INTERNATIONAL JOURNAL OF HYDROGEN ENERGY ] ( ]]]]) ]]] ]]] Available at journal homepage:

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1 HE : 46 Available at journal homepage: Effect of GDL permeability on water and thermal management in PEMFCs I. Isotropic and anisotropic permeability Dewan Hasan Ahmed, Hyung Jin Sung, Joongmyeon Bae Department of Mechanical Engineering, Korea Advanced Institute of Science and Technology, -, Guseong-dong Yuseong-gu, Daejeon -, Republic of Korea article info Article history: Received January 2 Received in revised form 8 July 2 Accepted April 28 Keywords: PEMFC High current density In-plane permeability Through-plane permeability Cathode overpotential Ohmic loss. Introduction abstract The performance of proton exchange membrane fuel cells (PEMFCs) with various isotropic and anisotropic permeabilities of the gas diffusion layer (GDL) was investigated using computational fluid dynamics analysis. A three-dimensional, non-isothermal model was employed with a single straight channel; both humidification and phase transportation were included in the model. The total water and thermal management for systems operating at high current densities was obtained. The results showed that the cell performance deteriorated for low isotropic permeability of the GDL. Water removal from the cathode GDL was significantly reduced in systems with low isotropic permeability or anisotropic systems with low permeabilities in both the in-plane and through-plane directions. Moreover, both the in-plane and through-plane permeabilities were found to affect water and thermal management in PEMFCs, especially in the low permeability ranges. Variations in GDL permeability had a greater influence on ohmic losses than on cathode overpotentials because the former losses depend on water and thermal management. In addition, the results showed that water and thermal management was good in systems in which the permeability in at least one direction (in-plane or through-plane) was high, whereas systems with low permeability in both the in-plane and through-plane directions exhibited poor water and thermal management. However, heat removal in PEMFCs was negatively affected by low permeability, leading to higher temperatures in the cell. The present numerical results suggested that modeling with isotropic permeability conditions may overpredict the cell performance, and inaccurately predict the water and thermal management in PEMFCs. & 28 Published by Elsevier Ltd. on behalf of International Association for Hydrogen Energy. In proton exchange membrane fuel cells (PEMFCs), water and thermal management is a critical determinant factor of cell performance. However, efforts to improve water and thermal management are complicated by the fact that many variables either directly or indirectly affect thermal and water transport phenomena within PEMFCs. The permeability of the gas diffusion layer (GDL) is one of the major parameters influencing reactants and water transportation in PEMFCs. In general, the transport of reactants from channels to the reacting areas, water transportation from anode to cathode Corresponding author. Tel.: ; fax: address: hjsung@kaist.ac.kr (H.J. Sung). 6-/$ - see front matter & 28 Published by Elsevier Ltd. on behalf of International Association for Hydrogen Energy. doi:.6/j.ijhydene Isotropic and anisotropic permeability. Int J Hydrogen Energy (28), doi:.6/j.ijhydene

2 HE : Nomenclature A cv specific surface area of the control volume, m Area cv surface area of the control volume, m 2 C wa C wc D H2;l D O2;l D W F H H H2;l H O2;l h rxn h fg I I avg I o,k L l M m,dry M n m w,l mass n n n d P sat w;k P P n R r S t f concentration of water vapor at the anode, mol m concentration of water vapor at the cathode, mol m diffusion coefficient of H 2 in a liquid water film, 6. m 2 s diffusion coefficient of O 2 in a liquid water film, 2.4 m 2 s diffusion coefficient of water, m 2 s Faraday constant, 6 48 C mol half of the cell height, m Henry s law constant for H 2 in a liquid water film, 8. Pa Henry s law constant for O 2 in a liquid water film, 2.2 Pa enthalpy of water formation, kj kmol enthalpy of vaporization of water, kj kg local current density, A m 2 average current density, A m 2 exchange current density for reaction K, A m 2 length, m distance between two applied forces (in Fig. ), m equivalent weight of a dry membrane, kg mol molecular weight of species n, kgmol mass fraction of liquid water mass of species n, kg No. of electrons electro-osmosis drag coefficient saturation vapor pressure of water in stream k, Pa pressure, Pa partial pressure of species n, Pa universal gas constant, 8.4 J (mol K) condensation rate, s source term liquid water film thickness, m by electro-osmosis, and water removal from the cathode GDL to the cathode gas channel depend strongly on the GDL permeability. Thermal management in PEMFCs also depends on the effective removal of the water produced by the chemical reactions at the cathode. Computational fluid dynamic analysis can be helpful to predict and understand the effects of GDL permeability on water and thermal management in real PEMFCs. In PEMFCs, the GDL is located between a membrane and bipolar plates. The major task of this very important component is to transfer the reactants from the channel to the reacting area (catalyst layer), to remove the produced water (gas and liquid) to the channel, and to transport the heat produced by the chemical reactions. GDLs are manufactured via a process consisting of various chemical and mechanical processes as well as thermal treatments []. The sequence of these processes and treatments affects the t m T V V OC V cell W X i,k Greek symbols membrane thickness, m temperature, K velocity, ms open circuit voltage, V cell voltage, V width, m mole fraction of species i in stream k a net water flux per proton b permeability, m 2 e porosity of the gas diffusion layer Z overpotential, V l water content in the membrane m dynamic viscosity, kg s m r m,dry density of the dry membrane, kg m r density of the mixture, kg m s m membrane conductivity, S m x stoichiometric rate Subscripts and superscripts a avg c ch cv e glif H 2 K l O 2 reac sat v z anode average cathode channel control volume electrochemical reaction gas liquid interface hydrogen anode or cathode liquid oxygen reacting saturated vapor dummy variable for direction x, y or z physical properties of the final GDL; in particular the permeability of the GDL, especially in the in-plane (length and width direction) and through-plane (height direction) directions is often sensitive to the processing conditions. GDLs are fabricated either by pressing chopped carbon fibers into a sheet or by weaving bundles of fibers into a cloth [2]. In addition, many GDLs contain a thin micro-porous layer, which usually makes them denser. This thin micro-layer reduces the through-plane permeability by several orders of magnitude but leaves the in-plane permeability almost unaltered [2,]. In addition, many GDLs contain a thin micro-porous layer, which usually makes them denser. This thin micro-layer reduces the through-plane permeability by several orders of magnitude compared with bare gas diffusion media [2,]. However, recently, Gurau et al. [4] showed through experiments that the GDLs having micro-porous layers with the higher polytetrafluoroethylene (PTFE) content Isotropic and anisotropic permeability. Int J Hydrogen Energy (28), doi:.6/j.ijhydene

