Application of CFD Techniques in the Modelling and Simulation of PBI PEMFC ~

Transcription

1 DOI: /fuce Application of CFD Techniques in the Modelling and Simulation of PBI PEMFC ~ G. Doubek 1 *, E. Robalinho 1,E.F.Cunha 1,E.Cekinski 2, and M. Linardi 1 1 IPEN Av. Prof. Lineu Prestes, 2242, , São Paulo, Brazil 2 IPT Av. Prof. Almeida Prado, 532, , São Paulo, Brazil Received November 29, 2010; accepted February 3, 2011 Abstract In the present work two 3-D models, for the catalytic layer, were employed in order to simulate the responses of a PBI high temperature polymeric membrane fuel cell. The simulations made use of an agglomerate model and a pseudohomogenous model, both implemented taking into account the temperature influence over their parameters. The overall simulation was performed also as two models, linked by the variable pressure, one for the whole graphite plate simulating the distribution channels, and the other dealing with the MEA and thereof the catalytic layer. A discussion over the two models was done and the experimental results demonstrated that the pseudo-homogeneous obtained the better fits. Keywords: CFD, High temperature fuel cell, Modelling, PBI 1 Introduction ~ Paper presented at the Second CARISMA International Conference Progress in MEA Materials for Medium and High Temperature Polymer Electrolyte Fuel Cells, La Grande Motte, France, September The need for highly efficient and low emission energy conversion devices has attracted attention towards fuel cells world over. Out of several families of fuel cells, proton exchange membrane fuel cells (PEM) are an important class of fuel cells for which the technology is mature enough for practical usage. PEM fuel cells composed by polybenzimidazole (PBI) doped with phosphoric acid forms a new line of research enabling a higher operational temperature and dismissing complex humidification systems. The operating temperature has an important influence over the PEM fuel cell performance, since its increase improves the reaction rates and mass transfer rates. In addition, at high temperature, CO poisoning can be decreased by reducing chemisorptions of CO [1]. In order to further develop this class of fuel cell a computational model would reduce prototype costs and accelerate future production. The application of computational fluid dynamic (CFD) [2] is a very useful tool to simulate hydrogen and oxygen fuel cells. The two main fundamental models designed to simulate polymer-electrolyte fuel cells were those of Bernardi and Verbrugge [3] and Springer et al. [4]. Both of them treat the fuel cell MEA (membrane, diffusion media and catalyst layers) as being isothermal and 1-D. Since 1990s, an increasing number of models have been generated, typically more complex and focused on multidimensional, transient and microscopic effects. Ridge et al. [5] implemented the agglomerated model by the first time, to examine the microstructure of the cathode catalytic layer in more detail. Other CFD models have been published, as Siegel et al. [6] studying the effects of the agglomerate radius and catalyst loading on fuel cell s performance [7], showing a good comparison with the experimental data. Nowadays many authors are concerned with high temperature PEM (HT-PEM) modelling, as presented in the work of Cheddie et al [8 10], Lobato et al. [11], Shamardina et al. [12], Jiao and Li [13] and Jiao et al. [14]. However, there are still many challenges to overcome in order to obtain a more reliable and accurate model to analyse and predict the HT- PEM fuel cell response. At this work a more refined discussion is done over the traditional model used to simulate the polymeric fuel cell s response, with the objective of increase its applicability to the PBI PEMFC operating at higher temperatures and with dry feed gases. The numerical results were corroborated by the experimental data. [ * ] Corresponding author, doubeksi@gmail.com, efcunha@ipen.br, gdoubek@ipen.br FUEL CELLS 00, 0000, No. 0, WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim 1

