International Journal of Multiphase Flow 91 (2017) 120–129

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International Journal of Multiphase Flow

journal homepage: www.elsevier.com/locate/ijmulflow

Investigation of pressure drop in horizontal pipes with different diameters

F.A. Hamada,∗ , F. Faraji a, C.G.S. Santimb, N. Bashaa, Z. Ali a
a
School of Science & Engineering, Teesside University, Middlesbrough, TS1 3BA, UK
b
Faculty of Mechanical Engineering, University of Campinas, CEP: 13083-860, Campinas, Brazil

artic l e i nf o abstrac t

Article history: The pressure drop has a significant importance in multiphase flow systems. In this paper, the effect of the volumetric quality and
Received 27 August 2016 mixture velocity on pressure drop of gas-liquid flow in horizontal pipes of different diameters are investigated experimentally
Revised 8 January 2017
and numerically. The experimental facility was de- signed and built to measure the pressure drop in three pipes of 12.70, 19.05 and
Accepted 23 January 2017
25.40 mm. The water and air flow rates can be adjusted to control the mixture velocity and void fraction. The measurements are
Available online 27 January 2017
performed under constant water flow rate (CWF) by adding air to the water and constant total flow rate (CTF) in which the flow
Keywords: rates for both phases are changed to give same CTF. The drift-flux model is also used to predict the pressure drop for same cases. The
Air-water flow present data is also compared with a number of empirical models from the literature. The results show that: i) the pressure drop
Pressure drop increases with higher volumetric qualities for the cases of constant water flow rate but decreases for higher volumetric qualities of
Horizontal pipes constant total flow rate due to the change in flow pattern. ii) The drift-flux model and homogenous model are the most suitable
Experimental measurement Drift- models for pressure drop prediction.
flux model
© 2017 Elsevier Ltd. All rights reserved.

1. Introduction In horizontal flow, the phases tend to separate due to the dif- ference in
densities and the effect of fluid gravity, thereby causing a form of stratification. The
The application of single and multiphase flow has been fre- quently heavier fluid tends to concentrate at the bottom of the pipe whereas the lighter
observed in many diverse fields of science and engineer- ing such as agricultural, fluid concentrates at the top. Several flow patterns can be observed during the flow
biomedical, chemical, food science and petroleum engineering. It is necessary to of mixed phases as flow rates of water and air are varied. These flow patterns also
predict design parame- ters such as friction factor, pressure drop, bubble size, void depend on the physical properties of the fluids such as the density and viscosity,
fraction, heat and mass transfer coefficient in order to determine the de- sired surface tension and the flow system geometry.
operating conditions and the size of the equipment required for the specific According to Awad (2012) the formation of specific flow pattern is governed by
application. The pressure drop in horizontal pipes is the parameter to be competition of different forces in the system such as momentum, viscous,
investigated in this paper gravitational, and surface tension. When the momentum force in two-phase flow is
The pressure drop in horizontal pipes has been studied by a number of dominant, the bubbles tend to disperse uniformly into the pipe. This usually
researchers to develop empirical models to use in the design of new equipment. occurs at high mixture flow rate, which leads to a bubbly flow.
However, there is no general model available to predict the pressure drop within The pressure drop of a fluid is due to the variation of kinetic and potential
acceptable accuracy (Michaelides, 2006). This is attributed to the complexities energy of the fluid and that is due to friction on the walls of the flow channel.
inher- ited from the single-phase flow like the non-linearity, transition to turbulence Therefore, the total pressure drop is represented by the sum of the static pressure
and instabilities plus additional two-phase characteris- tics like motion and drop (elevation head), the momentum pressure drop (acceleration) and the fric-
deformation of the interface, non-equilibrium effects and interactions between the tional pressure drop. Here the most problematic and important term is the
phases (Ghajar, 2005). frictional pressure drop, which can be expressed as a function of the two-phase
friction factor.
Two distinct approaches are available from engineering point of view in
∗
Corresponding author. accounting for the behaviour of multiphase flow sys-
E-mail addresses: f.hamad@tees.ac.uk (F.A. Hamad), foadfaraji5@gmail.com
(F. Faraji), christianosantim@gmail.com (C.G.S. Santim), n.mehboobbasha@tees.ac.uk (N. Basha),
z.ali@tees.ac.uk (Z. Ali).

