Post on 13-May-2023
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INFLUENCE OF PARALLEL FLOW FIELD DESIGN ON THE PERFORMANCE OF PEM
FUEL CELLS
E. Barakat1, K. Ahmed
2, M. Ahmed
1,*, Ali K. Abdel-Rahman
1 and Ahmed Hamza H. Ali
1
1Department of Mechanical Engineering, Assiut University, Assiut 71516, Egypt
2Department of Mechanical and Industrial Engineering, Qatar University, Qatar
*Corresponding Author: aminism@aun.edu.eg.
ABSTRACT
Flow field design in PEM fuel cells has an important influence on both the power density and
efficiency of fuel cell systems. In order to effectively utilize the active area, flow distribution and current
density should be as homogenous as possible. In addition, pressure losses should be minimized. The main
objective of this work is to provide a comprehensive study of the flow field characteristics for different
parallel flow channel configurations. The investigated channel configurations are parallel with various
cross-sectional configurations. For each channel configuration pressure drop, species mass fraction,
velocity, and current distributions are numerically predicted. In addition, performance curves are
presented and discussed. The predicted performance parameters are compared with the corresponding
available experimental data. Based on the computed results the optimum channel design is selected.
Detailed results are presented and discussed. The present work would help PEM fuel cell manufacturers,
companies and researchers to choose the optimum configuration for their applications and products to
achieve the best possible performance.
KEYWORDS: PEM fuel cell, PEM flow field design, PEM fuel cell performance
1 INTRODUCTION
Proton Exchange Membrane (PEM) fuel cells can be considered as the best candidate to replace the
fossil fuel job in different applications. Modeling and optimization of the fuel cell and its components are
critical tasks to the fuel cell researchers and companies. The flow field design plays an important role in
controlling the PEM fuel cells performance. It can be used to direct the gas flow into the gas diffusion
layer through a channel system, provide uniform reactant flow over the active area, water management,
and make the cell mechanically stable (Li & Sabir 2005). Typical flow field designs are parallel,
serpentine, interdigitated and many other modified and/or combined configurations of channel designs.
The geometric parameters of flow field design that have a significant effect on the performance of fuel
cells include; active area, pattern type, cross-sectional shape, flow channels area, flow channel to the rib
width ratio, and the flow channel aspect ratio.
Many researchers studied the influence of such parameters in order to improve the fuel cell
performance. Wang et al.(2008) studied the effects of two flow field design (on cathode side) parameters
such as the flow channel aspect ratio, and cross-sectional area, on the cell performance and local transport
phenomena. They found that the channel aspect ratio and cross-sectional area had little effects on the cell
performance. Bachman et al. (2012) experimentally studied the effect of channel length on the
performance of fuel cell. In their work, three lengths of 5, 15 and 25 cm were selected to be investigated.
They concluded that the longer the channel length the better the cell performance. Camci et al. (2011)
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studied numerically, using COMSOL software, the effect of making obstacles inside the flow channels of
the bipolar plates. In addition, the effects of the inlet velocity, the outlet pressure, and the channel length
on the fuel cell performance were investigated. Results indicated that increasing outlet pressure, inlet
velocity and depth of the obstacles through the channels enhanced the cell performance. Wang et al.
(2009) studied numerically using a two-phase 3-d model, the effect of active area on the cell performance
using interdigitated and serpentine flow channel design. They found that in general increasing the active
area significantly improved the cell performance. In addition, in the case of using parallel flow field, the
performance at low voltages did not increase with increasing size of active area. They reported that this
could be partially due to their 100% humidified anode and cathode reactant feed gases. Other study was
conducted by (Wang et al. 2009) in order to study the effect of widths of flow channel and rib for the
various flow channel area ratio on the cell performance. They found that at higher operating voltages, the
cell performance is independent of the above reported parameters and the operating conditions while at
lower operating voltages, these parameters affect cell performance.