3 HE : 46 INTERNATIONAL JOURNAL OF HYDROGEN ENERGY] ( ]]]]) ]]] ]]] L W H Z 4 Z 2 Z Z Z Z have higher permeability coefficients. Thus, all GDLs, regardless of their particular make-up, have very different structures in the in-plane and through-plane directions, with the in-plane permeability typically being higher than the through-plane permeability []. Attempts have been made to measure the in-plane permeability [,6] and through-plane permeability of GDLs with different Teflon loadings [], with and without a micro-porous layer [,,] and with varying thicknesses []. Moreover, Gostic et al. [] showed experimentally that compression of a GDL to half of its initial thickness causes its permeability to decrease by an order of magnitude. Collectively, these findings highlight the importance of considering both in-plane and through-plane permeability effects on water and thermal management and also water transportation in PEMFCs. Over the past decade, numerous computational analyses of different aspects of PEMFCs have been conducted with the aim of enhancing cell performance and to better understand water and thermal management [ 4]. Lum and McGuirk [] and Shimpalee et al. [6] carried out numerical analyses of PEMFCs with GDLs with different isotropic permeabilities and showed that the cell performance deteriorates at low isotropic permeability because the reactants struggle to reach the reacting area and transportation processes are slow. Lin and Nguyen [] investigated the effects of varying the inplane water permeability of the GDL while keeping the through-plane permeability constant, and found that the mass transfer limitation in PEMFCs improves with increasing in-plane permeability. They reported that as the liquid water needs to cover both in-plane and through-plane permeability in the shoulder region, higher in-plane permeability leads to a significant reduction of liquid water saturation in that region. Pharoah [2] showed in a recent study that as the in-plane permeability of a GDL is increased, the pressure drop across the GDL decreases and the in-plane permeability becomes more dominant over the through-plane permeability. However, to our knowledge, no detailed study has yet been made of water and thermal management in PEMFCs under either isotropic or anisotropic permeability conditions. In the present study, we therefore performed numerical simulations to investigate the water and thermal management in PEMFCs under different isotropic conditions as well as various anisotropic permeability conditions achieved by varying the in-plane and through-plane permeabilities of the GDL. In particular, we examined the distribution of reactants, the local current density, and the details of water and thermal management for PEMFCs under high current density operation. Moreover, we showed that the various overpotentials and water removal process depended on the permeability conditions. In our sequel paper (Part 2) [8], we examined the effects on PEMFCs of applying clamping forces to the GDL in particular the effects on water and thermal management. A three-dimensional model with a single straight channel geometry was employed in the computational analysis. The simulation results were validated by comparison with previous experimental results. 2. Numerical simulation A schematic diagram of the conventional PEMFC with a channel-to-shoulder width ratio of is shown in Fig.. The system consists of two channels (for hydrogen and air) between which the membrane electrode assembly (MEA) is sandwiched. There are bipolar plates (also known as shoulders) on both the anode and cathode sides, which function as current collectors with high electronic conductivity. Humidified hydrogen and air are introduced into the respective channels, where the quantities of the two gases are determined by the stoichiometric rate and average current density. The following assumptions are made in the model: ideal gas mixture, steady state, laminar flow, isotropic and homogeneous porous GDL, homogeneous two phase flow, and negligible potential drop in the bipolar plates. The governing equations for the numerical simulation are conservation of mass, momentum transport, species transport, and energy equations. () Conservation of mass equation: rðr~uþ ¼S ma þ S mc. () Shoulder or Bipolar Plate Anode Gas Channel MEA (Z 6 ) Gas Diffusion Electrode (GDE) Cathode Gas Channel Fig. Single straight channel flow field for a PEMFC. (a) geometry, (b) cross sectional view Isotropic and anisotropic permeability. Int J Hydrogen Energy (28), doi:.6/j.ijhydene