http://dx.doi.org/10.1016/j.ijmultiphaseflow.2017.01.007 0301-9322/©
2017 Elsevier Ltd. All rights reserved.
 F.A. Hamad et al. / International Journal of Multiphase Flow 91 (2017) 120–129 121

tem. The first is a global approach that relies on the practical method in Table 1
The values of coefficient C (Holland and
developing simplified models that contain parameters,
Bragg, 1999).
which are evaluated from the experimental data (Lockhart and
Martinelli, 1949; Friedel, 1979; Mishima and Hibiki, 1996; Chen et al., 2001). The Liquid Gas C

second is a continuum approach in which more complex physically-based Turbulent Turbulent 20

models are used to describe the flow phenomena (Ivor, et al., 2004; Beattie and Viscous Turbulent 12
Whalley, 1982; Awad and Muzychka, 2014a, b). The two-phase frictional pressure Turbulent Viscous 10
Viscous Viscous 5
drop in gas-liquid flow is determined by either finding of two-phase fric- tion
factor (homogeneous flow model) or a two phase friction mul- tiplier (separated
flow model). A summary of the empirical models is given hereafter.
2.2. Separated flow models
2. Review of two-phase frictional pressure drop correlation
2.2.1. Lockhart-Martinelli (1949)
2.1. Homogeneous flow model The Lockhart-Martinelli pressure drop correlation is the most typical form of
separated flow model. A majority of correlation that has been proposed by many
In Homogenous model, it is assumed that there is no slip be- tween the two researchers such as (Friedel, 1979; Mishima and Hibiki, 1996; Chen et al., 2001)
phase flow at similar velocities. However, with an exception for very small were proposed on the basis of two-phase friction multiplier suggested by Lockhart
values of void fraction (bubbly flow region) there exists a significant slip and Martinelli (1949) and the fitting correlation of the multipliers from Chisholm
between the two phases (Bhagwat and Ghajar (2014)). (1983).
The frictional pressure drop equation is the Darcy equation which uses Lockhart and Martinelli (1949) performed the most represen- tative
Blasius relation to calculate the friction factor from the average mixture investigation that developed the theory of separated flow model. Their work
properties. The Blasius equation for two-phase flow is represented by: based on experimental analysis of a circular pipe with the diameter ranging from
1.48 to 25.83 mm using two phase mixture of air with benzene, kerosene, water
and several oils. Their work was based on two hypotheses, the first assumption
states that the static pressure drop for both liquid and gas phases
m,
fTP = 0.079/Re−0.25 (1) are the same regardless of the flow pattern as long as the changes
where Rem = Gmd/μm is the mixture Reynolds number, fTP is the two-phase in radial direction are not significant and the second assumption states that the total
flowfriction factor, Gm: mass flus (kg/m2s), d isthepipe diameter (m) volume of the pipe is equal to sum of the vol- ume occupied by gas and liquid at
The mixture viscosity (μm) is represented as in Awad (2014), in terms of the any instant (continuity equa- tion). Based on these assumptions and their
mass quality (x): experimental analysis, Lockhart and Martinelli (1949) developed the concept of two-
μm = xμg + (1 − x)μl, (2a) phase flow multipliers which can be used to calculate the two-phase flow pressure
2 drop (dp/dx)TP as ((Holland and Bragg, 1995):
Where x is the mass quality, μg is the gas viscosity (N.s/m ), μl is . Σ . Σ
dp dp
the liquid viscosity (N.s/m2) .
= φl
2 (5)
Rodrigo et al., (2016) studied experimentally the pressure drop dx dx
TP l
of multicomponent zeotropic mixtures boiling in small channels Chisholm (1983) developed the theoretical basis to calculate the liquid phase
over temperatures ranging from 100 K to room temperature along multiplier φ2 from the following simplified correla-
l
with the sensitivity of frictional pressure drop to parameters such tion,
as mass flux, pressure, tube diameter, and mixture composition. The measured
φ2 = 1 c 1 , (6)
data were compared to several pressure drop cor- + + 2
l
relations available in the literature. They found that Awad and Muzychka X X
(definition 1) correlation (Awad and Muzychka, 2008) where
,
for multiphase flow viscosity was able to predict the pressure drop over the range of X = (dp/dx)l/(dp/dx)g. (7)
experimental data considered, with an Absolute Average Deviation (AAD) of 17%.
The values of C are into the range of 5 ≤ C ≤ 20 for different flow regimes,
Awad and Muzychka (2008) (defi- nition 1) is also used in this study to predict the
as given in Table 1.
pressure drop for all the tests in present work. The viscosity is given as:
2.2.2. The Friedel correlation (1979)
2μl + μa − 2(μl − μa)x Friedel model is one of the most accurate methods to deter- mine the pressure
μ2ph =μ l (2b)
2μ +l μa + (μ −l μa)x drop in two-phase flow (Quiben (2005)). Friedel
Whereas, the mixture density ( ρ m) can be evaluated as (Awad and Muzychka, developed a correlation based on 16.000 measured data points and for wide
2008; Awad 2015): range of pipe diameters. The model includes the gravity effect through the
Froude number (Fr), the effects of sur- face tension and total mass flux using the
ρm = αρg + (1 − α)ρl (3) Weber number (We) (Suwankamnerd and Wongwises, 2014).
Where α is void fraction, ρg is the gas density (kg/m ), ρl is the liquid density,
3
The two-phase flow pressure drop, ( dp)TP candxbe obtained as:
3
(kg/m ) on the above average properties, two phase frictional
Based
. Σ . Σ
pressure drop for horizontal tube of internal diameter, d is calcu- dp dp . (8)
lated as: dx =φ 2lo dx
2 TP lo
2 fTPG l 2
Op = ρmdm (4) Where φlo is the two-phase friction multiplier based on pressure
gradient for total flow assumed liquid. It can be calculated from
Where l is the length of the pipe. The homogenous model becomes the following equation:
more accurate for density ratio lower than 10 and mass flux lower 2 3.24F H
2
than 2000 kg/m s (Crowe, 2006). φlo = E + , (9)
Fr0.45We0.035
122 F.A. Hamad et al. / International Journal of Multiphase Flow 91 (2017) 120–129

