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Effects of agglomerate model parameters on transport characterization and performance of PEM fuel cells
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y x x x ( 2 0 1 8 ) 1 e1 3
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Effects of agglomerate model parameters on transport characterization and performance of PEM fuel cells Shian Li a, Jinliang Yuan b, Gongnan Xie c, Bengt Sunden a,* a
Department of Energy Sciences, Lund University, P.O. Box 118, SE-22100, Lund, Sweden Faculty of Maritime and Transportation, Ningbo University, 315211, Ningbo, China c Department of Mechanical and Power Engineering, Northwestern Polytechnical University, Box 24, 710072, Xi'an, China b
article info
abstract
Article history:
A three-dimensional, non-isothermal and two-phase flow model for proton exchange
Received 19 November 2017
membrane (PEM) fuel cells is developed. In the cathode catalyst layer, a spherical
Received in revised form
agglomerate model with consideration of catalyst layer structure and liquid water effect is
21 February 2018
applied to determine the electrochemical kinetics. The size and structure of the agglom-
Accepted 15 March 2018
erates are determined by the following parameters, i.e., the agglomerate radius (ragg), the
Available online xxx
volume fraction of ionomer within the agglomerate (Li,agg), and the thickness of the ionomer film over the agglomerate (di). It is noted that a random combination of the three
Keywords:
above parameters is widely used in agglomerate models by researchers. In this paper, the
PEM fuel cells
effects of ragg and Li,agg on the cell performance and local transport characteristics are
Electrochemistry
numerically investigated by using the developed model with consideration of the re-
Agglomerate model
lationships between agglomerate parameters. It is concluded that the cell performance is
Agglomerate structure
significantly improved by decreasing ragg and increasing Li,agg at medium and high current
Mass transport
densities when the volume fractions of the solid phase (LPt/C) and ionomer phase (Li) are maintained constant. In addition, the distributions of oxygen concentration, liquid water saturation, volumetric current density and effectiveness factor are also strongly influenced by the variation of the two parameters. © 2018 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.
Introduction Proton exchange membrane (PEM) fuel cells have been widely considered as the most promising alternative power sources for a wide variety of applications due to their attractive advantages [1]. However, the commercialization of PEM fuel cell systems is limited by the cost, durability and stability issues.
Over the past few years, cell performance improvement has been gradually obtained by increased platinum utilization, appropriate flow field design, thermal and water management strategies. Operating conditions were optimized to obtain the maximum performance of a PEM fuel cell [2]. Raman et al. [3] developed a dynamic model to investigate the water induced pore blockage and mitigation strategies in PEM fuel cells. The performance of PEM fuel cells with in-line and staggered
* Corresponding author. n). E-mail address: [email protected] (B. Sunde https://doi.org/10.1016/j.ijhydene.2018.03.106 0360-3199/© 2018 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved. Please cite this article in press as: Li S, et al., Effects of agglomerate model parameters on transport characterization and performance of PEM fuel cells, International Journal of Hydrogen Energy (2018), https://doi.org/10.1016/j.ijhydene.2018.03.106
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Nomenclature a A c CP D E f F h H i j k K L m M n P Q r R s S t T ! u V X Y
1
Effective surface area, m /Water activity Area, m2 Mole concentration, mol m3 Specific heat, J kg1 K1 Diffusivity, m2 s1 Effectiveness factor Platinum mass ratio to Pt/C Faraday constant, 96,485 C mol1 Enthalpy change, J kg1 Henry's constant, Pa m3 mol1 Exchange current density, A m2 Volumetric current density, A m3 Thermal conductivity, W m1 K1/Reaction rate constant, s1 Permeability, m2 Volume fraction Mass loading, kg m2 Molecular weight, kg mol1 Osmotic-drag coefficient Pressure, Pa Mass flow rate, kg s1 Agglomerate radius, m Universal gas constant, 8.314 J mol1 K1 Liquid water saturation Source term/Entropy, J mol1 K1 Thickness, m Temperature, K Velocity vector, m/s Voltage, V/Volume, m3 Mole fraction Mass fraction
Greek Symbols a Transfer coefficient g Water phase change rate, s1 d Thickness, m ε Porosity h Over-potential, V q Contact angle l Water content m Dynamic viscosity, Pa s
blockages were experimentally studied by Heidary et al. [4]. In addition, a novel convergent-divergent serpentine flow field was proposed and investigated by Chowdhury [5]. PEM fuel cells consist of several components including the current collectors (CCs), the gas flow channels (GFCs), the gas diffusion layers (GDLs), the catalyst layers (CLs) and the membrane. The CL is the most important component of PEM fuel cells as the chemical energy conversion to electrical energy via the electrochemical reactions occurs here. The hydrogen oxidation reaction (HOR) and oxygen reduction reaction (ORR) simultaneously take place within the anode and cathode CLs, respectively. In comparison with the HOR, the ORR is relatively slow and becomes the dominant factor that
x r s f F
Stoichiometric ratio Density, kg m3 Electron/Proton conductivity, S m1/Surface tension, N m2 Potential, V Theile's modulus
Subscripts and Superscripts a Anode agg Agglomerate c Cathode/Carbon con Condensation d Osmotic-drag/Dissolved water eff Effective eq Equilibrium evap Evaporation g Gas i i th species/Ionomer j j th species l Liquid lg Liquid and gas water m Membrane/Mixture mom Momentum equation oc Open circuit ref Reference rl Liquid relative rg Gas relative phase Phase change Pt Platinum sat Saturation s Solid/Liquid water saturation vd Vapor and dissolved water w Water wv Water vapor Abbreviations CC Current collector CL Catalyst layer GDL Gas diffusion layer GFC Gas flow channel PEM Proton exchange membrane
determines the cell performance. During the past decades, numerical simulations have been widely applied to improve the understanding of transport characterization inside PEM fuel cells. Generally, there are three models to describe the cathode CL, i.e., (a) the interface model [6e9], (b) the homogeneous model [8,10e14], and (c) the agglomerate model [8,15e28]. Among the three mentioned models, the agglomerate model has the capability to capture oxygen concentration loss at high current densities. A comprehensive study of different cathode CL models on cell performance was conducted by Harvey et al. [8], showing the advantage of the agglomerate model on predicting the mass transport resistance at high current densities. The effects of ionomer and
Please cite this article in press as: Li S, et al., Effects of agglomerate model parameters on transport characterization and performance of PEM fuel cells, International Journal of Hydrogen Energy (2018), https://doi.org/10.1016/j.ijhydene.2018.03.106
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platinum loadings on cell performance were numerically investigated by Sun et al. [15]. The results showed that there is an optimal value of the ionomer loading under a constant platinum loading. A multi-variable optimization work was carried out to improve the performance of PEM fuel cells by using an agglomerate model for description of the cathode electrochemical kinetics, and Kriging surrogate model for the implementation of optimization procedure [16]. PEM fuel cells with non-uniform agglomerate cathode CLs, which are achieved by applying several sub-layers with varying agglomerate radius, porosity and ionomer volume fraction within the agglomerate, were numerically investigated by Song et al. [17] and Yin et al. [18]. Due to the operating temperature of PEM fuel cells below 100 C, water may exist in either liquid phase or vapor phase, which is dependent on local temperature and saturation pressure. The presence of liquid water is beneficial to increase the protonic conductivity, decrease the ohmic loss, and thereby improve the cell performance. However, excessive liquid water can block the pores in GDLs and CLs for gas transport and influence the electrochemical reaction rates in CLs. For the mathematical models of PEM fuel cells, the mass diffusivity and electrochemical reaction rate are commonly modified by multiplication of a term (1-s)n to account for the effect of liquid water. The influence of exponent n on the cell performance was extensively examined by Wang et al. [14]. The driving force for liquid water transport in porous regions is the capillary pressure, which is determined by either the Leverett function or correlations obtained by different researchers. Although the values of the capillary pressure do not agree very well with each other, the Leverett function is still widely used in PEM fuel cell models. In addition, the water transport mechanisms through the membrane are electroosmotic drag, back diffusion and hydraulic permeation [6]. Generally, a combined model is adopted to model the process of water transport in the membrane. In addition, the hydraulic permeation term is commonly neglected in the model because it is much smaller than the electro-osmotic drag and back diffusion terms. For the agglomerate model, each spherical agglomerate particle is assumed to be evenly coated with a thin ionomer film, followed by a thin liquid water film. Agglomerate models with consideration of liquid water have been extensively developed and applied in numerical studies of PEM fuel cells. The effect of liquid water on cell performance was numerically studied by Rao et al. [19]. The cathode CL microstructure of PEM fuel cells was optimized to improve the platinum utilization [20]. Recently, the water film formation and transport characteristics of PEM fuel cells under low humidity operating conditions were numerically investigated by Jo et al. [21]. For implementation of the agglomerate model to PEM fuel cells models, the size and structure of the agglomerates are determined by the following parameters, i.e., the agglomerate radius (ragg), the volume fraction of ionomer within agglomerate (Li,agg), and the thickness of the ionomer film over the agglomerate (di). It is noted that different agglomerate model parameters are used by different researchers in the open literature. As shown in Table 1, ragg ranges from 50 to 1500 nm, di ranges from 0 to 100 nm, and Li,agg ranges from 0.1 to 0.6. Therefore, this study focuses on the effects of the agglomerate
Table 1 e Review of agglomerate model parameters.