4 HE : 46 4 The source terms are rðrm n ~uþ ¼rðJ n ÞþS s, () S ma ¼ S H2 þ S wvp þ S wlp þ S awve at z ¼ z, (.) S mc ¼ S O2 þ S wvp þ S wlp þ S cwve at z ¼ z 2, (.2) where S H2 and ¼ M H2 A cvi 2F at z ¼ z S O2 ¼ M A O2 cvi at z ¼ z 2. (.) 4F The mass contributions of the water vapor at the anode and cathode sides are S awve ¼ M H2OA cv ai at z ¼ z, (.4) F S cwve ¼ S cwvp þ S cwvt ¼ M H2OA cv I þ am H2OA cv I 2F F ¼ ð þ 2aÞM H2OA cv I at z ¼ z 2. (.) 2F The change of phases between water vapor and liquid water depends on the partial pressure, and is defined as [] P M H2O n of v S wlp ¼ S wvp ¼ Psat wv P mass n of v M n of v P sat wv P wv r P at z pzpz, (.6) where r is the condensation rate (set to s in the model). Eq. (.6) shows that phase changes of water can be detected by monitoring the partial pressure of water vapor compared with the saturated pressure. Specifically, if the partial pressure of water vapor exceeds the saturated pressure, the water vapor will condense, whereas if the partial pressure of water vapor is lower than the saturated pressure, the liquid water will evaporate. In Eqs. (.4) (.), a is the net water transfer coefficient per proton through the membrane, which is defined as a ¼ n d FD W½C wc C wa Š. (.) It m Here D W is the water diffusion coefficient. The electroosmotic drag coefficient (n d ) can be correlated with the membrane water content (l) [2]: n d ¼ :2l 2 þ :l :4. (.8) (2) Momentum transport equation: rðr~u~uþ ¼ rpþrðmr~uþþs p;i. (2) Here S p,i is the sink source term for porous media in the x, y and z directions. The pressure drop in porous media can be accounted for using Darcy s law [2]. The source term is defined as S p;i ¼ mu i at z pzpz 2 and z pzpz 4. (2.) b i Here, b is the permeability. () General species transport equation: where n denotes H 2, O 2, water vapor, or liquid water. The source terms are the same as those for the conservation of mass equation. The transportation of the species is solved with bulk mixture velocities and with diffusion mass fluxes. The diffusion mass flux of each species is evaluated with binary diffusion coefficients [22] and is reduced by % in the diffusion layer to account for the effect of the porosity and tortuosity of the pores []. It is assumed that the liquid water is in the form of small droplets freely suspended in the gas flow. This means that the two phases flow together (homogeneous two phase flow) under normal, steady-state operating conditions but not under supersaturated conditions. The diffusion mass flux (J) of species n in direction z is qm K;n J x;n ¼ rd x;n qx, (.) where x is a dummy variable for direction x, y or z. (4) Energy equation: rðr~uhþ ¼rðkrTÞþS h. (4) The source term S h contains contributions from energy losses and heat associated with phase transformations. The heat source from the electrochemical reaction is given by the difference between the total energy released by the electrochemical reaction at the cathode membrane surface and the electrical energy extracted out of the fuel cell [2]: IA cv S he ¼ h rxn ðiv 2F cell A cv Þ z¼z2 at z ¼ z 6. (4.) z¼z2 The heat source due to a phase change can be expressed as S hp ¼ S wlp h fg at z pzpz, (4.2) where h fg is the enthalpy of formation of water. The local current density of the cell is calculated from the open circuit voltage (V OC ) and the losses according to: I ¼ s m fv OC V t cell Zg, () m which can be rewritten as V cell ¼ V OC Z t m I. (6) s m The last term on the right-hand side of Eq. (6) corresponds to the ohmic loss, where t m is the membrane thickness and s m is the membrane conductivity, both of which are calculated as functions of the water content on the membrane surface at the anode interface. The membrane conductivity can be expressed as [] s m ¼ :4 M m;dry r m;dry C wa :26! exp 268 T T, () where T ¼ K. The water vapor concentration is defined as C w;a ¼ r m;dry l, (8) M m;dry where r m,dry and M m,dry are the material density and the equivalent weight of a dry proton electrode membrane, respectively. The water content in the membrane (l) is Isotropic and anisotropic permeability. Int J Hydrogen Energy (28), doi:.6/j.ijhydene

5 HE : 46 INTERNATIONAL JOURNAL OF HYDROGEN ENERGY] ( ]]]]) ]]] ]]] defined as Table Physical and electrochemical parameters l ¼ð:4 þ :8a K :8a 2 K þ 6:a K Þ if a Kp, l ¼ð4 þ :4ða K ÞÞ if a K 4, () where the subscript K stands for the anode or cathode. a a is the water activity and is defined as a a ¼ X w;ap P sat, () w;a where P is the cell pressure, X w,a is the mole fraction of water on the anode side, and P sat w;a is the saturation pressure of anode water. The local overpotential (Z) for a PEMFC is used for both the anode overpotential and cathode overpotential and can be written as [24] Z ¼ RT a c F ln " # IP I O2 P O2 þ RT a a F ln " # IP, () I H2 P H2 where P is the pressure, a a and a c are the transfer coefficients for the anode and cathode respectively, and I is the exchange current density. The partial pressures of oxygen and hydrogen are calculated as P O2 ¼ X O2 P and P H2 ¼ X H2 P; where X O2 and X H2 are the oxygen and hydrogen mole fractions, respectively. By including the partial pressures, the overpotential terms also include the activation and concentration overpotentials. In the present model, the source terms of different conservation equations correspond to the control volume, not to the boundary conditions at the anode or cathode interface. To determine the concentrations and activities at the membrane GDL interface correctly, the mole fraction of each species is extrapolated to the membrane surface. This extrapolation procedure is not, however, performed when a liquid water film is generated on the membrane surface. If liquid water is present at the MEA, the model accounts for the mass transfer resistance of the gas diffusing through the film of water. To achieve this, Henry s law is used to calculate the solubility of the reactants in the liquid water film [2]. The diffusion length of the dissolved gas is determined by the thickness of the film of water on the MEA corrected for the porosity of the GDL. Moreover, the average pore flooding is accounted for by considering an average film thickness on membrane surface. The resulting equations are as follows: " I 4F M ¼ r D X O2;glifP glif H O2;l X # O2 O2 O2 O2;l at z ¼ z 2, I 2F M ¼ r D H2 H2 H2;l t f;c " X H2;glifP glif H H2;l X # H2 t f;a at z ¼ z, (2) where P glif is the pressure at the gas liquid water interface, H is the Henry constant of the reactants in the liquid water film, and t f,k is the liquid water film thickness for the anode and cathode, which is defined as t f;k ¼ m w;lð P mass n Þ. () r wl Area cv Here, e is the porosity of the GDL, m w,l is the liquid water mass fraction at the membrane GDL interface, and mass n is the mass of species n. The velocity at the inlet of anode and cathode can be calculated by the operating current density and species Parameter Value (base case) Value (case studies) Anode pressure (atm) Cathode pressure (atm) Stoichiometric rate at anode.2.2 Stoichiometric rate at cathode Cell temperature (C) Anode inlet temperature (C) 8 8 Cathode inlet temperature (C) Open circuit voltage (V).6. Relative humidity at anode (%) Relative humidity at cathode (%) Oxygen inlet mole fraction Oxygen exchange current 2 density (A/m 2 ) Hydrogen exchange current 2 density (A/m 2 ) Anode transfer coefficient.2. Cathode transfer coefficient.6. Porosity.. Permeability (isotropic) (m 2 ) 2 Varied Anode top surface temperature (z-direction) (C) Cathode top surface temperature (z-direction) (C) concentrations which are determined from the inlet pressure and humidity conditions. V a ¼ x airt a A reac, (4) 2FPX H2 A ch V c ¼ x cirt c A reac. () 2FPX O2 A ch The exits of the anode and cathode sides assume ambient pressure to be the boundary conditions. Other detailed boundary conditions used in the model can be found in Table. The above governing equations are solved under appropriate boundary conditions by employing the user coding capabilities of STAR-CD that employ a finite volume method. The solution procedure used in this commercial flow solver is based on a SIMPLE algorithm. At each iteration, three momentum equations corresponding to three coordinates are solved; follow by a pressure correction equation that does the mass balance. After the bulk flow calculations, enthalpy and species transport equations are solved. The mixture properties at each control volume are calculated based on the local species content, where, the anode side gas mixture contains hydrogen, water vapor and liquid water. On the other hand, cathode side gas mixture contains oxygen, water vapor, liquid water and nitrogen. Therefore, the density and viscosity of the two flow channels are different and vary from one location to the other Isotropic and anisotropic permeability. Int J Hydrogen Energy (28), doi:.6/j.ijhydene

