optimising the extraction of rosemary oleoresin. A comparison
between the yields obtained by a Soxhlet extractor and a percolator on an immersed fixed bed has
led to select the latter. Oleoresin diffusivities have been determined by using a mathematical
model. These ones have been affected positively by decreasing the solvent flow rate, the vegetal
weight and the stocking duration, and increasing the bed porosity and the operating temperature.

Key words: Rosemary, solvent extraction, oil, operating parameters, kinetics modelling, diffusivity.

INTRODUCTION

Rosemary, one of the most prevalent plants in Algeria and Mediterranean countries, is the
typical example since it has innumerable virtues. Actually, this plant is used since the dawn of time
by Greeks and Romans then by Arabs as flower of commemoration or reverence for the ones and
for its curative properties for the others [1, 2]. During this last decade, great efforts have been
focused on its very strong antioxidative properties, intending this oil to food preserving industry [3,
4]. It is important to emphasise that very few studies have been undertaken concerning the
Algerian rosemary and particularly on the solvent extraction kinetics of this plant. Among the few
works found in literature, those of Spiro & Chen [5] and Chen & Spiro [6]. As result, the aim of the
present work deals with hexane extraction of rosemary leaves oil originated from the Bibans (Bordj-
Bou-Arreridj, Algeria) in a semi-batch extractor, in order to bring to the fore the effect of the
diffusion coefficient on the operating parameters, solvent flow rate Q, vegetal material weight Wd,
bed porosity ε, stocking duration St and operating temperature T.

EXPERIMENTAL

Extracting process

In order to define the most suitable process to use it is advertisable to remember that the
solvent extraction can be done by three different ways in batch mode, in semi-batch or in
continuous mode. Inspired by the literature results the second extracting mode has been chosen
because it gathers the advantages of the two others without their drawbacks.
Nevertheless, two kinds of extractors are based on the semi-batch mode principle, the Soxhlet
generally chosen as reference and the percolator on immersed fixed bed. A comparison of the
extraction yields obtained by these two extractors, using three kinds of solvents as it is hexane,
ethanol and a 50% hexane+ethanol mixture of these two solvents, has shown that the two
extractors are equivalent, since very close yields have been obtained (Fig. 1).

1
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International Conference Engineering and Food

80

Perco lato r 6 0 .8 4 5 8 .9 0
60
Extraction yields (%)

So xh let

40 3 4 .7 5
3 3 .3 6

20

7 .0 5 6 .3 3

0
H ex an e E t h an o l H ex an e+E t h an o l

S ol ve n t type

Figure 1. Extraction yield-extractor type histogramm for three kinds of solvents

(hexane, ethanol and hexane+ethanol (50%))

Consequently, it is the percolator, which will be used in this paper because the Soxhlet has
the drawback of exposing continuously the oleoresin to the intense heat of a boiler favouring thus
its degradation.

Solvent extraction apparatus

The percolator in immersed fixed bed used is illustrated by the figure 2.

Figure 2. Experimental apparatus of semi-batch solvent extraction

A continuous circulating of hexane, at a constant flow rate, is insured by a distillation

system. This one is essentially constituted by a round-bottomed flask with a three-necked top (2),
filled with solvent. A boiler (1) insures the heating of this one until its boiling point. The solvent level
in the flask is maintained constant by using a separating funnel (3). A Vigreux column (5) is fitted
above the flask in order to rectify solvent vapours. Thermometers (4, 6) allow reading temperature
respectively in the flask and on the top of the Vigreux column. The vapours flow out by percolation
with the help of two condensers (7, 8) on the top of a thermostatted extractor (9). This one is made

2
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International Conference Engineering and Food

of two glass cylinders one inside the other. The cylinder containing the plant is of 36 cm length and
2.5 cm diameter. The exterior cylinder has a function of a water jacket. Rosemary leaves were
disposed in stages of 2 cm height, by using filter discs in order to assure, a uniform repartition of
the fluid in contact with the vegetal material and to avoid its compacting in the bottom of the
column. The solvent flow rate is regulated by a tap (10) in the bottom of the extractor. The miscella
is collected in an erlenmeyer (11). The solvent/oleoresin mixture (miscella) is subject to a vacuum
distillation with the help of a Rotavapor. The oleoresin obtained at each time is then weighted and
the yields deduced.

Plant material

The solid phase is formed by rosemary leaves air-dried at room temperature and cut from
the same mother shrub, from Bordj-Bou-Arreridj (Algeria). The average particle thickness is about
0.64 mm. While the liquid phase is constituted by hexane manufactured by Merck. The plant
moisture content was measured by Dean and Starck method; it was found about 6%. All the
experiments were based on the plant dry weight.

RESULTS AND DISCUSSION

Kinetics study

The effect of several operating parameters has been brought to the fore previously by Krim et
al. [7] both on oleoresin concentration in the solid and on the corresponding extraction rate. The
kinetics plots have shown therefore the presence of a constant rate step followed by a decreasing
rate one, called respectively washing and diffusion step. According to microscopic cross-section of
rosemary leaves, it has been assumed that the first one corresponded to the interfacial transfer of
the oil situated in exogenous glands (solid-liquid transfer) and the second one to the recovering of
the oil stocked in endogenous glands, by molecular diffusion through the solid. The latter being the
slowest stage, the mechanism of this extraction is assumed to be controlled by the molecular
diffusion. Otherwise, the kinetics plots have shown parabolic curves, so we can conclude to a
controlling Fickian diffusion. An example relating to the stocking duration is given in figures 3 and 4.

T=35°C, Wd=20g, 20
T=35°C, Wd=20g,
20
Q=2.3mL/min, ε=0.71 R a t e .1 0 4 Q=2.3mL/min, ε=0.71
Y e (% )
( g o /g d w m n )

16 16

M onths
12 M on th s 12

8
8
8 8
17
17
4 4

tim e (m in )
t im e ( m in )
0 0
0 50 100 150 200 250 300 350 0 50 100 150 200 250 300

Figure 3. Effect of stocking duration on extraction Figure 4. Effect of stocking duration on

yields –time plots extraction rate –time plots

The stocking duration impact of rosemary leaves, in the shade and at ambient moisture, over
a period spreading out 8 to17 months has revealed as shown on figures 3 and 4 a decreasing of
both the extraction yields and the washing step rate and a stabilisation of the diffusion step rate as
attested by the confounded curves observed in this case. These results suggest that, only the
superficial oil evaporates during the plant storage.

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Diffusivity determination

In order to determine diffusion coefficient under the different operating conditions

considered here a diffusion model has been proposed which assumes rosemary leaf as a slab of
infinite length (eq. (1)).
∂CS r
= div(Da gradCS ) (1)
∂t
The boundary conditions and the simplifying hypotheses have been also previously
presented [7], the solution obtained is a Fourier Serie (eq. (2)).

∞
CS  D 
C *cr = = ∑ B n exp − q 2n 2a (t − t cr ) (2)
C cr n =1  a 

The extraction front being displaced from the initial concentration of the solid to the critical
one corresponding to the transition between the washing and diffusion steps, a new relative
concentration has been defined by CS/Ccr. Da is the apparent diffusion coefficient and a
characteristic dimension of the solid corresponding to the half thickness of the leaf. The values of
Bn and qn are given by Crank [8] and Schwartzberg & Chao [9].
Actually this equation can be simplified for the short times (Ccr* > 0.40 ; τ < 0.29) by the
equation (3).

1 − C *cr = 2 τ (3)
π

Where the calculus of the Fick’s number τ leads to determine graphically the diffusion coefficient Da
(eq. (4)).
D a (t − t cr )
τ= (4)
a2

Whereas, for the long times (Ccr* < 0.61 ; τ< 0.12) the equation 2 is reduced to its first term.
The diffusivities are then obtained graphically in a semi-logarithmic scale (eq. (5)).

8 π2Da
ln C = ln 2 −
*
cr (t − t cr ) (5)
π 4a 2
Operating parameters effects on diffusivity

Şaşmaz [10] reported that the extraction rate constant depends on the solid shape and
dimension, on the cells permeability and on the operating temperature. Indeed, the diffusivity
values gathered in tables 1 to 5, have shown that this diffusion coefficient depends also on these
parameters, since it depends on the solvent flow rate, the vegetal weight, the bed porosity, the
vegetal stocking duration and the temperature. Furthermore, these values are in good agreement
with those of Reverchon et al. [11] and Boutekedjiret et al. [12] respectively 2.8 .10-9 and 2.1 .10-9
cm²/s.

Table 1. Solvent flow effect on diffusivity

Q(mL/min) 2.3 4.3 6.3
Da.109 (cm²/s) 2.79 2.45 0.40

Table 2. Vegetal weight effect on diffusivity

Wd(g) 20 40
Da.109 (cm²/s) 12.92 2.97

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International Conference Engineering and Food

Table 3. Bed porosity effect on diffusivity

(-) 0.61 0.71
Da.109 (cm²/s) 8.03 9.64

Table 4. Stocking duration effect on diffusivity

St(months) 8 17
Da.109 (cm²/s) 12.92 9.64

Table 5. Operating temperature effect on diffusivity

T(°C) 25 35 45
Da.109 (cm²/s) 0.68 1.09 1.77

The variation of the diffusivity under the different parameters studied follows the same
evolution as that of the kinetics plots shown in figures 3 and 4 for the stocking duration and
presented by Krim et al. [7] for the other parameters.
Actually, the solvent flow rate has shown a negative effect on the diffusivity; it decreases very
slightly between 2.3 to 4.3 ml/mn and more strongly for a flow rate of 6.3 ml/mn (Table 1).
The effect of the vegetal weight is similar; the diffusivity increases of 5 folds from 40 to 20 g
(Table 2).
While the bed porosity has a slightly positive effect on the diffusion step; the diffusivity
decreases of about 16% from a porosity of 0.71 to 0.61 (Table 3).
The stocking duration seems as shown on the figure 4 affecting negatively but not significantly
on the diffusion step. Indeed, the diffusivity decreases of about 24 % between 8 and 17 months of
vegetal storage (Table 4).
Finally, the operating temperature has a positive effect on diffusivity between 25 and 45 °C.
Anyway, it has been shown previously by Krim et al. [13], that the diffusivity can be correlated to
temperature according to Arrhenius law (Table 5).

CONCLUSION

Following to this study, one can conclude that the percolator in immersed fixed bed is the most
suitable extractor to use in order to carry out a semi-batch extraction.
Additionally, rosemary oleoresin extraction by hexane is governed by two transfer phenomena
and the global kinetics is controlled by a molecular diffusion.
Finally, the operating parameters have shown a negative effect on diffusivity for the vegetal
weight and the stocking duration, and a positive effect for the bed porosity and the temperature.

Nomenclature

Latin letters

a : characteristic dimension, cm
CS : mean concentration of the oil in the solid phase, go/gdm
Ccr : mean concentration of the oil in the solid phase at the critical time, go/gdm
Ccr : relative concentration depending on a critical reference, go/gdm
Da : Diffusion coefficient, cm2/s
Q : solvent flow rate, mL/min
St : stocking duration, months
T : operating temperature, °C
T : extraction time, min
t0 : initial time of extraction, min
Ye : Extraction yield, %.
Greek letters

: bed porosity,
: Fick’s number.
Indices

5
ICEF9 - 2004
International Conference Engineering and Food

dm : dry material,
o : oil,
s : solid phase.

References

1. Gildmeister E. and Hoffmann F., « Les huiles essentielles ». T. I, 2ème édition J. B. Baillère &
Fils, 1912.

2. Vernon F.and Richard H., « Quelques épices et aromates et leurs huiles essentielles ». APRIA.
2, 151-161, 1976.

3. Kim S. Y., Kim J. H., Kim S. K., Oh M. J. and Jung M. Y. Antioxidant activities of selected
oriental herb extracts. JAOCS, 71, 633-640, 1994.

4. Cuvelier M. E., Richard H. and Berset C. Antioxidative activity and phenolic composition of
pilot plant and commercial extracts of Sage and Rosemary. JAOCS, 73, 645-652, 1996.

5. Spiro M. and Chen S. S. Kinetics of Solvent Extraction of Essential Oil from Rosemary Leaves.
Flav. and Frag. J., 9, 187-200, 1994.

6. Chen S. S. and Spiro M. Kinetics of Microwave Extraction of Rosemary Leaves in Hexane,

Ethanol and a Hexane+Ethanol mixture. Flav. and Frag. J., 10, 101-112, 1995.

7. Krim S., Boutekedjiret C. and Bentahar F. Mass transfer during extraction of rosemary
(Rosmarinus officinalis L.) leaves oil with hexane. Compact disc of the 14th International
Congress of Chemical and Process Engineering, CHISA’ 2000, Prague, 2000-a.

8. Crank J., “The Mathematics of Diffusion”. Oxford University Press, Oxford, 45-56, 1975.

9. Schwartzberg H.G. and Chao R. Y. Solute diffusivities in leaching processes. Food

Technology, 73-86, 1982.

10. Şaşmaz D. A. Evaluation of the Diffusion Coefficient of Rapeseed Oil During Solvent Extraction
with Hexane. JAOCS , 73, 669-671,1996.

11. Reverchon E., Donsi G. and Osseo L. S. Modelling of supercritical fluid extraction from
herbaceous matrices. Ind. Eng. Chem. Res., 32, 2721-2726, 1993.

12. Boutekedjiret C., Bentahar F., Belabbes R. Study of solvent extraction of essential oil from
rosemary leaves. Compact disc of the 14th International Congress of Chemical and Process
Engineering, CHISA’ 2000, Prague (Czech Republic), 2000.

13. Krim S., Boutekedjiret C. and Bentahar F. Modélisation de la cinétique d’extraction par solvant
volatile de la concrète de romarin. Effet de la température. Disque compact des 3èmes
Journées Tunisiennes sur les Ecoulements et les Transferts, JTET2000, Mahdia (Tunisia),
2000-b

6
ICEF9 – 2004
International Conference Engineering and Food

Mathematical modelling of Saccharomyces sp. yeast growth

Kurz, T (1)

(1) Technische Universität Berlin

Fachgebiet Lebensmittelverfahrenstechnik
Amrumer Str. 32
D-13353 Berlin
T.Kurz@lb.tu-berlin.de

Abstract. A metabolic model of Saccharomyces sp. growth on synthetic and industrial media is
introduced. It represents the basis for the development of precise control strategies for cultures of
Saccharomyces sp.. Predictive simulations matched data from literature and (sequencing) batch
experiments with a deviation below 6% and indicated limits of controlability after implementation of
moduls describing temperature and oxygen dependency as well as yeast flocculation.

Keywords: metabolic model, Saccharomyces, model based simulation, growth

Introduction. Saccharomyces cerevisiae is one of the best-examined microorganisms in

biotechnology. To describe the growth and the ethanol formation in the bakers’ yeast propagation
process many structured and unstructured modelling approaches are known from literature. Structured
approaches consider balanced growth or are specified to describe particular biochemical pathways
inside structured models and therefore represent the basis for the modelling approach introduced in
this work [1].
In most cases the validity of these approaches, however, is limited to defined states of the metabolism
(oxidative, oxidoreductive, fermentative). Temperature dependency and maintenance energy are not
considered. Also, a lag-time function to describe the adaptation of the microorganisms to the
surrounding growth medium, including the time for formation of enzymes, is merely included in single
approaches using different equations [2,3]. The maintenance energy of the microorganisms is only
considered in single approaches, e.g. Pham et al. [2]. However, this approach is only valid if oxygen is
available. Most of the reports in literature used full media as a growth medium to avoid undesired
limitation effects during the growth process. This is not possible in industrial applications, e.g. if
industrial produced beer wort is used as growth medium. Combined limitation and inhibition effects,
e.g. caused by high ethanol concentrations, are usually not considered. Therefore, the applicability of
the mentioned approaches for industrial purposes, in particular considering the usage of nutrient
deficient, limiting or inhibiting media, is not guaranteed without qualifications. So, with a
comprehensive modelling approach considering the aforementioned inhibition and limitation effects,
knowledge can be gained towards a process control tool for industrial applications.
In particular, for the bottom fermenting brewing yeast strain Saccharomyces uvarum var.
carlsbergensis (W34/70) no comprehensive modeling approach is available, which takes into account
flocculation as well as the very limiting composition of the specific growth medium, i.e., brewer’s wort.
This work introduces a metabolic modelling approach, which represents the basis for the development
of control strategies during research and industrial applications. The first objective of this work was to
develop a metabolic modelling approach for yeast growth considering limiting and inhibiting effects of
industrial media and to validate it with literature and experimental data from brewery and bakery
applications. The second target was to show the potential of a model based predictive simulation to
evaluate process control strategies for Saccharomyces cultures and to extract the limits of
controllability using practice relevant case scenarios.

Materials and Methods. A 150 litre (net volume) propagator with an integrated continuous aerator
(Frings TRG) and defoamer unit was used. The propagator was equipped with online measurement
devices for temperature (PT 100) and dissolved oxygen (Mettler-Toledo, InPro6100). Underlying
control loops guaranteed accurate control of the manipulated variables temperature (+/- 0.1°C) and
dissolved oxygen (+/- 0.1 ppm).
A bottom fermenting brewery yeast strain Saccharomyces uvarum var. carlsbergensis W34/70 was
used for the experiments. For the propagator experiments, yeast suspension was taken from the
aforementioned propagator system. For the experiments industrial wheat beer wort (OG 12.5 w/w%)
was used as growth medium. Zinc (0.2 ppm) was added to avoid limitation effects. The initial
ICEF9 – 2004
International Conference Engineering and Food

concentration of free amino acids was nearly constant over all trials at about 220 ppm. Yeast
fermentable extract was determined using the SCABA measurement system.
Cell counts were made with a haemocytometer. For the simulation software, biomass concentration
was calculated using the dry weight of the yeast, the yeast count, and the molecular weight of the
biomass was set to 25.01 g/mol, according to the literature [4].
Modelling and simulations were carried out using the software package MATLAB 6.5®. For each
simulation the starting conditions including concentrations of biomass, gravity, nitrogen, ethanol and
dissolved oxygen in the growth medium as well as the progression of the manipulated variables were
required. During the parameter estimation procedure, in a first step ftemp (temperature coefficient for
the substrate uptake rate) and tlag (lag time coefficient) were fitted to the reference data of substrate
concentrations. In a second step, the maximum specific oxygen uptake rate qO2,max was fitted to all
reference data (substrate-, ethanol- and biomass concentrations).

Mathematical modelling. In this work a new metabolic modelling approach is introduced, that
describes the states of metabolism dependent on the surrounding medium, following the approaches
of Heijnen [5], van Gulik et al.[6] and Krzystek et al. [7]. Considered substances and defined turnover
rates were rS (substrate as glucose equivalent), rX (biomass equivalents), rn (nitrogen source), ro
(dissolved oxygen), rc (carbon dioxide), rw (water), re (ethanol), rgly (glycerol), rNADH2 (NADH/H+) and rATP
(ATP). Biomass composition was adopted from Sonnleitner and Käppeli [4].
As the metabolic pathways were known, stoichiometric relationships were formulated with eight
reactions r1-r8 as shown in Table 1.
Table 1: Description of the relevant metabolic pathways for the yeast propagation process.
(1) Oxidative degradation out of glucose r1
C6H12O6 + 6 H2O → 6 CO2 + 12 NADH2 + 2 ATP
(2) Respiratory chain r2
NADH2 + ½ O2 → δ ATP + H2O
(3) Formation of biomass out of glucose r3
g C6H12O6 + 0,15 NH3 + K ATP →
CH1,79°0,57N0,15 + c CO2 + n NADH2 + w H2O
(4) Formation of ethanol out of glucose r4
C6H12O6 → 2 C2H5OH + 2 CO2 + 2 ATP
(5) Formation of glycerol out of glucose r5
C6H12O6 + 2 NADH2 + 2 ATP → 2 C3H8O3
(6) Maintenance r6
ATP → ADP
(7) Oxidative degradation of ethanol r7
C2H5OH + 3 H2O → 2 CO2 + 6 NADH2
(8) Biomass formation out of ethanol r8
e C2H5OH + 0,15 NH3 + Ke ATP + we H2O →
CH1,79O0,57N0,15 + ce CO2 + ne NADH2

The rate of metabolic turnover of one substance can be formulated as the sum of the turnover in the
single reactions. So, it is possible to define linear equations for the relation between the turnover of all
substances and the rates of all reactions r = A · v with r representing the vector for the turnover of the
single substances. A the matrix of stoichiometry and v the vector for reaction rates (see Table 1).
It was assumed, that NADH/H+ and ATP are neither accumulated in the cell nor excreted (rNADH2 = 0
and rATP = 0). Therefore for this modelling approach a linear equation system with 10 equations and 16
unknown rates (rs, rx, rn, ro, rc, rw, re, rgly, r1, r2, r3, r4, r5, r6, r7, r8) was formulated:
The coefficients δ, K and Ke were calculated using the known yield coefficients for purely aerobic
growth on glucose, purely anaerobic growth on glucose and aerobic growth on ethanol (δ = 1.5,
K = 2.2 and Ke = 5.1). Coefficients in the same order of magnitude are presented in literature [5,6,7].
The yield coefficients were assumed to be constant. Table 2 shows the final applied parameters taken
from the literature. So, the stoichiometry of this modeling approach is fixed.
In order to solve the equation system six rates have to be determined first. Kinetic equations for the
characterisation of the different metabolic states have to be taken into account. Known are rates for
oxidative growth OG (re=rgly=r7=r8=0), oxidoreductive growth ORG (rgly=r7=r8=0) and fermentative
growth FG (rO=r1=r7=r8=0) on sugar and for oxidative growth on ethanol OGE (r1=r3=r4=r5=0),
respectively. Merely four different rates remain unknown including rS, r6, rO ( for oxidative growth on
glucose) and rO ( for oxidative growth on ethanol). The missing rates for OG (rS, r6), ORG (rS, rO, r6),
ICEF9 – 2004
International Conference Engineering and Food

FG (rS, r6) and OGE (rS, r6) must be calculated for the different metabolic states using kinetic equations
describing rates for substrate turnover and maintenance.
Table 2: Stoichiometric and kinetic parameters used in the modelling approach for the brewery yeast propagation
process.
Parameter Value Unit Reference
Stoichiometric parameters
Yx/sox 3.527 mol/mol Sonnleitner and Käppeli [4]
Yx/sf 0.72 mol/mol Heijnen [5]
Yx/e 1.12 mol/mol Heijnen [5]
HX 1.79 mol/mol Sonnleitner and Käppeli [4]
NX 0.15 mol/mol Sonnleitner and Käppeli [4]
OX 0.57 mol/mol Sonnleitner and Käppeli [4]
C 0.095 mol/mol Krzystek and Ledakowicz [7]
Heijnen [5]
ce 0.266 mol/mol Heijnen [5]
Kinetic parameters
mATP 0,013 mol/mol/h Heijnen [5]
qs,max 0.4863 mol/mol/h Sonnleitner and Käppeli [4]
KS 2.8 mmol/L Sonnleitner and Käppeli [4]
KO 0.00121 mmol/L Hartmeier [8]
Ki,eth 500 mmol/L Hutter and Oliver [9]
Ki,eth,o 1000 mmol/L Sonnleitner and Käppeli [4]
Keth 2.2 mmol/L Sonnleitner and Käppeli [4]
KN 2 mmol/L Cartwright et al. [10]

Kinetics for substrate uptake and oxygen uptake are expressed by Monod-Terms. Monod kinetics are
only suitable to describe the exponential and the stationary state of the propagation. After inoculation,
the yeast cells need a certain time (lag-time tlag) to get adapted to the surrounding medium. For a
description a lag-time coefficient Lt is introduced as a sigmoid function of time t. Summarising, the
specific substrate uptake rate can be formulated as (valid for growth on glucose during OG, ORG, FG)

S K i ,eth N
qS = qS ,max ⋅ ⋅ ⋅ f temp ⋅ Lt (1)
S + K s K i ,eth + E N + K n
The specific oxygen uptake rate, qO2, is limited by the oxygen concentration and inhibited by the
ethanol concentration in the growth medium with Ki,eth = 1000 mmol/L [4] and Ko = 0.00121 mmol/L [8].
The value of qO2 is limited by a maximum specific oxygen uptake rate qO2,max, which is a measure for
the oxidative capacity of the yeast cell.
O K i ,eth ,o
qO 2 ≤ qO 2,max ⋅ = qO 2,lim (2)
O + K O K i ,eth ,o + E

At a critical specific substrate uptake rate qS ,the oxidative capacity of the cell is reached. With an
increase of qS the metabolism changes from pure oxidative to oxidoreductive metabolism, that means
that the glucose is no longer degraded using only the oxidative pathway, but a portion is degraded
fermentatively as well. At the critical substrate uptake rate, qO2 reaches its limit qO2,lim. This
phenomenon is known as the ‘Crabtree effect’.
For yeast growth on ethanol (OGE) the specific oxygen uptake rate is different from equation 2. As no
metabolism regulation effects such as the ‘Crabtree effect’ have to be considered, a sufficient
description of the metabolism can be achieved with one specific uptake rate. Therefore, additionally to
equation 2, the specific oxygen uptake rate is limited by available ethanol and nitrogen sources. In
addition, as glucose is the preferred substrate, growth on ethanol is only possible if the glucose
concentration is very low. According to Sonnleitner and Käppeli [4], this aspect was expressed by an
extra inhibition term (KiS = Ks). During growth on ethanol equation 3 describes the kinetics for the
specific oxygen uptake rate qO2,e,lim.
O E N K i,eth,o Ks
qO 2,e,lim = qO 2,e,max ⋅ ⋅ ⋅ ⋅ (3)
O + KO E + K e N + K n Ki ,eth,o + E K s + S

It is assumed that the specific demand on maintenance energy of yeast cells is constant. If the energy
demand mATP is known, the rate r6 can be calculated.
ICEF9 – 2004
International Conference Engineering and Food

The kinetic is herewith determined for each metabolic state. Reaction rates ri are calculated by means
of ri = qi * xi. The switch between the different metabolic states is realised at the critical specific
substrate uptake rates for oxidative, oxidoreductive and fermentative metabolism. Critical rates are
calculated by combining conditions of two states and solving the equations for qs.

Model identification and sensitivity analysis. A first rough validity of the developed modelling
approach could be verified with literature data from baker’s yeast batch propagations [4,11,12] and
with experimental data from brewery propagations. Reference data on biomass, substrate and ethanol
concentrations were compared to model based simulation runs. For the required propagations yield
coefficients, maximum specific oxygen uptake rate qO2,max, temperature coefficient ftemp and lag-time tlag
were extracted as parameters with a high influence on the progression of the considered
concentrations in a sensitivity analysis. In this work, only the latter three parameters were intended for
the parameter estimation procedure in order to fit model based simulation runs on experimental data.
On the other hand, yield coefficients and parameters with low sensitivity were assumed to be constant.
The accuracy of the simulation concerning the biomass concentration was validated with the deviation
between simulation and reference values. A mean value for the deviation of 5.6% could be reached
(not shown). Considering the measurement error of yeast count of ±5%, it can be stated that the
simulation represents the reference values accurately, which could be reproduced also with different
propagation plants and different yeast strains with a conventional discontinuous aeration system (not
shown). So, the validity of the modelling approach for industrial applications could be proven.

Process management. Concerning the influence of temperature, in the field of baker's yeast
propagation work was done on a comparably small scale. In contrast to this, several authors described
the temperature dependence of microbial growth in general or for specific bacteria. The most common
approaches were exponential following the Arrhenius equation or parabolic Bĕlehrádek-type
equations.
The main objective of this work is to replace the variable parameters by model equations of their
temperature dependency in order to allow a predictive simlation of non isothermal propagation runs.
Figure 1 presents the observed temperature dependency of the estimated parameters qO2,max and the
temperature coefficient ftemp of the specific sugar uptake rate (dots).
0,2
0,18 1
0,16
qO2 ,max 0,8
ftemp
0,14
0,12
0,6
0,1
0,08
0,4
0,06
0,04 0,2
0,02
0 0
2 70 2 80 2 90 T/K 300 310 320 27 0 28 0 290 T/K 300 310 320

Figure 1: Schoolfield model (lines) fitted on data sets (dots) of the specific oxygen uptake rate qO2,max and the
temperature coefficient ftemp of the specific sugar uptake rate.
Four different modelling approaches were tested, a square-root approach, a potential approach of
Bĕlehrádek, the Schoolfield model and an Arrhenius approach of Mohr and Krawiec, to describe the
temperature dependency of the parameters ftemp and qO2,max. The Schoolfield model (see equation 4
and lines in Figure 1) could describe the temperature dependency of both parameters best along the
entire temperature range.

T ⋅ exp ∆H° ⋅  1 − 1 
 
r(15°C) ⋅   
288K  R
 288K T 
f (T ) = 
(4)

 ∆H
°  1 1 
 
 ∆H
°  1 1 


1 + exp T
⋅  −  + exp H 
⋅ − 
 R
  T0,5 T T   R
  T0,5 H T 

with r(15°C) specific growth rate at 15°C [h-1], ∆H° activation enthalpy of the limiting enzyme reaction
[J⋅mol-1], ∆HT° change of the activation enthalpy by inactivation of the enzyme at low temperatures
[J⋅mol-1], T0,5 T temperature [K], when half of the enzymes are inactivated by low temperatures, ∆HH°
change of the activation enthalpy by inactivation of the enzyme at high temperatures [J⋅mol-1] and
ICEF9 – 2004
International Conference Engineering and Food

T0,5 H temperature [K], when half of the enzymes are inactivated by high temperatures. The rate of the
enzyme catalysed reaction (growth rate) is modelled only by the numerator, if all enzymes are active.
The exponential expression in the denominator model the transition in an inactive form caused by high
or low temperatures. Belonging values for the parameters are given in Table 3.
Table 3: Final parameters of the Schoolfield model. Units are given in the text.
r15°C ∆H0 ∆HHo T0,5H ∆HTo T0,5T
ftemp 0.22 61742.66 513434.54 308.57 -713399.45 277.20
qO2,max 0.14 6695.79 1100795.40 303.11 -236498.15 289.09

Other approaches (not shown) could not reach the accuracy of the Schoolfield description. Especially
the transition from the sub-optimal to the superoptimal temperature range could not be represented by
the other three aproaches with an adequate accuracy. Hence, the variable parameters of the applied
metabolic modelling approach was replaced by the Schoolfield temperature model.
For the regarded experiments already adapted yeast, inoculated in an exponential state, was used for
the propagation. Less than one hour for the lag time resulted by the parameter estimation for all
experiments. Therefore the parameter lag time was fixed to zero. Experiments with dried yeast (not
presented here) yielded a temperature dependency of the lag-time similar to trials described in
literature. However the results could not be confirmed statistically.
Practice relevant concentrations of dissolved oxygen in the required range of 0.1 to 0.8 ppm for
experiments at 15°C exerted only a minor influence on the biomass growth compared to the
temperature. However, lower dissolved oxygen concentrations than 0.1 ppm decreased the specific
growth rate due to oxygen limitation effects, e.g. to 70% at 0.05 ppm dissolved oxygen concentration.
This confirmed results of Hartmeier [8] or Cho et al. [13] and therefore is not presented in more detail.
An implementation of the dissolved oxygen dependency in the specific growth rate was not necessary,
because the relation was represented by the temperature dependent maximum specific oxygen
uptake rate qO2,max and the fixed half saturation constant Ko without an individual adaptation.
Flocculation of bottom fermenting yeast strains was described by a discrete model based on Stokes
sedimentation equation (unpublished work).

Case scenarios. With the formulation of the variable parameters ftemp and qO2,max as ftemp(T) and
qO2,max(T), respectively, and a fixed set of stoichiometric and kinetic parameters a predictive simulation
of the yeast propagation process was possible even for the application of temperature and dissolved
oxygen profiles.
Herewith a prerequisite for the realisation of an active process control and evaluation tool for control
strategies could be established. In order to show this potential, case scenarios were carried out, which
simulate a delay in a preliminary production step. Figure 2 presents a case scenario for a brewery.
600 300
Concentration [mmol/L]

400 294
Temperature [K]

200 288

0 282

Figure 2: Application of a temperature scenario for the yeast propagation process. A temperature profile (293-283-
293 K) was applied (dotted line). Reference values for the progressions of biomass (!) and substrate (♦) and
belonging simulations (lines) are shown.
Here, the yeast propagation has to be delayed for several hours due to a disturbance in a preliminary
production step. Progressions of reference values (dots) and model based predictive simulations
(lines) of the concentrations of biomass and substrate (as glucose equivalents) for the given
temperature profile are presented. The change of temperature caused a deceleration and
acceleration, respectively, of the propagation process, which can be found in the progressions of the
ICEF9 – 2004
International Conference Engineering and Food

reference values as well as in the belonging predictive simulation runs. The deviation between
measurement and simulation was around 6%. Also in other scenarios applying temperature and/or
dissolved oxygen as manipulated variable it could be shown, that with a precise adjustment of
trajectories the crop time of the inoculum could be varied within a period of 7 to 50 hours by
maintaining a high fermentation activity for the subsequent anaerobic fermentation. The results could
also be confirmed at industrial propagations in a 200 hL propagation plant as well as with other yeast
strains in the described 150 L pilot plant (not shown). Similar to aerated and stirred yeast propagation
anaerobic batch fermentations could be simulated with a satisfying accuracy after implementation of
the discrete sedimentation model.

Conclusions. A reasonable modelling approach for research and industrial yeast propagation was
developed and validated with literature data and experiments. Model based simulations matched
experimental data very well and the validity of the modelling approach for the required brewery
propagations could be proven. Therefore, an automatic adaptation of the parameters of the model, as
it is proposed in other works to reach a higher accuracy of the model-based simulation, was not
indicated in the required application. With only three variable parameters an easy manageable
simulation tool is provided for the engineer.
The benefit for the engineer from this work, lies in the gain of process knowledge about both the
influence of manipulated variables and the growth medium on biomass growth and resulting biomass
activity as well as about the limits of controllability. Though using an industrial growth medium,
process control strategies can be simulated and evaluated. The knowledge gained about the process
behaviour allows the employment of optimisation algorithms, e.g. genetic algorithms, in order to plan
propagation strategies more efficient than before. Mistakes in process strategies can be avoided and
active yeast can be provided for inoculation even considering practice relevant scenarios. The
applicability of the developed system is not limited to the considered case. Conceivable are
applications for fed-batch and continuous cultures as well as industrial fermentations, where
economical or traditional aspects prohibit the usage of customised growth media, such as for the
production of vinegar, wine, single cell proteins or secondary metabolites.

References
1 Sweere, A.P.J., Giesselbach, J., Barendse, R., de Krieger, R., Honderd, G., Luyben, K.C.A.M.
Modelling the dynamic behaviour of Saccharomyces cerevisiae and its application in control
experiments. Applied Microbiology and Biotechnology, 28, 116-127,1988.
2 Pham, H.T.B., Larsson, G., Enfors, S.-O. Growth and Energy Metabolism in Aerobic Fed-Batch
Cultures of Saccharomyces cerevisiae: Simulation and Model Verification. Biotechnology and
Bioengineering, 4, 474-482, 1998.
3 Zhang, Z., Scharer, M., Moo-Young, M. Mathematical model for aerobic culture of recombinant
yeast. Bioprocess Engineering, 17(4), 235-240, 1997.
4 Sonnleitner, B., Käppeli, O. Growth of Saccharomyces cerevisiae is controlled by its limited
respiratory capacity: formulation and verification of a hypothesis. Biotechnology and Bioengineering,
28, 927-937, 1986.
5 Heijnen, J.J. Macroscopic approach and mathematical modelling of microbial processes. In: BODL-
Advanced Course Microbial Physiology and Fermentation Technology, Delft, 1996.
6 van Gulik, W.M., Heijnen, J.J. A metabolic network stoichiometry analysis of microbial growth and
product formation. Biotechnology and Bioengineering, 48, 681-698, 1995.
7 Krzystek, L., Ledakowicz, S. Yield and maintenance coefficients in s. cerevisiae cultures. Journal of
Chemical Technology and Biotechnology, 71, 197-208, 1998.
8 Hartmeier, W. Untersuchungen über die Kinetik der mikrobiellen Sauerstoff-Aufnahme und den
Einfluß des Sauerstoff-Partialdruckes auf den Stoffwechsel von Saccharomyces cerevisiae. Ph.D.
Thesis. Technische Universität Berlin, 1972.
9 Hutter, A., Oliver, S.G. Ethanol production using nuclear petite yeast mutants. Applied Microbiology
and Biotechnology, 49, 511-516, 1998.
10 Cartwright, C.P., Rose, A.H., Calderbank, J., Keenan M.H.J. Solute Transport, In:The Yeasts, Vol.
3, 2nd edn., A.H. Rose and J.S. Harrison Eds., Academic Press: London, pp.5-56, 1989.
11 Barford, J.P. A mathematical model for the aerobic growth of Saccharomyces cerevisiae with a
saturated respiratory capacity. Biotechnology and Bioengineering, , 23, 1735-1762, 1981.
12 Barford, J.P. A general model for aerobic yeast growth: batch growth. Biotechnology and
Bioengineering, 35, 907-929, 1990.
13 Cho, M.H., Wang S.S. Practical method for estimating oxygen kinetic and metabolic parameters.
Biotechnology Progress, , 6, 164-167, 1990.
ICEF9 – 2003
International Conference Engineering and Food

FEM BASED ADVANCED TOOLS FOR SIMULATION OF

FOOD PRESERVATION PROCESSES
C. Maggiolo (1), E. Balsa-Canto(2), M. Chiumenti(3),
M. Cervera(4) and E. Oñate(5)
(1 − 5)CIMNE, Barcelona-Spain; email:cmagg@cimne.upc.es;, ebalsa@cimne.upc.es
chiumenti@cimne.upc.es, cervera@cimne.upc.es, onate@cimne.upc.es

Keywords: food preservation, simulation, finite element method

ABSTRACT

Complexity of mathematical models plus the often complex geometry of foodstuffs, makes the sim-
ulation of food preservation processes a rather complicated task, often requiring the use of appropriate
numerical techniques. The development of a new numerical tool, which makes use of the Finite Element
Method (FEM), for the simulation of most comon food preservation techniques is presented here. This
new tool allows users from food companies: to select geometries (from ISO databases) or to ”draw” their
own geometries, to select food nutrients and microorganisms, to select processing conditions, to perform
simulations based on the FEM approach and to visualize results in tabular, figure or video format, all
included in a very convenient easy to use environment.

1 Introduction
One of the major concerns of food industry is offering high quality and safe products to the consumers.
Food spoilage is a gradual process occurring because of enzymatic or chemical reactions, improper tem-
perature control or microbial growth, which results in undesirable changes in the colour, flavour, odour
or texture. Food safety and quality control ensures that the desirable characteristics of food are retained
throughout the production, handling, processing, packaging, distribution and preparation stages.
It is well known that the use of adequate preservation techniques results in a longer shelf life of the
product. Food preservation through processing is an extremely broad area in food science and there are
several possible technologies, we will focus here on the thermal processing of foods.
The different nature of food products results in different responses to the preservation treatments.
Moreover different processing conditions will result in different final product characteristics. This has lead
to an increasing demand from the industry of tools which allow a better knowledge of the processes, the
design of better processes and the computation of optimal operation policies. The modern computer aided
process engineering tools can be used for these purposes (see for example [1]), allowing a considerable
reduction of cost and time if compared with the traditional experimental ”try and error” method.
This work presents a new user-friendly environment based on the use of the finite element approach
for the simulation of the most common preservation processes (sterilization, pasteurization and freezing).
This new tool offers a number of advantages allowing the simulation of nonlinear cases (e.g., thermo-
physical properties depending on temperature), anisotropic and/or non homogeneous food loads and
complex geometries. The numerical results have been experimentally validated and some examples are
also presented here.

2 Mathematical formulation
Most of the mathematical models for the thermal processing of food are based on the energy and/or mass
and/or momentum conservation laws plus the equations describing quality and safety related factors.
The resulting mathematical models consist of sets of Partial Differential Equations and/or Ordinary
Differential and Algebraic Equations (PDAEs) subject to adequate boundary and initial conditions:
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φt = −v(φ)∇φ + f (φ)∇(k(φ)∇φ) + q(φ, ∇φ, ξ) (1)

where φ is the distributed variable, ξ are the spatial variables, and v(φ), k(φ), correspond to the convective
and conductive terms and q(φ, ∇φ, ξ) represents a possible source (for example, a heat source due to the
presence of an electromagnetic field). Note that equation 1 can be used to describe almost any type of
heat treatment, including solid and liquid foods.
Considering temperature evolution inside a solid food load (1) becomes:

ρ(T )c(T )Tt = ∇(k(T )∇T ) (2)

Considering now the concentration of microorganisms and nutrients, and noting that the generation
term in this case corresponds to a pseudo-first order kinetic following the thermal death time model ([2]),
(1) becomes:

d ln Ci (t) ln 10 T (ξ, t) − Ti,ref

= −( ) exp( ) (3)
dt Di,ref zi,ref

where subscript i refers to microorganism spores or to nutrients and D and z are kinetic parameters.

3 Numerical solution approach

Because for realistic cases there are not analytical solutions for the set of equations (1) and (3 ), the use
of numerical methods is necessary. Several approaches have been proposed in last years for the numerical
solution of these sets of PDAEs (see reviews in Schiesser, 1994 and Oh, 1995). Most of them apply
standard spatial discretization techniques: the finite differences or finite elements approaches proceed
dividing the domain of interest into many smaller sub-domains, and applying an approximation method
within each sub-domain.
Although quite popular, the finite differences approach has a number of drawbacks. This has lead
to the use of the finite element in this work as it allows the efficient handling of nonlinear terms and
complex geometries.
The method of finite elements proceeds as follows (see details in [5] and [6]:

• Step 1: The area of interest is divided into a number of simple ”elements”. In this way, the complete
system may be complex and irregularly shaped, but the individual elements are easy to analyze. The
elements may be, in general, 1-D, 2-D (triangular or quadrilateral), or 3-D (tetrahedral, hexaedral,
etc.).
• Step 2: The dependent variables are approximated within each element using simple functions of
their values at the edges of the elements or at certain discrete nodes along its edges. This allows
the ease introduction of the boundary conditions.
• Step 3: All elements are assembled to generate an overall system description. Since the behavior of
each element has been described in terms of its behavior at its edges, and at certain discrete nodes
along its edges, the assembly of element matrices into an overall system matrix forces that nodes
shared by two elements must have the same dependent variable value when considered as part of
either element.

As a result a set of ordinary differential equations is obtained which must be solved using an adequate
initial value problem solver (IVP solver). These solvers usually proceed dividing the time domain into
a number of time steps and approximating the time dependent variables using simple polynomial func-
tions. This has lead to a large variety of approaches: Euler methods, Runge-Kutta methods, backward
differentiation (BDF) methods, etc... which are appropriate for the solution of different types of problems
(see [7] for further information).
The implementation considered in this work is based on the use of triangular and tetrahedral linear
elements (see [8] for further details) and it has been prepared to allow the simulation of phase changes
appearing in the freezing of food process. In this regard, the use of BDF approach was selected for
the resolution of the initial value problem to deal with the solution of stiff problems as the ones to be
considered in this work.
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4 User graphical interface

The numerical kernel was linked to GiD the pre- and post- processor which was adapted for the food
processes so as to simplify the introduction of geometry, food load properties and operating conditions
but also the post-processing and visualization of the results.
The overall tool offers the following advantages to the possible users:
Regarding problem statement:
• Possibility of introducing any geometry or selecting one from the database implemented. An image
acquisition system can be experimentally used to extract the food geometry, GiD can be used to
generate the geometry and mesh. These two possibilities are illustrated in Figure 1.

a) b)

Figure 1: a) Geometry of a salmon filet generated with GiD. b) Geometry of half asparagus obtained
through digitalization.

• Possibility of assigning time dependent food properties (k, c, ρ) but also possibility of selecting
several kinetic parameters for both nutrients and microorganisms (Tref , D, z).

• Possibility of studying non-homogeneous food products.

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• Any type of time dependent boundary conditions. Realistic processing temperature profiles can be
approximated by step-wise functions. Non-uniform initial conditions are also allowed.

Regarding visualization of results:

• All relevant variables (temperature, nutrient and microorganisms concentration, lethality at the
critical point, average lethality, average nutrient retention) can be viewed in tabular or graphical
formats.
• For space dependent variables contour plots and videos are automatically generated.

5 Case studies
With the purpose of validating the tool presented here several tests both numerical and experimental
were performed, next sections show some results.

5.1 Numerical validation

The objective was to compare results with the ones provided by a different numerical tool. With this aim
a realistic case regarding the thermal sterilization of caned tuna in olive oil was considered, as it is one
of the most important canned products worldwide. Table 5.1 summarizes the parameters and processing
conditions selected:

Diameter of cylindrical can (cm) 8.75

Height of cylindrical can (cm) 11.6
Thermal diffusivity (m2/s) 1.544 × 10−7
Microorganism Clostridium
Reference Temperature (o C) 121.11
Z Reference (o C) 10
D Reference (s) 240
Initial temperature (o C) 71.11
Heating temperature (o C) 122
Cooling temperature (o C) 20
Heating time (s) 5514
Cooling time (s) 7830

Table 1: Data for the numerical validation.

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Figures 2 a) and b), illustrate the results obtained for two relevant variables, the temperature and
the lethality at the critical point respectively. From the figures it is clear that results are almost indis-
tinguishable with maximum relative error being 0.5% for the temperature and 1.0% for the lethality at
the critical point.

a) b)
140 16

120 14 Fc (min), FEM

Temperature ( ºC)

12
100 Fc (min) , FD

Lethality (min)
10
80
8
60 Tc FEM
6
40 Tc FD
4
Processing Temperature
20
2
0 0
0 1200 2400 3600 4800 5814 6414 7014 7614 0 1200 2400 3600 4800 5814 6414 7014 7614
Time (s) Time (s)

Figure 2: Finite elements vs finite differences.

5.2 Experimental validation

In order to validate the capabilities of this tool to predict experimental results a number of experiments
were performed at the Food Engineering School, Universidad Técnica Federico Santa Marı́a in Chile. The
results obtained for the thermal sterilization of canned pre-cooked lentils are summarized here.
A number of experiments were performed for a standard heating process and temperatures at the
retort and at critical point were measured using ELLAB (Cu-CuNi) thermocouples connected to an
OM-220 portable data acquisition system.
In order to use the simulator in a reliable way the model must be calibrated. In this regard two
approaches can be used, one possibility consists of using experimental data and the solution of an opti-
mization problem so as to minimize differences between model prediction and measured data (parameter
estimation problem) other possibility is based on the use of composition based formulas, as the ones
proposed by Choi and Okos ([9]) which describe thermal properties of food products in terms of the
macro-molecule composition and temperature. Second approach was selected for this work, although it
is expected to implement an estimation parameter module in the tool in the near future as predictions
provided are usually more close to reality.
The results are illustrated in Figure 3 where measured temperature at the retort is represented in
black, measurements at the critical point for two different experiments are represented in blue and green
and numerical prediction is plotted in red.
Note that predictions are reasonable good considering the limitations of using composition based
formulas instead of a more rigorous approach based on the solution of a parameter estimation problem.

6 Conclusions and future work

A new tool based on the finite element approach has been presented in this work for the simulation of
the thermal processing of foods. This new tool offers a number of advantages over the ones being used
currently, such as the fact of being customized for the food sector, the possibility of considering any type
of geometry, non-linearity, anisotropy and non-homogeneous food products.
Future work includes the extension of this tool to new processing technologies and to the solution of
the parameter estimation as well as the design and dynamic optimization problems.
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140
T Exp A
120 T Exp B
T Predicted
100
T Retort
Temp ºC

80

60

40

20

0
0 1000 2000 3000 4000 5000 6000 7000 8000
Time (s)

Figure 3: Finite elements predictions vs experimental results.

ACKNOWLEDGEMENTS: This work was supported in part by the the Spanish Government (FP-
2001-1036). Authors are specially thankful to Prof. Simpson group at the Universidad Técnica Federico
Santa Marı́a in Chile for their support in the experimental validation.

References
[1] A. Datta. Enabling computer-aided food process engineering. In Computational Techniques in Food
Engineering, E. Balsa-Canto, J. Mora, J.R. Banga, E. Oñate Eds., pages 3–14, CIMNE, Barcelona.
2002.
[2] C. R. Stumbo. Thermobacteriology in Food Processing. Academic Press, New York, 1973.
[3] M. Oh. Modelling and Simulation of Combined Lumped and Distributed Processes. PhD thesis,
Imperial College, University of London, London, U.K., 1995.
[4] W. E. Schiesser. Computational Mathematics in Engineering and Applied Science: ODEs, DAEs and
PDEs. CRC Press, Inc., 1994.
[5] O.C. Zienkiewicz and R. L. Taylor. El Método de los Elementos Finitos. Vol.1. CIMNE, 1994.
[6] O.C. Zienkiewicz and R. L. Taylor. El Método de los Elementos Finitos. Vol.2. CIMNE, 1994.
[7] K. E. Brenan, S. L. Campbell, and L. R. Petzold. Numerical Solution of Initial-Value Problems in
Differential-Algebraic Equations. North-Holland: New York, 1989.
[8] M. Cervera, C. Agelet de Saracibar, and M. Chiumenti. Thermo-mechanical analysis of industrial
solidification processes. International Journal for Numerical Methods in Engineering, 46:1575–1591,
1999.
[9] Y. Choi and M.R. Okos. Efects of temperature and composition on the thermal properties of foods,
chapter Food Engineering and Process Applications. Elsevier, m. le maguer and p. jelen edition, 1986.
ICEF9 – 2004
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MODELLING OF TEXTURE AND COLOUR DURING VEGETABLES BLANCHING

A.Olaverri(1); T. Fernández(1); C. Arroqui(1) and P. Virseda(1)

(1) Technology, Control and Food Safety Group. Universidad Pública de Navarra. 31006 Pamplona.
SPAIN.
email: arantxa.olaverri@unavarra.es
Abstract
Changes in potatoes texture and green peas colour in a blanching process in hot water (85, 90, 95ºC)
during 10 min were studied. Texture was measured as the maximum compression force in a TA:XT2i
Texture Analyzer and colour as –a*/b* in a spectrophotometer Minolta 2500-d. Two models of first
order were obtained to describe texture and colour degradation.

Key words: blanching, potato, green peas, texture, colour, modelling

Introduction
Blanching is a thermal treatment at high temperature (75 -100ºC) applied during a short period of time
(from few seconds to several minutes), applied to raw vegetables before preservation processes as
sterilisation, freezing and dehydration. The main objective of this treatment applied before freezing
and dehydratation is the inactivation of enzymes responsible of the deterioration of the final product.
Nevertheless, a negative consequence of this treatment could be the obtaining of a product with an
inadequate quality (i.e. undesirable texture or colour) that can derivate in the product rejection by the
consumer.
In potatoes, texture is one of the most important sensory attribute (1). For practical purposes it is
important to develop simple methods of predicting the behaviour of tissue during certain thermal
treatments (2).
Many researchers have studied the kinetics of thermal softening of potatoes (3-10) and they found
different values of apparent rate constants and energy of activation.
On the other hand, colour is a very important characteristic of green vegetables and its proper control
or modification is needed. Thermal processes in green vegetables result in a colour change from the
natural green to what is described as an olive-brown colour. The colour change is attributed to the
conversion of the chlorophyll to pheophytin, through the substitution of magnesium by hydrogen.
Several researchers have studied the kinetics of colour losses in green peas (11, 12) obtaining
different values of reaction rate constants for each temperature and for the activation energy.
According to the importance of these quality attributes in the above mentioned vegetables and the
differences observed between the models founded in literature, it was considered interesting to
develop models to describe the softening of potatoes (cv. Monalisa) and colour losses in green peas
(cv. Utrillo), both very consumed in Spain, during a 10 min blanching at temperatures of 85, 90 and
95ºC.
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Materials and methods

Potatoes (Solanum tuberosum, cv. Monalisa) were stored at 5ºC and 85% RH until use. Cylindrical
samples of 22 mm height and 16 mm in diameter were prepared using a cork borer.
Green peas (Pisum sativum, cv. Utrillo) were stored at 0 - 5ºC and 85% RH until use.
Samples were blanched in hot distilled water at 85ºC, 90ºC and 95ºC in a temperature controlled
water bath. The samples were taken out of the water bath at intervals of 20 s from 0 to 600 s, cooled
in iced distilled water until ambient temperature and strained.
The breaking force of potatoes ( average of 15 samples for each treatment) was determined by
compression of individual cylinders by a TA-XT2i Texture Analyzer equipped with a cylindrical probe
(75mm diameter). Compression was stopped at strain level of 0,6 and texture was characterised by
the first peak on the force-deformation curve.
The processed green peas were subjected to colour measurements using a spectrophotometer
Minolta 2500-d. Twelve measurements at each time-temperature combination were taken in different
parts of the samples. For the colour study the CIE 1976 L*a*b* system was used. The parameter –
a*/b* was used as a degree of the greenness of the vegetables.
Potato softening and green peas colour losses during water blanching could be described as a first-
order kinetic model. (11, 13)
The dependence of the studied quality parameters on blanching time for each temperature are
described by the equation [1]:

Ln (Q) = Ln (Q0) – k·t [1]

Q is the quality parameter (texture, colour) at a determinate time, Q0 is the initial quality parameter
(texture, colour), k is the kinetical rate constant (min–1) and t is the blanching time (min).
The dependence of kinetical rate constants on blanching temperature is described by the Arrhenius
equation [2]:

Ln kt = Ln k0 – Ea/R·1/T [2]

where kt is the kinetical rate constant at t (min-1), k0 is the kinetical rate constant of unblanched
vegetables (min-1), Ea is the activation energy (KJ/mol), R is the gas constant (J/mol·K) and T is the
absolute temperature (K).
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Results and discussion

Figure 1 shows the evolution of maximum compression force (F) in potatoes during blanching at
different temperatures. The first order rate constant for each temperature are shown in Table 1.

5,5

5
LnF

4,5
Blanching at 85ºC
4 Blanching at 90ºC
Blanching at 95ºC
3,5
0 100 200 300 400 500 600 700
Time
Fig.1. Evolution of the maximum compression force during blanching of potatoes at 85, 90 and 95ºC,
where F is expressed in N and time in s.

Table 1. Values of first order rate constants (k) for softening of potatoes at 85, 90 and 95ºC
Temperature (ºC) First order rate R2
constant, k (min-1)
85 0,0008 0,7087
90 0,0023 0,9568
95 0,0028 0,9393

Figure 2 shows the evolution of –a*/b* parameter in green peas during blanching at temperatures
between 85, 90 and 95ºC. Kinetic constants for each temperature are shown in Table2.
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-0,4
Ln -a*/b*

-0,8

-1,2 Blanching at 85ºC

Blanching at 90ºC
Blanching at 95ºC
-1,6
0 100 200 300 400 500 600 700
Time (seconds)

Fig 2. Colour evolution during blanching of green peas at 85, 90 and 95ºC
.

Table 2. Values of first order rate constants (k) for degradation of colour in green peas at 85, 90 and
95ºC.
Temperature (ºC) First order rate R2
constant (k) (min-1)
85 0,0005 0,6416
90 0,0008 0,8408
95 0,0011 0,7549

The activation energy (Ea) of the thermally induced quality degradation in potatoes and green peas
were calculated based on the Arrhenius relationship described by Eq. [2]. The Ea for softening of
potatoes is 137,57 KJ/mol and for the green peas colour losses is 86,39 KJ/mol.
Alvarez and Canet (10) reported an activation energy of 104,40 KJ/mol for thermal treatment of potato
cv. Monalisa at the temperature range of 50-100ºC and longer periods of time. Verlinden et al. (14)
reported an activation energy of 102 KJ/mol for potato cv. Bintje at temperature range of 60-100ºC and
also longer periods of time. Those activation energies are smaller than the activation energy obtained
in this study..
The Ea obtained in this study for the degradation of colour in green peas, 86,39 KJ/mol, is also higher
than those founded in bibliography. Hayakawa and Timbers (11) and Rao et al. (12) worked with
frozen green peas applying a higher range of temperatures (79,4-148,8ºC and 98.8-126.6º C,
respectively) during longer periods of time. The Ea reported by these authors were 75,68 and 73,15
KJ/mol respectively.
The difference between the values of activation energy could be the consequence of the different
temperature range applied as well as of the different cultivars used.
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Conclusions
Thermal softening of potatoes cv. Monalisa at temperatures between 85, 90 and 95ºC followed a first
order reaction kinetic with an activation energy of 137,57 KJ/mol. The reaction rate constants for
texture softening at 85ºC, 90ºC and 95ºC were 0,0008, 0,0023 and 0,0028 min-1, respectively.
Colour evolution in green peas cv. Utrillo during blanching at 85, 90 and 95ºC also followed a first
order reaction kinetics. The activation energy was 86,39 KJ/mol and the reaction rate constants were
0,0005, 0,0008 and 0,0011 min-1 for the blanching at 85ºC, 90ºC and 95ºC respectively.
Therefore, the evolution of quality parameters, i.e. texture and colour, in vegetables, i.e. potatoes,
green peas, during a blanching process have to be studied for each cultivar and process conditions.

Acknowledgements
We acknowledge the financial support of the Navarra Government (research project 1010, 2001-2002)
and for the scholarship of formation and specialisation granted to A. Olaverri.

References
1. Van Marle, J.T., Van de Vuurst de Vries, R., Wilkinson, E.C., Yuksel, D. Sensory evaluation of the
texture os steam-cooked table potatoes. Potato Research, 40, 79-91, 1997.
2. Harada,T., Tirtohusodo, H., Paulus, K. Influence of the composition of potatoes on their kinetics.
Journal of Food Science, 50, 463-468, 1985.
3. Kozempel, M.F. Modelling the kinetics of cooking and precooking potatoes. Journal of Food
Science, 53, 3, 1988.
4. Rahardjo, B., Sastry, S.K. Kinetics of softening of potato tissue during thermal treatment.
Transactions of the Institution of Chemical, 71, C, 1993.
5. Mittal, G.S. Thermal softening of potatoes and carrots. Lebensmittel-Wissenschaft und-
Technologie., 27, 253-258, 1994.
6. Rizvi, A.F., Tong, C.H. Fractional conversion for determining texture degradation kinetics of
vegetables. Journal of Food Science, 62, 1, 1997.
7. Sebök, A., Bontovics, P., Bleszkán, M. A kinetical approach of texture changes of vegetables during
blanching. Acta Alimentaria, 28, 3, 279-290, 1999.
8. Stoneham, T.R., Lund, D.B., Tong, C.H. The use of fractional conversion technique to investigate
the effects of testing parameters on texture degradation kinetics. Journal of Food Science, 65, 6, 968-
973, 2000.
9. Blahovec, J., Esmir, A.A.S. Precise study of cooked potatoes texture. Journal of texture studies, 32,
165-184, 2001.
10. Alvarez, M.D., Canet, W. A comparison of various rheological properties for modelling the kinetics
of thermal softening of potato tissue (c.v. Monalisa) by water cooking and pressure steaming.
International Journal of Food Science and Technology, 37, 41-55, 2002.
11. Hayakawa, K.E., Timbres, G.E., Influence of heat treatment on the quality of vegetables: changes
in visual green colour. Journal of Food Science, 42,3, 1977.
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12. Rao, M.A., Lee, C.Y., Katz, J., Cooley, H.J. A Kinetic Study of the Loss of Vitamin C, Color, and
Firmness During Thermal Processing of Canned Peas. Journal of Food Science, 46, 636, 1981.
13. Huang, Y.T., Bourne, M.C. Research Note: Kinetics of thermal softening of vegetables. Journal of
Texture Studies, 14, 1-9, 1983.
14. Verlinden, B.E.; Nicolaï, J.; De Baerdemaeker, J. The starch gelatinization in potatoes during
cooking in relation to the modelling of texture kinetics, Journal of Food Engineering, 24,165-179, 1995.
ICEF9-2004 International Conference Engineering and Food

A product design system based on kansei engineering for functional orange-juice based drinks

Pagidas N. (1) and Oliveira J.C.* (2)

(1) Dept. of Process Engineering, University College Cork, Ireland. n.pagidas@mars.ucc.ie

(2) Dept. of Process Engineering, University College Cork, Ireland. j.oliveira@ucc.ie
* Author to whom correspondence should be addressed

ABSTRACT

A basic kansei engineering method was applied to establish the influence of design factors of a soft drink
based on orange juice in consumer perception, expressed in terms of feelings and emotions associated
with the drinking experience. Prototypes combined different options regarding 7 design factors (base,
flavour, stimulants, information, carbonation, sweetener, colour). The kansei adjectives were grouped by
PCA in 7 main components, which were then analysed with a multilinear model using dummy variables.

Keywords: kansei engineering, consumer perception, flavours.

1. Introduction

Kansei engineering (also called “emotional engineering” in the US) is a methodology emerging
from Japan with great promise for product design engineering systems (1). Its application in food product
development is still very incipient (2). Kansei engineering of products such as cars, furniture and garments
has led to various and sophisticated developments which enable the development of products with
combinations of design factors that correspond better to satisfaction and emotional design intent. The
ultimate goal is to go “beyond the voice” of the consumer, searching for the emotional and physical effects
that underpin satisfaction. Kansei is a Japanese word (pronounced like “can-say”) that can be translated
by “ill-defined feelings or emotions”. Product design with kansei therefore implies to design emotional
satisfaction and excitement.
The most basic kansei engineering method, as developed originally by Prof. Mitsuo Nagamachi
(1) can be considered with two major parts: (i) one is the interface with the consumers, and how to try to
extract from them the underlying emotions and sensations without asking rational questions; (ii) the
second is the handling of the data in a functional model that relates the product descriptors extracted in (i)
with the design factors. The second part is similar to conjoint analysis using multilinear models (which is a
limitation of this basic technique, as interactive effects are not considered), while the first is a very
interesting concept that deserves greater consideration. Koster (3) has recently pointed out the fallacies
that consumer research most often falls into considering the usual assumptions at the light of modern
knowledge from neurophysiology and behavioural psychology. As stressed by Oliveira (4), one of the main
implications is that asking rational questions and expecting rational answers from consumers regarding
prototype evaluation may be misleading, and is unlikely to uncover the real “emotional driving force”
behind the actual buying decisions.
Nagamachi (1) based his basic kansei method in a typical social sciences approach. First, a
questionnaire is prepared with a large number of pairs of adjectives (the kansei database). This can be
done from focus groups, trade journals, etc., and thus build a comprehensive collection of words that
consumers use to express feelings and sensations regarding the product. The adjectives can be paired as
antonyms (e.g. nice<->unpleasant) or as the adjective and its negation (e.g. nice<-> not nice). It is
intended that the questionnaire will have a large number of pairs (e.g. 30 to 60) to avoid that respondents
spend too much time thinking about the meaning of a particular word. The idea is to try to have the first,
instinctive, reaction to the product/adjective and not a rational analysis of how an adjective fits a product.
Consumers are instructed to treat words loosely, not to worry about meanings, and just express what they
feel first hand. The questionnaire consists of a semantic differential scale between the two extremes of a
pair of adjectives (5 to 7 are the most common gradings).
The main feelings/emotions are extracted as major product descriptors from this data by applying
a Principal Component Analysis (PCA). Looking at the adjectives with higher loadings in a PC that were
thus grouped uncovers a meaning, a type of feeling or idea that in general was consistently being
expressed via those words. The response can then be considered wither in terms of these PC’s, or of the
ICEF9-2004 International Conference Engineering and Food

key adjectives (those with higher loadings in the main components). Adjectives that spread over several
components without being particularly relevant in any may be disregarded, as this may be due to different
people using the word in different ways (linked to different feelings). The application of neural networks to
deal with this step has also been discussed (5).
The PC’s, and/or key adjectives, thus identified are then related to the design factors and their
options by a multilinear model. The Japanese literature refers to the Quantitative Method Type I
nomenclature (6), which unfortunately is not available in English. In previous research (unpublished), the
authors have obtained best results to mimic the Japanese method by using a multilinear model with
dummy variables. Each variable corresponds to a design option, and can only have the value of 1 (if the
prototype has that particular design feature), or zero (if it does not). The general model is therefore:

n mi
Re sponse = ao + ∑ ∑ aij Xij (1)
i=1j=1

where ao is the average of all responses, n is the number of design factors that are changed in the
various prototypes, mi is the number of options that the design factor i may have, i designates the design
factor, j the design option, Xij are the dummy variables and aij the coefficients of the model.
The full model is evaluated first to have an idea of how accurate we can expect the analysis to be,
looking at the coefficient of correlation, which in a sense expresses the possible quality of the conclusions.
Then, the importance of each design factor is assessed by calculating its partial correlation coefficient
(PCC), and the coefficients of the partial model indicate the effect of each of the design options. This is
visualised neatly in a kansei table, with the coefficients represented as bars (similar to a Pareto chart).
Kansei engineering has evolved immensely in Japan in the last decade, in particular, with the
incorporation of biomimetics. The use of physical sensors and brain-activity sensors (e.g. EEG, MRI, PET)
can go even better beyond the voice of the consumer than a questionnaire. The International Journal of
Kansei Engineering (published by the Kansei Engineering Society of Japan) is a good source of literature
in this area.
The objective of this work was to apply a basic kansei engineering approach to the design of
functional soft drinks. Orange juice was selected as one of the standard design basis in itself, as it has an
image of healthy and refreshing drink on its own merit.

