effect of the prominent catalyst layer surface on reactant gas
TRANSCRIPT
Applied Energy 87 (2010) 1386–1399
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Applied Energy
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Effect of the prominent catalyst layer surface on reactant gas transportand cell performance at the cathodic side of a PEMFC
Shiang-Wuu Perng a, Horng-Wen Wu b,*
a Department of Accounting Information, Kun Shan University, No. 949, Da Wan Rd., Yung-Kang City, Tainan Hsien 710, Taiwan, ROCb Department of Systems and Naval Mechatronic Engineering, National Cheng Kung University, Tainan, Taiwan, ROC
a r t i c l e i n f o
Article history:Received 3 June 2009Received in revised form 16 July 2009Accepted 3 August 2009Available online 2 September 2009
Keywords:Cell performance enhancementProminent catalyst layerPEM fuel cell
0306-2619/$ - see front matter � 2009 Elsevier Ltd. Adoi:10.1016/j.apenergy.2009.08.006
* Corresponding author. Tel.: +886 6 2740718x223E-mail address: [email protected] (H.-
a b s t r a c t
The cell performance enhancement of a proton exchange membrane fuel cell (PEMFC) has been numer-ically investigated with the prominence-like form catalyst layer surface of the same composition at thecathodic half-cell of a PEMFC. The geometries of the prominence-like form catalyst layer surface areassigned as one prominence, three prominences, and five prominences catalyst layer surfaces with con-stant distance between two prominences in the same gas diffusion layer (GDL) for the purpose of inves-tigating the cell performance. To confine the current investigation to two-dimensional incompressibleflows, we assume that the fluid flow is laminar with a low Reynolds number 15. The results indicate thatthe prominence-like form catalyst layer surface can effectively enhance the local cell performance of aPEMFC.
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1. Introduction
Fuel cell (FC) converts the chemical energy from the reaction ofa fuel (usually hydrogen) and an oxidant (usually oxygen in ambi-ent air) directly into electricity with high efficiency and high envi-ronment compatibility. FC technology offers the prospect of zeroemission energy production for applications ranging from station-ary power generation for electric utilities networks to automotivetransportation. Among several types of fuel cells, the proton ex-change membrane fuel cell (PEMFC) operates at significantly lowtemperature (80–90 �C) than other types. It has been consideredas a potential candidate of the power sources in the future; there-fore, recent papers [1–3] experimentally or mathematically inves-tigated the transport phenomena in a PEMFC system.
The catalyst layer, being the host to several competing transportmechanisms, plays an important role in the overall cell perfor-mance of a PEMFC system. In the past, therefore, many researchershave investigated on the catalyst layer to enhance the PEMFC per-formance. The emphasis of these studies was mainly to investigatehow the thickness and structure for the catalyst layer influencedthe PEMFC performance. Weber and Newman [4] employed themathematical, pseudo two-dimensional simulations to investigatehow the cell performance is varied with four different along-the-channel thickness distribution of both the membrane and cathodecatalyst layer. Das et al. [5] developed a three-dimensional, steady-state, multi-agglomerate model of cathode catalyst layer in PEM
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fuel cells to assess the activation polarization and the currentdensities in the cathode catalyst layer. For the performance of aPEMFC, the cathode is regarded as the dominant component. Thisidea is due to the slow kinetics of oxygen reduction [6] and the cellperformance depends strongly on the oxygen transport rate to thecathode. Therefore, the modeling of the cathodic half-cell of a PEM-FC has been emphasized [6,7]. Das et al. [8] found that the opti-mum catalyst layer thickness is 9–11 lm for the platinumloading 0.20 mg/cm2 at the cell voltage 0.8 V. In addition, the cellpotential increases with an increase in catalyst layer thicknessfor the thickness <10 lm. For the thickness >10 lm, the cell poten-tial decreases slowly with increasing catalyst layer thickness dueto the limited rate mass diffusion in the catalyst layer as well aslower active surface per unit volume. In other words, the influenceof catalyst layer thickness 5–10 lm on the cell potential is slight.Moreover, the 10 lm thickness of catalyst layer is slight for the0.1 mm GDL thickness used in the present study. The catalyst layeris therefore considered to be an ultra-thin layer, and the fast andcomplete reaction of oxygen thus occurs only on the surface ofthe catalyst layer.
