Energy 169 (2019) 338e343
Contents lists available at ScienceDirect
Energy
journal homepage: www.elsevier.com/locate/energy
Three-dimensional study of stack on the performance of the proton
exchange membrane fuel cell
B.H. Lim a, E.H. Majlan a, *, W.R.W. Daud a, b, M.I. Rosli a, b, T. Husaini a
a
b
Fuel Cell Institute, Universiti Kebangsaan Malaysia, 43600, UKM Bangi, Selangor Darul Ehsan, Malaysia
Department of Chemical and Process Engineering, Universiti Kebangsaan Malaysia, 43600, UKM Bangi, Selangor Darul Ehsan, Malaysia
a r t i c l e i n f o
a b s t r a c t
Article history:
Received 12 September 2018
Received in revised form
30 November 2018
Accepted 4 December 2018
Available online 11 December 2018
The distribution of reactant in the proton exchange membrane fuel cell (PEMFC) is crucial because the
performance of the fuel cell is determined by the lowest performance cell. The reactant is distributed
from the manifold to the cells in the stack and further distributed into the flow field channels (depending
on the flow field design). The three-dimensional PEMFC is comparatively studied as a dual-cell, a quadcell and a hexa-cell stack. The previously investigated modified parallel flow field is used as the anode
flow field. The dual-, quad- and hexa-cell stacks are connected in series to study the effect of PEMFC
performance when the number of cells increases in a PEMFC stack. Computational fluid dynamics (CFD)
is used to study the current density generation of a PEMFC stack. The results demonstrate that when the
quantity of cells rises in a stack, the current density decreases. Six equations are formed at different cell
potentials to predict the PEMFC performance as the quantity of cells increases.
© 2018 Published by Elsevier Ltd.
Keywords:
PEMFCs stack
CFD modeling
Manifold
1. Introduction
Fossil fuels which are the main source of energy, have put the
environment in an alarming stage. Carbon emission has reached an
unsustainable level and caused air pollution and greenhouse effects, which change the global climate [1,2]. The fuel cell, which has
low emission and high efficiency, is a promising alternative solution
to reduce the carbon emission [3,4]. Among all fuel cells, the proton
exchange membrane fuel cell (PEMFC), which works at temperatures below 100 C, has gained more attention because it can substitute for the current internal combustion engine in automotive
applications [5e7]. However, the major problem of introducing the
PEMFC to mass production of automotive applications is the uncertainty of the PEMFC reliability and life span [8,9]. The PEMFC life
span is affected by water and reactant management, where
improper management of water and reactant will degrade the gas
diffusion layer (GDL) and membrane electrode assembly (MEA)
[10e12]. In a PEMFC stack, the reactant is distributed from the
manifold to the cell and further into the flow field channels. The
uneven reactant distribution from the manifold to the cells will
reduce the performance of the PEMFC because the overall performance of a fuel cell stack is reduced by the weakest cell in the stack
* Corresponding author. Tel.: þ60 389118521; fax: þ60 389118530.
E-mail addresses: edy@ukm.edu.my, edyhm71@gmail.com (E.H. Majlan).
https://doi.org/10.1016/j.energy.2018.12.021
0360-5442/© 2018 Published by Elsevier Ltd.
[13]. Adding the quantity of cells in the stack will affect the reactant
distribution because a longer manifold tends to have an uneven
reactant distribution to cells further from the inlet [14].
Previous literature have numerically studied the effects of the
type of manifold configuration on the performance of a PEMFC
[14e16]. Chen et al. [15] studied the effect of the manifold
dimension on the pressure distribution and reported that larger
manifold widths improved the flow distribution. Mustata et al. [14]
investigated the Ue and Z-configuration stacks and found that the
Z configuration had a more uniform flow distribution. Wang [17]
and Pandiyan et al. [18] investigated the effect of the bipolar flow
field pattern on the PEMFC stack performance. Both investigation
reported that the optimization of the flow field design can improve
the performance of the PEMFC stack. Le & Zhou [19] numerically
studied the effect of water presence on the physical and transport
characteristics. They showed that the presence of water in the
model affected the stack performance because the current density
of a PEMFC stack is determined by the lowest current density cell.