2. Materials and Methods

A kansei database (collection of adjectives used to express feelings and sensations about soft
drinks) was built from two sources: (i) 35 young adults (aged 18-22) were shown slides of various
packages of drinks and asked to write down what words and feelings came to mind about them (circa 50%
were novel drinks from foreign markets, unknown to the individuals); (ii) a collection of transcripts (3) of
focus groups that had been assembled to discuss drinks was scanned and the most frequently cited
adjectives were collected. A set of 45 pairs was then selected for the kansei questionnaire.
Product prototypes were produced by mixing the relevant combination of design options pertaining
to 7 factors: base of the drink (either orange juice or water), flavouring, stimulant ingredients (a mix of
caffeine, 320 mg/L, taurine, 2,500 mg/L and ginseng, 320 mg/L), information (what the participants were
told the drink was), carbonation, sweetener and colour. The set of design factors and the options of each
are detailed in table 1. Twenty prototypes were produced, selecting the combination of design options in
accordance with blocking and specific comparisons that were inte3nded to be assessed subsequently.
Details are given in table 1. It is noted that information was treated as an independent design factor, which
means that in some cases consumers were testing samples that were not what they believed them to be.
A group of 48 young adults (aged 18-22, circa 2/3 males) was assembled for testing. Each
individual tasted 5 samples in 35 ml clear plastic cups and was requested to fill the kansei questionnaire
after consumption.
ICEF9-2004 International Conference Engineering and Food

Table 1: Product prototypes, design factors and options used in the study
base flavour stimulant information fizzyness sweetener colour
Prototype No.

orange drink
energy drink
orange juice

taurine,gins.

natural juice
orange peel

carbonated
forest fruits

aspartame
mandarin

flavoured

yellowish
caffeine,

fructose
sucrose

orange
peach
water

water
none

none

none

none
still

red
oil
1 9 9 9 9 9 9 9
2 9 9 9 9 9 9 9 9
3 9 9 9 9 9 9 9
4 9 9 9 9 9 9 9
5 9 9 9 9 9 9 9
6 9 9 9 9 9 9 9
7 9 9 9 9 9 9 9
8 9 9 9 9 9 9 9
9 9 9 9 9 9 9 9
10 9 9 9 9 9 9 9
11 9 9 9 9 9 9 9
12 9 9 9 9 9 9 9
13 9 9 9 9 9 9 9
14 9 9 9 9 9 9 9
15 9 9 9 9 9 9 9
16 9 9 9 9 9 9 9
17 9 9 9 9 9 9 9
18 9 9 9 9 9 9 9
19 9 9 9 9 9 9 9
20 9 9 9 9 9 9 9

3. Results and Discussion

Principal Component Analysis (extraction of the product descriptors)

The PCA was performed using the Varimax rotation method with Kaiser normalisation using the
Statistica software (release 5.1, 97 edition, Statsoft, Tulsa, Oklahoma, USA). Seven principal components
(PC) would explain 81% of the variance. This is a larger number of PC’s than usual in similar kansei
studies. The pairs of adjectives that had high loadings in several PC’s (13) were eliminated and a second
PCA was performed using only the remaining 32 pairs. Seven PC’s explained 80% of the variance.
The PC’s combined various adjectives in a given direction of the rating, from –2 to +2. The groups
are shown in table 2. From the combination, the following interpretation emerges: PC1 expresses a feeling
of interest and curiosity which is sparkled by the product or not, with a low rating meaning “traditional and
boring” and a high rating “novel, interesting and exciting”; PC2 expresses a sensation of “refreshment,
renewal and cleanliness” on the high rating as opposed to a sensation of “tiredness and dirtiness” on the
low rating. It is interesting to note that the adjective “sweet” comes in this PC, together with “energetic”
while “bitter” comes together with toxicity. This may show an inherent correlation between sweetness and
energy and between bitterness and toxicity; PC3 expresses a feeling of pureness and health on the high
rating, versus artificiality and misleading on the low rating; PC4 expresses a sensation of comfort
associated to appealing taste with high ratings versus a sensation of impersonality and tastelesness with
low ratings; PC5 opposes a sense of sophistication, but possible danger on the high end of the scale to a
sense of simplicity but safe on the low end; PC6 is similar to PC1, with a greater strength of emotion:
“stylish” and “exciting” on the high ratings to “plain” and “pathetic” on the low ratings. Finally, PC7 is mostly
the rather trivial sensation of fizziness which is obviously correlated to the carbonated samples, but
ICEF9-2004 International Conference Engineering and Food

interestingly was combined with “syrupy”, suggesting a possible greater perception of sweetness from
carbonation, as opposed to a watery feeling in the still samples.

Table 2 – PCA grouping of the kansei adjectives

(those shown in each PC are the ones with loading factors above 0.55)
+2 PC1 -2 +2 PC2 -2 +2 PC3 -2
new dated
original typical
sweet bitter
different normal
refreshing tiring pure fake
smooth rough
simple complicated beneficial useless
interesting <-> ordinary
clear <-> confusing natural <-> artificial
unusual standard
detoxifying toxic healthy unhealthy
alternative usual
energetic passive
cool unfashionable
fresh stale

+2 PC4 -2 +2 PC5 -2 +2 PC6 -2

warm cold
intense mild
balanced unbalanced stylish plain
fruity <-> watery
complex <-> basic
exciting <-> pathetic
dangerous safe
tasty tasteless
+2 PC7 -2
fizzy still
syrupy <-> watery

Multilinear design model

The coefficient of correlation of the global model for the most relevant first 6 PC, and the partial
coefficients of correlation (PCC) in each case, are shown in table 3. It can be seen that the multilinear
model is quite good (high global coefficient of correlation), except for PC1 where it is just fair. The feeling
of novelty, interest and excitement (PC1) is mostly influence by flavour, carbonation and colour and it does
not really matter whether the base is orange juice or water. The feeling of renewal and cleanliness (PC2)
is mostly affected by the base, flavour, and to a lesser extent information and sweetener. The feeling of
pureness and healthiness (PC3) and that of comfort and appealing taste (PC4) are influence mostly by the
same design factors as PC2. The feeling of simplicity but safe is primarily influenced by carbonation,
sweetener and colour, and the feeling of style and excitement comes mostly from base, flavour and colour.
It is worthy to note that in relation to the influence of the factor stimulants, the “energising” could
not be felt with this evaluation, which focuses mostly on the organoleptic sensations of tasting. Still, due to
their influence on the flavour profile and on expectations, this factor showed some influence on PC2 and 3
specially.

Table 3 – Global (GCC) and partial (PCC) coefficients of correlations of the multilinear model The most
relevant design factors for each PC (higher PCC) are shown in bold
PCC (design factors)
PC GCC Base Flavour Stimulant Information Carbonation Sweetener Colour
1 0.89 0.07 0.61 0.12 0.17 0.45 0.31 0.39
2 0.97 0.86 0.88 0.52 0.66 0.55 0.68 0.65
3 0.99 0.89 0.91 0.53 0.76 0.55 0.79 0.50
4 0.97 0.88 0.90 0.33 0.68 0.34 0.69 0.68
5 0.99 0.00 0.17 0.35 0.30 0.56 0.44 0.47
6 0.93 0.59 0.62 0.03 0.37 0.27 0.46 0.61

The kansei design tables summarise all analysis and allow to select the best option for a given intended
result. These are too long for the space available in the paper, and so an example is shown. Table 4 is the
kansei design table for PC2. A simple modification is introduced: the thickness of the bars are proportional
to the PCC. This allows for a visualisation of which factors are more important, at the same time as which
options go towards a particular feeling.
ICEF9-2004 International Conference Engineering and Food

Table 4 – Kansei design table for PC2 (sense of renewal and cleanliness)

factor tiredness and dirtiness PC2 (r = 0.97) renewal, cleanliness PCC

orange juice
base .892
water

forest fruits

peach

flavour mandarin .913

orange peel oil

none

none
stimulant .527
mix

flavoured water

energy drink
informa-
.762
tion natural juice

orange drink

carbona- still
.547
tion fizzy

none

sweete- sucrose
.789
ner fructose

aspartame

none

red
colour .504
orange

yellowish

The table suggests that if one intended to produce a drink that would provide a sense of renewal
and cleanliness to the consumer, the best combination of design options would be: a pure orange juice
with no added flavour nor sweetener nor colouring with a label claiming to be natural fruit juice but with
added stimulants (caffeine, taurine and ginseng). Obviously, to achieve both goals of being natural and
having the stimulants would imply using natural sources of these ingredients, such as guaraná and herbal
teas and extracts. The drink should be just a mixture of natural products that provide a stimulation but
have a flavour profile as close as possible to a fresh orange juice.
A similar approach can be used for the other PC’s
The overall product design therefore depends on which emotions or feelings the product intends to
satisfy. The optimum combination depends on which emotional goal the consumer wishes to target. A
comprehensive product design system would be able to handle more than one specification (for instance,
a product that is interesting and novel (high PC1), cleanses and renewals (high PC2) and is simple but
safe (low PC5). This would require the minimisation of an objective function composed of the various
requirements, such as suggested by Matsubara and Nagamachi and co-workers (7) for hybrid kansei
systems. More sophisticated approaches include the dual simplex method and a genetic algorithm (8).
ICEF9-2004 International Conference Engineering and Food

4. Conclusions

Following a kansei engineering questionnaire it was found that the main emotional descriptors of
soft drinks can be grouped in 7 principal components: (i) a sense of novelty and interest, (ii) a feeling of
renewal and cleanliness, (iii) a sensation of naturality and health, (iv) a feeling of comfort and tastiness, (v)
a sensation of sophistication yet of possible danger, (vi) sense of stylishness and excitement and (vii) the
perception of fizziness.
The design factors that generally had the greatest influence were flavour (dominant in 5 of the 6
main PC’s), the base of the drink (dominant in 4 of the 6) and colour (relevant in 5 out of 6, though
dominant in only 1). What is important however depends on which emotion is targeted: for instance, for a
sense of novelty and interest (PC1) and sophistication versus simplicity (PC5) whether the drink was
made of orange juice or water with added ingredients made no difference at all. In spite of the evaluation
not considering after-drink effects, only the immediate sensory perception, the addition of stimulants (a mix
of caffeine, taurine and ginseng) had a relevant effect in 2 of the emotions and a possible small role in 2
others.
While the kansei table drawn for the various PC’s, or for key pairs of adjectives, are valuable tools
for a speedy analysis of optimum design combinations for specific intents, it will be necessary to continue
with the development of kansei techniques to more sophisticated methods. The necessity of assuming
multilinearity is the main limitation of the technique shown here and better functional models, such as
neural networks, need to be developed. Seeking other forms of interactions with the consumer, from the
use of pictures instead of kansei words to express emotions, to physiological and neurological
measurements, also shows enormous potential to perfect product design engineering systems for foods.

References
1. Nagamachi, M. (1995). Kansei engineering: a new ergonomic consumer-oriented technology for product development.
International Journal of Industrial Ergonomics, 15 (1): 3-12
2. Oliveira, J. (2003). Role of Kansei Engineering in Product Design Engineering. Int. Journal of Kansei Engineering, In Press
3. Koster, E.P. (2002). The psychology of food choice: some often encountered fallacies. Food Quality and Preference, 14: 359-373
4. Oliveira, J. (2003). Advances in Consumer-oriented Product Design Engineering of Foods. Food Science and Technology
Research, In Press
5. Ishihara, S., Ishihara, K., Nagamachi, M. and Matsubara, Y. (1995). An automatic builder for a Kansei engineering expert system
using self-organising neural networks. International Journal of Industrial Ergonomics, 15 (1): 13-24
6 Jindo, T., Hirasago, K. and Nagamachi, M. (1995). Development of a design support system for office chairs using 3-D graphics.
International Journal of Industrial Ergonomics, 15: 49-62
7. Matsubara, Y. and Nagamachi, M. (1997). Hybrid kansei engineering system and design support. International Journal of
Industrial Ergonomics. 19:81-92
rd
8. Nishino, T., Nagamachi, M., Tsuchyia, T., Matsubara, Y. and Cooper, D. (1994). In Proceedings of the 3 Pan-Pacific Conference
on Occupational Ergonomics, pp. 162-166
ICEF9-2003 International Conference Engineering and Food

A product design model for orange juice sensory quality as a function of sweetness, bitterness,
carbonation and orange flavour.

Pagidas N. (1), Oliveira J.C.* (2) and Jova L. (3)

(1) Dept. of Process Engineering, University College Cork, Ireland. n.pagidas@mars.ucc.ie

(2) Dept. of Process Engineering, University College Cork, Ireland. j.oliveira@ucc.ie
(3) Dept. of Process Engineering, University College Cork, Ireland. l.jova@mars.ucc.ie
* Author to whom correspondence should be addressed

ABSTRACT

A full factorial design was applied to study the interactive effects between carbonation and sweetness in
orange juice drinks. A second factorial design was applied to study the influence of bitterness and orange
flavour. Regression analysis was conducted and interaction tables were drawn in order to develop models
that relate consumer perception with product design elements.

Keywords: Product design engineering, kansei engineering, consumer perception, orange juice.

1. Introduction

The development of new food products is an essential requirement for keeping added value in a
strongly competitive environment where margins are progressively squeezed in undifferentiated products.
A new food product must have a new feature which sustains its higher value, which must be sufficient to
recover the development costs in addition to delivering the greater margin sought. This is a difficult
proposition in the food industry environment due to a variety of factors, but it remains a basic necessity of
food companies. New food product launching (in absolute numbers) has peaked in the late 90’s and
abated somewhat in the last couple of years, but is still very strong. Success rates are however dismaying,
and it is generally considered that only about 1 in 10 new products remains on the shelves after 1 year.
It is evident that continuing with strong product development activity depends on minimising
development costs and maximising the product features that underpin success. The ideal approach to
achieve these goals is therefore a consumer-oriented product design engineering system (1). In essence,
products should not be seen as static entities, but rather companies should engage in what IBM
Consulting Services terms “product lifecycle management”, where the design function, accessible to
customers, is part of the cycle. This allows customers to engage in production on demand more closely,
specifying design changes and options that the manufacturer delivers as the clients need.
Product design engineering of food products requires the development of functional models that
relate the product design factors and options with consumer perception. Kansei engineering (2) is a most
promising approach that has been emerging in Japan in the last decade, combining both a systematic
(systems engineering) nature and the incorporation of the cognitive (psychological) dimension of human
perception and feelings. The most basic kansei engineering methodology would be comparable to conjoint
analysis, with the difference that instead of asking rational answers to rational questions from consumers,
the method will attempt to extract product descriptors from stated feelings and emotions (kansei,
pronounced as “can-say”, is a Japanese word meaning ill-defined feelings or emotions). In the same way
as in conjoint analysis, the simplest functional models are multilinear expressions, and this is a significant
limitation as some factors can show strong interaction (that is, the effect of a given design option may
depend on the value of another design option).
In order to develop an effective design system, interactions need to be studied in detail to
establish the most suitable models. In this work, we are particularly interested in beverages, and primarily
orange juice based products.
The sensory profile of orange juice is like a benchmark for healthy drinks, offering a balance
between sweetness and bitterness which consumers have learned to appreciate over extensive use. It is
known that humans have an inborn preference for sweetness (3). The preference of sweet products
persists from birth till old age (4) even though the degree of likeness of sweetness varies with age (5).
Adults enjoy the sense of sweetness in their food and drinks, however they are concerned about other
healthy or nutritional factors related with sugar. Orange-based beverages may contain different types of
ICEF9-2003 International Conference Engineering and Food

sweeteners, with sucrose generally regarded as more or less natural but bad for teeth decay and calories,
TM
and ingredients such as Aspartame being regarded as artificial but suitable for dieting.
Conceptually, the perception of sweetness could be affected by carbonation. The tiny carbon
dioxide bubbles released in the mouth give a sensation of freshness to those that like it (not all consumers
do) and interfere with the layer of liquid adjacent to the tongue and hence to flavour perception. However,
literature data is conflicting. It has been reported that carbon dioxide can suppress the perception of
sweetness (6) and also that carbonation had no effect on sucrose sweetness perception (7).
Previous (yet unpublished) consumer research had shown that consumers may rate more bitter
drinks better when they consider the bitterness to be due to the use of natural oranges. The contextual
element of what a fresh orange juice is may actually suggest that bitterness may be a positive factor to
some extent, amenable to optimisation.
The objective of this work was to analyse the interactive effect between carbonation and
sweetness, as well as the role of (orange) flavour and bitterness in orange drinks, as a basis for further
development of a design engineering system for orange-based drinks.

2. Materials and Methods

Twenty-one participants (young adults, 2/3 males, aged 18-20, strong users of soft drinks and
juices) received three sets of different samples and were asked to evaluate them in a five-point scale
(coded -2, -1, 0, 1 and 2), in terms of fizziness, sweetness, taste, flavour and overall quality. They were
also asked which one they considered to be more natural, which they preferred, and finally to indicate how
likely they were to purchase any of these products.
All samples were made from freshly squeezed orange juice, coded, and served in clear 35 ml
cups. The participants only knew they were drinking orange juice drinks, and were not told of the actual
ingredients. Carbonation was performed in a small carbonating machine (Soda Stream, Soda Club Ltd.,
carbon dioxide E290), which produces tiny bubbles (similar to those of naturally sparkling mineral waters,
TM
such as Perrier ). Previous analysis showed that this type of fizziness is more acceptable than the large
bubbles of typical soft drinks for orange juice drinkers. All participants evaluated all drinks. The division of
samples in 3 groups, with plain orange juice as control, intended to minimise potential inconsistency
problems with continuous testing of too many samples. Participants cleaned their palate between sets of
samples with water and crackers.
In the first set of samples (testing sweetness for sucrose and aspartame without carbonation
interference), the participants received one sample with plain orange juice, one with added artificial
TM
sweetener (0.15 g/L aspartame ) and one with normal sugar (15 g/L sucrose, analytical quality). These
amounts were selected from the composition of commercially available drinks.
In the second set (testing for bitterness and orange flavour) the participants received one sample
with plain orange juice, one with added quinine (0.5 g/L, increases bitterness with no other flavour
component) and one with added orange peel oil (0.2 ml/L, increases orange flavour and also bitterness).
These amounts were selected for giving similar bitterness, as judged sensorially by the researchers, from
the orange peel oil addition being enough to bring out an orange flavour, but not overwhelmingly.
In the third set (testing for sweetness in the presence of carbonation) the participants received one
sample of plain orange juice, one of carbonated orange juice, one of carbonated juice with 15 g/L sucrose
TM
and one of carbonated juice with 0.5 g/L of aspartame .

3. Results and Discussion

Testing for statistically significant differences

Tables 1 and 2 show the Tukey HSD test results (using the Statistical Software for the Statistical
Sciences - SPSS) for the first set of data (testing for sweetness with no carbonation). It can be seen that
the panel considered that the artificial sweetener provided the greatest sweetness response, while adding
sugar increased the sweetness perception only slightly (though also part of the same group as the
aspartame sample). However, the panel was equally willing to buy the juice with added sugar or the plain
juice, but not the one with aspartame (negative values in table 3 indicate a negative response). This is
likely due to the aspartame flavour affecting the perception of quality of natural orange juice, and also
indicates that sweetness is not necessarily a plus regarding orange juice products.
ICEF9-2003 International Conference Engineering and Food

a a
Table 1. Tukey HSD test for sweetness. Table 2. Tukey HSD test for willingness to buy.
Subset for a = .05 Subset for a = .05
SAMPLES N 1 2 SAMPLES N 1 2
Plain orange juice 21 .4762 Juice & Aspartame 21 -.4286
Juice & Sugar 21 .6667 .6667 Plain orange juice 21 0.2857
Juice & Aspartame 21 1.2857 Juice & Sugar 21 0.3810
Sig. .779 .81 Sig. 1.000 0.888

In the second set (test for bitterness), which product was considered more natural and which
shows the greater overall quality was also investigated (in addition to sweetness and willingness to buy).
Tables 3 to 6 show the results.
The samples with quinine and orange peel oil were both considered bitter (negative values), but
with no statistically significant differences between them (table 3). The juice with added orange peel oil
was the most highly rated regarding “being natural”, although not statistically different from plain juice
(table 5). The plain juice and the orange peel oil were also on the same group regarding overall quality
(table 4), with the sample with added quinine rated negatively. This shows that although the quinine and
orange peel oil in the amounts used were considered roughly equal in terms of bitterness, the improved
orange flavour from the oil made the product acceptable in terms of quality, and like a natural orange juice.
That was however insufficient to improve the willingness to buy rating (table 6), where only the plain juice
fared well. It is interesting to note from tables 2 and 6 that the rating for “willingness to buy” of plain orange
juice was higher when the samples being compared against it were bitter rather than sweet.
a a
Table 3. Tukey HSD test for sweetness. Table 4. Tukey HSD test for overall quality.
Subset for a = .05 Subset for a = .05
SAMPLES N 1 2 SAMPLES N 1 2
Juice & Quinine 21 -.9524 Juice & Quinine 21 -.2381
Juice & peel oil 21 -.0476 Juice & peel oil 21 .3810
Plain orange juice 21 .9048 Plain orange juice 21 .6667
Sig. .051 1.000 Sig. 1.000 .525
a a
Table 5. Tukey HSD test for more natural. Table 6. Tukey HSD test for willingness to buy.
Subset for a = .05 Subset for a = .05
SAMPLES N 1 2 SAMPLES 1 2
Juice & Quinine 21 0.0000 Juice & Quinine 21 -.762
Plain orange juice 21 .3810 Juice & peel oil 21 -.952
Juice & peel oil 21 .6190 Pure orange juice 21 .4286
Sig. 1.000 .148 Sig. 1.000 1.000 0.888

Regarding the results of the third set, table 8 shows that sweetness does not affect the sensation
of fizziness, which is a trivial result. Table 8 shows that carbonation did not affect the sweetness
perception, which agrees with reference (7) instead of (6). However, it might be worthwhile to analyse
whether this result may depend on the type of carbonation (8), or whether large bubbles might give a
different result. Table 9 shows that carbonation clearly diminishes the perception of overall quality, for
which sweetness is unable to compensate, hence it is no surprise that regarding overall preference the
panel preferred the plain orange juice over any of the carbonated beverages.
a a
Table 7. Tukey HSD test for fizziness. Table 8. Tukey HSD test for sweetness.
Subset for a = Subset for
.05 a = .05
SAMPLES N 1 2 SAMPLES N 1
Plain orange juice 21 -.7143 Carbonated orange juice 21 .3810
Carbonated & sugar 21 .8571 Carbonated & sugar 21 .5238
Carbonated orange juice 21 1.000 Plain orange juice 21 .5714
Carbonated & aspartame 21 1.000 Carbonated & aspartame 21 .9048
Sig. 1.000 .976 Sig. .269
ICEF9-2003 International Conference Engineering and Food

a a
Table 9. Tukey HSD test for overall quality. Table 10. Tukey HSD test for preference.
Subset for a = Subset for a
.05 = .05
SAMPLES N 1 2 SAMPLES N 1 2
Carbonated orange juice 21 -.3810 Carbonated & sugar 21 .0952
Carbonated & sugar 21 -.3333 Carbonated & aspartame 21 .0952
Carbonated & aspartame 21 -.1905 Carbonated orange juice 21 .1429
Plain orange juice 21 .7619 Plain orange juice 21 .6667
Sig. .909 1.000 Sig. .975 1.000

Linear regression analysis

Following a basic kansei engineering approach (9), the responses were analysed in terms of the
product design factors and their options using a multilinear model with dummy variables. The overall
model is:
Re sponse = a o + a11X11 + a12 X12 + a13 X1 + a 21X 21 + a 22 X 22 (1)
where ao is the average of all responses, X11=1 when the formulation is “plain juice” (and is
otherwise equal to zero), X12=1 when sucrose was added (and is otherwise =0), X13=1 when aspartame
was added (and is otherwise =0), X21=1 when the drink was not carbonated (and is otherwise =0), X22=1
when the drink was carbonated (and is otherwise =0). The coefficients aij thus quantify the relevance of a
particular design option. The relative importance of each design factor is quantified by the partial
correlation coefficient (PCC) of the model truncated of the terms of equation 1 that relate to the other
factor. The model coefficients of the partial models are shown as horizontal bars in tables 11 to 14: the
longer the bar, the greater the importance of that option.
Table 11 states the trivial result that fizziness is influenced primarily by carbonation (very high
PCC). Table 12 states that sweetness is strongly influenced by added sweeteners and very little by
carbonation (low PCC), as discussed earlier, and also quantifies that aspartame gave a much stronger
sweetness sensation than sugar (in the amounts used). Tables 14 and 15 give very interesting results:
that taste and flavour were much more strongly influenced by carbonation than by sweeteners. Choosing
the design option “still” gave positive ratings to taste and flavour, while the option “carbonated” negatively
affected both. To the slight extent that sweetness affects the results (low PCC), adding sucrose gave
better taste and flavour ratings, while aspartame played a negative (though slight) role, specially in flavour.

Table 11. Regression analysis for fizziness.

Multiple Correlation Coefficient R = 0.997
Design PCC Options still <--------------------------- FIZZINESS ------------------------> fizzy
Factors -0.8 -0.4 -0.2 -0.1 0 0.1 0.2 0.4 0.8
Sweetness 0.21 Plain 0.025
Sugar 0.037
Aspartame 0.156
Carbonation 0.99 Still -0.737
Carbonated 0.858

Table 13. Regression analysis for sweetness.

Multiple Correlation Coefficient R = 0.978
Design PCC Options bitter <-------------------- SWEETNESS -----------------------> sweet
Factors -0.4 -0.2 -0.1 -0.05 0 0.05 0.1 0.2 0.4
Sweetness 0.90 Plain -0.095
Sugar 0.059
Aspartame 0.559
Carbonation 0.25 Still 0.319
Carbonated 0.104
ICEF9-2003 International Conference Engineering and Food

Table 14. Regression analysis for taste.

Multiple Correlation Coefficient R = 0.896
Design PCC Options bad <----------------------------- TASTE --------------------> very good
Factors -0.6 -0.3 -0.15 -0.1 0 0.1 0.15 0.3 0.6
Sweetness 0.17 Plain -0.012
Sugar 0.290
Aspartame 0.028
Carbonation 0.86 Still 0.605
Carbonated -0.399

Table 15. Regression analysis for flavour.

Multiple Correlation Coefficient R = 0.890
Design PCC Options bad <---------------------------- FLAVOUR-----------------> very good
Factors -0.6 -0.3 -0.15 -0.1 0 0.1 0.15 0.3 0.6
Sweetness 0.30 Plain 0.074
Sugar 0.260
Aspartame - 0.120
Carbonation 0.84 Still 0.519
Carbonated -0.404

Table 15 shows that the overall quality results are also strongly dominated by carbonation, with
the option of carbonating the drink having a negative effect, while still drinks improve the overall quality
perception. To the slight extent that sweetness affects the results (low PCC), aspartame would be the
option that negatively influences the overall quality perception.

Table 15. Regression analysis for overall quality.

Multiple Correlation Coefficient R = 0.931
Design PCC Options OVERALL QUALITY
Factors -0.6 -0.3 -0.15 -0.1 0 0.1 0.15 0.3 0.6
Sweetness 0.32 Plain 0.146
Sugar 0.180
Aspartame -0.105
Carbonation 0.90 Still 0.517
Carbonated -0.396

Analysis of the interactive effects

Figures 1 to 3 show the interactive effects between sweetness perception and carbonation
regarding taste, flavour and overall quality. The average values of all samples with a particular design
option are indicated in the corners of the squares. The sweetening was divided to compare sucrose with
plain juice and aspartame with plain juice. The direction of the arrows shows the direction of increased
rating, while its length is proportional to the average effect achieved when moving fro one design option to
the other.
Figures 1 and 2 illustrate similar conclusions: sweetening with sucrose has very little interaction
with carbonation, but sweetening with aspartame does have an interactive effect. When the drink is
carbonated, aspartame actually improves the taste and flavour ratings, while in still drinks aspartame
worsens the rating. It is also noted that in aspartame-containing drinks carbonating or not does not really
affect the results, while in non-sweetened juice carbonation worsens the result extensively. Figure 3 also
shows no relevant interactive effects between sweetness and carbonation when using sucrose, but a
significant interaction when using aspartame. Again, carbonation improves the quality perception if the
drink is carbonated, and worsens it if it is still. Carbonation of a still drink also significantly decreases
quality perception, except when sweetened with aspartame, when it does not affect the results significantly
(in this case, carbonation even had a slight, though not statistically significant, influence).
These conclusions can be explained by the contextual element of aspartame: consumers are
more used to it in fizzy soft drinks. Carbonation changes the context of the drink from what looks like an
orange juice to what looks like a soft drink, and in the later aspartame taste and flavour is tolerated. This
ICEF9-2003 International Conference Engineering and Food

would suggest that if one wishes to produce a low calorie drink, it is better to carbonate it regarding taste
and flavour.

Figure 1. Interactive effects between sweetness and carbonation regarding taste.

Plain Sugar Plain Aspartame

Still Still Still Still
0.85 1.05 0.85 0.38

-0.62 -0.05 -0.62 0.10

Plain Sugar Plain Aspartame
Carbonated Carbonated Carbonated Carbonated

Figure 2. Interactive effects between sweetness and carbonation regarding flavour.

Plain Sugar Plain Aspartame

Still Still Still Still
0.75 0.86 0.75 0.05

-0.62 -0.19 -0.62 -0.14

Plain Sugar Plain Aspartame
Carbonated Carbonated Carbonated Carbonated

Figure 3. Interactive effects between sweetness and carbonation regarding overall quality

Plain Sugar Plain Aspartame

Still Still Still Still
0.76 0.86 0.76 0.14

-0.38 -0.33 -0.38 0.19

Plain Sugar Plain Aspartame
Carbonated Carbonated Carbonated Carbonated

References
1. Oliveira, J. (2003). Role of Kansei Engineering in Product Design Engineering. Int. Journal of Kansei Engineering, In Press
2. Nagamachi, M. (1995). Kansei engineering: a new ergonomic consumer-oriented technology for product development.
International Journal of Industrial Ergonomics, 15 (1): 3-12
3. Desor J. A., Maller O., Turner R. E. Taste in acceptance of sugars by human infants. Journal of Comparative and Physiological
Psychology. 84, 496-501, 1973.
4. Zandstra E. H., De Graaf C. Sensory perception and pleasantness of orange beverages from childhood to old age. Food Quality
and Preference. 9, 1/2, 5-12, 1998.
5. De Graaf C., Zandstra E. H. Sweetness intensity and pleasantness in children, adolescents and adults. Physiology and Behavior.
67, 4, 513-520, 1999.
6. Passe D.H., Horn M., Murray R. The effects of beverage carbonation on sensory responses and voluntary fluid intake following
exercise. International Journal of Sport Nutrition. 7, 4, 286-297, 1998.
7. Cometto-Muniz J. E., Garcia Medina M. R., Calvino A. M., Noriega M. Interaction between CO2 oral pungency and taste.
Perception. 16, 629-640, 1987.4. Linneman A.R., Meerdink G., Meulenberg M.T.G., Jongen W.M.F. Consumer-oriented technology
development. Trends in Food Science and Technology. 9, 409–414, 1999
8. Odake S. Sweetness in low-carbonated beverages. Biomolecular Engineering. 17, 151-156, 2001.
9. Jindo, T., Hirasago, K. and Nagamachi, M. (1995). Development of a design support system for office chairs using 3-D graphics.
International Journal of Industrial Ergonomics, 15: 49-62
 ICEF9 - 2004 International Conference Engineering and Food

A numerical investigation on the effect of thermal diffusivity and convective heat transfer
coefficient on heating rate of foods

T. Koray Palazoglu

Department of Food Engineering

University of Mersin
Ciftlikkoy, Mersin 33343, Turkey
E-mail: koray_palazoglu@yahoo.com

ABSTRACT
Common knowledge is that an object with a higher thermal diffusivity will always heat faster in
comparison to that with a lower thermal diffusivity. To demonstrate that this is not always true, the effect of
thermal diffusivity and heat transfer coefficient (h) on heating rate was investigated by finite difference
modeling of heat transfer in a spherical particle. The study showed that depending on the h value, a
particle with a lower thermal diffusivity may heat faster than a particle with a higher thermal diffusivity.

Keywords: heating rate, thermal diffusivity, heat transfer coefficient

INTRODUCTION

Many thermal processing operations involve heat transfer between a solid food product and a fluid
medium. While heat is transferred to the surface of the food product by convection, heat transfer within the
solid food is governed by conduction. Rate of heat penetration within the solid food is a function of several
factors including thermal conductivity (k), density (ρ), and specific heat (cp) of the food. These properties
k
of food make up thermal diffusivity ( α = ) which is known as the ratio of the heat conducted to the
ρ cp

heat stored.
Common knowledge is that an object with a higher thermal diffusivity will always heat faster in
comparison to that with a lower thermal diffusivity. Özışık [1] and Singh [2] stated that the larger the
thermal diffusivity, the shorter the time required for the heat to propagate within the solid. Özışık [1]
demonstrated this by comparing the times it took several materials with different thermal diffusivity values
to cool from an initial temperature to half of this value. Incropera and DeWitt [3] also reported that
materials of large thermal diffusivity respond more quickly to temperature changes in their environment.
Wang et al. [4] somewhat pointed out to the varying effects of thermal diffusivity on heating rate in

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different heating media (different h values). They modeled heating of fruits in hot air and in hot water.
They used three different thermal diffusivity values (1.4 x 10-7, 1.6 x 10-7, and 1.8 x 10-7 m²/s) in their
simulations. They reported that changing the thermal diffusivity from its middle value to its lower and
upper values caused heating time to differ about 4% in hot air and 13% in hot water. The difference
between hot air and hot water was attributed to the difference in the magnitude of Biot numbers (h D/ k)
for the two different cases, which were between 1 and 3 for hot air, and 82 and 130 for hot water. The
reason why the heating time was more affected by the changing thermal diffusivity during water heating
was said to be the fact that the internal heat resistance was more dominant in controlling the heat transfer
to the fruit’s center when the heating medium was water.
The subject deserves investigation as by now no mention has been made in regards to the effect of
heat transfer coefficient, except by the study of Wang et al. [4]. Therefore, the objective of this study was
to investigate the combined effect of heat transfer coefficient and thermal diffusivity on the rate of heating,
and to analyze the effect of the heat storage (ρ cp) and conduction (k) terms individually.

METHODS

Numerical method

Spherical geometry was chosen as it is the simplest one to be numerically modeled. Spherical body
was divided into concentric spherical shells and a convective boundary condition was employed at the
surface. The explicit finite difference program was written in Visual Basic 6.0 (Microsoft Corporation 1998)
using the energy balance approach with a non-capacitance surface node (Figure 1).
A total of 10 nodes were used in the radial direction for a particle with a radius of 0.00635 m (1/4
inch), and the following energy balance equations were setup:

Node 10 (Surface node)

 
 T − Tn k A9 n  ∆t
n+1 ∞
= T10 +  (T9 − T10 )
n 10 n
T10 +
 1 + ∆r ∆r  ρ c p ∆V10
hA 2k A 
 10 

Nodes 9 – 2 (Interior nodes)

n+1 n k Ai n n k A i−1 n n  ∆t
Ti = Ti +  (Ti+1 − Ti ) + (Ti−1 − Ti )
 ∆r ∆r  ρ c p ∆Vi

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Node 1 (Center node)

n+1 n k A1 n n ∆t
T1 = T1 + (T2 − T1 )
∆r ρ c p ∆V1

T∞
h

1 8 9 10
∆V1
A1 ∆r

A8 ∆V9

A9 ∆V10
A10
A

Figure 1 - Node generation employing non-capacitance surface node

Thermophysical properties used in the study are given in Table 1, where Particle 1 represents potato
and Particle 2 is a plastic material. Simulations were run for a spherical particle with a radius of 0.00635 m
for an initial temperature of 20°C, ambient temperature of 140°C, heating time of 100 s, and heat transfer
coefficient values of 50 and 1,000 W/m².°C.

Table 1- Thermophysical properties of the particles

Particle 1 2
Density (kg/m³) 1,090 833
Thermal conductivity (W/m-K) 0.554 0.17
Specific heat (J/kg-K) 3,517 1,968
-7
Thermal diffusivity (m²/s) 1.45 x 10 1.04 x 10-7

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RESULTS AND DISCUSSION

Numerical vs analytical method

Numerical method was validated against the exact analytical solution and a close agreement was
found between numerical and analytical values (Table 2). An incremental time step of 0.025 s was found
satisfactory for convergence.

Table 2 - Comparison of numerical and analytical solutions

Temperature at center node Temperature at surface node
Particle h (°C) (°C)
(W/m².°C) Numerical Exact Numerical Exact
1 50 59.4 59.4 76.6 76.7
2 50 76.4 76.6 107.5 107.7
1 1,000 127.6 127.9 138.1 138.2
2 1,000 117.8 118.4 138.1 138.2
Particle radius = 0.00635 m Ti = 20°C
Time = 100 s T∞ = 140°C

Simulation results

Temperature profiles for the surface and center nodes of the two particles are presented in Figures 2
and 3. When heat input to the particle is limiting, small h value case, temperature increase at the surface
of the particle with the smaller specific heat and density (Particle 2) is greater (Figure 2a), resulting in a
steeper temperature gradient within this particle. Since conduction is governed by not only thermal
conductivity but also temperature difference, this steep temperature gradient could more than compensate
for the low k value. The same heat input resulted in a smaller temperature increase at the surface of
Particle 1, and hence a smaller temperature gradient within that particle as a result of its greater heat
storage term. Thermal conductivity value of this particle was simply not large enough to offset the small
temperature gradient effect. This can be seen from Figure 2a where the center of Particle 2 reached a
higher temperature than that of particle 1 after the same period of time.
However, when the h value was large, surface temperature profiles for the two particles were
comparable (Figure 2b), indicating that the heat input to the particles was not limiting. In this case, heat
propagation was faster within the particle having the larger thermal conductivity (Figure 3b).

CONCLUSION
This study established that individual roles of the storage and conduction terms must be considered
rather than the thermal diffusivity alone in heat transfer applications.

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 ICEF9 - 2004 International Conference Engineering and Food

a b

Figure 2. Surface temperature profiles for the two particles tested, a) h = 50 W/m².°C, b) h = 1,000
W/m².°C

a b

Figure 3. Center temperature profiles for the two particles tested, a) h = 50 W/m².°C, b) h = 1,000 W/m².°C

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SYMBOLS

A surface area of the spherical body m²

Ai heat transfer area between nodes m²
cp specific heat of particle J/kg.°C
D characteristic length m
h convective heat transfer coefficient W/m².°C
i node number in radial direction
k thermal conductivity W/m.°C
n time-step index
R radius of spherical body m
T∞ ambient temperature °C
Tin temperature at node i at time step n °C
Tin+1 temperature at node i at time step n+1 °C
∆r distance between nodes m
∆t incremental time step s
th
∆Vi volume of i nodal element m³

Greek letters
ρ density of particle kg/m³
α thermal diffusivity of particle m²/s

REFERENCES
1. Özışık, M.N. Heat Conduction. 2nd ed. John Wiley & Sons, Inc., New York, 692p, 1993.

2. Singh, R.P. Thermal diffusivity in food processing. Food Technology, 36, 2, 87-91, 1982.

3. Incropera, F.P. and De Witt, D.P. Fundamentals of Heat and Mass Transfer. 3rd ed. John Wiley & Sons,
Inc., New York, 919p, 1990.

4. Wang, S., Tang, J. And Cavalieri, R.P. Modeling fruit internal heating rates for hot air and hot water
treatments. Postharvest Biology and Technology, 22, 257-270, 2001.

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ICEF – 2004
International Conference Engineering and Food

Heat transfer in canned foods of big particles suspensions during sterilization

Rabiey Ladan, Duquenoy Albert

ENSIA Dep GIA – UMR Génial - Massy
rabiey@ensia.fr, duquenoy@ensia.fr

Abstract
Heating of cans containing water and several tomatoes (from 5 to 11) is performed using an agitated
water bath and recording the evolution of the temperature at five different positions in both liquid and
particles. A model based on heat balances is developed that includes heat transfer coefficients
between the liquid and the heating medium hf, and between the liquid and the particles hp. The heat
transfer inside particles, presumably spherical, is considered purely radial. The model is programmed
with Matlab and used to adjust the heat transfer coefficients to fit the experimental data. These
adjusted coefficients appear to vary with the number, size and position of the particles.

Key words: heat transfer, canned foods, particles

Nomenclature
-2 -1 3
h Heat transfer coefficient (W.m .K ) V Volume (m )
-3
r Radial position in a particle Specific mass (Kg.m )
-1 -1
rmax Radius of a particle Cp Specific heat capacity (J.Kg .K )
2 -1 -1
A Area (m ) Particle thermal conductivity (W.m .K )
H Distance from bottom of can Subscripts
R Radial position in the can f Liquid
T Temperature (°C) p Particle

Introduction
Thermal sterilization of foods has been one of the most widely used methods for food
preservation during the twentieth century and has contributed significantly to the
nutritional well being of much of the world populations. Typically, it consists of
heating food containers in retorts at specified temperatures for prescribed lengths of
time(Teixeira and Tucker,1997).To ensure that all parts of the product achieve the
required temperature exposure to guarantee a microbiologically safe product and at
the same time preserve the nutritional and sensory value of the product, the
knowledge of the heat transfer phenomena is required. Heat is transferred inside
cans by conduction, convection or a combination of both. When solid particles are
suspended in a liquid, convection occurs in the liquid and conduction in the solid
particles. In fact, even inside the same product fraction, the two modes of transfer
coexist and participate in the equilibration of the temperature. Thermal process
calculations are based on time–temperature data taken at the coldest point of the
particle(Abdul Ghani et al.,1999). Mathematical modelling serves as an important tool
in reducing the number and cost of experiments required in designing, validating and
optimising processing systems. With the use of a mathematical model, the
temperature distribution and the time–temperature profile in a particle can be
predicted from the knowledge of the size and number of the particles, the thermal
properties of both particles and liquid medium and the heat transfer
coefficients(Abdul Ghani et al.,2002). Several researchers(Chinesta et al.,2002;
Verboven et al.,1997)have proposed mathematical procedures to predict heat
transfer to particles and computer simulation programs for process evaluation.
Chinsta et al. used an homogenized thermal model and Verboven et al. used a
model based on Computational Fluid Dynamics.
The objective of the present study is to use and modify a model developed by
Binbonet and Duquenoy(1974) which are based on heat balances: an overall heat

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balance for the liquid, and punctual ones for the particles. The model includes heat
transfer coefficients between the liquid and the heating medium hf, and between the
liquid and the particles hp, and to study how they vary with the number and position of
the particles. The present paper is describes the preliminary approach concerning
static heat treatment applied to several spherical particles of uniform size suspended
in water.

Theory: Modelling convection and conduction

Binbenet and Duquenoy (1974) considered a container containing one - size
spherical particles suspended in a liquid. They described the heat exchanges as
follows:
• From the heating medium to the liquid, through two laminar layers and the wall,
• In the liquid by convection (The liquid is considered strongly agitated, therefore
without any temperature gradient),
• From liquid to particles surface through a laminar layer,
• In the particles by conduction.
They assumed the following hypothesis to write the heat balance for the liquid:
uniform temperature for the particles surface as well as for the liquid, uniform heat
transfer coefficients, constant thermo-physical properties for the liquid, and no energy
accumulation in the can wall. The balance then gives the evolution of the liquid
temperature:
dT f
h f Ac (T R T f ) h p A p (T f T p ) = V f f Cp f (1)
dt
For the particles immersed in the liquid, they assumed that they are spherical with a
spherical symmetry, uniform and constant physical properties. The heat balance can
then be written as:
2
Tp 2 Tp Tp
= ( + 2
) (2)
t p Cp p r r r

The initial and boundary conditions are: T(r,0)=Ti (3)

T (0, t )
=0 (4)
r
T ( rmax , t )
h p (T p Tf ) = (5)
We modified this modelling by considering different heat transfer coefficients for each
particle.

Materials and Methods

-Experimental apparatus: It consist of:
• A 80°C water bath as heating medium,
• 4/4 cylindrical metal cans as container,
• Water as filling liquid and tomatoes as particles.
Tomatoes are merely ellipsoid and have almost the same size with an average
“height” of 5,5 cm and an average “width” of 4 cm. They are blanched for one minute
in boiling water and then peeled.
Their specific mass is determined from the displaced volume of water and weight of
the tomatoes. Specific heat and thermal conductivity are measured using a CT-

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METRE (TELEPH Meylan, France). Water properties are obtained from the literature
data. Resulting values are given in Table 1.
Table 1 - Thermo-physical properties of tomato and water at 20°C
(W.m-1.K-1) Cp(KJ.Kg-1K-1) (Kgm-3)
Tomato 0.656 4.05 1029
Water - 4.18 998.2

-Thermocouple errors: Liquid and particles temperatures are measured using T

type needle thermocouples and are collected via a Fluke data logger. The main error
associated with a thermocouple is the conduction of heat along its wires. To evaluate
this error in our experimental situation, we first compared the temperature of the
canned liquid close to the can wall, given by a thermocouple passing across the hot
water bath, to the one given by a thermocouple the wires of which remained cool
(see figure 1a). We also compared the values at the centre of the can measured by
the first thermocouple, with that given by an autonomous recording thermal sensor
(NanoVACQ NVQ, Tmi-orion, Montpollier, France), thus with no wire. (See figure 1b).
Figure 1- Experiments for the evaluation of the error brought about by the conduction

5cm
Tmi temperature sensor

5 5
50
a cm 1cm b mm
cm

in the thermocouple wires.

-Experiments: Five thermocouples are inserted into the can through the lateral wall.
Three have their sensitive end in the liquid at locations defined by (H, R) couples of
(1, 4), (5, 2) and (10, 0) cm. The others are at the centre of 2 tomatoes. The first
tomato has its largest dimension set vertically, while it is horizontal for the other.
These two measures correspond to (H,R) positions of (3, 3) and (7, 2.25). See figure
2.
We measured the evolution of these temperatures in cans containing various
numbers of tomatoes 5,7,9 and11 tomatoes.
-Solving the heat balance equations and adjusting the model: We programmed
an explicit finite difference method to solve the particle heat equation, and this
method associated with an Euler method to solve the particles and liquid heat
equations simultaneously, using Matlab.
The adjustment of the heat transfer coefficients on a least squares criteria, is
achieved by the minimum seeking functions of this software. The two types of
coefficient, for liquid and for particles, are adjusted in a sequence: first hp then hf.
hp is adjusted so that the solution of equation 2, using recorded values as known
values of Tf , fits the experimental measurements of the temperature at the centre of
the tomato. As the 3 measured temperatures for the liquid are different, the required
local temperature at the same h as the considered particle, is assumed to be equal to

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ICEF – 2004
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the mean of the temperature measured in the liquid below and above h. As the two
measured temperatures in the particles are different, two coefficients are adjusted.
hf is adjusted so that the solution of the set of equations composed of equation 1 and
as many equations 2 as there are tomatoes, fits the mean value of the three
measured liquid temperature. Equations 2 differ by the value of hp. For the tomatoes
with no temperature record, this coefficient is extrapolated from the two adjusted
ones, using a simple linear function.
The validity of this procedure is estimated by the comparison of the experimental
temperatures at the centre of the particles, with those computed from the above set
of equations using all the adjusted coefficients.

N°2

N°1

Figure 2 – The arrangement plan of the thermocouple in the can

Results & discussion

-Thermocouples errors:
The temperature overestimation is shown at figure 3. The overestimation is greater
when the temperature is measured close to the can wall for two reasons. First the
longer the wire, the higher its resistance to heat transfer. Secondly the heat flow
transferred can be dissipated along the wire: the longer the wire, the less heat flow
reaching its end. This double effect makes the temperature correction hazardous. All
we can conclude that the error is less 1°C after 5 minutes of heat treatment.

7 80 2 80
Te m pe ra ture (°C)

6
Ove r e s tim atio n (°C)
Overstim ation (°C)

Tem perature (°C)

5 Temp. Through the 60 Temp. Through the 60

water bath water bath
4
Temp. Of the 40 1 Temp. Of sensor 40
3
other thermo.
2 overestimation 20 overestimation 20
1
0 0 0 0
0 200 400 600 800 0 200 400 600 800
a Time (s)
b Time (s)

Figure 3 - Overestimation of the temperature given by the thermocouple passing

through the water bath.
a) Compared to the other thermocouple b) Compared to the Tim sensor

-Temperatures evolutions: influence of the number of particles

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ICEF – 2004
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Figure 4 shows a typical time – temperature profile of the liquid and of the centre of 2
tomatoes. The liquid temperature increases quickly, while at the centre of the particle
temperature changes naturally much more slow. The further in the can, the faster the
particles and liquid heat transfer.

90 90

80 80

70 Liq.. H=10cm 70
Te m pe ratu re (°C )

Temperature (°C )
60
Liq. H=1& H=5 cm 60

50 50

40 Tom. Centre H=3 cm 40

30 Tom. Centre H=7 cm 30

20 20
10 10
0 500 10 00 150 0 200 0 0 500 1000 1500 2000 2500 3000 3500
a Ti m e (s ) b Time (s)

Figure 4 –Temperature profiles in the liquid and the particle centre.

a) 5 tomatoes b) 11 tomatoes

-Adjustment of the particles heat transfer coefficient:

Figure 5 shows that there is a good agreement between adjusted and experimental
temperature of tomato’s centre. Experimental data are the means of tow replications.

80 80

70 70

60 60
Temperature (°C)

computed(11tom)
Te mpe rature (°C)

computed(11 tom)
50 experimental(11 tom) 50 experimental(11tom)
computed(5 tom) computed(5tom)
40 40
experimental(5 tom) experimental(5tom)

30 30

20 20

10
10
0 500 1000 1500 2000 2500 3000 0 500 1000 1500 2000 2500 3000
a Time (S) b Time (S)

Figure 5 – Comparison of experimental and computed temperature in the centre of

the tomatoes. a) H = 3 cm; hp (5 tom)=328.27; hp (11tom)=135.95
b) H = 7 cm; hp (5tom)=198.85; hp (11tom)=82.24 Wm-2°C-1

-Adjustment of the liquid heat transfer coefficient:

A comparison of experimental liquid temperature with model predictions is presented
in Fig 6. Experimental data represent the means of tow replications. Computed and
measured particle and liquid temperatures are in close agreement throughout the
duration of the experiments.
-Validity of the procedure:
Finally we validate our model using hp and hf values obtained as described above as
inputs to the computer program. The computed curves are compared with the
experimental ones(Figure 7).

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 ICEF – 2004
International Conference Engineering and Food

2 2
H=1cm
1,5 H=5cm 1,5 H=1cm
H=10cm H=5cm
1 comuted 1 H=10cm
LOG(TR-Tf)

computed

LOG(TR-Tf)
0,5 0,5
0 0
-0,5 -0,5
-1 -1
-1,5 -1,5
a 0 500 Time (s) 1000 1500 b 0 1000 Time (s) 2000 3000

Figure 6 - Comparison of experimental and computed temperature in the liquid

a) 5 tomatoes hf=661,34 b) 11 tomatoes hf=455,96 W.m-2°C-1

90 90
80 80
70
Temperature (°C)
Temperature (°C)

70
60 60
50 computed particle 50 computed particle
computed liquid computed liquid
40 experimental particle 40 expental particul
experimental liq H=1 experimental liq H=1
30 experimental liq H=5 30 experimental liq H=5
20 experimental liq H=10 20 experimental liq H=10

10 10
0 500 1000 1500 2000 0 500 1000 1500 2000
a Time (s) b Time (s)

90 90
80 80
Temperature (°C)
Temperature (°C)

70 70
60 60
coputed particle 50 computed particle
50 computed liquid computed liquid
40 experimental particle 40 experimental particle
experimental liq H=5 experimental liq H=1
30 experimental liq H=10
30 experimental liq H=5
20 experimental liq H=10 20 experimental liq H=10

10 10
0 1000 2000 3000 4000 0 1000 2000 3000 4000
c Time (s) d Time (s)

Figure 7 – Validation of model a) particle H=3, 5 tomatoes; b) particle H=7, 5

tomatoes; c) particle H=3, 11 tomatoes d) particle H=7, 11 tomatoes

-Variation of hp and hf with tomato numbers and tomato position

Both heat transfer coefficients decrease with the number of tomatoes (figure8 and 9).
The lower distance of the particle from the can bottom, the smaller heat transfer
coefficient between the liquid and the particle. The more tomatoes in the can, the
worst movement of the liquid, thus the lower the heat transfers.

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ICEF – 2004
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400 5tom 700

7tom
9tom

hf(Wm-2°C-1)
300 11tom
h p (Wm-2°C-1)

600
200
500
100

0 400
1 3 5 7 9 5 7 9 11
H (cm) tomato number

Figure 8 – Variation of hp with the Figure 9 _ Variation of hf with the number

Position of the tomatoes in the can of tomatoes

Conclusions
A numerical convection-conduction heating model is modified successfully so that it
showed a good agreement between computed and experimental temperatures. Our
model is primarily validated by a comparison of the experimental temperatures at the
centre of the particles, with those computed using all the adjusted coefficients and
showed a close agreement throughout the duration of the experiments. Values oh hp
varied for different conditions and followed the expected trends of variation,
increasing of with the number of particles and their distance from the can bottom.
For the forthcoming work we shall use model product in order to control the size of
the particle perfectly.

Bibliographie

1.Teixeira, A. A. and G. S. Tucker. On-line retort control in thermal sterilization of canned foods. Food Control,
8, 1, 13-20, 1997.

2.Abdul Ghani, A. G., M. M. Farid, X. D. Chen and P. Richards. An investigation of deactivation of bacteria in
a canned food during sterilization using computational fluid dynamics. Journal of Food Engineering, 42, 207-
214, 1999.

3.Abdul Ghani, A. G., M. M. Farid and X. D. Chen. Numerical simulation of transient temperature and velocity
profiles in a horizontal can during sterilization using computational fluid dynamics. Journal of Food
Engineering, 51, 77-83, 2002.

4.Chinesta, F., R. Torres, A. Ramon, M. C. Rodrigo and M. Rodrigo. Homogenized thermal conduction model
for particulate foods. International Journal of Thermal Science, 41, 1141-1150, 2002.

5.Verboven, P., B. M. Nicolaï, N. Scheerlinck and J. Baerdemaeker. The llocal surface heat transfer coefficient
in thermal food process calculations : a CED approach. Journal of Food Engineering, 33, 15-35, 1997.

6.Bimbenet, J. J. and A. Duquenoy. Simulation mathématique des phénomènes intéressant les industries
alimentaires, 1-transferts de chaleur au cours de la stérilisation. Ind. Alimen. Agric., 91, 4, 359-375, 1974.

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ICEF 9 – 2003 International Conference Engineering and Food
Shelf-life prediction in minimally processed potatoes
Russo L. , Albanese D.1,Cinquanta L.2, Orilio P.1 and Di Matteo M.1*
1
1
Università di Salerno - Dipartimento di Ingegneria Chimica e Alimentare -
mdimatteo@unisa.it
2
Università del Molise - Dipartimento di Scienze e Tecnologie Agro-Alimentari Ambientali e
Microbiologiche
a
Department of Chemical and Food Engineering, University of Salerno, Via Ponte Don Melillo, 84084
Fisciano (SA), Italy E-mail mdimatteo@unisa.it
b
Department of Agricultural, Food, Environmental and Microbiological Science and Technology,
University of Molise, Via F. De Sanctis, 86100 Campobasso, Italy. E-mail cinquant@unimol.it

Abstract

In this research we studied the effects of pre-treatments with natural antioxidants on the shelf-life of
minimally processed potatoes. The physico-chemical parameters analysed showed that the two pre-
treatments improved the shelf-life elongation. Moreover, on the basis of the results obtained, a
predictive model of the shelf-life of such products was developed, by using the change in total phenol
content during the cold storage.

Keywords: colour, minimally processed food products (MPFP), modelling shelf-life, poliphenol oxidase
(PPO), potatoes.

Introduction

The purpose of minimally processed food products (MPFP) is to offer to the consumer a fresh-like
quality and, at the same time, to ensure food safety and to maintain nutritional and sensory quality.
Many processing operations help to preserve quality, spoilage, and the possible increase of safety
hazard. All elements of the processing, packaging and distribution must be nearly optimised for the
system to deliver safe and good quality food, especially in the case of the MPFP. In some cases
(minimally processed fruit and vegetables), it is very important to take in account pre-treatment of the
products to provide MPFP of good quality and safety (1). Potatoes processing, such as: peeling,
cutting, portioning, useful to produce convenience foods, tend to degrade the quality of the products
and, thus, to reduce their shelf-life, mainly due to the occurrence of enzymatic browning on raw
potatoes slices (2, 3). The browning is mainly related to the concentration of polyphenol oxidase
(PPO) substrates (free tyrosine, chlorogenic acid, caffeic acid), that are located mainly in the vacuoles
(4). Intracellular compartmentation of PPO, a plastide enzyme located in the chloroplast thylakoid
membranes, and phenols in the tuber, prevents the initiation of colour formation in undamaged tissue
(5). To start the colour reaction, the deterioration of intracellular membranes is necessary to make
contact between the enzyme and its substrates (6). The PPO catalyse the hydroxylation of
monophenols to o-diphenols and the oxidation of o-diphenols to o-quinones. These latter are then
subjected to further reactions leading to the formation of pigments, that differ widely in hue and
intensity. In this research we evaluated the quality of minimally processed (sliced) potatoes, pre-
treated with different natural anti-oxidants, during cold storage. Moreover, we developed a predictive
model to evaluate the shelf-life of such products, by using the total phenol content as deterioration
index.

Materials and methods

The experiments were carried out on two potato (Solanum tuberosum) cultivars, Agria and Merit.
Samples of about 250 g for each variety, peeled and portioned in 5 mm thickness slices, were
submitted to one of the following pre-treatments, before packaging in a semi-permeable film (Cryovac
MRX):
a) dipping in a natural antioxidant solution (F);
b) dipping in a natural antioxidant solution with humectant (G);
Moreover untreated packaged samples (U+film) and untreated samples, without package (U), were
used as references. The potatoes were stored at 6°C for 8 days and the relative humidity was 90%.
Daily the product quality was evaluated by measuring the following parameters: colour, total phenol
contents, and polyphenoloxidase activity (PPO).
Colour was assessed with a CR-200 Chromameter (Minolta, Japan) having an aperture size of 10
mm. The results were expressed with the Hunter scale (L*, a*, b*).
Total phenols were determined at 760 nm using the Folin-Ciocalteau reagent (with a
spectrophotometer Perkin Elmer, mod. Lambda Bio 40) and expressed as gallic acid (7)
Poliphenol oxidase activities (PPO) were assessed according to Chazarra et al. (8).
Shelf-life modelling. The quality of minimally processed potatoes was studied with a kinetic model
approach (9) of food deterioration reactions. Generally, recognizing the complexity of a food system
and based on some simplifying assumptions, quality loss can be represented by the loss of a
desirable quality factor or the increase of an undesirable factor. In our case, as measure of potatoes
degradation processes, we have chosen the concentration of total phenols. The assumption is that the
decrease of total phenols in time follows a kinetic model mathematically expressed by a power law.
More precisely, indicating with C the phenols concentration, we assume that the evolution of phenols
in time can be expressed by the following law :
dC
= −kC n (1)
dt
where k is the apparent reaction rate constant and n the reaction order. Obviously the Eq.(1) does not
represent the true reaction mechanisms and the reaction order is not necessarily true reaction order
but rather represents apparent order. The apparent reaction order and constant are determined by
fitting the measured data of phenols with time trough the eq.1. The rate equations can be analytically
solved allowing the expression of C as a function of time. One assumes different values of n and tries
a least square linear fit to the corresponding equations of the experimental data. The coefficient of
determination (R2) of the linear regression is in most cases a sufficient criterion to determine which
reaction order gives the best fit. Once time the model is validated and the parameters n and k are
estimated, the shelf-life of potatoes can be valuated by fixing a minimum value of phenols
concentration, Cmin, and by integrating in time the eq.1.In this way, the shelf-life prediction can be
given by the following expression:
C1− n − Cm1−inn
tsl = 0 (2)
k (1 − n )

The minimum value of phenols concentration, Cmin was estimated equal to about 0.5 g/100 g,
corresponding, in our experience, to the appearance of an undesirable degree of visible browning.

Results and discussion

The total phenols content on fresh potatoes was about 0.79 g/100g in Merit samples, and 0.79 g/100g
in Agria ones. During the cold storage the total phenols content decreased in all samples. As
expected, the pre-treatments with antioxidants caused a less decrease of phenols in both varieties,
with a similar behaviour for the different kind of samples. After 8 days of storage, the phenols
reduction on Merit potato slices varied from 55% in U samples, to 30% in G (Fig. 1); while in Agria the
decrease varied from 65% in U samples, to 20% in G samples, (Fig. 2). Thus the pre-treatments better
preserved the initial phenol content in sliced potatoes, limiting their involvement in oxidation reaction.

cv MERIT U
1 U + film
0,8 F
phenols (%)

G
0,6
0,4
0,2
0
0 1 2 days 3 4 7 8

Fig.1 – Total phenols changes during cold storage of different minimally processed Merit potatoes.
 1 cv AGRIA

0,8

phenols (%)
0,6
U
0,4 U + film
F
0,2 G

0
0 1 2 3 4 7 8
days

Fig.2 – Total phenols changes during cold storage of different minimally processed Agria potatoes.

The total poliphenol oxidase (PPO) activity was quite similar in fresh sliced potatoes of both varieties
(Figg. 3-4). During storage, the total PPO activity decreased in all samples. The highest initial PPO
values were due to the physical damage of processed potatoes tissues, and to their physiological
disorder, that enhanced the availability of such enzymes. The highest PPO reduction was detected in
pre-treated samples.

cv Agria
U
0,012
PPO activity [microkatal/gr]

U+film
0,01 F
0,008 G

0,006
0,004
0,002
0
0 1 2 3 4 7 8
days

Fig.3 – Total poliphenol oxidase activity changes during cold storage of different minimally processed
Agria potatoes.

cv Merit
PPO activity [microkatal/gr]

0,012
0,01
0,008 U
U+film
0,006
F
0,004 G
0,002
0
0 1 2 3 4 7 8

days

Fig.4 – Total poliphenol oxidase activity changes during cold storage of different minimally processed
Merit potatoes.
 Fresh sliced Agria and Merit minimally processed potatoes showed quite similar L* (lightness) values.
During storage, the L* values decreased, with differences between the pre-treated and untreated
samples, while the a* values (redness), slightly increased in both varieties. The total change in potato
slices colour was evaluated by means of the ∆E parameter (visual difference in the diagram L*a*b*),
measured on fresh minimally processed potatoes, and after 8 days of cold storage (Fig. 5). The data
showed the effectiveness of pre-treatments on the preservation of the colour, with respect to the
untreated and only packaged samples, in either cultivars.

cv AGRIA
cv MERIT
80 80
70 70
60
60
50
50
40
40
30
30

∆E
cv AGRIA

20
70
60
50
40
20
30

10
20
10
0
U U+film F G

10
0
0
U U+film F G U U+film F G

Fig. 5 – Colour changes (∆E) in fresh minimally processed potatoes and after 8 days of cold storage.

The enzymatic browning of the slices potatoes affects their quality. Enzymatic browning is connected
with the action of the mono-oxygenase which in presence of oxygen hydroxylates the colourless
monophenols to o-diphenols which are subsequently oxidized to coloured o-quinones. Through a series
of non-enzymatic reactions, o-quinones are then converted irreversibly to brown polymeric pigments.
Many authors have attempted to correlate browning results with the phenolic content and/or enzymatic
activity. With the modelling approach discussed in previous section, we have calculated the shelf-life,
both for Agria and Merit samples, with the eq.2.
In tab1-2 the results of the regression analysis of untreated and pre-treated samples of Agria and Merit
are reported. For the agria cultivar (tab.1), the total phenols content decreases by following a zero-order
kinetic both for untreated and pre-treated samples. The predicted shelf-life time is reported in the last
column, where it is apparent that F and G samples are less sensitive to the browning phenomenon.
Instead, for Merit cultivar (tab.2), the total phenols content decreases by following a two-order kinetic
both for untreated and pre-treated samples and, also in this case, the F and G treatments increase the
shelf-life time.

