Abstract A full three-dimensional, non-isothermal computational fluid dynamics model of a proton exchange membrane fuel cell (PEMFC)
with both the gas distribution flow channels and the membrane electrode assembly (MEA) has been developed. A single set of conserva-tion equations which are valid for the flow channels, gas-diffusion electrodes, catalyst layers, and the membrane region are developed and numerically solved using a finite volume based computational fluid dynamics technique. In this research some parameters such as Oxygen consumption and fuel cell performance according to the variation of porosity, thickness of gas diffusion layer, and the effect of the boundary conditions were investigated in more details. Numerical results shown that the higher values of gas diffusion layer porosity improve the mass transport within the cell, and this leads to reduce the mass transport loss. The gas diffusion layer thickness affects the fuel cell mass transport. A thinner gas diffusion layer increases the mass transport, and consequently the performance of the fuel cell. Furthermore, the study of boundary conditions effects showed that by insulating the bipolar surfaces, hydrogen and oxygen consumption at the anode and cathode sides increase; so that the fuel cell performance would be optimized. Finally the numerical results of proposed CFD model are compared with the available experimental data that represent good agreement.
Fuel cells convert the chemical energy of fuel into electrical energy. It has very important role to provide electrical energy in future world. Useful features such as high power density, safety, reliability and simple structure make those suitable to home appliance, vehicles and transportation tools.
Many parameters have effected fuel cell operation as hu-midity, temperature, pressure and membrane structure and feeding channel geometry, and etc. Therefore, the foremost problem is to foresee fuel cell operation.
Several coupled fluid flow, heat and mass transport proc-esses occur in a fuel cell in conjunction with the electrochemi-cal reaction. These processes have a significant impact on two important operational issues: (i) thermal and water manage-ment, and (ii) mass transport limitations. Water management ensures that the polymer electrolyte membrane remains fully hydrated to maintain good ionic conductivity and performance. Water content of the membrane is determined by the balance between water production and three water transport processes: electro-osmotic drag of water, associated with proton migra-
tion through the membrane from the anode to the cathode side; back diffusion from the cathode; and diffusion of water to/from the oxidant/fuel gas streams. Without control, an im-balance between production and removal rates of water can occur. This results in either dehydration of the membrane or flooding of the electrodes; both phenomena have a very det-rimental effect on performance and fuel cells have to be care-fully designed to avoid the occurrence of either phenomenon. Thermal management is required to remove the heat produced by the reaction in order to prevent the membrane drying.
The 3D flow and electrochemical simulations are based on single domain fuel cell model established by Um et al. [1]. The notable work has been done by Bernardi and Verbrugge [2, 3] and Springer et al. [4] that extended one dimensional, isothermal models of fuel cells. A two dimensional model emphasizing the effects of two-phase water and heat transport was developed by Fuller and Newman [5], Nguyen and White [6] and Gurau and Liu [7].
The present numerical model considers a single-domain for-mulation without requiring boundary conditions at interfaces internal to the fuel cell, thus facilitates implementation into a commercial computational fluid dynamics (CFD) package. Moreover, the model contains a detailed membrane electrode assembly (MEA) sub model where, the water content distribu-tion within the membrane. Hence, the spatial variations of
† This paper was recommended for publication in revised form by Associate Editor Yong-Tae Kim
2666 N. Pourmahmoud et al. / Journal of Mechanical Science and Technology 25 (10) (2011) 2665~2673
reaction rate and ionic resistance within the catalyst layer are fully resolved [1].
The hydrogen-rich fuel is fed to the anode, where the hy-drogen diffuses through the porous gas diffusion electrode (GDE). At the catalyst layer, the hydrogen splits into hydro-gen protons and electrons according to:
.
Driven by an electric field, the H+ ions migrate through the
polymer electrolyte membrane. The oxygen in the cathode gas stream diffuses through the gas diffusion electrode towards the catalyst interface where it combines with the hydrogen pro-tons and the electrons to form water as follows:
.
The overall reaction is regarded as exothermic, and be-
comes:
. Water management is a principal issue in PEMFC technol-
ogy because high water content results in high proton conduc-tivity of the membrane, thus decreasing ohmic voltage loss.