2 Since models that employ a CFD approach seems to be the best suitable for considering multidimensional effects, this work presents two 3-D implementations using different catalytic layer models, and their respective description. 2 Modelling and Simulation 2.1 Assumptions and Calculus Domains In order to study the simulation of transport phenomena of HT-PEMFC, a few hypotheses were made to simplify the implementation of the model. Due to the high temperatures, the water was considering to be always on the vapour phase. No hydrogen or oxygen crossover through the membrane was considered. Further the catalytic layers were modelled by two approaches: agglomerate model and pseudo-homogeneous model, whose responses were compared with the experimental result. The assumptions for the model were Ideal gas; Steady state, laminar and incompressible flux; Isothermal T = 443 K (170 C); Reactions were defined at the boundary of the calculus domain in the first simulation, and at the catalytic layer volume in the current simulation; The water in the system is in the gas phase; Polarisation voltage on the cathode side is constant along the channel; Gas flow in the channel is a plug flow with the constant velocity; Zero external forces; Isotropic and homogeneous materials; Thermodynamic and electrochemical properties are constants; Crossover through the membrane is negligible; Mono-phase (gas phase). In order to create the model, it is firstly defined five geometric domains for the problem: the H 2 gas distribution channel X channel H2, the anode GDL X GDLa, the proton exchange membrane X m, the cathode GDL X GDLc and the O 2 gas distribution channel X channel O2, as can be seen in Figure 1. Between the anode GDL and the membrane, and between the cathode GDL and the membrane it is also defined two layers being the anode catalytic layer X a and the cathode catalytic layer X c where the boundary conditions were applied. At the distribution channels, there are two inlets and two outlets subdomains, which are X in-h2, X out-h2, X in-o2 and X out-h2. The model was implemented in a commercial CFD, COM- SOL 4.0a, which is a sequential code using finite elements Fig. 1 Calculus domain for the 3D-parcial model. Adapted from ref [1]. method (FEM) and multifrontal massively parallel sparse direct solver (MUMPS). This solver uses parametric (V_cell in [0.2, 0.8] with step 0.05) and segregated features and has a convergence criterion in which the relative tolerance is 10 4.A mesh with about 38,400 hexahedral elements (297,272 degrees of freedom DOFs) was found to provide sufficient spatial resolution. The hardware was an Intel Quad Core Xeon Workstation with 16 GB RAM. In Table 1 the parameters that were used in this model are showed. 2.2 Mathematical Statements The numerical model is divided into two-parcial models linked by the variable pressure. The first one simulates the gas channel distribution and the orthogonal pressure to the GDL. The second partial model deals with the processes of the membrane-electrode-assembly (MEA) and uses the traditional mathematical formulations of Maxwell-Stefan, Darcy, Laplace, the electrochemical expressions of Butler-Volmer and a modified version of the agglomerate model of Springer and Raistrick [15]. The fluxes of gases are described by the Navier-Stokes equations: q u t g u ušt q u u p ˆ 0 (1) u ˆ 0 (2) in which g is the dynamic viscosity (kg m 1 s 1 ), u the velocity vector (m s 1 ), q the density (kg m 3 )ep is the pressure (Pa) WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim FUEL CELLS 00, 0000, No. 0, 1 11

3 Table 1 Parameters used in the model. Parameters and variables Values Channel length 0.02 m Channel width m Channel height m Rib m Operation conditions Inlet anode Mass fraction 0.9 Velocity 0.53 m s 1 Inlet cathode Mass fraction: 0.9 Velocity: 1.18 m s 1 Outlet anode and cathode Reference pressure Physical properties of gases Hydrogen Molar mass kg mol 1 Viscosity Pa s Reference concentration mol m 3 Oxygen Molar mass: kg mol 1 Viscosity Pa s Reference concentration mol m 3 Cell temperature 443 K Cell potential 0.2 to 0.8 V GDL Porosity 0.4 Permeability m 2 Thickness m Conductivity 1,000 S m 1 Electrode thickness m Electrolyte (membrane) Conductivity 1.4 S m 1 Thickness m Reference pressure Pa Permeability of porous electrode Anode and cathode m 2 The equations applied in the model incorporate the Brinkman s equations, combining the flow of the porous media with the free flow on the gas distribution channels, being thereof an extension of the Darcy s law, with a viscous transport term on the momentum balance: q u t gdu g u p ˆ 0 (3) kp u ˆ 0 (4) in which kp is the permeability