Tab 1 : shelf-life prediction in minimally processed Agria potatoes

n r2 K tshelf-life
Tq 0 0,9945 0,0749 1 gg
Tq + film 0 0,9685 0,0644 1,68 gg
F 0 0,9838 0,0427 4,53 gg
G 0 0,9970 0,0245 6,54 gg
Tab.2 : shelf-life prediction in minimally processed Merit potatoes
n r2 K tshelf-life
Tq 2 0,9565 0,2265 2 gg
Tq + film 2 0,9839 0,1285 4,9 gg
F 2 0,9914 0,1253 5,8 gg
G 2 0,9614 0,00832 7,6 gg
Furthermore, Merit cultivar samples have a higher shelf-life time than Agria cultivar samples, in
untreated and pretreated cases.

Conclusions

The main quality factor, affecting the shelf-life of minimally processed potatoes, is the enzymatic
browing. The influence on shelf-life of two anti-oxidant treatments (F and G) is studied on two different
potato cultivars (Agria and Merit).
The experimental study of physical-chemical parameters, related to the browing phenomenon, is
conducted by monitoring total phenols content, plolyphenol oxidase activity and colour parameters (L,
a, b, ∆E) during cold storage. The prediction of the shelf-life time is given by constructing a cinetic
model of the evolution time of the total phenols content. The decrease rate of total phenols in Agria
samples is fitted by a two order cinetic while a zero order cinetic is found for Merit cultivars. For both
cultivars the treatments F and G improve the shelf-life time.

References

1.Sapers, G.M., Miller, R.L., Choi, S.W.. Prevention of enzymatic browning in prepeeled potatoes and
minimally processed mushrooms. In: Lee, C.Y., Whitaker, J.R. (Eds.), Enzymatic Browning and its
Prevention. American Chemical Society, Washington, DC, USA, pp. 223–239, 1995
2.Matheis, G., Belitz, H.-D., 1977. Untersuchungen zur enzymatischen bra¨unung bei kartoffeln
(Solanum tuberosum). I. Phenoloxydasen und phenolische inhaltstoffe verschiedener sorten. Z.
Lebensm-Unters -Forsch. 163, 92–95.
3.Duangmal, K., Apenten R., 1999. a comparative study of poliphenoloxidase from taro and potato.
Food Chemistry 64, 351-359.
4.Lærke, P.E., Brierley, E.R., Cobb, A.H., 2000. Impact-induced blackspots and membrane
deterioration in potato (Solanum tuberosum L) tubers. J. Sci. Food Agric. 80,1332–1338.
5.McGarry, A., Hole, C.C., Drew, R.L.K., Parsons, N., 1996. Internal damage in potato tubers: a critical
review. Postharvest Biol. Technol. 8, 239–258.
6.Partington, J.C., Smith, C., Bolwell, G.P., 1999. Changes in the location of polyphenol oxidase in
potato (Solanum tuberosum L.) tuber during cell death in response to impact injury: comparison with
wound tissue. Planta 207, 449–460.
7. Singleton, V.L., Orthofer, R., Lamuela-Raventos, R.M., 1999. Analysis of total phenols and other
oxidation substrates and antioxidants by means of Folin-Ciocalteau reagent. Methods in Enzymology,
299, 152-178.
8.Chazarra, J., Escribano, J., Carmona, F.. Kinetics study of the suicide inactivation of latent
polyphenoloxidase from iceberg lettuce (Lactuca sativa) induced by 4-tert-butylcathecol in the
presence of SDS. Biochimica et Biophysical Acta 1339, 297-303, 1997.
9. Kilcast, E.D., & P.Subramaniam, 2000. “The stability and shelf-life of food”. Whodhead Publishing in
Food Science of Technology Cap 5, 107-128.
 ICEF9-2004
International Conference Food and Engineering

SIMPLIFIED SOLUTIONS FOR INVERSE HEAT CONDUCTION PROBLEMS USING NEURAL

NETWORKS

S. S. Sablani
Department of Bioresource and Agricultural Engineering
Sultan Qaboos University
P. O. Box-34, Al-Khod PC 123, Muscat, Oman
shyam@squ.edu.om

ABSTRACT

The Direct Heat Conduction Problem (DHCP) of transient heat conduction for two and three-
dimensional geometries with a convective boundary condition was solved using analytical and
numerical methods. The dimensionless temperature-time history at the center and geometry
parameters were then correlated with the corresponding Biot number using appropriate artificial
neural network models to predict the Biot number (0.01 ≤ Bi ≤10) from the slope of the dimensionless
temperature ratio versus Fourier number. The developed models may offer significant advantages
when dealing with repetitive estimation of the heat transfer coefficient/Biot number.

INTRODUCTION

Estimation of the heat transfer coefficient falls under the inverse heat conduction problems
(IHCP) category. This approach requires experimental measurement of the transient temperatures
inside a body of known geometry at a specified location, usually at the center, and estimation of
transient temperatures at the same location by solving the governing heat conduction equations with
an assumed convective boundary condition (i.e., the Biot number, Bi). In doing so, Bi is varied
systematically to produce computed temperature-time histories matching close to experimentally
measured temperature histories. The procedure involved is iterative in nature and needs a long
computation time. Although this approach for estimating Bi is more computationally intensive than
conventional approaches, it has the advantages of simplicity and low expensive cost [1]. Several
algorithms based on finite difference and finite element methods have been developed for solving the
IHCP. Excellent discussion of the difficulties encountered in solving the IHCP and several solution
methods used can be found in Beck et al. [2], Alifanov [3] and Ozisik and Orlande [4].
Artificial neural network (ANN) is a potent computer model that learns from examples through
iterations without requiring prior knowledge of the relationships of the process parameters. ANN is
also capable of dealing with uncertainties, noisy data, and nonlinear relationships. The salient feature
of ANNs that make them attractive for many different applications is their ability to learn and
generalize the relationship in complex data sets. The objective of the present study was to devise a
single and direct procedure for estimating the heat transfer coefficient from the numerically/analytical
solution generated temperature field in two dimensional geometries (finite cylinder and rectangular
bar) and three dimensional geometry (cube) using ANN as a means to avoid the need for a time-
consuming, iterative solution. This procedure was accomplished using the Finite Element Method and
a finite element based computer program FIDAP to generate transient temperatures at the center of
the given geometry. This temperature-time data values was then used in the development of ANN
models.
The problem considered in this work has relevance in food processing operations. For
examples transient heat transfer analysis during drying, frying and freezing of fruits, vegetables and
meats, sterilization of particulate liquids in continuous systems (aseptic processing), cooling of fresh
produce, and baking will require knowledge of heat transfer coefficients.

FORMULATION

The Direct Heat Conduction Problem (DHCP)

The problem considered here is transient heat conduction in an isotropic body exposed to a
forced flow of a viscous fluid. The thermophysical properties of the fluid and solid, as well as the heat
transfer coefficient at all faces of the geometry were assumed to be constant. The governing partial
differential equation of heat conduction in non-dimensional form is:
 ICEF9-2004
International Conference Food and Engineering

∂θ
∇ 2θ = (1)
∂Fo
The initial and boundary conditions that are imposed on Equation (1) are:

For Fo = 0; θ = 1 (2a)
∂θ
= − Bi θ at surface, Fo > 0 (2b)
∂n

where θ is the non-dimensional temperature, Fo is the Fourier number or dimensionless time and Bi is
the Biot number. The above equations were solved for a finite cylinder, an infinite bar with a
rectangular cross section, and a cube. The finite element based computer software FIDAP (Fluent
Inc., NH) was used to solve the conduction problem with a convective boundary condition. Since the
non-dimensional center temperature varied linearly with Fourier number when plotted on a semi-
logarithmic scale, the temperature profile could be characterized using the slope, S, of this curve. The
slope was obtained from calculated temperature histories at the geometric center for several Bi
values. The datasets were then used in the development of ANN models. The Biot number and the
corresponding slope data set for each geometry was divided into two groups. The first group was
used for training/testing of ANN models while the second group was used for validation of the ANN
model, chosen randomly from the original dataset (Table 1).

Analytical Solutions
With the advent of computer algebra packages all known analytical formulae [5] involving
solutions of nonlinear equations, differential equations by standard Laplace transforms, their
inversions, integration of Green-function representations, double-triple series can be reduced to
routines and brought to the desktop of engineers. For our specific case the separation of variables
calls for calculation of the product of two infinite sums from Carslaw and Yaeger [5].

Training of Artificial Neural Network Model

The feed forward network structure was used in this study [6]. Several ANN models were
trained and tested using the training data set. In the case of the inverse problem, the input layer
consisted of two neurons corresponded to each of the input parameters (slope, S, and geometric
ratio, Ν) while the output layer had one neuron representing the Biot number, Bi. In developing the
ANN model for the direct problem, Bi and S were switched. The number of hidden layers and the
neurons within each hidden layer can be varied based on the complexity of the problem and the data
set. In order to reduce the chances of memorization of the behavior among the data set (rather than
generalization), the number of hidden layers and neurons in these layers should be minimized [7]. In
our study, the number of hidden layers varied from one to two while the neurons in that layer were
varied from two to 10, in increments of two. This resulted in a total of 10 networks for each of the
geometries. The optimal configuration was based upon minimizing the difference between the ANN
predicted values and the desired outputs.
The commercial software package, Neural Works Professional II/Plus (Neural Ware,
Pittsburgh, PA), was employed in the study. The back-propagation algorithm was utilized for model
training. In order to train a model, several parameters including the learning rule, the transfer
function, the learning coefficient ratio, the random number seed, the error minimization algorithm, and
the number of learning cycles had to be specified. These parameters could be varied based on the
complexity of the problem. Given the lack of clear guidance in the literature concerning the selection
of the above parameters, a trial-and-error procedure must be followed. While some of the parameters
were kept constant during our study, others were varied to develop the optimum ANN configuration.
The parameters that were kept constant included the transfer function (the hyperbolic-tangent transfer
function); the learning rule (the normalized-cumulative delta-rule), the random number seed (257),
and the learning rate (0.9), momentum (0.6). The error-minimization process was achieved using the
gradient descent rule [6] while the number of training cycles was set at 200,000. All of the remaining
model parameters (as specified above) were kept constant throughout the training processes. Back-
propagation uses the supervised training technique where the network weights and biases are
initialized randomly at the beginning of the training phase.
The performance of various ANN configurations was compared using the mean relative error
(MRE) and the standard deviations in the relative (STDR) errors. The coefficient of determination, R2,
 ICEF9-2004
International Conference Food and Engineering

of the linear regression line between the predicted values from the neural network model and the
desired output was also used as a measure of performance.

RESULTS AND DISCUSSION

The Inverse Heat Conduction Problem

Finite cylinder: In the first attempt, the ANN models were trained using an original data set without
applying any transformation to the input and output parameters. The configuration of the ANN model
was varied, as discussed above. However, the performance of many ANN configurations was not very
satisfactory, since the MRE in the prediction of Bi always exceeded 75%. This was particularly true for
the prediction of Bi in the lower range (Bi = 0.01 to 1.0). An attempt was made to improve the results
by changing some of the neural network parameters such as transfer functions and learning rate.
However, this approach did not improve the predictive performance of the ANN models.
In principle, ANN models do not require any prior knowledge of the relationships between
dependent and independent variables. However, in some instances, transformation of the
independent and/or dependent variables is known to improve their predictive performance [7, 8]. A
plot of Bi versus S indicated an arctangent relationship between Bi and S [9, 10]. A plot of Bi vs S for
different l/a ratio of finite cylinder indicated tangent relationship between them. Analytical solutions of
the system of Equations 1-2 also showed a tangent relationship between Bi and one of the
parameters. Hence, both input and output parameters i.e. Bi, S and geometric ratio (Ν=l/a) were
transformed using the inverse tangent functions tan-1 Bi, tan-1 S and tan-1Ν before feeding to the ANN
model. This transformation led to a significant improvement in the prediction performance of all ANN
models. The optimal ANN configuration included eight neurons in each of the two hidden layers
(Table 2). The MRE for this optimal configuration was 4.4%, with a standard deviation of 14.7% (Table
2). Other trigonometric functions such as exponential transformation were also used but they did not
improve the prediction performance. The prediction errors (i.e. relative error) of an optimal network in
the higher range (0.05 < Bi < 10) and lower range of Bi (0.01 < Bi < 0.05) were 2.2 and 40%,
respectively. This is why the standard deviation in relative error was slightly higher than the mean
relative error.
One of the simplest ANN models with four neurons and one hidden layer also predicted Bi
with a very good accuracy (MRE < 8.5%) (Table 2). Considering the benefits of a non-iterative
procedure, an ANN model with four neurons and one hidden layer can be considered a very good
predictor. This particular model showed very good accuracy (MRE of 5.3%) for the prediction of Bi in
the range of Bi between 0.05 and 10.0. This model is recommended to users. The network weights
and coefficients associated with this ANN model are presented in the form of simple algebraic
equations in Appendix A. These equations can be used to predict Bi from the slope of experimentally
measured transient temperatures and geometric ratios (Ν=l/a or height/diameter) from 0.2 to 5.0 for
the finite cylinder.

Rectangular bar and Cube: ANN models for rectangular bars and cubes were developed using the
data that were transformed using arctangent functions. The prediction errors of ANN models for the
rectangular bar and the cube were lower compared to a finite cylinder. The optimal ANN configuration
for a rectangular bar included six neurons in each of the two hidden layers. The MRE for this optimal
configuration was 2.0%, with a standard deviation of 7.3%. While for the cube, an ANN model of eight
neurons in a single hidden layer was found to be optimal. The MRE for this configuration was less
than 1.5% (Table 2). The ANN models for the cube consisted only one input and one output variable
and hence the prediction accuracy of the ANN models was very good. The accuracy of simpler
models i.e. two neuron in single hidden layer for rectangular bar and cube was also very good
especially for Biot number in the range of 0.05 and 10. The network weights and coefficients
associated with the ANN models for rectangular and cube geometries are presented in the form of
simple algebraic equations in Appendices B and C.

Verification of ANN Models

The predictive performance of simpler ANN models (for inverse and direct problems)
presented in the appendices was validated using a data set (Table 1) that was not used in the initial
training of the ANN models. The ANN models for a finite cylinder, a rectangular bar and a cube
(appendices A, B and C) predicted Bi with a mean relative error of 8.7, 4.0 and 2.3%, respectively.
Once again the errors in predictive performance for Bi less than 0.05 were rather high (~100%).
Otherwise, the mean relative errors in prediction of Bi using ANN models were less than 5% in the
Biot number range between 0.05 and 10.0.
 ICEF9-2004
International Conference Food and Engineering

Experiments were carried to estimate heat transfer coefficients in different heating/cooling

systems such as in oven and freezer. Both conventional iterative procedure (i.e. using FIDAP) and the
ANN model developed were used to estimate convective heat transfer coefficient/Biot number from
experimentally obtained transient temperatures within the cube. Table 3 shows the values of heat
transfer coefficients/Biot numbers predicted using the ANN model and the FIDAP for different
experimental conditions. For most cases, the Bi predicted was very close to the Bi estimated using
FIDAP (error <4%). The mean relative error in the ANN-predicted Bi was 1.0% and the standard
deviation of relative error was 1.0%. This is well below the experimental error (~10%) observed in the
estimation of the heat transfer coefficients [10].

CONCLUSIONS

ANN models were presented to allow for the prediction of the convective heat transfer
coefficient at the surface of two and three-dimensional geometries from measurement of the
temperature-time history at the center point. The models were non-iterative, which yields results within
5% (for 0.05<Bi<10) of those obtained by iterative solution of the governing conduction equation.
Though analytical solutions to determine temperature in two and three dimensional regular
geometries subjected to convective heat transfer are available, estimation of the heat transfer
coefficient/Bi from know time temperature data still remains iterative in nature. The ANN models
presented here can easily be used without any elaborate programming.

ACKNOWLEDGMENTS

The author is pleased to acknowledge Dr. Anvar Kacimov and Professor M. F. A. Goosen for
stimulating discussions and critical evaluation of this manuscript.

NOTATIONS

2a side of cube, side of rectangular (m)

2b side of rectangular
Bi Biot number (h.a/k)
Fo Fourier number (αt/a2)
h Heat transfer coefficient (W/m2K)
k Thermal conductivity (W/mK)
2l Height of the cylinder (m)
2r Diameter of cylinder (m)
S Temperature-time slope
t Time (s)
T Temperature (K)
Ti Initial temperature (K)
Tf Fluid temperature (K)

Greek symbols
α Thermal diffusivity (m2/s)
θ Dimensionless temperature (Tf - T)/((Tf - Ti)
Ν Geometric ratio (l/a or b/a)

REFERENCES

1. Chantasiriwan, S. Inverse determination of steady state heat transfer coefficient, International

Communication in Heat and Mass Transfer, 27: 1155-1164, 2000.
2. Beck, J. V., Blackwell, B., St. Clair Jr., C. R. . Inverse Heat Conduction, John-Wiley-Interscience,
New York, 1985
3. Alifonov, O. M. Inverse Heat Transfer Problems, Springer Verlag, Berlin, Germany, 1994
4. Ozisik, M. N., Orlande, H. Inverse Heat Transfer, Fundamentals and Applications, Taylor and
Francis, New York, NY, 1999.
5. Carslaw, H.S., Jaeger, J.C. Conduction of Heat in Solids. London: Oxford University Press, 1959.
 ICEF9-2004
International Conference Food and Engineering

6. Hornik, K. Stinchombe, M., White, H. Multilayer feed forward network are universal approximators.
Neural Networsk 2: 359-366, 1989
7. Sablani, S. S., Shayya, W. H., Kacimov, A. Explicit calculation of the friction factor in pipeline flow
of Bingham plastic fluids: a neural network approach, Chemical Engineering and Sciences 58: 99-106,
2003
8. Porru, G., Aragonese, C. Baratti, R., Servida, A. Monitoring of a CO oxidation reactor through a
grey model-based EKF observer, Chemical Engineering Sciences, 55:331-338, 2000.
9. Sreekanth, S., Ramaswamy, H. S., Sablani, S. S., Prasher, S. O. A neural network approach for
inverse heat transfer problems. American Society of Mechanical Engineers, National Heat Transfer
Conference, Baltimore, MD, August 10-12, 1997.
10. Sablani, S. S. A neural network approach for non-iterative calculation of heat transfer coefficient in
fluid-particle systems, Chemical Engineering and Processing 40: 363-369, 2001.

APPENDIX A

C Direct estimation of Biot number, Bi from the height/radius (Ν=l/a) and slope (S) of
temperature ratio (on logarithm scale) versus Fourier number for finite cylinder

Y0=atan(Ν)
Y1=atan(S)
X2 = Y0 * (1.701) + (-1.336)
X3 = Y1 * (1.341) + (1.012)
C Estimating output of neurons in hidden layer
X4 = tanh((1.140) + (-0.606) * X2 + (-0.693) * X3)
X5 = tanh((-1.865) + (0.318) * X2 + (-1.894) * X3)
X6 = tanh((0.0487) + (0.833) * X2 + (-0.596) * X3)
X7 = tanh((0.105) + (-1.546) * X2 + (0.350) * X3)
C Estimating output of neuron in output layer
X8 = tanh((0.176) + (0.619) * X4 + (0.783) * X5 + (0.972) * X6 + (0.301) * X7)
Bi = tan(X8 * (1.218) + (0.741))

APPENDIX B

C Direct estimation of Biot number, Bi from the ratio of two sides, b/a (Ν) and slope (S)
of temperature ratio (on logarithm scale) versus Fourier number for rectangular bar

Y0 = atan(Ν)
Y1 = atan(S)
X2 = Y0 * (3.401) + (-1.671)
X3 = Y1 * (1.900) + (1.009)
C Estimating output of neurons in hidden layer
X4 = tanh((1.493) + (0.149) * X2 + (-1.053) * X3)
X5 = tanh((-0.168) + (-0.286) * X2 + (-0.788) * X3)
C Estimating output of neuron in output layer
X6 = tanh((-0.401) + (0.803) * X4 + (0.854) * X5)
Bi = tan(X6 * (1.218) + (0.741))

APPENDIX C

C Direct estimation of Biot number, Bi from the slope (S) of temperature ratio (on
logarithm scale) versus Fourier number for cube

Y=atan(S)
X2 = YI * (1.676) + (1.022)
C Estimating output of neurons in hidden layer
X3 = tanh((-0.354) + (0.444) * X2)
X4 = tanh((-1.700) + (-1.218) * X2)
C Estimating output of neuron in output layer
X5 = tanh((0.296) + (-1.185) * X3 + (0.884) * X4)
 ICEF9-2004
International Conference Food and Engineering

Bi = tan(X5 * 1.218 + 0.741)

Table 1. Variables used in generating dataset for different geometries

Geometry Geometric ratio # of Bi Number of cases in dataset

Total Test Validation

Finite cylinder l/a=0.2, 0.4, 0.6, 0.8, 85 765 660 105

1.0, 2.0, 3.0, 4.0, 5.0
Rectangular bar b/a=0.2, 0.25, 0.33, 0.4, 85 680 578 102
0.5, 0.6, 0.8, 1.0
Cube - 65 65 51 14

Table 2. Associated prediction errors of the Biot number, Bi, for different ANN
configurations after transformations of input and output data

# of Finite cylinder Rectangular geometry Cube

hidden
layers
and # MRE STDR R2 MRE STDR R2 MRE STDR R2
neurons (%) (%) (%)
in each
hidden
layer
1/2 26.4 71.3 0.937 4.13 7.43 0.983 2.16 4.55 0.999
1/4 8.40 21.5 0.984 3.26 7.77 0.995 2.03 4.54 0.999
1/6 7.69 25.4 0.995 4.70 16.2 0.995 1.61 1.68 0.998
1/8 7.58 26.0 0.994 2.98 10.2 0.996 1.39 1.55 0.999
1/10 6.59 18.9 0.993 3.11 9.58 0.997 1.79 3.04 0.998
2/2 25.6 56.6 0.907 7.18 15.2 0.981 3.38 9.22 0.999
2/4 8.44 26.8 0.992 4.69 10.9 0.996 2.95 7.53 0.999
2/6 6.62 14.9 0.996 2.01 7.31 0.998 2.08 4.45 0.999
2/8 4.38 14.7 0.996 2.20 6.75 0.998 2.38 5.52 0.999
2/10 7.08 20.1 0.994 4.17 9.85 0.997 2.15 3.43 0.999

Table 3. Biot number predicted using ANN model for cube and numerical method (FIDAP) under
different experimental conditions

System Fluid Side of Numerical method ANN Model (Appendix

cube* (FIDAP) A)
(cm) h (W/m2K) Bi h (W/m2K) Bi
Freezer Air, 1.4 56.4 1.07 56.4 1.07
-40oC 1.4 57.5 1.09 57.5 1.09
2.0 55.5 1.51 55.6 1.51
2.0 56.3 1.53 56.2 1.53
Convection Air, 70oC 1.4 278 5.27 282 5.35
Oven 1.4 282 5.35 285 5.40
2.0 271 7.35 262 7.10
2.0 274 7.42 265 7.17
*
Thermal conductivity = 0.369 W/mK, Thermal diffusivity = 1.51 x 10-7 m2/s
ICEF9-2004
International Conference Engineering and Food

SORPTION ISOTHERMS AND STATE DIAGRAM FOR EVALUATING STABILITY CRITERIA OF

ABALONE

S. S. Sablani1,2 *, S. Kasapis2, M. S. Rahman1,2, A. Al-Jabri1 and N. Al-Habsi1

1
Department of Bioresource and Agricultural Engineering
2
Department of Food Science and Nutrition
College of Agricultural and Marine Sciences, Sultan Qaboos University
P.O.Box-34, Al-Khod-123, Muscat, Sultanate of Oman
shyam@squ.edu.om

ABSTRACT

Water adsorption isotherms and the state diagram of abalone were developed to evaluate a
possible connection between two distinct stability criteria. The isotherms were measured at 23, 40 and
60oC using an isopiestic method. The state diagram was developed using freezing points, as derived
by the cooling curve method, and glass transition temperatures. Results indicate that there is a
considerable discrepancy in the temperature-related stability criteria predicted by the concepts of
water activity and the glass phenomenon.

Keywords: water activity; sorption isotherms; cooling curve; glass transition temperature
INTRODUCTION

The interaction of water with various ingredients determines the physical, chemical and
microbiological stability of food. The concept of water activity (aw) has been developed to provide a
reliable assessment of the microbial growth, lipid oxidation, non-enzymatic and enzymatic activities,
and the texture/mouthfeel of foods following manufacture [1]. In doing so, it is vital to establish a
relationship between water content and its activity measured at constant temperature. This is
achieved with the ‘water sorption isotherm’ [1]. Thus sorption isotherms are employed in process
design and control, such as in predicting the end-point of drying and optimizing ingredient selection in
food formulations [1, 2]. Furthermore, the heat of desorption, which is useful in assessing the energy
requirement for drying, can be estimated from sorption isotherms [2-4].
Recently, it has been argued that water activity is not sufficient to describe the secondary
processes of change-in-state in foodstuffs thus ushering in the concept of glass transition temperature
(Tg; [5]). Maximum utility of Tg is made in the state diagram which, in its simplest form, represents the
pattern of change in the state of a material as a function of increasing levels of solids [6]. Glass
transition temperatures were mainly recorded by differential scanning calorimetry (DSC). Recent
advances in microcomputer technology and system software allowed application of rheological
techniques to the investigation of vitrification phenomena in foods [7]. It is reported, and it is also our
experience, that dynamic mechanical techniques offer a sensitive probe in pinpointing glass transition
temperatures, as compared to DSC [8]. Compilation of isotherm data in the literature indicates that
there is some information on the physical parameters of seafood, namely: squid, fish flour, sardine,
and tuna meat [2, 4, 9-11]. However, there has been no attempt to assess the feasibility of developing
a link between the concepts of water activity and glass transition, which is the main thrust of the
present paper.
MATERIALS AND METHODS

Sample preparation
Fresh abalone was obtained from the Omani fish market (Salalah), iced and brought chilled
into the laboratory. The abalone was washed, frozen at -40oC for at least 48 hr and placed in an
automatically controlled freeze drier (VirTis SP Industries Company, New York, USA). The plate
temperature was set at -20oC with a vacuum of 800 mTorr (108 Pa) in the chamber while the
condensing plate temperature was set at -65oC. At the end of 72 hr drying, the moisture content was
about 4% (wet basis). Freeze-dried abalone was ground in a laboratory scale grinder (600 W Jaipan,
Mumbai, India) to form powder and samples were stored in an air-sealed container at 4oC for further
use. The water content and total solids were measured gravimetrically by drying samples in an air
convection drier at 105oC for at least 20 hr. Protein, fat, and ash were measured according to AOAC
(1990). Crude carbohydrate was estimated by difference. Five replicates were used for composition
analysis. Compositions were expressed on a wet basis (kg/100 kg sample).
ICEF9-2004
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Measurement and modeling of water activity

The water activity of abalone samples was determined using an isopiestic method [3]. Freeze
dried abalone samples were placed in open weighing bottles and stored in air-sealed glass jars while
maintaining equilibrium relative humidity with saturated salt solutions. The jars were placed in a
temperature controlled cabinet and maintained at a constant temperature of 23, 40 and 60oC. Details
of this method are given in Sablani et al. [10, 12]. The BET, GAB and Norrish equations were used for
modeling of the sorption isotherms of foods [11]. The net isosteric heat of sorption Qs (kJ/mol) was
determined from the Clausius-Clapeyron equation [2, 11].

Mechanical measurements
Rheological tests under low-amplitude oscillatory shear were performed using the Advanced
Rheometrics Expansion System (ARES), which is a controlled strain rheometer (Rheometric
Scientific, Piscataway, NJ, USA). ARES has an air-lubricated and essentially non-compliant force
rebalance transducer with the torque range being between 0.02 and 2000 g cm. For precise control of
sample temperature, an air convection oven was used which has a dual element heater/cooler with
counter-rotating air flow covering a wide temperature range (–60 to 130°C). This allowed recording of
the viscoelastic properties of abalone deep into the glassy state. In doing so, the parallel-plate
geometry was preferred with the diameter of the top plate being 5 mm. The measuring gap between
the plates was fixed at 3 mm. Samples were loaded onto the preheated platen of the rheometer at
room temperature and cooled at a scan rate of 1°C/min to –50°C. Heating runs to 90°C at the same
scan rate were interrupted periodically by frequency sweeps (0.1 to 100 rad/s).

Initial freezing point

The freezing points of freeze-dried abalone at different moisture contents were measured by
the cooling curve method [13]. Freeze-dried abalone samples were ground in a lab scale grinder to
form powder, homogenized with predetermined amount of distilled water and equilibrated for 24 hr in
air-sealed containers in refrigerator (4oC). The samples were filled in a stainless steel cylinder
(internal diameter, 2.2 cm; height, 4.5 cm; wall thickness, 1 mm), insulated at the top and bottom with
polystyrene foam and placed in a freezer set at –60oC (11, 13]. The initial freezing point and the end
point of freezing (maximal-freeze-concentration) Tm′ were determined from the cooling curve method
as developed by Rahman et al. [11]. The initial cooling rate was maintained at or below 1.5oC/min as
recommended earlier [13].

RESULTS AND DISCUSSION

Sorption Isotherm
The water content of fresh abalone was 76.6% (w.b.). The protein, fat, ash and crude
carbohydrate content were 13.2, 0.86, 0.88 and 8.46% (w.b.), respectively. As expected, the
equilibrium moisture content increased with increasing water activity. The constants of BET and GAB
equations are shown in Table 1. In BET, values of the monolayer moisture content of abalone was in
the range of 1.8 to 5.4% (d.b.) depending on temperature. This varied from 2.1 to 6.8% in the GAB
model. Results were in the range previously reported for fish flour (3.24 to 5.12% d.b.), sardines
(4.94% d.b.) and tuna meat (3.8 to 8.8%) [2, 10, 11]. The BET monolayer (Mb) is an effective method
for estimating the amount of bound water to specific polar sites in dehydrated food systems [1]. The
difference between BET and GAB (Mg) values are due to the nonlinear optimization techniques used
in the latter, which utilizes 3 parameters.
The net heat of sorption decreased from 29.2 to 1.2 kJ/mol as the moisture content increased
from 4.7 to 27.2% (d.b). Results are higher than those reported for fish flour (11.76 to 0.84 kJ/mol with
moisture content from 2 to 14%, d.b.), sardines (12.07 to 0.86 kJ/mol with moisture content from 2.76
to 37.5%, d.b) and tuna (13.54 to 0.90 kJ/mol with moisture content from 4.75 to 33.6%, d.b.) [2, 10,
11]. This indicates that water in abalone is strongly bound with the solid matrix compared to other fish
products. Data may be useful in the design of dryers and the estimation of the energy required for
evaporation of water from abalone.
ICEF9-2004
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Table 1. Model parameters of water adsorption isotherms of abalone at different temperature

Tempe BET GAB Norrish

-rature Mb B MRE Mg C K MRE E k MRE
(oC) (g/g dry (%) (g/g dry (%) (%)
matter) matter)
23 0.054 21.65 8.2 0.068 10.66 0.865 15.9 0.023 14.9 8.4
40 0.040 39.47 0.058 7.71 0.904 0.028 7.30
60 0.018 7.8x105 0.021 24.6 1.00 0.020 3.94
Combining the effect of temperature 0.075 9 x 10-7 0.796 7.7
in GAB Equations
Hc = 3.9x104 J/mol and HK = 149.5
J/mol

Mechanical measurements of vitrification phenomena

Many of the early investigations on the viscoelasticity of amorphous synthetic polymers and,
recently, on high-sugar polysaccharide or gelatin mixtures recorded the passage from the rubbery
plateau and the transition region to the glassy state [14, 15]. A notable feature of this work is an
extensive glass transition region covering 4 to 5 orders of magnitude where the viscous component of
the network is dominant (tan δ = G"/G' > 1). This allows application of the “synthetic polymer
approach”, which pinpoints the Tg at the conjunction of the free-volume driven transition and the
glassy state where the predictions of the reaction rate theory are more appropriate.
In contrast with the above findings, we observe that the transition region of dried foodstuffs is
not that clearly defined [13, 16). Thus the change in modulus is between one and two orders of
magnitude and the liquid-like response, which is the primary indication of glassy relaxation processes,
is substantially diminished (tan δ < 1). Clearly, drying produces tightly packed aggregates of reduced
molecular mobility, a result which diminishes the opportunity of applying the demanding synthetic
polymer approach to dried foodstuffs.
Nevertheless, headway can be made by considering a plot of the first derivative of shear
modulus as a function of the experimental temperature. The traces of G' and G" unveil three distinct
regions: i) a flat portion at temperatures above -10ºC which corresponds to the viscoelastic plateau in
a segment of the curve where dG/dT decreases rapidly to a minimum where the rate of increase in
modulus is accelerating and iii) the low temperature end where dG/dT levels off (G') or increases
rapidly (G") to match the decelerating rate of increase of viscoelasticity. The onset of the glassy state
is clearly demarcated at the low-temperature point of discontinuity in the first-derivative graph thus
defining the mechanical glass transition temperature (Tg = -28 ± 1ºC for abalone at 70% solids). The
glass transition temperature values at different solid content are listed in Table 2.

Freezing Point
Freezing point data of abalone as a function of solids content are given in Table 2. The
standard deviation of the freezing point increased with increasing solids content suggesting a higher
variability in experimental measurements. The pattern of freezing points was modeled by the
Clausias-Clapeyron equation in conjunction with an improved model based on the concept of bound
water.

State diagram
Figure 1 shows the state diagram of abalone meat incorporating the cooling and glass
transition curves. Curve AP represents the equilibrium between the solution and solids formed, and it
has a negative gradient showing the expected decrease in the freezing point with increasing
concentration of solids. Point P is shown as Tm′ in Figure 1 and its approximate value is –18oC at 68%
solids.
The intersection of the vertical extrapolation of the point P on the glass transition curve at
68% (point E) is identified as Tg′. At this stage, no water crystallizes to ice in concentrated
preparations of abalone and the system passes through the glass transition curve at Tg′, which is
about –44.3oC. Thus, the characteristic temperature of glass formation is lower than the point used to
denote the temperature of solvent (i.e. water) crystallization. The water content at point E is a good
estimate of the un-freezable water for abalone (Xw = 32%).
ICEF9-2004
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Table 2 Freezing point and glass transition temperatures of abalone

Xs TF T/m Xs Tg
o
(fraction) ( C) (oC) (fraction) (oC)
0.25 -0.9 (0.2) -18.1 (1.9) 0.70 -28
0.30 -1.2 0.755 -16
0.35 -1.9 0.80 -5
0.40 -2.8 (0.5) 0.855 6
0.45 -3.2 0.90 32
0.50 -4.3 0.95 88
0.55 -7.1 (1.0)
0.60 -8.9
0.62 -10.1
0.64 -14.1
0.66 -15.9
Note: average of 2 to 4 readings, values in the parentheses are standard deviation

Comparison of product stability criteria based on the concepts of water activity and glass
transition
Both water activity and glass transition have been used extensively in the literature to
evaluate the stability of a food product. The former argues that a product is most stable at its
monolayer moisture content, i.e. a water activity of about 0.2 [16]. The latter suggests that
formulations are stable at or below the corresponding glass transition temperature. We examined
closely the interrelationship of the two concepts and results are reproduced in Table 3 and Figure 1. It
is clear that the predictions of the glass transition model overestimate the stable temperatures range
at each level of solids. For instance, the sorption isotherm at 23°C indicates that dried abalone would
be stable at 94.6% solids (Point B in Figure 1). However, at the same level of solids, the glass
transition curve produces a Tg value of 73.5oC (point C in Figure 1). Moreover, from the glass
transition data in Table 3, abalone at 92.7% solids would be safe to store at 60oC or below whereas
sorption isotherms clearly point to a water activity of 0.66 at 60oC, which is too high for safe storage of
a food product. Finally, we do not fail to observe that at the experimental temperatures of sorption
isotherms the glass transition temperatures correspond to solid levels which focus on a water activity
value of 0.64 ± 0.02.

Table 3. Evaluating sorption isotherm and glass transition models

Sorption isotherm model Glass transition model

Temperature Solid Tg Tg Solid aw at
(oC) content at from glass (oC) content corresponding
0.2 aw transition (fraction) solid fraction
(fraction) model
(oC)
23 0.946 73.5 23 0.864 0.66
40 0.960 84.3 40 0.896 0.62
60 0.982 102.9 60 0.927 0.66
ICEF9-2004
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120
100
o
80 T g =73.5 C,
60 X s =0.946 C
40
B
Temperature (°C)

20
A aw=0.2,
0 T' m Xs =0.946

-20 P
o
-40 - 44.3 C
T' g (E) 68.3%
-60
-80
-100
-120
-140
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Solids (fraction)

Figure 1. State diagram of temperature vs. fraction of solids

obtained for abalone using freezing and glass transition curves

CONCLUSIONS

An attempt has been made to combine data of water activity and vitrification using well-
established criteria/requirements for product stability. Extensive work on the temperature dependence
of sorption isotherms and glass transitions for abalone indicates a gap in the way the two molecular
processes perceive stability at a molecular level. Surely, water activity relates to the equilibrium
condition that establishes a thermodynamic limit to a mechanism, whereas vitrification is at best a
kinetic equilibrium process at temperature below Tg. Nevertheless, the gap between the predictions of
the two approaches is staggering.
To account for this discrepancy, one should consider that vitrification reflects molecular
processes at best of up to 20% of the abalone matrix. It was discussed earlier that the mechanical
glass transition is limited as compared for amorphous synthetic and biological systems. In support of
this, we were unable to obtain discernable glass transition spectra using the standard technique of
modulated differential scanning calorimetry at various scan rates and annealing temperatures or
times.
It is intriguing to consider that systematic experimentation with samples bearing an increasing
amorphous character may unveil the whole picture of the relationship between the two approaches.
This should be facilitated by the plethora of results on water activity and glassy phenomena lying
scattered in the literature. In doing so, we should also derive a definitive answer as to the universality
or the product specific nature of the value of water activity (0.64 ± 0.02) at the corresponding glass
transition temperature.

REFERENCES

1. Rahman, M. S.; Labuza, T. P. Water activity and food preservation. In Handbook of Food
Preservation, eds. M. S. Rahman, Marcel Dekker, New York, pp. 339-382, 1999.

2. Labuza, T. P; Kaane, A.; Chen, J. Y. Effect of temperature on the moisture sorption isotherms and
water activity shift of two dehydrated foods. Journal of Food Science. 50: 385-391, 1985.
ICEF9-2004
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3. Spiess, W. E. L.; Wolf, W. Critical evaluation of methods to determine moisture sorption isotherms.
In Water Activity: Theory and Applications to Foods, eds. L. B. Rockland and L. R. Beuchat, Mercel
Dekker, New York, pp. 215-234, 1987.

4. Rahman, M. S. Food Properties Handbook. CRC Press, Boca Raton, FL, 1995

5. Slade, L.; Levine, H. Beyond water activity: Recent advances based on an alternative approach to
the assessment of food quality and safety. Critical Reviews in Food Science and Nutrition, 30:115-
360, 1991.

6. Roos, Y. H.; Karel, M. Applying state diagrams to food processing and development. Food
Technology, 45, 66-71, 1991.

7. Richardson, R. K.; Kasapis, S. Rheological methods in the characterisation of food biopolymers. In

Instrumental Methods in Food and Beverage Analysis, eds. D.L.B. Wetzel and G. Charalambous,
Elsevier, Amsterdam, pp. 1-48, 1998

8. Kasapis, S.; Al-Marhoobi, I.M.; Mitchell, J.R. Testing the validity of comparisons between the
rheological and the calorimetric glass transition temperatures. Carbohydrate Research. 338, 787-794,
2003

9. Rahman, M. S.; Chen, X. D.; Driscoll, R. H. Desorption isotherm of squid meat at 15oC. 23rd
Australian Chemical Engineering Conference Proceedings, Volume 3, Adelaide, South Australia, p.
139-142, 1995

10. Sablani, S. S.; Myhara, R. M.; Mahgoub, Al-Attabi; Z. H.; Al-Mugheiry, M. M. Water sorption
isotherms of freeze dried fish sardines. Drying Technology, 19(3): 671-678, 2001

11. Rahman, M. S.; Sablani, S. S.; Al-Ruziki, M. H.; Guizani, N. Water sorption isotherms of freeze-
dried tuna meet, ASAE Transaction, 45: 767-772, 2002

12. Sablani, S. S.; Rahman, M. S.; Labuza, T. P. Measurement of water activity using isopiestic
method. In Current Protocols in Food Analytical Chemistry Vol 1. editor-in-chief R. E. Wrolstad, John-
Wiley & Sons, Inc. pp. A2.3.1-A2.3.10, 2001

13. Rahman, M.S.; Kasapis, S.; Guizani, N.; Al-Amri, O. S. State diagram of tuna meat: freezing curve
and glass transition. Journal of Food Engineering, 57, 321-326, 2003

14. Ninomiya, K.; Ferry, J. D. Viscoelastic properties of polyvinyl acetates. I. Creep studies of
fractions. Journal of Physical Chemistry, 67, 2292-2296, 1963.

15. Kasapis, S. Advanced topics in the application of the WLF/free volume theory to high
sugar/biopolymer mixtures: A review. Food Hydrocolloids. 15, 631-641, 2001.

16. Rockland, L.B.; Nishi, S.K. Influence of water activity on food product quality and stability. Food
Technology. 34: 42-51, 1980.
ICEF 9 - 2004
International Congress on Engineering and Food

Effect of the characteristic behavior of roaster blowers

on coffee bean heating in batch roasters

Henry Schwartzberg [1]

[1] University of Massachusetts, Amherst MA 01003 USA
schwartzberg@foodsci.umass.edu

Abstract: In coffee roasters, the temperature of gas leaving the roasting chamber progressively rises
as roasting progresses. Gas mass-flow rates provided by blowers for most coffee roasters
progressively decrease because of the temperature rise. Methods for calculating how the temperature
rise affects the gas mass-flow rate and roasting are provided

Introduction: In most batch coffee roasters, a centrifugal blower draws hot gas through the roasting
chamber (roaster for short) and then cause it circulate through the rest of the roasting system. Figure
1 depicts the flow arrangement used when gas leaving the roaster recirculates, as it does in most

roaster gas stack

green
beans roaster gas blower
h bin g
i cyclone
2
e
t 1
roasted beans roasting chamber d bypass line
discharge gate

gas to roaster chaff

discharged gas 4

burner b
fuel gas
furnace
a air
3 air blower

Figure 1 Gas flow in a roaster system where gas recycling is used

large-scale roasters. Gas from the roaster first passes through the blower and a cyclone and then
enters a furnace, where it mixes with hot gas flowing out of the burner. The hot mixture leaving the
furnace splits into two streams. One stream flows into the roaster. The second flows out of the system
through a stack or an afterburner and stack. Black arrows show the direction of gas flow.

Mass-Flow Rates: The mass of gas in the system changes only moderately during a roast and is
very much smaller than the total mass of gas that flows through the system. Therefore, F, the mass
flow rate of hot gas entering the system through the burner, equals the mass flow rate of gas leaving
through the stack. G is the mass flow rate of gas through the roaster, blower and cyclone.
The mass flow rate of gas through the furnace is G + F. Hot gas enters the roaster at temperature
Tgi, transfers heat to the roasting beans and leaves at temperature Tgo. The roaster discharge gas
ICEF 9 - 2004
International Congress on Engineering and Food

then passes through the blower and cyclone and enters the furnace through a side port. In the
furnace, roaster gas mixes with products of combustion emanating from the burner at temperature Th,
producing mixed gas whose temperature is Tgi. In the blower, cyclone and ductwork between the gas
discharge end of the roaster and the side port of the furnace, the gas temperature is Tgo. In the
furnace and ductwork between the furnace and gas inlet to the roaster, the gas temperature is Tgi; and
in the roaster, the average gas temperature, Tga = (Tgi+ Tgo)/2.

Heat Transfer: Roaster gas transfers heat both to the roasting beans and roaster hardware. The
hardware transfers much of the heat it absorbs to the beans. Eq (1) describes the change in gas
temperature across the roasting chamber when the net rate of heat absorption by roaster hardware is
negligibly small [1].

(Tgi - Tgo) = (Tgi - Tb )[1 - exp (- UA/GCg )] (1)

Tb is the temperature of the beans, U is the effective overall heat-transfer coefficient between the gas
and beans and Cg is the heat capacity of the gas. Eq (2) describes the time rate of change of Tb if Eq
(1) applies [1].

dTb /dt = [GCg (Tgi - Tgo) + Rd {Λ(dX/dt) + Qr }]/[Rd (1 + X )Cb ] (2)

where Rd is the dry mass beans, X is their dry-basis moisture content, Cb their heat capacity, Λ is the
latent heat of vaporization of water from the beans, i.e. 2812 kJ/kg, Cg averages 1.48 (kJ/kg)/K over
the gas temperature range of interest. Qr the rate of exothermic heat generation, and -dX/dt the rate of
evaporation are provided by correlations presented in an earlier paper [1].
Eq (3) describes how G and F affect Tgi.

Tgi = (FTb + GTgo)/ ( G + F ) (3)

Thus G profoundly affects gas temperatures in the system and the rate of bean heating. G, in turn, is
affected by Tgo and TgI .

Blower Characteristics: Manufacturers describe blower performance in terms of how ∆P bs, the
pressure rise the blower provides for air at standard conditions (288.7 K and 101.3 kPa in the US),
depends on V, the volumetric flow rate of air through the blower. Over the operating range of interest,
∆Pbs is accurately predicted by the quadratic

∆Pbs = c + bV - aV
2
(4)

where c, b and a are best-fit parameters for the blower involved. ∆Pb, the pressure rise the blower
provides during roaster operation expressed in terms of G and Tgo is given by

∆Pb = (MgTs / MaTgo) [ c + bGTgo /L - a G Tgo /L ]

2 2 2
(5)

where Mg and Ma respectively are the average molecular weight of roaster gas and air, Ts is the
standard temperature, i.e. = 288.7 K, Tgo is also in degrees K, L = PMg /Rg. P is the absolute pressure.
3
Rg, the gas law constant, = 8.314 kPa(m )/[(kg mole)K]. In roasters local P usually do not deviate from
atmospheric pressure by more than 2%. Therefore it is assumed that P = 101.3 kPa. For a roaster
3
using a typical U.S. natural gas as fuel and Th = 1811 K, Mg = 27.99, L = 341.0 K(kg/m ), Mg/Ma =
0.966 and MgTs/Ma = 278.9 K.

Flow Pressure Drop: Flow pressure drops across sections of the roaster system between point 1 and
point 3 moving in the direction of gas flow are given by

∆Pj = Nj ρ gj vj = Nj G / [A j ρ gj] = Nj G Tgj / [A j L] = Kj Tgj G

2 2 2 2 2 2
(6)
ICEF 9 - 2004
International Congress on Engineering and Food

where vj is the linear gas velocity across area Aj in section j, ρgj is the gas density in section j, Nj, the
number of velocity heads = ∆P j /(ρgivj ) is a parameter characterizing the flow resistance of section j,
2
2
Kj = Nj /LAj and Tgj is the gas temperature in section j. Eq (6) also applies in the furnace section, i.e.
2 2
between point 3 and 4, and the duct between point 4 and point 1, but with (G + F) replacing G .
Thus, the total pressure drop in the system is

∆PT = G [KRTga + KcTgo + KFTgi(1 + F/G) + KITgi ]

2 2
(7)

where KR is the K between points 1 and 2, Kc is the K between points 2 and 3, KF is the K between
points 3 and 4 and KI is the K between points 4 and 1. ∆PT = ∆Pb. Thus the right-hand side of Eq (5)
can be equated to the right-hand side of Eq (7), forming a quadratic that can be solved for G if the a,
b, c, the various Kj, Tgi and Tgo are known. The Kj can be estimated from the layout and dimensions of
the duct and equipment or can be determined from pressure drop measurement obtained during tests
carried out while the blower circulates cold air through the roaster system with the roaster loaded.
Data from the blower manufacturer can be used to obtain a, b and c. Tgo can be obtained from Eq (1)
if Tgi, Tb and UA/GCg are known. Finding Tgi may require use of Eq (3) and Tgo. Eqs (1), (2), (3) and
Eqs (5) and (7) combined are highly interrelated and can be readily solved only through use of
machine computation. Computation may be further complicated by how G affects U. When the relative
velocity of beans with respect to the gas is mainly determined by gravitational acceleration and bean
motion imparted by moved parts of the roaster G affects U only slightly, but when the relative velocity
-0.4 -0.5
is linearly proportional to the gas flow rate UA/GCg will be proportional to G or G .

Computer Program: A computer program written in Quick Basic was used to determine how G, Tb
and Tgo vary with time t during a roast when Tbo, the initial Tb,, is known; Tgi is maintained constant by
feedback control that regulates F; UA/GCg is known at Gr, a reference value of G, and is inversely
proportional to G; and a, b, c, the various Kj and the initial weight and as-is moisture content of the
beans are known. Functions used in an earlier paper [1] were used in the program to determine Cb,
Qr and (dX/dt) for use in Eq (2), i.e. Cb(1+X) = 1.099 + 0.007Tb + 5.0X;
7 2 2
- dX/dt = (1.023x10 X / dp ) exp [ - 6,667/ Tb ] (8)

where dp is the bean diameter in mm; and

Qr = AR [(Het - He)/Het ] exp [-Ha /RgTb] (9)

where Ha is the energy of activation and AR in (kJ/kg dry coffee)/sec is the Arrhenius equation
prefactor times the amount of heat generated per unit amount of reaction, He is the amount of heat
o
already generated, Het is the maximum amount of heat that can be generated, Ha /Rg = 5,500 K, AR =
11600 (kJ/kg dry coffee)/s and Het = 232 kJ/kg.

Control Adjustments: In order to provide better control of roasting, G or Tgi is usually reduced near
the end of the roast. A reduction occurs when, Ta, the measured bean temperature, reaches a set
value. Then, a second reduction occurs when, Ta reaches a higher set value. In this paper the
reductions occur when Tb, rather than Ta, reaches set values. In the roaster being modeled, partial
closing of damper g (see Fig.1) is used to reduce G. The first reduction occurs when Tb reaches 454.2
K; and the second when Tb reaches 492.2 K. Partially closing damper g causes Kc to increase.
Therefore partial closing damper g was modeled by multiplying the original value of Kc by 1.5 for the
first G reduction and by 1.91 for the second G reduction.

Program Steps: The steps used in carrying out the program are described below.

1) Known constants and initial values are read in or are listed in program statements. These include:
a, b, c, NR, Nc, NF, NI, AR, Ac, AF, AI, Tbo, Tgi, Th, Tf, Λ, L, Cg, MgTs/Ma, Gi; (UA/GCg)o, the value of
UA/GCg when G = Gr, R and Xa, the initial weight and as-is moisture content of the beans,and
parameters involved in determining Qr and dX/dt
2) Rd and Xo are calculated from R and Xa. Rd = R (1 - Xa), Xo = Xa /(1 - Xa)
3) Initialize: Tb = Tbo; X = Xo; He = 0, Gi = Gr, G = Gi., t = 0
ICEF 9 - 2004
International Congress on Engineering and Food

4) Determine the numerical values of constant elements used in Eq (5), i.e. cMgTs/Ma, bMgTs/(LMa),
2
aMgTs/(L Ma), KR, Kco, KF, and KI
5) UA/GCg = (UA/GCg)o(Gr /G).
6) Determine Tgo from Eq (1), Tb, Tgi and UA/GCg.
2
7) Use Tgo to determine cMgTs /(MaTgo) and aMgTsTgo/(L Ma) in Eq (5). Note: bMgTs /(LMa) the
coefficient of G in Eq (5) does not depend on Tgo.
8) Use Tgi, Tgo and Th to determine F/G from Eq (3) rearranged
9) Use Tgo, Tgi, (1 + F/G) and the constants KR, Kc, KF, KI to determine the terms KRTga, KcTgo,
2
KF(1 + F/G) Tgi and KITgi used in Eq (7)
10) If Tb > 454.2 and < 492.2, KcTgo = 1.5KcTgo .
11) If Tb > 492.2, KcTgo = 1.91KcTgo .
2
12) Determine the constant term and coefficients of G and G in Eqs (5) and (7) combined. The
2
constant term is cMgTs /(MaTgo), the G coefficient is bMgTs /(LMa) and the G coefficient is
2 2
- (aMgTsTgo/L Ma) + KRTga + KcTgo + KF (1 + F/G) Tgi + KITgi.
13) Solve Eqs (5) and (7) combined (a quadratic) to determine G.
If this is the t = 0 step in the loop where G, X, Tgo and Tb are determined as t increases, and the
determined G does not = Gi, let G = the determined G and return to step (5).
14) Substitute X and Tb in the moisture-loss function, Eq (8), to determine -dX/dt.
15) Substitute Tb and He in the exothermic-heating function, Eq (9), to determine Qr.
16) Determine Cb (1+X) = 1.099 + 0.007Tb + 5.0X
17) Substitute G, Cg, Cb (1+X), Tgi, Tgo, Rd, Qr, Λ, and dX/dt in Eq (3) to determine dTb/dt.
18) Let Tb = Tb + (dTb/dt)∆t. ∆t is a small constant time step, e.g. 1 sec.
19) Let t = n∆t where n is the number of time steps taken
20) Let X = X + (dX/dt)∆t.
21) Let He = He + Qr∆t
22) Print out G, Tb, Tgo, X and He when t = 30 sec, 60 sec, 90 sec, etc.
23) If Tb is greater than or equal to Tf, print out final G, Tb, Tgo, X and He and stop. If not, go back to
step 5) and repeat steps 5) through 23).

Parameters: The program was solved for parameter values valid for a commercial roaster: Tgi =
774.4 K, Th = 1811 K, Tbo = 293.2 K, Tf = 532 K, Xa = 0.12, R = 240 kg, Cg = 1.481 (kJ/kg)K, dp = 6
mm, (UA/GCg)o = 1.7, Gr = 1.0569 kg/sec, Λ = 2790 kJ/kg, a = 350.9, b = 644.5, c = 3488.1, Nc =
2 2
5.725, NR = 0.75, NF = 0.95, NI = 0.575, 1/Aj = 187.8 (1/m ) for j, and the previously listed values of
parameters involved in determining Qr and dX/dt.
2
Effects of varying blower speed were modeled by leaving a unchanged and multiplying c by f and
b by f, where f is the ratio of the current blower speed to the normal blower speed. The program was
first run with f = 1. Then f was subjected to trial and error adjustment until Tb reached Tf in 720
seconds.
o
Results: Fig. 2 depicts the results obtained in the form of Tb, Tgo (in C) and G plotted versus t. The
step decreases in G can be readily discerned, but G also decreases gradually as Tgo increases. Tgo
decreases when step decreases in G occur, but to a smaller extent. In contrast, Tb varies smoothly.
Step decreases in G, by themselves, increase roasting time and increase He, the total exothermic
heat generation; but when blower speed is increased to prevent roasting time from increasing, the He
increase diminishes. Tb versus t profiles were computed for roasts with and without G step decreases
with roasting time kept at 720 seconds in each case by blower speed adjustment. With G step
decreases, Tb was 2.8 to3.7 K degrees higher between 150 and 390 seconds than when step
decreases were not used. The Tb increase was smaller at t nearer to 0 seconds and 720 seconds.
When larger G step decreases are used, the Tb increases in the 150 to 390 second t range
become larger. A Tb versus t profile was calculated for a 720 second roast with normal G decrease
steps but where G did not otherwise decrease as time increased. That profile was similar to the Tb
versus t profile shown in Fig. 2, but Tb was lower: 4.0 to 4.9 K degrees lower at t between 90 and 240
seconds and less depressed at other t.

Effects of Roasting Speed: The program was used to assess effects of roasting speed on roasting
behavior. If the same final Tb, is used, exothermic heat generation, He, decreases as roasting speed
ICEF 9 - 2004
International Congress on Engineering and Food

increases and roasting time decreases. If He is an indicator of roast flavor generation, higher final Tb
probably should be used when faster roasting is used.
.

Figure 2 Tb, Tgo and G versus elapsed roasting time during batch roasting of coffee beans

Program Variations: It is simple to change the program to account for UA/GCg being proportional to
0.4 0.5
(1/G) or (1/G) . With more complex changes, the program can be used for cases where Tgi is not
constant and F is first kept constant, then reduced when Ta exceeds a set values, and reduced again
when Ta exceeds a higher set value. Other methods are also used to reduce bean heating rates at
late stages of roasting, e.g. bypass valve i may be partly opened to reduce gas flow through the
roaster. More extensive program modification is required to account for use of such methods.
Nevertheless, in each case, Tgo progressively increases and G progressively decreases as roasting
progresses

References: 1. Schwartzberg H.G. Modeling bean heating during batch roasting of coffee beans,
st
“Engineering and food for the 21 century”, (Eds. J. Welti-Chanes, G.V. Barbosa-Canovas, J.M.
Aguilera) CRC Press, Boca Raton, Florida, Chapter 52, 871-890, 2002.
ICEF9 – 2004
International Conference Engineering and Food

Consumer-oriented Design of Sesame-Flavored Dressing

Using Gas Chromatography/Olfactometry and Artificial Neural Network

Tomizawa A(1), Ikeda G(1), Imayoshi Y(2), Iwabuchi H(2), Hinata T(3) and Sagara Y(1)

(1) Department of Global Agricultural Sciences, The University of Tokyo

Yayoi 1-1-1, Bunkyo-ku, Tokyo, Japan 113-8657
aa26291@mail.ecc.u-tokyo.ac.jp
(2) San-Ei Gen F.F.I, Incorporated
1-1-11, Sanwa-cho, Toyonaka, Osaka 561-8588
(3) Mitsukan Co., Ltd.
2-6, Nakamura-cho, Handa-shi, Aichi 475-8585

ABSTRACT
Gas chromatography/olfactometry (GC/O) and an artificial neural network (ANN) were applied to
design a new product of sesame-flavored dressing conforming the consumer preference. The GC/O
was used to evaluate the intensity and character of each flavor constituent. The non-linear relationships
between the characteristics of flavor and scores of sensory evaluation were analyzed by applying the
ANN. The applied procedures were demonstrated to be useful to design a novel flavored product.

KEYWORDS: artificial neural network, gas chromatography/olfactometry, kansei engineering,

sesame-flavored dressing, sensory evaluation

INTRODUCTION
The concepts of “Kansei Engineering” presented by Nagamachi about 30 years ago are now
providing the powerful tools to consumer-oriented technologies for designing and producing new
industrial products1) , and its specified paradigm and methodology related to foods has been proposed
recently as “Food Kansei Engineering” by Sagara2), coauthor of this paper. Since the Japanese word
“kansei” includes various interpretations, there is no exact equivalent in European languages. Thus it is
briefly defined as: 1) sensing abilities of sensory organs which involve perception in response to
external stimuli, 2) dynamics of emotions elicited by senses and 3) sensory desires that are considered
to be controlled by reason and the mind. Thus kansei can be proposed for adoption into the English
language. In Japan, kansei has become a keyword in research by professional societies in various
fields. Kansei engineering is science and technology that pursues the methods and systems based on
the quantified preference of each consumer. Concerning kansei related to food, measures are needed
to grade food preference and dislikes3). Thus it is desirable to develop a system for scientific
assessment and quantitation that has high reproducibility and objectivity. This should provide
innovative stimuli to new food development, product management and marketing strategies in the food
ICEF9 – 2004
International Conference Engineering and Food

industry.
In order to construct such a system, the physicochemical attributes of a food must be related to
psychological factors regarding eating habits. The former include the appearance, taste, flavor, texture,
temperature and sounds generated when being consumed. We should clarify the inter-relations
between such physical attributes and psychological factors, and thus finally quantify the kansei of
human beings towards foods3).
Gas chromatography/olfactometry (GC/O) has function to combine olfactometry or the use of
human detectors to assess odor activity in defined air streams with the gas chromatographic separation
of volatiles4). The method is useful for evaluating the intensity and character of each flavor constituent
contained in the sample. This methodology appeared as a useful tool in food kansei engineering and
was attempted to apply for the development of a sesame-flavored dressing based on consumer
acceptance. It is popular in Japan, and the determination of its flavor-active compound is desired for
designing a new product.
The objectives of the study are to elucidate the flavor constituents that contribute to consumer
preference, and to determine the optimum compounding ratio of ingredients based on the information
obtained from sensory evaluations.

MATERIALS AND METHODS

Test Samples
Seven commercially available sesame-flavored dressings and sixteen trial samples were prepared
as the test samples for instrumental and sensory analyses. The sesame-flavored dressings are
emulsified and composed of edible vegetable oil, vinegar, soy sauce, sesame, egg yolk, onion, salt,
sugar, xanthan gum and artificial flavors.

Sampling of Volatile Compounds

Both simultaneous steam distillation extraction (SDE) and headspace solid-phase microextraction
(SPME) methods were employed for sampling the volatile compounds in the test samples. The SDE
method is known to collect high-molecular-mass and low volatility compounds, while headspace-SPME
method to collect compounds of high volatility, representing the top-note of the sample5). For both
methods, the volatile compounds were prepared in three sets of dilutions by a constant factor of 3 for
the former and 2 for the latter. The former was prepared at the concentration ratio of 1, 1/3 and 1/9 by
dilution, while the latter by adjusting the SPME fiber length to be fully, approximately half and one-forth
exposed to the headspace gas.

Gas Chromatography/Olfactometry (GC/O)

TM
An extract from the test samples was injected into GC/O (Charm Analysis ) that has been
modified by DATU, Inc., Geneva, NY. Sniffer, an expert sensory technician, sat at the olfactometer
outlet and recorded what flavor was smelled in the stream of purified and humidified air at a linear
velocity. The sniffer recorded the time length and the character of each flavor being smelled. To
ICEF9 – 2004
International Conference Engineering and Food

characterize each flavor, 15 odor descriptors were extracted from Table 1. Odor descriptors
preliminary session (Table 1). For each compound with consistent
1. acidic/rancid
retention index (RI) and odor descriptor, odor intensity was calculated
2. burnt/smoky
as a charm value (CV) by integrating the time length being detected. 3. caramel
4. green/herb
CV = ∫ peak F n −1 di 5. fermented
6. metallic
where, F: dilution factor, n: number of dilution, di: RIend-RIbegin 7. mustard
8. nutty
9. oily
Sensory evaluation 10. roast/cooked
Eighteen trained panelists and 3 flavorists were employed for 11. sesame
12. soy sauce
sensory evaluation. The sensory 7-points descriptive analysis was 13. sulfur
used to profile the aroma, odor, taste and preference of the samples. 14. sweet
15. phenolic
The samples were described and discriminated by 44 sensory
attributes. The aroma was evaluated for the smell of the samples before they were put into the mouth,
and the odor, taste as well as preference were evaluated for the retronasal smell and taste in the mouth.
All samples were served in wine glasses with lid, and the orders of serving were completely
randomized.

PCA Analysis
Principal component analysis (PCA) was carried out on sensory data using the computer software
JMP 5 (SAS Institute, Inc.) in order to elucidate the sensory attribute for sesame-flavored dressings.

Kansei Transforming Model

Fig.1 shows the kansei transforming model proposed to analyze the preference for
sesame-flavored dressings. This model stands on the assumptions that volatile and non-volatile

sesame-flavored
constituent dressing
volatile aroma odor non-volatile
compound compound
【GC/O data】 【amino acid, etc.】

ANN ANN
perception
sensory
attributes
【sensory data】

MRA
preference
preference
【sensory data】
Fig.1 Kansei transformation model
ICEF9 – 2004
International Conference Engineering and Food

compounds are each converted to sensory attributes, and then they affect the preference scores. The
effects from cognition were ignored by giving no information such as price and brand. The artificial
neural network (ANN) analysis was carried out to investigate the quantitative relationships among the
compounds and the sensory attributes. The ANN model is usually used as an analytic tool to
approximate arbitrary non-linear functions, expressing the relationship between two groups of data
sets.

RESULTS AND DISCUSSION

Sensory Attributes
Factors for sesame-flavored dressings were extracted and interpreted through PCA. The first
factor is a characteristic feeling expressed in the term of “roasted sesame”, second “spice, citrus and
soy sauce”, third “residual”, fourth “mellow”, fifth “lightness”, sixth “caramel” and seventh “acid and
stimulus”. The correlations of these factors against preference were examined by multi regression
analysis (MRA), and the first, third and forth factors that satisfied p≦0.001 were employed as key
sensory attributes for sesame-flavored dressings.