Commonly, two methods are used to hydrate the membrane. One is to externally humidify inlet reactant gases. This strat-egy requires a humidifier making it complex and expensive to be applied to portable or mobile systems. The other way is to make full use of water production inside a PEMFC and hu-midify reactant gases internally. In the latter approach, Qi and Kaufman [8] proposed a counter-flow cathode flow field de-sign, where an inlet gas channel is placed next to an outlet channel in hopes that the moist air in the outlet channel will help humidify the dry air in the inlet channel. Such a self-humidification process is of technological interest as it has the potential to feed dry reactants without external humidification. While cell polarization experiments have been reported by Qi and Kaufman [8] for this flow field design, a fundamental understanding of the complex transport phenomena uniquely present in this flow configuration is absent.
In this article a single-phase, three dimensional, non-isothermal model for PEMFC is presented to describe the fundamental processes occurring in each component of a fuel cell–current collector, gas diffusion layer (GDL), catalyst layer (CL), and the membrane. Two electric potential field equations were solved in computational domain.
2. Physical parameter
Figs. 1 and 2 schematically show a PEMFC divided into the following sub-regions: the current collector, gas flow channel, gas diffusion layer, catalyst layer in the anode, cathode sides, and the membrane in the middle.
The middle planes of the flow channels and bipolar plates
are assumed as symmetry plane, because the structure of the fuel cell system in this model is supposed to repeat periodi-cally along the x-direction. Hence, here only half the domain is taken into account. This assumption seems to be logical until no cross-flow takes place between the channels that are placed next to each other. The reactant feed is conveyed by the gas flow channel and distributed onto the anode and cathode [9]. Reactants pass through the respective porous GDLs and reach the CLs where the electrochemical reaction occurs. The membrane acts as the gas separator, electrolyte and the proton conductor. The electrons are then collected by the anode cur-rent collector, which is connected to cathode current collector through the external load.
Fuel cell operating condition is illustrated in Table 1. It is used fully humidified inlet condition for anode and cathode inlet. The transfer current at anode and cathode can be de-scribed by Tafel equations.
Protons and electrons are the positively and negatively charged ions. The proton transfer in the proton conducting regions and the electron transfer in the electronic conducting regions determines the potential distribution in a cell. The polymer as electrolyte in the membrane and catalyst belongs to proton conducting region. While the catalysts, GDLs and BPs (Bipolar) including gas flow channels is regarded as elec-trode. Important geometrical parameters are listed in Table 2.
Fig. 1. Three dimensional schematic diagram.
Fig. 2. X-Y view of the Computational mesh of the domain.
N. Pourmahmoud et al. / Journal of Mechanical Science and Technology 25 (10) (2011) 2665~2673 2667
3. Numerical model
Governing equations of continuity, momentum, species concentrations of different component, electrical potential, and protonic potential equation are solved with various source terms. Electrical potential, protonic potential equations are coupled with chemical Reaction kinetics by introducing vari-ous source terms.
3.1 Model assumptions
The proposed model includes the following assumptions: (1) The system operates under a steady-state condition. (2) The incoming gas mixtures are incompressible ideal fluids.
(3) The flow in the channels is laminar because of small pres-sure gradients and flow velocities.
(4) The gas diffusion layers, catalyst layers and membrane are isotropic and homogeneous porous media.
(5) The membrane is considered impassable for reactant gases. (6) The water in the pores of diffusion layer is considered
separate from the gases in the diffusion layers, i.e. no in-teraction between the gases and the liquid water exists.
(7) The product water is considered as the liquid phase. (8) In the cell, because of the electrochemical reaction, the
process is non-isothermal, but the walls of the cell and inlet gases have constant temperature.
4. Governing equations
The proposed model is based on a single-domain approach for the governing equations, which are applicable for all the sub-domains used. So, at the interfaces between the sub-domains of the cell no interfacial conditions are employed. According to the preceding assumptions for the model, the governing equations can be written as below:
Mass conservation:
.( ) 0ερυ∇ = (1)
where ρ and v are the density of gas mixture and the fluid velocity vector, respectively.