at the porous media (m 2 ). It also used the Henry s law, which specifies the concentration of a reagent gas dissolved in the interface: c i ˆ pix i (5) K i in which K is the Henry constant (Pa m 3 mol 1 ). The computational algorithm solves the systems of equations and makes the coupling of these variables through the internal boundary conditions. The Brinkman s boundary conditions are the same applied for the Navier-Stokes solution: un ˆ u 0 p ˆ p 0 Inlet=Outlet Outlet=Pressure g u uš t Šn ˆ 0 Neutral (6) u ˆ 0 No slip ut ˆ 0; p ˆ p 0 un ˆ 0 Normalflux=Pressure Slip=Symmetry It is important to point out that three of the four walls on the distribution channels are considered dead ends, but the fourth one is a porous media or a GDL. For this porous media, the pressure drop is determined by the Darcy s law [16]: Dp ˆ g Q kp A L (7) in which g is fluid viscosity (kg m 1 s 1 ); Q volumetric flow rate (m 3 s 1 ); kp permeability (m 2 ); A cross section area of the flow field. (m 2 ); L is flow field length (m). Equation (7) can be used to determine the approximate pressure drop of any flow field, if it is considered to be laminar. The permeability constant kp is applied to the overall flow field and it is numerically estimated. At the interfaces electrodes/membrane, the hydrogen mass flow (consumed at the anodic catalytic layer) and oxygen mass flow (consumed at the cathodic catalytic layer) are related with the local current densities by Eq. (8): n= H2 ˆ i a 2F in X a n= O2 ˆ ic 4F in X c Those flows at the interfaces electrodes/membrane represent boundary conditions for the Darcy process (conservation of momentum). There is the need of defining the pressure inlet and outlet values: p ˆ p a;in in X in-h2 (9) p ˆ p ref in X out-h2 (10) p ˆ p c;in in X in-o2 (11) p ˆ p ref in X out-o2 (12) 8 FUEL CELLS 00, 0000, No. 0, WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim 3

4 The mass flow Eq. (8) is related with the rate of the electrochemical reactions, and they are linked by the material balance equations (Maxwell-Stefan): 2 X n4 N qx i 2 ˆ i a X n4 N qx i ˆ i c D ij jˆ1 D ij jˆ1 ( M M ) 3 p x j x j x M j x j D T T 5 i p T M j 13 ( M M ) 3 p x j x j x M j x j D T T 5 i p T M j 14 For the potential distribution calculation at the three desired regions: anodic collector, membrane, cathodic collector [5] utilised the routine Conductive Media DC: k e f e Š ˆ 0 in X a (15) k m f m Š ˆ 0 in X m (16) k e f e Š ˆ 0 in X c (17) in which k e is the electrical conductivity (S m 1 ) of the collectors (solid material), k m the ionic conductivity (S m 1 ) and f e e f m are the electrodes and membrane potentials, respectively. The boundary conditions for the current density at the interface anode/membrane, and at the interface cathode/ membrane, are given by, respectively: k e f e n ˆ i a in X a (18) k e f e n ˆ i c in X c (19) The current densities between the membrane and the electrodes are given by: k m f m n ˆ i a in X a (20) k m f m n ˆ i c in X c (21) Equations (18 21) represent the charge balance for the porous electrode. 2.3 Modelling the Catalytic Layer The catalytic layer has a crucial rule on the performance of a fuel cell, being where all the reactions and transport phenomena s meet their part for the power generation. It has a complex physical nano-structure with three simultaneous phases. There are several developed models that attempt to recreate the response of this complex structure with different degrees of complexity and applicability. These models include the pseudo-homogeneous model [17 20], the single pore model [21], the thin film model [22] and the agglomerate model [19, 22]. Among those models, the agglomerate model and the pseudo-homogeneous model are described as follow. The agglomerate model equation system involves diffusion and the electrode s kinetics parameters (Butler Volmer). At the COMSOL implementation, the agglomerate model was applied for the anode and cathode catalytic layers, as it has been successfully applied on previous works, by means of the following analytical expressions [23 25]:: " i a ˆ 6F D #" s s! # agg i 0;a S a i 0;a S a 1 R ag coth R agg R 2 agg c ag H2 cref H2 exp F RT g P 2Fc ref H2 D agg " i c ˆ 12F D # agg R 2 agg 2 v u i 0;c S a R 2 agg 41 t 4Fc ref O2 D exp agg c agg O2 2F RT g P 2Fc ref H2 D agg 22 v 3 u i 0;c S a R 2 agg coth 4Fc ref O2 D exp 