6 HE : Results and discussion A series of simulations were carried out on the base case with operating current densities ranging from low to high; the Table 2 Geometrical parameters Parameter Value (mm) Channel length 4. Channel width.8 Channel height Membrane length. Membrane thickness. Anode gas diffusion layer.2 Cathode gas diffusion layer.2 Cell voltage, V Voltage losses, V Present model Experiment (Cheng et al. [2]) Anode overpotential Cathode overpotential Ohmic loss Current density, A/cm 2 Fig. 2 (a) Polarization curve [2], (b) different types of voltage loss. physical and geometrical parameters for the base case are shown in Tables and 2, respectively. The polarization curve for the base case, shown in Fig. 2a, contains three distinct regions of losses. The variations in the anode and cathode overpotentials as a function of operating current density, shown in Fig. 2b, also follow the typical trend found in the literature [2,26]. It should be noted that the ohmic loss in Fig. 2b shows a nonlinear trend rather than the linear trend reported in literature because the present model was implemented with variable membrane conductivity. In order to study the effects of both in-plane and throughplane permeability on the cell performance, we conducted simulations using a wide range of permeabilities ( m 2 to m 2 ). Table shows different physical and electrochemical parameters for different case studies. Table shows the different combinations of in-plane and through-plane permeability conditions studied. In this table, x and y denote the in-plane and through-plane permeability respectively. Case xy (x ¼ y) represents isotropic permeability in the GDL, and all other combinations of x and y correspond to anisotropic permeability cases. Cases y, 4y, x and x4 represent anisotropic permeability cases (see Table ) and are analyzed in detail in the following sections. For example, Case y refers to the series of systems in which the in-plane permeability is maintained at a constant value of m 2 and the through-plane permeability is varied from m 2 to m 2. Similarly, Case x4 refers to the series of systems in which the through-plane permeability is maintained at a constant value of m 2 and the in-plane permeability is varied from m 2 to m 2. Note here that the porosity for all cases in Table is set to.. In the present study, we focused on systems with the same isotropic or anisotropic permeability throughout the GDL (i.e., at both the channel and shoulder regions) and its effect on high current density operation and cell performance. In our sequel paper, Part 2 [8], we focus on GDLs with different isotropic or anisotropic permeabilities in the channel and shoulder regions due to the clamping force of the two bipolar plates. Fig. shows the effects of permeability on cell voltage Table The combinations of in-plane and through-plane permeability in the cases studied Isotropic and anisotropic permeability. Int J Hydrogen Energy (28), doi:.6/j.ijhydene