Macedo-Valencia et al. [20] numerically investigated the thermal
distribution in a PEMFC stack. They observed the highest temperature near the ribs and outlet of the cathode. Multiple numerical
investigations of the PEMFC stack have been conducted to consider
the effects of the pattern, water and temperature on PEMFC stack
performance, but few investigations have been performed on the
effects of the number of cells on PEMFC performance. Thus, this
paper examines the effect of the quantity of cells in a stack on
B.H. Lim et al. / Energy 169 (2019) 338e343
339
PEMFC performance. The second part of this paper introduces
equations to predict the performance of a PEMFC stack when the
number of cells increases.
2. Modeling and simulation
A three-dimensional model of the dual, quad and hexa cells with
a single inlet/outlet for the cathode and a dual inlet/outlet for the
anode is shown in Fig. 1. The three-dimensional PEMFC stack model
includes the manifold of the anode and cathode, and each cell has a
MEA as well as GDL and bipolar plates. The cells are connected in
series; the conventional parallel flow field is used in the cathode, on
the anode a modified parallel flow field from previous studies is
used [21] (Fig. 2). Hydrogen and air are used as the reactant.
Hydrogen is supplied to each cell from two manifolds in the X-directions, and air is supplied through a single manifold in the
negative Z-direction. The parameters of the model are tabulated in
Table 1. Simulation was conducted using ANSYS where Design
Modular was used to create geometry and Meshing was used to
create mesh that will be used to solve the governing equations in
Fluent.
The governing equation was solved with the commercial software ANSYS, Fluent R15.0 was used to solve the governing equations. An additional add-on PEMFC module, which was developed
by ANSYS, was used to solve the fluid-based equation for the
PEMFC. The parameter inputs for the PEMFC add-on module were
set as suggested by the ANSYS manual [22]. In a previous study, a
grid independence test was performed for the flow field dimension.
Thus, in this study, only the MEA and GDL grid independence test
were performed. The result shows that approximately 1.2 million
elements were generated for each cell.
The boundary conditions to solve the governing equations are as
follows:
Inlet condition: minlet ¼ min
Outlet condition: Poutlet ¼ Pout
Boundary condition: no-slip boundary condition was imposed
for all channel walls
Two phases were considered in the model, where the liquid and
gaseous phases co-existed in the model. The governing equation to
solve the model is as follows:
The momentum conservation equation is given by
V$ðεrmuÞ ¼ εVp þ εmeff Vu þ Su
(1)
where p denotes pressure, and m denotes viscosity. Su in the above
equation results from the presence of porous media, where k is the
permeability of the porous media.
.
Su ¼ meff ε2 U k
(2)
Continuity equation, where the mass conservation in the channels and GDL is given by:
VðεruÞ ¼ Sm
(3)
where ε denotes porosity of the porous electrode, r denotes gas
mixture density, and u denotes fluid velocity vector. Sm indicates
the consumption and production of species during the electrochemical reaction in the PEMFC; it is zero in majority parts of the
model other than the anode and cathode catalyst layers. Sm denotes
the usage of reactant in anode and cathode as well as the generation of water in the cathode:
Fig. 1. Three-dimensional model: (a) dual cell; (b) quad cell; (c) hexa cell.
Sm ¼
X
Sk
(4)
k
Here, Sk is the source term of the kth species induced by the
electrochemical reaction in the active catalyst layers.
340
B.H. Lim et al. / Energy 169 (2019) 338e343
Fig. 2. Flow field: (a) anode; (b) cathode.
Table 1
Parameters for the simulation.
Parameters
Value
Active area (cm2)
Channel/rib width (mm)
Channel depth (mm)
Manifold width (mm)
GDL depth (mm)
Catalyst layer depth (mm)
Membrane depth (mm)
Operating temperature (K)
Operating pressure (atm)
Anode & cathode stoichiometry
1.69
1.0
0.8
2
0.5
0.005
0.06
353
1.0
2
SH2 ¼
1
(11)
4FCO2 jc
SH2 O ¼
1
2FCH2 O jc
(12)
Finally, the electrochemical reaction in the fuel cell simulation is
solved by the following two potential equations:
(5)
where leff is the effective thermal conductivity, Cp denotes isobaric
heat, and Sh denotes energy source term
Sh ¼ hreaction hja;c þ I 2 Rohm þ hphase
(6)
hphase ¼ rw h
(7)
rw ¼ cr max ð1 xÞ pwv psat R T MwH2 o :½sr1 g
(8)
where I denotes local current density, hreaction denotes water heat
formation, hphase is the rate of enthalpy change due to the formation
of water, ja and jc are the exchange current densities in the anode
and cathode, h is the over potential, rw denotes condensation rate
and x denotes liquid water.