Sun et al. [15] Xing et al. [16] Song et al. [17] Yin et al. [18] Rao et al. [19] Marquis et al. [20] Jo et al. [21] Secanell et al. [22] Yang et al. [23] Dobson et al. [24] Kamarajugadda et al. [25] Shah et al. [26] Li et al. [27,28]
ragg (nm)
di (nm)
Li,agg
1000 100e1000 300e1500 500e1500 100 150 100 250e1000 100 190e250 50e1000 200 1000
80 e e e e 12 e 0e80 10 e 0e100 15 22
0.5 e 0.1e0.4 0.2e0.6 e e e 0.5 0.39 0.17e0.25 0.2e0.5 0.2 0.5
model parameters on the cell performance and local transport characteristics. The parameters ragg and Li,agg are selected as the variables, and di is determined by the corresponding expressions when ragg and Li,agg are changed. The thickness of the liquid water film (dw) is determined by the local liquid water saturation level. The spherical agglomerate model is adopted in the cathode CL, which is fully coupled with the charge transport equation. In the present study, a three-dimensional, two-phase flow and non-isothermal agglomerate model based on the finite volume method is developed and applied to investigate the effects of the agglomerate model parameters ragg varying from 1.0 107 m to 9.0 107 m, and Li,agg varying from 0.2 to 0.5 on the transport phenomena and performance of PEM fuel cells. The structure of this paper is as follows. Firstly, the geometry of the computational domain is introduced, followed by description of the governing equations. Then, the catalyst layer composition and the agglomerate model are completely presented. Finally, the numerical results and conclusions are addressed.
Model description The three-dimensional computational domain considered in this study is a single channel unit of a PEM fuel cell, as shown in Fig. 1. The reactant gases hydrogen and oxygen (supplied in the form of air) are fed to the anode and cathode GFCs, respectively. The detailed information of the fuel cell geometry and operating condition parameters are summarized in Table 2 and Table 3. The fuel cell operating temperature and pressure are 353 K and 1 atm, respectively. In addition, 100% relative humidity is applied for both the anode and cathode reactant gases. In the PEM fuel cell mathematical model, the fluid flow is laminar; ideal gas law is applied for the reactant gases; the GDLs and CLs are homogeneous and isotropic; the reactant gases cannot diffuse across the membrane; the generated water in the cathode CL is in dissolved phase.
Governing equations With the above mentioned assumptions, the governing equations of mass, momentum, species, energy, charge, liquid
Please cite this article in press as: Li S, et al., Effects of agglomerate model parameters on transport characterization and performance of PEM fuel cells, International Journal of Hydrogen Energy (2018), https://doi.org/10.1016/j.ijhydene.2018.03.106
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Fig. 1 e Schematic of a PEM fuel cell: (a) three-dimensional computational domain, (b) the middle plane of cathode catalyst layer.
Table 2 e Fuel cell geometric dimensions [27,28]. Parameter Fuel cell length Fuel cell width GFC width GFC height CC width CC height GDL thickness CL thickness Membrane thickness
Value
Units
50 2 1 1 1 1.8 0.2 0.01 0.05
mm mm mm mm mm mm mm mm mm
V$ðr! u Yi Þ ¼ V$ rDeff ;i VYi þ Si
Reactant gas Operating pressure, Pa/Pc Stoichiometric ratio, xa/xc Relative humidity, RHa/RHc Operating temperature, Ta/Tc
Anode
Cathode
Hydrogen 1 atm 1.5 100% 353 K
Air 1 atm 2.0 100% 353 K
(1)
where r and ! u are the mixture fluid density and superficial velocity, respectively. Smass represents the source term of mass equation. The mass changes of hydrogen, oxygen and water vapor due to the processes of electrochemical reactions and phase change are completely considered in the corresponding layers. Momentum conservation equation: V$ðr! u! u Þ ¼ V$ðmV! u Þ VP þ Smom
V$ rCp ! u T ¼ V$ keff VT þ ST
(4)
where Cp and keff are the specific heat and effective thermal conductivity, respectively. The irreversible, reversible, ohmic heat generation and phase change terms are totally included in the energy equation source term, ST. Charge conservation equation:
water and dissolved water are used to describe the complex and coupled transport processes within fuel cells. Mass conservation equation: V$ðr! u Þ ¼ Smass
(3)
where Yi and Deff,i are the mass fraction and effective diffusivity for the i th species, respectively. Si represents the amount of consumption or generation of the i th species. The effective diffusivity (Deff,i) is obtained by the Bruggeman correlation which accounts for the tortuous path in the GDLs and CLs. Energy conservation equation:
Table 3 e Fuel cell operating conditions. Parameter
equation. The Darcy's law is adopted to describe the flow through the anode and cathode GDLs and CLs, which have the porous feature. Species conservation equation:
(2)
where P and m are the mixture pressure and dynamic viscosity, respectively. Smom denotes the source term of momentum
V$ seff ;s Vfs þ Ss ¼ 0
(5)
V$ seff ;m Vfm þ Sm ¼ 0
(6)
where seff,s is the effective electrical conductivity, seff,m the effective protonic conductivity, fs the electrical potential, fm the protonic potential. The Butler-Volmer equation and spherical agglomerate model are adopted to describe the HOR and ORR in the anode and cathode CLs, respectively. Liquid water transport equation: Krl mg ! u ¼ V$ðrl Ds VsÞ þ Sl V$ rl Krg ml
(7)
where Krl and Krg are the relative permeability of liquid and gas phase, respectively. Ds denotes the capillary diffusion coefficient. The source term, Sl, represents the phase change
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Table 4 e Parameters used in the mathematical model. Parameter
Value
mg cm2 kg m3 mg cm2 kg m3 kg m3 kg mol1 e A m2
10(0.03741*T16.96)
A m2
0.5 1 56.4
e e mol m3
Reference oxygen concentration, cO2 [32]
3.39
mol m3
Hydrogen Henry's constant, HH2 [33] Oxygen Henry's constant, HO2 [33] Thermal conductivity of CC/GDL/CL, kCC/GDL/CL [27] Thermal conductivity of membrane, km [27] Electrical conductivity of CC/GDL/CL, ss,CC/GDL/CL [27] Entropy of hydrogen oxidation, DSa [34] Entropy of oxygen reduction, DSc [34] Latent heat of condensation/evaporation, Dhlg [23] Liquid water viscosity, ml [23] Surface tension, s [23] Contact angle of GDL/CL, qGDL/CL [23] Condensation rate, gcon [33] Evaporation rate, gevap [33] Dissolved water phase change rate, g [33] Permeability of GDL, KGDL [27] Permeability of CL, KCL [27] Binary diffusivity, DH2 H2 O [9] Binary diffusivity, DO2 H2 O [9] Binary diffusivity, DO2 N2 [9] Binary diffusivity, DH2 ON2 [9]
4.56 103 0.101325e(666/Tþ14.1) 100/1.7/0.3 0.25 20,000/5000/2000 0.104 326.36 2.36 106 3.517 104 0.0625 110 /95 100 100 1 5.6e-12 1.0e-13 9.15 105 2.82 105 2.2 105 2.56 105
Pa m3 mol1 Pa m3 mol1 W m1 K1 W m1 K1 S m1 J mol1 K1 J mol1 K1 J kg1 Pa s N m1 e s1 s1 s1 m2 m2 m2 s1 m2 s1 m2 s1 m2 s1
ref
Anode reference exchange current density, ia [27] ref
Cathode reference exchange current density, ic [30] Anode transfer coefficient, aa [31] Cathode transfer coefficient, ac [31] ref
Reference hydrogen concentration, cH2 [32] ref
process between water vapor and liquid water, which is determined by the water vapor partial pressure and saturation pressure. Dissolved water transport equation: V$
Units
0.4 2.145 104 0.6 1.8 103 1.98 103 1.1 0.6 100
Platinum loading, mpt [29] Platinum density, rpt [27] Carbon loading, mc [27] Carbon density, rc [27] Dry membrane density, rm [27] Membrane equivalent weight, Mm [27] Porosity of GDL, εGDL [27]
n r d sm Vfm ¼ V$ m Dl Vl þ Sd F Mm
(8)
where nd and Dl are the electro-osmotic drag coefficient and water diffusivity in the membrane, respectively. The generated water in the cathode CL is in dissolved phase, and the absorption/desorption processes of ionomer in the anode and cathode CLs take place between water vapor and dissolved water. The parameters and complementary equations used in the mathematical model are summarized in Tables 4 and 5. In addition, the sources terms for the governing equations are given in Table 6.