Momentum conservation equation:
2.( ) ( )p Sυερυυ ε εμ υ∇ = − ∇ + ∇ + (2)
where ε and μ denote the effective porosity inside the porous mediums and the viscosity of the gas mixture, respec-tively. The source term in the momentum equation, is used to represent Darcy’s drag for flow through porous gas diffusion layers and catalyst layers as:
.vSkμν= − (3)
Here, k is the permeability inside porous mediums. Species conservation equation:
.( ) .i i iY J Sερυ∇ = −∇ + (4)
where i denotes the chemical species involving hydrogen, oxygen, nitrogen, and water. Therefore, J vector can be writ-ten as:
effi iJ D C= ∇
r r. (5)
eff
iD is the effective diffusion coefficient that is used to de-scribe the porosity effects in the porous gas diffusion layers and catalyst layers of species. It is defined by the Bruggeman equation as:
1.5( )eff eff
i iD Dε= . (6) Also, the diffusion coefficient is specified as a function of
temperature and pressure by the following correlation:
1.5( ) ( )o oi i
o
T PD DT P
= . (7)
The species source terms then becomes:
2
2
,
2w H
H a
MS R
F= − (8)
Table 1. Cell operating condition.
Parameter Symbol Value
Cell temperature (0C) Tcell 80
Pressure at the anode (atm) Pa 3
Relative humidity of inlet fuel RHa 1
Pressure at the cathode (atm) Pc 5
Relative humidity of inlet air RHc 1
Anode stoichiometry ζa 3
Cathode stoichiometry ζc 3
Reference current density A/cm2 Iref 1
Anode transfer coefficient αa 0.5
Cathode transfer coefficient αc 1
Table 2. Cell design parameter.
Parameter Value
Cell /electrode length (mm) 50
Gas channel height (mm) 1
Gas channel width (mm) 1
GDL thickness (mm) 0.26
Porosity of anode GDL (ε) 0.4
Catalyst layer thickness (mm) 0.0287
Porosity of catalyst layer (ε) 0.4
Membrane thickness (mm) 0.23
2668 N. Pourmahmoud et al. / Journal of Mechanical Science and Technology 25 (10) (2011) 2665~2673
2
2
.
4w O
O c
MS R
F= − (9)
2
2
, .2w H O
H O c
MS R
F= (10)
Charge conservation equation:
.( . )e Sε φσ φ∇ ∇ =r r
(11)
where eσ and eφ are the ionic conductivity in the mem-brane and the electrolyte phase potential, respectively. The source term in the charge equation, φS , in the catalyst layers is equal to exchange current density. In the other sub-layers no source term is needed.
The protonic conductivity of membrane is dependent on water content, and it has been correlated by Springer et al. [4]:
1 1(0.514 0.326)exp 1268( )
303e Tσ λ ⎡ ⎤= − −⎢ ⎥⎣ ⎦
(12)
2 30.043 17.18 39.85 36 ( 1)
14 1.4( 1) ( 1) .
α α α αλ
α α
⎧ + − + <⎪= ⎨⎪ + − >⎩
(13)
Here, λ is water content. The number of water molecules
for each sulfonate group in the membrane is called water con-tent. The water content is defined by the following equation as a function of water activity as:
Water activity is defined as:
wv
sat
PP
α =
2wv H oP x P= 5 2
7 3( 2.1794 0.02953( 273.17) 9.1873 10 ( 273.17)
1.4454 10 ( 273) )10T T
TsatP
−
−− + − − × −− × −= . (14)
wvP and satP refer to water vapor pressure and saturation
pressure. 2H ox is also the mole fraction of water.
The general energy equation can be written as:
.( ) .( )eff TvT T Sρ λ∇ = ∇ ∇ + (15)
where effλ is the effective thermal conductivity. The source term, that is TS , defined with the Eq. (15) in form of:
2
T ohm reaction a a c cS I R h i iη η= + + + . (16) In this equation, ohmR is the ohmic resistance of the mem-
brane. reactionh is the heat generated thorough the chemical reactions, aη and cη are the anode and cathode over poten-tials. They are calculated by:
m
ohme
tRσ
= . (17)
Here, mt is the membrane thickness.
2
lna H
aa o O
RT IPF j P
ηα
⎡ ⎤⎢ ⎥=⎢ ⎥⎣ ⎦
(18)
2
lnc O
ac o O
RT IPF j P
ηα
⎡ ⎤= ⎢ ⎥
⎢ ⎥⎣ ⎦ (19)
In these equations, aα and cα are the anode and cathode
transfer coefficients, respectively. oP is the partial pressure of hydrogen and oxygen, and
oj stands for the reference
exchange current density. The local current density of the cell is defined as:
( )eOC cell
m
I V Vtσ η= − − . (20)
Here, OCV is the open circuit voltage, and η represents
the losses.
