CFD simulation of velocity distribution of water-air two-phase flows in vertical helical coils
Hamid Saffari1, Rouhollah Moosavi, Edris Gholami
LNG Research Laboratory, School of Mechanical Engineering, Iran University of Science and
Technology, Narmak, Tehran 16844, Iran
Abstract
CFD simulation for single and two-phase flow and distribution of velocity and void fraction of fluid
flow in vertical helical coils by varying coil parameters has been investigated. The considered Reynolds
number is in the range of 16000 < Re < 80000, and the void fraction is in the range of 0.01 < α < 0.09.
To simulate the water-air two-phase flow in this article, the Eulerian-Eulerian model was employed.
The 3-D governing equations of continuity and momentum have been solved by using the finite volume
method. To calculate the turbulent fluctuations, the k-ε realizable turbulence model has been used. Also,
the SIMPLE algorithm was employed to solve the velocity and pressure fields. The close correlation
between the obtained numerical results and the numerical and empirical results of other researchers
confirms the accuracy of the applied method in mesh generation and in numerically solving the
governing equations.
Keywords: Numerical study; Flow field distribution; Bubbly flow; Eulerian-Eulerian
Nomenclature
a
tube radius

dynamic viscosity
d
tube diameter

kinematic viscosity
Dc
curvature diameter

density
1
Corresponding author: Hamid Saffari, Ph.D., Associate Professor of School of Mechanical Engineering, Iran
University of Science and Technology, Narmak, Tehran 16844, Iran. Tel./Fax: +98 21 77491228/ +98 21 77240488,
E-mail address: Saffari@iust.ac.ir
1

De
Dean number
helix angle
F
force term
f
frictional factor
subscripts
g
gravity acceleration
l
liquid phase
H
coil pitch
lg
from phase l to phase g
P
pressure
g
gas phase
Rc
curvature radius
k
phase(liquid or gas)
Re
Reynolds number
m
mixture
S
source term
pq
from phase p to phase q
u
velocity
TD
turbulence dissipation
V
volume
vm
virtual mass
Greek letters

void fraction

curvature ratio
2
Introduction
Helical coil tubes are used in various industries, including the food industry, nuclear
reactors, chemical processing, compact heat exchangers, heat recovery systems, low value heat
exchange, and medical equipment [1-3]. In comparison to straight pipes, coiled pipes have a
larger surface area and enjoy higher heat transfer and friction coefficients. The influence of
curvature and torsion on fully developed turbulent flow characteristics in straight, curved and
helically coiled pipe a direct numerical studied by Huttle et al. [4,5]. The results have shown
that the torsion effect is weaker than the curvature effect and performed several DNS of fully
developed flow through toroidal and helical pipes. Lin [6] studied the effects of inlet turbulence
on the development turbulent flow in the entrance region of a helically coiled pipe. They found
that bulk temperature kinetic energy for from the entrance is not affected by the inlet turbulence
level. Also Lin [7] investigated laminar forced flow and heat transfer in the entrance region of
helical pipes using a numerical method. For measuring the velocity in coiled pipes an
electrochemical technique was used by Sylvain Galier [8]. They observed that the high shear rate
was found at the outside and lowest value on the inside of the curve. Litster et al.[9] have 3D
numerical simulated the hydrodynamics and mass transfer inside helically wound hollow-fiber
membranes for the effect of the centrifugally induced Dean vortices on the mass transfer and
secondary swirling flow. They suggested a non-orthogonal pseudo-stream function to visualize
the flow.