The Froude and weber numbers are given respectively as Fr = 3. Experimental facility
G2m G2 d
and We = m , where σ is the surface tension. The dimen-
ρmσ The experimental facility shown in Fig. 1 is designed and built
m
gdρ2
sionless parameters F, H and E (Thome, (1990)) are defined as fol-
at Teesside University, to investigate the pressure drop for single and two-phase
lows:
flows pressure drop. The test rig has three PVC transparent pipes of 1 m in length
ρl fgo
E
=
(1 − x)2 +x2 , and inner diameters of 0.0127 m, 0.01905 m and 0.0254 m. The main components of
ρg flo the test rig are the water centrifugal pump, air compressor, water and air flow me-
ters, water tank, and differential pressure transducer.
F = x0.78(1 − x)0.224, To generate air-water mixture, the water is pumped from the
tank to the test section using a centrifugal pump. Then, the air is
Σ0.91. Σ0.19.
μ Σ0.7
.
ρl μ g supplied from the main compressor in the building via a filter and
H=
ρg μl pressure regulator, this is done to minimise the fluctuation in air
g flow rate. The air and water flow rates are measured by the flow
1− .
μl pressure regulator, this is done to minimise the fluctuation in air
flow rate. The air and water flow rates are measured by the flow
The flo and fgo can be calculated from the single phase fric- tion correlation meters at the upstream of the mixing point.
(Blasius equation) based on liquid Reynolds num- ber, (Relo = Gd/μl ) and gas In this investigation, the measurements are performed under constant water
Reynolds number (Rego = Gd/μg). From Blasius equation: flo = 0.079/Re0.25 and flow rate (CWF) by adding air to the water and con- stant total flow rate (CTF) in
fgo = 0.079/Re0.25. lo go which the flow rates for both phases are changed to give same CTF. The water flow
The pressure drop for assuming the total flow is liquid, (dp/dx)lo can be rate up to 40 l/min was measured by the digiflow 6710M meter. The air flow rate was
calculated as,
. dp Σ 2 floG2vl measured by Platon air flow meter with accuracy of ± 1.25%. The differential
= (10) pressure transducer (C9553 COMARK) is connected to the test section by two
dx d
lo flexible plastic tubes via two taps at inlet
Where vl is the liquid specific volume (m3/kg) is Thus, the two- phase flow and exit of the pipe. The images of flow patterns are obtained by a high-speed digital
pressure gradient can be obtained by substituting the Eqs. (9) and (10) in Eq. (8). camera (NiKon 1J1). Due to the limited length of the pipes, a perforated pate was
used a flow conditioned eliminate velocity profile distortion and uneven void
fraction distribution.
3.1.1. Muller-Steinhagen and heck
Muller-Steinhagen and Heck (1986) proposed the following two-phase
4. Numerical solution
frictional pressure drop correlation based on all liquid flow and all gas flow,
A Roe-type Riemann solver based on drift-flux model proposed by Santim and
. Σ Rosa (2016) was used to calculate the pressure drop
dp numerically. The model is assumed to be isothermal with no mass transfer between
= GMS (1 − x)
1/3
+ Bx (11) the phases. The system of equations for the con- servation laws is given by Eqs.
dx
TF (15)–(17). The first two equations
where the factor GMS is defined as, consist of mass formulations for each phase i.e, liquid and gas and
the last equation for the mixture momentum conservation.
GMS = A + 2(A − B)x. (12)
∂ ∂
Assuming the total flow is liquid, the pressure drop (dp/dx)lo can be [(1 − α) ρ l] + [(1 − α ) ρlu l] = 0, (15)
calculated as: ∂t ∂x
. Σ ∂ ∂
dp 2floG2vl (αρ ) + (αρ u ) = 0, (16)
A= dx = d . (13) ∂t g
∂x g g

