1. Proceedings of ICMM2005
2005 3rd International Conference on Microchannels and Minichannels
June 13-15, 2005, Toronto Canada
ICMM2005-75251
NUMERICAL SIMULATION OF FLOW THROUGH MICROCHANNELS IN BIPOLAR
PLATE
A. S. Rawool
Department of Mechanical Engineering
Indian Institute of Technology, Bombay
Mumbai, 400076
India
S. K. Mitra ∗
Department of Mechanical Engineering
Indian Institute of Technology, Bombay
Mumbai, 400076
India
Email: skmitra@me.iitb.ac.in
A. Agrawal
Department of Mechanical Engineering
Indian Institute of Technology, Bombay
Mumbai, 400076
India
S. Kandlikar
Department of Mechanical Engineering
Rochester Institute of Technology
Rochester,
NY 14623-5603
KEYWORDS
serpentine; bipolar plate; numerical; obstructions; two dimen-
sional; modeling
ABSTRACT
In this paper, the flow through a serpentine microchannel
with obstructions on wall is studied. Various obstruction geome-
tries ranging from rectangular to triangular are considered. For
each geometry pressure drop across single obstruction is stud-
ied at various Reynolds numbers. Also the effect of obstruc-
tion height on the pressure drop is investigated. A parametric
study is conducted for different obstruction heights, geometries
and Reynolds numbers.
NOMENCLATURE
µ Viscosity of liquid
ρ Density of liquid
u Velocity component in x-direction
∗Corresponding Author
v Velocity component in y-direction
P Pressure
Hobs Height of obstruction
l1 Streamwise length of obstruction at top
l2 Streamwise length of obstruction at bottom
L1 Length of longer section of channel
L2 Length of shorter section of channel
Re Reynolds number
1 Introduction
Serpentine channels are widely used in fuel cell bipolar
plates as flow passages for fuel (hydrogen) and oxidizer (air).
Serpentine channels have the advantage of compact size for
channel with a long length. The flow through these channels
is different from straight channels due to their serpentine geom-
etry. Various types of obstructions are placed on the walls of
these channels in order to improve momentum transfer and dif-
fusion through the corresponding anode/cathode diffusion layer.
The flow through channels and the effect of obstructions at the
entrance is studied in macro domain by Kabir et al. [1]. Pressure
1 Copyright c 2005 by ASME

2. losses in flow through fuel cell stack has been studied by Ma-
harudrayya et al. [2]. The pressure drop over wall obstructions in
microchannels is of interest, as it departs significantly from the
pressure drop calculated using classical sudden contraction and
expansion correlations [3]. This paper aims at numerically sim-
ulating the flow through a serpentine microchannel with obstruc-
tions placed on channel walls and studying the effect of various
parameters such as Reynolds number, obstruction geometry and
height.
2 Problem Statement
A schematic of the channel considered is shown in Fig. 1.
A two dimensional case is consider to reduce the computational
L2
L1
Figure 1. Geometry of serpentine channel
efforts required. The width of the channel considered is 100µm
with L1 = 1000µm and L2 = 700µm. The radius of curvature of
channel axis is 150µm. The enlarged view of the obstruction is
shown in Fig. 2. An aspect ratio for the obstruction is defined as
Figure 2. Geometry of obstruction.
A =
l1
l2
(1)
which is varied from 1(for rectangular obstruction) to 0 (for tri-
angular obstruction). Typical values of l1 and l2 for A = 0.5 are
50 µm and 100 µm, respectively. The height of the obstruction is
varied from 10µm to 50µm. A normalized height of obstruction
is defined as
h =
height of obstruction
width of the channel
(2)
h is varied from 0.1 to 0.5. Following assumptions are made in
the problem:
1. Steady flow of air through the channel.
2. Constant properties.
3. Two dimensional flow.
3 Results and Discussion
Commercial CFD code CFD-ACE+ [4] is used to numer-
ically simulate the flow through the channel. Constant veloc-
ity boundary condition is used at inlet and constant pressure is
specified at outlet. Velocities corresponding to Reynolds number
range of 10 to 50 are used for solving the problem. The velocity
solutions around the obstruction given by the model are shown
in Fig. 3 for the case of Re = 40, h = 0.1 and A = 1. The ve-
locity vectors show the recirculation of air around the corners
of the obstruction. Figures 4-6 show velocity and pressure pro-
Figure 3. Velocity vector map around obstruction.
files along channel cross section at upstream of obstruction, at
obstruction and at the downstream of obstruction respectively. It
can be seen that the velocity profiles correspond to parabolic pro-
file of laminar flow. Pressure across any section in the channel is
not uniform but it is fluctuating along the cross section.
2 Copyright c 2005 by ASME