The optimal Reynolds number for fully developed laminar forced convection in a helically
coiled tube have found by Shokouhmand and Salimpour [10]. Monisha and Nigam [11] studied
the pressure drop and heat transfer of turbulent flow in the tube in the tube helical heat
exchanger. They have proposed a relation for the friction coefficient and nusselt for the inner and
3
outer tubes. Banerjee et al. [12] the graph presented the effect of liquid velocity on the pressure
drop coefficient, especially for low-speed, liquid and gas show. Czop et al. [13] carried out
experiments on the adiabatic two-phase flow through a helically coiled tube and investigated
pressure drops, wall shear stress and void fraction. They have been observed in experiments that
the pressure drop in two-phase flow is very much different from Lokhart-Martinelli correction
but fairly good agreement with the Chisholm [14] correlation. Two-phase flow air-water in
helically coiled tube has been studied by Whalley et al. [15]. They have studied the flow pattern
transition between stratified and annular flow and also the local film thickness and pressure drop
for air-water flow has been measured. The effects of coil geometry and air and water flow rates
on the pressure loss of two-phase flows in horizontal and vertical helical pipes with three
different inside and outside diameters have been investigated by Xin et al. [16]. Frictional
pressure drops of a single and two-phase flow have been studied by Liejne et al. [17]. They
found that helix axial angles have little influence on the single phase frictional pressure drop,
while a variation of two-phase flow is high.
In this article, the numerical solution of fluid flow in a coiled heat exchanger pipe, in the
single-phase and two-phase (water-air) cases, has been investigated. The k-ε realizable
turbulence model has been used for calculating the turbulent fluctuations. Pipe diameter, coil
diameter, coil curvature, Reynolds number and void fraction on velocity profile and distribution
of void fraction in pipe have been studied.
Problem’s Geometry
The considered geometry, related coordinate systems and the mesh configuration used in the
problem have been shown in Fig. 1. The coiled pipe under investigation consists of 4 coil pitches
4
with a diameter “a” (d = 2a) and dimensionless curvature radius “Rc” (Dc = 2Rc). δ is the amount
of curvature, and H is the dimensionless coil pitch. The considered coil is installed vertically and
the two-phase fluid flows inside of it from bottom to top. It is worth mentioning that in these
types of coiled pipes, the cited geometrical features are constant throughout the coil. Similar to
the Reynolds number which is used for flows in straight pipes, the Dean’s number is employed
for flows inside helical pipes. The dimensionless Reynolds number and the Dean’s number are
defined as follows:
Re =
ρUi (2a)
2μ
De = Re√r⁄R
(1)
(2)
c
Governing equations
The governing equations of the two-phase flow comprise the volume fraction, continuity,
momentum and energy equations. The volume fraction of each phase includes the volume it
occupies from the total phase volume.
(3)
Vk = ∫ αk dV
where the sum of both phases is equal to 1.
αl + αg = 1
(4)
Continuity Equation
𝜕𝜌𝑘 𝛼𝑘
+ 𝛻. (𝜌𝑘 𝛼𝑘 𝑉𝑘 ) = ∑ ( 𝛤𝑝𝑞 − 𝛤𝑞𝑝 ) + 𝑆𝑘
𝜕𝑡
(5)
𝑝=𝑙,𝑔
5
Where Γpq − Γqp denotes the change of one phase to another; and since no phase change occurs
here, its value is zero. Also Sk is generation where its value is zero.