Correlations between Compounds and Preference

Fig.2 shows the correlation coefficients between odor strength CV summed up by each odor
descriptor against preference scores for the data obtained by both headspace-SPME and SDE
methods. The correlation coefficients for non-detected odor descriptors are not shown in this figure. As
shown in the figure, the volatile compounds collected by headspace-SPME showed mainly positive
correlations to preference, while those collected by SDE showed negative correlations.

0.8

0.6
correlation coefficient

0.4

0.2
nu om

e
t/s d

ca ky

in

odor descriptor
el

oy ed

0
i

13 uce
bu anc

ic
o
ee
o

no eet
hr

14 ur

ed
k
m

tty

ly
ra

oo
gr

sa
us

f
/r

ul
oi

/m
w
ic

s/

t/c
/m

.s
9.

.s
rn

SPME data
id

tru

lic
8.
3.

as

-0.2
ac

lic

.s
ci

. ro
al

12
2.
1.

SDE data
4.

he
et

10

.p
m

15
6.

-0.4

-0.6

-0.8

-1

Fig.2 Correlation coefficients of odor strengths against preference scores for volatile compounds
collected by headspace-SPME and SDE methods
ICEF9 – 2004
International Conference Engineering and Food

Fig.3 and Fig.4 show the estimated aroma ratio of volatile compounds in terms of CV, for the data
obtained by both headspace-SPME and SDE methods. The data of volatile compounds collected by
SDE method indicates that the mixture of weakly smelling compounds could obtain the optimum aroma
ratio. However, this behavior of results is considered to be unnatural because of higher preference
obtained by less compounds. Since sensory score obtained also support this consideration, indicating
positive correlations between preference and the strengths of aroma and odor, the data by
headspace-SPME method were considered appropriate for identifying the compounds affecting
preference. Thus several compounds collected by headspace-SPME method having higher correlation
against preference were chosen as affecting compounds on preference.

1. acidic/rancid
phenolic/medicine 15. 1400
1200 2. burnt/smoky
1000
sweet 14. 800 3. caramel
600
400
200
sulfur 13. 0 4. citrus/green

soy sauce 12. 6. metallic/mushroom

8. nutty adjustable area

10. roast/cooked
9. oily optimum mixture

Fig.3 Estimated optimum aroma ratio of volatile compounds by SDE method

1. acidic/rancid
2000
phenolic/medicine 15. 1800 2 .burnt/smoky
1600
1400
1200
sweet 14. 1000
800 3. caramel
600
400
200
0
sulfur 13. 4. citrus/green

soy sauce 12. 6. metallic/mushroom

8. nutty adjustable area

10. roast/cooked
optimum mixture

Fig.4 Estimated optimum aroma ratio of volatile compounds by headspace-SPME method

ICEF9 – 2004
International Conference Engineering and Food

Fig.5 shows the difference in preference scored for control and the newly designed sample by
adding some identified compounds. The designed sample exhibits higher scores of preferences for
both aroma and odor, and the identified compounds were confirmed to increase the preference scores.

5
preference

2
aroma odor
Fig.5 Difference in preference scores for control and designed sample by adding some identified
compounds (Data=Mean±SE, n=14) ( :control, :designed sample)

CONCLUSIONS
Sensory attributes that contribute to consumer preference were elucidated for the sesame-flavored
dressings, and the optimum compounding ratio of ingredients was determined based on the
characteristic preference of consumer. It was demonstrated that the procedure presented in this study
was useful to design a novel flavored product.

REFERENCES
1.Nagamachi M. Kansei engineering as a powerful consumer-oriented technology for product
development. Applied Ergonomics, 33, 3, 289-94, 2002

2.Sagara Y. “KANSEI” engineering for investigating food preference. Jpn. J. Taste Smell Res. 8,
153-159, 2001

3.Ikeda G., Hioki M., Nagai H. and Sagara Y. A study of designing techniques to incorporate
consumers’ ‘kansei’ into tea beverage (1). Jpn. J. Taste Smell Res. 9, 553-556, 2002

4.Acree T, Bioassays for flavor. In Flavor Science (Acree T. and Teranishi R. eds), American Chemical
Society, Washington DC, 1993

5.Jibao C., Baizhan L. and Qingde S. Comparison of simultaneous distillation extraction and
solid-phase microextraction for the determination of volatile flavor components. J. Chromatography A,
930, 1-7, 2001
 ICEF9 – 2004
International Conference Engineering and Food

Thermo-mechanical modeling during freezing

Tréméac B.(1), Lefeuve J.(2) Hayert M.(3) ,Le Bail A.(4) and Moes N. (5)

(1,3,4) UMR GEPEA (UA CNRS 6144 – SPI), ENITIAA, BP 82225, 44322 Nantes cedex 03, France
(2,5) Laboratoire de Mécanique des Matériaux, Ecole Centrale de Nantes, 44321 Nantes, France
(1) tremeac@enitiaa-nantes.fr;(2) jessy.lefeuve@ec-nantes.fr ;(3) hayert@enitiaa-nantes.fr
(4) lebail@enitiaa-nantes.fr;(5) nicolas.moes@ec-nantes.fr

ABSTRACT
Thermal stresses caused by the volume expansion of water during the freezing process are often
neglected in term of impact on the quality of food. Very few works related to food are available. This
work presents a 3D numerical model of the thermo-mechanical phenomena of a homogeneous food
model system (Tylose gel). Simulation data are in good agreement with our experimental data.

Keywords: thermo-mechanic, modeling, freezing, simulation, food model

INTRODUCTION
Freezing is one of the most satisfactory methods for long-term preservation foods. Although fast
freezing has the advantages of low drips loss and high end-product quality, some products will cracks.
One explanation has been that mechanical damage induced by fast freezing is due to volumetric
changes associated with the water-ice phase transition. Volume changes during freezing were
attributed to pure water at 0°C expanding by approximately 9% when transformed into ice at the same
temperature [1]. Nevertheless this thermal stresses induced by such phenomena have not been
theoretically analyzed. Indeed mechanical properties of ice are relatively unknown since they are
function of many parameters such as the temperature [2], the inner structure of the ice-crystal [3] and
the deformation rate of in ice [4]. In addition, the local deformation of an ice sample is difficult to
measure due to its volume expansion during the solidification. This deformation modifies the inner
structure (dendrites of crystallization) which is often unknown [5]. Lin et al. [6] modelized the volume
expansion of water during its solidification in a cylindrical brass tube. PROGCOMPSome hypotheses
(system in a state of quasi-balance during the freezing process, shear stress between tube and ice is
neglected, the mechanical properties) of the ice are constant and characteristics supposed to be those
of the ice polycrystalline isotropic were applied in first estimate. This model showed that the maximal
stress is localized in the interface between ice and water.

In the geologic domain, Yamabe et al. [7] have studied the thermo-mechanical properties of Sirahama
sandstone PROGCOMPand have showed that the transition into ice led to an increase of Young's
modulus. Moreover, contrary to the dry samples, the wet samples presented a viscoelastic behavior
attributed to the formation of microcracks in dilated pores.
Concerning the domain of biomaterials, Rabin et al. [8] have studied the tissues of rabbitPROGCOMP.
Some frozen tissues (liver and brains) had an elastic modulus close to the ice-crystal one whereas
others tissues (kidney) may have much higher moduli.

The qualitative aspect of the freezing of a cylindrical biomaterial was approached by Shi et al. [9; 10].
A potato cylinder was used as a model system. The progression of the freezing front freezing induced
field of radial and circumferential stresses field and deformationsPROGCOMP. The capacity of the
biomaterial to relax was stronger during ice formation than in frozen equilibrium state. The authors
also suggested to proceed the freezing process gradually in order to limit cracks in products.

Rubinsky et al. [11], who excluded the volumetric expansion in their calculation, demonstrated that the
amplitude of the induced stress was not only dependent of the material properties but also of the
product between external cooling rate and the square of the radial external surface.
It is thus clear that a detailed knowledge of the mechanical properties, deformations and relaxation
phenomena is necessary for a study of the freezing unit operation.

This work presents a numerical model of the thermo-mechanical phenomena of a homogeneous food
model system.

1
 ICEF9 – 2004
International Conference Engineering and Food

MATHEMATICAL MODEL
An uncoupled formulation is developed where the thermal and stress analyses are performed
independently. A rectangular geometry is used for this study where heat transfer is three-dimensional.
Moreover, the biomaterial is assumed to be isotropic and homogeneous.

Thermal analysis
Equation (1.) describes the heat transfer process for plane and axisymmetric cases:

∂ ( ρC p ,app T )
= ∇(k∇T ) 1.
∂t
The Neumann boundary and initial conditions are described respectively by:
− k∇T = h(T − T p ) 2.
T = T0 3.
where Tp is the temperature of the freezing medium and T0 is the constant initial temperature of the
material being frozen. In this study, an infinite value of h is used making the surface temperature equal
to Tp.

Mechanical analysis
It is assumed here that each component of the strain tensor can be additively decomposed into a
(e ) (T )
elastic strain å and a thermal strain å , that is,
ε = ε ( e ) + ε (T ) 4.
where the thermal strain is given by
T
ε (T )
= 1 ∫ αdT 5.
TR
with α, the thermal expansion coefficient, function of temperature [12] :
1 ρ dX
α (T ) = w 0 Φ I 6.
3 ρw dT
For an isotropic linear elastic model [12], the stress tensor is:
σ = λ Tr (ε)1 + 2µε 7.

This is given,
1 +ν ν
ε (e) = σ − Tr (σ )1 8.
E E
where ν is defined as:
εL
ν =− 9.
εa
where εa and εL are the strains in the axial and longitudinal directions, respectively.

And the displacement u is correlated to the stress by:

1
ε= {grad u + grad u'} 10.
2
The boundary conditions are:
T=T0 ;
t=0 , ∀x,y,z
u=0

y=0 ∀t,x,z { T=Tp(t)

ε=0
∀t on Ω σ ⋅n = 0

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 ICEF9 – 2004
International Conference Engineering and Food

To simplify the simulation, an x and y symmetries (the two horizontal directions) were used for the
calculation. So, only a quarter of slab is simulated.

FINITE ELEMENT FORMULATION

The governing equations were solved using the finite element computer code ABAQUS/Standard
(Hibbit, Karlsson and Sorensen Inc., Pawtucket, Rhode Island). A hexahedral finite element mesh was
used. The subroutine DISP was used to input the boundary condition Tp as an experimental data.

MATERIALS & METHODS

Experimental freezing data were collected to validate results obtained by the computational
simulations. Gel of methylcellulose or Tylose has been chosen as a model system. The humidity
(75.8 % w.c.) of this gel was determined by dehydration at 105°C. The freezing point (Tcc) of this gel or
Tylose is -1°C.
Freezing was carried out using a freezer plate. The sample was embedded in a polystyrene frame for
isolation. Temperature evolution was measured with five K-type thermocouples: four inserted to the
slab, and one fixed on the plate. For the variation of the volume during freezing, a displacement
transducer (VRVT050/E/TM, Penny and Giles, Christchurch, England) was used in the vertical
direction (y-direction).

During freezing, the temperature-time and displacement-time data were continuously recorded by a
digital data logger (Datalog 20, AOIP, Evry, France).

Table 1 gives some thermal and mechanical properties from our measured data (except for density
from Hseih et al. relation [13]). Fig. 1 shows the calculated α(T) for Tylose. The variation of the water
volume at +4°C is supposed here negligible.

Parameter Input unfrozen state frozen state

Initial dimensions (mm) 100*100*50
Initial temperature, T0 (°C) 23
Poisson’s ratio 0.47
Density (kg.m-3) 1100 800
Young’s modulus (MPa) 0.02 250
2 -1
Thermal conductivity (W.m .kg ) 0.48 1.2
Table 1: Some input parameters for the model

0.005
expansion coefficient (/°C)

-0.005

-0.01

-0.015

-0.02

-0.025
-20 -15 -10 -5 0
Temperature (°C)
Fig.1: Linear thermal expansion coefficient of Tylose, calculated for Eq.(6). For T> 0°C, α (T) = 0

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 ICEF9 – 2004
International Conference Engineering and Food

RESULTS & DISCUSSION

A typical global displacement in function of time, of a Tylose slab during freezing, is plotted in Fig. 2.
The global displacement in this direction is about 3mm after 7hrs of freezing.

3.50E-03

3.00E-03

2.50E-03

2.00E-03
U2 (m)

1.50E-03

1.00E-03

5.00E-04

0.00E+00
0 5000 10000 15000 20000 25000 30000 35000
t (s)

Fig 2: Experimental variation of the volume in the vertical direction of a Tylose sample during freezing

Fig 3: Numerical simulation of a quarter of a Tylose’s sample freezing: displacement at the bottom of
the sample in the vertical direction (U2 is in m) at t= 30 000s

Fig. 3 shows numerical results of the model developed. These results are for the bottom of a quarter
of sample. So, the maximal displacement is for the centre of the sample, and it is about 3.3 mm and is
closed to experimental data. The difference can result from the sensor’s position on the slab.
The non uniformity of U2 can be explained by the free surface that can expand in the other directions.
So, at the edges U2 is less that the center of the slab.

Effectively, Fig. 4 shows this global displacement in function of time. The quarter slab expands as the
freezing front progresses. As the Tylose material has been shown to have an elastic behavior

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 ICEF9 – 2004
International Conference Engineering and Food

whatever the temperature (elastic modulus is fourth time higher than plastic modulus at negative and
positive temperatures), the distortion front disappears when the slab is in thermal equilibrium. This
displacement can also be used as a front tracking.

t=343.3s t=1159s

t=2607s t=5867s

t=13200s t=30000s

Fig 4: Global displacement (U) during freezing at different step

CONCLUSION
This paper has developed a model for the thermo-mechanical phenomena during freezing. The 3D
model developed with a commercial code is in good agreement with our experimental measurements.
The continuity of this work will be to measure the fracture tensile of the Tylose to predict the crack
apparition with the stress numerical field.

NOMENCLATURE
Cp,app apparent specific heat J.kg-1.K-1
E Young’s modulus Pa
h heat transfer coefficient W.K-1.m-2
k thermal conductivity W.m2.kg-1
t time s
T temperature °C
Tcc initial freezing point °C
U displacement m

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 ICEF9 – 2004
International Conference Engineering and Food

XI ice ratio
Greek symbols
α thermal expansion coefficient °C-1
ε strain
λ Lamé’s coefficient
ρ density kg.m-3
σ stress Pa
µ Lamé’s coefficient
ν Poisson’s ratio
Ω free surface
Φ fractional volume due to phase
change of pure water ( = 0.087)
Subscripts
0 at t=0
2 y-direction
p plate

REFERENCES
1. Fennema, O. R. Freezing preservation.In: Principles of food science, Part II. Physical
principles of food preservation, O.R. Fennema and D.B. Lund. Marcel Dekker M.Karel, Inc.,
New York, 1975.
2. Dantl, G. Elastic Moduli of Ice.In: Physics of Ice, Plenum Press, 223-230, 1969.
3. Michel, B. Ice Mechanics, Laval, Quebec, Canada, 98, 1978.
4. Duval, P., Maitre, M., Manouvrier, A., Marec, G. and Jay, J. C. Primary creep and
experimental method for testing ice in various conditions of strain rates and stresses.
Proceedings of International Symposium on Ice, 11, 596-602, 1981
5. Kuon, L. G. and Jonas, J. J. Effect of strain rate and temperature on the microsctructure of
polycristalline ice.In: Physics and Chemistry of ice, The Royal Society of Canda, Laval,
Canada, Laval University Press, 370-376, 1973.
6. Lin, S., Gao, D. Y. and Yu, X. C. Thermal stresses induced by water solidification in a
cylindrical tube. Journal of Heat Transfer, 112, 1079-1082, 1990
7. Yamabe, T. and Neaupane, K. M. Determination of some thermo-mechanical properties of
Sirahama sandstone under subzero temperature condition. International Journal of Rock
Mechanics and Mining Sciences, 38, 7, 1029-1034, 2001
8. Rabin, Y., Steif, P. S., Taylor, M. J., Julian, T. B. and Wolmark, N. An experimental study of
the mechanical response of frozen biological tissues at cryogenic temperatures. Cryobiology,
33, 472-482, 1996
9. Shi, X., Datta, A. K. and Throop, J. A. Mechanical property changes during freezing of
biomaterial. Transactions of the ASAE, 41, 5, 1407-1414, 1998a
10. Shi, X., Datta, A. K. and Mukherjee, S. Thermal fracture in a biomaterial during rapid freezing.
Journal of Thermal Stresses, 22, 275-292, 1999
11. Rubinsky, B., Cravalho, E. G. and Mikic, B. Thermal stresses in frozen organs. Cryobiology,
17, 66-73, 1980
12. Lemaitre, J. and Chaboche, J. L. Mécanique des matériaux solides, Paris, 1988.
13. Hsieh, R. C., Lerew, L. E. and Heldman, D. R. Prediction of freezing times for foods as
influenced by product properties. Journal of Food Process Engineering, 1, 183-197, 1977

6
 ICEF9 – 2004
International Conference Engineering and Food

Computer model operation of a composition of combined foodstuff

Tujilkin V.I., Plaksin J.M., Filatov V.V.

vit@mgupp.ru, vit@mgupp.ru, filatov_vl@yahoo.com

The Moscow State University of Food Productions, Russia, 125 080 Moscow, Volokolamsky
shosse 11, fax (095) 158-03-71, tel. (095) 158-72-19

One of perspective directions in a food-processing industry is obtaining multicomponent

foodstuff, including the use of extrusion technology. One of these products is dry breakfasts and
foodstuffs of quick preparation. However, from the scientific point of view, the problem, connected
with production technology and receipts of such products are not worked out yet. In most cases the
deciding meaning has organoleptic analysis and degustation evaluation of obtained products but not
scientific substantiation of its composition.
The development optimal receipts of composition was carried out a method of computer
optimization on the basis of edible, biological value and function - processing behavior of builders of
combined foodstuff. Criteria of an optimality were biologically fissile substances (content of mineral
substances and vitamins), balance on amino acids to composition, relation of coefficients protein - fat,
protein - moisture, and also their edible value.
The mathematical model of a problem of optimization under the schema of linear programming
in the formalized view is represented.
By results of computer model operation the optimal relation of builders of combined foodstuff is
defined, and also experimental receipts are calculated. The chemical compositions of the designed
receipts of combined foodstuff is given.

Key words: combined foodstuff, сomputer modeling, receipts

Now in connection with increase of a level of pollution of an environment the organism of the
person tests undesirable external and internal actions. In opinion of many domestic and foreign
scientists, one of efficient ways of correction of breaking of metabolic processes in an organism is the
nutritive factor that causes of development and manufactures rigorous and optimally balanced on
irreplaceable alimentary substances of a food stuff [1]. For this purpose it is offered to adjust targeted
chemical composition of products and to improve in them the content of such substances as essential
amino asids, vitamins, mineral elements which delay inflow of harmful substances in an organism of
the person, protect from them separate systems, improve a common resistance of an organism.
By manufacture of a foodstuff with a heightened nutritive value it is desirable to prefer prime in
the use and to convenient food concentrates at transportation what are, in particular, krispies of type
a muesli.
Muesli are an express, combined product, from a grain of grain crops and other natural plant
roughage. Are used for a medical, prophylactic and daily feed. Are characterized by the heightened
content of alimentary filaments, microelements, inorganic salts and active agents. A muesli contain a
great many of protein, essential amino asids, carbohydrates, lipids, including, polyunsaturated fatty
acids (linolic and linolenic), nucleic acids (growth factors), the water-soluble (В1, В2, В6, Н, РР),
pantothenic both folic acids and fat-soluble (A, Е) vitamins, and as a great many macro and
microelements (iron, a potassium, a calcium, magnesium, manganese, fluorine and others). But
principal are grain which are compounded up to 80 % with a muesli: with them in an organism of the
person alimentary fibers, or so-called ballast substances hit. Muesli with correct the fitted prescription
structure can be recommended on a background of treatment antibiotics.
The nutritive value of different grades a muesli is stipulated by selection of components -
products which in themselves fall into to products of an able-bodied feed. In a mix they,
supplementing each other, frame the complex product keeping the balanced content of the basic

1
alimentary substances, giving power, and also high enough content of vitamins and inorganic
substances per unit calories.
Ratio of caloricity and the content of alimentary substances very important for performance of
products of an able-bodied feed. A muesli are characterized by high enough protein content. The lobe
of protein on caloricity compounds in a muesli about 12-13 % that corresponds to a correct balanced
ration of a feed.
The following alimentary properties a muesli as characterize products of an able-bodied feed:
1. The ratio of the basic alimentary substances giving power, corresponds to scientific
introducings about a product of an able-bodied feed.
2. Contain a high level of vitamins and inorganic substances per unit caloricities.
3. Contain only vegetable fats with the high content of polyunsaturated fatty acids and
reproduction vitamin, do not contain a cholesterine.
4. A muesli are affluent alimentary fibers which promote normal function of an intestines
5. Combine with any food liquors - milk, a kefir, yoghourts, juices.
6. A theoretical product for interested persons to control the weight or to lower it.
7. An irreplaceable product for the vegetarians, permitting to provide a rigorous able-bodied
feed at abandoning of animal products.
8. Have low salt content and clear saccharum. A muesli are sweetened with a fructose.
9. Allow to receive quickly a dish of an able-bodied feed without thermal culinary machining.
At formation of assortment of krispies and building of formulas the principal attention is
necessary for giving the following factors:
- Compatibility of the different components included in formulas, with the purpose of deriving in
a finished stock of desirable organoleptic indicators;
- A nutritive value of raw material and a main product;
- Abilities of a product it is long to be kept.
Krispies are stable enough at a storage as in a process of manufacture the raw material passes
high-temperature machining, and convenient in the use as do not demand padding culinary
machining.
It is known, that for satisfaction of requirement of an organism inflow alimentary components in
fixed quantity and a ratio - the philosophy of the theory of a balanced nutrition is necessary.
Development combined by a food stuff on the basis of an analytical assessment of quantity and
quality keeping in them components guesses the methodological approaches basing on secretion key
components, simulations and optimizations of its quality. This direction has received development in
series of analytical design techniques of quality proteinaceous amounting separate foodstuffs and
multicomponent compositions [2]. With development of introducings about a role of protein in security
of the major functions of an organism magnitudes of diurnal requirements have been definitely
revised. The due attention has become to be given its qualitative behaviors, in particular an amino-
acid score - to a parameter, which characterizes a degree of correspondence (in %) contents of each
essential amino asid in relation to its content in theoretical protein. Amino acid composition of
theoretical protein is specific and recommended specialists the CART.
At designing new foodstuffs with the purpose of increase their alimentary and a biological value
the problem posed to define lobes x j (l ≤ j ≤ n) of each of n - a formulation constituent so that weight
fractions c j (l ≤ i ≤ m) of essential amino asids in an obtained product were on an absolute value and
ratioes as much as possible approximative to weight fractions bi of essential amino asids of a
benchmark scale the CART .
The given problem mathematically falls into to optimum control where control action is the
r r
vector X = {xi } . It is necessary to specify a measure of proximity of a vector C = {ci } to a benchmark
r
vector B = {bi } which will be a criteriaon of performance (objective function).
Academician Lipatovym N.N. [3] gives definition of alimentary (combined) products of the third
generation. These are products, adequate traditional on organoleptic indicators and structural forms
of nutritive and ballast substances; weight fractions of components of these products pick up in such
a manner that at inclusion in diets ensure maintenance conditionally optimal material and the energy
balance of an organism of customers. Also the following design philosophies of structure of the
balanced products and rations keeping them are formulated:
- Correspondence to rationally balanced formula;
- Correspondence of balance of amino acid composition of protein bearing ingredients
statistically to the justified proteinaceous etalon;

2
 - A possibility targeted to variate fat - lead-acid structure addition padding жирсодержащих
ingredients;
- A maximal approaching to an assigned ratio between saturated, monounsaturated and
polyunsaturated fatty acids in any panel fataceous ingredients;
- A formula of the product which is included in a ration to calculate with the count of structure of
dishes and the products used simultaneously with projected;
- The structure of a multicomponent product, in one-time or diurnal rations, is balanced on
power value, a ratio macro and micronutritive and to a panel of ballast food items.
Also the following criteria of performance, designed on the grounding of a known principle of
the Mitchell-Bloсk [4] are known:
1) Quotient of utility of the amino acid composition, numerically describing balance of essential
amino asids in relation to physiologically necessary norm (etalon), lobes of a unit:

∑b
i =1
i
U = S min ⋅ m
(1)
∑c
i =1
i

Where S min - minimum it is fast essential amino asids of estimated protein in relation to
benchmark, and also
2) A potential biological value:
 l m 
BV p = 100 ⋅ 1 −  ⋅
 m ∑
Si − S min   (2)

  i =1  
Where Si = ci bi - it is fast i-essential amino asid of a product in relation to the etalon.
The purpose of optimization is search of a maximum of functions (1) or (2). In theoretical event
U=1; BV p = 100 %. However, in a statement of problem of optimization of amino acid composition, a
mix of projected foodstuffs measure (1) and (2) have some shortages. Magnitudes U also BV p will
r
increase at reduction of a vector magnitude C = {ci } , and it deletes from an optimal solution. Thus,
one of problems is development of a criteria on of performance (objective function) for optimization
r r
C = {ci } with the help of steering X = {xi } .
Let's mark out aij a weight fraction of i- essential amino asid in j- a component used in a
formula. We obtain

r r  m 

 j =1
∑
C = AX =  aij x j  (3)

r
( )
where a template A = aij of the dimension m × n . On a vector X = {xi } limitation is overlapped:
n

∑x
j =1
j = 1 (4)

Besides there are limitations on share ratio of mixture:

x j ≥ k j ≥ 0 (5)

where constants k j in the sum should be less than 1, or 100 %. Let's consider the module of a
r r
difference of vectors of amino acid composition of a product C = {ci } and the etalon B = {bi } :

r r m
J = C−B = ∑ (c − b )
i =1
i i
2
(6)

Apparently, that at the complete concurrence to the etalon J = 0 . The measure (6) allows to
apply the mathematical apparatus of optimum control, but has series of shortages.

3
 Magnitude J of the considerable degree is influenced by the greatest on an absolute value of
a lobe of amino asids. As the corollary, change of ratio of mixture on amino asids with small lobes
practically is not reflected in value J . Besides on values J it is practically impossible to judge
balance of projected products on amino acid composition.
To remove the indicated shortages, the following parameter is offered:
 l
m 
F = 100 ⋅ 1 − ∑ (Si − 1)2  (7)
 m i =1 
 
Thus, (7) is a convex function and extremums (6) and (7) are attained by the same optimal
r
solutions X = {xi } . Hence, the measure (7) with the count (3-5) puts a problem of finite-dimensional
convex conditional optimization [5]. At the complete concurrence of amino acid compositions of a
product and the etalon (and only in this case) magnitude F attains the global maximum of 100 %. The
closer magnitude F to 100 %, the amino asids in a product are better balanced.
Thus, development of optimal prescription structure a muesli was carried out a method of
computer optimization, with the help before designed software [6-7], on the basis of alimentary, a
biological value and function - processing behavior of components a muesli.
Basic the structure a muesli is given in tab. 1. Chemical composition of ingredients a muesli is
given in tab. 2. Amino acid composition of ingredients a muesli is given in tab. 3

Table 1
Basic the structure a muesli
Proteinaceous and carbohydrate components Futty components

Oat flakes "Gercules"; a rice extrudate (flakes); corn-flakes; The solid vegetable fat,
wheaten flakes from a bold kernel; an oatmeal; a whole grain a pounded coconut, a lecitine,
flour; seeds; an extrudate, an oat (the whole is express a milk chocolate, a hazel, cocoa
processed grain), rice starch. ground, a peanut, seeds of
Starch syrup, maltodextrins, honey, a banana powder, sunflower, a seed of a flux,
scraps of dehydrated berries and fruits: wild strawberry, a seeds cashews, an almond, a
dewberry, apples, bananas, a raspberry, apricots, a pear, a plum, coconut corrugated slices,
raisin, a concentrated fruit juice. vegetable oil.
.

Table 2
Chemical composition of ingredients a muesli on 100g. a product
Carbohydrates, g
Components Proteins, g Fats, g
Starch A cellulose Mono-, and
disaccharides
Oat flakes "Gercules" 11 6.2 48.9 1.3 1.2
Rice 7.5 2.6 55.2 9.0 0.9
Wheaten flakes 10.3 1.1 68.7 0.1 0.2
Corn-flakes 10.3 4.9 56.9 2.1 1.6
Soya bean 34.9 17.3 3.5 4.3 5.7
Sunflower (seeds) 20.7 52.9 - 2.9 3.4
Filbert 16.1 66.9 9.9 - -
Apricots 0.9 0.1 - 0.8 9.0
Raisin 0.6 0.2 - 0.6 15.0

4
 Table 3

Amino acid composition of ingredients "Muesli", mg on 100g a product

Amino asids Oat flakes Rice (rice Wheaten Corn-flakes A soya Sunflower A filbert Apricots Raisin
"Gercules" flakes) flakes bean (pips)
Valine 500 400 471 416 2090 1071 903 19 17
Isoleucine 398 283 430 312 1810 694 909 14 5
Leucine 635 689 806 1282 2670 1343 1046 23 12
Lysine 420 290 250 247 2090 710 539 23 13
Methionine 122 150 153 120 520 390 133 4 10
Threonine 380 260 311 247 1390 885 568 16 50
Indole amino- 195 90 100 67 450 337 192 9 2
propionic acid
Phenyl alanine 537 410 500 460 1610 1049 598 13 12

Alanine 486 390 330 790 1470 858 196 28 25

Arginine 736 600 400 411 2340 1785 2304 10 80
Aspartic asid 916 640 340 580 3820 1789 1280 191 72
Histidine 244 190 200 260 980 523 297 13 10
Glycine 1019 345 350 350 1420 1130 1192 14 5
Glutamic asid 1948 1280 3080 1780 6050 4124 3203 48 90
Proline 641 360 970 1091 1860 1180 773 22 100
Serine 514 315 500 514 2070 792 1295 23 70
Thyrosinum 443 290 250 380 1060 544 560 10 10
Cystine 282 140 200 170 550 396 121 8 15

5
 The mathematical model of a problem of optimization under the schema of a linear
programming in the formalized aspect looks like:
To minimize:
Z = 20 X 1 + 11X 2 + 9 X 3 + 15 X 4 + 20 X 5 + 180 X 6 + 80 X 7 + 80 X 8 → min
Under the following standardizing conditions:
 X 1 ≥ 0,2

 X 2 ≥ 0,1
 X 7 ≥ 0,1

110 X 1 + 75 X 2 + 103 X 3 + 349 X 4 + 207 X 5 + 161X 6 + 90 X 7+60 X 8 ≥ 120
4,9 X + 2,9 X + 2,5 X + 20,9 X + 7,1X + 5,4 X + 0,23 X +0,13 X ≥ 3
 1 2 3 4 5 6 7 8
3,8 X 1 + 2,6 X 2 + 2,5 X 3 + 13,9 X 4 + 8,9 X 5 + 5,7 X 6 + 0,16 X 7+0,5 X 8 ≥ 2

 X 1 + X 2 + X 3 + X 4 + X 5 + X 6 + X 7+ X 8 = 1
By results of computer simulation the optimal ratio of components a muesli has been
specific, and also experimental formulas a muesli are calculated some. In tab. 4. chemical
composition of an experimental formulas "Muesli" is given.

Table 4
Chemical composition of an experimental formulas "Muesli"
The basic Carbohydrates, g Amino asids, mg
alimentary Proteins, Fats, g
substances g Starch A Mono-, and A lysine Threonine
cellulose disaccharides
1 9.66 16.26 33.22 1.69 3.204 326,97 318,41
2 10,68 17,08 31,02 1,81 3,54 368,17 363,98
3 15,64 22,71 38,69 2,61 1,78 623,88 557,91
4 12,57 15,90 38,50 2,05 3,47 540,86 426,76
5 14,67 17,17 26,73 2,55 3,91 656,30 542,10

Breedings
1. The measure of an assessment alimentary and is offered to a biological value of combined
foodstuffs.
2. Check of measure at definition of balance on amino acid composition of combined foodstuffs
on the basis of groat crops has shown its objectivity.
3. By results of computer simulation the optimal ratio of components a muesli has been
specific, and also experimental formulas are calculated some.

The list of the literature

1. Lipatov N.N. Principle and design techniques of formulas of foodstuff, balancing diets //
Informations of high schools. Alimentary technologies. - 1990.-№ 6-p. 5.
2. Brazhnikov A.M., Rogov I.А. About a possibility of designing of combined meat products //
Meat the industries of the USSR. - 1984. - №5. - p.23.
3. Lipatov N.N. Some aspects of simulation of aminoacidic balance of foodstuffs // Alimentary
and process industry. - 1986.-№ 2-p.48.
4. Lipatov N.N., Rogov I.A. The methodology of designing by a food stuff with a required
complex of parameters of a nutritive value. // Informations of high schools. Alimentary technologies.
1987.-№ 2. -p.9.
5. Alekseev E.L., Pahomov V.F. Simulation and optimizations of manufacturing methods in the
food-processing industry. - M: Agropromizdat. 1987. – p.272
6. Plaksin J.M., Filatov V.V. Development of computer model for designing properties of
combined foodstuffs. Мaterials of international scientific - practical conference « The consumer
market: quality and safety of the goods and services. » Thom 2, December 18-21, Orel, 2001.
7. Plaksin J.M., Filatov V.V Computer simulation of formulas of combined foodstuffs. . Мaterials
of scientific - methodical seminar: Information science, concepts, the modern condition, perspectives
of development. – The Yelets state university of a name of I.A.Bunin, Yelets, 2003
ICEF – 2003
International Conference Engineering and Food

Finite difference modeling during immersion freezing of solid foods

Zorrilla Susana (1), Rubiolo Amelia(2)

Instituto de Desarrollo Tecnológico para la Industria Química (Universidad Nacional del Litoral –
Consejo Nacional de Investigaciones Científicas y Técnicas), Güemes 3450, S3000GLN, Santa Fe,
República Argentina. (1) zorrilla@intec.unl.edu.ar; (2) arubiolo@intec.unl.edu.ar

A finite difference method was used to solve a mathematical model to predict the heat and mass
transfer during the immersion freezing of foods for regular geometries. Sensitivity analysis showed that
the lower temperature or solute concentration of the immersion solution, the faster freezing rate and
the slower solute uptake. It was also observed that the higher heat transfer coefficient or the lower
diffusion coefficient, the lower solute average concentration in the solid.
Key words: numerical solution, immersion freezing, heat transfer, mass transfer.

Introduction
Immersion chilling and freezing (ICF) consists of direct soaking of foods in aqueous fluids (e.g.
solutions of NaCl, CaCl2 or sucrose) maintained at low temperature (e.g. from -10 to -40 °C). ICF is
one of the fastest chilling and freezing techniques, and it is associated to low costs and to high quality
of the final product. However, the main disadvantage is the uncontrolled solute uptake from the
refrigerated solution into the product [1]. Mathematical models may help to have a better
understanding of the transport phenomena associated with ICF and to control or optimize the main
variables. The mathematical formulation represents complex phenomena of heat and mass transfer
with phase change where the food properties strongly depend on temperature and composition. The
objectives of this work were to solve numerically a mathematical model previously obtained by the
authors and to perform sensitivity analysis considering the main heat and mass transfer parameters.

Numerical solution
Zorrilla and Rubiolo [2] developed a model for chilling and freezing of foods by immersion in aqueous
fluids maintained at low temperatures. Solid foods were assumed as a porous media with an occluded
solution. Three phases were considered, the rigid solid matrix, the liquid phase, and the ice phase.
Transport equations for a continuous media were applied to each phase. The averaging-volume
method developed by Whitaker [3] was used for obtaining comprehensive equations to predict solute
concentration and temperature as a function of space and time. The resultant set of equations is a
nonlinear problem that can be solved numerically.

Table 1 shows the equations to describe heat and mass transfer during immersion chilling and
freezing of foods considering a 1-D geometry [2]. The dominium 0 ≤ x ≤ a represents a 1-D region
where “a” may be the half thickness of an infinite slab, the radius of an infinite cylinder, or the radius of
a sphere. The system of equations (1) to (13) can be solved numerically. A finite difference method
based on the control-volume approach simplifies the numerical solution [4]. At the start, a grid must be
generated. Due to the dramatic changes of solute concentration near the surface during the ICF
process, a logarithmic grid reduces conveniently the computational times. A dimensionless variable
defined as
10 x / a − 1
η= 0≤η≤1 (14)
10 a / a − 1
helps to generate the logarithmic grid. The new dominium is divided into N equal subregions each of
thickness ∆η = 1 / N . Therefore, the distance to the internal grid points i = 1, 2, …, N+1 in the dominium
0 ≤ x ≤ a can be calculated by:
x i = a log10 (1 + 9(i - 1)∆η) (15)
The heat balance for a node i between time levels n to n+1 leads to
n+1 n ∆t  Q ni+1 − Q ni 
hi = hi + (16)
ρ  Si 

where
p p
x −x
i+ 1 i− 1
2 2
Si = (17)
p
ICEF – 2003
International Conference Engineering and Food

x i + x i±1 (18)
x =
i± 1 2
2

 T n − T n 
Q ni =A k
n  i i−1 
(19)
i− 1 eff i− 1
2 2 (x i − x i−1 )
n n
n k eff i + k eff i−1
k eff = (20)
i− 1 2
2
(p−1)
A =x (21)
i− 1 i− 1
2 2

Si and A are volume and area factors of the control volume that exclude terms common to both
i− 1
2
area and volume for the different geometries.

The mass balance for a node i between time levels n to n+1 lead to:
n+1  n n 
 ε ρ β  + ∆t Fi+1 − Fi 
n
 ε ρ β  = (22)
 β 2 i  β 2 i  Si 
 
where
 β
n
 β 
n
 ρ 2  −  ρ 2  
Fin = A 1 D eff 1 
n i i−1 
(23)
i−
2
i−
2 (x i − x i−1 )
n n
n D eff i + D eff i −1
D eff = (24)
i− 1
22
Q and F change according to the neighboring nodes and boundary conditions. Eqs. (16) and (22) for
nodes 1 and N+1 can be used considering
x1 = 0 (25)
2
x =a (26)
N+ 3
2
n
Q1 = 0 (27)

QNn + 2 = a (p −1)h c  T∞ − T 
n
(28)
 N+1 

F1n = 0 (29)
FNn+ 2= FNn +1 (30)
The mathematical description is completed with the estimation of the food thermal properties, of the
thermodynamic relation between temperature and solute fraction in presence of ice, and of the
effective diffusion coefficient [2]:


h i =  T i − Tref  C pf +
n n e 1 ∆H 0 T 0 − Tf
n
i

 n n
for T i ≤ Tf i
( ) (31)
  
 (T0 − T ref ) 
 T
 0
− T
n 

i 



Cpeff i = C pf +
n (
e1 ∆H0 T0 − Tf i
n
) for T
n n
≤ Tf i (32)
2 i
 T − T n

 0 i 

k eff i = k f + (k u − k f )
n (T
0 − Tf i
n
) for T
n n
≤ Tf i (33)
 T − T n

i
 0 i 

h
n
(n 
= Tf i − Tref C pf +
(
)
y 1 ∆H 0  
 + C pu  T
n
− Tf i 
n
for T
n n
> Tf i (34)
0 − Tref ) 
i
 T i  i

n n n
Cpeff i = Cpu for T > Tf i (35)
i
ICEF – 2003
International Conference Engineering and Food

n n n
k eff i = k u for T > Tf i (36)
i
n+1 n+1
For T i
≤ Tf i , the thermodynamic relation was estimated by
 n+1  n+1 
2
 n+1  
3
  ρ 2 β    ρ 2  
β
  ρ 2   
β
 i  i   i  
T i = T0 − b + c + d
n+1
(37)
 β  β   β  
 ρβ  ρβ   ρβ  
     
The effective diffusion coefficient was estimated by
n
n
D εβi
D eff i = (38)
τ
Eq. (37) can also be used to calculate Tf ni considering the initial liquid volume fraction
 n  n 
2
 n  
3
  ρ 2 β ε β    ρ 2 ε β  
β
  ρ 2 ε β   
β
 i  i   i  
= T0 − b + c + d
n (39)
Tf i
 β  β   β  
 ρ β ε β0  ρ β ε β0   ρ β ε β0  
     

Table 1. Summary of equations to describe heat and mass transfer during

immersion chilling and freezing of foods for a 1-D geometry*.

Heat and mass transfer equations (0 < x < a; t > 0)

∂h 1 ∂  ∂T 
ρ = (p−1) k eff x (p−1)  (1)
∂t x 
∂x  ∂x 
∂ •
 ε β ρ1
β  + m = 0
(2)
∂t  
 β 
∂
 εβ ρ2
β  = 1 ∂  D x (p−1) ∂ ρ 2 
∂t   x (p−1) ∂x  eff ∂x  (3)
 
∂ •
 ε α ρα
α  = m
(4)
∂t  

Boundary conditions (t > 0)

∂T
=0 x=0 (5)
∂x
∂T
k eff
∂x
= h c T∞ − T ( ) x=a (6)
β
∂ ρ2
=0 x=0 (7)
∂x
β
ρ2 = ρ 2∞ x=a (8)

Initial conditions (t = 0 ; 0 ≤ x ≤ a)
T = T 0 (9)
β β
ρ1 = ρ1 0 (10)
β β
ρ2 = ρ2 0 (11)
ε β = ε β0 (12)
ε α = ε α0 (13)
* p=1, 2, and 3 for rectangular, cylindrical and spherical coordinate systems, respectively.
ICEF – 2003
International Conference Engineering and Food

The finite difference scheme given by Eqs. (16) and (22) corresponds to an explicit method and
required a stability criteria analysis [5]. The stability criteria at the center ( i = 1) and at the surface
(i=N+1) are:
n n
2p k eff 1 2p D eff 1
1 i+ 1 i+
2 2
≥ ; ≥ i=1 (40)
∆t x i+1 Cpeff ρ
2 n ∆t x i+1
2
i

 (p−1)  x 1 (p−1) D eff n (p−1)

k eff 1  D eff 1 
n n
 x 1  i+ x 1
i− i− i+ 1 i− i−
(p−1)
p x i
2 2 
p
2 2 2 2 
hc + +
 (x i − x i−1 )   (x i+1 − x i ) (x i − x i−1 ) 
1    
≥   ; 1 ≥  
i=N+1 (41)
∆t  p p n ∆t  p p
 x i − x i− 1  C peff i ρ  x i+ 1 − x i− 1 
 2   2 2 
The calculation scheme consists of selecting the largest time increment ∆t that satisfies the stability
n n +1
criteria (Eqs. 40 and 41), computing Tf i (Eq. 39), thermal and mass properties (Eqs. 31 to 38), h i
n+1
(Eq. 16) and  ρ 2 ε β 
β n+1
(Eq. 22), and calculating T from the relation between temperature and
 i i

n+1
is calculated through Eq. (39) for  ρ 2 ε β 
n +1 β n+1 n+1
enthalpy. Tf i . If T ≤ Tf i then Eq. (37) is used
 i i

n+1 n+1
to calculate  ρ 2  . Then, ε β i is calculated from  ρ 2 ε β  , otherwise ε β i = ε β0 . Finally,
β n +1 β n+1
 i  i
thermal and mass properties are updated and the procedure is repeated. Similarly, equations and
procedures for 2-D and 3-D can be developed.

Results and discussion

The solute uptake during immersion freezing has been pointed out as one of the major drawbacks of
the process [1]. However, in some cases the solute uptake may be a desired result. The immersion
freezing of cheese using NaCl aqueous solutions at low temperatures may be an interesting
alternative to freeze the food and to incorporate the solute simultaneously.

A computer program for implementing the numerical scheme was written in Fortran language
(Compaq Visual Professional Edition, Version 6.1.0). Data used for calculations are shown in Table 2.
For the case of NaCl, b = 59.278, c = 7.332, and d = 544.427 [6].

Table 2. Data used for simulations.

Parameter Value Source

Physical properties
α β σ
ρα = ρβ = ρσ = ρ 1000 kg m-3 (a)
-10 2 -1
D/τ 6×10 m s (a)
CPu 3063 J kg-1 °C-1 (b)
CPf 2078 J kg-1 °C-1 (a)
ku 0.390 W m-1 °C-1 (b)
kf 0.973 W m-1 °C-1 (a)
hc 280 W m-2 °C-1 (a)
Initial conditions
ρ2 0
β 10 g L-1 (a)
εα0 0 (a)
εβ0 0.5 (a)
T 15 °C (a)
0
Immersion solution data
ρ2∞ 230 g L-1 (a)
T∞ -10 °C (a)
(a) Assumed for this study [2].
(b) Properties for the unfrozen state based on the cheese composition: 22% w/w fat content, 50% w/w water
content, 28% w/w non-fat solids [7].
ICEF – 2003
International Conference Engineering and Food

Table 3. Characteristic heat and mass transfer parameters for regular geometries.

3-D (ax=
1-D (a=0.01 m) 2-D (ax=ay=0.01 m)
ay=az=0.01 m)
Study Infinite
casea Infinite Finite Rectangular
Infinite slab Sphere rectangular
cylinder cylinder parallelepip.
rod
tcc d
ρ2 ave tc ρ2 ave tc ρ2 ave tc ρ2 ave tc ρ2 ave tc ρ2 ave
-1 -1 -1 -1 -1 -1
(min) (g L ) (min) (g L ) (min) (g L ) (min) (g L ) (min) (g L ) (min) (g L )
b
Nominal 39.14 18.98 17.85 23.26 11.67 26.62 20.54 23.99 13.66 27.65 15.07 28.32

T∞=-15°C 23.94 15.08 11.74 18.87 7.87 21.65 13.44 19.14 9.20 22.12 10.14 22.44
hc=560
-2 -1 31.35 16.99 14.48 20.75 9.49 23.80 16.84 21.52 11.27 24.80 12.55 25.48
W m °C
hc=840
-2 -1 28.52 16.13 13.19 19.58 8.65 22.30 15.45 20.38 10.36 23.46 11.58 24.20
W m °C
-1
ρ2∞=190 g L 38.57 16.03 17.78 19.47 11.59 22.14 20.35 19.89 13.57 22.77 14.99 23.22

-1
ρ2∞=270 g L 39.65 21.89 18.05 27.01 11.71 31.06 20.67 27.97 13.71 32.38 15.14 33.29
-10
D/τ=3×10
2 -1 36.94 14.42 17.27 17.68 11.36 20.20 19.79 18.19 13.28 20.90 14.65 21.40
m s
-10
D/τ=9×10
2 -1
m s
41.10 22.76 18.52 27.75 11.96 31.65 21.15 28.55 13.98 32.84 15.42 33.63
a
Study case: data similar to nominal case with the indicated value that changes.
b
Nominal: case associated with the data of Table 2.
c
tc : is the time that takes the geometric center to reach -5 °C.
d
ρ2 ave : is the average solute concentration in the solid at the immersion time tc.

The time that takes the geometric center to reach -5 °C (tc) and the average solute concentration in
the solid at the immersion time tc (ρ2 ave) for different regular geometries are shown in Table 3. The tc
and ρ2 ave values decrease when the temperature of the immersion solution decreases, when the heat
transfer coefficient increases, when the solute concentration of the immersion solution decreases, or
when the diffusion coefficient decreases. For 1-D geometries, tc decreases and ρ2 ave increases
according to the following order: an infinite slab, an infinite cylinder, and a sphere. For 2-D geometries,
tc decreases and ρ2 ave increases according to the following order: an infinite rectangular rod and a
finite cylinder. In the case of a rectangular parallelepiped, tc and ρ2ave were higher than for a finite
cylinder and for a sphere of similar characteristic dimensions.

Conclusions
The control-volume approach was used to solve satisfactorily the model for chilling and freezing of
foods. The time that takes the geometric center to reach -5 °C (tc) and the average solute
concentration in the solid at the immersion time tc (ρ2 ave) were calculated for regular geometries. The tc
and ρ2 ave values decreased when the temperature of the immersion solution decreased, when the
heat transfer coefficient increased, when the solute concentration of the immersion solution
decreased, or when the diffusion coefficient decreased. Multidimensional geometries improved heat
and mass transfer. The results obtained are promising and may help to optimize or control ICF
process.

Acknowledgements
This research was supported partially by Fundación Antorchas Grant # 13927/1 – 29, Consejo
Nacional de Investigaciones Científicas y Técnicas, and Universidad Nacional del Litoral (Argentina).

References
1. Lucas T., Raoult-Wack A.L. Immersion chilling and freezing in aqueous refrigerating media: Review
and future trends. International Journal of Refrigeration, 21(6), 419-429, 1998.

2. Zorrilla S.E., Rubiolo A.C. Mathematical modeling for immersion chilling and freezing of foods. Part
I: Model development. Journal of Food Engineering, submitted, 2002.
ICEF – 2003
International Conference Engineering and Food

3. Whitaker S. Simultaneous heat, mass, and momentum transfer in porous media: A theory of drying.
Advances in Heat Transfer, 13, 119-203, 1977.

4. Mannapperuma J.D., Singh R.P. A computer-aided method for the prediction of properties and
freezing/thawing times of foods. Journal of Food Engineering, 9, 275-304, 1989.

5. Mannapperuma J.D., Singh, R.P. Prediction of freezing and thawing times of foods using a
numerical method based on enthalpy formulation. Journal of Food Science, 53(2), 626-630, 1988.

6. Rahman S. “Food properties handbook”. CRC Press, Boca Raton, 1995.

7. Cleland D.J., Valentas K.J. Prediction of freezing time and design of food freezers. In K.J. Valentas,
E. Rotstein, R.P. Singh (Eds.), “Handbook of food engineering practice”. CRC Press, Boca Raton,
1997.

Nomenclature
CPeff effective specific heat (J kg-1 °C-1)
CPf specific heat of the completely frozen food (J kg-1 °C-1)
CPu specific heat of the unfrozen food (J kg-1 °C-1)
2 -1
D diffusion coefficient (m s )
Deff effective diffusion coefficient for the solute (m2 s-1)
e1 total initial mass fraction of freezable water
-1
h enthalpy per unit mass (J kg )
hc heat transfer coefficient (W m-2 °C-1)
∆H0 latent heat of fusion of ice (kJ kg-1)
keff effective thermal conductivity (W m-1 °C-1)
kf thermal conductivity of the completely frozen food (W m-1 °C-1)
ku thermal conductivity of the unfrozen food (W m-1 °C-1)
• -3 -1
m mass rate of water solidification (kg m s )

t time (s)
tc time that takes the geometric center to reach -5 °C (s)
T temperature (°C)
T0 freezing point of pure water (°C)
Tf initial freezing point (°C)
Tref reference temperature (°C)
Greek symbols
ε volume fraction
-3
ρ density (kg m )
τ tortuosity
ψ spatial average of a function ψ
ψδ phase average of a function ψδ

ψδ
δ intrinsic phase average a function ψδ
Subscripts / Superscripts
0 at initial time
1 water
2 solute
i at ith node
n at nth time level
x in the x direction
α ice phase
β liquid phase
∞ at the bulk immersion solution
ICEF9 - 2004 International Conference Engineering and Food

Modelling the untake of guar gum into potatoes with variable diffusion coefficient and external
mass transfer resistance based on experimental data
Carbonell, S. (1), Oliveira J.C.* (2) and Oliveira, F.A.R (3)

(1) Department of Process Engineering, University College Cork, Ireland; s_carbonellm@yahoo.es

(2) Department of Process Engineering, University College Cork, Ireland; j.oliveira@ucc.ie
(3) Department of Process Engineering, University College Cork, Ireland; f.oliveira@ucc.ie

* Author to whom correspondence should be addressed

ABSTRACT

The mass transfer process of guar gum uptake by potatoes during blanching was studied. Samples
were immersed in solutions with different initial gum concentrations (5, 7.5 and 10 g/L), at isothermal
conditions (70, 80 and 85 °C). Crank’s method was applied to obtain a concentration-dependent
apparent diffusivity which integrates the effect of internal effective diffusivity and external mass
transfer coefficient. Variation of the latter throughout the process was the most dominant effect.

Key words: blanching, diffusivity, mass transfer, viscosity.

1. Introduction

Convenience products are one of the few booming segments in the food sector. Long-term
storage convenience products are generally minimally processed and then frozen. This includes fresh-
cut vegetables for use directly from frozen. Freezing causes damage to the food tissue due to the
formation of ice crystals, resulting in a loss of texture after thawing, which strongly depends on
freezing rate. Additives that affect water mobility and ice crystallisation could be used to offer further
protection of the fresh tissue texture. Long chain carbohydrates are known to increase glass transition
temperature and would therefore be potentially applicable to obtain higher texture-quality products.
Lee et al. (1), studied the effect of various polysaccharide gums on the final texture after a freeze-thaw
cycle of sweet potato starch gel and found that guar gum was an excellent freeze-thaw stabilizer
acting at two levels: cooperative effect of gums with water, and with starch chains.
Blanching conditions can also have an effect on the ability of vegetable tissues to withstand
the stresses caused by freezing/thawing (2) and can be combined with additive infusion (3). Guar gum
can be infused into the cell food structure during blanching by simply using a gum solution to blanch
the food. The process must be designed to meet both the blanching target (peroxidase inactivation)
and the infusion of a suitable amount of gum. The latter requires a careful study of the mass transfer
process, as the transfer of gum from the solution to the vegetable will cause a substantial change of
the viscosity of the blanching solution and of the occluded solution inside the vegetable, through which
the mass transfer takes place. Therefore, the mass transfer parameters, which vary strongly with the
ICEF9 - 2004 International Conference Engineering and Food

viscosity of the medium, are expected to vary with concentration, and hence with time, and cannot be
treated as constants.
In spite of polysaccharide gums being widely used in food processing, there are no diffusion
studies that characterize a time-dependent mass transfer kinetics of gum uptake.
For viscous solutions it is expected that the external mass transfer coefficient is relevant.
However, it may be difficult to estimate with precision both the internal effective diffusivity and the
external mass transfer coefficient from experimental data, as shown by Azevedo et al., (4). The
problem becomes more cumbersome when both are time-dependent. In such cases, the process
should be analysed with significant external resistance and then again with minimum external
resistance to try to isolate the quantification of each.
The aim of this study was to analyse the mass transfer process of gum uptake by potatoes
during blanching in non-agitated solutions, quantified in terms of a concentration-dependent apparent
diffusivity which integrates the joint effect of viscosity variation on the external mass transfer coefficient
and on the internal effective diffusivity.

2. Materials and Methods

Experimental set-up
Potato slices of 4cm of diameter by 4mm of thickness were
placed in a 4 L thermostatic bath set to a constant temperature and
containing 2L of a gum solution. Eight slices were suspended in the
solution in each experiment, placed far apart (minimum of 2 cm
between samples), as shown in figure 1. The bath was covered to
minimise losses by evaporation and the volume monitored to ensure
constant volume conditions. Three initial gum concentrations were
tested: 5, 7.5 and 10 g/L. In each case experiments were performed
at 3 temperatures (70, 80 and 85 °C).

Figure 1. experimental set-up

Concentration measurement
The gum uptake to the potatoes was determined by a mass balance from the variation of the
concentration of gum in the solution. At any given time t:
 C o − C  V
 g g b
Mt = (1)
8Ws

where Mt is the average mass concentration of gum in a potato slice at time t in g/g, Ws is the
average mass of one potato slice, Vb is the volume of the gum solution (2L), Cgo is the initial mass
concentration of gum in the solution in g/L and Cg is the mass concentration of gum in the solution at
time t.
The concentration of gum in the solution was measured by calibrating the rheological
properties of the solution against concentration, using standards. The rheological properties of 30
ICEF9 - 2004 International Conference Engineering and Food

standards with concentrations between 0.1 and 10 g/L of guar gum were analysed in the range of 18-
300 s-1 of shear rate in a concentric cylinder rheometer (Rotovisco RV12, Haake instruments), at 20
°C. The Ostwald-de Waele model (also known as power-law) fitted well all the data, with concentration
affecting both the fluid behaviour and the fluid consistency indexes. The latter provided the most
accurate and precise indication of concentration.

Sampling
Samples of the bath solution were removed from the bath every 30 minutes and allowed to
cool to 20 °C before measuring the fluid consistency and behaviour indexes over the 18-300 s-1 range
of shear rates. The calibration curve yielded the corresponding concentration of gum in the solution
(Cg), and from equation 1 the concentration in the potato samples at that sampling time was obtained.

Data analysis
The method described in Crank (5) was applied. For variable external concentration and
negligible external resistance, the solution of the diffusion equation is:

Mt ∞ 2 α (1 + α)
= 1− ∑ exp ( −D q n2 t / l 2 ) (3)
M∞ n = 1 1+ α + α 2 2
qn

where D is the average diffusivity from time 0 to time t, qn are the non-zero positive roots

of tan q n = − α q n , and α is the molar ratio in equilibrium, i.e. α = Vb/K.Vs, with K being the partition
coefficient (ratio of the equilibrium concentration of the gum in the potato to that in the solution), Vb the
volume of the bath (2L) and Vs the volume of the 8 potato slices.
From the definition of average value of a function:
t
∫ D t dt
D= 0 (4)
t
where Dt is the instantaneous value of diffusivity at any time t. Therefore, simple manipulation
and application of Leibniz’s rule for derivating finite integrals yields:

Dt =
( )
dD× t
(5)
dt
The procedure to obtain instantaneous values of diffusivity is therefore straightforward. The
average diffusivities from time 0 to each sampling time are obtained from the experimental data with
equation 3. Plotting these values multiplied by the respective time as a function of time and fitting the
data to a smooth function then yields Dt from the derivative of that function at each sampling time, as
equation 5 shows..
It is noted that this simple analytical method implies negligible external resistance, which is not
the case. There are no analytical solutions for variable external resistance with finite volume. The
diffusivity thus obtained is an apparent value which integrates the resistance to mass transfer by
diffusion inside the potato and the resistance to mass transfer by convection from the solution to the
ICEF9 - 2004 International Conference Engineering and Food

potato surface. As the gum uptake progresses, the viscosity of the external solution decreases (as the
gum concentration decreases) and therefore the external resistance drops (which would increase the
mass transfer rate). Conversely, the viscosity of the occluded solution inside the potato increases
along the process, and therefore the effective diffusivity decreases (which lowers the mass transfer
rate). Hence, the evolution of the apparent diffusivity determined by this method will indicate which of
the variations causes a greater influence on the mass transfer process: if the apparent diffusivity
increases with time the fall of the external resistance has a greater influence; if the apparent diffusivity
decreases with time, then the fall of the effective diffusivity has a greater influence.
In relation to the relative importance of both resistances, it is also noted that performing
experiments with different initial gum concentrations in the solution will highlight the importance of the
external resistance: plotting the apparent diffusivities as a function of the concentration in the potatoes
will yield different curves for the different initial concentrations when external resistance is important. If
these curves differ, that will be due to the different absolute value of the concentration of the external
solution, that is, its viscosity and the absolute value of the external resistance.

3. Results and Discussion

Figure 2 shows the experimental data obtained. An example of the graphs of D x t versus t,
from where the instant apparent diffusivity is taken, is shown in figure 3. In most cases second order
polynomials provided a good fit for the smooth function from where the derivatives were calculated. It
is noted that axis are shown in min for visualisation, but calculations were performed using units of s.

10
2.50E-07
9

8 2.00E-07

7
1.50E-07
6
D.t (m )
2
Cg (g/L)

5 1.00E-07
4

3 5.00E-08

2
0.00E+00
1 0 100 200 300 400
t (min)
0
0 50 100 150 200 250 300 350 400
time (min)
Figure 3. Average diffusivity multiplied by time as a
function of time for the experiment at 80 °C
and 7.5 g/L initial gum concentration. The
Figure 2. Experimental data (concentration in the solution). Open smoothing function shown is a second order
symbols indicate initial gum concentration of 5 g/L, polynomial with correlation coefficient of 0.995
black symbols 7.5 g/L and grey symbols 10 g/L.
Squares indicate a temperature of 70 °C, losangles 80
°C and triangles 85 °C.
ICEF9 - 2004 International Conference Engineering and Food

Figures 4 to 6 show the apparent diffusivity at the 3 temperatures as a function of the

concentration of gum in the potatoes. It can be seen that 1.4E-10

with the exception of the lowest temperature and lowest 1.2E-10

initial concentration in the solution, the apparent 1.0E-10

diffusivity increased with the concentration in the

Da (m2/s)
8.0E-11

6.0E-11
potatoes, which means that it increased with time.
4.0E-11
Therefore, the influence of the decreased viscosity of the
2.0E-11
solution in lowering the external mass transfer resistance
0.0E+00

was more important than the increased viscosity of the 0 0.05 0.1 0.15
Mt (g/g)
occluded solution in the potato and consequently the
Figure 4. Variation of the apparent diffusivity with
greater resistance to internal diffusion. the concentration of gum in the potato
at 70 °C. Initial concentrations in
The different behaviour at the lowest solution … 5 g/L, ‘ 7.5 g/L U 10 g/L
temperature and lowest initial concentration can be
1.8E-09
attributed to the particularities of the functionality of the 1.6E-09

various influences. These conditions yielded the shortest 1.4E-09

1.2E-09
experimental range of concentrations of the solution and

Da (m2/s)
1.0E-09

hence of its viscosity, at the lowest values, and with low 8.0E-10

-10 2 6.0E-10
apparent diffusivities (1.2 - 1.3 x 10 m /s). In those
4.0E-10

conditions the external resistance variation was likely to 2.0E-10

0.0E+00
have been the smallest and hence the influence of the 0 0.1 0.2 0.3 0.4

decreasing internal effective diffusivity was relatively Mt (g/g)

more important. Figure 5. Variation of the apparent diffusivity with

the concentration of gum in the potato
Figures 4 to 6 also show that when the at 80 °C. Initial concentrations in
solution „ 5 g/L, ‹ 7.5 g/L S 10 g/L
concentration of the solution is higher the apparent
diffusivity is lower, which shows the significant influence 1.0E-08

of the external mass transfer resistance on its own. At 9.0E-09

8.0E-09

the two higher temperatures the apparent diffusivities 7.0E-09

6.0E-09
become similar at the two highest initial concentrations,
Da (m2/s)

5.0E-09

but it is noted that in those cases (and those alone) the 4.0E-09
3.0E-09
concentration of gum in the solution has also become 2.0E-09
1.0E-09
similar for those experimental points (see figure 2). 0.0E+00
0 0.1 0.2 0.3 0.4 0.5
Mt (g/g)

Figure 6. Variation of the apparent diffusivity with

the concentration of gum in the potato
at 85 °C. Initial concentrations in
solution „ 5 g/L, ‹ 7.5 g/L S 10 g/L
ICEF9 - 2004 International Conference Engineering and Food

4. Conclusions

The infusion of guar gum into potatoes during blanching in non-agitated media is significantly
affected by the external mass transfer resistance, to the point of the mass transfer rate increasing
significantly during the blanching process due to the decrease in viscosity resulting from the loss of
gum from the solution into the potato. This effect is much more important than the potential lowering of
the effective diffusivity due to the higher viscosity inside the potato. Therefore, while increasing the
gum concentration in the blanching solution increases the driving force, it significantly lowers the mass
transfer rate due to the greater external resistance, and hence there will be an optimum concentration
(which will depend on the blanching temperature) for maximum uptake of the gum.
Process modelling to estimate the optima will require the determination of a concentration-
dependent variable external mass transfer coefficient. This can be achieved by performing similar
experiments with sufficient agitation to eliminate the external resistance, from where the internal
effective diffusivity and its dependence on the gum concentration in the potato can be evaluated. The
experimental data reported here can then be used with an appropriate model to yield the external
mass transfer coefficient. Its dependence on viscosity can then be determined.

References:

1. Lee, M.H, Baek, M.H., Cha, D.S, Park, H.J. and Lim. S.T. (2002). Freeze-thaw stabilization of
sweet potato starch gel by polysaccharide gums. Food Hydrocolloids. 16: 345-352.
2. Agblor, A. and Scanlon M.G. (1998). Effects of blanching conditions on the mechanical properties
of french fry strips. American Journal of Potato Research. 75 (6): 245-255.
3. del Valle, J.M., Aránguiz,V. and León, H. (1998). Effect of blanching and calcium infiltration on PPO
activity, texture, microstructure and kinetics of osmotic dehydration of apple tissue. Food Research
International. 31 (8): 557-569.
4. Azevedo, I.C.A., Oliveira, F.A.R. and Drumond, M.C. (1998). A study on the accuracy and precision
of external mass transfer and diffusion coefficients jointly estimated from pseudo-experimental
simulated data. Mathematics and Computers in Simulation, 48 (1): 11-22
5. Crank, K. (1985). The Mathematics of Diffusion. Oxford University Press, Oxford, UK
ICEF9-2003 International Conference on Engineering and Food
Equivalences between diffusion, compartmental and transfer function models in drying:
application to the thin layer drying of rice

Francis Courtois and Gilles Trystram

UMR-GENIAL, 1 Avenue des Olympiades, 91744 Massy, France, email: courtois@umr-genial.org

Abstract
This paper shows the similarities between 3 different modeling approaches of the heat and mass transfers
in drying. The classic diffusion model, when discretized in n volumes, is equivalent to a n-compartment
model. The later, when linearized, can be rewritten in state-space representation and,easily converted in
a transfer function. A simple numerical application is given for thin layer drying of rice.