Su et al. (2005) studied experimentally and numerically the effect of parallel and serpentine flow
field on the cell performance. They found that the cell performance using serpentine design is better than
that using parallel one. Shimpalee et al. (2006) studied the effect of serpentine channel path length on the
cell performance using five different flow-field designs at constant active area of 200 cm2. They found
that the shorter path length gave more uniform current density distribution and less condensed liquid
water than the longer path. Karvonen et al. (2006) numerically investigated the effect of new distributor
channels (header) on the performance of a parallel flow channel design. They studied the flow distribution
across the channels and the total pressure drop across the flow field. They mentioned that using such
design could significantly reduce the pressure drop. Yan et al. (2006) experimentally studied the cell
performance of two parallel, two interdigitated, and one serpentine flow field channel. They
found that in a serpentine flow field the electrochemical reaction was raised as a result of
increasing in the channel numbers, the channel lengths and the number of corners.
Typically, the parallel channel configurations have a small hydraulic resistance and thus does not
generate a large pressure drop across the flow channel as reported by Karvonen et al. (2006). On the other
hand, the parallel channel flow field designs often have a non-uniform flow distribution (with respect to
other designs such as serpentine or interdigitated) and these configurations are consequently more
susceptible to flooding. However, these problems can partially be avoided with a careful design of the
flow field system. The objective of the present work is to find the optimal configuration of cross section
in order to achieve a better performance of fuel cells. Therefore, a complete 3-d PEM fuel cell model is
used to study the effects of the flow field channel designs on the cell performance for different parallel
flow fields. The local transport characteristics and the performance of cells with triangle, trapezoid (with
different aspect ratios), and half circle channels are compared to cell with a regular rectangular channel
design. A uniform flow distribution with the parallel channel system is presented, and the main result is to
show that uniform flow distributions can be achieved with parallel channel flow fields with relatively
slight changes in the flow field design.
2 MODEL GEOMETRY AND BOUNDARY CONDITIONS
2.1 MODEL GEOMETRY
A 3-d numerical model of one-channel cell is proposed in the current work to compare the channel
design effects on the cell performance by considering polarization curves of the cells. Details of the
governing equations are given in appendix. Different cell models are considered, depending on the
channel designs. A based reference model is developed using one channel based on the dimensions used
by Cheng et al. (2007), as shown in Table 1. The model shown in Figure 1 considers all fuel cell
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components; anode current collector, anode flow channel, anode gas diffusion layer, anode catalyst layer,
membrane, cathode catalyst layer, cathode gas diffusion layer, cathode flow channel and cathode current
collector. Mesh independency tests are performed to ensure that the model results are independent of the
grid size. A 130,000 cells mesh shown in Figure 2 is found to provide a sufficient resolution in the first
based reference model
Table 1: Cell dimensions
Geometrical parameters Units Value
Gas channel length mm 50.0
Height of gas channel mm 1.0
Width of the gas channel mm 1.0
Width of the cell mm 2.0
Thickness of catalyst layer mm 0.01
Thickness of gas diffusion layer mm 0.30
Thickness of current collector mm 2.0
Thickness of membrane mm 0.178
Figure 1: A single PEM fuel cell. (a) Complete cell with parallel flow channel and (b) model of one
channel
Figure 2: Model meshing
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2.2 BOUNDARY CONDITIONS
Anode and cathode boundary conditions are set as reactant species velocities at the inlets to model
the momentum transport. Reactant species mass fraction boundary conditions are applied at the inlets and
outlets for modeling the mass transport and diffusion phenomena. The motivating force for the
development of the electric current is the applied electric potential difference between the anode and
cathode electrodes. The anode voltage is set to zero (grounded) and the cathode voltage is set as the cell
operating voltage that take various volts starts from open circuit voltage. Polarization curves are obtained
by setting the cell voltage at constant value, solving the model, and integrating the local current density
value along the active layer, which gives the cell current density. Model boundary conditions are
summarized in Table 2.
Table 2: Model boundary conditions
B.C. Type Location Value Units Ref.