Momentum Equation
𝜕𝜌𝑘 𝛼𝑘 𝑉𝑘
+ ∇. (𝜌𝑘 𝛼𝑘 𝑉𝑘 𝑉𝑘 )
𝜕𝑡
(6)
𝑒𝑓𝑓
= −𝛼𝑘 ∇𝑃 + 𝛼𝑘 𝜌𝑘 𝑔 + ∇. [𝛼𝑘 𝜇𝑘 (∇𝑉𝑘 + (∇𝑉𝑘 )𝑇 ] + ∑ (Γ𝑝𝑞 𝑉𝑝𝑞 − Γ𝑞𝑝 𝑉𝑞𝑝 ) + 𝐹𝑙𝑔
𝑝=𝑙,𝑔
where
𝐷
𝐿
𝑉𝑀
𝑇𝐷
𝐹𝑙𝑔 = 𝐹𝑙𝑔
+ 𝐹𝑙𝑔
+ 𝐹𝑙𝑔
+ 𝐹𝑙𝑔
(7)
Turbulent Kinetic Energy Equation
𝜕
𝜇𝑡,𝑚
(𝜌𝑚 𝑘) + ∇. (𝜌𝑚 𝑢𝑚 𝑘) = ∇. (
∇𝑘) + 𝐺𝑘,𝑚 − 𝜌𝑚 𝜀
𝜕𝑡
𝜎𝑘
(9)
Dissipation Rate of Turbulent Kinetic Energy
𝜕
𝜇𝑡,𝑚
𝜀
(𝜌𝑚 𝜀) + ∇. (𝜌𝑚 𝑢𝑚 𝜀) = ∇. (
∇ε) + (𝐶1 𝐺𝑘,𝑚 − 𝐶2 𝜌𝑚 𝜀)
𝜕𝑡
𝜎𝜀
𝑘
(10)
As density and velocity average obtained from the following equations:
𝑁
(11)
𝜌𝑚 = ∑ 𝛼𝑖 𝜌𝑖
𝑖=1
𝜐𝑚 =
∑𝑁
𝑖=1 𝛼𝑖 𝜌𝑖 𝜐𝑖
∑𝑁
𝑖=1 𝛼𝑖 𝜌𝑖
(12)
Viscosity turbulence:
6
𝜇𝑡,𝑚 = 𝜌𝑚 𝐶𝜇
𝑘2
𝜀
(13)
Turbulent kinetic energy generation term:
𝐺𝑘,𝑚 = 𝜇𝑡,𝑚 (∇𝜐𝑚 + (∇𝜐𝑚 )𝑇 ): ∇𝜐𝑚
(14)
Results and Discussion
Table 1 shows the type of coil geometries used in this article. Diameter, coil pitch and coil
radius have been the considered parameters. There have been different inlet boundary conditions
based on the inlet velocity and void fraction, and the pressure gradient of zero has been
considered as the outlet boundary condition. Changes of pressure and shear stress in the singlephase and two-phase cases have been measured. These measurements have been taken initially
for the single-phase case from the Reynolds of 16000 to 80000; which according to Ito’s
proposed relation for critical Reynolds in coils, fall in the fully turbulent range.
Location of maximum velocity in the helical pipe
In all the geometries and flow cases (from the perspective of void fraction changes) in twophase (air-water) bottom-to-top flows, the maximum velocity point is observed at the outer
section of coiled pipe. In Fig 2, for coil No. 7 (with void fraction of 0.09 and Re = 72000), the air
velocity contour has been plotted at various cross sections for each of the phases at the inlet of
the pipe. In straight pipes, the central region of the pipe is where the maximum velocity forms in
single-phase flows. The reason for this phenomenon is that with the entrance of fluid into the
pipe, boundary layers are formed on pipe walls, and as the flow advances, these boundary layers
gradually develop and extend further.
7
The shear stress has a maximum value at the wall, and it decreases by moving towards the
pipe’s axis. As the flow advances inside the pipe, the boundary layers converge at the center of
the pipe; from this point on, the flow has a developmental state and the velocity profile assumes
a constant and unchanging form. Therefore, fluid velocity is higher in the central region of pipe,
which is less influenced by the shear stress of the wall; and the maximum velocity location in
straight pipes is on the pipe’s axis (central section of pipe).
However, in helical pipes, centrifugal forces affect the velocity field and cause the fluid
elements to move with different velocities along the pipe; in other words, the velocity profile is
not uniform in these types of pipes. In curved pipes, the fluid adjacent to the pipe’s outer wall
(due to having a larger curvature radius) generally has a higher velocity compared to the fluid
near the inner wall of the pipe. The centrifugal forces also affect the distribution of phases inside
the pipe. Regarding the two-phase (liquid-gas) flow, the process of phase distribution in the pipe
is significantly governed by the centrifugal forces that operate on the liquid phase. The shape of
velocity contours and void fraction at various pipe cross sections can provide a broader view on
the physics of the problem. The pipe curvature results in the creation of a centrifugal force which
affects the flow. This leads to a higher fluid velocity at the outer section of pipe, contrary to
flows within straight pipes in which the high velocity region is located at the center of the pipe.