2F t agg RT g 5 P 23 in which R agg is the agglomerate radius (m), S a the specific surface area of the catalytic layer (or active area experimentally determined from cyclic voltametry analyses) (m 1 ), F is the Faraday constant (C mol 1 ), c ref i and c agg i are the references concentrations of the used gases and their surface concentrations at the agglomerate interface (mol m 3 ), i 0 the exchange current density (A m 2 ), R the universal gas constant, T the temperature (K), g P is the overpotential of the anode or cathode(v), given by g P ˆ f e f m E 0;e (24) where f e is the electrode potential (anode or cathode) (V), f m the membrane potential (V) and E o,e the equilibrium potential of the anode or the cathode, being that E o,a is zero and E o,c is obtained through a temperature relationship for temperatures over 100 C given by Eq. (25) [24]. E o;c ˆ 1:17 2: T 373:15 4: ln p p H 2 p O2 p H2 O WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim FUEL CELLS 00, 0000, No. 0, 1 11

5 The anode and cathode exchange current densities (i 0,a and i 0,c ) depend on temperature according to an Arrheniuslike law expressed in Eq. (26) [26]. i ex ˆ i ref ex exp E A;ex 1 R T 1 T ref 26 In order to determine the gas diffusivity in the agglomerate, the model uses microscopic (e_mic) and macroscopic (e_mac) porosities, as D agg ˆ 1: e mac e micš 1:5 (27) in which e_mac = 0.4 and e_mic = 0.2. The equating of the pseudo-homogenous model is summarised by the Eqs. (28) and (29), in which a complete modified Butler Volmer relationship is used for the anodic side, and a Tafel-like modelling is used for the cathodic side.! 0;5 c H2 i a ˆ S a i 0;a c ref exp a afg p exp a cfg p RT RT H 2 i c ˆ S a i 0;c c O2 c ref O 2! exp a a a c Fg p RT ˆ S a i 0;c 28! c O2 c ref e g p=a c O 2 29 The A c is the cathode Tafel slope, its value was set up as 95 mv dec 1 according to the literature [27 30]. The parameters g P, i 0,a and i 0,c were obtained through Eqs. (24) and (26), respectively. The value of S a is the same used in the agglomerate model. 3 Experimental 3.1 MEA Assembling The way of preparing the membrane-electrode-assemblies (MEAs) is described below. On the top of a square gas diffusion media of 5 cm 2 (Carbon cloth impregnated with 15% of PTFE and carbon XC-72R, Cabot) a catalyst ink, composed of Pt/C powder (20% Pt on Vulcan XC-72, BASF) dissolved in a PBI solution (2 wt.-% in N,N-dimethylacetamide, DMAc) was hand painted to made the gas diffusion electrodes, letting it to dry in an oven after each layer applied to avoid the penetration of the catalyst into the bulk of the gas diffusion media. Then the electrodes were dried at 190 C for 2 h to remove the remaining DMAc. The final loading for both electrodes was 0.5 mgpt cm 2, and 0.1 mgpbi cm 2. The MEA was assembled by sandwiching a PBI membrane of 30 lm thickness, pre-doped in a solution of phosphoric acid 85% until a doping level of six molecules of H 3 PO 4 for each PBI repeated unit was reached, between the two gas diffusion electrodes described. The relation between the PBI and the catalyst powder, to prepare the catalyst ink, was made based on preview optimisation works [31,32], taking into account the loading of platinum and the amount of carbon in the catalyst powder. 3.2 Fuel Cell Test The cell hardware consists of two graphite plates into which channels were machined (0.8 mm width, 0.8 mm depth) in a multi channel serpentine geometry, copper goldcoated plates as current collectors and aluminium plates, with holes for the heating tubes, and to hold the cell together. During the measurements the cell was fed with pure hydrogen and oxygen, both dry, at a rate of 80 and 180 ml min 1, respectively, at atmospheric pressure. The temperature was fixed at 170 C. The polarisation curve was recorded by selecting a current with a dynamic load (Agilent 6060B) and the reading of correspondent potential response. 