Velocity-
inlet
Inlet anode flow
channel face
Anode inlet gas velocity 0.3 m/s
(Cheng et
al. 2007)
Anode inlet mass fraction of H2 0.445
Anode inlet mass fraction of H2O 0.555
Inlet Cathode flow
channel face
Cathode inlet gas velocity 0.5 m/s
Cathode inlet mass fraction of O2 0.212
Cathode inlet mass fraction of N2 0.709
Cathode inlet mass fraction of
H2O 0.079
Pressure
outlet
Outlet anode flow
channel face Anode outlet gas pressure 0
Pa
(gage)
Outlet cathode flow
channel face Cathode outlet gas pressure 0
Pa
(gage)
Wall
The terminal and
upper anode current
collector face
Specified electric potential 0
volts (ANSYS
Inc. 2011) The terminal and
lower cathode
current collector
face
Specified electric potential 0.95 –
0.3
All Outer cell faces Thermal condition constant
temperature 323 k
(Cheng et
al. 2007)
3 MODEL SOLUTION
3.1 SOLUTION TECHNIQUE
The physical model presented in this work is comprehensive and includes the transport equations of
gaseous species, ionic charge, energy, mass, momentum, and water in the dissolved phase within the
membrane as shown in appendix. These equations are solved over a 3-d computational domain. The
physical model is solved with a commercially available CFD package, ANSYS FLUENT 14.0 with a
PEM fuel cell add-on module, adapted to include the transport relations relevant to PEMFCs (ANSYS
Inc. 2011). The monitored residuals for converged solution are set at 1E-6 for; pressure, velocities and
current density. The history of calculated current density with iterations for cell voltage 0.6 volts is
shown in Figure 3. The model physical parameters, shown in Table 3, are kept constant throughout the
study. These parameters are needed to fully describe the transport processes taking place within the fuel
cell. These parameters are available in the literatures as reported in Table 3.
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Figure 3: Convergence history of the predicted current density
Note: the negative sign due to the current direction
Table 3: Model physical parameters
Physical parameters Units Value Ref.
Cell operating temperature 0C 323 (Cheng et al. 2007)
Cell operating pressure pa 101325 (Cheng et al. 2007)
Open-circuit voltage volts 0.95 (Obayopo et al.
2011)
Anode Reference exchange current density A/m2 10000 (ANSYS Inc. 2011)
Cathode Reference exchange current
density
A/m2 20 (ANSYS Inc. 2011)
Current collector Electric conductivity 1/ohm-m 4000 (Cheng et al. 2007)
GDL Electric conductivity 1/ohm-m 300 (Cheng et al. 2007)
Anode exchange coefficient 1 (Iranzo et al. 2011;
Iranzo et al. 2010;
Arvay et al. 2011)
Cathode exchange coefficient 1 (Iranzo et al. 2011;
Iranzo et al. 2010;
Arvay et al. 2011)
GDL Porosity 0.5 (Cheng et al. 2007)
CL Porosity 0.112 (Cheng et al. 2007)
3.2 MODEL VALIDATION
The I-V curve for the current numerical results and that experimentally obtained by Cheng et al. (
2007) are in good agreement as shown in Figure 4. There is only a minimal difference between the
simulation results and the experimental data. The standard deviation in the predicted current density
based on the definition made by Giri and Bannerjee (1975) is found to be 0.008 A/cm2.
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Figure 4: Comparison of the present base model and experimental results obtained by Cheng et al. (2007)
4 RESULTS AND DISCUSSION
4.1 EFFECT OF FLOW DIRECTION
The most common arrangements for flow paths within the anode and cathode channel are counter-
flow, parallel-flow and mixed. A counter-flow fuel cell is one in which the direction of the flow of one of
the working fluids is opposite to the direction to the flow of the other fluid. In a parallel flow, both fluids
in the channel flow are in the same direction. A mixed flow can be achieved by making the anode and
cathode in different channels.
The fuel cell performance is measured by polarization curves which relate the cell voltage to both;
the current and power densities. The counter flow channel shows better performance at all current
densities than parallel flow channel as shown in Figure 5 and Figure 6. The counter flow increases the
performance by 11% compared to that obtained using parallel flow. In addition, the parallel flow channel
produces maximum output power of 0.24 W/cm2 at 0.50 A/cm
2, while the counter flow channel produces
maximum output power of 0.28 W/cm2 at 0.55 A/cm
2, with a 19% increase in the maximum output
power.
The counter flow channel shows a better mass fraction of the reactants species and better current
distributions as well. Figure 7 shows mass fraction of H2 and O2 in a plane centered at the flow channel
in both cases at 0.50 A/cm2, the maximum power point. It is observed that the hydrogen mass flow rate is
less than the needed amount by the chemical reaction at this point, which explains the missing of
hydrogen mass fraction at channel end.