The catalyst layer composition and volume fraction
LPt=C ¼
(9)
mpt tCL
1 1f 1 þ rpt f rc
! (10)
where mpt is the platinum loading, tcl the thickness of the CL, rpt the density of platinum, rc the density of carbon. The parameter f is defined as the platinum loading divided by the sum of platinum loading and carbon loading. f¼
mpt mpt þ mc
(11)
where mc is the carbon loading. The volume fraction of the ionomer phase (Li) is expressed by: Li ¼
The catalyst layer consists of void space, Pt/C particles, and ionomer phase. The volume fraction of each component is determined by the following expressions [22,26,31]. The volume fraction of the void space (εCL) is given by: εCL ¼ 1 LPt=C Li
where LPt/C and Li are the volume fractions of Pt/C particles and ionomer phase, respectively. The volume fraction of the Pt/C particles (LPt/C) is determined by:
i h 3 L Pt=C r3agg Li;agg þ raggþdi r3agg r3agg 1 Li;agg
(12)
The ionomer phase consists of two parts: one part is inside the agglomerate, the other part is the ionomer film. When LPt/ C, Li, ragg, and Li,agg are given, the unique di is determined. It is assumed that the agglomerate is only occupied by Pt/C particles and ionomer phase. Li usually varies from 0.2 to 0.4 [33]. In
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Table 5 e Complementary equations and definitions. Description
Units 1:5 1:5
Effective mass diffusivity [10]
Deff ;i ¼ ð1 sÞ
Mass diffusivity
Di;m ¼ Pn
ε
m2 s1
Di;m
m2 s1
1Xi X =Di;j j¼1;jsi j
1:5
Binary mass diffusivity
P0 P
Di;j ¼ Di;j ðT0 ; P0 Þ
m2 s1
T T0
!0:5
Electrochemical kinetics [10]
ref
ja ¼ ð1 sÞia aeff
P
A m3
½eaa Fha =RT eac Fha =RT
H2 ref cH HH2 2
ha ¼ fs fm , hc ¼ fs fm Voc
Over-potential [10] Open circuit voltage [27]
Voc ¼ 1:229 8:456 104 ðT 298:15Þ þ 4:31 105 TLnðPH2 P0:5 O2 Þ
Active surface area [31]
aeff ¼
Proton conductivity [7]
sm ¼ ð0:514l 0:326Þe1268ð
Þ
S m1
Effective conductivity [27]
seff ;s ¼ ð1 εGDL Þ1:5 ss ; seff ;s ¼ ð1 εCL Li Þ1:5 ss seff ;m ¼ L1:5 i sm
S m1
Relative permeability
Krl ¼ Ks3 ; Krg ¼ Kð1 sÞ3
m2
mpt tCL
Ds ¼
m1
ð227:79f 3 158:57f 2 201:53f þ 159:5Þ 103 1 1 303T
Capillary diffusivity
V V
m2 s1
3
Ks dPc ml ds
Capillary pressure
0:5 Pc ¼ scosðqÞ Kε ð1:417s 2:12s2 þ 1:263s3 Þ
Saturation pressure
log10 Psat ¼ 2:1794 þ 0:02953ðT 273:15Þ 9:1837 105 ðT 273:15Þ þ
Pa 2
Pa
1:4454 107 ðT 273:15Þ3 Electro-osmotic drag coefficient [7] Dissolved water diffusivity [7]
l nd ¼ 2:5 22
Dl ¼ 1010 e½2416ð
1 1 303T
Equilibrium water content [35]
leq ¼
8 < 2:05l 3:25 Þ 6:65 1:25 : 2:563 0:33l þ 0:0264l2 0:000671l3
1:41 þ 11:3a 18:8a2 þ 16:2a3 10:1 þ 2:94ða 1Þ
e ð2≪l < 3Þ ð3≪l < 4Þ ð4 < lÞ
e
ða < 1Þ ða 1Þ
e
P þ 2s a ¼ XPwv sat
Water activity
m2 s1
m2 s1
TðjM Þ0:5 1012 m HV2 O0:6 H2 O O
Oxygen diffusivity in liquid water [36]
DO2 ;w ¼ 7:4
Oxygen diffusivity in ionomer [33]
DO2 ;i ¼ 2:88 1010 e½2933ð313TÞ
2
1
m2 s1
1
Table 6 e Source terms in the governing equations. Description
Units
Smass ¼ SH2 þ Swv Anode CL Smass ¼ SO2 þ Swv Cathode CL Smass ¼ Swv Anode and cathode GDLs S ¼ m! u Anode and cathode GDLs and CLs
kg m3 s1
SH 2 ¼
kg m3 s1
mom
SO 2 ¼
K ja 2FMH2 jc 4FMO2
Anode CL Cathode CL
Swv ¼ Sl Svd MH2 O Anode and cathode CLs Swv ¼ Sl Anode and cathode GDLs TDSa 2 2 2F ja þ seff ;m Vfm þ seff ;s Vfs þ Sl Dhlg Anode CL TDSc 2 2 ST ¼ jc hc 4F jc þ seff ;m Vfm þ seff ;s Vfs þ Sl Dhlg Cathode CL ST ¼ seff ;m Vf2m membrane ST ¼ seff ;s Vf2s þ Sl Dhlg Anode and cathode GDLs
ST ¼ j a ha
kg m2 s2 kg m3 s1 kg m3 s1 W m3
ST ¼ seff ;s Vf2s Anode and cathode CCs ¼ ja Anode CL ¼ þ jc Cathode CL ¼ þ ja Anode CL ¼ jc Cathode CL ¼ Sphase Anode and cathode GDLs and CLs 8 εð1 sÞ > > MH2 O ðPwv Psat Þ Pwv Psat < gcond RT Sphase ¼ > εs > : gevap MH2 O ðPwv Psat Þ Pwv < Psat RT Sd ¼ Svd Anode CL Sd ¼ Svd þ Sl Cathode CL Svd ¼ g Mrmm ðleq lÞAnode and cathode CLs
Ss Ss Sm Sm Sl
Sl ¼
jc 2F Cathode
A m3 A m3 kg m3 s1 kg m3 s1
mol m3 s1
CL
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Fig. 2 e Schematic of the ionomer and liquid water films covering the agglomerate.
this study, it is fixed at 0.4. Meanwhile, LPt/C is also a constant value, which can be obtained by Eq. (10). As a result, di is a function of ragg and Li,agg. The thickness of ionomer film (di) is obtained by: ffi # "sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 3 Li 1 Li;agg Li;agg þ 1 1 di ¼ ragg LPt=C
(13)
rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 3 3sεCL 3 dw ¼ ragg þ di þ ragg þ di 4pN
(17)
According to Eq. (13), The thickness di is increased from 8.63 109 m to 7.76 108 m when ragg is increased from 1.0 107 m to 9.0 107 m and Li,agg is fixed at 0.4. The thickness di is decreased from 9.78 108 m to 1.11 108 m
The total volume of the liquid water is: Vw ¼ sεCL VCL
(14)
where s is the liquid water saturation, VCL is the total volume of the CL. The volume of the liquid water covering the individual agglomerate can be obtained: Vw;i ¼
sεCL N
(15)
where N is the number of agglomerate particles per catalyst layer volume. N¼
3LPt=C 4pr3agg 1 Li;agg
(16)
The thickness of the liquid water film (dw) is obtained by:
Fig. 3 e Comparison of the numerical results with the experimental data.
Fig. 4 e Effect of agglomerate radius (ragg) on cell performance: (a) polarization curve, (b) power density curve.
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when Li,agg is increased from 0.2 to 0.5 and ragg is fixed at 5.0 107 m.
The cathode agglomerate model
1 1 1 FL tanhð3FL Þ 3FL
(19)
where the Thiele's modulus for chemical reactions is given as:
In the present model, the spherical agglomerate model [15,26] is used to calculate the volumetric current density. Fig. 2 depicts the structure of the agglomerates within the cathode CL. The identical agglomerates are uniformly distributed in the cathode CL, and the individual agglomerate is evenly covered and liquid water films. 1 by ionomer ragg þ di þ dw PO 1 di dw þ þ jc ¼ 4F 2 HO2 Er kc ð1 εCL Þ ragg aagg;i DO2 ;i aagg;w DO2 ;w (18) where P is the partial pressure of oxygen, H the Henry's constant, Er the effective factor, kc the reaction rate constant, aagg,i the ionomer effective agglomerate surface area, and aagg,w the liquid water effective agglomerate surface area. It is noted that the first term in the bracket represents the transport process within the agglomerate, and the second term denotes the transport processes through the ionomer and liquid water films. The effectiveness factor of the spherical agglomerate is defined as:
Fig. 5 e Effect of volume fraction of ionomer within agglomerate (Li,agg) on cell performance: (a) polarization curve, (b) power density curve.
Er ¼
FL ¼
ragg 3
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi kc L1:5 i;agg DO2
(20)
The reaction rate constant is computed as:
ref
kc ¼
ic aeff ref
4Fð1 εCL ÞcO2
eaa Fhc =RT þ eac Fhc =RT
(21)
The effective agglomerate surface area is obtained from: aagg;i ¼
2 3LPt=C εCL ragg þ di r3agg 1 Li;agg
aagg;w ¼
2 3LPt=C εCL ragg þ di þ dw r3agg 1 Li;agg
(22) (23)
According to Eq. (20), the effective surface area aagg,i is decreased from 5.15 106 m1 to 5.72 105 m1 when ragg is increased from 1.0 107 m to 9.0 107 m and Li,agg is fixed at 0.4. The effective surface area aagg,i is increased from 9.36 105 m1 to 1.09 106 m1 when Li,agg is increased from 0.2 to 0.5 and ragg is fixed at 5.0 107 m.
Fig. 6 e Effect of agglomerate radius (ragg) on oxygen concentration: (a) 0.7 V, (b) 0.3 V.
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Numerical implementation and boundary conditions The mathematical model of PEM fuel cells is developed by using the commercial software ANSYS FLUENT. The governing equations of charge, liquid water transport, and dissolved water transport are implemented by using user defined scalar (UDS) equations with an under relaxation technique developed by the authors. At the inlet of the GFCs, the mass flow rate, temperature, and species mass fractions are prescribed. The mass flow rates of reactants at both anode and cathode sides are calculated at a reference current density of 1.0 A/cm2, as given by Eqs. (24) and (25). Anode and cathode stoichiometric ratios (xa and xc) are given in Table 3. In addition, the inlet liquid water saturation is assigned to be zero. At the outlet of the GFCs, a pressure-outlet boundary condition is applied. The operating temperature and a constant electric potential, fs ¼ 0, are specified at the anode terminal. The operating temperature and a constant electric potential, fs ¼ Vcell, are applied for the cathode terminal. The corresponding current density is obtained when an operating cell voltage is specified. x MH (24) Qa ¼ a 2 Iref Am 2FYH2
Fig. 7 e Effect of volume fraction of ionomer within agglomerate (Li,agg) on oxygen concentration: (a) 0.7 V, (b) 0.3 V.