7 HE : 46 INTERNATIONAL JOURNAL OF HYDROGEN ENERGY] ( ]]]]) ]]] ]]] at the high operating current density of 2.4 A/cm 2 for Cases xy, y, 4y, x and x4 intable. This figure shows some interesting aspects of cell performance. Among the five cases, the cell performance is markedly lower for Cases 4y and x4, which correspond to constant low in-plane and low through-plane permeability, respectively. For isotropic Case xy, on the other hand, decreasing the permeability does not have a remarkable effect on cell performance until the permeability reaches around m 2. At an isotropic permeability of m 2 ( in Table ), the cell performance is much lower than at higher isotropic permeabilities. In the following sections, we investigate the effects of isotropic and Cell Voltage, V Current density, A/cm 2 H 2 O v,c mass fraction Case y Case 4y Case x Case x4 Case xy (x = y) Permeability, m Case 22 Case - Fig. Output cell voltage for different permeability cases at an operating current density of 2.4 A/cm 2. Oxygen mass fraction H 2 O l,c mass fraction anisotropic permeability in regard to water and thermal management... Isotropic permeability Fig. 4a shows the local current density distribution across the width at the exit of the cathode channel at the cathode GDL membrane interface for isotropic permeability cases. It is interesting to note that the local current density distribution moves higher as the permeability decreases, even though the cell performance deteriorated with decreasing permeability. At this high operating current density (I avg ¼ 2.4 A/ cm 2 ), the local current density is highest at the channelshoulder region for all cases, consistent with previous results for conventional PEMFCs obtained by our group [,2] and others [28]. Fig. 4b shows the variation in oxygen mass fraction across the width at the exit of the cathode channel at the cathode GDL membrane interface. The oxygen mass fraction decreases slightly with increasing permeability. The trend in oxygen mass fraction as a function of permeability can be explained by examining Fig. 4c and d, which show the variations in water vapor and liquid water mass fraction across the width at the exit of the cathode channel at the cathode GDL membrane interface. As the permeability decreases, the flow is increasingly restricted and hence smaller amounts of reactants take part of the chemical reaction, causing less water to be produced compared with systems with higher permeability. As a result, the oxygen mass fraction in the GDL increases with decreasing permeability W/W W/W Fig. 4 Variable distribution at the channel exit for different isotropic permeability cases at the cathode GDL membrane interface for an operating current density of 2.4 A/cm 2. (a) current density, (b) oxygen mass fraction, (c) cathode water vapor mass fraction and (d) cathode liquid water mass fraction. Isotropic and anisotropic permeability. Int J Hydrogen Energy (28), doi:.6/j.ijhydene

8 HE : Current density, A/cm Case 22 Case Oxygen mass fraction H 2 O v,c mass fraction.4.. H 2 O l,c mass fraction.. E W/W W/W Fig. Variable distribution at the channel inlet for different isotropic permeability cases at the cathode GDL membrane interface for an operating current density of 2.4 A/cm 2. (a) current density, (b) oxygen mass fraction, (c) cathode water vapor mass fraction and (d) cathode liquid water mass fraction. Current density, A/cm 2 H 2 O v,c mass fraction Case 22 Case W/W W/W H 2 O l,c mass fraction Fig. 6 Variable distribution at the middle of the channel for different isotropic permeability cases at the cathode GDL membrane interface for an operating current density of 2.4 A/cm 2. (a) current density, (b) oxygen mass fraction, (c) cathode water vapor mass fraction and (d) cathode liquid water mass fraction. Oxygen mass fraction as the amount of nitrogen in the cathode is fixed and nitrogen does not take part in any chemical reaction. Figs. and 6 show the same variables distribution along the width for inlet and middle of the channel, respectively. The reactant gradually decreases along the channel length and the production of water gradually increases. However, among the individual isotropic permeability cases, the lowest isotropic permeability case () shows extreme situation 4 Isotropic and anisotropic permeability. Int J Hydrogen Energy (28), doi:.6/j.ijhydene

9 HE : 46 INTERNATIONAL JOURNAL OF HYDROGEN ENERGY] ( ]]]]) ]]] ]]] of the variables distribution. For, the local current density is significantly reduced till the middle of the channel region. For oxygen distribution, at the inlet region there is bit different scenario compared with exit region, where decreasing the permeability causes to decrease the oxygen mass fraction. However, too low permeability exhibits to have higher oxygen mass fraction at cathode GDL membrane interface. As long as one goes towards the downstream, for all permeability cases, the oxygen mass fraction decreases from inlet to the exit region. However, comparing among the different permeability cases, the oxygen mass fractions for the low permeability cases have a tendency to have higher distribution at the cathode GDL interface than that for high permeability case, at least at the downstream regions. This shows that the produced water and the flow restriction in the GDL due to the lower permeability cause to increase the oxygen mass fraction at the downstream of the channel where the water is much more accumulated in the shoulder region. Fig. a shows the total pressure distribution along the height of cathode channel at W/W ¼. at the exit of the channel, and Fig. b shows the pressure distribution at the cathode GDL membrane interface along the channel length. It is clear from these plots that the total pressure is significantly higher for the low permeability cases. In systems with low permeability, the produced water cannot move easily from the cathode GDL to the cathode channel and hence the total pressure gradually increases along the channel. This pressure distribution is also consistent with the finding of Shimpalee et al. [6] that a lower (isotropic) permeability causes higher pressure in a GDL and restricts the transportation of species in and out of the GDL. On the other Pressure, Pa Pressure, Pa Case 22 Case H/H L/L Fig. Total pressure distribution for different isotropic permeability cases (a) along the height of the cathode channel at W/W ¼., (b) along the cathode channel at H/ H ¼.84. W velocity, m/s Temperature, K H/H Case 22 Case W/W Fig. 8 W velocity distribution along the height of the cathode channel at the channel exit at W/W ¼., (b) temperature distribution along width at the cathode GDL membrane interface for different isotropic permeability cases. hand, high permeability and porosity help to provide easy access for the produced water vapor and liquid water from the GDL to the channel and serve to lower the pressure in the exit region (Fig. b). The variation in the W velocity component at the cathode side at W/W ¼. with height (Fig. 8a) provides further evidence that the water removal process is slower at low permeability. As a result, the temperature in the fuel cell gradually increases with decreasing permeability (see Fig. 8b), suggesting that the heat removal process becomes worse as the isotropic permeability decreases..2. Anisotropic permeability We studied systems with a wide range of anisotropic permeabilities in the in-plane and through-plane directions, as shown in Table. The variation in output cell voltage among the systems with different in-plane and throughplane permeabilities operating at high current density (I avg ¼ 2.4 A/cm 2 ), shown in Fig., indicates that varying the anisotropic permeability has a significant impact on cell performance. Below we analyze in detail the effects of anisotropic permeability on water and thermal management. Fig. shows the local current density distribution at the exit of the cathode channel at the cathode GDL membrane interface for Cases y, 4y, x and x4 (see Table ). Case y (comprising Cases, 2, and 4) represents GDLs with a constant high in-plane permeability and varying throughplane permeability. The local current density distribution for Case y (Fig. a) does not show any significant variation, in contrast to the greater degree of variation shown by Cases 4y (Fig. b) and x4 (Fig. d). For Case y, however, the local current density slightly improves in the shoulder region as Isotropic and anisotropic permeability. Int J Hydrogen Energy (28), doi:.6/j.ijhydene