dx d
lo

Similarly, the pressure drop for assuming the total flow is gas ((dp/dx)go): ∂ ∂Σ Σ
[(1 − α)ρ u + αρ u ] + (1 − α)ρ u2 + αρ u2 + P = F ,
. Σ l l gg
∂x l l g g W
∂t
dp 2 fgoG vg 2 (17)
B=
dx
=
d . (14)
go where P is the pressure, α represents the void fraction, ρ is the
density, u is the velocity, with the subscripts l and g refer to the liquid and gas
The literature review presented above shows that in spite a number of
phases. The last term on Eq. (17), FW, is a momen- tum source term that represents
empirical models developed to predict the pressure drop of multiphase flow,
the wall friction force and is given as:
there is still a dearth of research work needed in this area as there are no reliable
models that can be
used for different geometries and flow patterns. Hence, the pur- pose of this paper ρm|um|um (18)
FW= f
is twofold. The first is to collect new experi- 2d
mental data on pressure drop for various pipe diameters with dif- ferent flow In which um = (1 − α)ul + αug represents the mixture velocity, ρm = αρg +
patterns (Teesside University) at Constant Water Flow rate (CWF) where the air is (1 − α)ρl is the density of mixture in terms of the void fraction, f represents
added to the water. In addition to Con- stant Total Flow rate (CTF) where the flow the friction factor and d is the ID pipe.
rates for both phases are changed to give CTF. The second is to examine the The friction factor (f) depends on Reynolds number of the mix- ture (Rem),
possibility of using the drift-flux model (utilizing the approximate Riemann which is defined as:
ρm|um|d
solver proposed by Santim and Rosa (2016) to predict the pressure Rem = , (19)
drop for two-phase flows by comparing the experimental data with μm
predictions from the model. In addition, the present experimental measurements are where μm is the mixture viscosity. The relation proposed by Beattie and
also compared with predictions from empirical models in the literature. Whalley (1982) is used: μm = (1 − α)μl (1 + 2.5α) + αμg in the range 0 < α
< 1.
 F.A. Hamad et al. / International Journal of Multiphase Flow 91 (2017) 120–129 123

Fig. 1. Schematic diagram of the experimental rig.

For laminar flows, the friction factor is defined as f = 64/Rem. The implicit length is too short or flow to fully develop and achieve a define defined flow
relation proposed by Colebrook, Eq. (21), is utilized pattern.
to calculate f for turbulent flows since the Eq. (20), proposed by , . Σ
ρ g −18α
Haaland, is assumed as an initial guess for Colebrooks´ equation. 2 ρl
1.2− 0.2 1−e
+ ,
6.9 Σ
.. Σ C0 = . Rem 2 Σ . 1000 Σ2 (24)
1
, = −1.8 log ε 1.11
, (20) 1+ 1+ Rem
3.7D + Re 1000

f m . Σ1/4
. Σ ud = C cos (θ ) + D gσ Oρ sin(θ ). (25)
1 ε/D 2.51 ρ2
l
, = −2 log + , , (21)
f 3.7 Rem f The discretization scheme used in the simulations is an upwind
discretization as demonstrated by Leveque (2002), in which the
discretization as demonstrated by Leveque (2002), in which the
where ε represents the equivalent roughness of the pipe, consid- ered as 10−9 vector U of conservative variables has its components Ui evaluated using an
m. explicit numerical procedure depicted below:
The thermodynamic state equations for the liquid and gas den- Σ _ +
Σ
m
. .
m
sities are expressed in terms of the sound velocities, cl and cg, as Ot (λp) wp (λ p w
p , (26)
presented below Uin+1 = Un i− Ox +
) , (26)
presented below i i
Ox p=1
i+1/2
p=1
i−1/2
P − Pl,0
ρl = ρ and ρ P
l,0 + g = , in which,
c2l c2g
βi−1/2 = R−1(Ui − U ) and wp = βi−1/2
p
rp, (27)
where ρ l,0 and Pl,0
i−1 i−1/2
are given as constants.
The system of the conservation laws, given by Eqs. (15)–(17), can be written where w represents the waves crossing the cells’ interface, λ− and
in the conservative form, as: λ+ are the characteristic velocities (superscript ’-’ means left going waves). The
∂U ∂F matrix R represents the right eigenvector matrix, and p is the counter of
+ = S, (22) eigenvalues (m is the total number).
∂t ∂x This explicit scheme must satisfy a CFL (Courant-Friedrichs- Lewy) condition
where U, F and S are the vectors of the conservative variables, fluxes and as stability criterion:
source terms written as follows: Ot
. Σ . Σ . Σ < 1.
U1 (1−α)ρl F1 |λmax|
Ox
(28)
U = U2 ≡ αρg F = F2 F3 The wall friction force source term is treated using the Fractional-Step
U3 (1 − α)ρlul + αρgug method studied by Leveque (2002). The hyperbolic
. Σ . Σ . Σ
(1 α ) ρ u l
− l S1 0 system is split into two sub-problems which are solved indepen- dently. The first
≡ αρgug S = S2 ≡ 0 . (23) consists of a homogeneous system using the up- wind scheme previously
(1 − α)ρlu 2 + αρgu2 + P FW presented in Eq. (26).
g S3 Σ
l
Σ .m
Ot (λ )
m _ + p
. p
Since the system has three equations and four unknowns, we U∗ = Un − (λp) wp + w (29)
need to obtain the system closure by using of a drift-flux rela- i i
Ox i+1/2 i−1/2
p=1 p=1
tion. The relation chosen was ug = C0um + ud, presented by Zuber
and Findlay (1965). The parameter C0 and the drift velocity ud are defined primarily The ODE must be solved in a second step, as
considering the fluid transport properties and
sometimes by the flow pattern regime. The drift parameters imple- Uin+1 = U ∗ −i OtS . 3 (30)
mented on the solver were proposed by Choi et al. (2012) and are pattern To obtain a numerical solution on pressure drop along a pipe, a spatial mesh
independent. This correlation was chosen since the pipe with 100 nodal points is chosen after a mesh test,
124 F.A. Hamad et al. / International Journal of Multiphase Flow 91 (2017) 120–129