As can be observed in Fig. 2, flow profile changes as we move forward in the coiled pipe. As
we advance through the pipe, centrifugal forces become more prominent and their impacts on the
flow become more obvious. These forces cause the fluid flowing in the outer region of coil to
have a higher velocity compared to the fluid that flows near the inner wall of the coil. Also,
contrary to straight pipes in which the flow is symmetrical, the fluid flow in a coiled pipe is
8
asymmetrical, and due to the influence of centrifugal forces, the phases are somewhat separated
from each other; in other words, the flow approaches a laminar flow.
Figures 3 and 4, the velocity profiles at different sections of the first and second coil and the
horizontal and vertical center line sections show. As is clear from the figures, the maximum
velocity is shifted towards the outer wall of the coil. In the helical tubes, due to the curvature of
the coil, and then the effect of the centrifugal force and the formation of secondary flow, the
velocity profiles are asymmetric and the radial direction this asymmetry can be seen as well.
Also can be seen as well as the effect of the return flow, as it is clear that we encounter in the
range of 0.4  r  0.4 to drop rapidly.
a
Impact of pipe diameter on velocity field
Figure 5 shows the air velocity diagrams for two pipes with diameters of 25 and 40 mm and
with the same coil radius of 200 mm, at two identical cross sections (outlet cross section). In two
spiral pipes with the same coil diameters and different pipe diameters, the one with the larger
pipe diameter has more curvature. Therefore, the centrifugal forces in this larger diameter pipe
are stronger due to the larger curvature, and they cause a larger difference between the velocities
of fluids near the outer and inner walls of the pipe. So the 40 mm diameter pipe has more
curvature compared to the pipe with 25 mm diameter, and stronger centrifugal forces are created
in this pipe as a result of its larger curvature. As is shown in Fig. 5, there is a larger difference
between the velocities of fluids near the outer and inner pipe walls in the 40 mm diameter pipe
than in the 25 mm diameter pipe. Also, because of the strong centrifugal force, the maximum
velocity that can be attained by the fluid in the larger diameter pipe is higher, which is clearly
seen in Fig. 5. The air velocity contours in two coiled pipes with the same coil radius of 200 mm
9
and different pipe diameters have been shown in Fig. 6 and 7, respectively. In the larger diameter
pipe, because of more curvature and a stronger centrifugal force, a stronger secondary flow is
created, which makes the fluid unstable and gives it a rotational motion. Therefore, as can be
seen from these two figures, in the smaller diameter coiled pipe, because of smaller curvature
and consequently, weaker centrifugal force, the flow develops sooner; meaning that it has a
shorter hydrodynamic inlet length.
Effect of coil diameter on velocity field
With the increase of coil radius, the curvature of the coiled pipe becomes smaller and
consequently, the centrifugal forces and their influence diminish as well. The larger the coil
radius gets, the smaller the pipe curvature becomes and the helical pipe turns more into a straight
pipe. As Fig. 8 illustrates, the air velocity profiles at two identical pipe cross sections are
different in two helical pipes with different coil diameters. The pipe with a smaller coil diameter
develops a stronger centrifugal force which causes a larger difference between minimum and
maximum values of flow velocity in the pipe’s cross section. This stronger centrifugal force also
causes the maximum velocity in the pipe with smaller coil diameter to be higher than the
maximum velocity in the pipe with larger coil diameter.
Fig. 8 illustrates the flow velocity contours in two helical pipes (pipes No. 5 and 8), both with a
pipe diameter of 25 mm, coil pitch of 60 mm, but with different coil radiuses.