3.3 Conductivity Measurements The conductivity of the doped PBI membrane was carried out in a sample of 8 mm diameter, sandwiched between gas diffusion layer which was pressed on the membrane faces by means of porous stainless steel discs. The membrane conductivity was determined as a function of temperature (from 100 to 180 C) by impedance spectroscopy in the frequency range 10 Hz 1 MHz at signal amplitude of 100 mv. This data was crucial and was added to the model as the intrinsic conductivity for the electrolyte. It was also performed, with the same fuel cell assembly described in Section 2.2, a series of in situ impedance spectroscopy measurements as a function of time, with a frequency range from 1 Hz to 10 KHz and amplitude signal of 10 mv in a fixed potential of 550 mv. The test was mainly performed due to possible rearrangements that this type of doped membrane might show during its operation. This fact could lead to a non reliable experimental data in order to validate the simulation. 4 Results and Discussion 4.1 In situ Impedance Spectroscopy Results In Figure 2 it can be seen a great change over the overall system s resistance at the start-up or first running hour, but no significant change after 5 h, indicating no further internal rearrangements in an appreciable level. It is also valid to mention that the behaviour shown in Figure 2 is a system characteristic at each start-up, but do not show the first startup behaviour. 4.2 Simulations for the Graphite Plate As mentioned before the simulation was made by the implementation of two models, the first one to simulate the velocity field and the orthogonal pressure on the catalytic FUEL CELLS 00, 0000, No. 0, WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim 5

6 Fig. 2 Nyquist plots for the in situ impedance spectroscopy as a function of time. layer for the complete graphite plate, and the second one dealing with the MEA for a single channel. As a response of the first model the values for the permeability and the anodic and cathodic pressures have been numerically determined and are shown in Figures 3 and 4. The result analyses suggest that the orthogonal pressure values, that should be used as the initial conditions for the MEA modelling, are the solutions found for permeabilities between and Some results of post-processing are shown below. Figure 3 represents the numerical response for oxygen, and Figure 4 shows the responses for hydrogen. This choice was made due to the fact that no significant change on pressure field was verified for permeability values above during the simulations at the end of the porous layer, as at the interface porous layer-distribution channels. The obtained orthogonal pressures for the oxygen were approximately four times greater when compared with the z-velocity / m s-1 Pressure / Pa Fig. 3 Velocity s flow field and orthogonal pressures for the whole plate simulations for oxygen with permeability values of z-velocity / m s-1 Pressure / Pa Fig. 4 Velocity s flow field and orthogonal pressures for the whole plate simulations for hydrogen with permeability values of WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim FUEL CELLS 00, 0000, No. 0, 1 11

7 hydrogen results, what was expected, since the experimental established flow for the oxygen was much higher that the hydrogen one. Both gases are being simulated as pure without humidification. The analysis made with this set of simulated responses creates a secure basis for the next step, in other words, the simulation of the MEA, in which is observed the chemical reactions and therefore a refined material balance for the settlement of the current densities of the fuel cell. 4.3 Discussion of the Catalyst Layer Modelling The agglomerate model, as the state of the art of catalytic layer 2-D model, was firstly used in this work. This model was deduced to describe the current density in a catalytic environment or layer, which consists of agglomerates made of ionic conducting material and electrically conducting particles partially covered by a catalyst [15]. The simulation of the MEA model was held after it had the parameters that are explicit affected by the temperature been adjusted, as densities, reagent gases viscosities and the anodic and cathodic exchanges current densities. Nevertheless, it could not predict the PBI-PEM fuel cell behaviour, as shows the first simulation response in Figure 5. Although, the agglomerate model provides a satisfactory response on simulating low temperature fuel cells [19, 23], the increase of the temperature and the different chemical affinities that the PBI/H 3 PO 4 system has over oxygen, could lead to a hard task on re-deducing the model and perhaps unnecessary work, if some other model could be used instead. One simplified approach for this issue was the use of the