Design of the flow channel in the bipolar plate plays the impor-tant role for the cell performance of a PEMFC system. Furthermore,the catalyst layer surface is considered as the boundary of thecomputational domain in the flow channel for investigating thePEMFC performance. Several papers [9–14] have dealt withthe numerical computations to perform the flow distribution andfuel gas diffusion. Wang et al. [9] developed a two-dimensionalnumerical model to study the two-phase flow transport in the aircathode of a PEMFC. In this paper, the model encompassed both
Nomenclature
A diffusion matrix of concentration equationC fluid concentration vector of nodal pointscO2 dimensionless oxygen concentration (mol m�3)cO2 ;ref reference oxygen concentration at inlet (mol m�3)cH2O dimensionless water vapor concentration (mol m�3)c�O2
oxygen concentrationc�H2O water vapor concentrationD divergence matrixDO2 binary diffusivity of oxygen in the water vapor (m2 s�1)DO2 ;eff effective diffusivity of oxygen in the gas diffusion layer
(m2 s�1)DH2O binary diffusivity of water vapor in the oxygen (m2 s�1)DH2O;eff effective diffusivity of water vapor in the gas diffusion
layer (m2 s�1)DP width of the prominence (mm)Da Darcy numberF Faraday’s constant (C mol�1)H flow channel height (mm)H1 gas diffusion layer thickness (mm)HP height of the prominence (mm)I averaged current density on the catalyst surface (A m�2)Io exchange current density (A m�2)Ix local current density along the catalyst surface (A m�2)Ilocal local-averaged current density on the effective catalyst
surface where the prominent catalyst layer surfaceinfluences in the PEMFC (A m�2)
K conduction matrixL flow channel length (mm)LS total length of the catalyst layer surfaceL1 distance between two prominences (mm)M mass matrixn dimensionless normal vector along the catalyst layer
surfacen� normal vector along the catalyst layer surfaceP pressure vector of nodal points
p dimensionless pressure (p�=qf u2in)
pin inlet pressurep� pressure (N m�2)Q imposition vector of concentration boundary conditions
on the catalyst surfaceR universal gas constant (mol�1 K�1)R ohmic resistance (X cm�2)Re Reynolds number (uinH=m)RM1, RN1 coefficients in Eq. (18)S diffusion matrix of the momentum equationSP length along the surface of prominences dimensionless length along the catalyst layer surfaceSci Schmidt number (ScO2 ¼ m=DO2 ;eff for oxygen; ScH2O ¼
m=DH2O;eff for water vapor)T operating temperaturet dimensionless time (t�=ðH=uinÞ)t� timeU velocity vector of nodal pointsu, v dimensionless velocity components (u = u�/uin, v ¼
v�=uin)~u dimensionless velocity vectoruin inlet average velocityu*, v� velocity components~u� velocity vectorx, y dimensionless x�, y� coordinates (x ¼ x�=H; y ¼ y�=H)x*, y* physical coordinatesZ pressure gradient matrix
Greek symbolse porosity of the gas diffusion layerg over-potential on the cathode sidej permeability of gas diffusion layerm fluid kinematic viscosityqf fluid densitys tortuosity of the gas diffusion layer
S.-W. Perng, H.-W. Wu / Applied Energy 87 (2010) 1386–1399 1387
single- and two-phase regimes corresponding to low and high cur-rent densities and was capable of predicting the transition betweenthe two regimes. Hontanon et al. [10] employed the Navier–Stokesequations and the Michaelis–Menten type two-step kinetics modelto study the performance of the grooved plate and porous flow dis-tributors at anode. The results implied that the fuel consumptionincreases with decreasing the permeability of the flow distributor.Also, they found that the porous materials are more advantageousthan the grooved plates considering the reactant gas under thesame pressure drop. Kee et al. [11] performed a generalized com-putational model for the mass and momentum transport in chan-nel networks of typical planar fuel cell layers/stacks. Kumar andReddy [12] studied numerically the flow field of the bipolar plateswith metal foam in a PEMFC. These results revealed that the use ofmetal foam renders the local current density distribution moreuniform. Perng and Wu [13] presented how the internal flow mod-ification affects the cell performance enhancement of a proton ex-change membrane fuel cell (PEMFC) using the finite-elementmethod (FEM). Perng et al. [14] numerically investigated the instal-lation of the transverse rectangular cylinder along the gas diffusionlayer (GDL) in the flow channel for the cell performance enhance-ment of a proton exchange membrane fuel cell (PEMFC). Their re-sults indicated that the transverse installation of a rectangularcylinder in the fuel flow channel effectively enhances the cell per-formance of a PEMFC.
Although many papers have been conducted on the enhance-ment of the cell performance of the PEMFC for various thicknesses
and structures of the catalyst layer [4–8], there are few reports onhow various geometric catalyst layer surfaces and these differentcatalyst layer boundaries are applied to the fuel flow channel.The enhancement technique investigated here is the employmentof the prominent catalyst layer surface to enlarge the contact areaof the fuel gas and accelerate the fuel flow in the gas diffusion layer(GDL). Examining the efficacy of the enhancement technique forthe cell performance of a PEMFC is a motivation to us frompractical consideration. The purpose of this paper is to quantifynumerically how the prominent catalyst layer surface influencesthe cell performance enhancement by changing the catalyst layersurface geometry. According to the results of the references[15,16], the liquid water effect does not change the trend of fuelcell performance enhanced by the internal flow modification. Inaddition, from the references’ discussion, how the temperaturevaries the fuel cell performance enhancement is slight using theinternal flow modification. Therefore, the temperature and two-phase effects are neglected in the model to investigate how inter-nal flow modification affects the cell performance enhancement ofa PEMFC. Hwang et al. [17] investigated how gas-distributor geom-etry and cathodic over-potential influenced the oxygen transportillustrated by the flow structure, oxygen concentration and currentdensity distributions.