Qc ¼
xc MO2 Iref Am 4FYO2
(25)
The Semi-Implicit Method for Pressure Linked Equations (SIMPLE) algorithm is used to handle the pressure-velocity coupling. The standard procedure is used for pressure, while the second order upwind discretization scheme is adopted for momentum, species, energy and UDS equations. A grid independence study was carefully performed to balance the accuracy and computation resources. The mesh system with the total control volume number of 172,000 was selected for the following simulations.
Results and discussions In this section, the effect of ragg ranging from 1.0 107 m to 9.0 107 m on the cell performance was investigated, when Li,agg is fixed at 0.4. The effect of Li,agg ranging from 0.2 to 0.5 on the cell performance was also investigated, when ragg is fixed at 5.0 107 m for all the corresponding cases. In addition, the local distributions of oxygen concentration, liquid water saturation, volumetric current density, and effectiveness factor in the cathode CL at the operating cell voltages 0.7 V and 0.3 V are presented and analyzed.
Fig. 8 e Effect of agglomerate radius (ragg) on liquid water saturation: (a) 0.7 V, (b) 0.3 V.
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Model validation The numerical results obtained by the developed model are compared with the experimental data reported by Yan et al. [37], as shown in Fig. 3. It is found that the numerical results show good agreement with experimental data. A 25 cm2 fuel cell with a platinum loading of 0.4 mg cm2 for both the anode and cathode CLs was tested under the operating temperature of 353 K, operating pressure of 1 atm, and relatively humidity of 100%. The information provided by the experimental work is limited, but the CL parameters and operating conditions of experiments are very similar to those of the present work. For the model validation, ragg ¼ 1.0 106 and Li,agg ¼ 0.44 are adopted in the agglomerate model, and the remaining parameters are the same as the present work.
Cell performance The cell performance is estimated and evaluated in terms of polarization curve (Vcell, Icell) and power density curve (Icell, Pcell). Fig. 4 presents the effect of variation of ragg on the cell performance. It can be seen that the current density is significantly affected by the ragg at medium and high current densities. The current density is gradually improved with decreasing ragg at the same operating voltage. For the
Fig. 9 e Effect of volume fraction of ionomer within agglomerate (Li,agg) on liquid water saturation: (a) 0.7 V, (b) 0.3 V.
operating voltage 0.3 V, the current density for the case with ragg ¼ 9.0 107 m is 0.682 A/cm2, while the current density for the case with ragg ¼ 1.0 107 m is 1.431 A/cm2 which is approximately 2.1 times higher than the previous one. In addition, the maximum power density is greatly improved from 0.564 W/cm2 to 0.303 W/cm2 when ragg is reduced from 9.0 107 m to 1.0 107 m. As shown in Fig. 5, the cell performance is also strongly affected by the variation of Li,agg at medium and high current densities. The current density is gradually improved with increasing Li,agg at the same operating voltage. The maximum current density for the case with Li,agg ¼ 0.2 is 0.747 A/cm2, while the maximum current density for the case with Li,agg ¼ 0.5 is 1.316 A/cm2 which is approximately 1.8 times higher than the previous one. In addition, the maximum power density is greatly improved from 0.325 W/cm2 to 0.505 W/cm2 when the Li,agg is increased from 0.2 to 0.5. Therefore, it is clear that the cell performance can be improved by either decreasing ragg or increasing Li,agg at the same operating voltage when the Lpt/C and Li are kept constant. At low current density, no significant difference is observed due to the low reaction rate in the CLs. The increase of the effectiveness factor and decrease of the oxygen transport resistance through the ionomer and liquid water films are caused by either decreasing ragg or increasing Li,agg, thereby leading to improvement of the cell performance.
Fig. 10 e Effect of agglomerate radius (ragg) on volumetric current density: (a) 0.7 V, (b) 0.3 V.
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Local transport characterization
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The oxygen concentration distributions in the middle plane of the cathode CL (Line-1) at operating voltages 0.7 V and 0.3 V are shown in Figs. 6e7. This is a key parameter affecting the ORR in the cathode CL. It is observed that the maximum oxygen concentration appears under the channel region, while the minimum oxygen concentration appears under the rib region due to the transport resistance from the channel to the region under the rib. The consumption amount of oxygen is proportional to the current density, so a lower oxygen concentration is obtained in the cathode CL when a higher current density is generated. The oxygen concentration is gradually decreased by either decreasing ragg or increasing Li,agg at the same operating voltage, which is caused by the increased current density as discussed above. It is also observed that the minimum oxygen concentration for the cases with ragg ¼ 1.0 107 m and Li,agg ¼ 0.5 at the operating voltage 0.3 V is extremely low (approaching zero for ragg ¼ 1.0 107 m), which means that the desired amount of oxygen is not satisfied by the transport process from the channel to CL and the cell performance is also limited by the concentration loss. The liquid water is formed when the water vapor partial pressure exceeds the saturation pressure which is a function of local temperature. The membrane needs to be well
hydrated to decrease the ohmic loss caused by the proton transport from the anode CL to the cathode CL. However, excess liquid water causes the water flooding issue which strongly affects the cell performance. Figs. 8e9 show the liquid water saturation distributions in the middle plane of the cathode CL (Line-1) at operating voltages 0.7 V and 0.3 V. The liquid water under the channel region can be easily transferred and removed away from the GDL to the GFC, so a lower liquid water saturation is observed in this region compared with that under the rib. It also can be seen that the liquid water saturation level is increased with decreasing ragg and increasing Li,agg, which is consistent with the trend of the current density. When the current density is improved, the amount of water generation is increased and more liquid water is also formed. The volumetric current density (jc) is determined by the spherical agglomerate model. A higher jc means that more oxygen is consumed and water is generated in the cathode CL. The jc distributions in the middle plane of the cathode CL (Line-1) at operating voltages 0.7 V and 0.3 V are shown in Figs. 10 and 11. For the operating voltage 0.7 V, the case with ragg ¼ 1.0 107 m and Li,agg ¼ 0.5 provides the maximum jc and the variation of jc is also the biggest compared to other cases. For the operating voltage 0.3 V, the case with ragg ¼ 1.0 107 m and Li,agg ¼ 0.5 provides the maximum jc
Fig. 11 e Effect of volume fraction of ionomer within agglomerate (Li,agg) on volumetric current density: (a) 0.7 V, (b) 0.3 V.
Fig. 12 e Effect of agglomerate radius (ragg) on effectiveness factor: (a) 0.7 V, (b) 0.3 V.
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numerically investigated by a PEM fuel cell model based on the finite volume method. The agglomerate model is applied in the cathode CL to describe the electrochemical kinetics due to the slow ORR. The thickness of the ionomer film (di) is obtained when the parameters of LPt/C, Li, ragg and Li,agg are given. Then the thickness of the liquid water (dw) is also determined according the liquid water saturation level. The thickness of the ionomer film (di) increases with increasing ragg and decreasing Li,agg, which increases the oxygen transport resistance through the ionomer film. The effective agglomerate surface area (aagg,i) increases with decreasing ragg and increasing Li,agg, which facilitates the oxygen transport process. The current density is greatly improved at medium and high current densities when the ragg is decreased and the Li,agg is increased. This is attributed to the decrease of the transport resistance within the agglomerate and through the ionomer and liquid water films. A lower oxygen concentration distribution and a higher liquid water saturation distribution are observed in the cathode CL when the current density is improved. The volumetric current density and effectiveness factor are largely improved at the region under the channel for the cases with ragg ¼ 1.0 107 m and Li,agg ¼ 0.5 compared to the corresponding cases. These numerical results improve the understanding of the agglomerate model and give useful guidance for manufacturing of PEM fuel cell catalyst layers.
Acknowledgments Fig. 13 e Effect of volume fraction of ionomer within agglomerate (Li,agg) on effectiveness factor: (a) 0.7 V, (b) 0.3 V.
The work was carried out at the Department of Energy Sciences, Lund University. The first author gratefully acknowledges the financial support from China Scholarship Council (CSC).
references under the channel region and minimum jc under the rib region. This is attributed to the oxygen concentration distributions, as shown in Figs. 8e9. At high current densities, the jc distribution is strongly affected by the oxygen mass transport. The effectiveness factor (Er) of the agglomerate represents the efficiency of the ORR process within the agglomerate. As shown in Figs. 12 and 13, Er is increased with decreasing ragg and increasing Li,agg, and Er is decreased with increasing current density due to the increase in reaction rate constant. According to Eqs. (19) and (20), Er is increased with decreasing ragg and kc, and increasing Li,agg. For the operating voltage 0.7 V, the case with ragg ¼ 1.0 107 m provides the maximum Er approximately 1.0, while the case with Li,agg ¼ 0.5 provides the maximum Er, approximately 0.85. For the operating voltage 0.3 V, the Er under the rib of all cases is relatively low and close to zero, while the Er under the channel of the case with ragg ¼ 1.0 107 m and Li,agg ¼ 0.5 is still relatively high approaching 0.85 and 0.18, respectively.