pseudo-homogeneous model, which relates the concentration dependent Butler Volmer relationship, considering the different assumptions for each electrode. In the same way of the agglomerate model, it is also necessary to take into account the diffusion of the involved species, here represented by means of their concentrations and the electrochemical Potential / mv Current Density / A.cm -2 Fig. 5 Current density versus cell voltage. The experimental conditions were pure oxygen (180 ml min 1 ), and hydrogen (80 ml min 1 ), both dry at 170 C. active area. To simulate the anode the complete Butler Volmer equation is used. As for the cathode, which determine the reaction rate, the option for a Tafel-like relation was made due to the mechanisms of the charge transfer process been summarised by the experimental slope. The electrodes used on the PBI fuel cell have the same amount of catalyst and a similar microscopic structure as the traditional electrodes in low temperature fuel cell, so one could think that the deduced agglomerate model should be also valid, but there are some parameters that have been priority considered for the conditions and temperatures ranges that usually PEM fuel cells are subjected to. According to Springer and Raistrick [15], the agglomerate model is a solution that considers not only the diffusion through the pore structure of the agglomerate region, defined as D agg, but also the diffusion through the thin film that holds the agglomerate together. In the case of a low temperature fuel cell, NAFION is the ionomer that creates this thin film, and for the DC solutions the thin film contribution on the overall resistance is neglected for potentials slightly far from the equilibrium, when compared with the agglomerate s diffusion resistance. In the case of a PBI/H 3 PO 4 system, where the doped membrane is the electrolyte on the agglomerate model, the poor oxygen solubility in the phosphoric acid leads to a much higher diffusion resistance through the thin film, making standard deduced Eqs. (22) and (23) not suitable to address the system s response as can be seen in Figure 5. Together with the equating modification of the catalytic layer, the way of implementing it was also modified from an electrode surface to a porous electrode. This adjustment is at certain point correcting the missing diffusivity on the Tafellike relation when compared with the agglomerate model. The D agg parameter, that was taking into account the macroscopic and microscopic porosities, was replaced by a thicker one, porous electrode, with a similar microscopic porosity. Therefore the impact of the catalytic layer thickness can now be evaluated. It was found that its thickness could considerably affect the activation response of the polarisation curve on the simulations. In Figure 6 this influence is showed, a thicker catalytic layer provides a better distribution for the active surface area on the model resulting in a higher current density for the same potential. But a thicker layer also introduces a thicker pathway for the proton transfer, the result of that is a non-linear increase of the current density due to the increased ohmic resistance. As can be seen in Figure 6, the current density seems to approach saturation on its increasing tendency around 50 lm. The porous electrode implementation brought another issue for the electrolyte conductivity analysis. The measured value obtained just with a membrane sample would indicate the conductivity of the membrane but not necessarily the ionic conductivity of the contained electrolyte on the porous catalytic layer, specially in the case of a PBI/H 3 PO 4 system where the acid concentration can change. To prevent this problem a measurement of the whole MEA was performed and the calculus of the specific electrolyte resistance, assumed FUEL CELLS 00, 0000, No. 0, WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim 7

