INTERNATIONAL JOURNAL OF APPLIED ENGINEERING RESEARCH, DINDIGUL
Volume 2, No 1, 2011
© Copyright 2010 All rights reserved Integrated Publishing Association
RESEARCH ARTICLE ISSN 09764259
Experimental and Numerical comparison between the performance of
Helical cone coils and ordinary helical coils used as dehumidifier for
humidification dehumidification in desalination units
Abo Elazm M.M. 1, Ragheb A.M. 1, Elsafty A.F. 1, Teamah M.A. 2
1
Arab Academy for Science, Technology and Maritime Transport, Alexandria, Egypt.
2
Faculty of Engineering, Alexandria University, Alexandria, Egypt.
Ragheb_9@yahoo.com
ABSTRACT
Helical and spiral coils were used for too long as heat exchangers in power and chemical
processes. This Numerical research is introducing the concept of helical cone coils and
comparing the performance of helical cone coils as heat exchangers to the ordinary helical
coils. Helical and spiral coils are known to have better heat and mass transfer than straight
tubes, that’s attributed to the generation of a vortex at the helical coil known as Dean Vortex,
this vortex is a secondary flow superimposed on the primary flow. The Dean Number which
is a dimensionless number used in describing the dean vortex is a function of Reynolds
Number and the square root of the curvature ratio, so varying the curvature ratio for the same
coil would vary the Dean Number. Experimental and Numerical investigation based on the
commercial CFD software fluent was made to understand the difference between ordinary
helical coils and helical cone coils. Two coils having different heights of 40 and 50 mm and
thicknesses 0.6 mm and 0.7 mm were used in the investigation. It was found that as the taper
angle enhances the heat transfer characteristics of the coil this increase is presented in an
increase in the coil exit temperature, the numerical simulation showed that the heat transfer
characteristics of the helical cone coil is better than the ordinary helical coils.
Keywords: Experimental, Numerical, Helical, Heat Exchanger, Heat Transfer
Nomenclature
a: Pipe radius (mm).
H: Helical coil height (mm).
h: Heat transfer coefficient (w/m2 K).
I: Inclined height (mm).
Murf: Relaxation factor of momentum.
P: Helical Pitch (mm).
Purf: Relaxation factor of pressure.
R: Coil radius of curvature (mm).
t: Tube Thickness (mm).
T: Temperature (k).
Twall : Wall temperature (k).
u: Inlet velocity (m/s).
De: Dean Number.
Nu: Nusselt Number.
Recr : Critical Reynolds number.
Re : Reynolds number.
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RESEARCH ARTICLE ISSN 09764259
Greek Symbol
Θ: Taper angle.
Ρ: Density.
1. Introduction
Helical coils have been long and widely used as heat exchangers in power, petrochemical,
HVAC, chemical and many other industrial processes. Helical and spiral coils are known to
have better heat and mass transfer compared to straight tubes, the reason for that is the
formation of a secondary flow superimposed on the primary flow, known as Dean Vortex
(Rohsenow et al., 1998). The Dean Vortex was first observed by Eustice; then numerous
studies have been reported on the flow fields that arise in curved pipes (Dean, White,
Hawthorne, Horlock, Barua, Austin and Seader)( Adrian and Allan, 2003). The first attempt
to mathematically describe the flow in a coiled tube was made by Dean, he found that the
secondary flow induced in curved pipes (Dean Vortex) is a function of Reynolds Number and
the curvature ratio, the Dean Number is widely used to characterize the flow in curved tubes:
De = Re * (1)
It has been widely observed that the flow inside coiled tubes remains in the viscous regime up
to a much higher Reynolds Number than that for straight tubes Srinivasan et al. (Rohsenow et
al., 1998). The curvatureinduced helical vortices (Dean Vortex) tend to suppress the onset of
turbulence and delay transition. The critical Reynolds Number which describes the transition
from laminar to turbulent flow is given by any correlations; the following correlation is given
by Srinivasan et al.( (Rohsenow et al., 1998):
Recr = 2100 * (1+12 ) (2)
Dennis and Ng (Dennis and Ng, 1982) numerically studied laminar flow through a curved
tube using a finite difference method with emphasis on two versus four vortex flow
conditions. They ran simulations in the Dean range of 96 to 5000. The four vortex solutions
would only appear for a Dean number greater than 956. Dennis and Riley (Dennis and Riley,
1991) developed an analytical solution for the fully developed laminar flow for high Dean
Numbers. Though they could not find a complete solution to the problem, they stated that
there is strong evidence that at high Dean Numbers the flow develops into an inviscid core
with a viscous boundary layer at the pipe wall.