The results show that the pressure drop increased significantly for small pipe
diameter. To have a better understanding of this effect, the variation of pressure
drop with volume fraction for the same water Reynolds number (Re = 26,000)
considering three pipes is given in Fig. 3d. The results show that reducing pipe di-
ameter lead to nonlinear increase in friction pressure drop similar to single phase
flow which can be approximated by the follow- ing formula: Op = 4.733d−1.45,
this formula is given by Bhagwat et al. (2012). A similar finding was reported by
Kaji and Azzopardi (2010) for air-water flow in vertical pipes of diameters in a
range of 0.010 m – 0.050 m.

5.3.1. Pressure drop and flow pattern

From the visual observation of the flow pattern during the pres- sure drop tests,
it is possible to verify that the flow pattern in the pipe is changed. To
investigate this in further detail, the wa- ter single phase flow of 40 l/min in 0.0254
m diameter is selected to observe and the flow pattern for both CWF and CTF at
Fig. 2. Comparision of measured single phase flow friction factor with prediction from Blasius different volumetric qualities. Fig. 4a shows the pressure variation for the
correlation. vomumetric qualities under investigation.
The corresponding flow pattern at points 1, 2, 3, 4, 5 and 6 are given in Fig. 4b
and c. The flow patterns are observed visually and recorded photographically using
and a temporal mesh with 20,000 points is used. Finally, the tran- sient simulation is
High Speed Camera for water flow rate of 40 l/min in 0.0254 m ID pipe. For CWF
halted to record the results when it reaches the steady state. cases (Fig. 4b), the photos show that two different zones of bubbly flow and water
can
5. Results and discussion be observed. For lower air flow rate of 5 l/min (β =11.1%), bubbly
flow of 1 cm height is formed in the upper part of the pipe while water zone of 1.5
5.1. Single phase pressure gradient cm height flow in the rest of the pipe separated by wavy interface. The thickness of
the bubbly flow zone expand further down to become 1.5cm for air flow of 15 l/min
The single-phase flow measurements are carried out to validate the experimental (β = 27.3%) and 2 cm for air flow rate of 25 l/min (β = 38.5%). The large long
facility along with the accuracy of instrumenta- tion and thereby set the reference bubbles appears near the upper pipe wall at the upper region of the bubbly flow
velocities to be used for the comparison with two-phase flow measurements. The zone for β = 38.5%.
pressure drop data for different water flow rates is recorded and this is used to For the CTF, the photos show that by replacing 5 l/min (12.5%) of water with
calculate the friction factor by applying Darcy equation for smooth pipe as: air, generates two layers of the flow similar to flow pattern at point 1 for CWF.
Opd Increasing the air to 15 l/min
fexp = . (31) (β = 37.5%) leads to an appearance of air of about 0.6 cm thickness
2Lρv2
at the top, water layer at the bottom of the pipe and this bottom layer is separated
Fig. 2 presents the comparison of the experimental friction factor fexp with by a middle layer of bubbly flow. The bubbly flow lies in the central region of
predicted values from Blasius correlation ( f = 0.079/Re0.25) for each flow rate the pipe. The flow in the middle layer is very chaotic and has unstable wavy
(Re). The error associated with the pressure drop measurements proves to be quite interface with air and water. A similar flow pattern is observed for higher air flow