The chemical reaction in the fuel cell, where hydrogen, oxygen
and water have a convective flow and a diffusion flow, is govern by
Fick's law equation
V$ðεruYi Þ ¼ V$ rDi:eff VYi þ Si
(10)
2FCH2 ja
SO2 ¼
The energy equation is
V$ leff VT ¼ V$ εrCp uT þ Sh
1
(9)
where Yi denotes mass fraction for species i and Di:eff denotes
effective diffusion coefficient for species i. Si denotes the source
term of oxygen consumption and water generation in the catalyst
layer and the species phase change in the liquid computation
domain. The subscript i denotes the sources terms in the fuel cell
given by the following:
V$ðss V∅s Þ þ js ¼ 0
(13)
V$ðsm V∅m Þ þ jm ¼ 0
(14)
where the first equation shows the potential equation of the electron transfer through a solid conductive material, such as the gas
diffusion layer and the current collectors. The second potential
equation describes the protonic transport through the membrane.
∅ is the electric potential, s denotes the electrical conductivity and
s and m represents solid and membrane phases.
The Butler-Volmer equation shown below is used to solve the
transfer current in the catalyst layer given by ja and jc , which are the
exchange current densities.
.
ja ¼ za jref
½A ½A
a
ref
.
jc ¼ zc jref
½C ½C
c
ref
!ga
!gc
aa F ha=
e
RT
ac F ha=
RT
e
a F h
a Fh
e c c=RT e a c=RT
(15)
(16)
where z is the surface-active area, g is the concentration dependence, a denotes transfer coefficient, F denotes Faraday constant
and R denotes universal gas constant. The term h denotes the
overpotential or activation losses, which is computed as follows,
where VOC is the open circuit voltage.
ha ¼ ∅s ∅m
(17)
hc ¼ ∅s ∅m VOC
(18)
B.H. Lim et al. / Energy 169 (2019) 338e343
341
Fig. 3. Comparison of the numerical and experimental data.
3. Results and discussion
The numerical investigation of PEMFC using Fluent has been
commonly demonstrated in many studies. Macedo-Valencia et al.
[20] reported their model development and validated their simulation results with experimental data. Thus, a model validation is
performed with their reported results, where their parameters,
such as the dimensions, membrane electrode assembly (MEA)
properties, operating conditions and geometric characteristics,
were used. The comparison results of the simulation with the
Macedo-Valencia et al. [20] data are shown in Fig. 3. The simulation
results show that there are differences with their experimental
data. However, Macedo-Valencia et al. produced a similar result for
the simulation data and reported that the difference in the
experimental and numerical data results from different component
properties for the experiment and numerical analyses. The author
simulation data are more consistent with the experimental data,
where the calculated current densities are less different from the
experimental data than the simulation data of Macedo-Valencia
et al. [20]. This result occurs because the multiphase condition
was used in the current simulation, which reduced the discrepancy
of water vapor existence in the model and the experimental condition, which caused the larger difference in current densities.
The main aim of this investigation is to obtain the performance
of the PEMFC stack for different quantities of cells. The single-cell
model was considered in this study, it is to understand the effect
of stacking the PEMFC on its performance. The simulation was
performed, and the polarization curves of the single-, dual-, quad-
Fig. 4. Polarization curve of the single, dual-, quad- and hexa-cell PEMFC models.
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B.H. Lim et al. / Energy 169 (2019) 338e343
Fig. 5. Change in current density as the quantity of cells changes in a PEMFC stack.
and hexa-cell PEMFC stacks are shown in Fig. 4. The cell potential is
the average potential of the number of cells considered in the
simulation. All the simulations were performed under the identical
operating condition for this study. Fig. 4 clearly shows that the
single-cell PEMFC model performs better than the dual-, quad- and
hexa-cell PEMFC stack models. When the number of cells increases
Table 2
Equations of the relationship between the current density and the number of cells.