When the coil radius changes, the velocity profiles will not be the same for different coils at
identical θ angles; in other words, the flow development lengths will be different. As the coil
radius gets larger, the formation of the high velocity region towards the outer section of coil
starts at smaller values of θ, due to the reduction of the centrifugal force. Therefore, in pipes with
10
a larger coil radius, because the curvature is small and the centrifugal forces arising due to
curvature are weak, the fluid gets to the high velocity region sooner.
Effect of Reynolds number on void fraction distribution
Fig. 9 shows the void fraction distribution in coil No. 3 at different Reynolds numbers. In
fluid flow inside coiled pipes, the centrifugal force tends to carry the fluid towards the outer wall
of the coil and the force of gravity tends to pull down the fluid towards the bottom section. The
equilibrium between these two forces is expressed by the Froud number. A low Froud number
means that the force of gravity has overcome the centrifugal force. As is observed, air
distribution at low Reynolds numbers is more uniform and air is dispersed throughout most of
the pipe’s cross section. Although the centrifugal force in helical pipes causes the denser fluid to
move towards the outer section of pipe, here at low Reynolds numbers, it is observed that the
centrifugal force has a lower influence compared to the force of gravity, and the gas phase of the
fluid is dispersed towards the upper section. The distribution of void fraction at Re = 16000
indicates that, as a result of low flow velocity and thus the minor effect of the centrifugal force,
with the increase of angle along the coil’s length, water (being denser and heavier) is pulled by
the force of gravity towards the bottom section of pipe, and air (with less density) occupies the
upper half of the pipe’s cross section. When the Reynolds number increases, the centrifugal force
exerts more influence and as a result, with the increase of angle θ, the liquid phase tends to move
towards the outer section of pipe. At θ = 270º, when Re = 16000, it is observed that the liquid is
at the bottom and the air is at the top of the pipe’s cross section; while at Re = 48000, the liquid
phase moves more towards the outer region of the pipe. As Fig. 9 shows, with the increase of
Reynolds number, the centrifugal forces influence the distribution of phases throughout the pipe
11
and cause the air bubbles to move away from the outer section of coiled pipe and get closer to
the inner section as the fluid moves along the pipe. These forces also cause the water phase,
which has a higher density relative to air, to be present at the outer region of helical pipe.
Velocity and pressure profiles in the two-phase case
In all the geometries and flow cases (from the perspective of void fraction changes) in twophase (air-water) bottom-to-top flows, the maximum velocity point is observed at the outer
section of coiled pipe. In Fig 10, for coil No. 7 (with void fraction of 0.09 and Re = 72000), the
air velocity contour has been plotted at various cross sections for each of the phases at the inlet
of the pipe. In straight pipes, the central region of the pipe is where the maximum velocity forms
in single-phase flows. The reason for this phenomenon is that with the entrance of fluid into the
pipe, boundary layers are formed on pipe walls, and as the flow advances, these boundary layers
gradually develop and extend further. The shear stress has a maximum value at the wall, and it
decreases by moving towards the pipe’s axis. As the flow advances inside the pipe, the boundary
layers converge at the center of the pipe; from this point on, the flow has a developmental state
and the velocity profile assumes a constant and unchanging form. Therefore, fluid velocity is
higher in the central region of pipe, which is less influenced by the shear stress of the wall; and
the maximum velocity location in straight pipes is on the pipe’s axis (central section of pipe).
However, in helical pipes, centrifugal forces affect the velocity field and cause the fluid elements
to move with different velocities along the pipe; in other words, the velocity profile is not
uniform in these types of pipes. In curved pipes, the fluid adjacent to the pipe’s outer wall (due to
having a larger curvature radius) generally has a higher velocity compared to the fluid near the
inner wall of the pipe. The centrifugal forces also affect the distribution of phases inside the pipe.