reasonable (± 10%). The discrepancy in the data compared to well-known rate of 25 l/min (β = 62.5%), but the layer of air becomes thicker and water layer
correlation developed by Blasius may attributed to the inaccuracy of flow me- ters becomes thinner.
and pressure transducer and the change in temperature due the heat added by the The changes in volumetric quality (β), flow structure and pres-
pump. The temperature affects the density and viscosity of the fluid used in sure drop in photos of Fig. 4b & c indicate the strong correlation between the
calculation of Renolds number used in calculation of friction factor. pressure drop and the flow structure. The pressure drop is a result of energy
dissipation, eddy viscosity and bubble induced turbulence. Energy dissipation
5.2. Two-phase flow measurements occurs due to the fluid vis- cosity and eddy viscosity occurs due the wall
generated turbu- lence. In case of two-phase flow, the turbulence becomes more
The frictional pressure drop in this study was investigated with two complicated due to: i) the interaction between the drop-induced turbulence
different methods of two-phase generation. In the first method, air is injected (bubble motion) and shear–induced turbulence (the ex- ternal force due to main
while the water flow rate kept is constant, hence that increases the total mass flow flow). ii) The modification of water ra- dial velocity distribution due to the radial
rate and β of mixture. This method is called Constant Water Flow (CWF). In the distribution of bubble slip velocity, bubble diameter and volume fraction. To add
second method, the total flow rate of the mixture is kept constant and the flow rate is to this, the introduction of bubble can either enhance or attenuate the liq- uid
changed for both the phases, this leads to a two-phase flow. This method is called turbulence (Serizawa and Kataoka (1990); Hamad and Ganesan (2015).
Constant Total Flow rate (CTF). For CWF, the results show that the increase in β The modification in energy dissipation (pressure drop) may be attributed to
lead to an increase in the mixture mass flux and the pressure drop. This is a (Hamad and Ganesan (2015): i) the breakup of large scale eddies containing higher
similar trend that was observed by Muller-Steinhagen and Heck (1986), Shannak energy by the bubble moving faster than water. ii) The drop wake turbulence due the
(2008) and Hamayun et al. (2010). In contrast to the CWF cases, the results show slip velocity be- tween the drops and the continuous phase in bubbly layers gen-
that an increase in β lead to a reduction in mass velocity and pressure drop. The erate additional turbulence as described by Risso et al. (2008). iii) The unstable
measured pressure drop for CWF and CTF are presented in Fig. 3a, b and c, relative fluctuating interface zone between the layers can be
to the 0.0254 m, 0.01905 m and 0.0127m ID, respectively.
 F.A. Hamad et al. / International Journal of Multiphase Flow 91 (2017) 120–129 125

a b

c d

Fig. 3. (a) Variation of measured pressure drop for the CWF and CTF rates in 0.0254 m pipe with volumetric quality. (b) Variation of measured pressure drop for the CWF and CTF rates in 0.01905 m pipe with
volumetric quality. (c) Variation of measured pressure drop for the CWF and CTF rates in 0.0127 m pipe with volumetric quality. (d) Effect of pipe diameter on pressure drop (Re = 26,000).