The effect of pitch on heat transfer and pressure drop was studied by Austin and Soliman
(Austen and Soliman. 1988) for the case of uniform wall heat flux. The results showed
significant pitch effects on both the friction factor and the Nusselt Number at low Reynolds
Numbers, though these effects weakened as the Reynolds number increased. The authors
suggested that these pitch effects are due to free convection, and thus decrease as the forced
convection becomes more dominant at higher Reynolds Numbers. The effect of the pitch on
the Nusselt Number in the laminar flow of helicoidal pipes was also investigated by Yang et
al (Yang, Dong, and Ebadian. 1995) Numerical results for fully developed flow with a finite
pitch showed that the temperature gradient on one side of the pipe will increase with
increasing torsion; however, the temperature gradient on the opposite will decrease. Overall,
the Nusselt Number slightly decreases with increasing torsion for low Prandtl Numbers, but
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Volume 2, No 1, 2011
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RESEARCH ARTICLE ISSN 09764259
significantly decreases with larger Prandtl Numbers. On the other hand Germano (Germano,
1982) introduced an orthogonal coordinate system to study the effect of torsion and curvature
on the flow in a helical pipe. In the results of the perturbation method indicated that the
torsion had a second order effect and curvature had a first order effect on the flow. Further
studies by Tuttle (Tuttle, 1990) indicated that the frame of reference (coordinate system)
determines if the torsion effect is first or second order.
Kalb and Seader (Kalb, and Seader. 1972) numerically studied the heat transfer in helical
coils in case of uniform heat flux using an orthogonal toroidal coordinate system. They have
found that for Prandtl Numbers greater than 0.7, it was shown that the local Nusselt Number
in the area of the inner wall was always less than that of a straight tube, and increasing less as
the Dean Number is increased till it reached a limiting value. The local Nusselt Numbers on
the outer wall continued to increase with increasing Dean Number. Fully developed laminar
flow and heat transfer was studied numerically by Zapryanov et al. (Zapryanov, Christov, and
Toshev, 1980) using a method of fractional steps for a wide range of Dean (10 to 7000) and
Prandtl (0.005 to 2000) numbers. Their work focused on the case of constant wall
temperature and showed that the Nusselt number increased with increasing Prandtl numbers,
even for cases at the same Dean number.
Spiral coils have received little attention compared to helical coils, though the reported results
of spiral coils show better performance than helical ones. Figueiredo and Raimundo
(Figueiredo and Raimundo, 1996) experimentally investigated the thermal response of a hot
water store and the thermal discharge characteristics from heat exchanger coils placed inside.
The classical cylindrical coil and the flat spiral coil were investigated. The results indicated
that the efficiency of flat spiral coil was higher than that of a cylindrical one. The results from
comparison between the model and experiments were in good agreement. Naphon and
Suwagrai (Naphon and Suwagrai, 2007) studied the Effect of curvature ratios on the heat
transfer in the horizontal spirally coiled tubes both experimentally and numerically, they have
found that due to the centrifugal force, the Nusselt number and pressure drop obtained from
the spirally coiled tube are 1.49, 1.50 times higher than those from the straight tube,
respectively.
Helical cone coils have even received lower attention than spiral coils, only very few
researchers have investigated the capabilities of these coils due to the complexity of the
structure, it was hard to investigate it both numerically and experimentally. Yan Ke et al.
(Yan Ke, Ge, Sue and Meng, 2011) have investigated the helical cone tube bundles both
numerically and still some foregoing experiments, the authors found that the cone angle has a
significant effect on enhancing the heat transfer coefficient, also they’ve found that the pitch
has nearly no effect on the heat transfer. The aim of this paper is to experimentally and
numerically investigate the effect of the taper angle on heat transfer characteristics.
2. Numerical Simulation
2.1 Helical Cone Coil Geometry
The Geometry of the helical cone tube is shown in Fig.1; both the curvature and torsion are
variable along the tube. The bottom radius of curvature is donated (R), the pipe diameter (a),
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Volume 2, No 1, 2011
© Copyright 2010 All rights reserved Integrated Publishing Association
RESEARCH ARTICLE ISSN 09764259
the helical pitch as (P), the straight height (H) and finally the inclined height (I). For a
straight helical coil the height (H) will be equal to (I) but when changing the inclination angle
(θ), the height of the coil (I) will change in accordance to that angle, while keeping (H)
constant.
Figure 1: Helical Coil Geometry
The bottom radius of
curvature (R) is 95 mm; the tube diameter (a) was 11 mm. two coil heights (H) were used 40
and 50 mm and two different tube thicknesses were used 0.6 and 0.7 mm.