8 Potential / mv Current Density / A.cm -2 Fig. 6 Influence of the porous electrode thickness on simulating the activation region. to be the overall ohmic resistance, was made considering the membrane and the catalytic layer thickness. The final result of this analysis and the choice of the right experimental electrode thickness provided a good agreement between the experimental data and the simulated response, as seen in the current simulation of Figure Results of the MEA Model The results of the current model provide valuable results in terms of gas flow distribution on the porous electrode, on the gas diffusion layer and gas channels. Figures 7 and 8 show the gas flow distribution at the anode and cathode at 400 mv of cell potential. It can be seen in Figure 7 that the hydrogen concentrations towards the channel under study is very homogenous, with a variation on its concentration ranging from to mol m 3. In Figure 8, for the cathodic side, the concentration distribution was more affected, ranging from to mol m 3, suggesting that the oxygen consumption is heterogeneous towards the distribution channel. The reason for this behaviour can be explained by the oxygen dilution due to the water vapour generated at the cathode. Figure 9 shows the electrolyte current density at the middle of the coordinate Z, which corresponds to the middle of the membrane at the fuel cell. It can be seen that the drawing Fig. 7 Hydrogen molar concentration isosurface at cell potential of 400 mv (cathode at the upper side and anode at the lower side units in mol m 3 ). Fig. 8 Oxygen molar concentration isosurface at cell potential of 400 mv (cathode at the upper side and anode at the lower side units: mol m 3 ) WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim FUEL CELLS 00, 0000, No. 0, 1 11

9 Fig. 9 Contour lines of electrolyte current density, at the middle of Z coordinate (XY slice). pattern of the current density s contour follows exactly the contour of the oxygen isosufaces at the cathode, when they meet the porous electrode. This fact is a consequence of the oxygen reduction reaction being the rate determinant step at the current production, and also indicates that the control over the oxygen molar distribution towards the channel would have a directly repercussions over the homogeneity of the reactions, the existence of hot spots and the electrolyte s ionic current distribution. Therefore Figures 8 and 9 are very useful in order to optimise the ionic current density towards the electrolyte and the homogeneity of the oxygen consumption by studying different flows or geometries that could lead to a better distribution and therefore improving the system s life time. To further study the distribution behaviour of the gases along the channel, a pressure profile for both sides was plotted. Figure 10 shows the result at the same cell potential of 400 mv. The oxygen pressure profile (upper side) was orthogonal to the catalytic layer and, as expected, the numeric response for the pressure was greater for the cathodic side. This pressure behaviour also supports the proposition of the oxygen dilution by the water vapour, rather than an abrupt pressure profile, in order to explain the accentuated molar variation seen in Figure 8 for the cathode. 5 Conclusion A three dimensional model for a high temperature fuel cell was successfully developed and implemented using a commercial CFD code, COMSOL 4.0a. The numerical model was divided into two-partial models linked by the variable pressure. The first one simulated the gas distribution channels and the orthogonal pressure to the GDL. The second partial model dealt with the MEA. The first partial model provided the basis for the MEA simulation, computing the values of the orthogonal pressures and providing a tool to estimate the porosities values, which were used as initial conditions into the second partial model. The value of was adopted as the porosity for the porous media once it was found no significant change on the pressure field for values above that at the end of the porous layer, as at the interface porous layer-distribution channels. On the second-partial model, two different approaches in order to simulate the catalytic layer response were attempted. The agglomerate model that have already been validated on low temperature fuel cell simulations, and a pseudo-homogenous model that makes use of a Tafel-like relationship for the cathode. The validation by the experimental data corroborates the pseudo-homogenous model rather than the agglomerate one in the way it was implemented on this work. The pseudohomogenous model provided a good agreement between the experimental and the simulated results, enabling enough parameters for the construction of a model for the catalytic layer. The simulated responses for