12
Regarding the two-phase (liquid-gas) flow, the process of phase distribution in the pipe is
significantly governed by the centrifugal forces that operate on the liquid phase. The shape of
velocity contours and void fraction at various pipe cross sections can provide a broader view on
the physics of the problem. The pipe curvature results in the creation of a centrifugal force which
affects the flow. This leads to a higher fluid velocity at the outer section of pipe, contrary to
flows within straight pipes in which the high velocity region is located at the center of the pipe.
As can be observed in Fig. 10, flow profile changes as we move forward in the coiled pipe.
As we advance through the pipe, centrifugal forces become more prominent and their impacts on
the flow become more obvious. These forces cause the fluid flowing in the outer region of coil to
have a higher velocity compared to the fluid that flows near the inner wall of the coil. Also,
contrary to straight pipes in which the flow is symmetrical, the fluid flow in a coiled pipe is
asymmetrical, and due to the influence of centrifugal forces, the phases are somewhat separated
from each other; in other words, the flow approaches a laminar flow.
Fig. 11 illustrates the contours of pressure at different angles from pipe surface. Angle θ is
measured from the pipe inlet cross section. The centrifugal forces that act on the fluid inside the
pipe cause a high pressure region near the outer wall of the pipe. The decreasing trend of
pressure along the pipe, at various cross sections, can be observed in this figure.
Conclusion
In this paper, the numerical solution of fluid flow and distribution of void fraction in a coiled
heat exchanger pipe, in the single-phase and two-phase (water-air) cases, has been investigated.
With regards to the effect of the centrifugal force resulting from curvature in coiled pipes, which
causes the velocity profile to become asymmetrical and makes the heavier fluid to move towards
13
the outer section of pipe and the maximum velocity point to shift in the same direction. Pipe
diameter, coil diameter, coil curvature, Reynolds number and void fraction on velocity profile
and distribution of void fraction in pipe have been studied. Numerical results indicate that with
the increase of curvature effect, friction coefficient increases due to the increase of the
centrifugal force. By increasing the pipe diameter and keeping the coil pitch and diameter
constant, the radius of coil curvature increases and as a result, the centrifugal force becomes
stronger. The impact of coil diameter on velocity field has also been examined. With the increase
of Reynolds number in a given coiled pipe, the centrifugal forces affect the distribution of phases
throughout the pipe and cause the gas phase bubbles to approach the inner section of pipe and the
liquid phase (with a higher density relative to gas) to move towards the outer region as the flow
advances inside the pipe. The higher the Reynolds number gets, the higher the percentage of gas
phase moving towards the inner wall of the pipe and of the liquid phase moving towards the
outer wall will become.
References
[1]
Berger SA. Talbot L. Yao LS. 1983. Flow in curved pipes. Ann. Rev. Fluid Mech., Vol. 15,
pp. 461-512.
[2]
Rabin Y. Korin E. 1996. Thermal analysis of a helical heat exchanger for ground thermal
energy storage in arid zones. International Journal of Heat and Mass Transfer, Vol. 39(5),
pp.1051-1065.
[3]
Bai B. Guo L. Feng Z. Chen X. 1999. Turbulent heat transfer in a horizontally coiled tube.
Heat Transfer-Asian Research, Vol. 28(5), pp.395-403.
14
[4]
Huttl T J. Friedrich R. 2001. Direct numerical simulation of turbulent flow in curved and
helically coiled pipes. Computers & Fluids Vol. 30, pp. 591-605.
[5]
Huttl TJ. Friedrich R. 2000. Influence of curvature and torsion on turbulent flow in helically
coiled pipes, International Journal of Heat and Fluid Flow Vol. 21, pp. 345-353.
[6]
Lin C X. Ebadian M A. 1999. The effects of inlet turbulence on the development of fluid
flow and heat transfer in a helically coiled pipe, International Journal of Heat and Mass
Transfer, Vol. 42, pp. 739-751.
[7]
Lin CX. Zhang P. Ebadian MA. 1997. Laminar forced convection in the entrance region of
helical pipes, International Journal of Heat and Mass Transfer, Vol. 40(14), pp. 3293-3304.