2.2 Simulation Model
The laminar flow in the helical spiral coil is simulated using the commercial CFD software
Fluent. In the simulation of the laminar fluid flow, the flow and pressure equations were
solved with SIMPLEC algorithm, which is one of the three widely, used velocity pressure
coupling algorithm in Fluent. The Second Order Upwind algorithm was employed in the
discretization of the equations because of its accuracy and iterating efficiency. The
parameters of laminar fluid flow model were in accordance with the default values of the
CFD software:
Purf = 0.3 Murf = 0.7 (3)
Where, the Purf and Murf respectively denote the Under Relaxation Factor of pressure
and momentum of the fluid flow inside the tube during the iterating of the calculation. The
commercial software Fluent uses both Navier – Stocks equation, continuity equation and the
energy equation in the solution, the equations are solved for laminar, steady and 3D flow.
The second step was to make mathematical model verification, and as stated previously, very
few experiments and mathematical simulations have been conducted on helical cone tubes. In
order to verify the accuracy of the mathematical model we are investigating, the finite
element model for the circular cross sectional area made by (Yan Ke et al)has been used in
the verification. Unstructured, nonuniform grid systems are used to discretize the main
governing equations. The sweep grids were used to discretize the whole volume of the spiral
coil. The skewness was kept below 0.5 for all of the models to have a good mesh quality.
The constant temperature and nonslip boundary conditions were applied. The results of the
mathematical model were found in agreement with the results of Yan Ke et al. (Yan Ke, Ge,
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Sue and Meng, 2011), this paper was discussing both elliptical and circular pipe cross section
for the helical cone coils, in the verification the results was only compared to the circular pipe
results and it was within 10% of these results.
3. Results and Discussion
3.1 Experimental and Numerical Results
Two numerical models were used to simulate the actual coils at various operating conditions;
table 1 shows the geometrical parameters for the experimental and numerical model. Coil 1
mathematical model data could be found in table 2 and coil 2 mathematical model data could
be found in table 3. Five experiments and numerical simulation were conducted on each coil,
vapor at various temperatures is used to heat the water in the coil.
Table 1: Helical Cone Coils Experimental and Mathematical Model Geometrical Parameters
Coil P R (mm) a Re u t (mm) H I (mm)
(mm) (mm) (m/s) (mm)
Coil 1 0.7 40 85
20 95 11 6360 0.58
Coil 2 0.6 50 95
Table 2: Coil 1 Mathematical Model Data
Number of Nodes 283124
Number of Cells 252384
Inlet Velocity inlet (0.58 m/s)
Outlet Pressure Outlet
Thermal Boundary Condition Temperature = Vapor Temperature for each
Case
Pressure, Momentum, Energy, Scheme Second Order upwind
Water Inlet Temperature Inlet Temperature in each Case
Table 3: Coil 2 Mathematical Model Data
Number of Nodes 341048
Number of Cells 310230
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RESEARCH ARTICLE ISSN 09764259
Inlet Velocity inlet (0.58 m/s)
Outlet Pressure Outlet
Thermal Boundary Condition Temperature = Vapor Temperature for each
Case
Pressure, Momentum, Energy, Scheme Second Order upwind
Inlet Temperature Inlet Temperature each Case
Figure 2: Coil 1 Experimental and Numerical Results Comparison
Figure 2 shows the vapor temperature, the water temperature at the coil inlet, the water
temperature at the coil outlet numerically and experimentally for coil 1. It can clearly
conclude from the figure that the difference between the experimental and numerical results
is less than 10 % so the numerical simulation is highly acceptable.
Figure 3 shows the vapor temperature, the water temperature at the coil inlet, the water
temperature at the coil outlet numerically and experimentally for coil 2. It can clearly
conclude from the figure that the difference between the experimental and numerical results
is less than 10 % so the numerical simulation is highly acceptable.
It can be concluded from the previous results that the numerical simulation can be used to
compare between the ordinary helical coils and helical cone coils.
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3.2 Helical Cone Coils and Ordinary Helical Coils Numerical Comparison
The comparison between the helical cone coils and the ordinary coils will be numerically as
the numerical simulation has shown good agreement with the experimentally results. Two
numerical models were built for the ordinary coils. Table 4 shows the geometric parameters
of the ordinary helical coils.