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 0.1 0.2 0.3 0.4 0.5
Cel
l volt
age
Vcell (
volt
s)
Current density i (A/cm2)
Present model
Experimental Cheng et al. (2007)
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Figure 5: Polarization curve for different flow arrangement
Figure 6: Power density curve for different flow arrangement
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 0.2 0.4 0.6 0.8 1
Cel
l volt
age
Vcell (
volt
s)
Current density i (A/cm2)
I-V counter flow
I-V parallel flow
0
0.05
0.1
0.15
0.2
0.25
0.3
0 0.2 0.4 0.6 0.8 1
Pow
er d
ensi
ty p
(W
/cm
2)
Current density i (A/cm2)
I-P counter flow
I-P parallel flow
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Figure 7: Mass fraction of H2 and O2 in both cases at 0.50 A/cm2 (a) H2 mass fraction parallel flow (b) H2
mass fraction counter flow (c) O2 mass fraction parallel flow (d) O2 mass fraction counter flow
4.2 EFFECT OF CHANNEL LENGTH
This study aims to investigate the effect of channel length on the cell performance. The base fuel
cell design that used before in model validation is used for this study with changing channel length to
various lengths; 40, 80, 100, 150, 200, 250 mm. The results of this study show that the shorter channel
lengths achieve a higher performance at all current densities than that of the longer channels. Table 4
shows the maximum power and the corresponding current density for each length.
Figure 8 and Figure 9 show the effect of channel length on the cell performances. Based on the
figures, increasing the channel length significantly reduces the performance of fuel cell for all studied
cases. Figure 10 shows the effect of channel length on the current density at various cell voltages. It is
obvious based on the figure that increasing the channel length results in a significant reduction in the
current density. This trend is observed for all values of voltages in the range of 0.4, 0.6, 0.8, and 0.9 volts.
Table 4: The maximum power and the corresponding current density for each length
Channel length (mm) 40 80 100 150 200 250
Maximum power (W/cm2 ) 0.33 0.28 0.26 0.24 0.241 0.22
Current density (A/cm2) 0.64 0.57 0.56 0.56 0.51 0.40
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Figure 8: Polarization curve for different channel lengths
Figure 9: Power density curve for different channel lengths
0
0.2
0.4
0.6
0.8
1
1.2
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
Cel
l volt
age
Vcell (
volt
s)
Current density i (A/cm2)
length 40 mm
length 80 mm
length 100 mm
length 150 mm
length 200 mm
length 250 mm
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
Pow
er d
ensi
ty p
(W
/cm
2)
Current density i (A/cm2)
length 40 mm
length 80 mm
length 100 mm
length 150 mm
length 200 mm
length 250 mm
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Figure 10: Effect of channel length on the current density at various cell voltages
4.3 EFFECT OF FLOW CHANNEL CROSS-SECTION
For each cross-section, the channel land length (1 mm) remains the same. In addition, the channel
height (1 mm) remains the same except for half circle case. The constant cross section constrain does not
adapt with the same channel land length so the same area is chosen. The same boundary conditions,
channel length and all other physical properties are used for all cases to eliminate any other factors to,
solely, find the effect of flow channel configuration. Table 5 shows the designed cross-sections.
Figure 11 and Figure 12 show the effect of different designed cross-sections on the performance
curves. The reversed trapezoidal cross-section is the highest performance for the same channel land
length and the same height, because it is the largest area of them.
Table 5: Cross-section designs
Configu
ration
Rectangular Triangle Trapezoidal Reversed
trapezoidal
Half circle
channel
height
1 mm 1 mm 1 mm 1 mm 0.5 mm
channel
land
length
1 mm 1 mm 1 mm 1 mm 1 mm
Dimensi
ons and
Shape
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
40 mm 80 mm 100 mm 150 mm 200 mm 250 mm
Cu
rren
t d
ensi
ty i
(A/c
m2)
0.9 volts 0.8 volts 0.6 volts 0.4 volts
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Figure 11: Polarization curve for different cross-sections
Figure 12: Power density curve for different cross-sections
0
0.2
0.4
0.6
0.8
1
1.2
0 0.2 0.4 0.6 0.8 1
Cel
l volt
age
Vcell (
volt
s)
Current density i (A/cm2)
Half circle
Trapezoidal
Triangle
Rectangular
Reversed trapezoidal
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0 0.2 0.4 0.6 0.8 1
Pow
er d
ensi
ty p
(W
/cm
2)
Current density i (A/cm2)
Half circle Trapezoidal
Triangle rectangular
Reversed trapezoidal
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5 CONCLUSIONS
The effects of varying the flow field designs on the PEM fuel cells have been numerically
investigated. The flow direction in anode and cathode, channel length, and channel cross section
geometry are considered in the present work. The governing equations are solved with a commercially
available CFD package, ANSYS FLUENT 14.0 with a PEM fuel cell add-on module (ANSYS Inc. 2011).