This paper describes a semi-implicit finite-element study thatinvestigated flow modification by means of the prominence-likeform catalyst layer surface at the cathodic half-cell of a PEMFCand how it affects the cell performance when changing the
1388 S.-W. Perng, H.-W. Wu / Applied E
cathodic over-potential. Semi-implicit finite-element method withthe projection technique proposed by Ramaswamy et al. [18,19] isa powerful numerical method for unsteady incompressible flows.They confirmed that this method generally requires much lesscomputer storage and CPU time than the conventional finite-ele-ment methods. The results of this paper may be of interest to engi-neers attempting to develop the optimization of a PEMFC and toresearchers interested in the flow modification aspects of the PEM-FC performance enhancement in the cathode.
2. Numerical modeling
The PEMFC with the prominent catalyst layer surface is simu-lated in this paper as shown in Fig. 1. The physical problem consid-ered in this paper is the two-dimensional half-cell model of thePEMFC system for the fuel gas mass and momentum transport inthe flow channel and the porous GDL at the cathode as indicatedin Fig. 2. The geometrical relations in this study are set forth: H1/H = 0.17, L/H = 16.67, L1/H = 1.33, DP/H = 0.33, HP/H = 0.096. Further-more, in this study, the geometries of the prominence-like formcatalyst layer surface are assigned as one prominence, three prom-inences, and five prominences catalyst layer surfaces with constantdistance between two prominences in the same gas diffusion layer(GDL). In our previous publication [13], the numerical modelingemployed in this study was verified to solve the above physicalproblem. Therefore, the following assumptions are employed inthe model of this study:
(1) Both the gas mixture and the separated component behaveaccording to the ideal gas model.
(2) The fluid flow is unsteady, laminar, and incompressible; allthe physical properties of the fluid are taken to be constant.
(3) Porous GDL is homogeneous and isotropic with uniformmorphological properties.
(4) Water in the electrode exists as vapor only.
Fig. 1. Schematic representation of a PEMFC w
(5) Catalyst ayer is considered to be an ultra-thin layer, and thefast and complete reaction of oxygen thus occurs only on the
surface of the catalyst layer [15,17].(6) The fuel cell operates at a constant temperature of 353 K.(7) The fluid field is isothermal and single phase.(8) The angle of the prominence catalyst layer is assigned to be
120o for considering the GDL thickness.
nergy 87 (2010) 1386–1399
2.1. Governing equations
The two-dimensional governing equations for the fuel flowchannel and gas diffusion layer in a half-cell of the PEMFC can beexpressed as:
r �~u� ¼ 0 ð1Þ
@~u�
@t�þ ð~u� � rÞ~u� ¼ � 1
qfrp� þ l
qfr2~u� � l
qf je~u ð2Þ
@c�i@t�þ ð~u� � rÞc�i ¼ Di;effr2c�i ð3Þ
where~u� is the velocity vector, p� the pressure, qf the fluid density,l the fluid viscosity, c�i the fluid concentration and Di,eff the effectivediffusivity. In addition, this study modifies the effective diffusivityDi,eff by the Bruggeman correlation [20] to account for the effectsof porosity and tortuosity (s) in the porous electrode, i.e.,
DO2 ;eff ¼ esDO2 ð4Þ
DH2O;eff ¼ esDH2O ð5Þ
where the tortuosity (s) of 1.5 was employed in previous studies[13–17,21] for the investigation of reactant gas transport in themainstream flow channel of a PEMFC.
The governing equations are normalized by first definingdimensionless independent variables of the form x = x*/H, and
ith the prominent catalyst layer surface.
BC1
H1
BC4
BC3
BC6
GDL BC5
L
BC2
x
H
u=1
v=0
p=pin
CO2= CO2,in
CH2O=0y
(a)
BC1
H1
BC4
BC6
BC3
BC5
yx
BC2
LDP L1
HP
GDL
L1 BC6
H
u=1
v=0
p=pin
CO2= CO2,in
CH2O=0
(b)
Fig. 2. The configuration of a PEMFC half-cell in a flow channel: (a) for a flat catalyst layer and (b) for a catalyst layer with prominences.
Table 1Geometric and physical parameters used in this study.