10 HE : 46 6 Current density, A/cm Case 2 Case Case 4 Case 4 Case Current density, A/cm Case 2 Case Case W/W W/W the through-plane permeability decreases due to slower water removal, as described above. Case x (Fig. c), characterized by constant high through-plane permeability and varying in-plane permeability, shows a similar pattern of local current density distribution to Case y, in that all of the GDLs in the x series exhibit similar distributions but the local current density improves slightly in the shoulder region as the in-plane permeability decreases due to slower water removal to the cathode channel. However, greater variability is observed in the local current density distributions for Cases 4y and x4, which represent the systems with constant low inplane permeability with varying through-plane permeability and constant low through-plane permeability with varying in-plane permeability, respectively. The local current density variations for these cases show a significant influence of the permeability, especially when the permeability is low. Furthermore, for all cases (Cases y, 4y, x and x4), the local current density of low permeability cases is higher or much more uniform than that of high permeability cases. Comparison of the curves in Fig. a d reveals that the local current density distributions are similar for systems in which the inplane or through-plane permeability is high regardless of the permeability in the other direction. On the contrary, when the in-plane or through-plane permeability is low while varying the through-plane or in-plane permeability, significant variations in the local current density distribution are observed (Figs. b and d). The local oxygen mass fraction distributions at the exit of the cathode channel at the cathode GDL membrane interface for the various cases, shown in Fig., are similar for all systems; this finding is consistent with the Case 4 Case 4 Fig. Local current distribution at the cathode GDL membrane interface at the channel exit for different anisotropic permeability cases. (a) Case y, (b) Case 4y, (c) Case x and (d) Case x4. results for the isotropic cases shown in Fig., and can be attributed to the high porosity of the GDLs. However, the local current density also depends on other variables such as the anode water activity, membrane conductivity, and the ohmic loss and anode and cathode overpotentials. The anode water activity distributions for Cases y, 4y, x and x4 at the exit of the anode channel at the anode GDL membrane interface are shown in Fig.. The trends in the anode water activity are similar to those observed for the local current density (Fig. ); that is, when the in-plane or through-plane permeability is fixed at a high value and the permeability in the other direction is varied (Cases y and x), no significant variations in anode water activity and cell performance (as shown in Fig. ) are observed. However, the anode water activity of Case 4y is much less than that of Case x4, especially in the shoulder region, indicating that fixing the in-plane permeability at a low value has a greater influence on anode water activity than fixing the through-plane permeability at a low value. The anode water activity generally depends on the water mole fraction at the anode side, total pressure and water saturation pressure, which in turn depends on the temperature, as shown in Eq. (). A possible explanation for the behavior of Case 4y can be arrived at by examining the distributions of water vapor, liquid water mass fraction, pressure and temperature at the anode GDL membrane interface (Fig. 2). It is noteworthy that in the present study the humidified hydrogen introduced at the anode inlet is C hotter than the cell temperature. Due to this temperature difference, the water vapor condenses to liquid water. However, as the through-plane permeability Isotropic and anisotropic permeability. Int J Hydrogen Energy (28), doi:.6/j.ijhydene

11 HE : 46 INTERNATIONAL JOURNAL OF HYDROGEN ENERGY] ( ]]]]) ]]] ]]] Oxygen mass fraction Case 2 Case Case 4 Case 4 Case Oxygen mass fraction..2. Case 2 Case Case W/W W/W Case 4 Case 4 Fig. Oxygen mass fraction distribution at the cathode GDL membrane interface at the channel exit for different anisotropic permeability cases. (a) Case y, (b) Case 4y, (c) Case x and (d) Case x4. Anode water activity Anode water activity Case 2 Case Case 4 Case 2 Case Case 4 Case 4 Case 4 Case 4 Case W/W W/W Fig. Anode water activity at the cathode GDL membrane interface at the channel exit for different anisotropic permeability cases. (a) Case y, (b) Case 4y, (c) Case x and (d) Case x4. Isotropic and anisotropic permeability. Int J Hydrogen Energy (28), doi:.6/j.ijhydene