Model validation is carried out by comparing the predicted results with the available experimental data.
Results indicate that counter flow direction in anode and cathode achieves a better performance of fuel
cells. In addition, a shorter length is recommended since it provides the maximum possible output power.
For the same channel land length and channel height, the reversed trapezoidal cross section shows the
best cell performance.
6 ACKNOWLEDGEMENT
Authors acknowledge Misr El Kheir foundation for its financial support provided to carry out
attend ICCE 2013 conference.
REFERENCES
ANSYS Inc., 2011. ANSYS FLUENT 14.0 fuel cells module manual.
http://cdlab2.fluid.tuwien.ac.at/LEHRE/TURB/Fluent.Inc/v140/flu_fcm.pdf.
Arvay, A. et al., 2011. Convergence criteria establishment for 3D simulation of proton exchange
membrane fuel cell. International Journal of Hydrogen Energy, 37(3), pp.2482–2489. Available at:
http://dx.doi.org/10.1016/j.ijhydene.2011.11.005.
Bachman, J. et al., 2012. Experimental investigation of the effect of channel length on performance and
water accumulation in a PEMFC parallel flow field. International Journal of Hydrogen Energy,
37(22), pp.I7172–I7179. Available at:
http://linkinghub.elsevier.com/retrieve/pii/S0360319912018253 [Accessed April 28, 2013].
Camcı, T. et al., 2011. MODELING OF GAS FLOW CHANNELS FOR PROTON EXCHANGE
MEMBRANE FUEL CELLS. In IGEC. pp. 381–388.
Cheng, C.-H., Lin, H.-H. & Lai, G.-J., 2007. Design for geometric parameters of PEM fuel cell by
integrating computational fluid dynamics code with optimization method. Journal of Power
Sources, 165(2), pp.803–813. Available at:
http://linkinghub.elsevier.com/retrieve/pii/S0378775306025584 [Accessed August 1, 2011].
Iranzo, A. et al., 2010. Numerical model for the performance prediction of a PEM fuel cell. Model results
and experimental validation. International Journal of Hydrogen Energy, 35(20), pp.11533–11550.
Available at: http://linkinghub.elsevier.com/retrieve/pii/S0360319910008311 [Accessed May 2,
2012].
Iranzo, A. et al., 2011. Update on numerical model for the performance prediction of a PEM Fuel Cell.
International Journal of Hydrogen Energy, 36(15), pp.9123–9127. Available at:
http://linkinghub.elsevier.com/retrieve/pii/S0360319911009670 [Accessed May 2, 2012].
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Karvonen, S. et al., 2006. Modeling of flow field in polymer electrolyte membrane fuel cell. Journal of
Power Sources, 161(2), pp.876–884. Available at:
http://linkinghub.elsevier.com/retrieve/pii/S0378775306008020 [Accessed December 31, 2011].
Li, X. & Sabir, I., 2005. Review of bipolar plates in PEM fuel cells: Flow-field designs. International
Journal of Hydrogen Energy, 30(4), pp.359–371. Available at:
http://linkinghub.elsevier.com/retrieve/pii/S0360319904003453 [Accessed April 13, 2011].
Obayopo, S., Bello-Ochende, T. & Meyer, J.P., 2011. Three dimensional optimisation of a fuel gas
channel of a proton exchange membrane fuel cell for maximum current density. International
Journal of Energy Research, 37(3), pp.228–241. Available at:
http://onlinelibrary.wiley.com/doi/10.1002/er.1935/full [Accessed June 25, 2013].
P.K.Giri & J.Bannerjee, 1975. Introduction To Statistics, Academic Publishers. Available at:
http://books.google.com.eg/books?id=E1zn5ukZemIC [Accessed June 25, 2013].