Quantity Value
Flow channel length, L (mm) 10Flow channel height, H (mm) 0.6Gas diffusion layer thickness, H1 (mm) 0.1Diameter of the prominence, DP (mm) 0.2Height of the prominence, HP (mm) 0.64226Operating temperature, T (K) 353Operating pressure (atm) 1Faraday constant, F (C mol�1) 96,487Permeability of gas diffusion layer, j (m2) 1.0 � 10�12
Universal gas constant, R (mol�1 K�1) 8.314Ohmic resistance, R (X cm�2) 0.16Open circuit voltage, Voc (V) 1.1Electrochemical coefficients, a 0.5Porosity of the gas diffusion layer, e 0.4Tortuosity of the gas diffusion layer, s 1.5Inlet average velocity, uin (m s�1) 0.25Relatively humidity of inlet oxygen 0%Exchange current density, Io (A m�2) 100Reference oxygen concentration at inlet, cO2 ;ref (mol m�3) 35.7Fluid viscosity, l (kg cm�1 s�1) 0.21 � 10�6
S.-W. Perng, H.-W. Wu / Applied Energy 87 (2010) 1386–1399 1389
y = y*/H. Moreover, dependent dimensionless variables may also bedefined as~u ¼~u�=uin, t = (t*uin)/H, p ¼ p�= qf u
2in
� �, Da = j/H2, Re = (-
uinH)/m, ci ¼ c�i =cO2 ;ref and Sci = m/Di,eff; the above governing equa-tions can be expressed as the non-dimensional form:
r �~u ¼ 0 ð6Þ
@~u@tþ ð~u � rÞ~u ¼ �rpþ 1
Rer2~u� 1
Re Dae~u ð7Þ
@ci
@tþ ð~u � rÞci ¼
1ReSci
r2ci ð8Þ
The momentum equations are valid in both the porous gasdiffusion layer and the fuel flow channel. They are reduced to theextended Darcy’s law for flow in the porous cathode with a smallpermeability [22], and become the Navier–Stokes equations insidethe flow channel with the porosity of unity and the permeability ofinfinite.
2.2. The initial and boundary conditions
The initial conditions are prescribed for t = 0, in the region,u ¼ v ¼ cO2 ¼ cH2O ¼ 0. We use the following boundary conditionsfor computations as shown in Fig. 2:
(a) At the oxygen inlet (BC1):
u ¼ 1;v ¼ 0;p ¼ p ; c ¼ c ; c ¼ 0 ð9Þ
in O2 O2 ;in H2O(b) At the both sides of the GDL (BC2 and BC5):
u ¼ v ¼ @cO2
@x¼ @cH2O
@x¼ 0 ð10Þ
(c) On the current collector surfaces (BC3):
u ¼ v ¼ @cO2
@y¼ @cH2O
@y¼ @p@y¼ 0 ð11Þ
(d) At the outlet (BC4):
@u@x¼ @v@x¼ @cO2
@x¼ @cH2O
@x¼ @p@x¼ 0 ð12Þ
0 2 4 6 8x* (
10mm)
0
4000
8000
12000
16000
20000
24000
I x (A
/m2 )
1 prominence10060 nodes and 9728 elements13065 nodes and 12800 elements15808 nodes and 15487 elements
(a)
0 2 4 6 8x* (
10mm)
0
4000
8000
12000
16000
20000
24000
I x (A
/m2 )
1 prominence0.000250.00050.001
(b)
Fig. 3. (a) Grid sensitivity and (b) time step size sensitivity of local current density distribution on the surface of the 1 prominence catalyst layer.
1390 S.-W. Perng, H.-W. Wu / Applied Energy 87 (2010) 1386–1399
(e) On the surface of the catalyst layer (BC6):
@pu ¼ v ¼@n¼ 0 ð13Þ
For the boundary conditions of the reactant concentrations onthe surface of the catalyst layer, the Butler–Volmer correlation[23] was employed to describe the rate of electrochemical reaction
S.-W. Perng, H.-W. Wu / Applied Energy 87 (2010) 1386–1399 1391
on the surface by the relationship of the local current density andthe reactant concentrations:
Ix ¼ I0c�O2
cO2 ;ref
� �exp
4aFRT
g� �� �
ð14Þ
0 0.5 1 1.5
I
0
0.2
0.4
0.6
0.8
1
1.2
VC
ell (
V)
Kazim anThe prese
Operating temperature = 8Operating pressure = 5.0 aCathode width = 0.18 cmCathode height = 0.02 cmBinary diffusion coefficienExchange current density =Number of electrons = 4Transfer coefficient = 2Ref. oxygen concentrationHydraulic permeability = 1Fluid viscosity = 0.21*10-6
Porosity = 0.6Inlet oxygen mole fraction
Bruggeman coefficient = 2
Fig. 4. Comparison of the results between the prese
0 2 4x
4000
5000
6000
7000
8000
I x (A
/m2 )
Fig. 5. The local current density distributions along d
a is the electrochemical coefficients depending on the exchange cur-rent density and the over-potential on the electrode surfaces. In thisstudy, it is considered to be constant. In Eq. (14), the first term is thereductive current representing the strength of forward reaction,while the second term is the oxidative current that has an opposed
2 2.5 3 3.5 4
(A/cm2)
d others' predictionsnt predictions
5oCtm
t = 0.05 cm2s-1
0.01 Acm-2
= 3.57*10-5 mol cm-3
.0*10-8 cm2
kg cm-1 s-1
= 0.21
nt prediction and Kazim and other’s prediction.