Keywords
drying, rice, diffusion, compartment, transfer function, model.

Introduction
Modelling is a single, and thus simple, word hidding many different aspects. Modelling is not a one step
ahead methodology. First of all, there are many approaches available. For instance, there are many
different drying models. Some are considered to be theoretically better than others. The diffusion model
is probably the favourite pick. To take over biased judgements, the purpose of this paper is to show how
close compartmental models and transfer functions (considered as black-box models) can be to diffusion
models (considered as white-box models).

Problem formulation
When considering drying models which take into account internal moisture content gradient and are
broadly validated on a large drying domain, only diffusion based models and compartmental models
appear competitive. In the following examples, the product is assumed having an internal moisture
content gradient and being uniform in temperature. Within the product, mass transfers occur only in
the liquid form and vaporization takes place only at the surface. The heat transfer is convective. The
product is typically a grain (e.g. rice) with an approximately spherical shape.

The equation sets correspond to thin layer models i.e. models for one average grain. Initial conditions
are similar: at the initial time, grain moisture content X is assumed uniform and equal to X0 , and grain
temperature Tg = Tg0 .

Diffusion model
The model is written in spherical coordinates since a spherical shape of radius R is assumed. The diffusion
coefficient D and the heat transfer coefficient h are assumed to be uniform (over the radius 0 < r < R)
and constant. The exact equation set follows (1-2):

δ2 X
 
dX 2 δX
=D + (1)
dt r δr δr2
and, for the heat balance, using ρg and Cpg , the density and heat capacity of the grain, we have:

dTg −ha(Tg − Ta ) − Ka(Xequ − XR ).Lv

= (2)
dt ρg Cpg

with the boundary condition at the surface (r = R) of the grain:

ICEF9-2003 International Conference on Engineering and Food

δXr=R
−D = K(Xequ − Xr=R ) (3)
δr
and at the center (r = 0) of the grain:
δXr=0
−D =0 (4)
δr
In equations (2-3), the mass transfer, at the surface, is assumed to be proportional to a difference of
moisture contents (with Xequ equilibrium moisture content for the air side) instead of a difference between
product and air partial vapour pressures. This is done only for linearizing reasons since the latter has a
stronger physical sense.

Before doing any calculation, let us remark that:

δ2 X 1 δ r2 δX


2 δX δr
. + = (5)
r δr δr2 r2 δr
Then, assuming the sphere can be divided in n (with n → ∞) concentric shells. The corresponding
separation radius are noted Ri with i ∈ {0, 1, . . . , n}. Then, the volumic mean derivative for moisture
content of shell #i (0 < i < n) is:
R Ri R Ri 2 h 2 δX δ2 X
i
2 δX(r) 3 r D . + dr
δXi R
4πr δt dr Ri−1 r δr δr 2
= i−1 R Ri = 3 3

(6)
δt 4πr2 dr Ri − Ri−1
Ri−1

using equation 5, and assuming D is uniform, it gives:

Ri
3D r2 δX

δXi δr Ri−1
= (7)
Ri3 − Ri−1
3


δt
Now, consider Ri the average radius of shell #i
R Ri 2
R Ri 3
Ri−1 4πr r dr Ri−1 4πr dr 3 Ri4 − Ri−1
4


Ri = = 4 3 3
=
with R0 = 0 (8)
4 Ri3 − Ri−1
3
R Ri

2
Ri−1 4πr dr 3 Ri − Ri−1

and assume shells are thin enough (i.e. n → ∞ ) to solve equation 7 by a finite difference, one obtains:

 
δXi 3D 2 δX(r = Ri ) 2 δX(r = Ri−1 )
= R − R
δt Ri3 − Ri−1
3 i
δr i−1
δr
 
3D 2 Xi+1 − Xi 2 Xi − Xi−1
= Ri − Ri−1 (9)
Ri3 − Ri−1
3
Ri+1 − Ri Ri − Ri−1

arranging the terms and forcing a surface to volume ratio to appear, gives:

2
δXi 4πRi2 D
4πRi−1 D

= 4 3 3

X i+1 − X i − 4 3 3

Xi − Xi−1 (10)
δt 3 π Ri+1 − Ri Ri+1 − Ri 3 π Ri − Ri−1 Ri − Ri−1

Introducing Si/i+1 surface area between shells #i and #i+1 and Vi volume of shell #i, equation 10
can be rewritten as:

δXi Si/i+1 D
Si−1/i D

= Xi+1 − Xi − Xi − Xi−1 (11)
δt Vi Ri+1 − Ri Vi Ri − Ri−1
Then, introducing, similarly, exchange coefficients:
Dρdm Dρdm
Ki/i+1 = and Ki−1/i = (12)
Ri+1 − Ri Ri − Ri−1
ICEF9-2003 International Conference on Engineering and Food
we obtain:

δXi Si/i+1 Ki/i+1
Si−1/i Ki−1/i

= Xi+1 − Xi − Xi − Xi−1 (13)
δt ρdm Vi ρdm Vi
For i = 1 (0 < r < R1 ), it is straightforward to obtain:

δX1 S1/2 K1/2

= X2 − X1 (14)
δt ρdm V1
and for i = n (Rn−1 < r < Rn ):

δXn Sn/air Kn/air
Sn−1/n Kn−1/n

= Xequ − Xi − Xn − Xn−1 (15)
δt ρdm Vn ρdm Vn
The full set of equation for this diffusion model (assuming n shells) is noted [Md]:



 δX1 S K1/2

= 1/2 X2 − X1




 δt ρ dm V 1



 δXi = Si/i+1 Ki/i+1 Xi+1 − Xi
− Si−1/i Ki−1/i Xi − Xi−1
f or 1 < i < n


δt ρdm Vi ρdm Vi

Sn−1/n Kn−1/n
S Kn/air

 δX


δt = − Xn − Xn−1 n/air Xequ − Xn

 n

 ρdm Vn ρdm Vn




 dTg = −hSn/air (Tg −Ta )−Kn/air Sn/air (Xequ −Xn ).Lv


dt ρg Vg Cpg
RR 2 Pn
Pn 4πr X(r) dr Vi X i
with Vg = 1 Vi and X = 0 R R 2 = 1Vg
4πr dr
0

n-Compartment model
Consider the general formulation of a n-compartment drying model, noted [Mc]:
S1/2 K1/2

δX1
 δt = ρdm V1 (X2 − X1 )

 δXi = i/i+1 Ki/i+1 (X
S Si−1/i Ki−1/i

i+1 − Xi ) − (Xi − Xi−1 ) f or 1 < i < n

δt ρdm Vi ρdm Vi
δXn Sn/air Kn/air Sn−1/n Kn−1/n
δt = ρdm Vn (Xequ − Xi ) − ρdm Vn (Xn − Xn−1 )


 dTg = −hSn/air (Tg −Ta )−Kn/air Sn/air (Xequ −Xn ).Lv


dt ρg Vg Cpg
Pn
Pn Vi X i
with Vg = 1 Vi and X = 1Vg
When n → ∞, there is an obvious analytical equivalence between [Md] and [Mc]. In practice, n is
generally equal to 2 or 3. In that case, the equivalence appears only at the numerical level, i.e. when
equation 1 is discretized with a n-shell finite difference scheme.

State-space representation
Assuming ρg Cpg , Ki/j , Si/j and Vi are constants ∀i ∈ [1, 2 · · · , n], models [Mc] and [Md] are linear in
their inputs (Ta and Xequ ). Grouping variables in input and state variable vectors:

u(t) = [Xequ , Ta ]0

x(t) = [X1 , X2 · · · , Xn , Tg ]0
Considering, that only X and Tg are actually measured, we introduce the output vector y:

y(t) = [X, Tg ]0
Model [Md] (and, thus, [Mc]) can be compacted in its state-space representation noted [Mss]:
ICEF9-2003 International Conference on Engineering and Food

ẋ(t) = Ax(t) + Bu(t)
y(t) = Cx
where A, B and C are constant matrices:

S1/2 K1/2 S1/2 K1/2

 
− ρdm V1 ρdm V1 0 ··· ··· 0
 S1/2 K1/2 S K1/2 S2/3 K2/3 S2/3 K2/3 

 ρdm V2 − 1/2
ρdm V2 − ρdm V2 ρdm V2 0 ··· 0 

 .. .. 
A=
 0 ··· . . ··· 0 

Sn−1/n Kn−1/n S Kn/air
0 ··· ··· − n/air 0
 
 ρdm Vn ρdm Vn 
.. ..
 
Kn/air Sn/air Lv −hSn/air
0 ··· . . − ρg Vg Cpg ρg Vg Cpg

 
0 0
 .. .. 

 . . 

B= 0 0 
Sn/air Kn/air
 

 ρdm Vn 0 

Kn/air Sn/air Lv hSn/air
ρg Vg Cpg ρg Vg Cpg
 V1 V2 Vn 
Vg Vg ··· Vg 0
C=
0 ··· 1

Analytical solution
Using the fact that matrices A, B and C are constant, it is possible to solve analytically [Mss] when
u is constant (i.e. drying under constant conditions). Additionally, we assume A is non-singular (i.e.
invertible). First, we define a new state variable vector z as:

z = x + A−1 .B.u (16)

thus, it is obvious that

ż = ẋ (17)
and

ż = ẋ = Ax + Bu = Az (18)
thus

ż = Az (19)
which is easy to integrate analytically since A is a constant matrice. For that purpose, we first need
to diagonalize A assuming that:

A = P.D.P −1 (20)
where D is a diagonal matrice and P is a transformation matrice (formed with the eigenvectors of A).
Thus, (19) becomes:

ż = P.D.P −1 .z (21)
which should be rewritten as

P −1 .ż = D.P −1 .z (22)

Let us create now another state variable vector w as
ICEF9-2003 International Conference on Engineering and Food

w = P −1 .z = P −1 .(x + A−1 .B.u) (23)

Thus, (21) is equivalent to

ẇ = D.w (24)
which is integrated straightforward as:

w = eD.t .w0 (25)

with

w0 = P −1 .z0 = P −1 .(x0 + A−1 .B.u)7 (26)

x = P.w − A−1 .B.u (27)

Thus, the final solution appears:

x = P.eD.t .P −1 .(x0 + A−1 .B.u) − A−1 .B.u (28)

Transfer function
Since the model [Mss] is linear in its inputs and state variables, it is possible to apply the Laplace
transform to it (s ∈ C
l is the Laplace variable):

L.T. sx(s) = Ax(s) + Bu(s)
[M ss] →
y(s) = Cx(s)
furthermore, it is easy to obtain an input / output relationship :

(pI − A)x(s) = Bu(s) where I is identity matrix

y(s) = C(pI − A)−1 u(s)

the expression C(pI − A)−1 is the transfer function hmatrix (2x2 transfer i functions). If only X is
V1 V2 Vn −1
actually measured, y and C change to y = [X] and C = Vg , Vg , · · · , Vg , 0 and C(pI − A) becomes a
single input - single output transfer function (between Xequ and X).

It is possible to discretize the [Mss] system from continuous to discrete system and obtain a discreet
transfer function using the Z-transform instead of Laplace-transform. The resulting discreet transfer
function can be easily identified using experimental data and a computer with appropriate software.

Application to rice drying

Abud Archila [1, 2] have extensively worked on the modeling of rice drying. We have taken one sample
thin layer kinetic noted MARIZ804 where drying conditions are approximatly constant (T a = 80◦ C and
Xequ = 0.012 dry basis). We approximate the average rice grain by a sphere of 0.001 m radius with a
dry matter density ρdm of 1500.0 kg per m3 . We do not consider, here, the heat transfer part included
in above models: we focus only on the simulation of the mass transfer.

According to [3] and [4], and assuming ∀t X(r = R) = Xequ , the solution of the diffusion model (part
of [Md]) is:
∞
X(t) − Xequ X 6 −Dn2 π2 t
= 2 n2
e R2 (29)
X(t = 0) − Xequ n=1
π

which can be easily computed (D = 27.10−12 m2 .s−1 here) .

ICEF9-2003 International Conference on Engineering and Food

We consider also a 10-compartment model, with equal volumes for each compartment (V i = Vg /10),
and K coefficients calculated from (12) except Kn/air = 9.33 10−4 kg.m−2 .s−1 . Simulation is done from
the analytical solution given in (28).

1
exp
diff
10 comp.
0.9 Abud
2 comp.

0.8

moisture content X (d.b.)

0.7

0.6

0.5

0.4

0.3

0.2
0 500 1000 1500 2000 2500 3000 3500 4000
time t (s)

Figure 1: Comparison of diffusion, compartmental (10 and 2 compartments) models versus experimental
data and reference model (Abud Archila’s).

Simulations are compared with experimental data from Abud Archila [1, 2] on figure 1. Abud Archila’s
model and diffusion model are the closest. There is a noticeable difference between 10-compartment and
2-compartment models and experimental data. Nevertheless, Abud’s model is a 2-compartment model
but with very specific exchange coefficients K depending on internal temperature and moisture content.
In our simulations of the 2- and 10-compartment models, K are calculated according to equation 12 and
given D. Also, Kn/air has been tuned empirically.

As a concluding remark, diffusion-based models, compartment-based models or control oriented mod-

els (e.g. state space models or transfer functions) are very similar as long as they remain linear in their
parameters. Analytical solutions are available and performances are close. Some converting rules where
stated.

References
[1] Abud Archila, M., Courtois, F., Bonazzi, C., Bimbenet, J.J. A compartmental model of thin layer
drying kinetics of rough rice, Drying Technology, 18(7): 1389-1414, 2000.
[2] Abud Archila, M. Modélisation simultanée des transferts et de l’évolution de la qualité technologique
du riz paddy en vue d’optimiser les conditions de séchage. PhD report, ENSIA, Massy, France, 2000.
[3] Crank, J. The mathematics of diffusion, Clarendon Press Publishers, Oxford, UK, 1967.
[4] Parry, J.L. Mathematical modelling and computer simulation of heat and mass transfer in agricultural
grain drying: a review. NIAE report R.44, 1984.
ICEF9 – 2003
International Conference Engineering and Food 1

Modeling the Spaghetti Hydration Kinetics During Cooking and Overcooking

M. A. Del Nobile1, G. G.Buonocore2, A. Conte1, G. Gambacorta1

1
Department of Food Sceince, University of Foggia, Via Napoli, 25 – 71100 Foggia, Italy.
E-mail: ma.delnobile@unifg.it
2
Institute of Composite and Biomedical Materials, National Research Council, P.le Tecchio, 80 –
80125 Naples, Italy.
E.mail: gbuonoco@unina.it

Abstract
A study on the influence of raw materials and processing conditions on hydration kinetics during
cooking and overcooking of spaghetti is presented. Water sorption tests on commercially available
spaghetti and on three different types of home-made spaghetti were run at 100 °C. The spaghetti
hydration process was quantitatively resolved into the controlling phenomena by fitting a novel
mathematical model to the experimental data. Results suggest that the processing conditions
influence at a higher extent the quality of spaghetti with respect to raw materials.

Key Words: Modeling, Water sorption kinetic, Spaghetti, Moving boundary

Materials and methods

Four different types of spaghetti were used to run the tests; specifically: a commercially available
spaghetti from a single source (Barilla), with a diameter equal to 1.60 ± 2.6·10-2 mm (in the following it
will be referred to as Sample A), and three experimental samples of spaghetti produced with three
different types of semolina: Simeto (a durum wheat cultivar, in the following it will be referred to as
Sample B), Dicocco Garfagnana (a selected strain of strain of Triticum turgidum spp dicoccum, in the
following it will be referred to as Sample C) and Linea 324 (a new genotype from the cross between
durum wheat and T. turgidum spp dicoccum, in the following it will be referred to as Sample D). As
reported above, the investigated samples differ either for the raw materials or for the processing
conditions. In particular, it is reasonable to assume that sample A and B differ only for the processing
conditions, while samples B, C and D differ only for the raw materials (1).
Sorption tests were performed using 5 ± 0.64 cm long samples. Culture tubes containing about
70 cm3 of distilled water were equilibrated at 100 °C in a thermostatic bath (± 0.5 °C accuracy).
Afterwards, the samples were immersed into the tubes, one for each tube. The sample external
diameter was measured by means of a chathetometer (Galileo, Florence, Italy) with an accuracy of
1/760 mm, while a gauge with an accuracy of 1/20 mm was used to evaluate the length.
The position of the central core was determined by means of an optical microscope (NIKON,
model OPTIPHOT-2) equipped with cross polarized light.

Modeling
The water uptake kinetic during cooking and overcooking depends on four phenomena: 1) starch
crystalline domain melting kinetic; 2) water diffusion; 3) macromolecular matrix relaxation kinetic; 4)
“residual deformation” release kinetic. In the following, each of the above phenomena will be
presented separately.
Melting kinetics of the starch crystalline domains
The crystals melting kinetic is generally very fast if compared to the phenomenon controlling the
water uptake kinetic at the early stage of the hydration process (i.e., the diffusion of water molecules
into spaghetti). Therefore, it is reasonable to assume that as the local water concentration reaches
(ρ ⋅C )
*

W
(that is, the value of the local water concentration at which the melting temperature of the
starch crystals is equal to that of boiling water), the local degree of crystallinity falls to zero (fully
gelatinized starch).
Water diffusion and macromolecular matrix relaxation
The diffusion of low molecular weight compounds in macromolecular systems is generally
governed by two simultaneously occurring phenomena: 1) a substantially stochastic phenomenon
(related to Brownian motion), where the penetrant flows exclusively driven by a concentration gradient;
2) a relaxation phenomenon driven by the distance of the local system from the equilibrium (2).
Water diffusion related to Brownian motions is generally described by means of the Fick’s model.
In the specific case of diffusion through a long cylinder (mono dimensional geometry), the Fick’s model
reduces to the following expression:
ICEF9 – 2003
International Conference Engineering and Food 2

r
J = −DF ⋅
( )
∂ ρ⋅ C W r 
⋅ r = − A1 ⋅exp
−1 (
 ⋅
)
 ∂ ρ⋅ C W r
⋅r (1)
∂r  A2 + A 3 ⋅ ρ C⋅ W  ∂r
r
where: J is the diffusive mass flux, ρ is the density of the macromolecular matrix (i.e., starch plus
proteins) defined as the ratio between the weight of the macromolecular matrix and the volume of the
mixture (i.e., water plus r macromolecular matrix), C W is the local water concentration, DF is the water
diffusion coefficient, r is the radial unit vector, r is the radial coordinate, Ai are constants to be
determined by fitting the model to the experimental data.
Assuming that the pasta and water volumes are additive on mixing (3), it can be easily
demonstrated that ρ depends on the local water concentration through the following expression:
 1 CW 
ρ = 1/  +  (2)
 ρp ρ W 
where: ρp is the initial density of spaghetti strand, ρW is the water density. Since it was assumed that
( )
*
starch crystals melt as soon as the local water concentration reaches ρ ⋅CW , the dependence of DF
on the local degree of starch gelatinization can be described simply by providing the ratio between the
water diffusion coefficient of no-gelatinized spaghetti and that of the fully gelatinized spaghetti. Based
on the above arguments, the complete description of the water diffusion coefficient is given by the
following expressions:
  −1 
( )
*
DF = A 1 ⋅ exp  if ρ⋅ CW ≥ ρ⋅ C W
  A 2 + A3 ⋅ ρ ⋅CW 
 (3)
  
−1
( )
*
 DF = K ⋅ A1 ⋅ exp A + A ⋅ ρ C 
⋅ W 
i f ρ⋅ C W < ρ⋅ CW
  2 3

where: K is the ratio between the water diffusivity of no-gelatinized spaghetti and that of the fully
gelatinized spaghetti. Several approaches are reported in the literature to describe solvent induced
polymer relaxation (2). Among them, one of the simplest is that proposed by Long and Richman (4).
The rate at which the water concentration at the boundaries gradually increases is directly related to
the relaxation of the macromolecular matrix, which in turn depends on two factors: the macromolecular
mobility and the distance of the system from its equilibrium state. In this investigation the following
empirical expression is proposed to describe the boundary condition relaxation rate:
()
dα t
dt
() { [( ( ))]}
= α1 ⋅ α t  ⋅ 1 − exp − 1 − α t
 
(4)
where: α(t) is the normalised water volume fraction at the boundaries of the spaghetti strand at time t,
() ()
defined by the following equation: α t = νBW t / νeq. W ()
, νBW t is the water volume fraction at the
spaghetti boundary at time t, νeq.
W
is the equilibrium water volume fraction sorbed in the spaghetti
strand, α1 is a constant to be evaluated by fitting the model to the experimental data. α(t) spans from
zero to one, and represents the driving force of the macromolecular matrix relaxation phenomenon.
“Residual deformation” release kinetic
The release kinetic of the “residual deformation” is similar to a creep recovery test (5). Therefore,
to quantitatively describe the above phenomenon the expression used to describe the creep recovery
test of a Voigt-Kelvin element (6) was used:
()
Lm.m. t
= 1−
∆Leq.   t
⋅ 1 − e x p−
 
m.m.
(5)
L0 L0   τ 
where: Lm.m.(t) is the length of the macromolecular matrix at time t (it decreases as the system
approaches its equilibrium dry length), L0 is the initial length of the spaghetti strand, ∆Leq. m.m.
is the
difference between the initial length of spaghetti strand and its dry length at infinite time (i.e., the
length that the dry spaghetti would have if the macromolecular matrix were in the equilibrium
conformation), τ is the relaxation time of the “residual deformation” release kinetic.
Water concentration profile
The time course during cooking and overcooking of the local water concentration profile inside
the spaghetti strand was calculated by solving a set of differential equations obtained by writing the
integral water mass balance equation for each of the “n” concentric elements in which the spaghetti
strand was divided. For each of the “n” elements it is possible to write the following equation:
ICEF9 – 2003
International Conference Engineering and Food 3

 r r
∫ ( ) ( )
∂
∫
d
⋅ ρ ⋅CW ⋅d V = DF ⋅ ∂r ρ⋅ CW ⋅ r • n  ⋅ dS (6)
dt V( t) S( t)  
where: V(t) is the volume that contains ran amount of macromolecular matrix equal to the initial one,
S(t) is the surface of the volume V(t), n is the unit vector normal to the surface. Equation (7) was
derived neglecting amylose depletion (7, 8). The set of “n” equations, obtained by writing (7) for the “n”
elements, were solved numerically using the following initial and boundary conditions:

C = 0 ⇒ t= 0 ; 0< r < R0
 W

C W = C W t
B
()
⇒ ∀ t ; =R r t () (7)

(
 ∂ ρ⋅ CW

)= 0 ⇒ ∀ t; r= 0
 ∂r
where: R0 is the initial radius of the spaghetti strand, R(t) is the radius of the spaghetti strand at time t,
()
CBW t is the water concentration at the spaghetti boundary at time t. The value of V(t) was determined
by evaluating the evolution during hydration of the length and the diameter of each element. The
evolution of the spaghetti length was evaluated by solving the longitudinal force balance equation (i.e.,
the balance on the force acting on the spaghetti strand along its longitudinal direction). The
longitudinal force balance equation was derived under the following assumptions: the influence of the
radial component of the stress tensor on the longitudinal one was neglected; each of the elements
composing the spaghetti strand have the same length during the entire hydration process; each
element behaves as a purely elastic media; the spaghetti elastic modulus depends on the local water
concentration through the following empirical expression:
(
E = E 0 ⋅exp −E1 ⋅ ρ C ⋅W ) (8)
where: E is the spaghetti’s elastic modulus, E0 is the initial value of the spaghetti’s elastic modulus, E1
is constant to be determined by fitting the model to the experimental data, it is a measure of the ability
of the water to reduce the spaghetti’s elastic modulus (i.e., to plasticize the macromolecular matrix).

Results and Discussion

Model Validation
To validate the proposed model, hydration tests were performed at 100 °C on four different types
of spaghetti. In particular, the weight, the length and the diameter of the investigated spaghetti were
monitored during hydration (i.e., over a period of about 200 minutes). As an example figure 1 shows
the results obtained for Sample A. The curves showed in the above figure were obtained by fitting the
model simultaneously to the sets of experimental data available for each type of spaghetti (i.e., weight,
length and diameter plotted versus time).
6

1.2

4
0.8

2
0.4

0 0.0
0 4.103 8.103 1.104
Time [s]
Figure 1: (W (t ) − W )/ W , (L(t) − L ) /L and (R(t) −R ) /R plotted as a function of time for sample A.
0 0 0 0 0 0

( ) ( W (t ) − W )/ W , ( ) (L(t ) − L ) /L , ( ) (R(t ) −R ) /R . (L(t) is the length of the spaghetti strand at time t,

0 0 0 0 0 0
W(t) is the weight of the spaghetti strand at time t, W0 is the initial weight of the spaghetti strand).

The values of the model’s parameters obtained are listed in table 1. The goodness of fit was
ICEF9 – 2003
International Conference Engineering and Food 4

evaluated by means of the relative percent difference, E% (9). The calculated values of E% are
listed in table 2. As it can be inferred from the values of E% , the proposed model satisfactorily fits the
experimental data corroborating the hypothesis used to derive it.
Model’s Parameter Sample A Sample B Sample C Sample D
( ) [ ]
*
0.494 0.290 0.255 0.285
ρ ⋅CW
3
g/cm
E1 [cm3/g] 7.42 5.89 5.22 4.66
()[
CBW 0 g H2O / g d r y s p a g h e t t i ] 1.33 1.76 1.76 1.81
3
A1 [cm /g] 2.05·10-3 1.65·10-3 1.46·10-3 1.70·10-3
A2 0.132 0.137 0.131 0.140
A3 [cm3/g] 0.180 0.153 0.166 0.144
K 0.187 7.98·10-2 9.53·10-2 7.16·10-2
α1 [1/s] 7.44·10-4 5.06·10-4 4.91·10-4 5.14·10-4
( ∆L ) / L
eq.
m.m. 0
0.202 0.179 0.177 0.195
τ [s] 6.18·10-2 4.55·10-27.45·10-24.45·10-2
Table 1: Values of the model’s parameter obtained by fitting the proposed model to the experimental data. ( C 0 is the water
B
W ()
concentration at the spaghetti boundary at time zero, it represents the instantaneous response of the system to the increase of
the external water activity)

E%
SAMPLE A SAMPLE B SAMPLE C SAMPLE D
( W(t ) − W ) / W
0 0 3.38 3.61 3.42 3.53
(R(t ) − R ) /R
0 0
6.12 5.37 4.53 6.74
(L( t) − L ) /L
0 0
6.88 9.69 10.07 9.48
Table 2: Values of E% for each of the experimental data set fitted.

Figures 2 shows the enlarged photographs of Sample A cross section taken at different stages of
the cooking process. The above figure show the presence of a traveling discontinuity that moves
towards the center of the spaghetti as the hydration process proceeds. Figures 3 shows the evolution
of the local water concentration profile during the hydration process as predicted by means of the
proposed model using the data listed in table 1. As shown in figure 9, there is a discontinuity that
moves from the spaghetti’s boundary towards its center. This finding is in agreement with the data
showed in figure 2, further corroborating the hypothesis used to derive the proposed model.

Figure 2: Enlarged photographs of the

spaghetti cross section taken at different
stages of the hydration process for sample
A.

Hydration time = 0.5 mi n Hydration time = 4.5 min

Hydration time = 8 mi n Hydration time = 10 mi n

ICEF9 – 2003
International Conference Engineering and Food 5

Figure 3: The evolution of the local

0.8 water concentration profile during
hydration at the 100 °C as predicted by
the model using the data listed in table
1. ( ) 60 s, sample A; ( )
0.6 300 s, sample A; ( ) 60 s,
sample B; ( ) 300 s, sample B;
( ) 60 s, sample C; ( )
300 s, sample C; ( ) 60 s,
0.4 sample D; ( ) 300 s, sample D.

0.2

0.0
0.00 0.04 0.08 0.12 0.16
r [cm]
Influence of Raw Materials and Process Conditions
As pointed out in the modeling section, the spaghetti hydration process can be quantitatively
resolved into the three controlling phenomena (i.e., water diffusion, macromolecular matrix relaxation
kinetic, and “residual deformation” release kinetic) by fitting the presented model to the experimental
data. In the following the influence of raw materials and process conditions on the hydration kinetic of
the investigated spaghetti will be discussed by analyzing each of the three phenomena involved during
hydration.
As showed in figure 3 there is a substantial difference between the evolution of the water
concentration profile of sample A and that of the other three samples investigated. In particular, the
water concentration at the spaghetti’s boundary is lower in the case of sample A than in the case of
the other three samples (see also figure 4).
3
Figure 4: ()
CBW t plotted as a
function of time. ( ) sample
A, ( ) sample B, ( )
sample C, ( ) sample D.

1
0 200 400 600 800
Time [s]
Moreover, the traveling discontinuity relative to sample A is always closer to the center of the
spaghetti strand than that relative to the other three samples. With respect to the water concentration
at the spaghetti’s boundary, the samples differing only for the raw materials (i.e., samples B, C and D)
show a similar behavior, while the samples differing for the processing conditions (i.e., samples A and
B) show a different behavior. Considering the characteristics of the four investigated samples, the
observed differences should be attributed to the different processing conditions (extrusion and
desiccation process), which most probably have promoted the formation of a different structure of both
protein and starch phase in the two examined samples (i.e., samples A and B).
As reported above, the time that the traveling discontinuity requires for reaching the center of the
sample differ from sample to sample. In particular, samples B, C and D need almost the same time to
reach the center of the sample. On the contrary, sample A requires a shorter time. The above results
are in agreement with that showed in figures 5 and 6, where the water diffusion coefficient is plotted as
a function of ρ.CW, in the case of no-gelatinized spaghetti and in the case of fully gelatinized spaghetti
respectively. In fact, the water diffusion coefficient of sample A is always higher than that of the other
ICEF9 – 2003
International Conference Engineering and Food 6

three samples. Considering the different characteristics of the four examined samples, in terms of raw
materials and processing conditions, the obtained results seems to corroborate the idea that the
processing conditions influence at a greater extent the properties of the macromolecular matrix if
compared to the raw materials.

References
(1) Novaro, P., D’Egidio, M. G., Mariani, B. M., Nardi, S.. Combined effect of protein content and high-
temperature drying systems on pasta cooking quality. Cereal Chem. 70:716-719, 1993
(2) Del Nobile, M. A., Mensitieri, G., Netti, P. A., Nicolais, L. Anomalous Diffusion in Poly-Ether-Ether-
Ketone. Chemical Engineering 49:633-644, 1994.
(3) Del Nobile, M. A., Massera, M. Modeling of Water Sorption Kinetic in Spaghetti during
Overcooking. Cereal Chem. 77(5):615-619, 2000.
(4) Long, F. A., Richman, D. Concentration gradients for diffusion of vapors in glassy polymers and
their relation to time dependent diffusion phenomena. Journal of American Chemical Society
82:513-519, 1960.
(5) Rosen, A. L.. Fundamentals Principles of Polymeric Materials. Page 241. New John Wiley & Sons:
New York. 1982a
(6) Rosen. A. L.. Fundamentals Principles of Polymeric Materials. Page 243. John Wiley & Sons: New
York. 1982b
(7) Dexter, J. E., Matsuo, R. R., Morgan, B. C. Spaghetti stickiness: some factors influencing
stickiness and relationship to other cooking quality characteristics. Journal of Food Science
48:1545-1551, 1983
(8) Grant, L. A., Dick, J. W., Shelton, D. R. Effects of drying temperature, starch damage, sprouting
and additives on spaghetti quality characteristics. Cereal Chem. 70:676-684, 1993.
(9) Boquet R., Chirifie J., Iglesias H. A., Equations for Fitting Water Sorption Isotherms of Foods. II.
Evaluation of various Two-Parameters Models, J. Food Technol. 13 319-327, 1978.

Figure 5: Water diffusion

coefficient of no-gelatinized
8.0.10-6 spaghetti plotted as a function
( )
of ρ ⋅CW . ( ) sample A,
( ) sample B, ( )
sample C, ( ) sample D.
4.0.10-6

0.0.100

0.0 0.2 0.4 0.6

[
ρ⋅ C W g / c m
3
]
Figure 6: Water diffusion
4.10-5 coefficient of fully gelatinized
spaghetti plotted as a function
( )
of ρ ⋅CW . ( ) sample A,
( ) sample B, ( )
2.10-5 sample C, ( ) sample D.

0.0 0.2 0.4 0.6

[
ρ⋅ C W g / c m 3
]
ICEF9-2004
International Conference on Engineering and Food

Process evaluation and simulation of apple juice pasteurization on plate heat exchangers

Welti-Chanes, J., Vergara-Balderas, F., and Martínes-Gordillo, R.

Departamento de Ingeniería Química y Alimentos

Universidad de las Américas, Puebla,
Cholula, Puebla, 72820
MEXICO
jwelti@mail.udlap.mx

Abstract
Apple juice pasteurization using plate heat exchanger is analyzed by computational software based on
heat and momentum transport, equipment specifications, and kinetic data for microbial and quality
factors inactivation. This analysis shows that the industrial pasteurization process is overestimated. By
means of the same software, new conditions for process pasteurization are proposed in order to
optimize the process.

Key words: Pasteurization, plate heat exchanger, apple juice

Introduction
The time/temperature history of a thermal process is essential for a better design of this kind of
processes in order to obtain the desired inactivation level of microorganisms and enzymes, as well as
minimize the loss of quality factors (1). In addition, it is important to consider the final cost of the
product and to avoid superfluous expenses during production. It is necessary to analyze and evaluate
these processes to obtain safe products, keeping sensorial characteristics, and taking into account
expenses.
On the other hand, fruit juices, as in the case of apple juice, usually have pH value below 4, so they
are subjected to a light thermal process or pasteurization. This process has several applications in
food industry; however, in some products, equipment design and operation conditions are not studied
in detail, adapting information from other applications, and frequently overestimating the process.
Plate heat exchanger is the most used equipment for pasteurization of liquid foods. In a plate heat
exchanger, the product flows between two heated surfaces in a very thin film, resulting in a rapid
increase in temperature of the product and usually requiring only a single pass over a given heat-
transfer surface (2).
The objectives of this work are to analyze and evaluate the pasteurization process of apple juice with
a computational software and to generate a proposal with new conditions to improve the thermal
process to obtain stable and safe products minimizing energy expenses and taking care of sensorial
characteristics.

Materials and Methods

Apple juice
Apple juice is prepared in an industrial facility and it is subjected to the following tests in order to
characterize it: pH was measured with a pH-meter. ° Brix were measured with a refractometer at 25
°C. Titratable acidity was determined according to AOAC standard methods (3). Vitamin C was
determined according to AOAC standard methods (3), using the 2,6-dichlorophenolindophenol
reagent. Counts of mesophiles, molds and yeasts, and thermoduric microorganisms are realized using
standard microbiological techniques. Some samples of juice processed in specific conditions were
incubated at 35 an 55°C to promote possible microbial growth.

Software for analysis, evaluation, and simulation of pasteurizations processes

This software was developed in Delphi, ver. 4, for Windows 95/98 (4). This software has 4 modules:
(a) configuration, (b) microbiology, (c) calculation, and (d) production. In this study we use modules (a)
and (c). The configuration module is a data base with four sections: pasteurizers, product properties, F
and z values, and vapor cost. This information is used to make calculations in module (c). In the
“pasteurizers” section, it is required information about plate heat exchangers: dimensions, number of
plates, number of channels, area for heat transfer, conductivity, etc. The “product properties” module
needs food composition, and with this information the software calculates properties as: density,
viscosity, specific heat, and thermal conductivity. In the “F and z values” section, values of these
parameters for microorganisms and quality factors are needed. The “vapor cost” section allows to
ICEF9-2004
International Conference on Engineering and Food

evaluate the cost associated to energy expenses. Module (c), “calculations”, is used to evaluate the
equipment performance and process simulation with new conditions. This module has 4 sections: (a)
“Data” section handles information about process operation (operation temperatures). (b) “Results”
section is used to evaluate the pasteurization process, generating information about temperatures,
heat transferred, Reynolds number, transfer coefficients, cost, etc. (c) The “temperature profile”
section generates a temperature profile of the pasteurization stages (heating, holding, and cooling).
(d) The calculated value of F is presented here, and compared against a theoretical value of F as a
reference. The specific structure and application of this software has been reported previously (4).

Apple juice pasteurization

The equipment for apple pasteurization is a plate heat exchanger APV, model R-56S and it is used
only for heating (the cooling section is not used, because it is a hot-filling process). The heat
exchanger has the following characteristics: number of plates: 12, generating 6 channels for flow of
the heating medium and 5 channels for flow of juice; the wide, large and thickness of plates are 125,
430 and 0.6mm, respectively; the distance between plates is 2.62 mm and the heat transfer area is
0.032 m2. The heat conductivity of plates is 17.3 kJ/s-m°C and the heating medium is hot water. The
holding zone in the pasteurization process is a tube 53.4 m long and 4.73 cm diameter. The
pasteurization temperature is 91-93 °C during 60 s if the pH is < 3.9, or 93-97 °C when pH is 3.9 – 4.1.
After thermal treatment, the juice is conveyed to the filling machine where glass jars are filled and then
cooled in a tunnel operating with a water spray at 27 °C during 310 s. Final product temperature is
expected to be < 42 °C. A remote distance thermocouple was put into a glass jar with juice to obtain
the temperature evolution during the cooling process.

Results and Discussion

Apple juice characteristics
Table I shows the specifications of apple juice before and after of pasteurization

Table I. Apple juice specifications before and after the

pasteurization process
Parameter Before After
°Brix 12.5-13.5 12.5-13.5
Maximum pH 3.9 3.9
Total acidity (%) 0.22-0.41 0.22-0.41
Vit. C (mg/100g) 50-54 42.46

A historic evaluation was done to determine how different are the juice characteristics and process
conditions with respect to the specifications established by the industry. This evaluation has data from
January, 2001 to April, 2002. During the evaluation time the °Brix level in juice with and without
pasteurization was in the range 12.7 to 13.1 with an average of 13.0°. In the case of juice without
pasteurization, the vitamin C had levels in the range 51.9 to 61.1 mg/100g with an average of 56.2
mg/100g, and the pasteurized juice had an average vitamin C content of 51.3 mg/100g (46 to 59.6
mg/100g), value higher than that specified in Table I and it represents losses of 10% during the
thermal process.

Evaluation of pasteurization process

The historic registers showed that holding temperature had values from 92 to 97.2°C with an average
temperature of 93.3°C; however, even when that average is a level adequate to reach the objective of
the pasteurization, temperature changes could be a problem and overprocessing is expected in a
normal process. The juice flow had historic registers between 3800 and 4560 kg/h with an average
flow of 4355 kg/h; this flow provokes a residence time of 75 s in the holding time, being higher than the
required one (60s). Computer simulation of the thermal process was done using the minimum and
maximum temperature levels in the holding zone and the average flow.
Table II shows the lethality of several processes in terms of Fo values (which were obtained with the
software afore mentioned), and other information important to characterize the transfer phenomena
involved in the pasteurization process. There are specific data of the operation in each section of the
process. It is important to observe the contribution to letality of each zone in terms of the F value. As it
can be seen, around 96% of the total F value comes from the holding zone and the remaining 4 %
ICEF9-2004
International Conference on Engineering and Food

comes from the heating in the heat exchanger and cooling in the final step. These F values are
compared to a theoretical Fo value required for this evaluation which was calculated using a reference
temperature of 93.3 °C and a z value of 8.89 °C. Overprocessing is observed in all cases evaluated; it
means that the product is receiving a process greater than need to obtain a safe and stable product,
with a greater degradation of vitamin C and a greater energy expense.

.
Table II. Simulation results and evaluation of apple juice pasteurization at different holding
temperatures (Holding time = 79 s, W=water, J= Juice)
Holding 93 94 95 96 97
temperature
(°C)
Heating zone
Variable W J W J W J W J W J

Tin (°C) 120 32 120 32 120 32 120 32 120 32

Tout (°C) 76.6 93 77.5 94 78.4 95 79.4 96 80.3 97
Heat transfer 283 283 288 288 293 293 297 297 302 302
(kJ/s)
Flow (kg/h) 5579 4355 5785 4355 6013 4355 6251 4355 6501 4355
Velocity (m/s) 0.06 0.17 0.06 0.17 0.06 0.17 0.06 0.17 0.07 0.17
Reynolds
number 2343 4130 2446 4165 2560 4201 2681 4236 2808 4272
Heat transfer 987.7 1684 1020 1691 1056 1699 1093 1706 1132 1714
coefficient (J/s
m2°C)

Evaluation of pasteurization process

Frequired 1.0808 1.0808 1.0808 1.0808 1.0808
Fheating 0.049 0.045 0.081 0.106 0.137
Fholding 1.313 1.702 2.205 2.856 3.701
Fcooling 0.004 0.004 0.004 0.004 0.004
Ftotal 1.366 1.751 2.290 2.966 3.842
Overprocess 26% 62% 112% 174% 255%

Overprocessing is coming originally from the use of a time higher (79 s) than that required (60 s). This
difference represents the original 26% of overprocessing when a holding temperature of 93°C is used;
when this temperature is increased with the same retention time, the overprocessing is increased to
levels higher than 200%. It is possible to do some changes in the process conditions to reduce
overprocessing; these modifications could be oriented to reduce the retention time (increasing the
juice flow or reducing the size of the holding tube) and /or reducing the temperature in the holding
section.

Operation improvement
By means of the mentioned software, several operation conditions (temperatures, flow of fluids, etc.)
were modified to obtain Fo values closer to the theoretical Fo value. Decision was taken to evaluate
the safety and microbial quality of juices processed at holding temperatures of 89-90.5°C (the range
represents the sensitivity of the temperature control of the industrial heat exchanger) and a juice flow
of 4600 kg/h. These conditions are enough to reach the expected F value. After of the process, the
juice samples were microbiologically evaluated and the results obtained are shown in Table III.
Results show that it is possible to modify the thermal process through a phenomenological and
microbial (kinetic) analysis as the one used in the software applied to improve the process. More
research is needed to improve the mentioned analysis and to evaluate the possible safety problems to
be considered in the future taking into account different microorganisms to those considered in the
classic analysis.
ICEF9-2004
International Conference on Engineering and Food

Table III. Microbial quality of apple juice process with a holding

temperature of 89-90.5°C and a flow of 4600 kg/h
Sample Mesophiles, Thermoduric Yeast Molds
(cfu/ml) (cfu/ml) (cfu/ml) (cfu/ml)
1 <1 <1 <1 <1
2 <1 <1 <1 <1
3 <1 <1 <1 <1
Incubate juice at 35°c
4 <1 <1 <1 <1
5 <1 <1 <1 <1
6 <1 <1 <1 <1
Incubated juice at 55°C
7 <1 <1 <1 <1
8 <1 <1 <1 <1
9 <1 <1 <1 <1

Conclusion
It is demonstrated that the juice is overprocessed. In this condition, the process can be re-evaluated to
optimize it, obtaining a safe product with a lesser loss of quality factors, and with less energy expense.

Acknowledgements

This work was funded by Universidad de las Américas, Puebla.

References

1. Adams, J.C., Simunovic, J., Smith, K.L. Temperature Histories in a UHT Indirect Heat Exchanger.
Journal of Food Science, 49 (); 273-277, 1984.
2. Heldman, D.R. and Singh R.P. Food Process Engineering. 2nd. Edition. AVI Publishing Company,
Inc. Westport, Connecticut, U.S.A. 1981
3. A.O.A. C. Official Methods of Analysis. Association of Official Analytical Chemists., USA, 1996.
4. Welti-Chanes, J., Vergara-Balderas, F., Ruíz-Medina, A.L., Serna-Figueroa, F., Ramírez-Juárez,
J.L. Simulación y optimización de proceso en intercambiadores de calor de placas. Jugos y bebidas
de frutas. 3er Congreso Iberoamericano de Ingeniería de Alimentos (CIBIA III); Valencia, Spain, 2001.


  
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ICEF9 - 2003
International Conference Engineering and Food

ADVANCES TOWARD COMPUTER-AIDED FOOD PROCESS ENGINEERING

Ashim K. Datta
Cornell University, Dept. of Biol. and Env. Engineering, Riley-Robb Hall, Ithaca, NY 14853, USA.
akd1@cornell.edu

ABSTRACT: Computer-aided engineering (CAE) can benefit food product, process and equipment
design. Commercial software can simulate many, but not all of the important food processes. The
most critical need seems to be to develop comprehensive and consistent mathematical descriptions of
food processes. A comprehensive overview of the status and needs of computer-aided food process
engineering is provided through careful analysis of the ongoing modeling and related work worldwide
in academia, industry and software manufacturers.

KEYWORDS: Computer-aided engineering, modeling, simulation, problem formulation

INTRODUCTION

This article describes the potential and some of the missing key parts of Computer-Aided Engineering
(CAE) as applied to food processing. Use of CAE can be roughly divided into two major purposes—
improved understanding and prediction. The most common use of computer-aided engineering has
been to have a better understanding of the physical process by seeing the relationships between its
input and output parameters. For example, in modeling a sterilization process one would like to know
the effect of steam temperature (input parameter) on the extent of lethality or bacterial death (output
parameter). It is the research objective that prompted the earliest studies of computer-aided food
process engineering [1]. As computing techniques and computational hardware and software went
through a revolution, the second major objective emerged—to use the model in design or to check
“what if” scenarios for industrial processes [2, 3, 4]. In this article, we will try to discuss the specific
bottlenecks to the use of CAE in food processing—various components and their integration that can
make CAE of food processing less of a challenge.

ISSUES OF IMPORTANCE TO FOOD PROCESSING

Food materials are biological materials that vary considerably in any property—mechanical, electrical,
thermal, diffusional, and so on. Such variations are due to composition (particularly moisture),
structure and other factors. Due to biological variability, properties may not be isotropic; for example,
thermal conductivity of muscle tissue is different along the fiber as compared to perpendicular to the
fibers. One of the most important sources of variation in properties is the change during processing
itself. We are ultimately interested in food quality. Having temperature, moisture or residence time of
food during processing is only part of the story. We need to know the rates of reactions for
biochemical (nutrient, color, flavor, etc.) or microbial changes. Food materials always contain
moisture. Whether desired or not, the moisture in food is constantly undergoing either loss (due to
evaporation, especially when heated) or gain (from humid surroundings). Food materials are often
solid-liquid mixtures. Flow and heat transfer in such mixtures during sterilization (aseptic processing)
is an important food processing operation. The physics of such multiphase flow is, however, quite
complex and is not readily solvable in commercial software. Food materials are hygroscopic. They
shrink upon drying or swell upon gaining moisture. Heating and cooling of food is never uniform
throughout the material and this differential expansion or contraction over the volume leads to stress
development and sometimes cracking. Thus, heat and mass transfer in foods are often coupled with
solid mechanics issues.
ICEF9 - 2003
International Conference Engineering and Food

MOST IMPORTANT CAE NEEDS IN FOOD PROCESSING

Some of the generic components of the computational tools are 1) Problem formulation (governing
equation, boundary and initial conditions); 2) Computational software that is able to solve the
formulated problem; 3) Material properties; 4) Ability to input geometry and generate mesh; 5)
Visualization; 6) Validation and 7) Sensitivity/uncertainty analysis. Due to space limitations in this
article, only the first and the most important topic of Problem Formulation is now discussed.

Problem formulation
Perhaps the most important need in being able to apply CAE more readily to food processing is to be
able to define the food process appropriately in mathematical terms. This process is often overlooked,
but this is where the biggest uncertainty lies today. The mathematical formulation often requires
intelligent simplification of an otherwise complex problem. The goal is to keep as many details of the
process as possible, without creating unnecessary computational complexity or time commitment.
Said in another way, the problem formulation needs to be “As simple as possible, but no simpler.”
Many food processes have not been understood in non-empirical quantitative engineering terms. In
other words, the governing equations and the boundary conditions that apply to a particular process
are far from clear. What we need is a knowledge base of various food processes and their accurate
mathematical representations.

(1a) (1b)

(1c) (1d)

Figure 1. Different formulations of the frying process as example to possibilities in the formulations of
various food processes. 1a) formulation with a sharp interface where evaporation occurs; 1b)
formulation with distributed evaporation (no sharp interface); 1c) formulation with evaporation
occurring at the surface only; 1d) empirical formulation that considers total moisture loss with time,
without any regard to transport mechanisms.

An example would illustrate the point. Between 1996 and 1999, there has been a flurry of papers on
modeling of frying processes [5, 6, 7, 8, 9, 10, 11, 12, 13]. Most of these papers have different
ICEF9 - 2003
International Conference Engineering and Food

formulations (governing equation and boundary conditions) of the frying process. This is illustrated in
Figure 1. In one formulation, a sharp boundary is assumed for evaporation. Here two separate sets of
equations are written for the two zones—core and crust. A separate equation is written for the location
of boundary (interface) between the two zones. In another formulation, evaporation is considered
distributed throughout the porous material, with rates that are dependent on local temperature,
saturation and pressure. The governing equations for this formulation are quite different from the
previous one. In yet another formulation, heat and water transport inside the material are considered
to be simple diffusion, with all of the evaporation occurring at the surface. A still simpler formulation
(Figure 1d) is empirical and provides a simple rate equation for water loss with the kinetic parameter
for water loss estimated from the same experimental data. There are two points to be made here. The
first is that depending on the formulation, the governing equations and therefore the numerical
methods used are quite different. Any given software is unlikely to be able to accommodate all
formulations of the problem in a satisfactory manner (i.e., it may not be able to solve the sets of
equations in all possible formulation). Thus, depending on which formulation we decide to be the best
one, the software would have to be chosen that can solve for this best formulation. The second point
here is a decision to the level of empiricism that is ideal. For the purposes of CAE, even the fourth
formulation (Figure 1d) that is completely empirical is acceptable, since it will still allow computer-
based manipulation of processes. However, such an empirical formulation is unlikely to be very
flexible, i.e., as we change to different products and processes, new empirical parameters will be
needed that would rely entirely on experimental data. This goes against the advantages of computer-
aided engineering where we are trying to reduce our dependence on physical prototypes. Thus, overly
empirical models should be avoided as we build general-purpose CAE tools for food processing.

If the frying process is to be designed using a CAE software available commercially, we have to agree
on either a formulation of the frying process or a number of equivalent formulations where the
equivalence can be clearly demonstrated. Without such agreement on the framework, there will be
disagreements on whether the mathematical model mimics the real physical process.
Another way to look at the relative importance of problem formulation is that over the years, with
increase in computing power and user-friendliness, processing (equation solvers) and post-processing
(e.g., visualization) parts of CAE have been dramatically improved. Many parts of pre-processing
(setting up of problem) have also been improved, e.g., mesh generation. Problem formulation, which
is a part of pre-processing, however, does not depend on computing power, but the user’s ability to
simplify a physical problem in mathematical terms. Very little of it can be automated. Today, a very
significant fraction of the total time needed for CAE of food processes would be spent on the problem
formulation.

As mentioned earlier, governing equations and boundary (and initial) conditions are the two main parts
of problem formulation. Mathematical descriptions of many food processes and their solution
possibilities in typical commercial software are discussed [4].

As part of problem formulation, boundary conditions can also be difficult to decide for specific food
processing situations, although it is not as much of an issue. The other component of problem
formulation is the source term for the energy or the species equation. In the energy equation, the
energy source term can be due to electromagnetic or ultrasonic heating or from the heat of respiration.
For electromagnetic heating, the source term would come from the solution of Maxwell’s equations.
For ultrasonic heating, the source term would come from the equations for acoustics, but sometimes
can be simplified to an exponential decay of energy characterized by the absorption coefficient for the
particular food. Heat of respiration data are available for some food products from experiment (e.g.,
[14]). Examples of source terms in species equation are biochemical and microbiological changes in
the food during processing, such as destruction of nutrients or bacteria. Such kinetic data are
available for nutrients or bacteria, but are not so easily available for other quality factors such as
texture. Some of these issues are described in more details [4].

Beyond problem formulation, there are several other issues that require developments in the context of
food processing applications. Some details of these issues are provided elsewhere [4]. Material
property data are often the other most important missing link. Material property data for food are
strongly variable depending on its composition, structure and temperature. Material property also
varies during processing. Large material property databases exist for other material processing [15].
However, for food materials, this has not happened yet. Some databases are beginning to appear for
food processing [16, 17], but their scope is limited in terms of availability of food data for different
ICEF9 - 2003
International Conference Engineering and Food

composition, temperature, etc. For computer-aided engineering, availability of simple prediction

formulas that relate property with composition (e.g., thermal properties [18]; dielectric properties [19])
would go a long way. When specific properties data is not available, perhaps the most useful route to
CAE is to perform sensitivity analysis with respect to the unavailable data.

Closely coupled with accurate formulation of the problem is the validation of the model computations.
This can include mesh convergence study, checking for mistakes, checking if the results can be
explained using common sense physics and comparing the results with experimental data.

Physics appropriate for food processing applications need to be included in the software. Examples of
processes that are difficult to accomplish using today's commercial software include, for example,
sterilization (aseptic processing) of a flowing solid-liquid mixture with large particulates. The
commercial software of today still lack the ability to handle processes where internal evaporation is
very significant and can develop pressures, such as high intensity drying, microwave heating, and
deep-frying.

Food processes quite often involve more than one discipline of engineering. For example, microwave
food processing involves at least the two subject areas—electromagnetics and heat transfer.
Sometimes, there is strong coupling between electromagnetics and heat transfer, since heating
changes the dielectric properties that can change the electromagnetics [20]. Calculations of
electromagnetics and heat transfer in a transient process need to go on simultaneously, but, as of this
writing there is almost no commercial software that implements this coupled computation. More
software that couple different physical processes, such as the multiphysics module from ANSYS [21]
or better linkages between software will be necessary for food processing.

Uncertainty (in input parameters, process variables) in food processing can be greater than in other
materials processing. For example, to design a sterilization process, one would like to know the initial
load of bacteria, which can be extremely variable. Such uncertainty in model parameters is not
implemented in most commercial software, although some software is beginning to include such
analysis [21]. In the absence of built-in ways to calculate the uncertainty, Monte-Carlo simulation
(repeated simulation of a process for a range of parameter values chosen from a probability
distribution) may be possible provided the computation times are not prohibitive.

SUMMARY

Computer-aided engineering is a rapidly growing field. Food processing use of computer-aided

engineering can only grow in the future. In order for food processors to increase the CAE use,
software needs to be customized for food applications, by delivering solutions to sets of equations of
relevance to food processing. However, the current user base for the food industry is so small that the
software companies are reluctant to invest the resources needed to develop specific capabilities of
interest to food processing. This is a chicken-and-egg situation. To prime the process, perhaps
collaboration between software developer, industry and academia can be developed so that individual
resource commitments are reduced. A systematic study of the bottlenecks in the CAE steps (such as
problem formulation) and developing the needed knowledge base by combined effort would help the
food industry enjoy the same benefits of computer-aided engineering as in other industries. This will
benefit society through increased convenience, reduced costs and reduced wastage of foods.

REFERENCES

[1] Teixeira, A. A., J. R. Dixon, J. W. Zahradnik and G. E. Zinsmeister. Computer optimization of

nutrient retention in the thermal processing of conduction-heated foods. Food Technology,
23(6):137-142, 1969.

[2] Scott, G. and Richardson, P. The application of computational fluid dynamics in the food
industry, Trends in Food Science and Technology, 8:119-124, 1997.

[3] Datta, A. K. Computer-aided engineering in food process and product design. Food
Technology. 52(10):44-52, 1998.
ICEF9 - 2003
International Conference Engineering and Food

[4] Datta, A. K. Enabling computer-aided food process engineering: Status and needs. In
Computational Techniques in Food Engineering, Edited by E. Balsa-Canto, J. Mora, J. R. Banga
and E. Onate. International Center for Numerical Methods in Engineering (CIMNE), Barcelona,
Spain. pp. 3-14, 2002.

[5] Dincer, I. and M. Yildiz. Modeling of thermal and moisture diffusions in cylindrically shaped
sausages during frying. International Journal of Food Science and Technology, 24:183-187,
1996.

[6] Farkas, B. E., R. P. Singh and T. R. Rumsey. Modeling heat and mass transfer in immersion
frying: Model development. Journal of Food Engineering, 29:211-226, 1996.

[7] Ikedalia, J. N., L. R. Correia, G. A. Fenton and N. Ben-Abdallah. Finite element modeling of
heat transfer in meat patties during single-sided pan frying. Journal of Food Science, 61
(4):796-802, 1996.

[8] Chen, Y. and R. G. Moreira. Modeling of a batch deep-fat frying process for tortilla chips.
Transactions of the Institution of Chemical Engineers, Part C: Food and Bioproducts
Processing, 75(C3):181-190, 1997.

[9] Vijayan, J. and R. P. Singh. Heat transfer during immersion frying of frozen foods. Journal of
Food Engineering, 34 (3): 293-314, 1997.

[10] Farid M. M. and X. D. Chen. The analysis of heat and mass transfer during frying of food using
a moving boundary solution procedure. Heat and Mass Transfer, 34(1):69-77, 1998.

[11] Costa R. M. and F. A. R. Oliveira. Modelling the kinetics of water loss during potato frying with a
compartmental dynamic model. Journal of Food Engineering, 41 (3-4): 177-185, 1999.

[12] Ni, H. and A. K. Datta. Moisture, oil, and energy transport during deep-fat frying of food
materials. Transactions of the Institution of Chemical Engineers: Food and Bioproducts
Processing. 77C(9):1-11, 1999.

[13] Sahin, S., S. K. Sastry and L. Bayindirili. Heat transfer during frying of potato slices.
LEBENSMITTEL-WISSENSCHAFT & TECHNOLOGIE , 32 (1): 19-24, 1999.

[14] Kole, N. K. and S. Prasad. Respiration rate and heat of respiration of some fruits under
controlled atmosphere conditions. International Journal of Refrigeration, 17(3):199-202, 1994.

[15] Anonymous. Some material property databases. On the web at http://www.gi.rwth-

aachen.de/mebsp-b/datab-list.html, 2002.

[16] Nelfood. Food properties database. On the web at http://www.nelfood.com/ , 2002.

[17] Singh, R. P. Food properties database v2.0 for Windows, CRC Press, Boca Raton, Florida.
1995.

[18] Choi, Y. and M. R. Okos. Thermal properties of liquid foods-- Review, in Physical and Chemical
Properties of Foods, edited by M. R. Okos, American Society of Agricultural Engineers, St.
Joseph, MI, 1996.

[19] Sun, E., A. K. Datta and S. Lobo, Composition-based prediction of dielectric properties of foods.
The Journal of Microwave Power and Electromagnetic Energy 30(4):205-212, 1995.

[20] Datta, A. K. Analysis of microwave heating of foods. In Food Processing Operations Modeling:
Design and Analysis. Edited by J. Irudayaraj, Marcel Dekker, Inc., New York, NY, 2001a.

[21] ANSYS. ANSYS products capabilities chart. On the web at http://www.ansys.com/

ansys/pdf/capabilities_chart_61.pdf , 2002.
ICEF 9 – 2004

International Conference Engineering and Food

Modelling and Optimisation of Solid Door Refrigerated Display Cabinets for Chilled Liquid
Foods
Love R.J. (1), Cleland D.J. (2)

(1) Institute of Food, Nutrition and Human Health.

Massey University
Palmerston North
NEW ZEALAND
r.j.love@massey.ac.nz
(2) Institute of Technology and Engineering.
Massey University
Pamerston North
NEW ZEALAND
d.cleland@massey.ac.nz

Abstract: A model of a refrigerated display cabinet for chilled liquid foods was developed and
validated against measured data for pull down of the product from ambient temperatures to the
storage conditions. The model includes consideration of refrigeration system performance, air
distribution throughout the cabinet, product cooling and energy use. The model can be used to
evaluate alternative cabinet designs in terms of pull-down rate and energy consumption.

Keywords: refrigerated display cabinets, modelling, optimisation

Introduction

Many retail products, including drinks and convenience foods, are displayed for sale in glass fronted
chiller cabinets. A schematic of a typical cabinet is shown in Figure 1.

k B
iii
θc,out hc,out
l ii
iv
θamb
Ps θs θc
j i Pc
θa,off v
θe i

Pd
Duct
θa,on hc,in
Cans

Door

Figure 1. Two dimensional schematic of a typical chiller cabinet (not to scale). Blow out [A] indicates
the air/product node network, where each product unit (can) is surrounded by 4 air nodes and air flows
between the air nodes. Blow out [B] indicates refrigeration system: (i) Compressor, (ii) Condenser, (iii)
Suction line heat exchanger, (iv) Capillary Tube expander, (v) Evaporator.

The product items (cans, in this case) are stacked in layers on shelves. The cabinet is cooled by a
top-mounted, single-stage vapour compression refrigeration system. Cool air enters the cabinet, from
the evaporator, via a perforated duct. Air can flow horizontally through channels between the layers
ICEF 9 – 2004

International Conference Engineering and Food

and vertically up between cans and in the space between the front cans and the cabinet door. Air
returns to the evaporator at the top of the cabinet. A common variation is to mount the refrigeration
system beneath the cabinet.

One aspect of successfully designing and optimising chiller cabinets is the pull-down performance. A
typical pull-down test involves loading the cabinet with product at ambient temperature and running
the cabinet until the refrigeration system starts to cycle on thermostat control. Key performance
indicators include:
1. the time that the system requires to complete the pull-down;
2. the variation in product temperatures during and at the end of pull-down; and
3. the energy use both during the pull-down and during cycling.

Cabinet design is often based upon the steady-state (cycling) performance of the refrigeration system
components, because pull-down performance is more difficult to predict. Consequently, time-
consuming and expensive tests of a prototype must be performed to check pull-down performance.
An accurate and fast model of the chiller cabinet performance during pull-down would enable the time,
cost and uncertainty of prototyping to be minimised.
1
Some workers have modelled chiller cabinets using computational fluid dynamics (CFD) models .
While these models can be accurate they are computationally expensive and may take many hours of
computer time to solve. Additionally, CFD models usually focus on the prediction of air flows and heat
transfers within the cabinet while the refrigeration system performance is often modelled too
simplistically to predict pull-down performance. The aim of this paper is to develop a simple model of
chiller cabinet performance and to validate it against measured data.

Model Description

The following key assumptions were made in development of the model:

1. Variation in conditions across the width of the cabinet were neglected. That is, the cabinet
was modelled as a two-dimensional cross-section (as shown in Figure 1).
2. Heat transfer inside the cabinet is by convection only (conduction and radiation are ignored).
3. The cabinet door remains closed, so air-interchange with ambient was ignored.
4. Heat from lighting is transferred only to the air nodes adjacent to the lights.
5. Water va pour transport was ignored. That is, only sensible heat transfer was modelled.
6. Refrigerant superheat at the evaporator exit, sub-cooling at the condenser exit and line
pressure drops were assumed to be constant.
7. Refrigerant flow rate was assumed constant throughout the refrigeration circuit and the
compressor response to changes in operating conditions was assumed instantaneous.

Refrigeration System
A single stage, air-cooled, mechanical vapour recompression refrigeration system with a capillary tube
expander and a suction line heat exchanger is often used in refrigerated display cabinet applications
(see Figure 1 [B]). The refrigeration system was modelled using a quasi-steady state approach similar
2
to that taken in the RADS simulation package .

The refrigerant evaporation and condensation temperatures were modelled by:

dθ e Eq 1.
(MC )e = (UA)e (θ a,on − θ e ) − m& r (he ,out − he, in )
dt
dθ c Eq 2.
(MC )c = m& r (hc, in − hc , out ) − (UA)c (θ c − θ a, amb )
dt
The refrigerant flow-rate through the refrigeration circuit was calculated from:
Qrη v Eq 3.
m& r =
vr
The performance of the suction line heat exchanger was represented by:
θ s = θ e ,out + ε (θ c, out − θ e ,out ) Eq 4.