Shimpalee, S., Greenway, S. & Van Zee, J.J.W., 2006. The impact of channel path length on PEMFC
flow-field design. Journal of Power Sources, 160(1), pp.398–406. Available at:
http://linkinghub.elsevier.com/retrieve/pii/S0378775306003673 [Accessed May 24, 2011].
Su, A., Chiu, Y.C. & Weng, F.B., 2005. The impact of flow field pattern on concentration and
performance in PEMFC. International Journal of Hydrogen Energy Research, 29, pp.409–425.
Wang, X. et al., 2008. Effects of flow channel geometry on cell performance for PEM fuel cells with
parallel and interdigitated flow fields. Electrochimica Acta, 53(16), pp.5334–5343. Available at:
http://linkinghub.elsevier.com/retrieve/pii/S0013468608003435 [Accessed April 9, 2011].
Wang, X.-D. et al., 2009. Determination of the optimal active area for proton exchange membrane fuel
cells with parallel, interdigitated or serpentine designs. International Journal of Hydrogen Energy,
34(9), pp.3823–3832. Available at: http://linkinghub.elsevier.com/retrieve/pii/S0360319908017564
[Accessed December 13, 2011].
Yan, W. et al., 2006. Experimental studies on optimal operating conditions for different flow field designs
of PEM fuel cells. Journal of Power Sources, 160(1), pp.284–292. Available at:
http://linkinghub.elsevier.com/retrieve/pii/S0378775306000760 [Accessed May 21, 2011].
APPENDIX
This section discusses the model parameters based on ANSYS FLUENT fuel cell module manual
(Arvay et al. 2011; Iranzo et al. 2011; Iranzo et al. 2010; ANSYS Inc. 2011). The transport of gas
mixtures in the gas channels and in the electrodes conforms to the mass, momentum, species conservation
principles, and electrochemical reactions. The 3D fluid flow and heat transport is solved using CFD
techniques, which include conservation of mass, momentum and energy that can be expressed in the
Naviere-Stokes equations are written as follows:
(1)
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The conservation equation in this form states that the rate of change quantity plus the transport
due to convection plus the transport due to diffusion is equal to the source. is the transported quantity
(energy, momentum), t is time, A is the surface area, V is volume, is the diffusivity coefficient , S is the
source term.
Equations for the surface over-potential, the driving force behind the electrochemical reactions
within the fuel cell simulation, are solved according to the following two equations
(2)
The first equation describes the difference between the phase potential of the solid materials which
governs the transport of electrons through the GDL porous material and current collectors. The second
equation describes ionic transport of ions through the membrane. represents the electrical
conductivity ( ); is the electric potential (volts); is the volumetric transfer current (
) in the solid or membrane.
Transfer currents are computed within the catalyst layers using the Butler-Volmer function.
(4)
(5)
is the specific active surface area ( ). is the reference exchange current density per active
surface area . The quantities in the brackets represent the local species concentration );
is the concentration dependence; is the transfer coefficient. F is Faradays constant and R is the
universal gas constant. The quantity is the local surface over-potential or activation loss which is
computed using the following equations where is the open circuit voltage.
(6)
(7)
Mass conservation is obeyed using volumetric species mass terms.
(8)
(9)
(10)
Where represents the species source term (Kg/s.m3); is the molecular mass of the species
(kg/kmole). The sign of the equations indicate that hydrogen and oxygen are consumed while is
generated. The electric current is conserved by obeying the following equation.
(3)
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(11)
Volumetric sources for thermal energy are required because not all of the chemical energy is
converted to electrical work. This is accounted for by using a thermal energy (rate of enthalpy change, )
equation
(12)
where is the net rate of enthalpy change (J/s) due to the electrochemical reactions.
is the product of the transfer current and the over-potential in the anode or cathode.
is the ohmic resistivity of the conducting media and I is the current (A). is the rate of enthalpy
change due to phase changes of the water.
Flow within the porous media of the GDLs and catalyst layers is modeled by adjusting the source
term by adding a negative source which represents fluid flow pressure drops in the species equations and
calculating species diffusivities.
( 13)
Si indicates the source in i direction. is the kinematic viscosity (m2/s), the fluid density (kg/m
3),
are the velocity and magnitude of the velocity (m/s), C2 is the inertial resistance factor (m-1
).