considered as an addition wall due to the velocity difference be- tween the two to predict the pressure drop. For all simulations the system shows to be hyperbolic.
layers which lead to generation of addition eddies. Fig. 5 represents a comparison between the experimental pres- sure drop and the
numerical prediction as a function of the mix- ture Reynolds number. The results
5.3.2. Experimental uncertainties show that there are different representative zones: i) for 0 < Re < 75,000, the
The experimental uncertainty is a combined effect of pipe di- mensions data is not scat- tered, ii) for 75,000 < Re < 125,000, there is a high scatter and
(length and diameter and surface roughness), the accu- racy of instrumentation (flow iii) Re> 125,000 the pressure drop increases smoothly. These three zones are similar
meters and pressure transducer), the fluid properties (density, viscosity and surface to laminar, transition and turbulent flow for sin- gle phase flow. The comparison
tension) and the op- erating conditions (flow rate and temperature). The effect of proves that the drift-flux model can be used for pressure drop prediction of two-
these variables will lead to some error in pressure drop measurements. The error phase flows.
can be estimated using the available statistical correla- tion and incorporated into
the plotted graph as error bars. Fig. 4d present the experimental data for two-phase
5.5. Comparison of present pressure drop data with empirical models
flow with error bar. The height of the bars reflects the level of uncertainty at the
dif- ferent Reynolds numbers. It can be observed that the uncertainty is peaked for
The investigation was carried out for three horizontal pipes of different
Re in the rage of 75,000 −125,000 reflecting the high instability of the flow this
diameters using air-water mixture. Table 2 provides the range of various
parameters used in the experiments.
5.4. The drift-flux model The measured pressure drop values have been compared with the predictions
from the most common existing empirical models, the models selected for this
The model takes into account the effects of non-uniform veloc- ity and void purpose are Lockhart and Martinelli (1949), Friedel (1979), Müller-Steinhagen and
fraction profiles as well as effect of local relative ve- locity between the phases Heck (1986), Awad and Muzychka, (2008) and the homogeneous model. The
(Shen et al., 2014). The relative motion between the phases is governed by a subset most of the above-mentioned models are applicable for smooth pipes. Therefore,
of the parameters in- herent to the flow. The model comes from the Two-Fluid the test conditions of the present experimental data in transparent acrylic pipes are
model (TFM) through neglecting the static head terms and assuming the applied to the above-mentioned mod- els. The comparison between the
momentum conservation of the mixture. Therefore, a third bound- ary condition is measurements and the predic- tions are presented in Figs. 6–9.
not necessary at the inlet region and the interfacial friction term is cancelled out. The accuracy of the predictions can be measured by calculating the average
Other advantage is that the equa- tions can be put in a conservative form, percent error (APE) and average absolute percent error (AAPE) of each data source.
facilitating to discretize by finite volume methods. The system of the conservation The percentage error at each point (PE) can be calculated as:
laws is generally hyperbolic depending on the slip law used.
Σ (dp/dx) − (dp/dx) Σ
The approximate Roe-type Riemann solver proposed by Santim and Rosa pred exp
PE =100. (32)
(2016), which is based on the Drift-Flux model, is applied (dp/dx)exp
126 F.A. Hamad et al. / International Journal of Multiphase Flow 91 (2017) 120–129

a b

Fig. 4. (a) Variation of the pressure drop with CWF and CTF in the pipe of 0.0254 m. (Water flow rate = 40 l/min). (b) Photographs of CWF cases (d = 0.0254 m, 40l/min). (c) Photographs of CWF (d = 0.0254 m, 40 l/min).
(d) Experimental data for pressure drop with error bars.

Table 2
Experimental measurements.

Pipe ID (m) No of tests Flow Type Usw (m/s) Usa (m/s) β (%) Op (Pa) Rem

min max min max min max min max min max

0.0254 19 CWF 0.66 1.32 0 0.822 0 55 260 1300 15,000 65,000

0.0254 14 CTF 0.16 1.32 0 0.82 0 75 160 750 15,000 46,000
0.0191 24 CWT 0.585 0.234 0 1.46 0 72 1000 4800 130,005 95,000
0.0191 20 CTF 0.29 2.33 0 1.4 0 83 240 2800 13,300 77,000
0.0127 24 CWF 1.21 5.26 0 3.28 0 71 5000 33,000 33,000 190,000
0.0127 19 CTF 0.65 5.26 0 3.28 0 83 1200 21,000 24,000 125,000

The average percentage error is defined as follows: the absolute errors are considered so that the positive and nega-
. Σ ΣΣ tive errors are taken into account (the positive and negative errors
1.
n (dp/dx) pred − (dp/dx) exp arenot cancelled out). Theequationisgiven as:
APE = 100. (33)
n (dp/dx)exp
k=1

Eqs. (32) and (33) are used to estimate the error of individual points and ⎡ ⎤
average error of the data. The average abolute percent- Σ. Σ2 Σ1/2
n
. 1 ( dp/dx )pred − (dp/dx )exp
age error (AAPE) is calculated to evaluate the prediction capability
AAPE = ⎣ ⎦ 100. (34)
of the emprical correlation. Unlike the average percent error (APE), n (dp/dx)exp
of the emprical correlation. Unlike the average percent error (APE), k=1
(dp/dx)exp
 F.A. Hamad et al. / International Journal of Multiphase Flow 91 (2017) 120–129 127

Fig. 5. Comparision between the experimental data and prediction from drifit flux model.