The enthalpy of the refrigerant entering the condenser was estimated from:
ICEF 9 – 2004

International Conference Engineering and Food

his L Eq 5.
hc .in = hs + −
η i m& r
The temperature of the air leaving the evaporator was given by:
(UA)e Eq 6.
θ a, off = θ a ,on −
m& a c a
(θ a , on −θ e )

The parameters in these equations were based upon manufacturer’s data for the evaporator,
compressor, condenser and suction line heat exchanger. The refrigerant 's (HFC-134a)
thermodynamic properties (h as a function of θ and P, his as a function of Ps , Pd and θs , Pe and Pc from
θc and θe and vr from Ps and θs ) were estimated using the curve-fit relationships developed by
3
Cleland .

Cabinet Air
The air in the cabinet was modelled as a two-dimensional network of well-mixed zones, connected by
lines of flow (see Figure 1 [A]). Each zone has a temperature associated with it, up to two flows
leaving the zone (vertically, up and horizontally, right) and up to two flows entering from adjacent
zones. The network of zones was defined so that each product item in the two-dimensional cross-
section of the cabinet was surrounded by 4 nodes. Additional air zones were defined to represent the
air delivery ducting, the air adjacent to the cabinet door and the air return ducting to the evaporator.
The air flow rate and velocity between each node is pre-determined by either measurement or CFD
predictions.

Mechanisms for energy transfer into and out of an air zone include:
1. Air flow entering from or leaving to an adjacent zone.
2. Convective heat transfer from adjacent product items.
3. Heat input due to external sources, either electrical heat loads (for example, cabinet lights) or
conduction from the ambient through the cabinet walls.

The general form of the differential equation that governs the temperature of the ith air zone was:
dθ Eq 7.
(MC )a ,i a ,i
& a ,i→ k c aθ a ,i + ∑ α l→ i Al →i (θ p, l − θ a ,i ) + E i
= ∑ m& a, j →i c aθ a , j − ∑ m
dt j k l
The air to product heat transfer coefficient was estimated as a function of the velocity of the flow
passing over the product surface between adjacent air zones.

Product
Each product unit interacts with the four surrounding air zones by convection. Each product unit is
assumed to be well-mixed so that the equation describing the temperature of the lth unit is:
dθ Eq 8.
(MC ) p ,l p, l
= ∑ α l →i Al →i (θ a, i − θ p,l )
dt i

Ambient and Electrical Heat Loads

The ambient temperature was assumed to be constant. Heat loads from the ambient (conduction
through the walls of the cabinet) were modelled as proportional to the temperature difference between
the cabinet air and the ambient temperatures. Heat load and energy use due to electrical sources
such as cabinet lighting, door heater and fans were each assumed to be constant.

Model Implementation

For a typical cabinet, the model consisted of over 150 differential equations (one for each product
item, each air zone and two for the refrigeration system) and over 15 algebraic relationships. The
system of equations was solved using a variable time-stepping Runge-Kutta numerical solution
4
method . The model was implemented as a C++ computer program, and run upon a Pentium III, 866
MHz PC. The model took less than 60s to simulate 24 hours of cabinet performance.

Results and Discussion

ICEF 9 – 2004

International Conference Engineering and Food

The following graphs compare the modelled predictions to experimental measurements for the pull-
down of a cabinet contained 355 ml drink cans. The measurements were performed on a prototype
chiller cabinet, developed by a New Zealand manufacturer. All temperatures, times and other data
and results have been scaled for confidentiality reasons. Likewise, the exact cabinet specifications
are commercially sensitive. The key performance requirement was to pull the product from an
o o
ambient temperature of 35 C to a storage temperature of about 2.5 C within a 26 hour period. The
cabinet performance was measured in a calorimeter test facility.

40 40
Predicted-Air onto Evaporator
Predicted Measured
Predicted-Air off Evaporator

30 Measured- Air onto Evaporator

30
Measured- Air off Evaporator

Temperature [o C]
Temperature [ C]
o

20 20

10 10

0 0
0 10 20 30 40 50 0 10 20 30 40 50
Time [h] Time [h]

Figure 2. [A] Predicted and measured can temperature. Error bars represent the range of values
throughout the cabinet. [B] Predicted and measured temperature of air onto and off the evaporator.

Measured- Evaporation Predicted- Evaporation

Mesaured- Condensation Predicted- Condensation
90 Measured- Suction Predicted- Suction
Measured- Discharge Predicted- Discharge

70
o
Temperature [ C]

50

30

10

-10
0 10 20 30 40 50
Time [h]
Figure 3. Predicted and measured refrigeration system temperatures (evaporation, condensation and
compressor suction and discharge).

Figure 2 [A] summarises the predicted and measured can temperatures. The pull-down time of about
24 hours is accurately predicted. The model predicts a narrower range of can temperatures for most
of the pull-down, except near the end. This is almost certainly due to both significant variation in
ICEF 9 – 2004

International Conference Engineering and Food

temperature across the width of the measured cabinet (because of imperfect air distribution) and
significant radiation effects. These shortcomings are currently being investigated in a revision of the
model.

The predictions of the can temperatures during pull-down are on average slightly higher than the
experimental results. This is due to the predicted air temperature difference across the evaporator
being greater than measured (Figure 2 [B]). This discrepancy is probably due to the evaporator
performance being assumed constant whereas it is likely that the capillary tube expander will stave the
evaporator of refrigerant early in the pull-down when the difference between Pc and Pd is less.

Figure 3 compares the predicted and measured refrigerant temperatures. All temperatures are
predicted reasonably accurately, given the simplicity of the model. The regular cyclic variation in the
measured condensation and discharge temperature after about 10 hours is due to variation in the
ambient temperature due to imperfect control in the test facility. Variation between measured and
predicted temperatures may be due to differences between the actual performance of installed
equipment and the performance data quoted by the manufacturer.

Once pull-down has been achieved (after about 24 hours) the system begins to cycle to maintain the
temperature of the cabinet. The predicted cycling is about the same rate as the measured, which
suggests that the values used for the evaporator and condenser thermal mass are appropriate. The
cabinet was observed to consume about 9.5 kW h of energy for each 24 h of cycling, the model
predicted only 8.7 kW h. Detailed analysis suggested that this variance was due to the measured
compressor energy-use being greater than that indicated by the manufacturer’s data. Although the
predicted energy use is significantly different to that measured, comparisons between predictions for
would be expected to give an accurate indication of the relative effect of design changes on energy
use.

40
Original Base Case
20% smaller evaporator and condenser

30 20% smaller compressor

Temperature [o C]

20

10

0
0 10 20 30 40 50
Time [h]
Figure 4. Predicted can temperatures for three design cases (base case, 20% smaller evaporator and
condenser and 20% smaller compressor).

The model can be used to investigate the effect of incremental design changes. Figure 4 plots the
predicted pull-down profile of the can temperatures for three different design cases: the first is the
case already described, the second case has a 20% smaller evaporator and condenser installed, the
third case has a 20 % smaller compressor. The case with a 20% smaller evaporator and condenser
takes about 26 h to achieve the pull-down and is predicted to use 8.6 kW h / 24 h of energy during
ICEF 9 – 2004

International Conference Engineering and Food

cycling. The case with the 20% smaller compressor is predicted to take about 28 h to achieve the
pull-down and use only 8.2 kW h / 24 h of energy during cycling. The model predicts that installing a
smaller compressor will save energy during cycling but will cause a large increase in the pull-down
time. Alternatively installing a smaller condenser and evaporator is predicted to save little energy
during cycling, but has a smaller impact on the pull-down time. This information could be used to
guide prototyping work.

Conclusions

A model has been developed that describes the pull-down performance of a chiller display cabinet.
Although the model under-predicts the energy use in the cabinet it does accurately predict the time
required to achieve a pull-down test, the refrigeration system conditions and the spread of
temperatures in the cabinet at this time. Use of such a model should increase the speed and
accuracy of the cabinet design process, particularly when evaluating the effect of incremental design
changes.

Nomenclature

Variables Subscripts
m& mass flow rate kg s
-1
→ between two nodes (indicated by indices)
2
A product surface area m a air
-1 -1
c specific heat capacity J kg K amb ambient air condition
E external energy input W c condenser / condensation
-1
h refrigerant enthalpy J kg d compressor discharge condition
L compressor energy losses W e evaporator / evaporation
-1
MC thermal mass JK i air node index
P refrigerant pressure Pa in refrigerant entry condition
3 -1
Q compressor swept volume m s is isentropic change
t time s j adjacent air node (upstream)
-1
UA heat transfer rating WK k adjacent air node (downstream)
3 -1
v refrigerant specific volume m kg l product unit index
-2 -1
α heat transfer coefficient Wm K off air off condition
ε heat exchanger effectiveness - on air on condition
ηi compressor isentropic - out refrigerant exit condition
efficiency
ηv compressor volumetric - p product
efficiency
o
θ temperature C r refrigerant
s compressor suction condition

References

1. Cortella, G, Manzan, M, Comini, G, “CFD Simulation of Refrigerated Display Cabinets”,

International Journal of Refrigeration, 24, 250-260, 2001.
2. Cleland, AC, Cleland, DJ, RADS Software User Manual, Massey University, 1991.
3. Cleland, AC, "Polynomial Curve-Fits for Refrigerant Thermodynamic Properties: Extension to
include R134a", International Journal of Refrigeration, 17, 245-249, 1994.
4. Press, WH, Teukolsky, SA, Vetterling, WT, Flannery, BT, Numerical Recipes in C++: The Art of
Scientific Computing, Cambridge University Press, Cambridge UK, 2002.
ICEF 9 2003
International Conference Engineering and Food

Effective Scraping in a Scraped Surface Heat Exchanger: Some Fluid Flow

Analysis

D. L. Pyle (1), K.-H. Sun (1), M. E. M. Lee (2), C. P. Please (2), A. D. Fitt (2), S. K. Wilson
(3), B. R. Duffy (3), N. Hall-Taylor (4)

(1) School of Food Biosciences, University of Reading, RG6 6AP, UK

(2) School of Mathematics, University of Southampton, SO17 1BJ, UK
(3) Department of Mathematics, University of Strathclyde, G1 1XH, UK
(4) Chemtech International Ltd, Reading, RG2 0LP

Abstract
An outline of mathematical models that have been used to understand the behaviour of scraped
surface heat exchangers is presented. In particular the problem of the wear of the blades is
considered. A simple model, exploiting known behaviour of viscous flow in corners and in
wedges, and accounting for the forces on the blade is derived and solutions generated. The
results shows initial rapid wear but that the wear rate goes to zero.

Keywords: Scraper blade, wear, Newtonian fluid.

Introduction
Scraped surface heat exchangers (SSHE) are used in a variety of food processes. Central to the
operation is the careful design of the scraping blades as these generate circulating flow field to
continuously renew the food material on the outer heat exchange surface. The developments
by the current research team are produced within a multidisciplinary research framework and
a number of mathematical models have been used to create a theoretical framework to aid
understanding of the flow regimes within SSHEs. Our general approach is to consider foods
that are shear-thinning, heat-thinning fluids and then to study the resulting flow using a blend
of numerical techniques and analytical approaches. In addition we have considered a number of
elucidating paradigm problems that involve some geometric or rheological simplification in order
to gain insight though analytical solutions. Within this introduction we give a brief description
of the various aspects of our work studying the SSHE.
We have exerted a significant amount of research effort in computing numerical solutions for
steady-state flow of heat-thinning and shear-thinning fluids in a prescribed geometry. A 2-D lid-
driven cavity [1,2] considers the limit where the blades close off a rectangular or parallelogram
region and one surface moves at prescribed velocity over the stationary blades. We have found
how the location of the primary eddy’s centre is determined by the shear-thinning index and the
Reynolds number. A two dimensional annular cross-section of the SSHE with a periodic array
of blades has also been simulated [3] and compares well with available data. The angle and
length of the blades have been varied to understand their influence on the flow pattern. In all
these calculations a small amount of fluid has been allowed to travel under the blade in order to
remove the stress singularity that occurs where the sliding surface is in contact with the blade.
One of the natural extensions to [2] is being presented at this meeting [4] where a steady 3D
simulation of the SSHE is examined.
In the aforementioned numerical approaches the blades are given a fixed position and shape.
Because of the central role of the blades in the scraping process we have also considered the

1
ICEF 9 2003
International Conference Engineering and Food

movement of freely pivoted blades. In particular we have looked at a periodic array of blades
[5] in a slender channel where the reduced Reynolds number of the flow is sufficiently small that
the assumption of lubrication flow is appropriate. We have found that in such cases the blade
can have multiple steady-state positions. In addition for the cases of more practical application
to SSHEs, no steady state solution exists and it is necessary to consider the blade tip to come
into contact with the channel walls. When contact does occur the force due to the outer moving
surface can be included but a singularity in the fluid stress then arises. We have considered a
number of different theories to alleviate this problem including use of a fluid slip condition, a
power law fluid and, as in this paper, a small flow through the blade contact region.
Other problems of relevance to SSHE behaviour include the paradigm problem of parallel flow
shear flow in a channel for a heat-thinning and shear-thinning fluid [6]. There is a particularly
interesting limit where pressure gradient along the channel tends to zero. It is well known
that when this pressure gradient is non-zero there can exist multiple steady state solutions and
even non-existence of a steady states [7,8], and that for zero-pressure gradient there is a unique
solution in cases where the wall velocity is prescribed. We have been studying the structure of
these various solutions, particularly in the non-unique case.
Another class of paradigm problem we have considered are high Peclet-number flows in a
lid-driven cavity [9]. There are a number of analytical simplification that can be made to help
understand the underlying mechanisms that drive heat transfer in an SSHE. These approaches
also will help clarify issues related to numerical diffusion that can cause difficulties with our
numerical solutions particularly in the narrow thermal boundary layers present in SSHEs.
Finally, the problem that we will discuss in more detail in this paper are how the resultant
forces acting upon the blade affect the quality of scraping. Blade wear is very important and
poorly designed blades can lead to excess fouling on the heated/cooled surface and unwanted
significant blade fragments in the finished food product.

The Blade Wear Problem

The wear of scraper blades is due to rubbing between the blade tip and the moving hard outer
surface. To simplify the analysis consider the fluid in the exchanger to be Newtonian and neglect
any of the effects of temperature on either the fluid or the wear rate. The basic idea is to consider
the fluid dynamics around the scraper and to use this to identify the forces acting on the tip.
The flow under the blade tip changes as the blade wears thereby altering the forces on the blade
and we show how these effects interact to determine the tip wear rate.
In order to simplify the analysis, but still remain relatively close to the physical problem,
consider the scraper to be straight, pivoted at its end point and to be “touching” the outer
moving surface. The scraper will be taken to be at a small angle, α, to the moving surface
under the scraper. In addition the flow above the scraper will be taken to be very simple (the
scraper is assumed to be a long way from the inner surface) so that we can take the flow to be
at pressure pa (this infers that the scraper must be held on the outer surface due to suction of
the fluid behind the blade rather than by fluid pressing to get over the blade).
One of the more controversial aspects of the modelling is to decide the mechanisms whereby
fluid can get under the tip, between the scraper and the moving surface. Here the ideas usually
applied to flow of fluid in cracked rock seem applicable. The tip behaviour will first be modelled
by presuming that where the scraper touches the outer surface there is still a small tortuous gap
of small height h∗ that the fluid can pass through. This height will effectively be determined
by the asperity height on the hard outer surface. A simple and realistic model is to take h∗ to

2
ICEF 9 2003
International Conference Engineering and Food






























 






































































pivot



















































































  














p = p














































 





































a




































  











































































 h





 = h ∗ +αx








































































  































 


α 






































h∗ l(t)
0 L

Figure 1: The basic geometry of the scraper blade being considered

be the asperity height and hence, because of the sliding action, this is independent of the force
applied to the blade. There is extensive discussion about the appropriate law for flow through
such a set of touching surfaces but, in general, they employ a “tortuocity” parameter to account
for the tortuous path the fluid takes.
A second modelling difficulty is to identify the mechanisms that cause wear. Again there are
many different models but the basic parameters in these are usually the normal stress applied
between the two surfaces and the relative tangential speed of the two surfaces (the aim being
to estimate the shear stress induced in the asperities). The simplest model is to take the wear
rate as proportional to the normal stress times the sliding velocity

The Model
The basic problem to be studied is outlined in Figure 1. Here the tip is “touching” the outer
surface in the region −l(t) < x < 0 where l(t) is the length of the contact region between the
tip and the moving outer surface which will increase as the scraper wears. Using the basic ideas
given above we can write the following system of equations down. In the contact region under
the blade tip, −l(t) < x < 0, the flux of fluid, Q(t), is given by

U h∗ β(h∗ )3 (p(0, t) − p(−l(t), t))

Q(t) = − , (1)
2 12µ l(t)
where the constant β < 1 is the tortuocity parameter, and we have to determine the pressures
at the two ends p(0, t) and p(−l(t), t).
To find the pressures we consider the flow in front of the blade and in the wedge under the
blade. We consider the addition of two classical fluid flow problems concerning flow in a wedge.
These are a “driven corner flow” (one stationary wall and one moving wall) together with a low
Reynolds number version of “Jeffrey-Hamel flow” (both walls stationary and a given flow into
the corner) [9]. These solutions depend on the radial distance from an assumed sharp corner.
For this problem we take the solutions to be valid until a radial distance equal to h∗ where we

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ICEF 9 2003
International Conference Engineering and Food

anticipate the solution changes to the solution in the contact region. Hence the flow will only
be approximate. In addition the pressure in the corner depends on both the radial distance and
the angular variable. We have taken an average of the pressure over this angle as representing
the pressure exerted at the end of the contact region. For the flow in the wedge of angle α under
the blade such analysis gives
µU µQ
p(x, t) = pa − Aα + Bα . (2)
x + h∗ (x + h∗ )2

while for the flow in front of the blade, where the wedge angle is π/2 we get the result

µU µQ
p(−l(t), t) = pa + A π2 − B π2 ∗2 . (3)
h∗ h
Here Aα and Bα are constants defined as :
1 − cos α sin α
Aα = 2 , Bα = 2 . (4)
α − sin α sin α − α cos α
while A π2 and B π2 are these evaluated with α = π/2.
The force applied in the region of contact is due to the moment around the pivot point. This
consists of an integral of the pressure in the wedge under the blade (2) and to the pressure in
the contact region under the tip. Hence the stress taken by solid-solid contact in the tip area is
given by

1
Z L 
Aα µU Bα µQ
 (Aα − A π2 )µU (Bα − B π2 )µQ
σ= (L − x) − dx + − . (5)
lL 0 x+h ∗ (x + h∗ )2 2h∗ 2h∗2

Finally we have to model how the contact length, l(t), will change due to the wearing of
the blade. If the rate at which the blade material is worn away is given by γU σ, where γ is
a coefficient related to the hardness of the blade material, then the behaviour of length of the
contact region is determined by
dl γU
= σ. (6)
dt sin α
From the pressure equations and the definition of Q(t) we get

U h∗ βU (h∗ )2
+ (Aα + A π2 )
2 12 l(t)
Q(t) = . (7)
βh∗
1+ (Bα + B π2 )
12 l(t)

We wish to solve the equations (5), (6) and (7) for σ(t), l(t), and Q(t) given the initial condition
that the blade is new and hence l(0) = 0.

Nondimensional Formulation
To get some basic understanding of the behaviour of this system we non-dimensionalise the
equations. To do this we take
µU h∗ l0 sin α
x = Lx̄, l = l0 ¯l, σ= σ̄, t= t̄, Q = U h∗ Q̄ .
h∗ γ µ U2

4
ICEF 9 2003
International Conference Engineering and Food

In doing this we have decided to look at behaviour of the problem when the contact region is of
length l0 . The precise value chosen for this scale is unimportant, the solutions remain the same,
however, since typical SSHEs have h∗  l0  L choice of this lengthscale allows us to make
simplifications later. Doing some elementary simplifications we therefore get

d¯l
!
δ
Z 1
Aα Bα Q̄(t̄) (Aα − A π2 ) (Bα − B π2 )Q̄(t̄)
=¯ (1 − x) − dx + − , (8)
dt̄ l(t̄) 0 x+ (x + )2 2 2

where
12¯l(t̄) + δβ(Aα + A π2 )
Q̄(t̄) = . (9)
12¯l(t̄) + δβ(Bα + B π ) 2

with ¯l(0) = 0 and where we have introduced the two non-dimensional parameters
h∗ h∗
= , δ= .
L l0
The solution therefore is determined by the values of , δ and α. All these parameters are
conventionally very small in practice and numerous approximations can be made to exploit
these.

Discussion
Development of the mathematical model has identified the time scale of the wear and its depen-
dence on the basic physical parameters. The key results of a detailed analysis of (8) and (9) are
as follows. There is a short initial period where the flux through the contact region is controlled
by the huge pressure difference between the two ends and this flux is constant. During this time
the contact region increases in length like the square root of time. This behaviour quickly gives
way to the flux being dominated by fluid transported by the moving surface. Interestingly the
flux in this period is also constant, but different, corresponding to Q̄ ≈ 1. During this later
period, because  is small the downward force on the blade is dominated by the large pressures
in the wedge very near the contact point and the governing equation is approximately.

d¯l δ (−Aα − Bα − Aα − Bα ) ln  (Aα − A π2 − Bα + B π2 )

≈ ¯l(t̄) + (10)
dt̄ 2
This is easily solved and solutions for a typical practical case are given in Figure 2.

We again find that the contact region length increases proportional to the square root of time.
However, as time progresses the force due to the pressure under the contact region increases and
the wear rate decreases rapidly with the contact region tending to a fixed length of
2 (Aα + Bα + (Aα + Bα ) ln )
l∞ =
(Aα − Aπ − Bα + Bπ )
These formula give insight into the setting of the blade angle, α, and how this will affect the wear
process. We are currently investigating the stability of the solutions for the contact region length
in order to understand the possible reduction in scraping efficiency. In particular we anticipate
that as the contact region reaches its maximum length the blade will become very sensitive to

5
ICEF 9 2003
International Conference Engineering and Food

5E-5
0.00025

4E-5
0.0002

3E-5
0.00015
l(t) l(t)

2E-5
1E-4

5E-5 1E-5

0 0
0 0.05 0.1 0.15 0.2 0 0.05 0.1 0.15 0.2
t t

Figure 2: The length of the contact region as a function of time (in nondimensional units) using
(8) and (9) for the cases i)  = 10−4 , δ = 10−2 , α = π/6 and ii)  = 10−3 , δ = 10−2 , α = π/6

pressure variations due to the dependence of the motion on the pressure in the contact region.
We are also considering the inclusion of elastic deformation effects in the blade and how they
interact with the flow problem outlined here.

Acknowledgement
This research has been supported by the Smith Institute Faraday Partnership in Mathematics
and Computations and funded by EPSRC (grant GR/R93032/01)

References
1. Sun K.-H., Pyle D. L., Hall-Taylor N., Baines M. J., Fitt A. D. Velocity profiles and frictional
pressure drop for shear thinning material in lid driven cavities with fully developed axial flow.
(submitted to Chem. Eng. Sci. 2003)
2. Sun K.-H., Pyle D. L., Fitt A. D., Please C. P., Hall-Taylor N., Baines M. J. Heat transfer and
thermal entrance length with shear thinning materials in lid driven cavities with fully developed
axial flow. (submitted to Int. J. Heat and Mass Transfer 2003)
3. Sun K.-H., Pyle D. L., Fitt A. D., Please C. P., Baines M. J., Hall-Taylor N. Numerical
Study of 2D Heat Transfer in a Scraped Surface Heat Exchanger. Int. J. Computers and Fluids.
(accepted for publication 2003)
4. Pyle D. L., Sun K.-H., Hall-Taylor N., Fitt A. D., Please C. P., Baines M. J. Numerical studies
of heat transfer with shear thinning fluids in scraped surface heat exchangers. (submitted to
ICEF 9)
5. Duffy B. R., Wilson S. K., Lee M. E. M., A model of fluid flow in a scraped-surface heat
exchanger. (to be submitted)
6. Martin B. Some analytical solutions for viscometric flows of power law fluids with heat
generation and temperature-dependent viscosity. Int. J. Nonlinear. Mech. 2, 285-301, 1967.
7. Stroh F., Pita J., Balakotaiah V., Luss D. Thermoflow multiplicity in a cooled tube. AICHE
Journal, 13(3), 397-408, Mar. 1990.
8. Lee. M. E. M., Please C. P. High Peclet number flows in a lid-driven slender cavity. Internal
report 2003.
9. Batchelor G. K., An Introduction to Fluid Mechanics, CUP, 1967, p224 and p294.

6
ICEF9 – 2004
International Conference Engineering and Food

An Approach of “KANSEI” Engineering for Designing the Novel Bitter Beverage

Based on Consumer Characteristics in Acceptance of Bitter Taste

Hioki M (1), Ikeda G (1), Nagai H(2), Sagara Y(1)

(1) Department of Global Agricultural Sciences, The University of Tokyo,

Yayoi 1-1-1, Bunkyo-ku, Tokyo, JAPAN 113-8657
aa26295@mail.ecc.u-tokyo.ac.jp

(2) New Products Development Division, Suntory Limited

Motoakasaka 1-2-3, Minato-ku, Tokyo, JAPAN 107-8430

Abstract
Consumer preferences were investigated for designing a novel bittersweet beverage, introducing
an approach of “kansei” engineering. It was revealed that 16% of the subjects had a potential to prefer
bitter taste. The response surface methodology (RSM) applied to analyze non-linear relationships
among bitter-sweet component values, sensory scores and hedonic ratings. The applied approach was
demonstrated to be useful to design a novel beverage conforming the consumer preferences.

Keywords
kansei engineering, bittersweet beverage, Response Surface Methodology, sensory evaluation,
consumer preference

Introduction
“Food Kansei Engineering” has been proposed by Sagara1), that provides the methodologies to
consumer-oriented designing and producing new food products. Though “kansei” in Japanese words
includes various interpretations, it is briefly explained as: 1) sensing abilities of sensory organs which
involve perception in response to external stimuli, 2) consumer emotions elicited by senses, and 3)
sensory desires that are considered to be controlled by reason and the mind. In an earlier study,
methodology related to foods, such as green tea 2, 3) has been proposed. For the purpose of developing
new food products which suite specified tastes of consumers, it is strongly required to develop a new
methodology for characterizing individual preferences for the new products and to clarify the marketing
target.
Foods and beverages that have prominent bitter taste are generally rejected by a number of
people, and constitute only a small portion of total calories in industrial countries 4). However, some
items with a bitter flavor are constantly consumed and enjoyed in process of growing into adulthood. As
shown in coffee with sugar or bitter-tasting products in the market, the bitterness is often modified by
ICEF9 – 2004
International Conference Engineering and Food

sweetener. It is suggested that the sweetener play an important role in facilitating to acquire a
preference for bitter taste.
The objectives of this study are to 1) evaluate the effects of sweet and bitter components
concentrations on the hedonic ratings of consumers against novel bittersweet beverages, 2) to classify
consumers into clusters having similar preference characteristics, and 3) to investigate the optimum
concentration ratio of bitter-sweet components for the targeted consumers.

Materials and Methods

Stimuli
Nine novel bittersweet beverages were prepared as
the test samples. Two flavor profiles, sweetener and 7 8 9
122.5
bitter component, were added to the base sample

[g/L]
according to a full factorial design (Fig. 1). Three levels

Concentration of sweet
of concentrations were set for sweetener (40, 70, 122.5 4 5 6
70
g/l) and bitter (0.1, 0.3, 0.53 g/l). A sugar concentration
range was designed to fit those usually included in
commercially-available beverages. Concentration levels
1 2 3
40
were fixed based on the results obtained from the
0.1 0.3 0.53
preliminary experiments to ensure the perception of Concentration of bitter [g/L]
taste differences by ordinary people. All test samples
Fig.1 Experimental design
were prepared 24 h before the sensory evaluation.

Subjects
Eighty-nine students of the University of Tokyo participated as the panel. Subjects were consisted
of 53 males and 36 females, and mean age was 19.6 years old. They were informed that the aim of this
meeting was to evaluate palatability of the beverage samples.

Sensory meeting
All subjects firstly evaluated a “warm-up” sample containing 70 g/l sucrose and 0.3 g/l bitter
ingredient. They evaluated their expectation of palatability for the sample before tasting, then they
tasted to rate the sample with regard to liking and taste notes such as sweet, bitter, sour, salty,
aftertaste and smoothness, on a seven-point category scale.
Secondly, each subject performed the evaluations for 6 samples in a fully randomized block design.
All samples of 70 ml were distributed in a plastic cup at room temperature and they were presented in a
random order. Subjects were instructed to rinse their mouths with spring water and a salt-free cracker
to cleanse their palates between each sample. They were also requested to answer questionnaires
about their preferences for foods and beverages, their dietary habits and selected personality traits.
ICEF9 – 2004
International Conference Engineering and Food

Data analysis
General data analysis was preformed using JMP statistical software (SAS institute, Inc). For the
purpose of revealing characteristics of each cluster, the relationships among component index of
bitter-sweet concentrations, sensory scores and hedonic ratings were investigated using Response
Surface Methodology by Spline, in Visual Nesia software (Yamatake co. Ltd, Japan).

Results and Discussions

Cluster analysis
Hedonic ratings for 9 samples varied among stimuli, exclusively for the samples with high
concentrations of bitter component. It was indicated that there were some latent groups that have
different preferences for the flavor stimuli. Therefore, correlation coefficient values were calculated
between hedonic and sensory scores of the taste, as an index of individual preference characteristics.
Applying cluster analysis on these index values, the subjects were divided into 3 clusters; the largest
cluster 1 (75%), cluster 2 (16%), and a minority of cluster 3 (9%). As shown in Fig. 2, the individual
correlation coefficients between a) bitterness and sweetness and b) total intensity and smoothness with
preference were plotted. Ellipses in the figures cover 50% of each cluster in the figures. Thus these
figures illustrated the characteristics of 3 clusters. In the cluster 1, preference showed a negative
correlation with perception of bitterness, and a positive with sweetness. Although the cluster 2 showed
a preference for sweetness, no significant correlation was observed between pleasant ratings and
perception of bitterness. Comparing with cluster 1 and 2, the cluster 3 showed a negative correlation
between preference and sweetness.
Correlation coefficients with smoothness
甘味 with sweetness

1 1

Cluster 1
0.5 Cluster 2 0.5
Cluster 3
Correlation coefficients

0 0

Cluster 1
-0.5 -0.5
Cluster 2
Cluster 3

-1 -1

-1 -0.5 0 .5 1 -1 -0.5 0 .5 1
Correlation coefficients
苦味 with bitterness Correlation coefficients with intensity

a) Correlation coefficients of bitterness and b) Correlation coefficients of intensity and

sweetness with hedonic ratings smoothness with hedonic ratings
Fig. 2 Preference characteristics of 3 clusters

Relationship between hedonic ratings and sensory data

Using thin plate spline methodology, the relationship between sensory data and pleasantness
ratings were determined for each cluster. As a typical result the relationship between perception of
ICEF9 – 2004
International Conference Engineering and Food
6

Predicted scores of preference

5.5
bitterness and liking was presented in Fig.3.
5
Cluster 2
The preference for the cluster 3 showed the
peak with scores for bitterness ranging from 5 4.5

to 7, whereas the other two clusters showed 4

Cluster 1
marked decrease as perception of bitterness 3.5 Cluster 3

increased. These results indicated that the 3

cluster 2 had a potential to have a preference 2.5

for bitter taste. 2

1 2 3 4 5 6 7
Scores for bitterness

Fig. 3 Predicted curves of preference vs. bitterness

Relationship between sensory data and bitter-sweet concentrations

Fig. 4 illustrated a curved surface in three-dimensional space showing the contour of sweetness
ratings against the relationship between bitter-sweet concentrations among a) cluster 1 and b) cluster 2.
These results indicated that the cluster 2 had tendency to perceive sweetness for the samples with high
bitterness in concentration comparing with the cluster 1.
Concentration of sweetness log C [g/L]

Concentration of sweetness log C [g/L]

Concentration of bitterness log C [mg/L] Concentration of bitterness log C [mg/L]

2 7 2 7
Scores for sweetness Scores for sweetness

a) Cluster 1 (75%) b) Cluster 2 (16%)

Fig. 4 Perception of sweetness vs. bitter-sweet concentrations

Relationship between hedonic ratings and bitter-sweet concentrations

As shown in Fig. 5, the response surfaces of hedonic scores for 3 clusters were determined based
on the relationship between bitter and sugar concentrations. The cluster 1 which contained 75 % of
the subjects showed the marked preference for the sample with lower bitter and higher sweet
components in concentration. However, the counters for the cluster 2 and 3 showed significantly
different characteristics for their preference. The cluster 2 showed a preference for the bitterer
concentration samples, if its sugar concentration was maintained relatively at a high level. The cluster 3
 ICEF9 – 2004
International Conference Engineering and Food

Concentration of sweetness log C [g/L]

Concentration of sweetness log C [g/L]

a) Cluster 1 b) Cluster 2

Concentration of bitterness log C [mg/L] Concentration of bitterness log C [mg/L]

6 2 6
Scores for preference
Concentration of sweetness log C [g/L]

c) Cluster 3

Fig. 5 Preference vs. bitter-sweet concentrations

a) Cluster 1
b) Cluster 2
c) Cluster 3

Concentration of bitterness log C [mg/L]

2 6
Scores for preference

seemed to disrelish in proportion to concentrations of both components. These results indicated that
there were some potential clusters hiding behind the biggest cluster, in this case the cluster 1, by the
segmentation of consumers according to the individual preferences.

Conclusion
Consumer preferences for a novel bitter beverage were investigated to design the optimum
combination of bitter-sweet concentrations and to find a target cluster. It was demonstrated that the
segmentation of consumers based on their individual characteristics of taste preference was useful to
find the latent clusters having potentially preferences against novel products.

References
1. Sagara Y. “Kansei” engineering for investigating food preference. The Japanese Journal of Taste
and Smell Research. 8, 2, 153-159, 2001
ICEF9 – 2004
International Conference Engineering and Food

2. Ikeda G. Hioki M. Nagai H. Sagara Y. A study of designing techniques to incorporate consumers’

“kansei” into tea beverages (1). The Japanese Journal of Taste and Smell Research. 9, 3, 553-556,
2002

3. Hioki M. Ikeda G. Nagai H. Sagara Y. A study of designing techniques to incorporate consumers’

“kansei” into tea beverages (2). The Japanese Journal of Taste and Smell Research. 9, 3, 557-560,
2002

4. Mattes R.D. Gustation as a determinant of ingestion: methodological issues. The American Journal
of Clinical Nutrition. 41,4, 672-683, 1985
ICEF9-2004 International Conference Engineering and Food

Modelling-based analysis of the influence of product image and information on consumer

evaluation of functional orange drinks

Pagidas N. (1) and Oliveira J.C.* (2)

(1) Dept. of Process Engineering, University College Cork, Ireland, n.pagidas@mars.ucc.ie

(2) Dept. of Process Engineering, University College Cork, Ireland, j.oliveira@ucc.ie
* Author to whom correspondence should be addressed

ABSTRACT

A full factorial design was applied with two levels regarding formulation and three levels regarding
information. The study was performed over two weeks, supplying a panel of consumers with four 250 ml
bottles each week, to consume at home. The response was evaluated with various descriptors using a
semantic differential scale. The descriptors were analysed by PCA and the principal components and key
descriptors were then modelled with a multi-parametric function to yield the design model.

Key words: Product design engineering, kansei engineering, functional foods

1. Introduction

The evaluation of food, even in terms of sensory quality, has a very strong contextual element.
Consumers may strongly like or dislike the same product depending on what they think it is that they are
eating. However, there is little information available that quantifies the so-called placebo effect in foods.
This is a particularly important issue regarding energy drinks. Consumers generally associate
these drinks with higher levels of energy, but to what extent is the effect influenced by belief and
expectation? How much of the boost can be attributed to the product image, even to marketing, and how
much is an objective effect on the human metabolism caused by stimulant ingredients such as caffeine
and taurine?
Consumer research tends to isolate the product image from its sensory quality by performing
sensory evaluation of formulations on their own. The marketing image of the product is generally
developed separately, often by a totally different team. However, from the point of view of the consumer,
the product is an integrated reality. When a consumer buys and consumes an actual product, he/she does
so in a specific context and not in a vacuum. Koster highlighted this problem well in his description of the
most common fallacies of consumer research (1).
The system of values and beliefs and expectations of individuals can play a major role in the
assessment of the product. It would therefore be logical to treat information as a design factor of the
product, which needs to be considered in the same way as any other (such as formulation), and in
particular integrated with all others. This would correspond to the concept of “seeking the gemba”. Gemba
is a Japanese word that signifies “real location”, which in this context means “to look for the evaluation of
the product in real conditions of use, with all factors that influence that judgement working in normal ways”
(2).
The objective of this work was to apply a product design engineering approach to the consumer
evaluation of functional drinks, studying in detail the interactive effect between formulation and
information, treating the latter as an independent design factor. Orange juice and orange juice fortified with
caffeine, taurine and ginseng in concentrations typical of commercially available energy drinks were the
two formulations considered. Samples were provided to a panel of consumers (young adults) for
evaluation at home, in their own time. The samples provided were however labeled independently of the
actual formulation, with 3 types of information given: (i) simple orange juice; (ii) a healthy orange juice,
fortified with vitamins and minerals; (iii) a stimulant drink, with added caffeine, taurine and ginseng. A full
factorial design of these two factors means that consumers received samples with totally wrong
information: normal orange juice with a label claiming to be a stimulant drink, fortified orange juice with
added stimulants labelled as simple orange juice, etc. If information played no role, than consumers
should be able to feel an energy boost with the fortified product, even if they do not know it is fortified,
ICEF9-2004 International Conference Engineering and Food

while they should never feel an energy boost if they drink a simple orange juice, even if they believe it to
have been fortified.
In addition to the energy boost feeling after consumption, other factors were to be evaluated,
namely rational aspects of likeness and willingness to buy (which are used in conjoint analysis), and a
small kansei engineering type of questionnaire.
Kansei engineering is a novel Japanese method of product design (3) which focuses on
developing combinations of design factors according to the feelings and emotions that their use causes in
the consumer. Kansei is a Japanese word (pronounced “can-say”) meaning ill-defined emotions or
feelings, and has been termed “emotional engineering” in some American popular press. Its application in
developing food products has been briefly discussed by Oliveira (4). In broad terms, the essential
difference between kansei engineering and methods more common in Europe such as conjoint analysis is
the specification of product descriptors not by rational answers that consumers give to objective questions,
but precisely by avoiding rationality altogether, and seeking the emotions and feelings that are difficult to
be verbalised, going “beyond the voice of the consumer”.

2. Materials and Methods

Subjects
Twenty-seven subjects (18 males, 9 females) aged 18-20 participated in the study. 52% of them
were exercising regularly (33% seldom and 15% never). 85% of the participants were paying attention to
their nutrition, while 15% were paying a little attention. The panel was representative of young people that
consume energy drinks.

Samples
In terms of actual formulation, there were only two product prototypes: (i) commercially available
orange juice lightly pasteurised (not made from concentrate), bought in a local supermarket (brand
Dunnes Florida Premium), which had sensory quality close to that of a freshly squeezed juice; (ii) the
same juice, but fortified with caffeine (320 mg/L), taurine (2,500 mg/L) and ginseng (320 mg/L), which are
concentrations typical of commercially available energy drinks.
The products were bottled in 250 ml plastic (PET) bottles, with one of three possible labels: (i) a
normal orange juice, (ii) a healthy orange juice, with extra natural vitamins and minerals; (iii) an energy
drink made from orange juice with added caffeine, taurine and ginseng.
A full factorial design of these two factors with two and three levels each therefore corresponded
to 6 different product prototypes, as described in table 1

Table1. Product prototypes

Code Formulation Information ((lable)
AI Plain orange juice Healthy drink
AII Plain orange juice Energy drink
AIII Plain orange juice Pure orange juice
BI Orange juice with stimulants Healthy drink
BII Orange juice with stimulants Energy drink
BIII Orange juice with stimulants Pure orange juice

Gemba evaluation
The participants were asked to take the bottles home and consume them at their own
convenience and time, as they would do with beverages they would normally buy. They were asked to fill
a questionnaire for each product after consumption, with two sets of issues: rational questions (like, willing
to buy, and energy boost effect felt) and a small kansei questionnaire using a five-point semantic
differential scale (SD) to express their feelings and opinions about the experience (table 2).
ICEF9-2004 International Conference Engineering and Food

Table 2. Summary of the questions included in the questionnaire

Rational questions
like dislike
strong energy boost no effect
willing to buy not willing to buy
Kansei adjectives
pleasant taste weird taste
original conventional
relaxed depressed
hyperactive calm
beneficial useless
stimulating normal
healthy unhealthy
energising draining
different usual
refreshing tiring
interesting ordinary
balanced unbalanced

Each participant received four products in the first week and three in the second. In the first week
two had the same formulation but different information and two had different formulation but the same
information. The participants were divided in three groups and each group received a different set of
products. During the second week of the study, each group received the two remaining drinks that they
had not received in the first week, plus one that was the same for both weeks.

Data analysis
Tuckey HSD tests were applied to establish statistically significant differences between
prototypes. The responses analysed were “likeness”, “willingness to buy” and “boost energy effect felt
after consumption”.
The small kansei questionnaire was handled in the simple way proposed by Nagamachi in basic
kansei engineering (3). The kansei adjectives were grouped by a Principal Components Analysis (PCA).
From the type of words (adjectives) that are combined in this way, each principal component is interpreted
in terms of an emotion or feeling. The influence of the various design factors and options in each of these
principal components (or on the key adjectives, that is, the pairs with higher loadings in the PCA) is then
visualised by considering a multilinear model using dummy variables:

Re sponse = ao + a11X11 + a12 X12 + a21X21 + a22 X22 + a23 X23 (1)

where ao is the average of all responses, X11=1 when the formulation is “plain juice” (and is
otherwise equal to zero), X12=1 when the formulation is “fortified juice” (and is otherwise =0), X21=1 when
the information on the label is “healthy drink” (and is otherwise =0), X22=1 when the information on the
label is “energy drink” (and is otherwise =0), X31=1 when the information on the label is “plain juice” (and is
otherwise =0). The coefficients aij thus quantify the relevance of that particular design option. The partial
correlation coefficients for the two design factors were also determined, each quantifying the relative
importance of that factor (this was done by using equation 1 truncated of all terms but those of the factor
being analysed).
The main limitation of this type of basic kansei engineering is the assumption of linearity and
independence of the design options.

3. Results and Discussion

Analysis of rational questions

Tables 3 and 4 show that there were no significant differences between the beverages in terms of
likeness and willingness to buy. The participants liked and were willing to buy either orange juice or
fortified orange juice in roughly the same manner.
ICEF9-2004 International Conference Engineering and Food

a a
Table 3. Tuckey HSD for likeness Table 4. Tuckey HSD for willingness to buy
Subset for Subset for
a = .05 a = .05
Sample N 1 Sample N 1
BIII 27 .4815 AII 27 1.1852
BI 27 .6667 AIII 27 1.1852
BII 27 .7407 AI 27 1.2222
AII 27 .8148 BII 27 1.2953
AIII 27 .8148 BI 27 1.4074
AI 27 .9630 BIII 27 1.4074
σ .568 σ .537
Legend: A - plain juice; B - fortified juice; I - healthy label; II - energy label; III - plain label

Table 5 shows significant differences between the prototypes regarding the energy boost effect
reported by the panel of consumers, with very interesting results. The prototype that caused the greatest
effect was indeed a fortified juice (and the one with that label), although the plain juice with the label
claiming to be fortified with stimulants fell in the same statistical group. On the other hand, the group with
the lowest boost effect response includes the plain orange juice with its correct label and also the fortified
orange juice with the label indicating that it was a plain product.
Therefore, when consumers were told that the product contained stimulants they felt a boost,
whether it did in fact contain them or not, and when told that the product was orange juice they did not feel
any boost, even when the stimulants were actually there. This suggests that the placebo effect is stronger
than the actual metabolic effect of these ingredients in these amounts.
This also suggests that the consumers correlated healthy formulations (extra vitamins and
minerals) with energy and well being, as they placed the products introduced as healthy drinks in between
the pain and fortified labels. The juice that was fortified, but with the label claiming to have only extra
vitamins and minerals also fell in the same group as the two energy labelled samples, albeit with a clearly
lower rating which was not statistically different from the plain products either (sample BI fell in all three
groups).
a
Table 5. Tuckey HSD for after-drink energy boost effect
Subset for a = .05
Sample N 1 2 3
AIII (plain juice + plain label) 27 1.1852
BIII (fortified juice + plain label) 27 1.1852
AI (plain juice + healthy label) 27 1.2963 1.2963
BI (fortified juice + healthy label) 27 1.3074 1.3074 1.3074
AII (plain juice + energy label) 27 1.6667 1.6667
BII (fortified juice + energy label) 27 1.7407
σ .561 .149 .149

Analysis of the kansei questionnaire

The responses of the participants on all adjective pairs of the SD scale were analysed using data
reduction analysis, and three principal components were identified, explaining 91.3% of the variance. The
adjectives that appeared distributed with similar loadings in more than one PC were then eliminated (it is
interpreted that such split may be caused by different individuals giving different meanings to the words, or
using them to express different feelings). A second PCA was then run on the remaining 9 pairs, forcing all
pairs of adjectives to lay in only one PC. The three main PC then explained 90.4% of the variance. Table 6
shows the results.
ICEF9-2004 International Conference Engineering and Food

a
Table 6. Rotated Component Matrix for selected adjective pairs.
Component
Adjective pairs 1 2 3
Weird Taste ↔ Pleasant .957
Conventional ↔ Original .865
Depressed ↔ Relaxed .880
Calm ↔ Hyperactive -.886
Useless ↔ Beneficial .808
Normal ↔ Stimulating .866
Unhealthy ↔ Healthy .784
Usual ↔ Different -.898
Ordinary ↔ Interesting .919
Extraction Method: Principal Component Analysis.
Rotation Method: Varimax with Kaiser Normalization.
a. Rotation converged in 5 interactions

The emotions/feelings behind the grouping must now be identified. Note that negative loading
factors imply switching the words at the extremes. The first PC seems broadly related to the drinking
experience in itself, with the higher end of the scale (2) being good and satisfying (“pleasant”, “beneficial”,
“healthy”, “usual”), while the lower end (-2) would be generally unappealing (“weird taste”, “useless”,
“unhealthy”, “different”). The second component relates to novelty and interest, as opposed to
conventionality, with the higher end of the scale being appealing (“original”, “stimulating”, “interesting”) and
the lower end of the scale somewhat boring (“conventional”, “normal”, “ordinary”). The third PC groups the
adjectives related to action and relaxation, with the higher end of the scale meaning peacefulness
(“relaxed”, “calm”) and the lower end energetic with a negative connotation (“depressed”, “hyperactive”).
This extraction must be treated with some caution as the kansei questionnaire was small and
limited, but it seems to indicate that the most important emotion of consumers in assessing these products
is the actual drinking experience and how the product feels and looks like. The curiosity and interest for
novelty that it sparkles would come as second major factor, while an actual energetic effect comes only
third.
The kansei engineering design tables are shown in tables 7 to 9. All correlation coefficients of the
multilinear model (equation 1) were above 0.85, which has been considered quite acceptable in similar
studies of kansei engineering (5, 6). The partial correlation coefficients (PCC) are then analysed to see
which of the two design factors is more important and whether any is negligible. The importance of the
design options is visualised by bars which correspond to the coefficients of the multilinear partial model
(the longer the bar, the greater the importance of that option).
Thus, it can be seen from table 7 that the drinking experience was always considered positively
for all prototypes, but the formulation played the most important role in satisfying the consumers (higher
PCC), and the best option is a plain juice (this may be due to the slight bitter taste conceded by caffeine
and taurine). Regarding the sense of novelty and interest, table 8 shows that it is dominated by the label
and formulation is not really important. An energy label claim gives a higher rating (more interest). In terms
of the energetic effect it is the label again, not the formulation, that is the dominant factor. The highest
rating (relaxing) is obtained with a healthy label, while an energy label gives the opposite result
(energetic).

Table 7. Kansei analysis for principal component 1.

Multiple Correlation Coefficient R = 0.866
Design PCC Design PC1 (Drinking Experience)
Factors Options -0.4 –0.2 0 0.2 0.4
Formulation 0.79 Fortified 0.860
Plain 0.221
Information 0.33 Healthy 0.518
Energy 0.209
Plain 0.454
ICEF9-2004 International Conference Engineering and Food

Table 8. Kansei analysis for principal component 2.

Multiple Correlation Coefficient R = 0.850
Design PCC Design PC2 (Sense of Normality)
Factors Options -0.4 –0.2 0 0.2 0.4
Formulation 0.07 Fortified 0.242
Plain 0.193
Information 0.84 Healthy 0.176
Energy 0.531
Plain -0.171

Table 9. Kansei analysis for principal component 3.

Multiple Correlation Coefficient R = 0.948
Design PCC Design PC3 (Energy Effect)
Factors Options -0.4 –0.2 0 0.2 0.4
Formulation 0.21 Fortified 0.152
Plain 0.025
Information 0.92 Healthy 0.353
Energy -0.283
Plain 0.207

4. Conclusions

The results showed that information given on what a beverage contains plays a greater role in the
response to it than the actual content of the drink. The concentrations of caffeine and taurine that are used
in energy beverages can be adjusted taking into consideration this placebo effect. This work suggests that
an image of energetic and boosting product may compensate lower amounts of stimulant ingredients. The
fact that they are there, rather than the concentration, appears to be the most relevant factor.
A brief kansei analysis suggested that the three main emotions/feelings involved in consumer
assessment of energy beverages are (i) the drinking experience in itself, with the lower end of the scale
being good and satisfying, while the higher end would be generally unappealing; (ii) a sense of novelty
and interest, as opposed to conventionality and (iii) a sense of action and relaxation, with the lower end of
the scale meaning peacefulness and the higher end energetic (with a negative connotation). Formulation
is only a relevant factor in the first, with the two latter being clearly dominated by information.

References

1. Koster, E.P. (2002). The psychology of food choice: some often encountered fallacies. Food Quality
and Preference, 14: 359-373
2. Oliveira, J. (2003). Role of Kansei Engineering in Product Design Engineering. International journal of
Kansei Engineering, In Press
3. Nagamachi, M. (1995). Kansei engineering: a new ergonomic consumer-oriented technology for
product development. International Journal of Industrial Ergonomics, 15 (1): 3-12
4. Oliveira, J. (2003). Advances in Consumer-oriented Product Design Engineering of Foods. Food
Science and Technology Research, In Press
5. Jindo, T., Hirasago, K. and Nagamachi, M. (1995). Development of a design support system for office
chairs using 3-D graphics. International Journal of Industrial Ergonomics, 15: 49-62
6. Jindo, T. and Hirasago, K. (1997). Application studies to car interior of Kansei engineering.
International Journal of Industrial Ergonomics, 19: 105-114
Numerical Analysis of Design Parameters and their Influence on Continuous Flow
Microwave Processing of Liquid Foods

Sabliov, C.M.* and K.P. Sandeep**

* Biological & Agricultural Engineering Dept., Louisiana State Univ., Baton Rouge, LA
70803
E-mail: csabliov@bae.lsu.edu, Phone: 225-578-1055, Fax: 225-578-3492

** Department of Food Science, North Carolina State University, Raleigh, NC 27695-

7624
E-mail: kp_sandeep@ncsu.edu, Phone: 919-515-2957, Fax: 919-515-7124

ABSTRACT:

Temperature uniformity within a liquid product heated by microwave energy depends on

three components-- electromagnetics, fluid flow, and heat transfer. The objective of this
study was to describe the process of continuous microwave heating of liquid foods by
coupling all three components above, using numerical methods.

Modeling studies completed in ANSYS (ANSYS Inc., Pittsburgh, PA) were designed to
assess the influence of design parameters on uniformity of outlet temperature for liquid
foods processed in a 5 kW continuous microwave unit. Processing parameters of interest
included dielectric properties, initial temperature, flow rate, microwave power level,
applicator diameter, and geometry of the focusing cavity.

INTRODUCTION
Several studies have been conducted in the area of mathematical modeling of the
multimode microwave systems (Lui et al., 1994; Dibben and Metaxas, 1994; Ma et al.,
1995; Zhao and Turner, 1996; Iwabuchi et al., 1997; Zhang and Datta, 2000). The goal of
this study was to describe the process of microwave heating of liquid foods using a
continuous microwave system. Modeling studies were designed to assess the influence of
design parameters such as dielectric properties, initial temperature, flow rate, microwave
power level, applicator diameter, and geometry of the focusing cavity on uniformity of
outlet temperature for liquid foods processed in a continuous microwave unit.

MATERIALS AND METHODS

Dielectric properties of apple sauce, skim milk, tomato sauce, and nacho cheese
were measured experimentally as a function of temperature, at a frequency of 915 MHz
using a HP 8753C Network Analyzer and a HP 85070B dielectric probe kit (Hewlett-
Packard, Palo Alto, CA). The food products were selected so as to encompass a wide
range of dielectric properties -- low loss tangent (apple sauce), medium loss tangent
(skim milk), and high loss tangent (tomato sauce and nacho cheese). The behavior of the
chosen food systems subject to high-frequency field was studied numerically. The outlet
temperature of apple sauce, skim milk, and tomato sauce heated in the 5 kW microwave
unit at 915 MHz, was computed.

1
 The influence of dielectric properties (and other processing parameters) on the
heating pattern of low, medium, and high dielectric loss products was assessed using
numerical modeling. An algorithm was developed to couple the high frequency
electromagnetics module with the thermal module and the fluid flow module, using
ANSYS (ANSYS Inc., Pitsburgh, PA) as outlined in Figure 1. The coupling between the
modules is reciprocal. First, the microwave power converted into heat leads to a
temperature increase in the food product. The temperature change, in turn affects the
dielectric, physical, and thermal properties of the product. Consequently the microwave
power converted into heat changes and the loop continues.

Start

Initial
Temperature (Ti)

Dielectric Properties Thermal Properties Physical Properties

ε’, tanδ = f (T) k, ρ, cp = f (T) ρ, µ = f (T)

High Frequency Electromagnetics Module

(HF Emag)

Volumetric Heating
(Joule Heat)
Thermal Module Fluid Dynamics
(Heat Equation) (Momentum Equation)

Temperature and Velocity

T, v = f (x,y,z,t)

∆T > ∆Tset

x
Stop

Figure 1. Proposed algorithm for coupling High Frequency Electromagnetics with Heat
Transfer and Fluid Flow

2
RESULTS AND DISCUSSION
Heating time, as well as temperature distribution in a product is dictated by its
dielectric properties, among other parameters. The effect of temperature on the dielectric
properties of the products studied is shown in Figure 2.

80 3.2

70 2.8

60 2.4
Dielectric constant (ε')

Loss tangent (tan δ)

50 2
apple sauce skim milk tomato sauce
40 1.6

30 1.2

20 0.8

10 0.4

0 0
0 20 40 60 80 100
Temperature (°C)

Figure 2: Effect of temperature on dielectric properties

The influence of dielectric properties on the heating pattern of low, medium, and
high dielectric loss products was assessed using numerical modeling. Maxwell’s
equations were solved using the High Frequency Electromagnetics Module of the
commercially available Finite Element Package, ANSYS (ANSYS Inc., Pittsburgh, PA).
The simulations confirmed that lower loss tangent products absorbed less microwave
power as compared to higher loss tangent products as seen from Table 1.

Table 1: Influence of dielectric properties on microwave power converted into heat

Product Dielectric constant (ε') Loss tan (tan δ) Power loss (W)
Apple sauce 68.4 0.12 3437.7
Skim milk 64.6 0.31 4771.1
Tomato sauce 69.3 0.92 4987.8

3
 The first step in better understanding how microwave energy is spatially
distributed in the food product requires an analysis of the electromagnetic field
distribution in the microwave cavity. The effect of dielectric properties and the diameter
of the applicator tube on the electric field distribution was determined for food products
processed in the 5 kW microwave unit operating at 915 MHz (Figures 3 and 4).

Figure 3: Influence of average dielectric properties on electric field distribution

a) Apple Sauce and b) Tomato sauce

Figure 4: Influence of applicator diameter on electric field distribution (in nacho cheese)
b) Applicator diameter D = 1.5” and b) Applicator diameter D = 2”

Next, temperature distribution in apple sauce, skim milk, and tomato sauce heated in
a 5 kW continuous microwave unit were computed based on the algorithm outlined in
Figure 1. The results showed that in milk, the highest temperature was reached at the
center of the tube, and lowest, close the wall. For tomato sauce, a high loss tangent
product, the highest temperature area was skewed toward the wall facing the back of the
cavity. This heating pattern resulted in a less-uniform outlet temperature of the flowing
product, as compared to milk. The validation of the numerical results against
experimental data makes the object of future research.

4
CONCLUSIONS
Modeling studies were used to understand the interaction between products of
different dielectric properties and microwaves, in a continuous microwave system.
Numerical modeling was a great tool to quickly determine the temperature distribution in
the processed product and to determine the best configuration of the processing system,
such as the applicator diameter for a certain product. It was found that products with
higher dielectric properties heated faster than those of low properties at the extent of
temperature uniformity in the system studied. The heating process can be improved by
changing the size of the microwave applicator and the geometry of the focusing cavity.

REFERENCES
Dibben, D., Metaxas, A.C. 1996. Time-domain finite-element analysis of multimode
microwave applicators. IEEE Transactions on Magnetics. Vol. 32(3): 942-945.
Iwabuchi, K., Kubota, T., Kashiwa, T., Tagashira, H. 1997. Analysis of electromagnetic
fields using the finite-difference time-domain method in a microwave oven loaded with
high-loss dielectric. Electronics and Communications in Japan. Vol. 78(7): 41-50.
Lui, F., Turner, I., Bialkowski, M. 1994. A finite-difference time-domain simulation of
power density distribution in a dielectric loaded microwave cavity. Journal of Microwave
Power and Electromagnetic Energy. Vol. 29(3): 138-148.
Ma, L., Paul, D., Pothecary, N., Railton, C., Bows, J., Barratt, L., Mullin, J., Simons, D.
1995. Experimental validation of a combined electromagnetic and thermal FDTD model
of a microwave heating process. IEEE Transactions on Microwave Theory and
Techniques. Vol. 43(11): 2565-2572.
Zhang, H., Datta, A.K. 2000. Coupled electromagnetic and thermal modeling of
microwave oven heating of foods. Journal of Microwave Power and Electromagnetic
Energy. Vol. 35(2): 71-81.
Zhao, H., Turner, I.W. 1996. An analysis of the finite-difference time-domain method for
modeling the microwave heating of dielectric materials within a three-dimensional cavity
system. Journal of Microwave Power and Electromagnetic Energy. Vol. 31(4): 199-214.

5
 Food process design using computer spreadsheets

Saravacos, G.D. (1) and Maroulis, Z.B. (2)

National Technical University of Athens, 15780 Greece
(1) gsaravac@otenet.gr (2) maroulis@chemeng.ntua.gr

Abstract

Application of computer packages to food process design is limited by inadequate process modeling
and insufficient food property and engineering data. PC spreadsheets, utilizing simplified models and
approximate food property data, can be used in simulation and design of food processes. Typical ap-
plications of the spreadsheet technique include thermal processing of foods (in-container and continu-
ous flow) and food dehydration.

Keywords: process design, spreadsheets, pasteurization, sterilization, drying

Introduction

Process and plant design are well developed fields of Chemical Engineering, which can be applied to
Food Technology and Engineering for the efficient and economic design and operation of food proc-
essing plants (1). However, in contrast to simple gases and liquids of Chemical Engineering, the engi-
neering properties of most foods (complex solid or semi-solid materials) are not well known or predict-
able accurately.
Beyond the engineering and economic aspects of classical process design, food process de-
sign must take into serious consideration food safety and quality, since food products must be safe,
nutritious and acceptable to the consumer.
Recent advances on engineering and transport properties of foods are discussed by Rahman
(2), and Rao et al. (3). Of particular importance are the transport properties of foods (4).
Engineering process design is a procedure of sizing and rating of a process in order to
achieve a specific goal, such as economic production, product quality, and environmental protection.
Modern process design is preceded by mathematical modeling and simulation, which can predict the
performance of the process.
Computer packages (software) have been developed that simulate the operation of process
units or process systems in Chemical Engineering. Such packages require extensive data of physical
and engineering properties of the materials, which are available or can be predicted accurately for
gases and liquids.
Commercial computer packages are difficult to apply to food processes, since data on physi-
cal and transport properties are limited and they cannot be predicted accurately.
Modeling and simulation of some food processes has been reported by Skjoldebrand et al. (5),
which require detailed programming for each specific application. Simplified computer spreadsheets
have been proposed for the effective design of various food processes (6, 7).

Spreadsheet Implementation

The implementation of the Excel (Microsoft) spreadsheet system in food processes is outlined briefly
in the following:
Modeling and simulation are useful tools in process design. Modeling consists of the equa-
tions describing the physical laws applicable to the specific process. The equations are obtained from
material and energy balances, thermodynamic equilibria, transport phenomena, reaction kinetics, and
equipment and economic characteristics.
Simulation is the appropriate software, which predicts the actual performance of a process. It
is based on mathematical modeling plus the appropriate graphics interface in a computer environ-
ment.
ICEF9-2004 International Conference Engineering and Food

A process is characterized mathematically by the degrees of freedom (F), which is the number
of variables (M) minus the number of process equations (N).The degrees of freedom are broken down
to the design specifications and the design variables. Typical design specifications are product feed
rate and temperature, utility temperatures, and quality constrains.
Design variables are decided by the design engineer, such as geometry of the equipment and
fluid velocity. The remainder set of equations (M-N) is solved using mathematical techniques. In food
engineering applications, the system of equations can be solved sequentially (down triangle matrix) or
by using a few trial variables. The values of the design variables are selected so as to optimize the
economic design of the process. Process optimization involves the process mathematical model, the
process specifications, and technical and economic data.
The process simulator, represented in a spreadsheet, consists of the process model work-
sheet (model, variables, data), the problem solution visual basic model (visual basic, solver), the data-
base worksheet (properties), and the graphics interface worksheet. (specific problem, problem specifi-
cations, results presentation - tables, charts). Figure 1 shows the spreadsheet implementation of a
food process.

Economic Data Economic Model Excel Solver

Technical Data

Process Model Excel Table

Process
Specifications Process Constraints

Design Variable Excel Graph

Data Equations Excel Tools

Figure 1. Spreadsheet implementation of a food process

Thermal Processing of Foods

The spreadsheet technique has been applied to the design of thermal processing of foods. Two typical
examples are described here, i.e. in-container sterilization and continuous flow thermal processing (7).
Continuous flow thermal processing includes pasteurization and sterilization of fluid foods (8).

In-Container Sterilization
In-container sterilization of a solid food was simulated using the spreadsheet technique. The process
variables of the system are 15 and the process equations 9. The 6 degrees of freedom are all consid-
ered process specifications (feed rate, cylindrical can size, steam, cooling water, and ambient tem-
peratures), leaving zero design variables.
Solid pack corn was sterilized in 1/1 cans (EU) of dimensions 99mmx122mm (900 mL capac-
o
ity), which is close to the US No 2 1/2 cans. Assumed temperatures, steam 120 C, cooling water 15
o o
C, and ambient 25 C. Decimal reduction time 0.3 min and reduction exponent 12.
The thermal diffusivity of the product was estimated from literature data of physical and trans-
-7 2
port properties as α = 1.6x10 m /s (2, 4). Assuming conduction heating, the calculated heating pa-
rameter is fh = 79.3 min. The simulated time-temperature profile of the can center is shown in Figure 2.
The thermal destruction of the target spoilage microorganism (bacterial spores) is simulated in Figure
3. The destruction of heat sensitive food nutrients can be simulated in similar diagrams. It should be
noted that the entire heating and cooling period of the can is taken into consideration in the calculation
of thermal destruction of bacteria and nutrients.
ICEF9-2004 International Conference Engineering and Food

The thermal process time, defined as he time the can is exposed to the processing tempera-
o
ture (120 C), is estimated from Figure 2 as t = 88 min. The classical Ball formula method (9, 10) esti-
mates the thermal process time in the given system as tB = 79 min. The difference in process time is
due to assumption of a cooling lag factor j = 1.41 in the Ball method, while the spreadsheet technique
neglects the lag phase (j = 1).