[8]
Galier S. Issanchou S. Moulin P. Clifton MJ. Aptel P.2003. Electrochemical Measurement of
Velocity Gradient at the Wall of a Helical Tube, AIChE Journal, Vol. 49(8), pp. 1972-1979.
[9]
Litster S, Pharoah JG. Djilali N. 2006. Convective mass transfer in helical pipes: effect of
curvature and torsion, Heat Mass Transfer, Vol. 42, pp. 387–397.
[10] Shokouhmand
H. Salimpour MR. 2007. Optimal Reynolds number of laminar forced
convection in a helical tube subjected to uniform wall temperature. Int Comm Heat Mass
Transf, Vol. 34(6), pp. 753–761.
[11] Mandal
MM. Nigam KDP. 2009. Experimental Study on Pressure Drop and Heat Transfer of
Turbulent Flow in Tube in Tube Helical Heat Exchanger, Ind. Eng. Chem. Res. Vol. 48, pp.
9318–9324.
[12] Banerjee
S. Rhodes E. Scott DS. 1969. Studies on concurrent gas–liquid flow in helically
coiled tubes – I, Flow patterns, pressure drop and holdup, Can J Chem Eng, Vol. 47(5), pp.
445–453.
15
[13] Czop
V. Barbier D. Dong S. 1994. Pressure drop, void fraction and shear stress
measurements in an adiabatic two-phase flow in a coiled tube, Nuclear Engineering and
Design, Vol. 149(1-3), pp. 323-333.
[14] Chisholm
D. 1967. A theoretical basis for the Lockhart-Martinelli correlation for two-phase
flow, International Journal of Heat and Mass Transfer, Vol. 10(12), pp. 1767-1778.
[15] Walley
PB. 1980. Air-Water two-phase flow in helically coiled tube, Int. J. Multiphase Row
Vol. 6, pp. 345-356.
[16] Xin
RC, Awwad A, Dong ZF, Ebadian MA. 1996. An investigation and comparative study of
the pressure drop in air–water two-phase flow in vertical helicoidal pipes, Int J Heat Mass
Transfer, Vol. 39, pp. 735–43.
[17] Liejin
G. Ziping F. Xuejun C. 2001. An experimental investigation of the frictional pressure
drop of steam-water two-phase flow in helical coils. International journal of heat and mass
transfer, Vol. 44, pp. 2601-2610.
16
Table 1- Geometrical characteristics of studied cases
Case No.
PCD [mm]
Pitch [mm]
Diameter [mm]
1
100
20
16
2
100
40
16
3
100
60
16
4
200
60
16
5
200
60
25
6
200
60
40
7
300
60
25
8
400
60
25
17
Fig. 1- Geometry and mesh configuration of the problem
18
  0
  45 
  90 
  135 
  180 
  225 
  270 
  360 
  450 
  540 
  765 
  900 
  1125 
  1260 
  1440 
Fig. 2- Velocity distribution [m/sec] at different angles
19
Fig. 3 Air velocity profiles in the radial direction
20
Fig. 4 Air velocity profiles in the direction perpendicular to the radius of the coil
21
Fig.5- air velocity in two different diameter pipes
22
θ=450
θ =900
Fig. 6- air velocity in helical coil with diameter 25 mm in two different sections
23
θ=450
θ =900
Fig. 7- air velocity in helical coil with diameter 25 mm in two different sections
24
Case 8
Case 5
  45 
  90 
  135 
  45 
  90 
  135 
Fig. 8 - Effect of coil diameter on velocity [m/s] distribution
25
Re = 16000,
  270

  360 
  540 
  630 
  360 
  540 
  630 
  360 
  540 
  630 
Re= 48000,
  270 
Re= 80000,
  270 
Fig. 9 - Void fraction distribution at different Reynolds numbers
26
Fig. 10- the air velocity contours in the helical coil
27
Fig. 11- the pressure contours in the helical coil
28