12 HE : H 2 O v,a mass fraction H 2 O l,a mass fraction Pressure, Pa decreases for Case 4y (i.e., Cases 4 44), the water in the GDL eventually becomes trapped. The resulting build-up of water also significantly influences the thermal management, and as a result the cell temperature gradually increases with decreasing through-plane permeability (see Fig. 2d). As a consequence of this, the water vapor and liquid water mass fraction gradually increase and decrease, respectively, as shown in Figs. 2a and b. However, the significant influence of permeability on anode water activity (e.g., Case 4y) derives from the pressure distribution. Note that a pressure gradient is created in the GDL (see Fig. 2c) as hydrogen and water vapor are consumed at the membrane surface. This pressure gradient is steeper for low permeability cases due to the greater flow restriction in such systems, similar to the trend reported by Shimpalee et al. [6]. The variation in net water flux per proton (alpha) across the width at the exit of the cathode channel at the cathode GDL membrane interface is shown in Fig.. It is evident from these distributions that the permeability has a significant influence on water transportation. For Case 4 in the 4y series, electro-osmosis dominates in the shoulder region and back diffusion takes place in the channel region. However, the dominance of this electroosmosis shifts towards the channel shoulder interface region as the through-plane permeability decreases and eventually diminishes once the through-plane permeability is low enough. The membrane conductivity distributions at the exit of the channel for Cases y, 4y, x and x4 are shown in Fig. 4. These distributions exhibit a similar trend to the anode water activity distributions, which is expected as the membrane conductivity strongly depends on the anode water activity []. Temperature, K 6 6 Case 4 Case W/W W/W Fig. 2 Different variables distribution for Case 4y at the exit of the channel at anode GDL membrane interface (a) anode water vapor mass fraction, (b) anode liquid water mass fraction, (c) pressure and (d) temperature. The variation in ohmic loss across the width at the exit of the cathode channel at the cathode GDL membrane interface, which depends on the local current density and membrane conductivity, is shown in Fig. for Cases y, 4y, x and x4. The results indicate how the ohmic loss could influence the overall cell performance with variations in the in-plane and through plane permeabilities. Consistent with the previous results for GDLs with isotropic permeability, our GDLs with low in-plane and through-plane permeabilities show significantly poorer cell performance. By contrast, the distributions of cathode overpotential (Fig. 6) at the exit of the channel are similar for all cases, indicating that the permeability has little effect on cathode overpotential. In a similar manner, the ohmic loss at the inlet and middle of the channel and the cathode overpotential at the inlet and middle of the channel are shown in Figs. 2, respectively, and show that the cell performance is significantly influenced by the ohmic loss especially at the low permeability cases. However, for the cathode overpotential, slight variation is found in the shoulder region especially from the inlet to the middle part of the channel and no significant variation is observed at the channel region even for the low permeability cases. The lack of sensitivity of the cathode overpotential distribution to the GDL permeability can be explained by the fact that in the present model, the cathode overpotential consists of both activation and concentration losses, and hence the flow restriction of the reactants with low permeability in GDLs allows to increase the loss is offset by the higher pressure and temperature in such systems. However, the major influence of GDL permeability on PEMFC perfor Isotropic and anisotropic permeability. Int J Hydrogen Energy (28), doi:.6/j.ijhydene

13 HE : 46 INTERNATIONAL JOURNAL OF HYDROGEN ENERGY] ( ]]]]) ]]] ]]] Alpha Alpha Membrane conductivity, S/m Membrane conductivity, S/m Case 2 Case Case 4 Case 2 Case Case 4 Case 2 Case Case 4 Case 4 Case 4 Case 4 Case W/W W/W Fig. Net water flux per proton at the cathode GDL membrane interface at the channel exit for different anisotropic permeability cases. (a) Case y, (b) Case 4y, (c) Case x and (d) Case x4. Case 4 Case 4 2 Case 4 Case 2 8 Case Case 4 Case W/W W/W Fig. 4 Membrane conductivity at the cathode GDL membrane interface at the channel exit for different anisotropic permeability cases. (a) Case y, (b) Case 4y, (c) Case x and (d) Case x4. Isotropic and anisotropic permeability. Int J Hydrogen Energy (28), doi:.6/j.ijhydene

14 HE : Ohmicloss, V Case 2 Case Case 4 Case 4 Case Ohmicloss, V Case 2 Case Case 4 Case 4 Case W/W W/W Fig. Ohmic loss at the cathode GDL membrane interface at the channel exit for different anisotropic permeability cases. (a) Case y, (b) Case 4y, (c) Case x and (d) Case x4. Cathodeoverpotential, V Cathodeoverpotential, V Case 2 Case Case 4 Case 4 Case 4.6 Case 2 Case Case 4 Case 4 Case W/W W/W 4 Fig. 6 Cathode overpotential at the cathode GDL membrane interface at the channel exit for different anisotropic permeability cases. (a) Case y, (b) Case 4y, (c) Case x and (d) Case x4. Isotropic and anisotropic permeability. Int J Hydrogen Energy (28), doi:.6/j.ijhydene

15 HE : 46 INTERNATIONAL JOURNAL OF HYDROGEN ENERGY] ( ]]]]) ]]] ]]]. 6 Ohmicloss, V Case 2 Case Case 4 Case 4 Case Ohmicloss, V.4.4 Case 2 Case Case 4. Case 4. Case W/W W/W Fig. Ohmic loss at the cathode GDL membrane interface at the channel inlet for different anisotropic permeability cases. (a) Case y, (b) Case 4y, (c) Case x and (d) Case x4. Ohmicloss, V Ohmicloss, V Case 2 Case Case 4.2 Case 2 Case Case 4 Case 4 Case 4 Case 4 Case W/W W/W Fig. 8 Ohmic loss at the cathode GDL membrane interface at middle of the channel for different anisotropic permeability cases. (a) Case y, (b) Case 4y, (c) Case x and (d) Case x4. Isotropic and anisotropic permeability. Int J Hydrogen Energy (28), doi:.6/j.ijhydene

16 HE : Cathodeoverpotential, V.. Case 2 Case Case 4 Case 4 Case Cathodeoverpotential, V.. Case 2 Case Case W/W W/W Case 4 Case 4 Fig. Cathode overpotential at the cathode GDL membrane interface at the channel inlet for different anisotropic permeability cases. (a) Case y, (b) Case 4y, (c) Case x and (d) Case x4. Cathodeoverpotential,V Cathodeoverpotential,V Case 2 Case Case 4 Case 2 Case Case 4 Case 4 Case 4 Case 4 Case W/W W/W 4 Fig. 2 Cathode overpotential at the cathode GDL membrane interface at middle of the channel for different anisotropic permeability cases. (a) Case y, (b) Case 4y, (c) Case x and (d) Case x4. Isotropic and anisotropic permeability. Int J Hydrogen Energy (28), doi:.6/j.ijhydene