Cell Potential, V (V)
Equation
0.4
I ¼ 0:679 þ 1:7988e1:6926n
0.5
I ¼ 0:615 þ 2:1275e2:0445n
0.6
I ¼ 0:530 þ 1:4601e1:9377n
0.7
I ¼ 0:440 þ 0:9550e1:723n
0.8
I ¼ 0:339 þ 0:5576e1:4496n
0.9
I ¼ 0:226 þ 0:2013e0:6592n
from 1 to 2, Fig. 4 shows that at the cell potential of 0.6 V, there is a
23.4% current density reduction because of the addition of manifold
in the PEMFC simulation model. The addition of a manifold into the
model decreases the performance of the PEMFC because the variation of flow resistance for each cell affects the reactant distribution. The captured current density was determined by the lowest
cell performance. Thus, the current density is higher for the singlecell PEMFC model. Further comparison of the dual-, quad- and
hexa-cell PEMFC stack current densities shows that the current
density decreases when the number of cells increases. However,
the current density almost did not deteriorate as the quantity of
cells increases from quad-to hexa-cell. Thus, the increase in the
quantity of cells in a stack stabilizes the PEMFC stack performance.
Fig. 4 shows that the performance decreases with the increase in
quantity of cells in a PEMFC stack. To predict the performance of a
larger PEMFC stack, the correlation amid the current density and
the quantity of cells is plotted and shown in Fig. 5. It was shown
Fig. 6. Prediction of the current density for different numbers of cells at 0.6 V.
B.H. Lim et al. / Energy 169 (2019) 338e343
that as the number of cell increases, the reduction rate of the current density in a stack is reduced. Thus, Table 2 shows the equations
of the relationship of different cell potentials between the current
density and the number of cells in Fig. 5. The equations in Table 2
can be used to predict the current density generation with the increase in number of cells in a stack.
From Table 2, the prediction of the current density generation
for different numbers of cells can be calculated. Therefore, the
current density of a 40-cell PEMFC stack at a cell potential of 0.6 V
was predicted in this study. The equation at 0.6 V from Table 2 was
used to predict the current density of the 40-cell PEMFC stack. Fig. 6
shows the predicted current density at 0.6 V from a single cell to
40 cells. The predicted current density for 40 cells is 5.3 A/cm2.
There was almost no change in current density from 20 cells to
40 cells because the PEMFC stack performance had reached
stability.
The equations in Table 2 to predict the polarization curve of a
PEMFC stack are limited to only the author design because changes
in the flow field design, manifold design and stacking method will
affect the performance of the PEMFC.
4. Conclusion
In this study, a numerical simulation was performed on threedimensional dual-, quad- and hexa-cell PEMFC stacks. The results
show that as the quantity of cells rises, the performance of the
PEMFC decreases. The largest difference in calculated current
density is between the single- and dual-cell models at 0.6 V the
current density difference was 23.4%. When the number of cells
increases from 2 to 6, the difference in calculated current density is
reduced dramatically. This research was carried out to predict the
performance of a PEMFC stack as the number of cells in stack increases. A set of equations was built to predict the current density
as the quantity of cells increases in a PEMFC stack. Equations was
built at different cell potential and performance of PEMFC stack
could be calculated based on the equations. The predicted current
density for 40 cells has shown almost no change in current density
from 20 to 40 cells. The equations formed in this study can reduce
the time and cost to predict the current density of a PEMFC stack.
Acknowledgements
The authors are grateful to the Ministry of Higher Education,
Malaysia (LRGS/2013/UKM-UKM/TP-01) and Universiti Kebangsaan
Malaysia (GUP-2016-044) for funding this work.
References
[1] Mesjasz-Lech A. Urban air pollution challenge for green logistics. Transp Res
343
Procedia 2016;16:355e65.
[2] Kumar P, Imam B. Footprints of air pollution and changing environment on
the sustainability of built infrastructure. Sci Total Environ 2013;444:85e101.
[3] Elmer T, Worall M, Wu S, Riffat SB. Fuel cell technology for domestic built
environment applications: state of-the-art review. Renew Sustain Energy Rev
2015;42:913e31.
[4] Garland NL, Papageorgopoulos DC, Stanford JM. Hydrogen and fuel cell
technology: progress, challenges, and future directions. Energy Procedia
2012;28:2e11.