150

125
Steam

100
Temperature ( oC)

75

50

25

Cooling Water
0
0 30 60 90 120 150

Processing time (min)

Figure 2. Simulated time-temperature profile of the can center

1.E+00

1.E-03
Surviving fraction

1.E-06

1.E-09

Sterilizer Cooler

1.E-12

1.E-15
0 30 60 90 120 150
Processing time (min)

Figure 3. Simulated thermal destruction of spoilage bacteria spores

Continuous Flow Sterilization

A system of plate heat exchangers was used to pasteurize milk, with hot water for heating, and cold
water and refrigeration for cooling. The total system involves 30 variables and 18 process equations.
The 12 degrees of freedom consist of 7 process specifications (feed flow rate, product and utility tem-
peratures, bacterial inactivation, and quality damage) and 5 design variables (product temperature in
the holding tube, residence time, refrigerant temperature). The time-temperature profile of the product
during the entire process is shown in Figure 4.
ICEF9-2004 International Conference Engineering and Food

Thermal sterilization of milk was simulated using indirect steam heating and steam injection
systems. Both heating systems have 6 process specifications (feed flow rate, and feed, product,
steam and cooling water temperatures. The indirect system has 3 design variables (regenerator tem-
perature, holding tube temperature, and time), while steam injection has an added variable, i.e. the
residence time in the flash vessel.
Figure 4 shows the simulated time-temperature profiles of milk sterilization, using both indirect
heating and steam injection (7). The entire heating and cooling periods of each process are taken into
consideration, while conventional calculations consider only the residence time in the holding tube.
The computer spreadsheet technique can be applied to the simulation and design of steriliza-
tion of particulate foods, i.e. food liquids containing suspended particles, such as pulps, emulsions and
soups.

150
Sterilization
(Injection) Sterilization
125
(Indirect)
Temperature ( oC)

100

75

50
Pasteurization
25

0
0.0 0.5 1.0 1.5 2.0 2.5
Processing Time (min)

Figure 4. Temperature – time profiles of pasteurization and sterilization.

Data from Maroulis and Saravacos (7).

Convective Drying of Foods

Computer spreadsheets have been applied to the design of convective food dryers, e.g. conveyor belt
and rotary dryers (7). As a typical application, the simulation and design of a belt dryer for potato
pieces is discussed briefly here. The system consists of 37 variables and 24 process equations. The
13 degrees of freedom are broken down into 9 design specifications (feed flow rate, moisture con-
tents, material size, loading depth, ambient temperature and humidity, and steam temperature) and 4
(design variables (drying air velocity, temperature, and humidity, and belt width).
The drying kinetics of potato pieces, expressed as the drying time constant (tc) or the drying
rate constant (K), can be estimated from the following empirical model, obtained from experimental
measurements (7):
c1 c2 c3 c4
tc = 1/K = co d u T Y (1)

where co = 0.581, c1 = 1.49, c2 = -1,85, c3 = -0.345, and c4 = 0.151

o
For the process and design specifications u = 1.5 m/s, d = 1 cm, T = 65 C, Y = 0.025 kg/kg
dry basis, the drying time constant becomes tc = 0.91 h.
When experimental drying rate data are not available, the time constant tc can be estimated
from literature diffusivity (D) data, assuming that mass (moisture) transport is controlled by diffusion
within the potato piece (4):
2 2
tc = d / 4π D (2)
ICEF9-2004 International Conference Engineering and Food

where d is the equivalent spherical diameter of the potato pieces (1 cm). For a diffusivity of moisture in
o -10 2
potato at 65 C, D = 10x10 m /s, the drying time constant becomes tc = 0.7 h.
The following process specifications and design variables were considered: feed rate F=100
kg/h dry basis, characteristic size 1 cm, moisture content from 6 to 0.1 kg/kg dry basis, air temperature
o
65 C, ambient air humidity 0.010 kg/kg dry basis, drying air humidity 0.025 kg/kg dry basis, air velocity
o
1.5 m/s, steam temperature 160 C, and belt width 2 m.
Some of the important results obtained by the spreadsheet technique are: drying time (resi-
2
dence time in the dryer) 4.16 h, drying rate 590 kg/h, dryer area 23 m , dryer length 11.5 m, dryer
2
mass holdup 3 ton, belt velocity 2.7 m/h, and air heater area 90 m .
Sensitivity analysis of the belt dryer yielded diagrams of belt area, thermal load, and cost ver-
sus the design variables. Figure 5 shows the annual cost as a function of air temperature and velocity.
The air velocity is near the optimum but the air drying temperature is not, due to the quality con-
o
straints, which suggest that air drying temperature should not be greater than 65 C.

400

Total

300
Annual cost (k$/yr)

Operating

200

100
Equipment
(annualized)

0
50 60 70 80 90 100
o
Temperature ( C)

400
Total

300
Annual cost (k$/yr)

Operating

200

100
Equipment
(annualized)

0
0 1 2 3 4
Air velocity (m/s)

Figure 5. Effect of air temperature and velocity on the drying cost

ICEF9-2004 International Conference Engineering and Food

References

1. Saravacos G.D., Kostaropoulos A.E. “Handbook of food processing equipment.” Kluwer Aca-
demic/Plenum Publ., 710 p, New York, 2002.

2. Rahman S. “Food properties handbook.” CRC Press, 500 p, New York, 1995.
rd
3. Rao M.A., Rizvi, S.S.H., Datta, A. “Engineering Properties of Foods” 3 ed. Marcel Dekker, New
York, 2004.

4. Saravacos G.D., Maroulis Z.B. “Transport properties of foods.” Marcel Dekker, 425 p, New York,
2001.

5. Skjoldebrand C., Sundstrom B., Janestand H., Anderson C.G. Simulators of food processes. In
“Automatic control of food and biological processes.” J.J. Bimbenet,E. Dumoulin, G. Trystram eds.
Elsevier, Amsterdam, 1994.

6. Maroulis Z.B., Saravacos G.D. Modeling, simulation and design of drying processes. In “Drying
th
2002 - Proceedings of the 13 International Drying Symposium” pp 33-48, Beijing, China, 2002.

7. Maroulis Z.B., Saravacos G.D. “Food process design.” Marcel Dekker, 520 p, New York, 2003.

8. Lewis M., Heppel N. “Continuous thermal processing of foods.” Aspen Publ., New York, 2000.
”
9. Teixeira A. Thermal process calculations. In “Handbook of food engineering D.R. Heldman and
D.B. Lund, eds. Marcel Dekker pp 563-619, New York, 1992.

10. Ramaswamy H.S., Singh R.P. Sterilization process engineering. In “Handbook of food engineering
practice” K.J. Valentas, E. Rotstein, R.P. Singh eds. CRC Press, pp 37-69, New York, 1997.
ICEF9 – 2004
International Conference on Engineering and Food

Shelf-life prediction of fresh orange juice

Zanoni Bruno, Pagliarini Ella, Galli Antonietta
DiBa – Food Technology Section - University of Florence – Via Donizetti, 6 – 50144 Florence - Italy
bruno.zanoni@unifi.it
DiSTAM – Food Technology Section - University of Milan - Via Celoria, 2 – 20133 Milan – Italy
ella.pagliarini@unimi.it
DiSTAM – Food Microbiology Section - University of Milan - Via Celoria, 2 – 20133 Milan – Italy
antonietta.galli@unimi.it

Abstract
Fresh orange juice is successful on the market because of its taste and nutritional value. On the other
hand, it requires accurate control of the cold chain during storage and distribution. A kinetic study was
carried out both on growth of spoilage microorganisms and on decrease of nutritional value of fresh
orange juice during storage. The kinetic equations were used to set up a mathematical model to
predict shelf-life under isothermal and non-isothermal conditions.

Key words
Orange juice, shelf-life, predictive modelling.

Introduction
Consumers of fresh orange juices wish a safe product that keeps both sensory characteristics and
nutritional value either for some days, when orange juice is unpasteurized, or for 40-60 days, when
orange juice is pasteurized (Eleftheriadou et al., 1998; Polydera et al., 2003). These consumer
expectations may be translated into concentration of yeasts and level of heat and oxidative damage.
Heat and oxidative damage may be measured by determining ascorbic acid and anthocyanin (i.e. for
blood orange juice) contents. These product characteristics are significantly dependent on the cold
chain during storage and distribution.
The aim of this work was to set up a mathematical model to predict shelf-life of fresh orange juice
under isothermal and non-isothermal conditions.

Materials and Methods

Commercial pasteurized fresh blood orange juice in 750 ml multiwall paper bags (polyethylene-paper-
polyethylene-aluminium-polyethylene) provided with a plastic screw was used to determine kinetics of
both yeast growth and ascorbic acid and anthocyanin degradation at different times and temperatures
of storage.
Juice was inoculated with 10 CFU/ml of yeasts, which were isolated from unpasteurized orange juice.
They were stored at 4, 10.6, 15 and 20°C for several days. At varying time intervals 100 ml juice was
poured into sterile stomacher bags and homogenized. Samples (10 ml) were collected and diluted
1:10 in a sterile tryptone-salt solution. Yeast concentration was determined on Yeast Glucose
Chloramphenicol Agar (serial dilutions were spread on a surface plate and incubated at 30°C for 72 h).
Juice was stored at 3, 10.6, 15 and 20°C for several days to determine ascorbic acid and anthocyanin
degradation. At varying time intervals 50 ml juice was collected. Ascorbic acid content was determined
by HPLC at 254 nm, anthocyanin content was determined by spectrophotometer at 510 nm according
to Rapisarda et al. (1994).
TM
Linear and non-linear regression analyses were carried out by TableCurve (Jandel Scientific
Software, Erkrath, Germany). The mathematical model of shelf-life was solved by a numerical solution
in Fortran programming language (Microsoft Developer Studio 97, Microsoft Co., Redmond, USA).

Results and discussion

Experimental data were processed as a function of time and temperature by empirical reaction
kinetics, as reported in Table 1.
Kinetics was used to set up a chart for storage optimisation of pasteurised fresh blood orange juice
(Figure 1). Circles represent equivalent time-temperature conditions to have 3 log-cycles of yeasts
growth, which is a critical limit for product stability. Triangles and diamonds represent equivalent time-
temperature conditions to cause 50% anthocyanin and ascorbic acid losses, respectively; these losses
are a significant level of oxidative damage of product.
It can be seen that shelf-life is significantly dependent on yeast growth. A microbial stability for 40-60
days is consistent with storage at ≤ 5°C; on the other hand, oxidative damage is small at all storage
temperatures.
 ICEF9 – 2004
International Conference on Engineering and Food

Table 1. Reaction kinetics data.

Characteristics Variation Rate Kinetics and constants

kinetics constants as a function of temperature

A = a + b ⋅T c
(power law model)
c
a = -9.90; b = 12.20 1/°C ;
c = 0.234 (r = 0.99)
at 4°C (r = 0.99):
A = 6.90; µ m = 0.014 1/h; λ = 177.5 h  Ea 
µ m = µ mo ⋅ exp − 

  µ m ⋅ 2.718  at 10.6°C (r = 0.99):  R ⋅T 
N  ⋅ 
Yeast growth ln = A ⋅ exp − exp

A  A = 11.74; µ m = 0.028 1/h; λ = 131.3 h (Arrhenius equation)
No  ⋅ (λ − t ) + 1  
   µmo = 5.2 1020 1/h; Ea = 120100
(Gompertz equation at 15°C (r = 0.99): J/mol (r = 0.98)
modified by A = 12.35; µ m = 0.090 1/h; λ = 41.81 h
Zwietering et al. (1990)) p
at 20°C (r = 0.99): ln λ =
A = 14.96; µ m = 0.222 1/h; λ = 19.63 h (T − Tlim )
(Adair equation)
p = 139.7 h°C; Tlim = -21.92°C
(r = 0.92)

 E 
K = K o ⋅ exp − a
-4
K3°C = 1.65 10 1/h (r = 0.85) 
 R ⋅T
-4
K10.6°C = 2.81 10 1/h (r = 0.98) 
Loss of C = C o ⋅ exp( − K ⋅ t ) -4
K15°C = 4.17 10 1/h (r = 0.95) (Arrhenius equation)
ascorbic acid st
(pseudo 1 order equation)
-4
K20°C = 4.53 10 1/h (r = 0.97) K0 = 15778 1/h
Ea = 42066 J/mol
(r = 0.98)

 E 
Loss of C = Co − K ⋅ t K3°C = 0.019 mg/Lh (r = 0.89) K = K o ⋅ exp − a 
anthocyanins K10.6°C = 0.035 mg/Lh (r = 0.94)  R ⋅T 
(pseudo 0 order equation) K15°C = 0.056 mg/Lh (r = 0.96) (Arrhenius equation)
10
K20°C = 0.094 mg/Lh (r = 0.97) K0 = 7.79 10 mg/Lh
Ea = 66934 J/mol
(r = 0.99)

Kinetics was also used to set up a chart for storage optimisation of unpasteurised fresh blood orange
juice. This chart was validated by experimental data reported by Laureati (2003). Yeast growth
followed analogous kinetics in pasteurised and unpasteurised juices; loss of ascorbic acid and
anthocyanins was faster in unpasteurized juice, since no enzyme inactivation occurred during
processing.
Kinetics was finally used to set up a mathematical model able to predict quality variations in
pasteurised fresh blood orange juice during shelf-life under non-isothermal conditions.
Reaction kinetics was transformed into dynamic models, i.e. their prediction ability should also include
systems at steadily varying temperatures. Dynamic models were developed by the numerical
integration approach.
The dynamic development of Gompertz equation was processed according to Zanoni et al. (1997)
method, assuming that: (i) during the lag phase the effect of temperature shifts resulted in a new lag
phase that was equal to the relative part of the lag phase still to be completed: (ii) during the
exponential phase the effect of temperature shifts resulted in a growth that continued immediately with
the specific rate without a new lag phase.
The mathematical model was also used to predict yeast growth in unpasteurised fresh blood orange
juice. Figure 2 shows an application of this model. Two hypothetical temperature profiles during
factory storage, transport to dealer, shop storage and home storage were supposed. Temperature
profile A describes a wrong cold chain, which is not so unfrequent. Critical effect of temperatures on
yeast growth is well evidenced. Orange juice only keeps microbial stability for 3 days with respect to
the wrong cold chain against a predicted shelf-life of 7-10 days with respect to the cold chain B.
ICEF9 – 2004
International Conference on Engineering and Food

1000

100
50% of
ascorbic acid loss
Time (days)

50% of
anthocyanin loss
10

3 log-cycles of
yeast growth

1
4 8 12 16 20 24
Temperature (°C)

Figure 1. Chart for storage optimisation of pasteurised fresh blood orange juice.

500 16

450
14

400 Yeast growth

for T.P. A 12
350
Yeast concentration (UFC/ml)

Temperature 10
300 profile A

Temperature (°C)
250 Temperature 8
profile B
200
6

150
4
100

2
50
Yeast growth
for T.P. B
0 0
0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00
Time (days)

Figure 2. Prediction of shelf-life of unpasteurised fresh blood orange juice.

References
1. Eleftheriadou M., Quantick P., Nolan M., Akkelidou D. Factors affecting quality and safety of freshly
squeezed orange juice (FSOJ). Dairy, Food and Environmental Sanitation, 18, 14-23, 1998.

2. Polydera A.C., Stoforos N.G., Taoukis P.S. Comparative shelf life study and vitamin C loss kinetics
in pasteurised and high pressure processed reconstituted orange juice. Journal of Food Engineering,
60, 21-29, 2003.

3. Rapisarda P., Fanella F., Maccarone E. Reliability of analytical methods for determining
anthocyanins in blood orange juice. Journal of Agriculture and Food Chemistry, 48, 2249-2252, 2000.

4. Zwietering M.H., Jongenburger I., Rombouts F.M., van’t Riet K. Modeling of the Bacterial Gowth
Curve. Appled and Environmental Microbiology, 56, 6, 1875-1881, 1990.
ICEF9 – 2004
International Conference on Engineering and Food

5. Laureati M. Studio per l’ottimizzazione della conservabilità di spremute di arancia fresche da

agricoltura biologica. Thesis, University of Milan, Italy, 2003.

6. Zanoni B., Peri C., Garzaroli C., Pierucci S. A Dynamic Mathematical Model of the Thermal
Inactivation of Enterococcus faecium durino Bologna Sausage Cooking. Lebesmittel Wissenschaft und
Technologie, 30, 727-734, 1997.
ICEF9 ö 2003
International Conference Engineering and Food

Com puter Simulation of Sugar Crystallization in Confectionery Produc ts

Eyal Ben-Yoseph (1), Richard W. Hartel (2)

(1)Carmel Consulting EMB LTD, Hertzel 37 Petach-Tiqva, Israel
eyal@carm el-consulting.com
(2)Food Science Departm ent, University of Wisconsin, 1605 Linden Drive, Madison, WI, USA
rwhartel@wisc.edu

1. Abstract
A com puter sim ulation was developed to m odel drying, moisture sorption and crystallization, during
processing and storage of confectionery products. The three-dim ensional model analyzed
sim ultaneously heat and m oisture transfer. Crystal gro wth wa s evalu ated from crystallization kinetic s
based on supersaturation and tem perature. The m odel predicted quality and storage stability based on
correlations with the calculated sugar concentration, crystallinity and phase state.
Key words: Sugar, Crystallization, Confectionery, Drying, and Modeling.

2. Introduction
Controlling crystallization o f sugars in confe ctionery pro ducts is critical to develo pm ent of their
proper appearan ce, texture and storage stability. Sugar crystals in the product m ay be desirable (e.g.
sugar she ll, fondant, toffee and fudge), or undesirable (e.g. hard candy, jelly and caramel). However, our
understanding of the para m eters that influence those attributes is severely lacking, since hea t transfer,
m ass transfer, and phase transition phenomena, which determine crystallinity, are com plex and
interrelated. A computer sim ulation can model these phenomena, and predict crystallization during the
production pro cess and storage of confe ctionery products. The use of c om puter sim ula tion can result in
faster and cheaper pro cess developm ent, help optim ize existing processes, and im prove our
und erstanding of the pro duc t properties.
The objective of this work was to develop a model that determines quality and storage stability of
confectionery pro ducts. W e chose to m odel the sim plest c onfection ery system , i.e., sucrose solution,
which is applied as a thin film on a solid surface as m ight be found in a panned confection. T he quality
attribute m odeled was the appearance of the coating, which was directly related to the surface area
coverage of crysta ll inity of the coating. Storage stability was predicted based on the water activity and
glass transition tem perature. The m odel in its current configuration can be used to m odel crystallization
of sugar shell in Hard Panning process. For more com plex system s, the m odel needs to be m odified.
For exam ple, to m odel a system of sucrose, corn syrup and water (e.g. Hard Candy) the governing
equations need to be cha nged; nam ely for diffusivity of sucrose and water, glass transition tem perature
equation, water activity equation and sucrose crystallization kinetics in the presence of corn syrup.

3. Theory/Modeling
Th e m ode ling phase c onsisted of the following eight m ajor steps:
1. The temperature of the film as function of tim e was calculated from the heat transfer equation.
2. The sugar concentration as function of tim e and location was c alculated from the unstea dy state
m ass transfer equation.
3. Crystal growth rate was predicted based on local supersaturation, film tem perature , and growth
kinetics (found experim entally).
4. Crystal size was calculated based on the crystal growth rate at each point in space and tim e.
5. The influence of crystal growth on the film concentration and tem perature was evaluated.
6. Gla ss tran sition concentration was calculated from the film tem perature, and local am orphous
areas within the film were defined.
At this point we were able to define thre e different reg ions in the film : a) c rystalline reg ion – its
am ount, location, and crystals number and size; b) solution region – amount, location, and the
concentration profile; and c) amorphous region – its am ount, location, concentration, and the g lass
tran sition tem perature . Th is inform ation was used in the last 2 ste ps o f m odel develo pm ent:
7. Crystal area coverage wa s predicted from the crystal size and d istribution in the film.
8. Storage stability was predicte d base d on glass transition tem perature and water activity, which
were calculated from the sugar concentration of the solution phase and the am orphous phase.
ICEF9 ö 2003
International Conference Engineering and Food

3.1 Heat and mass transfer

The system of nonlinear partial differential equations for heat transfer in tim e and for m ass transfer
in tim e and three dim ensions was solved num erically. The sucrose solution was subdivided into many
sm all rectangular elements in order to apply the finite difference method. A detailed description of the
m ethodology used to predict the tem perature and concentration in the film are found in Ben-Yoseph et
al, (1).

3.2 Predicting the state of solution, and crystal growth rate, size, shape and distribution
The information about temperature and concentration at any location in the solution during the
drying pro cess lo cated each point in the solu tion in the phase diagram; either it was an undersaturated,
m etastable, labile or glassy solution. A region was considered glassy if the temperature at that point was
below the glass tran sition tem perature , T g . Roos and Karel (2) suggested a m eth od to calculate T g for
sucrose-water by applying the Gordon and Taylor equation:

(1)

where w 1 and w 2 are weight fraction s of com ponent com pounds, T g1 and T g2 are the abso lute glass
transition tem pera tures (/K) o f the com ponent com pounds, and k is con stan t. In our case , T g1 =138/K (T g
of water), T g2 =335/K (T g of pure sucrose), and k for sucrose-water equal to 4.7 (2).
Growth kine tics of suc rose c rystals were studied in a m ethod described by Howell at al. (3), and the
results were correlated to the solution cond itions using the following equation (4):

(2)

where d is the th ickness of th e su rface sub layer, r s is the density of sucrose crystal, C is the bulk
concentration, C i is the solute concentration at crystal-solution interface, and D A B is the m utual diffusion
coefficients in water-sucrose system , which is a function of solution tem perature and concentration.
Equation 2 includes two term s that depend on the solution concentra tion. T he diffu sion coefficient,
D A B , decreases with conce ntration, while the supersaturation (C-C i ) increases with concentration. The
growth rate is zero when the supersaturation equa ls zero or when the diffusivity equals zero. Plotting the
gro wth rate as function of c oncentration gives a convex cu rve with a m axim um gro wth rate at a specific
solution concentration.
Durin g growth, when the volume of a seed reached the element volume, growth continued in the
adjacent elem ents (as long as there were no crystals in these elem ents). Growth continued from the
center of the adjacent element (Figure 1) with growth rate proportional to the surface concentration in
this volum e elem ent. One or m ore se eds c an be placed at any point in the m atrix.

a) b) c)

Figure 1: Illustration of the way growth wa s modeled in a discrete matrix of volume element (in the x-z
plane). a) Seed is placed in a ce nte r of volume element. b) When the volume of the seed reaches the
element volume, growth continued in the adjacent element., c) Growth rates are fun ctio n o f the
conditions in each volume element, therefore some faces grow fas ter than others. In this case the face
in the top of crystal grew faster, therefore growth continued in adjacent elements around this face.
ICEF9 ö 2003
International Conference Engineering and Food

3.3 Evaluation of the influence of crystal growth on the temperature and concentration
Sugar crystals growing within the solution exert an influence on the surrounding environ m ent.
The following phenomena were taken into account in the sim ulation program :
1) Reduction in concentration: When a crystal grew, sucrose molecules were removed from the
solution and the concentration around the crystal decreased. The change in concentration was
calculated from a m ass balance on sucrose and water.
2) Generation of fusion heat: Crystal growth generated heat that raised the candy tem perature . A
term wa s added to the heat transfer equation, relative to the m ass that was built on the crystal.
3) Decrease in diffusivity: The volume of a crystal acted as a barrier for diffusion of sucrose and
water. To m odel this influence, a mass transfer of zero was used between two points when a crystal
was present between them .
4) Decrease in drying rate: Crystals that grew on the surface decreased the surface area for water
m igration from the solution to the air. In order to take this into account, the drying surface area was
m ultiplied by one m inus the ratio of crystal cross sectional area to solution cross sectional are a in the
directio n of water flux.

3.4 Predicting the appearance

The overall abundance of sugar crystal coating was determ ined in a visual descriptive sensory
analysis by 33 panelists. The panelists were asked to indicate their assessm ent of the appearance,
where 1= sugar c rystal coa ting n ot app aren t (absent, coating lo oks c lear as the solution is glassy)
and 7= extensive sugar crystal coating (extrem ely abundant, coating appears wh ite, as m ost sugar is
crystallized). The crystal area coverag e, A, was correlated to the film crystallinity, x, to get equation 3:
A = -3.8912x 2 + 9.0155x + 1 R 2 = 0.9285 (3)
This correlation was combined into the m odel. Since the m odel predicted the crystallinity of the
coating, using equation 3 it can determ ine the appearance of the coating.

4. Results
4.1 Simu lating the effect of process conditions on crys tallizatio n ra te
The program was used to determ ine growth rate of sucrose in thin film s und er various process
con ditions. Re sults were com pared to experim ental work conducted by Howell and Hartel (5). In
general, good agreem ent between pre dicte d and experim ental results was ac hieved. Both
experim ental and simulated results showed the significant im pact of tem perature a nd relative
hum idity on growth rate and the m inor im pact of air velocity and initial film concen tration (Figure 2).
The growth rate increased substantially with air temp erature. Above 40/C volum e diffusion
governs sucrose crystal growth ra tes and a s the tem pera ture incre ased , the diffusivity of sucrose
m olecules was higher and the growth rate increased. On the other hand, increasing the tem perature
decreased the supersaturation due to lower solubility, which would tend to inhibit growth. However, in
this case, temperature elevation also increased the drying rate and the concentration in the film, so a
dec rease in supersaturation was no t obtained. Air velocity had alm ost no effe ct on crystal gro wth
becau se it had no effect on drying rate (under the sim ulated conditions internal water diffusion
determ ined the drying rate) and had no effect on the internal conditions in the film . Relative hum idity
of the air directly affected the film concen tration. W hen the air was moist (40-50% R H) the film
concentration was low (~80%), resulting in lower supersatura tion and slower gro wth. W hen the air
was very dry, the film concentration became so high that the decrease in m obility inhibited crystal
growth. At the o p tim a l 3 5 % RH the film concentration was approxim ately 90%, which gave m axim um
gr ow th rate at 80/C. Initial concentration in the range of 75 to 85% had only a minor effect on cr ystal
growth. Observing the conc entration p rofiles in the film in the sim ulation output gave an explanation:
drying occurred so rapidly that the solution approa ched high supersaturation very quickly regard less
of initial concentration.

4.2 Growth velocity of the crystal’s faces and concentration fields

A sim ulation of growth of three 10 :m seed crystals, that were virtually placed in a sugar film, was
perform ed in order to follow the change of crystal size and shape and the concentration fields. The
crystal faces grew at rates proportional to their respective surface concentration. At initial stages of
drying, when the film con centration w as at its lo west, the crystal faces that were clo ser to the air
interface grew faster since the concentratio n a t the surface was higher. Later, when the film
ICEF9 ö 2003
International Conference Engineering and Food

concentration was high and m olecular m obility restricted growth, the fac e closer to the bottom of th e
film grew faster since the concentration at that surface was now lower. The concentration below the
crystals was low com pared with other regions in the same horizontal layers due to a combination of
growth desaturation and the crystals acting as a barrier for moisture migration upward (Figure 3).

Figure 2: Predicted and experimental growth rates (:m/min) of sucrose crystals during drying of
thin sucrose films on microscope slides in different drying temperatures as function of air relative
humidity (left chart) and initial film concentration (right chart). The lines represent the predicted
results, and the marks w ith the error bars – the experimental results (from Howell and Ha rtel, 2001).

Figure 3: Concentration
fields (in % total solids)
around gro wing crys tals
after 115 seconds of drying
of thin sugar film. Seed
crys tals we re initially
placed in 3 locations in film.
Sucrose solution
conditions: initial
concentration 83% TS,
temperature 71.0/C. Film
thickness 103.8 :m. Drying
air conditions: temperature
80/C, velocity 1.0 m/s,
relative humidity 10%.
ICEF9 ö 2003
International Conference Engineering and Food

4.3 Appearance of coating

For a given seed density and location, the drying conditions had the same effect on the crystal
area coverage as on grow th rate (section 4.1). An initial high density of seeds in the film led to m ore
crystal growth and resulted in m ore crystalline m aterial. Therefore, den se se eding is an advantage in
order to get m axim um crystalline appearance. The sim ulation results showed that the best location for
seed s, in order to m aximize c rystal gro wth, wa s at th e b ottom of the film. During drying of thin film s,
the film concentration closer to the surface increased above the optim al concentration for growth and
inhibited crystallization. At the bottom of th e film , the c oncentra tion was the lowest and was close r to
the optim al concentration for growth. Therefore, the growth rate was faster at the bottom . Also, when
seeds are located at the bottom of the film, a larger layer of crystalline m aterial that inhibits further
drying of the film was not formed.

4.4 Pre diction of C rystal Are a C overage and Storage stability of sugar-coated substrate
Two drying processes of sugar-coated substrate at 80/C were sim ulated. Both processes started
with applying warm aqueou s sugar solution over substrate in a thin film and seeding. The m ain
difference be twe en the proc esses was tha t proc ess (A ) includ ed intense d rying, while process (B)
included drying in 2 steps, optim ized to achieve highest crystal gro wth rate .
Drying conditions for process B were chosen in the following way: Based on Equation 2,
m axim um gro wth rate at 80/C is achieved at 94%. Process (B) included step of fast drying to reach
this concen tration, and a long er step of mild drying to m aintain this concen tration, while the crystals
grew. The 94% concentration was controlled by the hum idity of the drying air. The Norrish equation
(reference 6) gives the equilibrium film concentration for a given relative hum idity of the surrounding
air. T o achieve a concentration of 94 %, the re lative hum idity of the drying air wa s ad justed to 15.4%.
The process conditions and simula tion results are described in Tables 1 and 2. While conveying
the product at room temp erature (step 1), the film s were cooled and the seed crystals started to grow.
The drying duration was 4 m inutes in b oth pro cesses (step 2), bu t pro cess B g ave higher crystallinity
(97% com pared to 56%), and higher crystal coverage area because of its optim al conditions for
growth. In addition the film in process A re ached higher concentra tion (98.8% TS), which correspond
to high T g (44.8/C). When drying process ended, film A cooled below this tem perature, it becam e
glassy and no m ore crystal growth occurred. Film B ha d lower conc entration, lower T g , and did not
becom e gla ssy. At the end of the pro cess (step 3), film B w as in a more stable condition for storage:
99% was crystallized, compared to film A where only 59% was crystallized, and the remaining
solution had a w of 5% and T g of 2 9.7/C. With this low water activity, film A would probably pick up
m oisture from the air and becom e stick y. Even if it was wrapped with a m oisture barrier, at
tem perature s ab ove 29.7/C its glassy structure would collapse and it would start to crystallize.

Table 1: Process conditions for intense drying of sugar-coated substrate (pro ce ss A) , and the
simulation results.

Process Conditions Results (end of stage)

Stage Description
T im e Air Air Air Sugar coating Crystal Tg aw
temp. velo city hu m idity Phase state area
(min) (/C) (m /s) (g.w/g.da) coverage (C/)

99% solution (81% TS)

Transp ort to 0.009
1 0.2 26 0.11 1% crystalline 1.06 -41 .6 67%
dryer (40% RH)
No g lassy material
44% solution (99% TS)
0.003
2 Drying 4.0 80 1.0 56% crystalline 4.81 44 .8 0.3%
(1.5% RH)
No g lassy material
0% solution
0.004
3 Cooling 2.0 21 1.0 59% crystalline 4.97 29 .7 5%
(30% RH)
41% glass @ 96.4% TS
ICEF9 ö 2003
International Conference Engineering and Food

Table 2: Proce ss co nditions for op timized dry ing of sugar-coated substrate (process B) and
the simulation results.

Process Conditions Results (end of stage)

Description T im e Air Air Air Sugar coating Crystal Tg aw

Stage
temp. velo city hu m idity Phase state area
(min) (/C) (m /s) (g.w/g.da) (end of stage) coverage (/C)

99% solution (81% TS)

Transp ort to 0.009
1 0.2 26 0.11 1% crystalline 1.06 -41 .6 66%
dryer (40% RH)
No g lassy material
91% solution (95% TS)
Intens e short 0.003
1.0 80 1.0 9% crystalline 1.78 24 .9 9.2%
drying (1.5% RH)
No g lassy material
2
3% solution (94% TS)
Mild long 0.046
3.0 80 1.0 97% crystalline 6.09 17 .7 14%
drying (15% RH)
No g lassy material
1% solution (95% TS)
0.08 (30%
3 Cooling 2.0 26 1.0 99% crystalline 6.12 23 .6 10%
RH)
No g lassy material

5. Summ ary
A m odel to predict the concentration profile and growth of sugar crystals in a thin film has been
developed and utilized to study various conditions of sucrose crystal growth. The m odel solves the
unsteady state m ass transfer equation coupled with an appropriate growth kine tic m odel to predict
crystal size during drying of a thin film of sucrose with seed crystals im bedded in the film . By
coupling this m odel with sensory m easurem ents of fil m appearance based on area of crystal
coverage, the crystal area coverage, as related to sensory appearance, can be m odeled fo r different
ope rating and storage c ond itions.

6. References
1. Ben-Yoseph, E ., H artel R .W ., H owlin g, D., T hre e-D im ensional Model o f Phase Tra nsition of T hin
Sucrose Films during Drying. Journal of Food Engineering, 44, 13-22, 2000.
2. Roos, Y., a nd Karel, M. Applying State Diagrams to Food Processing and Development. Food
Technology 45: 66-71, 1991.
3. Howell, T.A., E. Ben-Yoseph, C. Rao and R.W . Hartel, Sucrose C rystallization Kin etics in Thin
Films at E levated Tem pe ratures and Supe rsaturations. C rysta l G rowth and Design, 2(1), 67-72, 2002.
4. W ey J.S. Basic Crystallization processes in silver halide precipitation. In Preparation and
Properties of Solid State Materia ls. V olume 6. Wilcox W .R. (ed.). Marcel Dekker, inc. NY, New York,
1981.
5. How ell, T .A., Jr. and R.W . Hartel, D rying and Crystallization of Sucrose Solutions in Thin Films at
Elevated Tem peratures, J. Food Science., 66(7), 979-984, 2001.
6. Norrish, R.S. An Eq uilib riu m fo r the Ac tivity Coefficients and Eq uilib riu m Rela tive Hum ilitie s of
W ater in Confectionery Syrups. Journal of Food Technology, 1: 25-39. 1966.
ICEF9 – 2004
International Conference Engineering and Food

AN INTERACTIVE SOFTWARE FOR COMPUTER AIDED LEARNING

IN INDUSTRIAL PLANTS OPERATING

Authors : Bernard GROS (Laboratoire Gestion et Cognition, IUT Paul Sabatier, 115 route de
Narbonne, 31077 Toulouse Cedex 04, bernard.gros@iut-tlse3.fr), Jean-Louis SELVES (same
address, selves@meph.iut-tlse3.fr), Robert DESCARGUES (same address, descargu@cict.fr)

Abstract : The authors present an interactive software for computer aided learning, based on the
TM
simulator PROSIM . The objective is to give new skills to persons who operate industrial plants,
because these persons have often to do very important choices in more and more complex
economical environment, and they have to do these choices in cooperation with other sectors of firm,
which now adopt a network structure. The authors briefly present the software.

Key words : learning, knowledge management, industrial plants operating, simulation, industrial
systems.

THE RESEARCH CONTEXT

In process industries, producers are : operators, intermediate responsibles, plant responsibles.

a) Operators are « on the field », in contact during 8 hours (« 3X8 ») with the plant, they operate the
plant.
b) Intermediate responsibles verify that the plant is well operated, they do a balance each day, they
program the maintenance operations, they are the links between operators and plant responsibles…
c) Plant responsibles work with firm managers and with intermediate responsibles. If they note
market evolutions, they can decide to do evolutions in : production, raw materials, plant operating …
They can decide to program structure modifications in the plant and they do the technical
management (raw materials management, energy management, …).
Intermediate responsibles and plant responsibles manage the human resources of the production
sector of the firm..

Functions have changed for operators, intermediate responsibles, and plant responsibles, in some
years, above all for operators.
-10 or 15 years ago, operators had very manual functions, and each one of the members of a
team (generally, 10 or 12 men) operated a small part of the plant. The operators functions were :
orders reading, valves manipulating, and above all, no understanding…
The relations between operators and intermediate responsibles were quite similar to the relations
between soldiers and officers in an army. Operators’ level was very low, and operators’ functions were
very poor.
-Now, plants are very automated, operators work in small teams, they use a personal
computer to operate the plant, they survey the whole plant, and they have to master the whole plant.
Operators have now important resources to work, and then intermediate responsibles and plant
responsibles have more important demands. Operators must take initiatives, and know how to
manage technical crisis. They must take quality, safety, and environment constraints into account in
plant operating.
Plant responsibles must more and more take legal rules (more and more complex), economic
constraints, market evolutions, into account. Firms have to react very rapidly, plant responsibles have
to give more and more flexibility to the plant, and they have to explain these constraints to operators
and intermediate responsibles.
Now, operators’ level is growing, and level of their tasks is growing. And, so the relations between
operators and intermediate responsibles are changing and are becoming conversations between
persons who have quite similar levels. Generally, operators have now a « Bac+2 » level.
-Tomorrow, operators will have also to take economic constraints into account in plant
operating.
ICEF9 – 2004
International Conference Engineering and Food

Operators’ functions are now growing, and in the next future, they will have better skills : autonomy,
whole firm complexity understanding (not only plant understanding). They must perfectly take their
places in the firm which now adopt a network structure, and work in cooperation with other sectors of
firm. Intermediate responsibles will become coordinators of small plant operating teams, but operators
and intermediate responsibles will have common knowledge and skills, and they will use common
tools. Now, probably, people will use the common name « producers » (for operators or intermediate
responsibles) to take this evolution into account. And then, the authors of this paper think that in small
firms, the intermediate responsible function will disappear, because differences between tasks is more
fuzzy than in large firms.
Plant responsibles will have to do more and more management tasks, and so, producers will work with
more and more autonomy.
Firms now adopt a network structure, linking the different sectors inside the firm, but also the outside
partners : production, technical management, financial resources management, maintenance, sub-
contractors, customers, suppliers, other plants producers, outside experts, outside databases, … This
new structure, more flexible, is the consequence of the economic constraints and the complexity :
globalisation, rapid market evolutions, more and more rigorous rules above quality, safety, and
environment constraints.
The research presented in this paper is in the field of industrial plants operating, particularly in process
industries, and the authors are very concerned by the producers’ problems who take charge of plant
operating. These problems are the consequence of very important evolution of their tasks. They must :

- Understand the plant complexity, but also the whole firm complexity, and the environment
complexity.
- Take technical problems (plant operation), but also economic problems (costs, quality),
and social problems (safety, environment constraints) into account.
- Take their places in the firm network structure, and co-operate with other sectors of the
firm.

Then, producers give up simple plant operation tasks, and have to do now very complex tasks : on-
line industrial plant management, in co-operation with other sectors of the firm. This paper presents
AN INTERACTIVE SOFTWARE FOR COMPUTER AIDED LEARNING (ISCAL) IN INDUSTRIAL
PLANTS OPERATING, to train producers to carry out their new tasks. The authors of this paper have
19 years experience of operators’ training in industrial firms, and are convinced of the software
usefulness. We think that in food industries, problems concerning quality, safety, environment
constraints, economic constraints, are similar to these problems in process industries, and operation
units are similar too. So, we think that our software will be very useful in food industries.

BIBLIOGRAPHY

In the field of industrial plants operating, a lot of papers exist about digital control for a part of a
plant, or for a whole plant. The problem studied by the authors of the present paper is very different
from these ones. But, here, we do comments about some of these works applied to flexible plants
operating, because they have common aspects with our own research : flexible plants are more and
more used in process industries, the production is generally low, the flexibility allows the producers to
adapt themselves to market demands in producing by different campaigns, and each campaign needs
a modification of operation sequence and modification of plant variables..
These papers are written about studies to do plant simulation and about studies to determine the best
operation sequence to improve the plant operation [1], [2], or there are written about studies to
determine the best method of production management [3]. Some of these papers are written about
computer aided decision to determine the best operation sequence [4]. But, none of these studies is
applied to producers learning.
In the learning field, many general studies exist, not only applied to industrial plants operating, but they
give a good point of view, very useful, about process engineering learning [5], or specifically about
learning inside firms [6]. These contributions insist upon the importance of preparing women and men
ICEF9 – 2004
International Conference Engineering and Food

to very big modifications in the fields of production and management, and they encourage us in our
research.
Some authors [7] present a virtual laboratory, using Internet, dedicated to process engineering
learning, but not specifically applied to plants operating. And we think that this tool is more useful for
students who discover process engineering than for producers who have yet an experience and who
want to improve their practice. Some papers are written about simulation software use to learn plants
operating, but they are limited to technical aspects [8], [9], [10].
Some authors [11] present a « learning game to analyse the operations management in an industrial
plant». The users may be producers or managers, students or operators. The objective is to discover
production system failures and imagine improvements, particularly to go to more autonomy. It is
different from our study, because this tool may be used by a very large public, and the pedagogical
objective is less specific. And, the authors are more concerned by plants design than by plants
operating.
The OPERA project [12] has the objective to do a pedagogical tool, based on simulation, dedicated to
producers training. This project is different from our study, because his principle is that production
system must operate with a very rigorous hierarchy between men, and that operators' skills must be
different than intermediate responsibles' skills, so autonomy is not the main objective of this project.

In conclusion, we can write that, generally, authors search above all the best ways to operate
industrial plants, and do tools dedicated to plants operating on-line optimisation. Problems about
interactions between system and man are generally neglected, and we can read very few studies
about learning, not adapted to the future of firms : network structure.

ISCAL DESCRIPTION

We are not only interested by dynamic complex system automatisation, but we study problems of
interactions between man and system. The objective is to train producers to carry out their new tasks,
and to improve their autonomy.
This paper presents AN INTERACTIVE SOFTWARE FOR COMPUTER AIDED LEARNING (ISCAL)
IN INDUSTRIAL PLANTS OPERATING, based on PROSIM [13] simulation software, dedicated to be
applied to learning in process industries. Our laboratory has a very good experience about these tools.
It is necessary to :
- training producers to taking a lot of simultaneous informations into account,
- increasing the number and the level of producers’ knowledge, to improve plants operating
and to facilitate their insertion in the network firm,
- training producers to exchange informations and to co-operate with other sectors of firm,
- training producers to take very important decisions,
This ISCAL needs :
- a knowledge modelling to understand the learning mechanisms . The ISCAL must adapt
itself to the learner.
- different skills, about technical problems to plants operating, but also about knowledge
management.
Our laboratory, named « Laboratoire Gestion et Cognition », have these different skills, because three
teams work : a management team, a modelling and digital simulation team, and an industrial systems
team.
An ISCAL contains many skills, about simulated system, about system operating, about learning,
about pedagogical resources, and must adapt itself and improve its’ skills. Using a multi-agent system
is the best way to build this tool, a study realized in our laboratory [14] demonstrated this idea. Each
agent has a part of the skills, and each agent can learn and adapt itself to different conditions. This
choice is made here.

When the learner uses the ISCAL, he must search the solution to a problem represented by the
simulation software. So, he can build his own experience. Access to the simulation software is free,
using a graphic screen, similar to this one that he has in front of him when he really operates the
industrial plant. A window on the screen contains the pedagogical guidance and helps the learner to
go to the best solution.
ICEF9 – 2004
International Conference Engineering and Food

The structure of the ISCAL is not detailed here, but some indications are given above the two main
parts :
-The part dedicated to knowledge about the simulated plant.

Simulated plant Knowledge base about the Technical

experts simulated plant documents

Simulation Graphic
software screen

-The part dedicated to the skills about plant operating. The learner must acquire these skills,
there are sequences of tasks that the producer must do when a particular situation occurs. These
skills must be larger in the future than now, and with these skills, producers will take into account
technical constraints, but also economic and social constraints presented at the beginning of this
paper.
We use the results of a research done in our laboratory about modelling of skills for firms.[15].

Teachers Knowledge base about Technical

experts skills documents

Survey of the Teacher’s Pedagogical

Acquisition of
learner's methods guidance
knowledge
sessions

These two drawings represent the environment in which the agents move and animate the ISCAL.

METHOD, RESULTS, CONCLUSION

Good operating of an industrial plant depends on a lot of constraints about : production

quantity, production quality, production cost, effluents rejected in the environment, raw materials
quantity used, energy quantity used, safety for the human beings, the environment, the plant, the
products, …
Events may occur : incidents with partial or total stopping of the production, raw materials changing,
legal rules changing about production quality, about effluents rejected in the environment,
ICEF9 – 2004
International Conference Engineering and Food

about safety, product cost changing, market demand changing, production campaign changing,
customer’s exceptional demand…
The decision may be : starting or stopping of a part of the plant, or of the whole plant,
modification of the plant variables values, modification of raw materials flow, modification of energy
flow, modification of raw materials, modification of operation sequences…
Method used for building the ISCAL is :
- Building of the knowledge base about skills, and building of pedagogical scenarios, first using
TM
the simulator PROSIM , then using pilot plants.
-Using these pedagogical scenarios : Building of an ISCAL prototype, then testing it, using the
TM
simulator PROSIM and using the pilot plants.

The first prototype build by the authors is based upon a batch distillation column. Some examples of
pedagogical sessions will be presented during the ICEF9 by demonstration.

In conclusion, we think that our research explores new fields in process engineering, and a lot of
applications may be done, particularly in food industries, because operation units are similar than
those of process industries. We think that, using this ISCAL, learners will have new skills, and they will
be able to take their places in the firm network structure, and co-operate with other sectors of the firm.
TM
And, finally, our research use very strong tools : pilot plants, and the simulator PROSIM .

REFERENCES

1 : BAUDET P., AZZARO-PANTEL C., DOMENECH S. et PIBOULEAU L., « Simulation d’ateliers

ème
discontinus de la chimie fine », 5 Congrès Français de Génie des Procédés, Lyon, France, 19-09-
1995, in : Automatique et Maîtrise des Procédés Complexes, coord. Charpentier J.C., Récents
Progrès en Génie des Procédés, Paris, Lavoisier, Vol. 9, N°40, pp. 117-122, (1995).

2 : PIBOULEAU L. , AZZARO-PANTEL C. , DOMENECH S., et FLOQUET P., « Simulation par

événements discrets pour l’ordonnancement à court terme d’ateliers discontinus de la micro-
ème
électronique à la chimie fine », 3 Congrès International de Génie Industriel : L’intégration des
ressources humaines et des technologies : Le défi, Montréal, Québec, (Mai 1999).

3 : BERARD F., « Stratégies de gestion de production dans un atelier flexible de chimie fine », Thèse
de Doctorat, Institut National Polytechnique de Toulouse, France, (26-01-2000).

4 : BAUDET P., « Ordonnancement à court terme d’un atelier discontinu de chimie fine. Cas du
fonctionnement job-shop », Thèse de Doctorat, Institut National Polytechnique de Toulouse, France,
(1997).

5 : PERKINS J., « Education in process systems engineering », Computers and Chemical

Engineering, , Vol. 24, N° 2-7 2000, pp. 1367, (July 2000).

6 : « La formation moteur de l’adaptation de l’entreprise », Techniques de l’Ingénieur, traité de Génie

Industriel, A 4 700 – 23.

7 : DONGIL SHIN, EN SUP YOON, SANG JIN PARK et EUY SOO LEE, « Web-based interactive
virtual laboratory system for unit operations and process systems engineering education », Computers
and Chemical Engineering, Vol. 24, N° 2-7 2000, pp. 1381-1385, (July 2000).

8 : MAHONEY D., YOUNG B. et SVRCEK W., « A completely real-time approach to process control
education for process systems engineering students and practitioners », Computers and Chemical
Engineering, , Vol. 24, N° 2-7 2000, pp. 1481-1484, (July 2000).
ICEF9 – 2004
International Conference Engineering and Food

9 : JAE HAK JUNG , MOONYONG LEE, JIETAE LEE et CHONGHUM HAN, « A development of
experimental education program : computer control of multi-stage level control system », Computers
and Chemical Engineering, Vol. 24, N° 2-7 2000, pp. 1497-1502, (July 2000).

10 : COOPER D. et DOUGHERTY D., « A Training Simulator for Computer Aided Process Control
Education », Chemical Engineering Education, Vol. 34, N°3, (Summer 2000).

11 : VOLSY R. et SODERQUIST K., « Jeu pédagogique d’analyse des processus dans le

ème
management des opérations », 3 Congrès International de Génie Industriel : L’intégration des
ressources humaines et des technologies : le défi, Vol. III, Montréal, Québec, (Mai 1999).

12 : RENAULT P., USLANDER T., INDESTEEGE L., THEUNISZ J., MALIK T., JOURDA L.,
« OPERA : Operators Training Distributed Real-Time Simulations », European Commission Funded
Esprit Project N° 24950, Final Report, (Février 2000).
TM
13 : PROSIM , www.prosim.net/english.html

14 : RICHARD L., « Un Système Multi-Agents pour la modélisation d’Environnements Interactifs

d’Apprentissage avec Ordinateur basés sur la simulation. Application à la formation de personnels de
maintenance aéronautique », Thèse de Doctorat, Université Paul Sabatier Toulouse III, France,
(1999).

15 : MONTALAN M. A., « Modélisation des compétences pour l’entreprise : conception et validation

d’un système d’évaluation formative des compétences en comptabilité financière », Thèse de
Doctorat, Université des Sciences Sociales Toulouse I, France, (1998).
ICEF9 - 2004 International Conference Engineering and Food

Texture testing of composite foods

Martin G. Scanlon(1) & Alok Anand(2)

(1) Department of Food Science, University of Manitoba, Winnipeg, Canada R3T 2N2
scanlon@cc.umanitoba.ca
(2) Food Development Centre, Portage la Prairie, Manitoba, Canada R1N 3J9
Aanand@gov.mb.ca

Composites were fabricated as bi-layer foodstuffs comprised of a core and a "harder"

crust. Indentation was performed to evaluate the overall mechanical response (texture)
of the composites. Mechanical properties of individual components were independently
measured. These independent measurements of mechanical properties were used as
inputs for models used to predict theoretical textural values for the composite that could
be compared with the experimentally-derived ones.

Key words: composite foods; texture; mechanical properties; modelling; indentation

Introduction
A large number of foods possess a layered composite structure. Fruits and vegetables
comprised of skin and flesh are Nature’s examples of such composites [1,2], while many
processed foods are deliberately manufactured with a layered composite structure:
examples are bread, french fries and many frozen desserts. In such cases, the
processing operations are performed with the objective of developing regions such as
crust and core which will exhibit distinct structural and mechanical differences [3]. The
contrast in mechanical properties between the two regions is important in imparting a
pleasurable textural sensation when the food is consumed [4]. In some instances,
processed foods have coatings added to the crust region to enhance this contrast in
mechanical properties [5] or to reduce the calorie content while mimicking desirable
taste attributes of the original food [6].

Predicting the texture of composite systems, so that individual unit operations can be
tailored to enhance textural contrast, is complicated by the heterogeneity of the food and
by the interaction between the two regions when stresses are applied to the food.
Therefore, an evaluation of the mechanical properties that contribute to the texture of the
food composite must consider the relative dimensions of the two regions and their
respective mechanical properties [7,8]. The evaluation becomes more complicated
when applied stresses are not uniformly distributed, as is the case in indentation (or
puncture) tests [9]. An indentation study of a model “french fry” composite, where crust
properties had been manipulated by frying time, showed that prediction of the
mechanical response of the composites was unsuccessful [8]. This was likely due to the
non-uniform structure of the french fry crust layer [8].

The objective of this study was to examine how food composite structure and properties,
and indentation (puncture) testing protocols, affected our ability to predict composite
ICEF9 - 2004 International Conference Engineering and Food

texture (overall mechanical response). Model composite foods were fabricated as

two-component bi-layer foodstuffs comprised of a core and a "harder" crust (covering a
range of “strengths”), so that the results might be generally applicable to foodstuffs such
as french fries, some frozen desserts and many baked goods.

Materials & Methods

Model layered composite foods were prepared from a crust of dry pasta on a core of 3%
agar gel or from a crust of 3% agar gel on a core of 1% agar gel. Agar of either 1% or
3% concentration was prepared [10] to a thickness of 4 cm to serve as core material.
Dry pasta, purchased from a local supermarket (thickness of 1.1 ± 0.10 mm), or 3% agar
gel (thickness of 2 mm or 4 mm) were used as crust materials. The cross-sectional area
of the pasta/gel composites was 4 cm x 4 cm, while that of the gel/gel composites was 6
cm x 6 cm. A high-speed hand-held cutting tool (Dremel, Racine, WI) was used to cut
the pasta into squares. Crust and core were bonded either with a thin (30 ±10 µm) layer
of superglue (pasta/gel composites) or a thin layer of hot 3% agar (gel/gel composites).
Bonding was performed just prior to indentation testing to prevent moisture migration
altering the mechanical properties of the individual components.

The mechanical properties of the individual components of the composites were

determined in separate experiments. Uniaxial compression between lubricated
compression platens was used to determine the mechanical properties of cylinders of
the gels [10,11]. Tensile testing (ASTM D828) was used to measure the mechanical
properties of strips of dry pasta.

Indentation was performed with flat-ended axisymmetric indentors applied to the top
crust of the composites at a crosshead speed of 1 mm min-1. Indentor diameters ranged
from 1 to 7 mm. Indentation load-displacement response was recorded continuously
until failure occurred in the composite. The mechanical parameters derived from these
load-displacement curves were indentation stiffness and indentation failure load.

Results & Discussion

Mechanical Properties of Composites
The indentation stiffness of the composites is shown in Figure 1. The fabricated
composites exhibit a good range in their
values of stiffness, and this range
encompasses the indentation response
of some real composite foods, such as
fries [8] and baked goods (Scanlon,
2000, unpublished results). Indentation
failure loads were also distributed over a
range of values (results not shown). For
the gel/gel composites, indentation
stiffness increased as indentor size
increased, so that composite behaviour is
similar to that of homogeneous materials
Fig. 1. Indentation stiffness as a function of indentor
subjected to indentation [10-12], whereas
radius for model composites (pasta, 4 mm gel, 2 mm no indentor size effect was discernible for
gel) and some real food composites. the pasta /gel composites.
ICEF9 - 2004 International Conference Engineering and Food

The elastic moduli and failure stresses of the three materials used to fabricate the
composites are shown in Table 1. The results from these independent measurements of
the mechanical properties of the components of the composites were used in
mechanical models to predict the indentation stiffnesses and failure loads of the
composites.

Table1. Mechanical properties of agar gels and dry pasta

Mechanical property 1% gel 3% gel pasta

Elastic modulus / kNm-2 12±2.1 74±18.4 2,900,000±400,000
Failure stress / kNm-2 9±0.9 57±5.5 4,100±970

Composite Modelling by Bending Analysis

The first model considered was that of flexure of an elastic plate (the crust) which is
supported by a Winkler foundation (the core) [13]. Details of the model, as applied to
prediction of the indentation stiffness of model french fries, have been previously
reported [8]. In Figure 2, the normalized stiffness (experimental value divided by
theoretical value) is plotted against the parameter b/l (indentor radius divided by the
radius of relative stiffness of the composite [14]). For a given composite, variation in b/l
is achieved by varying indentor diameter. It can be seen that this elastic flexure model
poorly predicts the indentation stiffness
of the gel composites: not only is there
an indentor size effect that should have
been eliminated, but the results are also
displaced from the y = 1 line. For the
pasta on gel composite, the indentor
size effect is eliminated. However, the
model over-predicts the indentation
stiffness, inferring a greater contribution
from the more compliant core.

Since the elastic plate on a Winkler

foundation model showed some promise
Fig. 2. Normalized stiffness as a function of b/l (see in predicting indentation stiffness, the
text) for gel/pasta and gel/gel composites. same model was used to predict
indentation failure loads [13]. The
failure load (P) is given by:
P = πb2σtoph2 / [3bl(1 + ν)·kei′(b/l)] (1)
where h is thickness of the pasta plate (crust), ν is its Poisson’s ratio (assigned as π-1)
and σtop is its tensile strength. Values for the derivatives of the imaginary parts of the
modified Bessel functions (kei′(b/l)) were obtained from the formulae given by McLachlan
[15] based on the ratio of indentor radius to radius of relative stiffness of the composite
(b/l). The results (Fig. 3) indicate that strength prediction is very poor. Despite the lack
of an indentor size effect, experimental strengths are very much larger than the
predicted ones. It was surmised that this discrepancy is attributable to the large load-
spreading capacity of the stiff pasta layer on the more compliant gel [16]. Support for
such a view comes from the magnitude of the radius of relative stiffness (l) for this
ICEF9 - 2004 International Conference Engineering and Food

composite. Based on this parameter,

the pasta on gel composites should
have had a cross-sectional area of 66
cm2 if a bending analysis of the pasta
plate was appropriate for modelling the
mechanical response [16], rather than
the 16 cm2 actually used, which was the
maximum size attainable with the pasta
that was available for purchase.
Therefore, load spreading effects
considerable compression of the
composite as a whole prior to the failure
Fig. 3. Normalized strength as a function of b/l (see of the crust in tension on its underside
text) for a gel/pasta composite. beneath the indentor; the result is
increased experimental indentation
failure loads. Such load spreading is used to good effect in consumer evaluations of the
freshness of bread crumb. The perception of crumb properties during squeezing of the
loaf is mediated by the dimensions and the properties of the crust. Effective spreading
of the applied load by the crust ensures that the crumb’s yield stress is not exceeded
and that elastic resilience of the crumb dominates in the consumer’s perception of crumb
freshness.

Composite Strength Modelling by Perforation Analysis

On the basis of Figure 2, a bending analysis of the failure load of the composite was
untenable for the gel on gel composites. Therefore, an approach used to analyse the
failure of sandwich panels under indentation was employed [2,17]. This model examines
whether core yielding or crust failure is the dominant mechanism affecting the strength of
the composite as a whole. The indentation failure load (P) is calculated from [17]:
P = 2πbhτtop + πb2σcore (2)
where τtop is the shear strength of the crust (assigned as compressive yield stress
divided by 2.33 [18]), h is crust thickness, and σcore is the yield stress of the core. By
normalizing each of the experimental indentation failure loads by either the first or

Fig. 4. Indentation failure load normalized by core Fig. 5. Indentation failure load normalized by crust
yielding load as a function of indentor radius for shear yielding load as a function of the ratio of
gel/gel composites of two crust thicknesses. crust thickness to indentor radius for gel/gel
composites of two crust thicknesses.
ICEF9 - 2004 International Conference Engineering and Food

second terms on the right hand side of Equation 2, it is possible to determine whether
crust failure under shear or core yielding is the dominant mode contributing to the failure
of the composite.

The contribution of core yielding to composite failure is shown in Figure 4. It is apparent

that this mechanism is not the dominant mode of failure for the gel on gel composites:
not only is there an effect of indentor size, but the composites of different crust thickness
do not reside on a common curve. In contrast, the results of Figure 5 indicate that shear
failure of the crust is critical during composite failure of these soft composites since there
is no crust thickness effect, and the results lie close to the y = 1 line.

Conclusions
A model for flexure of an elastic plate on a Winkler foundation showed some promise in
predicting the indentation response of “strong” food composites. Deficiencies in the
model’s predictive capacity arose from an interaction between the mechanical properties
of the composite and the dimensions of its constituent components. For “softer”
composites, a shear failure model indicates the importance of the mechanical properties
of the crust in predicting the failure response of the composite.

Acknowledgement
The authors are grateful for research support from NSERC Canada, and to Dr Z. Liu for
conversion of the file into pdf format.

References
1. Grotte M., Duprat F., Loonis D., Piétri E. Mechanical properties of the skin and the
flesh of apples. International Journal of Food Properties, 4, 149-161, 2001.
2. Bourne M.C. Method for obtaining compression and shear coefficients of foods using
cylindrical punches. Journal of Texture Studies, 5, 459-469, 1975.
3. Pinthus E.J., Weinberg P., Saguy I.S. Deep-fat fried potato product oil uptake as
affected by crust physical properties. Journal of Food Science, 60, 770-772, 1995.
4. Brown W.E., Eves D., Ellison M., Braxton D. Use of combined electromyography and
kinesthesiology during mastication to chart the oral breakdown of foodstuffs: relevance
to measurement of texture. Journal of Texture Studies, 29, 145-167, 1998.
5. Lonergan D., Larsen M. Emulsion glaze for dough products. US Patent 5 989 603,
1999.
6. Higgins C., Qian J., Williams K. Water dispersible coating composition for fat-fried
foods. US Patent 5 976 607, 1999.
7. Roy I., Campanella O.H., Normand M.D., Peleg M. Uniaxial compression of double
layers of solid foods. Journal of Texture Studies, 20, 443-455, 1989.
8. Scanlon M.G., Ross K.A. A mechanical model to characterize crust development
during french fry processing. “Proceedings of the 2nd International Symposium on Food
Rheology and Structure.” P. Fischer, I. Marti, E.J. Windhab (eds.), Laboratory of Food
Process Engineering, ETH Zürich, Zürich, 277-282, 2000.
9. Liu Z., Scanlon M.G. Modelling indentation of bread crumb by finite element analysis.
Biosystems Engineering, 85, 477-484, 2003.
10. Anand A., Scanlon M.G. Dimensional effects on the prediction of texture related
mechanical properties of foods by indentation. Transactions of the American Society of
Agricultural Engineers, 45,1045-1050, 2002.
ICEF9 - 2004 International Conference Engineering and Food

11. Ross K.A., Scanlon M.G. Analysis of the elastic modulus of an agar gel by
indentation. Journal of Texture Studies, 30, 17-27, 1999.
12. Sneddon I.N. The relation between load and penetration in the axisymmetric
Boussinesq problem for a punch of arbitrary profile. International Journal of Engineering
Science, 3, 47-57, 1965.
13. Wyman M. Deflections of an infinite plate. Canadian Journal of Research, 28A,
293-302, 1950.
14. Dempsey J.P., Zhao Z.G., Li H. Axisymmetric indentation of an elastic layer
supported by a Winkler foundation. International Journal of Solids & Structures, 27,
73-87, 1991.
15. McLachlan N.W. “Bessel Functions for Engineers (2nd edn.).” Clarendon Press,
Oxford, 239 p, 1955.
16. Terzaghi K. Evaluation of coefficients of subgrade reaction. Geotechnique, 5,
297-326, 1955.
17. Wen H.M., Reddy T.Y., Reid S.R., Soden P.D. Indentation, penetration and
perforation of composite laminates and sandwich panels under quasi-static and
projectile loading. Key Engineering Materials, 141-143, 501-552, 1998.
18. Hill R. “The Mathematical Theory of Plasticity.” Clarendon Press, Oxford, 356 p,
1950.
 ICEF9-2004
International Conference Engineering and Food

An Efficient Dynamic Simulation Environment for the Operation of Food

Processing Plants

Vilas, C., García, M.R., Villafín, M., Banga, J.R., Alonso, A. A. (1)
Process Engineering Group, IIM-CSIC, Eduardo Cabello 6. 36208 Vigo, Spain
(1)
antonio@iim.csic.es

Abstract
Food processing plants are good examples of hybrid systems where highly non-linear continuous
dynamics are coupled with discrete events. We present a user friendly interface and a library of unit
operations for food industry. This simulation environment use new methods in model building and is
able to reconstruct plant operation at different levels of detail. The architecture allows the embedment
of product transformations into different unit operations, and these into an economic model.
Keywords: hybrid systems, dynamic simulation, food processing, economic dynamic processes

1. Introduction.
Daily production in food industry combines continuous as well as discrete processes and decisions.
Typical examples of continuous processes and actions involve heat and mass transfer in units such as
cooking, frying or sterilization. These operations, which are usually carried out in batch mode are
commanded by the operator and/or through recipes previously defined and automated. Consequently,
food processing industries are excellent representatives of hybrid systems, with highly non-linear
continuous dynamics coupled with a variety of time and state driven discrete events [1]. Typical
examples of discrete time events include the actions of digital feedback controllers regulating the
appropriate temperature sterilization while state driven events include minimum temperature or
pressure values defining the cooking/sterilization cycle or drying policies [2] . the objective of this work
is the development of a multipurpose and efficient dynamic simulator environment to be employed in
food processing plants. In addition to efficiently handle discrete-continuous scenarios, the tool must be
user friendly and compatible with control, real time prognosis, information analysis and decision
making tools such as optimization. The purpose of this paper is to give an outline of the different
elements and methods employed in the construction of such a general tool, and illustrate its capability
on a number of representative examples of application.

2. The Modeling Structure of Food processing Plants

Our simulation environment is constituted by a set of equations describing the different components
that collect the inherent characteristic of processes, units and auxiliary equipment such as retorts, heat
exchangers, cooker vessels, boilers, controllers and valves or pumps, for instance. The continuous
world is represented by conserved properties such as material, energy and momentum transfer.
Mathematically, these components are expressed by coupled sets of non-linear partial, and ordinary
differential equations (PDEs and ODEs, respectively). The description is finally completed with a given
number of non-linear algebraic equations which take into account the constitutive relationships
 ICEF9-2004
International Conference Engineering and Food

between the states and the physical parameters. Formally, the different classes of PDAES (Partial
Differential Algebraic Equation Systems) are of the form:

xt + ∇( v k x ) = ∆(κx ) + f (t ,ξ , x, u ) (1)

x t = f ( x ) + g ( x )u (2)

where x is a field vector (or states) which, for instance, might represent the temperature or mass
product distribution in a solid or fluid, and ∇ and ∆ in (1) are the well-known gradient and Laplace
operators, respectively. Equation (2) represents a typical set of non-linear ordinary differential
equations in affine form with u being both in (1) and (2) the control actions.