6 8* (mm)
10
Re=15, =0.4flat
1 prominence
3 prominences
5 prominences
η
ifferent catalyst surfaces at Re = 15 and g = 0.4.
1392 S.-W. Perng, H.-W. Wu / Applied Energy 87 (2010) 1386–1399
effect on the oxygen reduction reaction (ORR). According toO2 + 4H+ + 4e�M 2H2O, the oxygen consumed rate on the reactionsurfaces by the ORR should be equal to the produced current. There-fore, the balance of oxygen concentration on the reaction boundarybecomes
0 2 4x
4000
8000
12000
16000
20000
24000I x (
A/m
2 )
Fig. 6. The local current density distributions along d
0 2 4x
0
0.002
0.004
0.006
0.008
0.01
oxyg
en m
ass
flux
(kg
/m2 s
)
Fig. 7. The local distributions of oxygen mass fluxes alo
�DO2 ;eff
@c�O2
@n�¼ Ix
4Fð15aÞ
DH2O;eff
@c�H2O
@n�¼ Ix
2Fð15bÞ
6 8* (mm)
10
Re = 15, = 0.9flat
1 prominence
3 prominences
5 prominences
η
ifferent catalyst surfaces at Re = 15 and g = 0.9.
6 8* (mm)
10
Re = 15, = 0.4flat
1 prominence
3 prominences
5 prominences
η
ng different catalyst surfaces at Re = 15 and g = 0.4.
S.-W. Perng, H.-W. Wu / Applied Energy 87 (2010) 1386–1399 1393
According to Eqs. (14) and (15), we can obtain the Eq. (16).
DO2 ;eff
@c�O2
@n�þ Io
4F
c�O2
cO2 ;ref
� �exp
4aFRT
g� �
¼ 0 ð16aÞ
DH2O;eff
@c�H2O
@n�þ Io
2Fc�O2
cO2 ;ref
� �exp
4aFRT
g� �
¼ 0 ð16bÞ
During the non-dimensional process, the non-dimensionalboundary conditions can be written as:
@cO2
@nþ RM1cO2 ¼ 0 ð17aÞ
@cH2O
@nþ RN1cO2 ¼ 0 ð17bÞ
where the non-dimensional parameters are described as follows:
RM1 ¼IoH � exp 4aF
RT g�
4FcO2 ;ref DO2 ;effð18aÞ
RN1 ¼IoH � exp 4aF
RT g�
2FcO2 ;ref DH2O;effð18bÞ
Fig. 8. The local distributions of velocity for different catalyst layer geometries at Re = 1catalyst layer.
2.3. Numerical methods
Applying the standard Galerkin finite-element to the spatial dis-cretization of Eqs. (6)–(8) leads to the following systems of thecoupled ordinary equations [18,19]:
MdUdtþ ZPþ 1
ReSðUÞ þ KðUÞU ¼ � e
ReDaMUdi1 ð19Þ
MdCdtþ 1
ReSciACþ KðUÞC ¼ 1
ReSciQ ð20Þ
DU ¼ 0 ð21Þ
where M is the mass matrix, K the pressure gradient matrix, Z theconvection matrix, and D = ZT the divergence matrix. S is thediffusion matrix of the momentum equation, and A is the diffusionmatrix of the concentration equations. Vectors U, C, and P representfinite-element solutions of velocity, concentration, and pressure,respectively. The right hand side vector Q results from the imposi-tion of the concentration boundary conditions on catalyst layer sur-face. By adopting a second-order Adams–Bashforth scheme for theadvection terms and an implicit Euler representation for the diffu-sion term, we may obtain the finite-element version of the semi-im-plicit projection scheme as described in previous paper [18].