5. Water transport
In polymer electrolyte fuel cells, the water molecules trans-port in the membrane is performed by electro-osmotic drag and the molecular diffusion. The water transport through the polymer electrolyte membrane by the hydrogen protons is called Electro-osmotic drag mechanism. Also, because of the oxygen reduction reaction in the cathode catalyst layer, water vapor is produced. The following conservation equation de-termines water transport through the polymer electrolyte membrane:
2 2.( . .( )) 0mem mem d
H o H onD C iF
∇ ∇ −∇ = (21)
where
2
memH oD is the water diffusion coefficient in the membrane
and dn is the water drag coefficient from anode to cathode. The drag coefficient of water is determined as the number of water molecules carried by each hydrogen proton. The water drag coefficient can be expressed as [10]:
1 ( 9)
0.117 0.0544 ( 9) .
λλ
λ λ
⎧ <⎪= ⎨− ≥⎪⎩
(22)
The water diffusion coefficient in the membrane is defined
as a function of the water content of the membrane and is expressed as [11]:
7 0.28 ( 2346/ )
9 ( 2346/ )
3.1 10 ( 1) 0 3
4.17 10 (1 161 ) .
Tmem
w T
e e
e e otherwiseDλ
λ
λ λ
λ
− −
− − −
⎧ × − < ≤⎪= ⎨× +⎪⎩
(23)
The terms are therefore related to the transfer current
through the solid conductive materials and the membrane. The transfer currents or source terms are non-zero only inside the
N. Pourmahmoud et al. / Journal of Mechanical Science and Technology 25 (10) (2011) 2665~2673 2669
catalyst layers. The transfer current at anode and cathode can be described by Tafel equations as follows:
( )/2
2
[ ][ ]
ca a
aaFF RTref RT
a aref
HR j e eH
γ
α ηα η −⎛ ⎞= −⎜ ⎟⎜ ⎟
⎝ ⎠ (24)
( )/2
2
[ ][ ]
ca c
ccFF RTref RT
c aref
OR j e eO
γα ηα η −⎛ ⎞
= − +⎜ ⎟⎜ ⎟⎝ ⎠
. (25)
6. Boundary conditions
The computational domain is divided into 240000 cells. Boundary conditions are set as follows: constant mass flow rate at the channel inlet and constant pressure condition at the channel outlet. The inlet mass fractions are determined by the inlet pressure and humidity according to the ideal gas law. Gradients at the channel exits are set to zero.
The inlet velocities are defined as:
2
,,
,
1 12
ref a ina in a MEA
a in H in ch
I RTv A
F P X Aς= (26)
2
,,
, ,
1 14
ref c inc in c MEA
c in o in ch
I RTv A
F P X Aς= (27)
where R, inT , inP , and ς
are the universal gas constant,
temperature in the inlet, pressure in the inlet, and stoichi-ometric ratio which is defined as the ratio between the amount supplied and the amount required of the reactant on the basis of the reference current density refI , respectively. At outlet gas-flow channels, the pressure is expressed as the electrode pressure.
7. Results and discussions
To validate the numerical simulation model used in this study, the performance curves of voltage and current density are compared with the experimental data of Ticianelli et al.
[12] in Fig. 3. The computed polarization curve is in favorable agreement with the experimental data. Power density curve also is shown in this figure, which can be evaluated by well known electric equation P=VI.
7.1 Oxygen distribution
Oxygen mole fraction distribution at the middle of cathode catalyst layer is shown in Fig. 4. It shows that oxygen is high at the entrance of flow channel and then decrease along the cathode channel direction because of consumption at cathode chemical reaction surface.
Water concentration at the cathode channel increased along the flow channel (Fig. 5). This increase of water concentration was associated with the fact that the water was formed by electrochemical reaction along the channel, and the water was transported from anode side by electro-osmotic drag simulta-neously.
The oxygen mole fraction along the cathode channels de-creased along the channel due to oxygen consumption by wa-ter formation.