Conclusions The effects of agglomerate model parameters (ragg and Li,agg) on cell performance and transport characteristics were
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Effects of agglomerate model parameters on transport characterization and performance of PEM fuel cells Shian Li a, Jinliang Yuan b, Gongnan Xie c, Bengt Sunden a,* a
Department of Energy Sciences, Lund University, P.O. Box 118, SE-22100, Lund, Sweden Faculty of Maritime and Transportation, Ningbo University, 315211, Ningbo, China c Department of Mechanical and Power Engineering, Northwestern Polytechnical University, Box 24, 710072, Xi'an, China b
article info
abstract
Article history:
A three-dimensional, non-isothermal and two-phase flow model for proton exchange
Received 19 November 2017
membrane (PEM) fuel cells is developed. In the cathode catalyst layer, a spherical
Received in revised form
agglomerate model with consideration of catalyst layer structure and liquid water effect is
21 February 2018
applied to determine the electrochemical kinetics. The size and structure of the agglom-
Accepted 15 March 2018
erates are determined by the following parameters, i.e., the agglomerate radius (ragg), the
Available online xxx
volume fraction of ionomer within the agglomerate (Li,agg), and the thickness of the ionomer film over the agglomerate (di). It is noted that a random combination of the three
Keywords:
above parameters is widely used in agglomerate models by researchers. In this paper, the
PEM fuel cells
effects of ragg and Li,agg on the cell performance and local transport characteristics are
Electrochemistry
numerically investigated by using the developed model with consideration of the re-
Agglomerate model
lationships between agglomerate parameters. It is concluded that the cell performance is
Agglomerate structure
significantly improved by decreasing ragg and increasing Li,agg at medium and high current
Mass transport
densities when the volume fractions of the solid phase (LPt/C) and ionomer phase (Li) are maintained constant. In addition, the distributions of oxygen concentration, liquid water saturation, volumetric current density and effectiveness factor are also strongly influenced by the variation of the two parameters. © 2018 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.
Introduction Proton exchange membrane (PEM) fuel cells have been widely considered as the most promising alternative power sources for a wide variety of applications due to their attractive advantages [1]. However, the commercialization of PEM fuel cell systems is limited by the cost, durability and stability issues.
Over the past few years, cell performance improvement has been gradually obtained by increased platinum utilization, appropriate flow field design, thermal and water management strategies. Operating conditions were optimized to obtain the maximum performance of a PEM fuel cell [2]. Raman et al. [3] developed a dynamic model to investigate the water induced pore blockage and mitigation strategies in PEM fuel cells. The performance of PEM fuel cells with in-line and staggered
* Corresponding author. n). E-mail address: [email protected] (B. Sunde https://doi.org/10.1016/j.ijhydene.2018.03.106 0360-3199/© 2018 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved. Please cite this article in press as: Li S, et al., Effects of agglomerate model parameters on transport characterization and performance of PEM fuel cells, International Journal of Hydrogen Energy (2018), https://doi.org/10.1016/j.ijhydene.2018.03.106
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Nomenclature a A c CP D E f F h H i j k K L m M n P Q r R s S t T ! u V X Y
1
Effective surface area, m /Water activity Area, m2 Mole concentration, mol m3 Specific heat, J kg1 K1 Diffusivity, m2 s1 Effectiveness factor Platinum mass ratio to Pt/C Faraday constant, 96,485 C mol1 Enthalpy change, J kg1 Henry's constant, Pa m3 mol1 Exchange current density, A m2 Volumetric current density, A m3 Thermal conductivity, W m1 K1/Reaction rate constant, s1 Permeability, m2 Volume fraction Mass loading, kg m2 Molecular weight, kg mol1 Osmotic-drag coefficient Pressure, Pa Mass flow rate, kg s1 Agglomerate radius, m Universal gas constant, 8.314 J mol1 K1 Liquid water saturation Source term/Entropy, J mol1 K1 Thickness, m Temperature, K Velocity vector, m/s Voltage, V/Volume, m3 Mole fraction Mass fraction
Greek Symbols a Transfer coefficient g Water phase change rate, s1 d Thickness, m ε Porosity h Over-potential, V q Contact angle l Water content m Dynamic viscosity, Pa s
blockages were experimentally studied by Heidary et al. [4]. In addition, a novel convergent-divergent serpentine flow field was proposed and investigated by Chowdhury [5]. PEM fuel cells consist of several components including the current collectors (CCs), the gas flow channels (GFCs), the gas diffusion layers (GDLs), the catalyst layers (CLs) and the membrane. The CL is the most important component of PEM fuel cells as the chemical energy conversion to electrical energy via the electrochemical reactions occurs here. The hydrogen oxidation reaction (HOR) and oxygen reduction reaction (ORR) simultaneously take place within the anode and cathode CLs, respectively. In comparison with the HOR, the ORR is relatively slow and becomes the dominant factor that
x r s f F
Stoichiometric ratio Density, kg m3 Electron/Proton conductivity, S m1/Surface tension, N m2 Potential, V Theile's modulus
Subscripts and Superscripts a Anode agg Agglomerate c Cathode/Carbon con Condensation d Osmotic-drag/Dissolved water eff Effective eq Equilibrium evap Evaporation g Gas i i th species/Ionomer j j th species l Liquid lg Liquid and gas water m Membrane/Mixture mom Momentum equation oc Open circuit ref Reference rl Liquid relative rg Gas relative phase Phase change Pt Platinum sat Saturation s Solid/Liquid water saturation vd Vapor and dissolved water w Water wv Water vapor Abbreviations CC Current collector CL Catalyst layer GDL Gas diffusion layer GFC Gas flow channel PEM Proton exchange membrane
determines the cell performance. During the past decades, numerical simulations have been widely applied to improve the understanding of transport characterization inside PEM fuel cells. Generally, there are three models to describe the cathode CL, i.e., (a) the interface model [6e9], (b) the homogeneous model [8,10e14], and (c) the agglomerate model [8,15e28]. Among the three mentioned models, the agglomerate model has the capability to capture oxygen concentration loss at high current densities. A comprehensive study of different cathode CL models on cell performance was conducted by Harvey et al. [8], showing the advantage of the agglomerate model on predicting the mass transport resistance at high current densities. The effects of ionomer and
Please cite this article in press as: Li S, et al., Effects of agglomerate model parameters on transport characterization and performance of PEM fuel cells, International Journal of Hydrogen Energy (2018), https://doi.org/10.1016/j.ijhydene.2018.03.106
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platinum loadings on cell performance were numerically investigated by Sun et al. [15]. The results showed that there is an optimal value of the ionomer loading under a constant platinum loading. A multi-variable optimization work was carried out to improve the performance of PEM fuel cells by using an agglomerate model for description of the cathode electrochemical kinetics, and Kriging surrogate model for the implementation of optimization procedure [16]. PEM fuel cells with non-uniform agglomerate cathode CLs, which are achieved by applying several sub-layers with varying agglomerate radius, porosity and ionomer volume fraction within the agglomerate, were numerically investigated by Song et al. [17] and Yin et al. [18]. Due to the operating temperature of PEM fuel cells below 100 C, water may exist in either liquid phase or vapor phase, which is dependent on local temperature and saturation pressure. The presence of liquid water is beneficial to increase the protonic conductivity, decrease the ohmic loss, and thereby improve the cell performance. However, excessive liquid water can block the pores in GDLs and CLs for gas transport and influence the electrochemical reaction rates in CLs. For the mathematical models of PEM fuel cells, the mass diffusivity and electrochemical reaction rate are commonly modified by multiplication of a term (1-s)n to account for the effect of liquid water. The influence of exponent n on the cell performance was extensively examined by Wang et al. [14]. The driving force for liquid water transport in porous regions is the capillary pressure, which is determined by either the Leverett function or correlations obtained by different researchers. Although the values of the capillary pressure do not agree very well with each other, the Leverett function is still widely used in PEM fuel cell models. In addition, the water transport mechanisms through the membrane are electroosmotic drag, back diffusion and hydraulic permeation [6]. Generally, a combined model is adopted to model the process of water transport in the membrane. In addition, the hydraulic permeation term is commonly neglected in the model because it is much smaller than the electro-osmotic drag and back diffusion terms. For the agglomerate model, each spherical agglomerate particle is assumed to be evenly coated with a thin ionomer film, followed by a thin liquid water film. Agglomerate models with consideration of liquid water have been extensively developed and applied in numerical studies of PEM fuel cells. The effect of liquid water on cell performance was numerically studied by Rao et al. [19]. The cathode CL microstructure of PEM fuel cells was optimized to improve the platinum utilization [20]. Recently, the water film formation and transport characteristics of PEM fuel cells under low humidity operating conditions were numerically investigated by Jo et al. [21]. For implementation of the agglomerate model to PEM fuel cells models, the size and structure of the agglomerates are determined by the following parameters, i.e., the agglomerate radius (ragg), the volume fraction of ionomer within agglomerate (Li,agg), and the thickness of the ionomer film over the agglomerate (di). It is noted that different agglomerate model parameters are used by different researchers in the open literature. As shown in Table 1, ragg ranges from 50 to 1500 nm, di ranges from 0 to 100 nm, and Li,agg ranges from 0.1 to 0.6. Therefore, this study focuses on the effects of the agglomerate
Table 1 e Review of agglomerate model parameters.