5 and g = 0.4: (a) flat, (b) 1 prominence, (c) 3 prominences and (d) 5 prominences
1394 S.-W. Perng, H.-W. Wu / Applied Energy 87 (2010) 1386–1399
3. Results and discussion
3.1. Model validation
In this paper, the prominence-like form catalyst layer surface isused to replace the flat catalyst layer surface to enhance the cellperformance in the PEM fuel cell. The geometries of the promi-nence-like form catalyst layer surface are assigned as one promi-nence, three prominences, and five prominences catalyst layersurfaces with constant distance between two prominences in thesame gas diffusion layer (GDL) for the purpose of investigatingthe cell performance. The geometric and physical parameters usedin the present study are listed in Table 1. After a series of mesh sen-sitivity tests for three finite-element meshes (10,060 nodes and9728 elements, 13,065 nodes and 12,800 elements, 15,808 nodesand 15,487 elements) for the 1 prominence catalyst layer surface,the calculation results are indicated in Fig. 3a. The local currentdensity difference between the second and the third mesh was lessthan 0.05% in test runs, so a finite-element mesh (13,065 nodes and12,800 elements) was chosen in all cases. The three time steps0.00025, 0.0005, and 0.001 were chosen to test the time step sizesensitivity for the 1 prominence catalyst layer surface. The timeincrement Dt was set at 0.0005 in all cases according to the resultsthat the predictions between time steps at 0.0005 and 0.00025 get
Fig. 9. The local distributions of dimensionless oxygen concentration for different channe(d) 5 prominences catalyst layer.
close in Fig. 3b. In this study, about 80,000 time steps werenecessary to obtain reasonably, reliable data. The CPU time wasvaried from 8 h 28 min 17 s to 9 h 11 min 57 s in a PENTIUM III1G PC.
To confirm that the program in this study can handle the cellperformance of a PEMFC, in our previous publication [13], weapplied the present numerical method to solve the oxygen gastransport through the cathode region of a PEMFC as described inKazim and others’ paper [23]. The physical problem is that theair is flowing into the channel and out from the other channeladjacent to the above one with interdigitated flow fields. Thephysical parameters and properties of the electrode are listed inFig. 4. The mesh employed compared with the reference was4280 nodes and 3985 elements. The steady-state solution isobtained by the numerical procedure as mentioned in the previ-ous section. As shown in Fig. 4, the result of the present predic-tions of the polarization curve agreeing fairly closely with Kazimand others’ predictions [23] gives one confidence in the use ofthe present program.
3.2. Influence of prominent catalyst layer surface
The local current density will be employed below to realizehow prominent catalyst layer surface influences the fuel cell
l geometries at Re = 15 and g = 0.4: (a) flat, (b) 1 prominence, (c) 3 prominences and
S.-W. Perng, H.-W. Wu / Applied Energy 87 (2010) 1386–1399 1395
performance in this study. The local current density along the cat-alyst layer for the steady-state is calculated by Eq. (15a) about80,000 time steps. In Fig. 5 (over-potential g is equal to 0.4), exceptfor the peak regions, the local current density along the catalystsurface decreases when the axial direction x increases. Moreover,the local current density around the prominent catalyst layer sur-face increases with changing the flat catalyst layer into the prom-inent catalyst layer, and the difference of the peak regions amongthree cases with the prominent catalyst layer is very small. Theelectrochemical reaction in the catalyst layer is expected to bestronger at a lower operating voltage or a higher operating currentdensity with constant over-potential. Therefore, the reactant oxy-gen consumes at a higher rate as it flows along the main flow direc-tion, which in turn causes the substantial variations in the localcurrent density. Fig. 5 also discloses that the better cell perfor-mance is noted for the fuel channel with a prominent catalyst layerat constant over-potential. The above phenomenon was also de-scribed in a previous study [16]. The reason for the phenomenonis that the fuel gas is accelerated to passes through the gas diffu-sion layer (GDL), and the contact area of the fuel gas is enlarged,which enhances the chemical reaction on the catalyst surface. Inthe prominent catalyst layer cases, the maximum local currentdensity occurs at the first crest of the prominence. At the both sidesof the prominence, the local current density reduces slightly be-
Fig. 10. The local distributions of dimensionless oxygen concentration for different chanand (d) 5 prominences catalyst layer.
cause of the axial velocity stagnation. At a higher over-potentialcondition (g = 0.9, Fig. 6), the local current density along the cata-lyst surface decreases along the axial location, and the trend of thelocal current density distribution around the prominent catalystlayer surface is similar to that as shown in Fig. 5. In Fig. 6, the dis-tributions of the local current density are almost the same in theupstream and downstream regions for the prominences. Thereduction of the local current density is less at g = 0.9 thang = 0.4 at the both sides of the prominence because the axialvelocity stagnation phenomenon becomes less obviously in theseregions for the higher over-potential condition.