Therefore, the water transport through the membrane is very
Fig. 3. predicted and experimental [12] cell polarization curves.
Fig. 5. Water mole fraction at cathode catalyst layer V=0.46 (V).
2670 N. Pourmahmoud et al. / Journal of Mechanical Science and Technology 25 (10) (2011) 2665~2673
crucial for simulating the water concentration and determining of water content in the membrane. The temperature variation along the width of channel is due to the fixed temperature and good thermal conductivity of both anode and a cathode bipo-lar plate, shown in Fig. 6. The slight temperature drop along the channel is because of the effects of heat generation from the electrochemical reactions, water evaporation, and finally fixed top surface temperature of both anode and cathode bipo-lar plates. Usually, the membrane water content falls at the beginning of the channel and causes to increase the tempera-ture sharply. Farther of the channel entrance, temperature de-creases slowly as the membrane water contents increase through the electrochemical reactions.
The profiles of the oxygen mole fraction at the membrane–cathode GDL interface shown in Fig. 7 and Fig. 8 for V=0.46 (V), respectively.
Oxygen scarcity in the shoulder region over the reacting area leads to higher concentration losses, which becomes worse in the downstream region of the channel due to deple-tion of the reactant with moving downstream. More often, at high operating current density, further molecules react and hence more water is produced. This results in larger quantities of water at the GDL, which reduces the oxygen diffusivity in the cell. This effect is particularly severe in the shoulder area, where water tends to accumulate. These contours and figures are displayed for half mono cell as a computational domain corresponds to Fig. 2.
7.2 Effect of GDL thickness
A thinner gas diffusion layer gives rise to the mass transport through it, and this leads to reduction in the mass transport loss. The molar oxygen fraction at the catalyst layer grows up with decreasing gas diffusion layer thickness due to the re-duced resistance to the oxygen diffusion by the thinner layer.
In Fig. 9 the effect of GDL thickness has been studied the
Fig. 6. Comparison of temperature at the membrane–cathode GDLinterface. Blue (entry region) and red (exit region).
Fig. 7. O2 mole fraction at the membrane–cathode GDL interface (exit region).
Fig. 8. O2 mole fraction at the membrane–cathode GDL interface (en-try region).
Fig. 9. The effect of GDL thickness on polarization curve.
N. Pourmahmoud et al. / Journal of Mechanical Science and Technology 25 (10) (2011) 2665~2673 2671
fuel cell potential and current density. Increasing the GDL thickness from 0.26 up to 0.3 mm causes the fuel cell potential clearly decreases. In the contrary decreasing from 0.26 to 0.22 mm helps to enhance of fuel cell performance.
7.3 Effect of GDL porosity
The porosity of the gas diffusion layer has two competing effects on the fuel cell performance. As the porous region provides the space for the reactants to diffuse towards the catalyst region, an increase in the porosity means that the on-set of mass transport limitations occurs at higher current densi-ties. The molar oxygen fraction at the catalyst layer increases with more distribution by increasing the porosity.
This is because a higher value of the porosity provides less resistance for the oxygen to reach the catalyst layer. Fig. 10 shows the effect of GDL porosity increase from 0.4 to 0.5 and also its decrease from 0.4 to 0.2 on polarization curves.
7.4 Effect of the boundary conditions
Figs. 11(a) and 11(b) show two kinds of boundary condi-tions. The temperature rise for the insulated boundaries along the flow path from inlet to outlet occurs because heat genera-tion is produced by electrochemical reactions. Hence, the temperature rise due to isothermal boundary conditions is less than insulated one. Temperature increase yields better and more reactions in the cathode catalyst layer. Thus the hydro-gen and oxygen consumption at the anode and cathode, as a parameter to judge the performance of the fuel cell, will in-crease.
Fig. 12 shows average mole fraction of oxygen in cathode catalyst layer at V=0.46 (V) for two boundary conditions. Insulating the boundary, given rise to the hydrogen and oxy-gen consumption, and decreases the average mole fraction of oxygen.
Fig. 10. The effect of GDL porosity on polarization curve.
Fig. 12. Average mole fraction of oxygen in cathode catalyst layer at V=0.46 for two boundary conditions.