At this point, it must be noted that the numerical solution of systems of the form (1) is in general
computationally involved as a result of the high dimensional structure of the usual discretization
schemes employed such as finite differences or finite elements (see, for instance [3] and [4]). This
translates into a extremely large number of ODE systems to be solved, what makes the approach
unsuitable for real time simulation or optimization. We overcome such limitation by taking advantage
of the dissipative structure of the PDE systems [5] which allows the extraction of a slow dimensional
dynamic manifold capturing the relevant dynamic behavior of the system. Different techniques such as
spectral decomposition [6] or Proper Orthogonal Decomposition POD [7] have been currently
implemented on an automated basis in our simulation environment

Finally, constitutive algebraic relations include degradation kinetics of nutrients and quality parameters
of interest such as growth and/or thermal death kinetics of microorganisms. As an example, the
following equation relates the thermal lethality as a function of temperature

 T − T (r0 ) 
( F0 )t = exp ref ln(10)  (3)
 z 
The other constitutive relations collected in the simulation environment express the installed flow
characteristics of valves through pipes and its relations with the control structure. See [8] for a
comprehensive overview of the different types of valves commonly employed in the process industry.

3. The simulation architecture

In order to ensure coherence among units and equipment, as well as transparency and user friendly
capabilities of the simulation environment, the software has been designed as an interconnected and
overlapped layer structure. Such architecture allows the consistency, inclusion/exclusion,
improvement and modification of both existing and/or new components encompassing the current
necessities of the users. A sketch of the different code layers and interrelationships between them has
been depicted in Figure 1. The basic level comprises a computational engine (EcosimPro) where
models are built in component form with inheritance and re-usability capabilities. This tool makes use
of a high level simulation language (EL) which efficiently handles and combines arbitrarily large hybrid
DAE systems through port technology (www.ecosimpro.com). The next level makes models and
 ICEF9-2004
International Conference Engineering and Food

computation algorithms accessible to the users through a highly interactive and visual interface built in
a high level language (Microsoft® Visual Basic 6.0, in our case). Such a layer allows, in an intuitive
way, the automatic translation of user prognosis demands and questions into the appropriate answers.
In this way, the different processes (products), units (e.g. retorts) or other equipment such as valves or
pumps are transformed into simple ActiveX objects (icons) organized in extendable libraries
graphically operated. Some details of the components and the interface can be seen in Figure 3. The
simulation environment is complemented with additional tools such as optimizers, state observers and
parameters estimators which via web record, complement and analyze both at the level of process or
economics the current performance of the plant (see Figure 2).

Figure 1: The different layers of Figure 2: Extensions of the simulation environment to the general
the software structure. information structure of the plant.

4. Some Representative examples

In order to illustrate some applications of the simulator two examples are presented. The first consists
of selecting the appropriate minimum energy consumption for a given number of sterilization
scenarios. The second example illustrate the advantages of the simulation environment in tuning a
digital proportional-integral temperature regulator for a given retort.

4.1. Comparison between scenarios

The problem consists on comparing a number of modes of operation (scenarios) in the sterilization of
a given quantity of albacore tuna. This comparison is made under economic and saving time points of
view. The simulation has been made by considering various autoclaves, one boiler, different kinds of
valves, a PI controller and three kinds of cans (RO85, RO1000 and RO3900). Figure (4) shows the
organization chart for one particular scenario. Segments represent sterilization cycles for the kind of
can indicated over each line, and the space between segments symbolizes the unload and load time.
By comparing the fuel cost, a saving of near 18% of fuel was found in one of the scenarios as
compared with the other alternatives. Furthermore, this scenario was also the one which reduced the
total amount of production time.
 ICEF9-2004
International Conference Engineering and Food

Figure 5 shows a typical output plot obtained by the simulator for a constant time-temperature
sterilization cycle of RO3900 type cans.

Figure 3: Example of a steam autoclave built in the simulator graphic interface. The different
units and equipment are selected from a component library (at the top left of the screen). As
shown in this case for the component retort has its own associated dynamic mathematical
model.

11
110
i 10
100 9
Temperature (oC)

90 8
80 ii 7
F0 (min)

70 6
60 5
iii 4
50
3
40 2
30 1
20
100 200 300 400
Time (min)
Figure 4: An example of the organization Figure 5: Output plot showing retort temperature (i),
chart for one scenario. temperature at the center of the can (ii) and lethality (iii)
for a typical sterilization cycle. RO3900 can.
 ICEF9-2004
International Conference Engineering and Food

4.2. Tuning of a PI controller

In this example the simulation environment has been employed to tune a PI-type controller. The
structure of the controller was made in the Internal Model Control (IMC) framework [2]. In velocity form
the resulting regulator has the form:
τ
uk = uk −1 + (ek − ek −1 ) + 1 ek (tk − tk −1 ) (4)
Kλ Kλ
where u is the valve opening, e represents the error between the desired set point and the actual
temperature measurement. Controller parameters are K and τ which represent the gain and time
constant for the open loop plant, linearized around the operation temperature of interest. Finally, λ is
the filter parameter related to the desired closed loop speed response. In order to test the effect on the
temperature response and movements of the manipulated variables, different λ parameter values
were tested in the example for τ = 35 s, K = 500, tk – tk-1 = 10 s. The evolution of retort temperature
and steam and bleeder valve opening are presented in Figure (6). As we can see in the Figure, the
lower the value of λ the faster the controller response. Note that extremely low values of λ may cause
valve saturation as illustrated in Figure 6(a).

(a) (b)

1 120 1
120 i 0.9
0.9
i 0.8
0.8 100
Temperature (oC)
Temperature (oC)

100 0.7
0.7
0.6 80 0.6
80 0.5

u
0.5
u

0.4 60 0.4
60 ii
ii 0.3 0.3
0.2 40 0.2
40 iii
iii 0.1
0.1
20 0 20 0
0 10 20 30 40 50 60 0 10 20 30 40 50 60
Time (min) Time (min)

(c)

140 1
0.9
120
i 0.8
Temperature (oC)

0.7
100
0.6
u

80 0.5
0.4
60 ii
0.3
0.2
40
iii 0.1
20 0
0 10 20 30 40 50 60
Time (min)
Figure 6: Representation of retort temperature (i), bleeder valve position (ii) and steam valve position
(iii) for: (a) λ = 0.5, (b) λ = 1 and (c) λ = 10.
 ICEF9-2004
International Conference Engineering and Food

5. Conclusions.
A user friendly interface for food processing plants was presented. The user can employ this
simulation environment to either analysis the effect of alternative technologies on plant production, to
design new production practices in the event of fluctuating supply conditions as well as controller
tuning without the need of expertise mathematical knowledge. The simulator can also be inserted in
via web management schemes that allows the access to the general information structure of the plant.

6. References

1. Barton P.I., Banga J.R., Galán S. Optimization of hybrid discrete/continuous dynamic systems.
Computers & Chemical Engineering, 24, 2171-2182, 2000.
2. Alonso A.A., Banga J.R., Perez-Martin R. Modeling and adaptive control for batch sterilization.
Computers & Chemical Engineering, 22, 3, 445-458, 1998.
3. Schiesser W.E. “The numerical method of lines.” Ed. Academic Press Inc., San Diego, 326p,
1991.
4. Reddy J.N. “An introduction to the finite element method.” Ed. McGraw-Hill, 684p, 1993.
5. Alonso A.A., Ydstie B.E. Stabilization of distributed systems using irreversible
thermodynamics. Automatica, 37, 1739-1755, 2001.
6. Alonso A.A., Fernández C.V., Banga J.R. Dissipative systems: from physics to robust
nonlinear control. Int. Journal of Robust and Nonlinear Control, accepted, in press, 2003.
7. Balsa-Canto E., Alonso A.A., Banga J.R. A novel, efficient and reliable method for thermal
process design and optimization. Part I: theory. Journal of Food Engineering, 52, 3, 227-234,
2002.
8. Smith C.A., Corripio A.B. “Principles and practice of automatic process control”. John Wiley &
sons Inc., 614p, 1985.
ICEF9 2004
International Conference Engineering and Food

Novel combination heating ovens: numerical modeling and experimental validation

Srikanth Geedipalli (1), Ashim K. Datta (2) and Marialuci F. Almeida(3)

(1) 27 Crows Nest Lane, 1L, Danbury, CT 06810

ssg24@cornell.edu
(2) Dept. of Biol. and Env. Engineering, Riley-Robb Hall, Cornell Univ., Ithaca, NY 14853
akd1@cornell.edu
(3) Riley-Robb Hall, Cornell University, Ithaca, NY 14853
mfa8@cornell.edu

Abstract

Combination microwave and hot air (or infrared) heating can be a successful means to
combine the benefits of each mode of heating and provide customized heating profiles
needed to obtain the desired quality of a prepared food. Several complex phenomena,
related properties and their interplay are involved in such a combination heating process.
Using a fundamental approach, combinations of heating modes are evaluated in terms of
rates and uniformity of heating.

Key Words: Microwave, Infrared, Jet impingement, Uniformity,

Introduction

Microwave ovens have had a tremendous impact on people’s cooking habits. They are
getting increasingly popular because they are quicker and more convenient than the
conventional ovens. However, the problems associated with microwaves are numerous such
as non-uniform heating, edge overheating, soggy texture, lack of browning and concerns
about inadequate microbial destruction.

To overcome the above disadvantages of microwave (mw) heating, researchers have

proposed various solutions like designing better ovens, changing food composition, using
active packages like shields and susceptors etc. Some ovens include mode stirrers to
change the electromagnetic field continuously while most ovens are provided with a turntable
to rotate food and hence heat more uniformly. But inspite of the above measures, major
issues remain about quality of food heated in a microwave oven.

Microwave combination ovens are ovens in which the food is heated by a combination of
heat transfer mechanisms, including microwave propagation, infrared radiation, convection,
jet impingement, high temperature bottom contact plates etc. These ovens are intended to
overcome some of the problems associated with microwave ovens while maintaining the
advantages of speed and convenience over conventional ovens. [1]

Objectives

The overall objective of this work is to evaluate the effectiveness of combination ovens over
microwave only ovens. The specific objectives are
ICEF9 2004
International Conference Engineering and Food

1. To develop a mathematical model to simulate the electromagnetic fields inside a

microwave oven and hence obtain power generated in the food

2. To combine with the above power generated a second mechanism of heating (Jet
Impingement, Infrared) and develop a thermal model to obtain temperature profiles
inside the food item.

3. To validate the mathematical models by comparing with experimentally measured

temperatures in real combination ovens available in the market.

4. To compare and contrast the individual heating mechanisms with their combinations
and evaluate their usefulness in obtaining a more uniformly heated food.

Mathematical Model

The electromagnetic field distribution inside a microwave cavity is governed by Maxwell’s

equations. The set of four Maxwell’s equation along with the three constitutive equations are
needed to define the system. The cavity walls are assumed to be perfectly conductive and so
a perfect electric conductor boundary condition is applied. The excitation is provided by a
waveguide in which electromagnetic (EM) waves propagate in the TE10 mode. The full set of
governing equations along with the boundary conditions and excitation are given in [2].

For the Jet Impingement, a simple model based on convection heating is used, instead of
detailed studies reported in literature (e.g., [3]). A basic thermal heating model is simulated
with surface convection heat transfer as the boundary condition. Heat transfer coefficients for
jet impingement heating are experimentally obtained. A better and more complex model of
combination mw and hot air heating, which includes moisture migration, is given in [4], but
the simple model would suffice for the present study. The infrared (IR) heating model is
based on radiative heat exchange between the hot halogen lamps, the food surface and the
cavity walls. The model is described in detail in [5].

Methodology

A finite element (FEM) software (Ansys 7.0, 2003) was used to solve for the EM Field inside
the microwave cavity. A minimum of 7 nodes per wavelength (as recommended) was used
and the results were verified for convergence. The total nodes used varied from 60,000 to
120,000 depending on the cavity and food size. The power generated inside the food is then
input in a thermal simulation model developed on another FEM software. (FIDAP 8.62, 2003)

To validate the simulation results, experiments were done on two commercially available
combination microwave ovens. (Thermador CJ302UB Double Jet/Microwave and GE
Advantium Combination Microwave/Infrared Oven). To measure temperature at different
locations in the food inside a mw cavity, fiber optic probes (from FISO Technologies, Quebec,
Canada) were used as they do not interfere with the EM field. Surface heat transfer
coefficient in Jet Impingement heating and surface radiation flux in Infrared heating were
measured using heat flux sensor provided by Omega Engineering (model HFS-3). Data
acquisition was done using a Fluke Hydra Data Bucket.

Potato was used as the food item of choice as its engineering properties have been
extensively studied and easily available. Since the model doesn’t consider any water
evaporation, experiments were limited to 60 seconds and below 600 C. Though some graphs
in results show trends beyond 600C, they should be considered as inaccurate
approximations.
ICEF9 2004
International Conference Engineering and Food

Input Parameters

For electromagnetic modeling, input excitation was obtained by doing an experiment with
water as a load as explained in [2]. The dielectric properties of potato are well documented
and were taken from [6]. Since dielectric properties of potato do not vary a lot with
temperature, constant properties were used. Test runs with changing dielectric properties
validate the use of constant values.

Figure 1 gives the heat flux on different surfaces of the food heated by hot air jet inside the
Thermador Double Jet/MW Oven. Temperature of the food surface were also obtained but
are not provided here due to the lack of space.

From the surface flux and surface

temperature, the heat transfer
coefficient was calculated to vary
from 50 to 80 W/m^2 K for the
different food surfaces. The jet
velocity in the oven was on the
lower side (around 1800 ft/min) and
the seemingly low heat transfer
coefficients are within range for
such low velocities. The calculations
were in agreement with similar
measurements done at Thermador
Inc.

Figure 1: Surface flux variation

with time for Hot air Jet heating

Air density 1.1614 kg/m3 Table 1. Input Parameters

Air Specific Heat 1030.0 J/kg-K used for solving the
radiation problem. The
Air Thermal Conductivity 0.04 W/m-K
optical properties were
Potato density 1000.0 kg/m3 experimentally measured
Potato Specific Heat 3900.0 J/kg-K and the details provided in
Potato Thermal Conductivity 0.4 W/m-K
[5]. The same thermal
properties of potato are
Oven surfaces emissivity 0.1
used in combination mw
Lamp surfaces emissivity 0.99 and jet impingement
Potato emissivity (gray) 0.88 heating.
Potato emissivity (non-gray) < 1350nm > 1350 nm
0.64 0.96
Stefan-Boltzmann constant 5.6697E10-8 W/m2-K4

Results

Microwave + Jet Impingement Combination Heating

ICEF9 2004
International Conference Engineering and Food

Figure 2: Experimental vs.

Simulated Curves for hot
spot for MW heating in MW –
Hot Air combination oven

Good match at lower

temperatures, but slightly off
at higher temperatures as
moisture loss is not included
in the model

Fig 3a: Microwave Oven Fig 3b: Hot Air Jet Oven

Figures 3a, 3b and 3c give the mean

temperature rise of the food and the 10
and 90 percentiles of the food
temperature distribution. Based on the
curves, we can say that for the same
mean temperature, combination oven
gives us the most uniform heating. The
two tables below quantify the uniformity
of heating. Two measures are used;
Coefficient of Variation (COV) and
difference in 10 and 90 percentiles. Both
measures show that combination heating
is way better than single mechanisms of
heating.
Fig 3c: Combination Oven
ICEF9 2004
International Conference Engineering and Food

Table 2. Heating Uniformity Comparison across different modes of heating (2 mins of

heating)
Jet Impingement MW Heating Combination
Heating Heating
Mean Temp. Rise 23.037 18.55 39.974
Std. Deviation 12.86 9.123 15.36
COV 0.558 0.492 0.382

Table 3. Heating Uniformity as shown by difference in hot and cold point temperatures
Jet Impingement MW Heating Combination
Heating Heating
Mean Final Temp. 48.037 43.55 64.974
Mean Temp. Rise 23.037 18.55 39.974
10 Percentile 31.5 33.2 45.0
90 Percentile 64.1 59.3 84.4
Difference 32.6 26.1 39.4
Difference/Rise 1.415 1.407 0.986

Microwave + Infrared Combination Heating

Figures 4a, 4b and 4c show the temperature contours on the food surface, which is heated
by infrared, microwave and combination IR/MW heating. From the figures and the data
obtained from simulations, it can be concluded that IR is good for surface heating only and
MW is too uneven. Combination IR/MW is a better alternative to either one of them used
individually.

Fig 4a: Infrared Heating

Fig 4b: Microwave

Fig 4c: Combination MW/IR heating

ICEF9 2004
International Conference Engineering and Food

Conclusions

1. The results from the model match favorably with the measured values for
temperatures below 550 C. But as the model doesn’t account for moisture, heating is
overestimated at higher temperatures where evaporation becomes significant.

2. The results show very definitely that combination heating leads to more uniform
heating, without compromising the speed or convenience.

3. COV and middle 80 percentile range are used as measures of non-uniformity. These
provide a good estimate of how good or bad the uniformity is for the whole food. But
there is a need to find a better statistic, like a one, which would account for local hot
and cold spots.

4. Uniform heating isn’t the only goal of combination heating appliances. Surface
browning to develop crispness is as important and we need to evaluate the
combination ovens’ usefulness in this area. A statistic like the one mentioned in point
3 above would be very helpful to do so.

References

[1] Nicolai B. M. et. al., Optimal control of microwave combination ovens for food heating.
ASAE/CSAE-SCGR Annual International Meeting, Toronto, 1999

[2] Zhang H. and Datta A. K., Coupled electromagnetic and thermal modeling of
microwave oven heating of foods. The Journal of Microwave Power and
Electromagnetic Energy, 35(2): 71-85, 2000

[3] Nitin N. and Karwe M. V., Heat transfer coefficient for cookie shaped objects in a hot
air jet impingement oven. Journal of Food Process Engineering, 24(1): 51-69, 2001

[4] Ni H. and Datta A. K., Infrared and hot air additions to microwave heating. Journal of
Food Engineering, 51(4): 355-364, 2002

[5] Almeida M. and Datta A. K., Radiative heating in an oven using near infrared source.
IFT Annual Meeting, Anaheim, California, 2002

[6] Sipahioglu O. and Barringer S. A., Dielectric properties of vegetables and fruits as a
function of temperature, ash and moisture content. Journal of Food Science, 68(1):
234-239, 2003
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ADVANCED TOOLS FOR SIMULATION, OPTIMISATION AND CONTROL OF FOOD

PRESERVATION PROCESSES

Maggiolo, C.(1), Balsa-Canto, E.(2), Chiumenti, M.(3), Cervera, M. (4), Oñate, E.(5),
Alonso, A. A (6) and Banga, J.R. (7)

(1-5) CIMNE, Barcelona, Spain. (6-7) IIM-CSIC, Vigo, Spain

e-mail: cmagg@cimne.upc.es e-mail: antonio@iim.csic.es
e-mail: ebalsa@cimne.upc.es e-mail:julio@iim.csic.es
e-mail: chiument@cimne.upc.es
e-mail: cervera@cimne.upc.es
e-mail:onate@cimne.upc.es

ABSTRACT

This work describes recent advances on the development of a new software package based on the
combination of user friendly interfaces with suitable numerical methods for the complete study of the
most relevant food preservation techniques (sterilization, pasteurisation, and freezing, among others).
This new tool will allow users from food companies to improve their processes in an effective way, to
guarantee safety and quality of foodstuffs, with less cost, reduced energy consumption and minimum
environmental impact.

Keywords: food preservation, simulation, optimisation, control, process engineering

1. INTRODUCTION

Food spoilage is a gradual process occurring because of enzymatic and/or chemical reactions,
improper temperature control or microbial growth, resulting in undesirable changes in the colour,
flavour, odour and/or texture. Typical effects of the food spoilage include nutrient loss, loss of
organoleptic quality and health damage. Therefore one of the major concerns of the food industry is to
develop new or to improve traditional processing techniques in order to offer high quality and safe
products to the consumers.

The objective of food preservation processes is to reduce the microbial load and render the final food
product shelf-stable. Food preservation through processing is an extremely broad area in food
technology, including processes like refrigeration, freezing, pasteurisation, sterilization, fermentation,
and drying, among others. Although the basic idea behind all these techniques is to either slow down
or eliminate the activity of the bacteria causing spoilage, not all these processes are suitable for all
types of food. Moreover, operating conditions must be carefully selected in order to guaranty a safe
product with the maximum possible content of nutrients.

During decades the better understanding of the processes and the selection of adequate operating
conditions were the result of an extensive experimental work with the subsequent time consumption
and economic cost. The increasing demand from industry of “automatic” tools which allow accelerating
this process and reducing economic impact, has lead to extensive research in several areas related to
food processing such as modelling, simulation, optimisation and control (e.g. see Teixeira et al, 1969;
Banga et al, 1991; Fryer, 1994; Alonso et al., 1998, among others). However, regardless of all the
advances in this field in the academic world, the use of these methodologies in industry is still very
limited, being the absence of user friendly customized software environments one of the main
reasons. Moreover, although there is a number of commercial tools that allow quite easy simulation of
many relevant food processes, this is certainly not the case for the solution of dynamic optimisation
and control problems.
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This work presents the advances on the development of a customized tool for the food preservation
industry. The features of this new tool include the following:

- Possibility of selecting specific geometries or drawing an arbitrary geometry.

- Possibility of selecting a food stuff from a list already included in the tool or including new
ones.
- Possibility of selecting a number of processing conditions.
- Automatic mesh generation through the use of the GiD personal pre and post processor
(http://gid.cimne.upc.es/, Domínguez and Soler, 1999, Ribó et al., 1999).
- Library of numerical routines for the simulation, model calibration, optimisation and control
of a number of relevant food preservation processes.
- A post-processing environment also based on GID which provides several result viewing
capabilities (figures, videos, tables).

2. MODELLING AND SIMULATION

Modern process system engineering methods rely on mathematical models based on sound first
principles, considering heat, mass and momentum transport phenomena, plus the corresponding
expressions for the kinetics and thermo-physical properties. Most of these processes are operated in
batch or semi-batch mode resulting in time-dependent mathematical models. Moreover, most of the
relevant variables of the processes, such as the temperature or the moisture content, have a
distributed character, that is, depend on the position inside the food (Singh and Heldman, 1993;
Tijskens et al., 2001).

Therefore, the resulting mathematical models consist of usually highly non-linear sets of partial
differential and algebraic equations (PDAEs) subject to appropriate boundary conditions which take
into account processes operation conditions whose solution usually relies on numerical techniques.

Most of these numerical approaches are based on the discretisation of the spatial domain, such as the
finite differences approach, the numerical method of lines (NMOL, Schiesser, 1991) or the finite
elements method (Zienkiewicz and Taylor, 2000; or Datta, 1998 for applications related in food
processing).

The tool presented here makes use of the Finite Element method due to the advantages it offers to
deal with complex three dimensional geometries. Moreover, it has been recently demonstrated that
the use of reduced order models can highly increase the efficiency of the simulation process (Alonso
et al., 2000, Balsa-Canto et al, 2002 a-b), therefore numerical tools for the calculation of reduced order
models will be also included in the tool.

3. MODEL CALIBRATION and DYNAMIC OPTIMIZATION

Model calibration consists of changing values of model parameters, for example heat transfer
coefficient, thermal diffusivity or kinetic parameters, in an attempt to match simulation results with
experimental observations. This problem can be formulated as a non-linear optimisation problem,
usually called inverse optimisation problem, being the objective function a measure of the error in the
model prediction and the decision variables the model parameters. Note that the solution of this
inverse optimisation problem requires the numerical solution of a PDAE system for each objective
function evaluation (NLP- PDAEs).

Dynamic optimisation involves the calculation of time-varying control profiles (e.g. the heating
temperature profile in a sterilization process) that optimise (minimise or maximise) a desired objective
functional (usually related to cost, quality of final product, energy consumption, etc.) subject to the
system dynamics and a number of constraints (e.g. microbiological safety).

During recent years, dynamic optimisation methods have been successfully applied to a number of
relevant processes from the food industry, such as thermal sterilization (Banga et al, 1991; Silva et al
1993; Durance, 1997) or drying (Banga and Singh, 1994).
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Most of the works on dynamic optimisation of food processing make use of the so called Control
Vector Parameterisation approach, which transforms the original dynamic optimisation problem into a
non-linear optimisation problem, which again requires the solution of a PDAE system for each
objective function evaluation (NLP-PDAEs).

As many of the NLPs considered are multimodal the use of global optimisation methods is necessary
(Banga et al., 2002; Banga et al., 2003). Although several possibilities are being studied, stochastic
approaches currently seem the best candidates to be included in the tool presented here, as they are
able to arrive to the close vicinity of the solution in reasonable times, without the need of any
assumptions or changes in the model.

5. CONTROL

In order to implement the optimal operating policies obtained through the solution of the dynamic
optimisation problems, it is necessary to use adequate control methodologies, usually based in the
model predictive control scheme. This type of controllers has been applied to several food processes
such as extrusion (Nikolau, 1996), drying and refrigeration (Trelea et al, 1998) and thermal sterilization
(Alonso et al, 1998; Chalabi et al, 1999).

6. CALISO FEATURES

CALISO will remedy some of the current software limitations providing a customized software not only
for simulation but also for optimisation and control. It will consist of three main elements:
A user friendly interface: in order to make work very simple, it will provide information
regarding the modelling of different preservation processes, geometries, plus simulation,
optimisation and control capabilities.
Pre and post processor: Users can easily introduce the desired geometry, either drawing it,
selecting from some databases or capturing it through the data from a digital vision system.
GiD will provide different mesh generation options, adaptability to simulation codes and
visualization facilities, such as temperature distributions, animated sequences for dynamic
analysis, graphics related to quality of products, etc.
New modules with suitable and efficient numerical techniques will ensure the rapid solution of
the simulation, optimisation and control problems.

Examples
The current capabilities of CALISO may be shown through an example.

Thermal sterilisation of canned foods.

Step 1: Introduce a geometry. A cylindrical can may be selected from the data-base which includes
all standard cans, or any other type of geometry can be considered.
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Can 202 x 214 is selected.

Step 2: Generate the mesh, material properties, and processing conditions.

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International Conference Engineering and Food

Step 3: Compute and visualize results:

(a) Temperature distribution at a given time.

(b) Nutrient concentration
(c) Lethality at critical point
(d) Optimal control profile for the maximisation of nutrient retention while achieving a certain lethality
value.

CONCLUSIONS

Although there are a number of simulation tools based on the finite element method which could be
somehow programmed to simulate food processing operations, this is not the case for dynamic
optimisation and control. CALISO is a new, user friendly, easy to use environment which will allow the
systematic application of computer-aided process engineering techniques to food preservation
processes. This new tool will allow the modelling and simulation of highly complex food preservation
processes and geometries, plus the possibility of computing their optimal operating conditions and
designing closed loop controllers. This software environment will allow the food industry to improve
both the performance of their processes and the quality of their products.

Acknowledgements

This work is supported by the Spanish Government (McyT projects AGL2001-2610-C02-01 and
AGL2001-2610-C02-02).
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REFERENCES

1. Teixeira, A.A., Dixon, J.R., Zahradnik, J.W. and Zinsmeinster, G.E. “Computer optimisation of
nutrent retention inthermal processing of conduction heated foods”. Food Technol., 23:137-142,
1969.
2. Banga, J. R., Perez-Martin, R. I., Gallardo, J. M. and Casares, J. J. “Optimization of the thermal
processing of conduction-heated canned foods: study of several objective functions”, J. Food Eng.
14(1): 25-51, 1991.
3. Fryer P, “Mathematical-Models In Food-Processing”, Chem Ind-London (13): 515-518, 1994.
4. Alonso, A. A., Banga, J.R. and Martín, R.I.P. “Modeling and adaptive control of a batch
sterilization process”, Comput. Chem. Eng. 22(3):445-458, 1998.
5. Domínguez, N. and Soler P. , “GID User Manual”, Ed. CIMNE, Spain,1999.
6. Ribó, R., de Riera, M. and Solano, E., “GID Reference Manual”, Ed. CIMNE, Spain, 1999.
7. Singh, R.P. and Heldman, D.R. “Introduction to Food Engineering”, Academic Press, California,
USA, 1993.
8. Tijskens, L.M.M., Hertog , M.L.A.T.M. and Nicolaï, B. “Food process modelling”. Woodhead
publishing limited, 2001.
9. Schiesser, W. E. “ The numerical method of lines”. Academic Pres, New York, 1991.
10. Zienkiewicz, O.C. & R. L. Taylor (2000), “The Finite Element Method”, 5ª Ed. Butterworth-
Heinemann, 2000.
11. Datta A.K. “Computer-aided engineering in food process and product design”, Food Technol-
Chicago 52 (10): 44-52, 1998.
12. Alonso, A.A., Banga, J.R. and Sánchez, I. “Passive Control Design for Distributed Parameter
Process Systems: Theory and Applications”, AICHE J., 46, 8, 1593-1606, 2000.
13. Balsa-Canto, E., A. A. Alonso and J. R. Banga. “ A novel, efficient and reliable method for thermal
process design and optimization. Part I: Theory”, J. Food Eng., 52, 227-234, 2002.
14. Balsa-Canto, E., Balsa-Canto, E., J. R. Banga y A. A. Alonso . “A novel, efficient and reliable
method for thermal process design and optimization. Part II: Applications” J. Food Eng., 52, 235-
247, 2002.
15. Silva, C. L. M., Oliveira, F. A. R. and Hendrickx, M. “Modelling optimum processing conditions for
the sterilization of prepackaged foods”, Food Control 4(2): 67-78, 1993.
16. Durance, T.D., “Improving canned food quality with variable retort temperature processes”, Trends
In Food Sci. & Tech. 8(4):113-118, 1997.
17. Banga, J. R. and Singh R. P. “Optimization of the air drying of foods”, J. Food Eng., 23:189-211,
1994.
18. Banga, J.R., Balsa-Canto, E., Moles, C.G. and Alonso, A.A., “Global Optimisation in Food Process
Engineering”, in Computational Techniques in Food Engineering, CIMNE, 2002.
19. Banga, J. R.; Balsa-Canto, E.; Moles, C. G.; Alonso, A. A (2003) Improving food processing using
modern optimization methods. Trends in Food Science and Technology, 14(4):131-144.
20. Nikolaou, M., “Computer-aided process engineering in the snack food industry”, Chemical Process
Control (CPC-V) Conference, January 7-12, Tahoe City, CA, 1996.
21. Trelea, I.C., Alvarez, G. and Trystram, G., “Non linear predictive optimal control of a batch
refrigeration process”, J. Food Process Eng. 21:1-32, 1998.
22. Chalabi, Z.S, L.G. van Willigenburg and G. van Straten. “Robust optimal receding horizon control
of the thermal sterilization of canned foods”, J. Food Eng, 40(3):207-218, 1999.
ICEF9-2004
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Prediction of thawing and freezing of bulk palletised butter

Nahid A(1), Bronlund J.E.*(2)., Cleland D.J.(3), Oldfield D.J.(4)., and Philpott B(5).

(1) Institute of Technology and Engineering, Private Bag 11222, Massey University,
Palmerston North, New Zealand. A.Nahid@massey.ac.nz
(2) Institute of Technology and Engineering, Private Bag 11222, Massey University,
Palmerston North, New Zealand. J.E.Bronlund@massey.ac.nz.
*Corresponding Author.
(3) Institute of Technology and Engineering, Private Bag 11222, Massey University,
Palmerston North, New Zealand. D.J.Cleland@massey.ac.nz
(4) Institute of Food, Nutrition and Human Health, Private Bag 11222, Massey University,
Palmerston North, New Zealand. D.J.Oldfield@massey.ac.nz
(5) Fonterra, Palmerston North, New Zealand Bruce.Philpott@fonterraresearch.co.nz

ABSTRACT

Butter keeping quality and pallet stability during transport and storage are dependent on the
temperature distribution through the product. This paper outlines work done on mathematically
modelling transient conductive heat transfer in bulk palletised butter. The model utilises effective
thermal properties to include the presence of packaging and entrapped air within the product.
Validation of the model against experimental data collected in a dairy factory is also presented.

Keywords: modelling, heat transfer, effective properties, bulk butter

INTRODUCTION

Bulk butter is often stored and transported at low or freezing temperatures. Such conditions help
to maximise butter keeping quality due to prevention of oxidation and microbial spoilage reactions
and also increase product rigidity and so avoid pallet instability. In order to meet customer
requirements the product is then later tempered to chilled temperatures prior to delivery in some
cases. Due to manufacturing and handling considerations a large amount of the heating and
cooling of the butter is frequently done on whole pallets of product.

Pallets of butter generally consist of a number of blocks of product (25kg) wrapped in a polymer
liner and placed in corrugated cardboard cartons. Many of these cartons (48 to 56) are then
stacked on a pallet. As a result the bulk system contains product, packaging material and air
entrapped between the packaging and butter and between adjacent cartons.

This paper outlines preliminary work on the formulation of a mathematical model for heat transfer
in the bulk butter pallet and compares the model predictions with experimentally collected
measurements carried out in a commercial cold storage facility.

EXPERIMENTAL DATA COLLECTION

A series of measurements of palletized butter cooling and thawing were set up in a commercial
cold storage facility. A single pallet (see figure 1) of freshly manufactured butter was used, made
up of 56 cartons, each containing 25kg of butter. The butter cases were made of corrugated
cardboard with single layer (4 mm) of cardboard on each face and two layers on the top and
bottom. The butter inside the cases was wrapped in polyethylene liners of thickness 0.85 mm.

The cases were re-stacked on the pallet after placing 45 thermocouples at different positions
inside and outside the butter cases. The thermocouples were then connected to a Grant Squirrel
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data logger and a Campbell data logger to record temperatures profiles throughout the pallet. The
whole pallet was then tightly wrapped in polyethyene stretch-wrap.
o
Before starting the trial, the pallet was held at 10 C for a month to ensure uniform initial
o
temperatures. The pallet was then shifted to a cool store at approximately -11 C. Temperature
readings were recorded every hour for 28 days. The pallet was kept in the cool store for another
30 days before beginning the thawing trial. At this time uniform initial temperatures were achieved
o
and the pallet was shifted to a cheese store at 10.4 C. The readings were collected every hour for
28 days.
1034

Plan
Layer 1,2,4,6 Layer 3,5,7

2042

772.5

1034 (0,0,0,)

Figure 1: Plan and elevation of butter pallet (approximate outer dimensions in mm)

MODEL DEVELOPMENT

A conduction only model (Eq 1) was developed to predict heat transfer in the butter pallet using
an enthalpy formulation and convective boundary conditions. The following assumptions were
made in formulation of the model:
*Constant density *Uniform initial temperature
*Symmetrical geometry *Homogenous medium of butter, packaging and air
*Uniform surface heat transfer *No internal heat generation
*No mass transfer or nucleation rate limitations to ice or fat crystallisation
*No evaporation or condensation occurs on the surfaces.
T
Heat transfer equation:
a3

dH ∂ ∂T ∂ ∂T ∂ ∂T
= k (T ) + k (T ) + k (T )
L dt ∂x ∂x ∂y ∂y ∂z ∂z
z

ha3 0 < x , y , z < L x , L y , Lz and t>0

T = f (H )
Boundary conditions:
ha2 ∂T ∂T
Ly Ta2 h1 (Ta1 − Ts1 ) = −k(T ) at x = 0 & t > 0 h2 (Ta 2 − Ts 2 ) = −k(T ) at x = Lx & t > 0
H(T ) ,k (T),T
∂x ∂x
∂T ∂T
h3 (Ta3 − Ts3 ) = −k(T ) at y = 0 & t > 0 h4 (Ta 4 − Ts 4 ) = −k(T ) at y = Ly & t > 0
∂y ∂y
∂T ∂T
h5 (Ta5 − Ts5 ) = −k(T ) at z = 0 & t > 0 h6 (Ta6 − Ts 6 ) = −k(T ) at z = Lz & t > 0
∂z ∂z

Lx

Initial conditions:
T = Tinitial at t =0 and 0 < x, y, z < Lx , Ly , Lz
(Eq 1)
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The model was solved numerically using MATLAB with an explicit finite difference scheme with
21x41x21 nodes in the x, y and z directions respectively. The solution was tested for
mathematical correctness by comparison with analytic solution in simplified scenarios.

SYSTEM PROPERTIES

Dimensions and composition: The pallet consists of butter, two types of packaging material and
air entrapped within the packaging and between adjacent cartons. The air and packaging present
on the outside surface of butter pallet was included in the external heat transfer coefficient (h),
whereas the air gaps and packaging inside the pallet affected the internal thermal properties of
pallet. The volume and mass fraction of different components of pallet were calculated from
physical dimensions of the pallet, butter blocks and cartons.
3
Density: Density was assumed to be constant. A value of 942 kg/m for butter was used which is
an average of over the whole temperature range [1]. The effective density of the pallet was
calculated using (Eq 2) with air, packaging and butter as the principal components.
1 n
Xi
= (Eq 2)
ρ eff i =1 ρi

Thermal conductivity: Average values of the thermal conductivity for butter were calculated from
the data reported by Middleton [1], for the frozen and unfrozen temperature ranges (Eq 3).
k = 0.2161 W / mK T >0
(Eq 3)
k = 0.2688 W / mK T ≤0
The effective thermal conductivity of the pallet depends on its configuration in terms of the
location of the packaging and entrapped air relative to the butter. The Maxwell model (Eq 4) [2]
was used to calculate the thermal conductivity, using butter as the continuous phase, and
packaging and air as discrete phases.
kd + 2kc − 2Vd (kc − kd )
keff = kc (Eq 4)
kd + 2kc + Vd (kc − kd )
This gave an effective value for the pallet of 1.9 W/mK.

Enthalpy: Enthalpy was measured using differential scanning calorimetry (DSC, Perkin Elmer
o
DSC 7). Two types of measurements were performed: By freezing the sample to -20 C and
o
then heating it up at a rate of 1 C/minute, an enthalpy curve was recorded that showed little
o
evidence of ice melting. By freezing the sample to -40 C and then heating it up at a rate of
o
1 C/minute, a significant of ice melting peak was observed. The curves were fitted with Eq (5)
without freezing and Eq (6) with freezing:

H = 2.37T + 46.74 − 20 ≤ T < 0

(Eq 5)
H = 3.997T + 46.74 0 ≥ T ≤ 20

H = 0.073T 2 + 4.0094T + 91.522 − 20 ≤ T < −3.9528

H = 1.7706T + 19.5532T + 126 .4392
2
− 3.9528 ≤ T < 0 (Eq 6)
H = 4.0252T + 126.4392 0 ≤ T < −3.9528

Heat Transfer coefficient: The effective surface heat transfer coefficient was calculated assuming
only convection from the packaging surface; with the inclusion of the additional resistance to heat
ICEF9-2004
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transfer caused by the packaging and entrapped air present on the outer surface of the pallet (Eq
7).
1 1 xp xa
= + + (Eq 7)
h ha kp ka
2 2
A value of 4 W/m K was used on the four vertical faces and 3 W/m K on top and bottom surfaces
and of the pallet due to an extra layer of packaging.

Initial and air temperatures: Air temperatures were measured on three sides of the pallet and an
average of these air temperatures was used for predictions. Initial product temperatures were
taken from the experimental data.

RESULTS AND DISCUSSION

Figure 2 shows the experimentally measured temperature profiles of the butter pallet along the
diagonal from the top left hand side corner to the centre of the pallet. Figure 2-1 shows the
general trend for freezing the butter. It was observed that the temperature inside the butter pallet
did not reach the store temperature. The offset between the butter and ambient temperature is
not due to the offset due to the thermocouples as all the thermocouples were tested in water and
ice slurry prior to the experiment.

Figure 2: Experimental data for the diagonal of the pallet layer by layer (2-1) Freezing (2-2) Thawing.
(The positions indicated are relative to bottom of the LHS of pallet as depicted in Fig 1)

Another important observation is the absence of a plateau that would normally be expected
around the freezing temperature of the water in the butter. This result is consistent with the DSC
measurements which showed an absence of a water melting peak for butter which had been
o
frozen to -20 C. The results indicate that the water in the butter is super-cooled and the latent
heat is released more slowly after 400 hours.

In contrast, the ice melting can be clearly seen in the thawing data (Fig 2-2). It is thought that ice
crystallisation occurred gradually during the time that the butter pallet was held at low
temperature before commencing the thawing trial.

Figure 3 shows comparisons between model simulations and the experimental measurements for
the pallet centre. In figure (3-1) for freezing of the butter, curve-b are the predictions if the latent
heat for water freezing is included in the enthalpy equation (Eq 6). This gives the expected
plateau around the freezing point but there is no evidence of this in the experimental data. When
the model was run with the enthalpy measured without water freezing (Eq 5), much better
predictions were achieved (curve d). This supports the hypothesis that significant super-cooling
occurs in the water droplet phase of the butter. Walstra [3] explains that super-cooling can occur
in water in oil (W/O) emulsions due to the dividing of the water phase into such small droplets that
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International Conference Engineering and Food
nucleation origins are not present in most of the particles. In addition a nucleation event in a
water droplet does not trigger nucleation in any other droplets so crystallisation in each droplet is
purely independent.

Fig3: Comparison of model predictions with experimental data (3-1) Pallet freezing: (a) Experimental data
(b) Predictions with latent heat (c) Packaging effect. (d) Without latent heat. (3-2) Pallet thawing: (a)
Experimental data (b) Predictions with latent heat (c) Predictions without latent heat.

The effects of the inclusion of packaging on the thermal conductivity can be seen by comparing
Figure 3, curves c (reduced k due to packaging) and d (k for butter only). Ignoring packaging
effects is partially valid because from the surface to the centre of pallet from its four faces there is
only a single layer of packaging in the butter and the bulk of the heat transfer occurs in the butter.
As discussed above, the packaging present on the outside of the pallet has been included in the
surface heat transfer coefficient. On the other hand, heat transfer vertically and from the other
faces flows across several layers of packaging and entrapped air so packaging cannot be ignored
completely. These results do show however that uncertainty in butter thermal properties have at
least as much importance on predictions as the presence of packaging in the pallet.

Figure (3-2) gives a comparison of experimental and model predictions for butter thawing. Two
predictions are given. Curve-c gives the predictions using (Eq 5) and over predicts the data due
to not including the latent heat of ice melting in the enthalpy data. Curve-b gives the model
predictions using (Eq 6) and is close to the experimental data. It appears from comparison of
curves-a and c that either the thermal conductivity of the butter is higher than the values used in
the simulations or the ice thawing occurs over a narrower temperature range.

CONCLUSIONS

Experimental measurements of heating and cooling of palletised butter has demonstrated that
model based prediction of heat transfer in bulk butter is not trivial. In particular water droplet
freezing is clearly mass transfer (nucleation) limited and as such, accurate time temperature
predictions require inclusion of nucleation kinetics into the model. It is also clear from these initial
studies that more accurate thermal data (thermal conductivity and enthalpy) is also required along
with consideration of the most suitable approach to characterise the effect of internal packaging
on the effective properties of the pallet.
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REFERENCES

1. Middleton J. “Physical properties of dairy products”, MAF Quality Management Ministry of

Agriculture, New Zealand. 120p, 1996.
2. Rahman S. “Food properties handbook.” CRC Press, Inc, Florida. 320p, 1995.
3. Walstra P. “Physical chemistry of foods” Marcel Dekker, Inc. New York. 571p, 2003.

NOMENCLATURE

h heat transfer coefficient Subscripts

H enthalpy
k thermal conductivity p packaging
L length of pallet i component i
T temperature d discrete phase
t time c continuous phase
V volume fraction a air
x x-direction or thickness s surface
X mass fraction eff effective
y y-direction x x-direction
z z-direction y y-direction
density z z-direction
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Modelling the small scale production of speciality malts

Robbins P.T. and Fryer, P.J.

Centre for Formulation Engineering, Chemical Engineering, University of Birmingham, UK.

Email: p.t.robbins@bham.ac.uk

Centre for Formulation Engineering, Chemical Engineering, University of Birmingham, UK.

Email: p.j.fryer@bham.ac.uk

Abstract

To improve the quality and consistency of speciality malt products greater understanding of the
processes are needed. A mathematical model of the roasting process has been developed and tested
on a spouted-bed roaster (500 g batch size). The model allows the average temperature and moisture
content of the malt to be predicted throughout the roast time. This information together with
expressions for colour development enables changes to be modelled as a function of roasting control
parameters such as temperature and time.

Keywords: Heat and Mass Transfer Modelling, Grain Roasting, Colour generation, Malt Barley.

I. Introduction
The brewing process has been in existence for millennia. It is in essence a fairly simple process using
a malted cereal and water (and more recently hops) to produce a medium which is then fermented
using brewers yeast. Few speciality malts are used in lager production as the product is low in colour
and flavour, whereas the full range of speciality malts is used in the production of the various ales
available. Speciality malts are highly coloured and flavoured products that are added into the grist (a
grind of the solid material used to make the beer) in small quantities (3 – 10%) to adjust the colour and
flavour of the beer being produced. They come in numerous varieties (1, 2) and are typically made or
finished in roasting drums with heated walls. Batch sizes of around 3 tonnes are common in industry.
In the UK, roasting was first permitted under the ‘Roasted Maltsters’ Act’ of 1842; as the process was
patented, roasted malts were sometimes referred to as patent malts (3). Speciality malts can be
divided into two main categories, dry roasted (e.g. roast barley, roast malt) and wet roasted (e.g.
crystal malt). Crystal Malt is used in premium lagers and most real ales, roast barley and other dry
roasted products are used in some ales and in stouts and porters.

The production of speciality malts is currently an artisan operation in which operators adjust the
temperature and length of run by observing product changes in colour by eye. Over-processing leads
to the incorrect product and in an extreme case can lead to combustion of the grains. As precise
flavours and colours are required by the industry, a better understanding of the process is required.
The work described here was carried out as part of a joint project between industry and academia, in
collaboration with Brewing Research International to develop such understanding.

Within a rotating drum a number of operational modes are possible depending on the rotational speed.
Differences in the trajectories and hence the temperature-time history of the grains can be expected
with consequent differences in quality between grains. The differing qualities of grains in the drum
make it unsuitable for determining fundamental kinetic data. To enable a sample of grain to be
processed uniformly a spouted bed roaster was designed and built. This system is easier to
characterise than the commercial system and allows a mathematical model of the roast process to be
developed and tested under well-defined conditions.

Two products were studied in this work. Roast barley, a dry roasted product (typical initial moisture
content 15% dry basis (db)) with a final grain temperature of ~ 220°C and Crystal Malt, a wet roasted
product (typical initial moisture content 90% db) with a final grain temperature of ~ 130°C.
ICEF9 – 2004
International Conference on Engineering and Food 2
II. Experimental Method
The spouted bed, shown schematically in Figure 1, is made of stainless steel and 70 mm in diameter
and 360 mm tall. Five 1.5mm K-type thermocouples (tc 1 to tc 5 see figure 1) are used to measure
the air inlet temperature, three bed temperatures and the exit air temperature. Air was supplied from
the compressed air main and the flowrate controlled by means of a rotameter board. A Secomak
process air heater (model 571/1) was used to heat the incoming air (150 – 350 l/min, ~ 1bar(g)) in the
range 20 – 245°C. The bed and associated pipe work is well lagged. Data is recorded and the heater
controlled by means of a National Instrument DAQ card and Labview™ software. Experimental
protocols are detailed in (4): it is possible to produce ca 300 g of product up to a maximum product
temperature of 240°C.

Flange
70

tc5

360
tc4
50
tc3
50
tc2
Cone 20 50

tc1

perforated plate 120

Flange and
Hot Air 38 gasket
25

Figure 1: Schematic cross section of Spouted Bed, all dimensions in mm. (NB tc = thermocouple).
The two parts of the bed where bolted together (not shown) through the flange and gasket.

III. Model Development

The work by Bruce (5) and then extended by Sokhansanj and Bruce (6) gave a good starting point for
simulating barley drying. A similar model was developed by Jumah et al., (7) specifically for the
spouted bed drying of corn. The model assumptions include that:

i. The grain kernels are uniform in size, are homogenous and can be considered as isotropic
spheres of radius R.
ii. The grains are perfectly mixed in the bed; hence all have the same temperature-time and
moisture-time profiles.
iii. Moisture loss is controlled by internal diffusion; water diffuses to the surface of the grain where
it is evaporated into the air stream.
iv. The grain surface moisture content is at equilibrium with the air in the bed (this comes from
(iii)).
v. The grain and the air are fully mixed within the bed, such that the properties of the exit air are
the same as the air in the bed.
vi. Conduction of heat and moisture between bed particles, heat losses and particle shape
change are negligible.

The general premise of the model is that air enters the bed at dry flowrate, ma (kg/s), temperature Tai
(K) and humidity Yai (kg water/kg dry air). This air mixes with the grain of dry mass mg (kg), average
moisture content Mav (kg water/kg dry grain) and average temperature Tgav. The air then leaves the
bed with dry air flowrate of ma, temperature Tax and humidity Yax.
ICEF9 – 2004
International Conference on Engineering and Food 3
An overall water balance across the bed gives
dM av
ma (Yax − Yai ) = −mg (1)
dt
i.e. moisture gained by air = water lost from grain

Similarly, an overall heat balance across the bed gives.

dM av
m& a ⎡⎣( Ca + CvYai ) Tai − ( Ca + CvYax ) Tax ⎤⎦ − Lg mg
dt
(2)
= mg ( Cg + Cw M av ) gav
dT
dt
i.e. change in enthalpy of air – latent heat x water loss = change in enthalpy of grain

where Ca is the specific heat of dry air (J kg-1 K-1), Cv is the specific heat of water vapour, Lg is the
latent heat of evaporation of water from the grain (J kg-1), Cg is the specific heat of dry grain and Cw is
the specific heat of water.

A set of transport equations can be used to describe water and temperature movement within the
grain. Using the assumptions noted above mass transport can be written:

∂M ( r , t ) ⎛ ∂ 2 M 2 ∂M ⎞
= D (Tgav , M av ) ⎜ 2 + ⎟ (3)
∂t ⎝ ∂r r ∂r ⎠
Initial condition assuming uniform moisture across the grain:
M ( r, 0) = M 0 0≤r ≤ R (4)

Boundary conditions:
M ( R, t ) = M e (5)
∂M ( 0, t )
=0 (6)
∂r
The average moisture content is defined by
R
4π
M av ( t ) =
∫ r ⋅ M ( r, t ) dr
2
(7)
V
0

The heat transfer can be described by:

ρ g C pg g = h ⋅ a (Tai − Tg ) + Lg ρ g
dT dM av
(8)
dt dt
with initial condition:
Tg = Tg 0 at t = 0 (9)

These equation were solved numerically with a Crank-Nicolson method being used for equation (3).
Values for the required physical properties were either found in the literature or measured
independently of the experiments (further details for roast barley can be found in (6) and for crystal
malt in (4)). The kinetics of colour change for crystal malt were found by Trauth (9), and for roast
barley by Robbins (4). They take a similar form:
dC ⎛ −B ⎞
= −k k = A exp ⎜
⎜ Tg ⎟⎟
(10)
dt ⎝ ⎠
i.e. that over some range the behaviour is essentially zero-order.
ICEF9 – 2004
International Conference on Engineering and Food 4
IV Results
The above models can be used to predict temperature, moisture and colour change of the grains with
processing time and air temperature. Figure 2 shows a typical result for the production of roast barley.
Good agreement is seen between the measured and predicted moisture and temperature of the grains
using data from the literature (4). Figure 3 shows a typical result for the production of crystal malt
using a fitted diffusion coefficient. Again good agreement is seen between the measured and
predicted grain moisture and temperature.

Figure 2: Measured and Modelled response for a roast barley experiment. Final grain temperature of
188°C.

160 100

90
140

80
120
70 Air Inlet Temp
Air Inlet Temperature
100
60 Model Grain
Temperature (°C)

Temp
%Moisture (db)

Grain Temperature Measured

80 50 Grain Temp
Model
Moisture
40
60 Measured
Grain Moisture Moisture
30
40
20

20
10

0 0
0 20 40 60 80 100 120 140
Time (mins)

Figure 3: Measured and Modelled response for a crystal malt experiment. Final grain temperature of
140°C.

Figure 4 shows the comparison of the final predicted and measured colour (from the spouted bed) for
a number of roast barley experiments. Once more good agreement is seen between the predicted
and measured results.

Figure 5 shows the comparison between the colour development during a crystal malt production on
the spouted bed and a commercial production. These are significantly different. This is because in
the commercial drum the wall is at a very high temperature, significantly hotter than the air and
average grain temperatures. The grain is only close to the hot wall infrequently but it is enough to
cause temperature spikes, which results in much greater colour development than would be predicted
from the measured average grain temperature alone. In the spouted bed, no such temperature spikes
occur and there is close agreement between the measured and predicted colour in this equipment.
ICEF9 – 2004
International Conference on Engineering and Food 5
1800

1600

1400

Colour EBC predicted

1200

1000 New data

Fit data
800 1:1 line

600

400

200

0
0 200 400 600 800 1000 1200 1400 1600 1800

Colour EBC measured

Figure 4: Comparison of the measured and predicted EBC colour for a number of roast barley
experiments. The data used to fit the model is given a square symbol, whereas new data is given the
cross symbol. There is good agreement between the model and experimental data across the whole
range of colours.

140 200

180

120
160 Commercial
Spouted Bed Grain Temperature Grain Temp

140
Spouted Bed
Temperature (°C)

100
Grain Temp
Colour (EBC)
120
Commercial Grain Temperature
Commercial
80 100 Colour

Commercial Colour 80 Predicted

Colour
60 Development
60
Spouted Bed
Measured
40 Colour
40
Modelled Colour 20

20 0
0 20 40 60 80 100 120 140

Time (mins)

Figure 5: Colour development during the roast for crystal malt seen commercially and on the spouted
bed. Both predicted and measured colour are shown for the spouted bed, whereas only the measured
colour of the commercial system. Greater colour development is seen commercially.

EBC colour is a brewing colour unit, with 0 EBC being a no colour (e.g. water) and 1600 EBC being a
very dark colour (e.g. a very dark stout). A standard larger is about 10 EBC.

V Conclusions
Speciality malts play a small but important part in the brewing process, adding unique colour and
flavour to the final beer. This project has provided quantitative information on the roast process; in
particular the grain temperature, moisture and colour changes during roasting that could enable better
control of the process.

A spouted bed has been used to study the roasting of two products roast barley (a dry roasted
product) and crystal malt (a wet roasted product) in the laboratory. A heat and mass transfer model
has been successfully used to predict the grain temperature and moisture changes during the roast.

Colour predictions where within ± 10% for both products produced on the spouted bed, however
colour development in the commercial system is seen to be greater for the same measured grain
temperature-time profile, for both roast barley and crystal malt production. This difference is due to a
hot wall effect.
ICEF9 – 2004
International Conference on Engineering and Food 6
VI Acknowledgements
Financial support for this project was provided via a LINK scheme project (AFM 88), supported by
MAFF (now DEFRA) UK, and comprising, Brewing Research International, Omron Electronics Ltd,
Pure Malt Products and J.P. Simpson & Co (Alnwick) Ltd.

VII Notation
a Specific area m2 m-3
A, B Fitted constants
C Colour EBC
Ca, Cv, Cw, Cg, Cpg Specific Heat Capacity of air, water vapour, water, J kg-1 K-1
dry grain, grain
D Diffusion coefficient m2 s-1
h Heat transfer coefficient W m-2 K-1
k Zero-order rate constant EBC s-1
Lg Latent heat of evaporation J kg-1
M, Mav, M0 Moisture content of grain, average, initial kg water per kg dry grain
ma mass flowrate of air kg s-1
mg mass of dry grain kg
r Radial co-ordinate m
R Equivalent spherical radius m
Tai, Tax Air temperature bed inlet, bed exit K
Tg, Tgav, Tg0 Grain temperature, average, initial K
V Volume of grain m3
Yax, Yai Air humidity bed exit, bed inlet kg water per kg dry air
ρg Density of grain kg m-3

VIII References
(1) Bemment D. W. (1985) Speciality Malts, The Brewer, 71, 457-460.

(2) Breiss R. C. (1986) Speciality malts and applications in brewing, Brewers Digest, 61(10), 20-21.

(3) Briggs D. E. (1998) Malts and Malting, 1st Edition, Blackie Academic & Professional, ISBN 0 412
29800 7.

(4) Robbins P.T. (2003) The Roasting of Speciality Malts, PhD Thesis, University of Birmingham.

(5) Bruce D. (1985) Exposed-layer Barley Drying: Three Models Fitted to New Data upto 150°C,
Journal of Agricultural Engineering Research, 32(4), 337-347.

(6) Sokhansanj S. and Bruce D. M. (1987) A Conduction Model to Predict Grain Temperatures in
Grain Drying Simulation, Transactions of the American Society of Agricultural Engineers,
30(4), 1181-1184.

(7) Jumah R. Y., Mujumdar A. S. and Raghavan G. S. V. (1996) A mathematical model for constant
and intermittent batch drying of grains in a novel rotating jet spouted bed, Drying Technology,
14(3,4), 765-802.

(8) Robbins, P.T. and Fryer P.J. (2003) The spouted-bed roasting of barley: development of a
predictive model for moisture and temperature, Journal of Food Engineering, 59, 199 – 208.

(9) Trauth E. (2000) Modelling of the Maillard Reaction during the Roasting of Malt, MSc Thesis,
University of Leeds.
Keyword list Modelling tools for design understanding and control

ABALONE COLD CHAIN DISCRETE ELEMENTS

AIR CURTAINS COLOUR DISPERSING
AIR FLOW COLOUR GENERATION DISTILLATION
AIR VELOCITY FIELDS COMBINED FOODSTUFF DOMESTIC REFRIGERATOR
AIRFLOW COMPARTMENT DRAG COEFFICIENT
ALCOHOL COMPOSITE FOODS DRYING
ANALYTICAL SOLUTIONS COMPOSITION DRYING OF YEAST
APPLE JUICE COMPUTATIONAL FLUID DYNAMICS (CFD) DYNAMIC GAUGING
AROMAS COMPUTER MODELING DYNAMIC SIMULATION
ARTIFICIAL NEURAL NETWORK COMPUTER SPREADSHEETS
CONFECTIONERY ECONOMIC DYNAMIC PROCESSES
BEAN HEATING CONSUMER MODELS EDIBLE BARRIER FILMS
BITTERSWEET BEVERAGE CONSUMER PERCEPTION EFFECTIVE PROPERTIES
BLANCHING CONSUMER PREFERENCE EFFECTIVE THERMAL CONDUCTIVITY
BLOWERS CONTROL EHEDG
BLOWING DUCT COOLING ELASTICITY
BULK BUTTER CRYSTALLIZATION ELECTRICAL CONDUCTIVITY
CYLINDER EMULSION
CAD ENERGY
CANNED FOODS DARCY-FORCHHEIMER-BRINKMAN ENERGY SAVINGS
CASEINS DARCY-FORSCHHEIMER ENZYMATIC COAGULATION
CFD DECONTAMINATION ERROR
CHEESE DIFFUSION
COCONUT OIL DIFFUSIVITY FERMENTATION
COFFEE ROASTERS DIPHASIC MEDIUM FINITE DIFFERENCE METHODS
Keyword list Modelling tools for design understanding and control

FINITE ELEMENT METHOD HEAT AND MASS TRANSFER JET IMPINGEMENT

FINITE ELEMENTS METHOD HEAT AND MASS TRANSFER MODELLING
FLAVOURS HEAT AND MASS TRANSFER PARAMETERS KANSEI ENGINEERING
FLOW HEAT EXCHANGER KNOWLEDGE MANAGEMENT
FLUID DYNAMIC HEAT TRANSFER
FLUID FLOW HEAT TRANSFER COEFFICIENT LASER LIGHT SCATTERING
FOAM HEAT TRANSFER HETEROGENEITY LEARNING
FOAMED PRODUCT MACROPOROUS MEDIA
FOOD MODEL HEAT- AND SHEAR-THINNING FLUIDS MACERATION
FOOD PRESERVATION HEAT-WATER TRANSFER MALT BARLEY
FOOD PROCESS MODELING HEATING RATE MASS TRANSFER
FOOD PROCESSING HOT AIR MATHEMATICAL MODELLING
FOOD QUALITY HYBRID SYSTEMS MECHANICAL PROPERTIES
FOOD SAFETY HYDRATION KINETICS METABOLIC MODEL
FOULING HYDROCOLLOID SOLUTIONS MICROBIAL KINETICS
FRACTURE HYGIENIC DESIGN MICROWAVE
FREEZING MICROWAVE HEATING
FUNCTIONAL FOODS IMMERSION FREEZING MICROWAVES
IMPINGEMENT MIGRATION MODELLING
GAS CHROMATOGRAPHY OLFACTOMETRY INDENTATION MILK
GLASS TRANSITION TEMPERATURE INDUSTRIAL PLANTS OPERATING MILK PASTEURIZATION
GREEN PEA INDUSTRIAL SYSTEMS MINIMALLY PROCESSED FOOD PRODUCTS (MPFP)
GREEN TEA INFINITE GEOMETRY APPROXIMATION MIXING
GROWTH INFRA-RED MODEL BASED SIMULATION
INVERSE HEAT INVERSE MODELING
Keyword list Modelling tools for design understanding and control

MODELIZATION PARTICLE BREAKAGE PRODUCT DESIGN ENGINEERING

MODELLING PARTICLES PROSIMPLUS
MODELLING SHELF-LIFE PARTITION COEFFICIENT PROTEIN PRECIPITATES
MOISTURE TRANSFER PASTA
MOVING BOUNDARY PASTE QSPR
MULTIDOMAIN APPROACH PASTEURIZATION QUALITY
MULTIPLE JETS PENICILLIUM CAMEMBERTII
PEPT RECEIPTS
NATURAL CONVECTION PHENOLS EXTRACTION REFRIGERATED DISPLAY CABINET
NEURAL NETWORK PHYSICAL REFINING REFRIGERATED DISPLAY CABINETS
NEUTRAL OIL LOSS PLATE HEAT EXCHANGER REFRIGERATION
NEWTONIAN FLUID PLATE HEAT EXCHANGERS RESPONSE SURFACE METHODOLOGY
NUMERICAL METHODS POLIPHENOL OXIDASE (PPO) REVERS FLOW VISCOMETER
NUMERICAL MODELLING POROUS MEDIA RFC
NUMERICAL SIMULATION POSTHARVEST STORAGE RICE
NUMERICAL SOLUTION POTATO RIPENING
POTATOES ROSEMARY
OHMIC HEATING POWER LAW
OHMIC THAWING PREDICTIVE MICROBIOLOGY SACCHAROMYCES
OPERATING CONDITIONS PREDICTIVE MODELLING SCRAPED SURFACE HEAT EXCHANGERS
OPTIMISATION PRESSURE DROP SENSITIVITY ANALYSIS
OPTIMIZATION PROBLEM FORMULATION SENSORY EVALUATION
ORANGE JUICE PROCESS DESIGN SEPARATION
PROCESS ENGINEERING SESAME-SEASONED DRESSING
PROCESS SIMULATION SHELF-LIFE
Keyword list Modelling tools for design understanding and control

SHELF-LIFE PREDICTION TUBULAR HEAT EXCHANGER

SIMULATION TURBIDIMETRY
SMOKE TURBULENCE
SOLID-STATE FERMENTATION TYLOSE
SOLVENT EXTRACTION
SORPTION ISOTHERMS UNIFORMITY
SPAGHETTI
SPOUTED VELOCITY
SST VELOCITY MEASUREMENT
STATE DIAGRAM VISCOELASTIC
STERILIZATION VISCOSITY
STRENGTH VISCOUS DISSIPATION
SUGAR VISCOUS FOODS

TEMPERATURE WATER ACTIVITY

TEXTURE WATER DIFFUSION
TEXTURE ANALYSER WEAR
THAWING WHEY PROTEINS
THERMAL DIFFUSIVITY WINE
THERMAL EXPANSION WINE CHARACTERISTICS
THERMAL LETHALITY WINE FERMENTATION PROCESS
THERMAL PROCESS WINE MAKING
THERMO-MECHANIC WIRE CUTTING
TRANSFER FUNCTION YEAST GROWTH-CYCLE
TRANSIENT TRANSFER YOGHURT