3. Figure 4. Velocity and pressure profile before obstruction.
Figure 5. Velocity and pressure profile at obstruction.
Figure 6. Velocity and pressure profile after obstruction.
The pressure drop predicted by the simulation across single
obstruction is considered to study the effect of various parame-
ters on the flow.
3.1 Effect of obstruction height:
Figure 7. Variation of pressure drop with height at Re = 10
Figures 7 to 11 show the effect of the height of obstruction
on the pressure drop across the channel, for various channel ge-
ometries. It can be seen that the pressure drop increases nonlin-
early with height of obstruction. Initially pressure drop increases
slowly, but as the height of obstruction increases there is a rapid
increase in the pressure drop. This is due to the decrease in flow
area with corresponding increase in velocity. The pressure drop
across a sudden contraction-expansion is directly proportional to
square of maximum velocity (i.e. the velocity at the obstruction),
hence there is a second order increase in the pressure drop with
increasing height of obstruction. The rate of increase is high-
Figure 8. Variation of pressure drop with height at Re = 20
3 Copyright c 2005 by ASME

4. Figure 9. Variation of pressure drop with height at Re = 30
Figure 10. Variation of pressure drop with height at Re = 40
est for rectangular obstruction and it goes on decreasing as the
geometry is changed towards triangular obstruction. As the ge-
ometry is changed from rectangular to triangular, the change in
velocity is more gradual. It is also observed that the nature of
variation of pressure drop with height is similar for the given
Reynolds number range. The rate of increase of pressure drop
is the same for all Reynolds numbers, if all the other parameters
remain the same.
3.2 Effect of Reynolds number:
The effect of Reynolds number on pressure drop variation is
depicted in Fig. 12-16. It can be seen that the pressure drop
in this case also changes nonlinearly with Reynolds number,
but this non-linearity is not as severe as the case with chang-
Figure 11. Variation of pressure drop with height at Re = 50
Figure 12. Variation of pressure drop with Re at Hobs = 10µm
ing obstruction height. This may be due to very small values of
Reynolds number used, which are typical of microchannel flows.
The effect of obstruction geometry is the same as previous case,
i.e., for rectangular obstructions the pressure drop is highest and
as the geometry is changed to triangle, the pressure drop goes on
decreasing.
3.3 Effect of obstruction geometry:
Figures 17 to 21 show the effect of the obstruction geom-
etry on the pressure drop. It can be seen from the figures that
with increasing the aspect ratio, the pressure drop across the ob-
struction increases almost linearly. This is expected since, as the
aspect ratio is changed from 0 (for triangular obstruction), to 1
(for rectangular obstruction), the transition from lower to higher
velocity takes place more suddenly. Hence, there is more pres-
sure drop for rectangular obstruction. Also, as the geometry de-
parts from rectangular shape the relations for sudden expansion
and contraction become inapplicable as the change in velocity is
4 Copyright c 2005 by ASME

5. Figure 13. Variation of pressure drop with Re at Hobs = 20µm
Figure 14. Hobs = 30µm
Figure 15. Variation of pressure drop with Re at Hobs = 40µm
more gradual and not sudden.
4 Conclusion:
The effect of three parameters, obstruction height, geome-
try and Reynolds number on pressure drop is studied for flow
Figure 16. Hobs = 50µm
Figure 17. Variation of pressure drop with aspect ratio at Re = 10
Figure 18. Variation of pressure drop with aspect ratio at Re = 20
through a serpentine microchannel with obstructions on wall. It
is found that the pressure drop across the obstruction increases
in a non-linear fashion with increase in obstruction height. The
pressure drop also increases with increasing Reynolds number
but the non-linearity is less pronounced in this case. The pressure
drop is found to decrease as the obstruction geometry is changed
from rectangular to triangular.
5 Copyright c 2005 by ASME

6. Figure 19. Variation of pressure drop with aspect ratio at Re = 30
Figure 20. Variation of pressure drop with aspect ratio at Re = 40
Figure 21. Variation of pressure drop with aspect ratio at Re = 10
5 Acknowledgment
The support of Suman Mashruwala MEMS Laboratory,
IITB is highly appreciated.
REFERENCES
[1] Kabir, M. A., Khan, M. M. K., and Bhuiyan, M. A., 2004.
“Flow phenomena in a channel with different shaped ob-
structions at the entrance”. Fluid Dynamic Research, 35 ,
pp. 391–408.
[2] Maharudrayya, S., Jayanti, S., and Deshpande, A. P., 2004.
“Pressure losses in laminar flow through serpentine channels
in fuel cell stacks”. Journal of Power Sources, 138 , pp. 1–
13.
[3] Fox, R. W., McDonald, A. T., and Pritchard, P. J., 2001. In-
troduction to Fluid Mechanics. John Wiley and Sons.
[4] “CFD-ACE+ software manuals”. CFD Research Corpora-
tion.
6 Copyright c 2005 by ASME