2672 N. Pourmahmoud et al. / Journal of Mechanical Science and Technology 25 (10) (2011) 2665~2673
8. Conclusions
In this article a full three-dimensional, non-isothermal com-putational fluid dynamics model of a proton exchange mem-brane fuel cell (PEMFC) has been investigated for both the gas distribution flow channels and the Membrane Electrode Assembly (MEA). Among from many parameters that affects this type of fuel cell operation, such as humidity, temperature, pressure, membrane structure, feeding channel geometry, and etc., therefore the present numerical study investigates the GDL porosity and thickness and also the insulating of the bipolar walls effects on fuel cell performance.
The obtained numerical results show that a thinner gas dif-fusion layer increases the mass transport. This leads to the reduction of the mass transport loss. The molar oxygen frac-tion at the catalyst layer increases with decreasing of gas dif-fusion layer thickness due to the reduced resistance to the oxygen diffusion by the thinner layer. Fuel cell potential clearly decreases as GDL thickness increases.
The molar oxygen fraction at the catalyst layer rises consid-erably by increasing of the porosity. This is because a higher value of the porosity provides less resistance for the oxygen to reach the catalyst layer. Insulating the boundaries helps to increase the hydrogen and oxygen consumption and decreas-ing of the average mole fraction of oxygen; then fuel cell per-formance would be increased.
a : Water activity C : Molar concentration (mol/m3) F : Faraday constant (C/mol) I : Local current density (A/m2) J : Exchange current density (A/m2) K : Permeability (m2) M : Molecular weight (kg/mol)
dn : Electro-osmotic drag coefficient P : Pressure (Pa) R : Universal gas constant (J/mol-K) T : Temperature (K) T : Thickness ν : Velocity vector V : Cell voltage Voc : Open-circuit voltage W : Width X : Mole fraction
Greek letters
α : Water transfer coefficient effε : Effective porosity ρ : Density (kg/m3) μ : Viscosity (kg/m-s)
eσ : Membrane conductivity (1/ohm-m)
λ : Water content in the membrane ς : Stoichiometric ratio η : Overpotential (v)
A : Anode C : Cathode Ch : Channel K : Chemical species M : Membrane MEA : Membrane electrolyte assembly Ref : Reference value Sat : Saturation W : Water
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Nader Pourmahmoud was born in 1969 in Oshnavieh city in Iran. He re-ceived BS degree in Mechanical Engi-neering in Shiraz University in 1992. After achieving some of practical engi-neering projects till 1997 he started Msc. degree in mechanical engineering (en-ergy conversion field) in Tarbiat Modar-
res University in Tehran and finally he received his Ph.D de-gree in mechanical engineering (energy conversion field) in 2003 at the same university in Iran. He is an assistance profes-sor in the mechanical engineering department at faculty of engineering of Urmia University. His professional interests are in the field of CFD of Turbulent fluid flow, energy conversion problems and especially in fabricating of specific Vortex Tube.
Sajad Rezazadeh was born in Urmia in1984. He passed entrance exam of Technical University of Urmia in me-chanical course in 2002. Immediately after finishing B.S, he accepted in Master De-gree of the same course (Energy conver-sion tendency). He finished his M.S with thesis about computational fluid dynamics
modeling of proton exchange membrane fuel cell. During that year he accepted in Ph.D and now he is in second year of his Ph.D studying. During this nearly 8 years, He has presented several articles in internal and international seminars about main me-chanical topics such as fuel cells and heat exchangers.
Iraj Mirzaee was born in 1960 in Ahar city in Iran. He received BS de-gree in Mechanical Engineering in Mashhad University in 1986. He started Msc. degree in mechanical engineering (energy conversion field) in Esfehan University in Iran and finally he re-ceived his Ph.D degree in mechanical
engineering (energy conversion field) in 1997 at the Bath University in England. He is an associated professor in the mechanical engineering department at faculty of engineering of Urmia University. His professional interests are in the field of CFD, turbulent, fluid flow, energy conversion problems and turbine gas.
Vahid Heidarpour was born in 1980 in Salmas city in Iran. He received Bs degree and Msc degree in Mechanical Engineering of Bu Ali Sina and Urmia University, Iran, respectively in 2004 and 2008. During that year he accepted in Ph.D degree and now he is in second year of his Ph.D studying. His interest
in research is in the field of CFD and heat transfer and rotating systems.