Fig. 7 indicates how the prominent catalyst layer influences theaxial distribution of oxygen mass flux along the catalyst surface.The oxygen decreases generally along the catalyst (with anincrease in the axial coordinate x), but some hump regions occuraround the crests of the prominent catalyst layer surfaces. Thesehump regions are caused by the strong forced convection, which en-hances the transport of oxygen. At the both sides of the prominence,the oxygen mass fluxes reduce slightly because the local convectionforce becomes weaker for the axial velocity stagnation. These re-sults in Fig. 7 give one confidence in the results of Figs. 5 and 6.
The velocity fields around the catalyst layer surface clearlydemonstrate the oxygen mass flow rate through the gas diffusionlayer. Fig. 8 illustrates the local distributions of the axial velocity
nel geometries at Re = 15 and g = 0.9: (a) flat, (b) 1 prominence, (c) 3 prominences
1396 S.-W. Perng, H.-W. Wu / Applied Energy 87 (2010) 1386–1399
for various catalyst layer geometries at Re = 15 and g = 0.4. In gen-eral, it can be observed that the velocity is higher in the gas diffu-sion layer with the prominent catalyst layer surface than with theflat catalyst layer surface, because the constricted flow channelarea above each crest of the prominent catalyst layer surfacegenerates a nozzle-type effect which accelerates the fuel flow.However, Fig. 8 presents that the axial velocity of the fuel gas re-duces in the trough regions of the prominences, especially at theboth sides of the prominences, which causes the trapping effecton the fuel gas in these regions of the gas diffusion layer, and thusincreases the supply of fuel to the catalyst layer near the promi-nences. The above phenomenon decreases the reduction of the lo-cal current density caused by the axial velocity stagnation at theboth sides of the prominence. Fig. 8 also shows that a strong con-vection force is induced along the prominent catalyst layer surface.
Fig. 11. The transient local distributions of velocity with 3 prominences catalyst layer at
This not only increases the supply of the fuel gas to the catalystlayer, but also improves the flow of the reaction byproducts outof the PEMFC. Thus, the cell performance is significantly improved,especially at higher current densities. The similar phenomenonwas also discussed in a previous study [24].
In this paper, the model is considered to be the half-cell on thecathode side, where the oxygen and the water vapor exist. Observ-ing the distributions of oxygen can help comprehend how theprominent catalyst layer influences the cell performance. Figs. 9and 10 reveal how various catalyst layer surfaces affect the con-tours of oxygen concentrations, but only for the local profiles ofthe oxygen concentrations to understand clearly. In Figs. 9 and10, the oxygen concentration decreases along-the-channel length,and some oxygen enters the gas diffusion layer. According to thecomparison of oxygen concentration profile between Fig. 9 and
Re = 15 and g = 0.9: (a) t = 36.0, (b) t = 37.0, (c) t = 38.0, (d) t = 39.0 and (e) t = 40.0.
S.-W. Perng, H.-W. Wu / Applied Energy 87 (2010) 1386–1399 1397
Fig. 10, a higher over-potential obtains a higher oxygen concentra-tion profile in the flow channel and in the porous GDL. This charac-teristic of oxygen concentration profiles leads to a higher reactionrate and a better overall cell performance at g = 0.9 than at g = 0.4.In Fig. 10, the distributions of oxygen concentration for variouschannel geometries have the same trend as those of oxygen con-centration presented in Fig. 9, and then the over-potential value al-most has little influence on the trend of oxygen concentrationprofiles for various channel geometries. Furthermore, it can be ob-served that the prominences which curve the catalyst layer out-ward to the flow field makes the catalyst layer approach thehigher oxygen concentration region. Because the prominent cata-lyst layer has curvature and approaches the higher oxygen concen-tration region, the variation of the oxygen concentration is more
Fig. 12. The transient local distributions of dimensionless oxygen concentration with 3 p(d) t = 39.0 and (e) t = 40.0.
obvious near the prominences than along the flat catalyst layersurface. The greater variation in the oxygen concentration withthe prominent catalyst layer surface is caused by the forcedconvection in the GDL. This phenomenon can interpret the localcurrent density distributions along the catalyst surface as shownin Figs. 5 and 6.
3.3. Transient behaviors
Transient behaviors of velocity and oxygen concentration arepresented in Figs. 11 and 12 with the 1.0 time increment (equalto 2000 time steps). In Fig. 11, the distributions of velocity are al-most the same for each time. Fig. 12 indicates that the value of oxy-gen concentration profile increases with increasing time slightly.
rominences catalyst layer at Re = 15 and g = 0.9: (a) t = 36.0, (b) t = 37.0, (c) t = 38.0,
Table 2In all cases of the various catalyst layer surfaces at Re = 15, values of effective local-averaged current density on the effective catalyst surface where the prominentcatalyst layer surface influences in the PEMFC.