Fig. 7. Comparison of experimental data with Lockhart-Martinelli model.

a

perimental data within acceptable error and can be recommended as a guide for
pressure drop prediction in multiphase flow systems. The Friedel model gives the
highest percentage of errors and not recommendable for pressure drop prediction of
multiphase flow in horizontal pipes.
Through analysis of Fig. 6a & b, it can be observed that the assumption of
multiphase flow as homogeneous flow is reason- able as the trend lines of
experimental and predictions are very close. Ghajar (2005) considers that the
homogenous model is more suitable for predicting pressure drop in bubbly flow
patterns. The present results also confirm this behaviour once the homogenous
model gives more accurate results for the bubbly flow cases of CWF and the low
air flow rate (5 l/min) for CTF. The error increases for the cases of CTF with high
volumetric quality when wavy strat- ified flow is observed. The discrepancy can be
related to the orig- inal assumption, which is made in the equation of the
homoge- neous model, that the flow is homogenous and the velocities of the
gas and liquid are the same.
b By analysis of Fig. 7, it can be verified that the Lockhart- Martinelliḿodel is
suitable for CWF cases as the error is lower compared to CTF. The higher error for
CTF may be attributed to the change in the flow pattern to wavy stratified flow
similar to ho- mogenous model. Spedding et al. (2006) found that the Lockhart-
Martinelli over/under predicts the data within ± 40% error espe- cially in higher
mass velocity values which are much higher than present study. Awad and
Muzychka (2014a) and Quiben (2005), recommended that Lockhart-Martinelli as
one of the best methods that can be used for predicting pressure drop in two-phase
flow as it can be used for any flow pattern. The results in Fig. 7 demon- strate that
at higher mass flux (Reynolds number) of the mixture, this method under predicts
the data. This may be attributed to the assumptions considered in the development
of the model such as:
i) interaction between the two-phases is ignored, ii) the accelera- tions and static
heads for the phases are neglected, therefore the pressure drop in gas and liquid
phases is assumed to be the same. From Fig. 8, it can be seen that the Friedel model
gives a high discrepancy compared to the other correlations which is reflected in
average error of 56% as given in Table 3. As it can be verified from the comparison,
this model over predicts the experimental data. The present finding is supported by
Fig. 6. (a) Comparison of experimental data with Homogenous model. (b) Compar- ison of
experimental data with Awad and Muzychka, 2008.
even higher error of 66% given by Xu et al (2012) and 83% by Awad and Muzychka
(2014b). In contrast, some authors (Quiben (2005) and Ghajar (2005)) rec-
ommended the Friedel correlation is capable of providing the most accurate results for
A summary of the error percentage calculated from Eqs. pressure drop analysis in two phase flows. The high discrepancy may be attributed to
(33) and (34) for all the models (empiricals and numerical) is given in Table 3. the difference in test oper- ating condition, pipe diameter and using fluids of
The error values in the table show that the drift-flux model and different densi-
homogenous model and Awad and Muzychka, (2008) model are the most accurate
models for pressure prediction as the values of AAPE, APE, average negative error
and average positive error are the lowest compared to the other models. The
Lockhart-Martinelli and Muller-Steinhagen & Heck models can predict most of the
ex-
128 F.A. Hamad et al. / International Journal of Multiphase Flow 91 (2017) 120–129

Table 3
Estimated error for each model.

Model APE (%) APE (-Ve%) APE (+Ve%) AAPE (%)

Drift-flux model 3 −15.2 17.2 16.2

Homogenous –1.9 −17.3 15.4 16.2
Awad and Muzychka (2008) 2.8 −16.2 19.7 18
Lockhart-Martinelli (1949) −10 −21 16.2 10
The Friedel Correlation (1979) 56 −9.5 67 60.7
Muller-Steinhagen and Heck (1986) −12.2 −22.5 14.2 18.6

various empirical correlations and by using of the drift-flux model. The superficial
water velocity in the range of 0.16 - 5.263 m/s and superficial air velocity in the
range of 0.16 – 3.289 m/s were used to give the different values of volumetric
qualities. The pressure drop measurements were performed under constant water
flow rate (CWF) and constant total flow rate (CTF). Through compari- son
between the pressure drop obtained by the models against the experimental
acquisitions, the main findings can be summarised as follows:

- Single phase flow tests were performed and the results con- firmed the
accuracy of the instrumentation and the suitabil- ity of the test facility which
can be used for two-phase flow investigation.
- The friction pressure drop enhanced with the increasing of gas flow rate for
CWF. On the other hand, it decreased with the increasing of gas flow rate for
Fig. 8. Comparison of experimental data with Friedel model. CTF. This behaviour is at- tributed to the flow patterns transition in pipes.
- Drift-flux model predicts the experimental data with good ac- curacy. The
average error is of around 0.8% which is the low- est compared to other
models.
- The prediction from Homogenous and Awad and Muzychka (2008) models
is concluded as the most accurate one com- pared to other empirical models
in the literature to measure the friction pressure drop with an average
percentage error less than 3%.
- The Lockhart-Martinelli and Muller-Steinhagen and Heck model are
considered as the second best empirical models from the literature to
predict the experimental data with satisfactory average percentage is
less than - 12%.
- The Friedel model can be used as a guide to predict the pres- sure drop but it is
not quantitatively reliable as the average percentage error is around 56%.

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