Sun et al. [15] Xing et al. [16] Song et al. [17] Yin et al. [18] Rao et al. [19] Marquis et al. [20] Jo et al. [21] Secanell et al. [22] Yang et al. [23] Dobson et al. [24] Kamarajugadda et al. [25] Shah et al. [26] Li et al. [27,28]
ragg (nm)
di (nm)
Li,agg
1000 100e1000 300e1500 500e1500 100 150 100 250e1000 100 190e250 50e1000 200 1000
80 e e e e 12 e 0e80 10 e 0e100 15 22
0.5 e 0.1e0.4 0.2e0.6 e e e 0.5 0.39 0.17e0.25 0.2e0.5 0.2 0.5
model parameters on the cell performance and local transport characteristics. The parameters ragg and Li,agg are selected as the variables, and di is determined by the corresponding expressions when ragg and Li,agg are changed. The thickness of the liquid water film (dw) is determined by the local liquid water saturation level. The spherical agglomerate model is adopted in the cathode CL, which is fully coupled with the charge transport equation. In the present study, a three-dimensional, two-phase flow and non-isothermal agglomerate model based on the finite volume method is developed and applied to investigate the effects of the agglomerate model parameters ragg varying from 1.0 107 m to 9.0 107 m, and Li,agg varying from 0.2 to 0.5 on the transport phenomena and performance of PEM fuel cells. The structure of this paper is as follows. Firstly, the geometry of the computational domain is introduced, followed by description of the governing equations. Then, the catalyst layer composition and the agglomerate model are completely presented. Finally, the numerical results and conclusions are addressed.
Model description The three-dimensional computational domain considered in this study is a single channel unit of a PEM fuel cell, as shown in Fig. 1. The reactant gases hydrogen and oxygen (supplied in the form of air) are fed to the anode and cathode GFCs, respectively. The detailed information of the fuel cell geometry and operating condition parameters are summarized in Table 2 and Table 3. The fuel cell operating temperature and pressure are 353 K and 1 atm, respectively. In addition, 100% relative humidity is applied for both the anode and cathode reactant gases. In the PEM fuel cell mathematical model, the fluid flow is laminar; ideal gas law is applied for the reactant gases; the GDLs and CLs are homogeneous and isotropic; the reactant gases cannot diffuse across the membrane; the generated water in the cathode CL is in dissolved phase.
Governing equations With the above mentioned assumptions, the governing equations of mass, momentum, species, energy, charge, liquid
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Fig. 1 e Schematic of a PEM fuel cell: (a) three-dimensional computational domain, (b) the middle plane of cathode catalyst layer.
Table 2 e Fuel cell geometric dimensions [27,28]. Parameter Fuel cell length Fuel cell width GFC width GFC height CC width CC height GDL thickness CL thickness Membrane thickness
Value
Units
50 2 1 1 1 1.8 0.2 0.01 0.05
mm mm mm mm mm mm mm mm mm
V$ðr! u Yi Þ ¼ V$ rDeff ;i VYi þ Si
Reactant gas Operating pressure, Pa/Pc Stoichiometric ratio, xa/xc Relative humidity, RHa/RHc Operating temperature, Ta/Tc
Anode
Cathode
Hydrogen 1 atm 1.5 100% 353 K
Air 1 atm 2.0 100% 353 K
(1)
where r and ! u are the mixture fluid density and superficial velocity, respectively. Smass represents the source term of mass equation. The mass changes of hydrogen, oxygen and water vapor due to the processes of electrochemical reactions and phase change are completely considered in the corresponding layers. Momentum conservation equation: V$ðr! u! u Þ ¼ V$ðmV! u Þ VP þ Smom
V$ rCp ! u T ¼ V$ keff VT þ ST
(4)
where Cp and keff are the specific heat and effective thermal conductivity, respectively. The irreversible, reversible, ohmic heat generation and phase change terms are totally included in the energy equation source term, ST. Charge conservation equation:
water and dissolved water are used to describe the complex and coupled transport processes within fuel cells. Mass conservation equation: V$ðr! u Þ ¼ Smass
(3)
where Yi and Deff,i are the mass fraction and effective diffusivity for the i th species, respectively. Si represents the amount of consumption or generation of the i th species. The effective diffusivity (Deff,i) is obtained by the Bruggeman correlation which accounts for the tortuous path in the GDLs and CLs. Energy conservation equation:
Table 3 e Fuel cell operating conditions. Parameter
equation. The Darcy's law is adopted to describe the flow through the anode and cathode GDLs and CLs, which have the porous feature. Species conservation equation:
(2)
where P and m are the mixture pressure and dynamic viscosity, respectively. Smom denotes the source term of momentum
V$ seff ;s Vfs þ Ss ¼ 0
(5)
V$ seff ;m Vfm þ Sm ¼ 0
(6)
where seff,s is the effective electrical conductivity, seff,m the effective protonic conductivity, fs the electrical potential, fm the protonic potential. The Butler-Volmer equation and spherical agglomerate model are adopted to describe the HOR and ORR in the anode and cathode CLs, respectively. Liquid water transport equation: Krl mg ! u ¼ V$ðrl Ds VsÞ þ Sl V$ rl Krg ml
(7)
where Krl and Krg are the relative permeability of liquid and gas phase, respectively. Ds denotes the capillary diffusion coefficient. The source term, Sl, represents the phase change
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Table 4 e Parameters used in the mathematical model. Parameter
Value
mg cm2 kg m3 mg cm2 kg m3 kg m3 kg mol1 e A m2
10(0.03741*T16.96)
A m2
0.5 1 56.4
e e mol m3
Reference oxygen concentration, cO2 [32]
3.39
mol m3
Hydrogen Henry's constant, HH2 [33] Oxygen Henry's constant, HO2 [33] Thermal conductivity of CC/GDL/CL, kCC/GDL/CL [27] Thermal conductivity of membrane, km [27] Electrical conductivity of CC/GDL/CL, ss,CC/GDL/CL [27] Entropy of hydrogen oxidation, DSa [34] Entropy of oxygen reduction, DSc [34] Latent heat of condensation/evaporation, Dhlg [23] Liquid water viscosity, ml [23] Surface tension, s [23] Contact angle of GDL/CL, qGDL/CL [23] Condensation rate, gcon [33] Evaporation rate, gevap [33] Dissolved water phase change rate, g [33] Permeability of GDL, KGDL [27] Permeability of CL, KCL [27] Binary diffusivity, DH2 H2 O [9] Binary diffusivity, DO2 H2 O [9] Binary diffusivity, DO2 N2 [9] Binary diffusivity, DH2 ON2 [9]
4.56 103 0.101325e(666/Tþ14.1) 100/1.7/0.3 0.25 20,000/5000/2000 0.104 326.36 2.36 106 3.517 104 0.0625 110 /95 100 100 1 5.6e-12 1.0e-13 9.15 105 2.82 105 2.2 105 2.56 105
Pa m3 mol1 Pa m3 mol1 W m1 K1 W m1 K1 S m1 J mol1 K1 J mol1 K1 J kg1 Pa s N m1 e s1 s1 s1 m2 m2 m2 s1 m2 s1 m2 s1 m2 s1
ref
Anode reference exchange current density, ia [27] ref
Cathode reference exchange current density, ic [30] Anode transfer coefficient, aa [31] Cathode transfer coefficient, ac [31] ref
Reference hydrogen concentration, cH2 [32] ref
process between water vapor and liquid water, which is determined by the water vapor partial pressure and saturation pressure. Dissolved water transport equation: V$
Units
0.4 2.145 104 0.6 1.8 103 1.98 103 1.1 0.6 100
Platinum loading, mpt [29] Platinum density, rpt [27] Carbon loading, mc [27] Carbon density, rc [27] Dry membrane density, rm [27] Membrane equivalent weight, Mm [27] Porosity of GDL, εGDL [27]
n r d sm Vfm ¼ V$ m Dl Vl þ Sd F Mm
(8)
where nd and Dl are the electro-osmotic drag coefficient and water diffusivity in the membrane, respectively. The generated water in the cathode CL is in dissolved phase, and the absorption/desorption processes of ionomer in the anode and cathode CLs take place between water vapor and dissolved water. The parameters and complementary equations used in the mathematical model are summarized in Tables 4 and 5. In addition, the sources terms for the governing equations are given in Table 6.