Figure 2: Coil 2 Experimental and Numerical Results Comparison
Table 3: Ordinary Coils Geometric Parameters
Coil P (mm) R (mm) a (mm) Re u (m/s) t (mm) H = I (mm)
Coil 1 0.7 40
20 95 11 6360 0.58
Coil 2 0.6 50
Ordinary helical Coil 1 mathematical model data could be found in table 5 and ordinary
helical coil 2 mathematical model data could be found in table 6. It’s worth noting that in the
helical cone coil having the structural parameters stated in table 1 that coil will be a six turns
coil, while ordinary helical coil with the structural parameters found in table 4 will be only
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RESEARCH ARTICLE ISSN 09764259
three turn though they have the same height. The coil will be simulated using the same vapor
temperature used in the previous section. Figure 4 shows a numerical comparison between
the exit temperature of the ordinary helical coil and the exit temperature of the helical cone
coil for coil 1, it can be clearly seen that the helical cone coil has better performance that the
ordinary helical coil though it utilizes less space.
Table 5: Coil 1 Mathematical Model Data
Number of Nodes 141450
Number of Cells 125952
Inlet Velocity inlet (0.58 m/s)
Outlet Pressure Outlet
Thermal Boundary Condition Temperature = Vapor Temperature for each
Case
Pressure, Momentum, Energy, Scheme Second Order upwind
Water Inlet Temperature Inlet Temperature in each Case
Table 6: Coil 2 Mathematical Model Data
Number of Nodes 197232
Number of Cells 178296
Inlet Velocity inlet (0.58 m/s)
Outlet Pressure Outlet
Thermal Boundary Condition Temperature = Vapor Temperature for
each Case
Pressure, Momentum, Energy, Scheme Second Order upwind
Inlet Temperature Inlet Temperature each Case
Figure 5 shows a numerical comparison between the exit temperature of the ordinary helical
coil and the exit temperature of the helical cone coil for coil 2, it can be clearly seen that the
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RESEARCH ARTICLE ISSN 09764259
helical cone coil has better performance that the ordinary helical coil though it utilizes less
space.
Figure 4: Coil 1 Ordinary and Helical Cone Coil Exit Temperature Comparison
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Figure 4: Coil 2 Ordinary and Helical Cone Coil Exit Temperature Comparison
4. Conclusion
The heat transfer characteristics of the helical cone coil were found to be better than the heat
transfer characteristics of the ordinary helical coils. The geometry of the coil was found to
have a significant effect of the coil exit temperature. The taper angle of the helical cone coil
has a significant effect on its heat transfer characteristics.
5. References
1. Austen, D. S., and H. M. Soliman. (1988), Laminar flow and heat transfer in helically
coiled tubes with substantial pitch. Experimental Thermal and Fluid Science, 1,pp 183
194.
2. Adrian B. and Allan D, E.B.,(2003), Heat Transfer Handbook, First ed. John Wiley &
Sons, New Jersey.
3. Dennis, S. C. R. and M. Ng. (1982), Dual solutions for steady laminar flow through a
curved tube. Quarterly Journal of Mechanics and Applied Mathematics, 35(3),pp 305324.
4. Dennis, S. C. R. and N. Riley. (1991), On the fully developed flow in a curved pipe at
large Dean number. Proc. R. Soc. London Ser. A 43(4), pp 473478.
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© Copyright 2010 All rights reserved Integrated Publishing Association
RESEARCH ARTICLE ISSN 09764259
5. Futagami, K. and Y. Aoyama. (1988), Laminar heat transfer in a helically coiled tube.
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6. Figueiredo AR, Raimundo AM. (1996), Analysis of the performances of heat exchangers
used in hotwater stores. Applied Thermal Engineering, 16,pp 605–11.
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Mechanics, 12(5),18.
8. Kalb, C. E. and J. D. Seader, (1972), Heat and mass transfer phenomena for viscous flow
in curved circular tubes. International Journal of Heat and Mass Transfer, 15,pp 801817.
9. Paisarn Naphon, Jamnean Suwagrai, (2007), Effect of curvature ratios on the heat transfer
and flow developments in the horizontal spirally coiled tubes, International Journal of
Heat and Mass Transfer 50, pp 444–451.
10. Tuttle, E. R. (1990), Laminar flow in twisted pipes. Journal of Fluid Mechanics, 219,545
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Transfer, Third ed. McGrawHill, New York.
12. Yan Ke, Ge Peiqi, Sue Yancai and Meng Haitao, (2011), Numerical simulation on heat
transfer characteristic of conical spiral tube bundle, Applied Thermal Engineering 31, pp
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13. Yang, G., F. Dong, and M. A. Ebadian. (1995), Laminar forced convection in a helicoidal
pipe with finite pitch. International Journal of Heat and Mass Transfer, 38(5), pp 853862.
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transfer in curved tubes. International Journal of Heat and Mass Transfer, 23,pp 873880.
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