Ilocal (A m�2)(flat catalyst layer)
Ilocal (A m�2)(prominent catalyst layer)
Increasepercentage (%)
1 prominenceg = 0.4 4874.82 5257.51 7.85g = 0.9 9053.62 9715.86 7.31
3 prominencesg = 0.4 4897.63 5317.89 8.58g = 0.9 9109.59 9827.46 7.88
5 prominencesg = 0.4 4955.62 5394.41 8.85g = 0.9 9222.40 9968.87 8.09
Note: Values in the italic font designating the percentage change relative to the flatcatalyst layer case.
1398 S.-W. Perng, H.-W. Wu / Applied Energy 87 (2010) 1386–1399
Therefore, in this study, about 80,000 time steps taken were neces-sary to obtain reasonable and reliable data for making comparisonsamong all cases.
3.4. Polarization curve
The purpose of this paper is to quantify numerically how theprominent catalyst layer surface influences the PEMFC cell perfor-mance enhancement. The overall cell performance of a PEMFC sys-tem is understood clearly by means of plotting the polarizationcurve. In the polarization curves, the abscissa is the averaged cur-rent density on the catalyst surface and the ordinate is the fuel cellpotential. The averaged current density on the catalyst surface isdetermined by:
I ¼ 1LS
Z LS
0Isds ð22Þ
0 2000 4000 6I (A
0
0.2
0.4
0.6
0.8
1
1.2
Vce
ll (V
)
Fig. 13. The polarization curves of the fuel cell performan
Furthermore, after the over-potential on the anode side is ne-glected, the fuel cell potential (the operating voltage) is calculatedas:
Vcell ¼ Voc � g� I � R ð23Þ
where Voc is the open circuit voltage kept constant, and the value ofVoc is listed in Table 1; g is the over-potential on the cathode side;the ohmic resistance R is set to be a constant value of 0.16 X cm�2
at T = 353 K throughout the electrode. In addition, in Table 2, the lo-cal enhancement of cell performance is understood clearly by theincrease of local-averaged current density on the effective catalystsurface where the prominent catalyst layer influences. The effectivelocal-averaged current density on the effective catalyst surface isobtained from
Ilocal ¼1SP
Z SP
0Isds ð24Þ
where SP is the length along the surface of prominence. The resultslisted in Table 2 with the increase percentage of effective local-aver-aged current density from 7.31% to 8.85% reveal that the promi-nence-like form catalyst layer surface can effectively enhance thelocal cell performance of a PEMFC. Fig. 13 illustrates the polariza-tion curves of the fuel cell performance for different catalyst layersurfaces to investigate how the prominent catalyst layer surfaceinfluences the overall fuel cell performance. An overall inspectionof Fig. 13 indicates that at the conditions of the higher operatingvoltage (lower over-potential on the cathode side), how the internalflow modification affects the overall fuel cell performance is negli-gibly small as compared with the non-prominent catalyst layer sur-face. At lower operating voltage conditions, on the other hand, howthe prominent catalyst layer surface affects the polarization curvesbecomes important. Moreover, for these three prominent catalystlayer surfaces, the overall cell performance increases when theamount of the prominence increases. This phenomenon is due to
000 8000 10000 12000/m2)
Polarization curves
no prominence
1 prominence
3 prominences
5 prominences
ce for different catalyst layer geometries at Re = 15.
S.-W. Perng, H.-W. Wu / Applied Energy 87 (2010) 1386–1399 1399
the fact that the fuel gas is accelerated to passes through the gas dif-fusion layer (GDL), and the contact area of the fuel gas is enlarged,as described previously in Figs. 5 and 6. From these results, the nextstudies are going to increase the numbers of the catalyst layerprominence for the purpose of accelerating the fuel flow and enlarg-ing the contact area of the fuel gas so as to enhance the overall fuelcell performance.
4. Conclusions
This study has accomplished a finite-element analysis of the cellperformance enhancement by changing the flat catalyst layer sur-face into the prominence-like form catalyst layer surface with thesame composition in the PEM fuel cell. The results of the polariza-tion curve computed in this paper are in good agreement withthose of other predictions. Both better local cell performance andgas reactant transport are generated around the prominent catalystlayer surface, especially around the crests of the catalyst layerprominence. Both worse local cell performance and gas reactanttransport occur at the both sides of the prominence, because thelocal convection force becomes weaker for the axial velocity stag-nation. The results have presented that the prominent catalystlayer surface generates a better convection performance and ahigher gas flow velocity than the flat catalyst layer surface, whichin turn improves the catalytic reaction efficiency. The better cata-lytic reaction efficiency obtains the better local cell performance.How the prominent catalyst layer surface influences the overallcell performance becomes important at lower operating voltageconditions. In addition, for these three prominent catalyst layersurfaces, the overall cell performance increases when the amountof the prominence increases.
Acknowledgement
The authors gratefully acknowledge the financial support of thisproject by the National Council of the Republic of China, undergrant NSC 97-2221-E-006-270-MY3.
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