17 HE : 46 INTERNATIONAL JOURNAL OF HYDROGEN ENERGY] ( ]]]]) ]]] ]]] Oxygen mass fraction Case 2 Case Case 4 Case 4 Case Oxygen mass fraction Case 2 Case Case 4 Case 4 Case H/H H/H Fig. 2 Oxygen mass fraction distribution along the height of the cathode channel at W/W ¼. for different anisotropic permeability cases. (a) Case y, (b) Case 4y, (c) Case x and (d) Case x4. W velocity, m/s W velocity, m/s Case 2 Case Case 4 Case 4 Case Case 2 Case Case 4 Case 4 Case H/H H/H Fig. 22 W velocity along the height of the cathode channel at W/W ¼. for different anisotropic permeability cases. (a) Case y, (b) Case 4y, (c) Case x and (d) Case x4. Isotropic and anisotropic permeability. Int J Hydrogen Energy (28), doi:.6/j.ijhydene

18 HE : mance comes from ohmic losses, which greatly influence water and thermal management. Above we have considered systems with various combinations of in-plane and through plane permeability. In practice, however, the in-plane permeability of GDLs is higher than the through-plane permeability. Hence, of the systems considered, Cases y and x4 are of greater relevance to the practical situation. Our results show that if the in-plane or throughplane permeability is fixed at a high value, varying the permeability in the other direction has little effect on the cell performance. However, if the in-plane or through-plane permeability is fixed at a low value, varying the permeability in the other direction has a considerable impact on the cell performance. Among the cases considered, the anisotropic GDL permeability configurations in Case x4 with higher inplane permeabilities are most relevant to the practical situation. Fig. 2 shows the oxygen mass fraction distribution at the exit of cathode channel at W/W ¼. as a function of cathode channel height for Cases y, 4y, x and x4. The results clearly show that the oxygen mass fraction gradually increases at the channel area (H/H ¼ to H/H ¼.22) for Cases 4y and x4. This indicates that the water removal process from the GDL to the cathode channel is slow in these systems, which will have a serious negative impact on cell performance, particularly for low permeability cases. Fig. 22 shows the W velocity distribution at the exit of the cathode channel as a function of the cathode channel height. The lower velocities observed for low permeability cases reflects the slower water removal from the cathode GDL to the cathode gas channel in such systems. 4. Conclusions In the present study, we carried out detailed numerical analyses of PEMFCs with a single straight channel geometry with varying the permeabilities of the GDL in the in-plane and through-plane directions over wide ranges. The major aim of the present study was to better understand water and thermal management in PEMFCs with different isotropic and anisotropic GDL permeability conditions, and to examine the link between GDL permeability and cell performance. The numerical results showed that the cell performance was greatly influenced by both isotropic and anisotropic permeability, especially when the permeability in one or both directions was low. Variations in GDL permeability were found to have a greater influence on ohmic losses than on cathode overpotential because the former losses strongly depended on water and thermal management. In addition, the results showed that water and thermal management was good in systems in which the permeability in at least one direction (in-plane or through-plane) was high, whereas systems with low permeability in both the in-plane and through-plane directions exhibited poor water and thermal management. In particular, water removal from the GDL to the cathode channel was greatly reduced in systems with low in-plane and through-plane permeabilities. Moreover, low permeabilities in both directions had a tremendous negative impact on thermal management as the low permeabilities slowed the heat removal process, leading to higher cell temperatures, especially at high operating current density. The results of our numerical study of GDLs with different anisotropic permeabilities suggested that modeling with isotropic permeability conditions may overpredict the cell performance, and inaccurately predict the water and thermal management in PEMFCs.. Uncited reference Q [8]. 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Interaction between the diffusion layer and the flow field of polymer electrolyte fuel cells experiments and simulation studies. J Power Sources 2;24: 84. [] Prasanna M, Ha HY, Cho EA, Hong SA, Oh IH. Influence of cathode gas diffusion media on the performance of the PEMFCs. J Power Sources 24;:4 4. [8] Williams MV, Kunz HR, Fenton JM. Influence of convection through gas-diffusion layers on limiting current in PEM FCs using a serpentine flow field. J Electrochem Soc 24;():A6 2. [] Lin G, Nguyen TV. Effect of thickness and hydrophobic polymer content of the gas diffusion layer on electrode flooding level in a PEMFC. J Electrochem Soc 2;2():A42 8. [] Dutta S, Shimpalee S, Van Zee JW. Numerical prediction of mass-exchange between cathode and anode channels in a PEM fuel cell. Int J Heat Mass Transfer 2;44: [] Gurau V, Liu H, Kakac S. Two-dimensional model for proton exchange membrane fuel cells. AIChE J 8;44(): [2] Um S, Wang CY, Chen KS. Computational fluid dynamics modeling of proton exchange membrane fuel cells. J Electrochem Soc 2;4(2):448. [] Ahmed DH, Sung HJ. Effects of channel geometrical configuration and shoulder width on PEMFC performance at high current density. J Power Sources 26;62:2. [4] Jung HM, Lee WY, Park JS, Kim CS. Numerical analysis of a polymer electrolyte fuel cell. Int J Hydrogen Energy 24;2:4 4. [] Lum KW, McGuirk JJ. Three-dimensional model of a complete polymer electrolyte membrane fuel cell model formulation, validation and parametric studies. J Power Sources 2;4: 24. [6] Shimpalee S, Dutta S, Lee WK, Van Zee JW. Effect of humidity on PEM fuel cell performance Part II numerical simulation Isotropic and anisotropic permeability. Int J Hydrogen Energy (28), doi:.6/j.ijhydene