The catalyst layer composition and volume fraction
LPt=C ¼
(9)
mpt tCL
1 1f 1 þ rpt f rc
! (10)
where mpt is the platinum loading, tcl the thickness of the CL, rpt the density of platinum, rc the density of carbon. The parameter f is defined as the platinum loading divided by the sum of platinum loading and carbon loading. f¼
mpt mpt þ mc
(11)
where mc is the carbon loading. The volume fraction of the ionomer phase (Li) is expressed by: Li ¼
The catalyst layer consists of void space, Pt/C particles, and ionomer phase. The volume fraction of each component is determined by the following expressions [22,26,31]. The volume fraction of the void space (εCL) is given by: εCL ¼ 1 LPt=C Li
where LPt/C and Li are the volume fractions of Pt/C particles and ionomer phase, respectively. The volume fraction of the Pt/C particles (LPt/C) is determined by:
i h 3 L Pt=C r3agg Li;agg þ raggþdi r3agg r3agg 1 Li;agg
(12)
The ionomer phase consists of two parts: one part is inside the agglomerate, the other part is the ionomer film. When LPt/ C, Li, ragg, and Li,agg are given, the unique di is determined. It is assumed that the agglomerate is only occupied by Pt/C particles and ionomer phase. Li usually varies from 0.2 to 0.4 [33]. In
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Table 5 e Complementary equations and definitions. Description
Units 1:5 1:5
Effective mass diffusivity [10]
Deff ;i ¼ ð1 sÞ
Mass diffusivity
Di;m ¼ Pn
ε
m2 s1
Di;m
m2 s1
1Xi X =Di;j j¼1;jsi j
1:5
Binary mass diffusivity
P0 P
Di;j ¼ Di;j ðT0 ; P0 Þ
m2 s1
T T0
!0:5
Electrochemical kinetics [10]
ref
ja ¼ ð1 sÞia aeff
P
A m3
½eaa Fha =RT eac Fha =RT
H2 ref cH HH2 2
ha ¼ fs fm , hc ¼ fs fm Voc
Over-potential [10] Open circuit voltage [27]
Voc ¼ 1:229 8:456 104 ðT 298:15Þ þ 4:31 105 TLnðPH2 P0:5 O2 Þ
Active surface area [31]
aeff ¼
Proton conductivity [7]
sm ¼ ð0:514l 0:326Þe1268ð
Þ
S m1
Effective conductivity [27]
seff ;s ¼ ð1 εGDL Þ1:5 ss ; seff ;s ¼ ð1 εCL Li Þ1:5 ss seff ;m ¼ L1:5 i sm
S m1
Relative permeability
Krl ¼ Ks3 ; Krg ¼ Kð1 sÞ3
m2
mpt tCL
Ds ¼
m1
ð227:79f 3 158:57f 2 201:53f þ 159:5Þ 103 1 1 303T
Capillary diffusivity
V V
m2 s1
3
Ks dPc ml ds
Capillary pressure
0:5 Pc ¼ scosðqÞ Kε ð1:417s 2:12s2 þ 1:263s3 Þ
Saturation pressure
log10 Psat ¼ 2:1794 þ 0:02953ðT 273:15Þ 9:1837 105 ðT 273:15Þ þ
Pa 2
Pa
1:4454 107 ðT 273:15Þ3 Electro-osmotic drag coefficient [7] Dissolved water diffusivity [7]
l nd ¼ 2:5 22
Dl ¼ 1010 e½2416ð
1 1 303T
Equilibrium water content [35]
leq ¼
8 < 2:05l 3:25 Þ 6:65 1:25 : 2:563 0:33l þ 0:0264l2 0:000671l3
1:41 þ 11:3a 18:8a2 þ 16:2a3 10:1 þ 2:94ða 1Þ
e ð2≪l < 3Þ ð3≪l < 4Þ ð4 < lÞ
e
ða < 1Þ ða 1Þ
e
P þ 2s a ¼ XPwv sat
Water activity
m2 s1
m2 s1
TðjM Þ0:5 1012 m HV2 O0:6 H2 O O
Oxygen diffusivity in liquid water [36]
DO2 ;w ¼ 7:4
Oxygen diffusivity in ionomer [33]
DO2 ;i ¼ 2:88 1010 e½2933ð313TÞ
2
1
m2 s1
1
Table 6 e Source terms in the governing equations. Description
Units
Smass ¼ SH2 þ Swv Anode CL Smass ¼ SO2 þ Swv Cathode CL Smass ¼ Swv Anode and cathode GDLs S ¼ m! u Anode and cathode GDLs and CLs
kg m3 s1
SH 2 ¼
kg m3 s1
mom
SO 2 ¼
K ja 2FMH2 jc 4FMO2
Anode CL Cathode CL
Swv ¼ Sl Svd MH2 O Anode and cathode CLs Swv ¼ Sl Anode and cathode GDLs TDSa 2 2 2F ja þ seff ;m Vfm þ seff ;s Vfs þ Sl Dhlg Anode CL TDSc 2 2 ST ¼ jc hc 4F jc þ seff ;m Vfm þ seff ;s Vfs þ Sl Dhlg Cathode CL ST ¼ seff ;m Vf2m membrane ST ¼ seff ;s Vf2s þ Sl Dhlg Anode and cathode GDLs
ST ¼ j a ha
kg m2 s2 kg m3 s1 kg m3 s1 W m3
ST ¼ seff ;s Vf2s Anode and cathode CCs ¼ ja Anode CL ¼ þ jc Cathode CL ¼ þ ja Anode CL ¼ jc Cathode CL ¼ Sphase Anode and cathode GDLs and CLs 8 εð1 sÞ > > MH2 O ðPwv Psat Þ Pwv Psat < gcond RT Sphase ¼ > εs > : gevap MH2 O ðPwv Psat Þ Pwv < Psat RT Sd ¼ Svd Anode CL Sd ¼ Svd þ Sl Cathode CL Svd ¼ g Mrmm ðleq lÞAnode and cathode CLs
Ss Ss Sm Sm Sl
Sl ¼
jc 2F Cathode
A m3 A m3 kg m3 s1 kg m3 s1
mol m3 s1
CL
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7
Fig. 2 e Schematic of the ionomer and liquid water films covering the agglomerate.
this study, it is fixed at 0.4. Meanwhile, LPt/C is also a constant value, which can be obtained by Eq. (10). As a result, di is a function of ragg and Li,agg. The thickness of ionomer film (di) is obtained by: ffi # "sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 3 Li 1 Li;agg Li;agg þ 1 1 di ¼ ragg LPt=C
(13)
rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 3 3sεCL 3 dw ¼ ragg þ di þ ragg þ di 4pN
(17)
According to Eq. (13), The thickness di is increased from 8.63 109 m to 7.76 108 m when ragg is increased from 1.0 107 m to 9.0 107 m and Li,agg is fixed at 0.4. The thickness di is decreased from 9.78 108 m to 1.11 108 m
The total volume of the liquid water is: Vw ¼ sεCL VCL
(14)
where s is the liquid water saturation, VCL is the total volume of the CL. The volume of the liquid water covering the individual agglomerate can be obtained: Vw;i ¼
sεCL N
(15)
where N is the number of agglomerate particles per catalyst layer volume. N¼
3LPt=C 4pr3agg 1 Li;agg
(16)
The thickness of the liquid water film (dw) is obtained by:
Fig. 3 e Comparison of the numerical results with the experimental data.
Fig. 4 e Effect of agglomerate radius (ragg) on cell performance: (a) polarization curve, (b) power density curve.
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when Li,agg is increased from 0.2 to 0.5 and ragg is fixed at 5.0 107 m.
The cathode agglomerate model
1 1 1 FL tanhð3FL Þ 3FL
(19)
where the Thiele's modulus for chemical reactions is given as:
In the present model, the spherical agglomerate model [15,26] is used to calculate the volumetric current density. Fig. 2 depicts the structure of the agglomerates within the cathode CL. The identical agglomerates are uniformly distributed in the cathode CL, and the individual agglomerate is evenly covered and liquid water films. 1 by ionomer ragg þ di þ dw PO 1 di dw þ þ jc ¼ 4F 2 HO2 Er kc ð1 εCL Þ ragg aagg;i DO2 ;i aagg;w DO2 ;w (18) where P is the partial pressure of oxygen, H the Henry's constant, Er the effective factor, kc the reaction rate constant, aagg,i the ionomer effective agglomerate surface area, and aagg,w the liquid water effective agglomerate surface area. It is noted that the first term in the bracket represents the transport process within the agglomerate, and the second term denotes the transport processes through the ionomer and liquid water films. The effectiveness factor of the spherical agglomerate is defined as:
Fig. 5 e Effect of volume fraction of ionomer within agglomerate (Li,agg) on cell performance: (a) polarization curve, (b) power density curve.
Er ¼
FL ¼
ragg 3
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi kc L1:5 i;agg DO2
(20)
The reaction rate constant is computed as:
ref
kc ¼
ic aeff ref
4Fð1 εCL ÞcO2
eaa Fhc =RT þ eac Fhc =RT
(21)
The effective agglomerate surface area is obtained from: aagg;i ¼
2 3LPt=C εCL ragg þ di r3agg 1 Li;agg
aagg;w ¼
2 3LPt=C εCL ragg þ di þ dw r3agg 1 Li;agg
(22) (23)
According to Eq. (20), the effective surface area aagg,i is decreased from 5.15 106 m1 to 5.72 105 m1 when ragg is increased from 1.0 107 m to 9.0 107 m and Li,agg is fixed at 0.4. The effective surface area aagg,i is increased from 9.36 105 m1 to 1.09 106 m1 when Li,agg is increased from 0.2 to 0.5 and ragg is fixed at 5.0 107 m.
Fig. 6 e Effect of agglomerate radius (ragg) on oxygen concentration: (a) 0.7 V, (b) 0.3 V.
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Numerical implementation and boundary conditions The mathematical model of PEM fuel cells is developed by using the commercial software ANSYS FLUENT. The governing equations of charge, liquid water transport, and dissolved water transport are implemented by using user defined scalar (UDS) equations with an under relaxation technique developed by the authors. At the inlet of the GFCs, the mass flow rate, temperature, and species mass fractions are prescribed. The mass flow rates of reactants at both anode and cathode sides are calculated at a reference current density of 1.0 A/cm2, as given by Eqs. (24) and (25). Anode and cathode stoichiometric ratios (xa and xc) are given in Table 3. In addition, the inlet liquid water saturation is assigned to be zero. At the outlet of the GFCs, a pressure-outlet boundary condition is applied. The operating temperature and a constant electric potential, fs ¼ 0, are specified at the anode terminal. The operating temperature and a constant electric potential, fs ¼ Vcell, are applied for the cathode terminal. The corresponding current density is obtained when an operating cell voltage is specified. x MH (24) Qa ¼ a 2 Iref Am 2FYH2
Fig. 7 e Effect of volume fraction of ionomer within agglomerate (Li,agg) on oxygen concentration: (a) 0.7 V, (b) 0.3 V.