[5] Abderezzak B, Busawon K, Binns R. Flows consumption assessment study for
fuel cell vehicles: towards a popularization of FCVs technology. Int J Hydrogen
Energy 2017;1e7.
€l S. Driver friendly: fuel cell/supercapacitor hybrid
[6] Thounthong P, Davat B, Rae
power sources for future automotive power generation. IEEE Power Energy
Mag 2008:69e76.
[7] Wilberforce T, El-Hassan Z, Khatib FN, Al Makky A, Baroutaji A, Carton JG, et al.
Developments of electric cars and fuel cell hydrogen electric cars. Int J
Hydrogen Energy 2017;42:25695e734. https://doi.org/10.1016/j.ijhydene.
2017.07.054.
[8] Pei P, Chen H. Main factors affecting the lifetime of Proton Exchange Membrane fuel cells in vehicle applications: a review. Appl Energy 2014;125:
60e75.
[9] Alaswad A, Baroutaji A, Achour H, Carton J, Al Makky A, Olabi AG. Developments in fuel cell technologies in the transport sector. Int J Hydrogen
Energy 2016;41:16499e508. https://doi.org/10.1016/j.ijhydene.2016.03.164.
[10] Fletcher T, Thring R, Watkinson M. An Energy Management Strategy to
concurrently optimise fuel consumption & PEM fuel cell lifetime in a hybrid
vehicle. Int J Hydrogen Energy 2016;41:21503e15.
[11] Ji M, Wei Z. A review of water management in polymer electrolyte membrane
fuel cells. Energies 2009;2:1057e106. https://doi.org/10.3390/en20401057.
[12] Cordiner S, Pietro Lanzani S, Mulone V. 3D effects of water-saturation distribution on polymeric electrolyte fuel cell (PEFC) performance. Int J Hydrogen
Energy 2011;36:10366e75. https://doi.org/10.1016/j.ijhydene.2010.09.063.
[13] Chang PAC, St-Pierre J, Stumper J, Wetton B. Flow distribution in proton exchange membrane fuel cell stacks. J Power Sources 2006;162:340e55. https://
doi.org/10.1016/j.jpowsour.2006.06.081.
~ o L, Barreras F, Gil MI, Lozano A. Study of the distribution of
[14] Mustata R, Valin
air flow in a proton exchange membrane fuel cell stack. J Power Sources
2009;192:185e9. https://doi.org/10.1016/j.jpowsour.2008.12.083.
[15] Chen C-H, Jung S-P, Yen S-C. Flow distribution in the manifold of PEM fuel cell
stack. J Power Sources 2007;173:249e63. https://doi.org/10.1016/
j.jpowsour.2007.05.007.
[16] Lim BH, Majlan EH, Daud WRW, Rosli MI, Husaini T. Numerical analysis of
flow distribution behavior in a proton exchange membrane fuel cell. Heliyon
2018;4:e00845. https://doi.org/10.1016/j.heliyon.2018.e00845.
[17] Wang J. Flow distribution and pressure drop in different layout configurations
with z-type arrangement. Energy Sci Technol 2011;2:1e12.
[18] Pandiyan S, Elayaperumal A, Rajalakshmi N, Dhathathreyan KS,
Venkateshwaran N. Design and analysis of a proton exchange membrane fuel
cells (PEMFC). Renew Energy 2013;49:161e5. https://doi.org/10.1016/
j.renene.2012.01.040.
[19] Le AD, Zhou B. A numerical investigation on multi-phase transport phenomena in a proton exchange membrane fuel cell stack. J Power Sources
2010;195:5278e91. https://doi.org/10.1016/j.jpowsour.2010.03.014.
[20] Macedo-Valencia J, Sierra JM, Figueroa-Ramírez SJ, Díaz SE, Meza M. 3D CFD
modeling of a PEM fuel cell stack. Int J Hydrogen Energy 2016;1e9.
[21] Lim BH, Majlan EH, Daud WRW, Rosli MI, Husaini T. Numerical analysis of
modified parallel flow field designs for fuel cells. Int J Hydrogen Energy
2016;42:9210e8.
[22] ANSYS FLUENT 12.0. Fuel cells module manual. Fuel Cells Bull 2001;4:97.
https://doi.org/10.1016/S1464-2859(01)80686-6.