Qc ¼
xc MO2 Iref Am 4FYO2
(25)
The Semi-Implicit Method for Pressure Linked Equations (SIMPLE) algorithm is used to handle the pressure-velocity coupling. The standard procedure is used for pressure, while the second order upwind discretization scheme is adopted for momentum, species, energy and UDS equations. A grid independence study was carefully performed to balance the accuracy and computation resources. The mesh system with the total control volume number of 172,000 was selected for the following simulations.
Results and discussions In this section, the effect of ragg ranging from 1.0 107 m to 9.0 107 m on the cell performance was investigated, when Li,agg is fixed at 0.4. The effect of Li,agg ranging from 0.2 to 0.5 on the cell performance was also investigated, when ragg is fixed at 5.0 107 m for all the corresponding cases. In addition, the local distributions of oxygen concentration, liquid water saturation, volumetric current density, and effectiveness factor in the cathode CL at the operating cell voltages 0.7 V and 0.3 V are presented and analyzed.
Fig. 8 e Effect of agglomerate radius (ragg) on liquid water saturation: (a) 0.7 V, (b) 0.3 V.
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Model validation The numerical results obtained by the developed model are compared with the experimental data reported by Yan et al. [37], as shown in Fig. 3. It is found that the numerical results show good agreement with experimental data. A 25 cm2 fuel cell with a platinum loading of 0.4 mg cm2 for both the anode and cathode CLs was tested under the operating temperature of 353 K, operating pressure of 1 atm, and relatively humidity of 100%. The information provided by the experimental work is limited, but the CL parameters and operating conditions of experiments are very similar to those of the present work. For the model validation, ragg ¼ 1.0 106 and Li,agg ¼ 0.44 are adopted in the agglomerate model, and the remaining parameters are the same as the present work.
Cell performance The cell performance is estimated and evaluated in terms of polarization curve (Vcell, Icell) and power density curve (Icell, Pcell). Fig. 4 presents the effect of variation of ragg on the cell performance. It can be seen that the current density is significantly affected by the ragg at medium and high current densities. The current density is gradually improved with decreasing ragg at the same operating voltage. For the
Fig. 9 e Effect of volume fraction of ionomer within agglomerate (Li,agg) on liquid water saturation: (a) 0.7 V, (b) 0.3 V.
operating voltage 0.3 V, the current density for the case with ragg ¼ 9.0 107 m is 0.682 A/cm2, while the current density for the case with ragg ¼ 1.0 107 m is 1.431 A/cm2 which is approximately 2.1 times higher than the previous one. In addition, the maximum power density is greatly improved from 0.564 W/cm2 to 0.303 W/cm2 when ragg is reduced from 9.0 107 m to 1.0 107 m. As shown in Fig. 5, the cell performance is also strongly affected by the variation of Li,agg at medium and high current densities. The current density is gradually improved with increasing Li,agg at the same operating voltage. The maximum current density for the case with Li,agg ¼ 0.2 is 0.747 A/cm2, while the maximum current density for the case with Li,agg ¼ 0.5 is 1.316 A/cm2 which is approximately 1.8 times higher than the previous one. In addition, the maximum power density is greatly improved from 0.325 W/cm2 to 0.505 W/cm2 when the Li,agg is increased from 0.2 to 0.5. Therefore, it is clear that the cell performance can be improved by either decreasing ragg or increasing Li,agg at the same operating voltage when the Lpt/C and Li are kept constant. At low current density, no significant difference is observed due to the low reaction rate in the CLs. The increase of the effectiveness factor and decrease of the oxygen transport resistance through the ionomer and liquid water films are caused by either decreasing ragg or increasing Li,agg, thereby leading to improvement of the cell performance.
Fig. 10 e Effect of agglomerate radius (ragg) on volumetric current density: (a) 0.7 V, (b) 0.3 V.
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Local transport characterization
11
The oxygen concentration distributions in the middle plane of the cathode CL (Line-1) at operating voltages 0.7 V and 0.3 V are shown in Figs. 6e7. This is a key parameter affecting the ORR in the cathode CL. It is observed that the maximum oxygen concentration appears under the channel region, while the minimum oxygen concentration appears under the rib region due to the transport resistance from the channel to the region under the rib. The consumption amount of oxygen is proportional to the current density, so a lower oxygen concentration is obtained in the cathode CL when a higher current density is generated. The oxygen concentration is gradually decreased by either decreasing ragg or increasing Li,agg at the same operating voltage, which is caused by the increased current density as discussed above. It is also observed that the minimum oxygen concentration for the cases with ragg ¼ 1.0 107 m and Li,agg ¼ 0.5 at the operating voltage 0.3 V is extremely low (approaching zero for ragg ¼ 1.0 107 m), which means that the desired amount of oxygen is not satisfied by the transport process from the channel to CL and the cell performance is also limited by the concentration loss. The liquid water is formed when the water vapor partial pressure exceeds the saturation pressure which is a function of local temperature. The membrane needs to be well
hydrated to decrease the ohmic loss caused by the proton transport from the anode CL to the cathode CL. However, excess liquid water causes the water flooding issue which strongly affects the cell performance. Figs. 8e9 show the liquid water saturation distributions in the middle plane of the cathode CL (Line-1) at operating voltages 0.7 V and 0.3 V. The liquid water under the channel region can be easily transferred and removed away from the GDL to the GFC, so a lower liquid water saturation is observed in this region compared with that under the rib. It also can be seen that the liquid water saturation level is increased with decreasing ragg and increasing Li,agg, which is consistent with the trend of the current density. When the current density is improved, the amount of water generation is increased and more liquid water is also formed. The volumetric current density (jc) is determined by the spherical agglomerate model. A higher jc means that more oxygen is consumed and water is generated in the cathode CL. The jc distributions in the middle plane of the cathode CL (Line-1) at operating voltages 0.7 V and 0.3 V are shown in Figs. 10 and 11. For the operating voltage 0.7 V, the case with ragg ¼ 1.0 107 m and Li,agg ¼ 0.5 provides the maximum jc and the variation of jc is also the biggest compared to other cases. For the operating voltage 0.3 V, the case with ragg ¼ 1.0 107 m and Li,agg ¼ 0.5 provides the maximum jc
Fig. 11 e Effect of volume fraction of ionomer within agglomerate (Li,agg) on volumetric current density: (a) 0.7 V, (b) 0.3 V.
Fig. 12 e Effect of agglomerate radius (ragg) on effectiveness factor: (a) 0.7 V, (b) 0.3 V.
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numerically investigated by a PEM fuel cell model based on the finite volume method. The agglomerate model is applied in the cathode CL to describe the electrochemical kinetics due to the slow ORR. The thickness of the ionomer film (di) is obtained when the parameters of LPt/C, Li, ragg and Li,agg are given. Then the thickness of the liquid water (dw) is also determined according the liquid water saturation level. The thickness of the ionomer film (di) increases with increasing ragg and decreasing Li,agg, which increases the oxygen transport resistance through the ionomer film. The effective agglomerate surface area (aagg,i) increases with decreasing ragg and increasing Li,agg, which facilitates the oxygen transport process. The current density is greatly improved at medium and high current densities when the ragg is decreased and the Li,agg is increased. This is attributed to the decrease of the transport resistance within the agglomerate and through the ionomer and liquid water films. A lower oxygen concentration distribution and a higher liquid water saturation distribution are observed in the cathode CL when the current density is improved. The volumetric current density and effectiveness factor are largely improved at the region under the channel for the cases with ragg ¼ 1.0 107 m and Li,agg ¼ 0.5 compared to the corresponding cases. These numerical results improve the understanding of the agglomerate model and give useful guidance for manufacturing of PEM fuel cell catalyst layers.
Acknowledgments Fig. 13 e Effect of volume fraction of ionomer within agglomerate (Li,agg) on effectiveness factor: (a) 0.7 V, (b) 0.3 V.
The work was carried out at the Department of Energy Sciences, Lund University. The first author gratefully acknowledges the financial support from China Scholarship Council (CSC).
references under the channel region and minimum jc under the rib region. This is attributed to the oxygen concentration distributions, as shown in Figs. 8e9. At high current densities, the jc distribution is strongly affected by the oxygen mass transport. The effectiveness factor (Er) of the agglomerate represents the efficiency of the ORR process within the agglomerate. As shown in Figs. 12 and 13, Er is increased with decreasing ragg and increasing Li,agg, and Er is decreased with increasing current density due to the increase in reaction rate constant. According to Eqs. (19) and (20), Er is increased with decreasing ragg and kc, and increasing Li,agg. For the operating voltage 0.7 V, the case with ragg ¼ 1.0 107 m provides the maximum Er approximately 1.0, while the case with Li,agg ¼ 0.5 provides the maximum Er, approximately 0.85. For the operating voltage 0.3 V, the Er under the rib of all cases is relatively low and close to zero, while the Er under the channel of the case with ragg ¼ 1.0 107 m and Li,agg ¼ 0.5 is still relatively high approaching 0.85 and 0.18, respectively.
Conclusions The effects of agglomerate model parameters (ragg and Li,agg) on cell performance and transport characteristics were
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Please cite this article in press as: Li S, et al., Effects of agglomerate model parameters on transport characterization and performance of PEM fuel cells, International Journal of Hydrogen Energy (2018), https://doi.org/10.1016/j.ijhydene.2018.03.106