the molar gases concentrations and pressures distribution along the channels was also important to analyse thoroughly the possible causes for fuel cell malfunction, or to clearly study the effects of the different phenomena occurring over the electrode s surfaces. This over view is important to optimise the operation condition of the actual fuel cell and to predict the response of new prototypes before it s manufacturing. It is also important to evidence that the simplicity of the pseudo-homogenous model accounts for a decrease on the computational time making easier the numerical implementations. Fig. 10 Pressure isosurface at cell potential of 400 mv (cathode at the upper side and anode at the lower side units: Pa). FUEL CELLS 00, 0000, No. 0, WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim 9

10 The agglomerate model, as implemented on this work, could not satisfactorily simulate the activation region of the polarisation curve. Although it is a more accurate mathematical model on a physical description point of view, it must be further modified taking into account the chemical interactions and microscopic mass transport resistances that the PBI ionomer dictate into the fuel cell behaviour, thus enabling for a more comprehensive computational model. Acknowledgements This work was supported by CNPQ and by Fuel Cell and Hydrogen Centre at IPEN/CNEN-SP. List of Symbols Latin Letters c ref H2 reference concentrations of the hydrogen (mol m 3 ) surface concentrations of the hydrogen at the agglomerate interface (mol m 3 ) O2 reference concentrations of the oxygen (mol m 3 ) surface concentrations of the oxygen at the agglomerate interface (mol m 3 ) diffusivity in the agglomerate thermal diffusion coefficient Fick s diffusivity matrix for ij components equilibrium potential of the anode or the cathode, being that E 0,a is zero and E 0,c is 1.23 V. c agg H2 c ref c agg O2 D agg D T i D ij E 0,e E A,ex potential energy (kj mol 1 ) e_mac macroscopic porosity in the agglomerate e_mic microscopic porosity in the agglomerate F Faraday constant (A s mol 1 ) = H2 hydrogen mass flow (kg s 1 ) = O2 oxygen mass flow (kg s 1 ) i 0,a anodic exchange current density (A m 2 ) i 0,c cathodic exchange current density (A m 2 ) i a anodic current density (A cm 1 ) i c cathodic current density (A cm 1 ) i ex exchange current density (A cm 1 ) k e electrical conductivity of the collectors (solid material) (S m 1 ) k m ionic conductivity (S m 1 ) k p permeability at the porous media (m 2 ) M molar weight (kg mol 1 ) n normal vector p pressure (Pa) p a,in anodic inlet pressure (Pa) p c,in cathodic inlet pressure (Pa) p ref reference pressure (Pa) R universal gas constant (m 3 Pa K 1 mol 1 ) R agg agglomerate radius (m) S a specific surface area of the catalytic layer (or active area) (m 1 ) T temperature (K) t time (s) u velocity vector (m s 1 ) V_cell cell potential Greek Letters X a anodic catalytic layer X c cathodic catalytic layer X in-h2 inlet of humidified H 2 X out-h2 outlet of humidified H 2 X in-o2 inlet of humidified O 2 X out-o2 outlet of humidified O 2 g dynamic viscosity (kg m 1 s 1 ) g P overpotential of the anode or cathode (V) f e electrodes potentials (V) f m membrane potentials (V) f e electrode potential (anode or cathode) f m membrane potential (V) x i, x j mass fraction: i and j components q density (kg m 3 ) References [1] Q. F. Li, R. H. He, J. O. Jensen, N. J. Bjerrum, J. Electrochem. Soc. 2003, 150 A159. [2] F. Seland, T. Berning, B. Børresen, R. Tunold; J. Power Sources 2006, 160, 27. [3] D. M. Bernardi, M. W. Verbrugge, J. Electrochem. Soc. 1992, 139, [4] T. E. Springer, T. A. Zawodzinski, S. J. Gottesfeld, J. Electrochem. Soc. 1991, 138, [5] S. J. Ridge, R. E. White, Y. Tsou, R. N. Beaver, G. A. Eisman, J. Electrochem. Soc. 1989, 136, [6] N. P. Siegel, M. W. Ellis, D. J. Nelson, M. R. von Spakovsky, J. Power Sources 2003, 115, 81. [7] A. Z. Weber, J. Newman, Chem. Rev. 2004, 104, [8] D. F. Cheddie, N. D. H. Munroe, Int. J. Hydrogen Energy 2007, 32, 832. [9] D. F. Cheddie, N. D. H. Munroe, J. Power Sources 2006, 156, 414. [10] D. F. Cheddie, N. D. H. Munroe, Int. J. Power Sources 2006, 160, 215. [11] J. Lobato, P. Canizares, M. A. Rodrigo, J. J. Linares, C. G. Piuleac, S. Curteanu, J. Power Sources 2009, 192, 190. [12] O. Shamardina, A. Chertovich, A. A. Kulikovsky, A. R. Khokhlov, Int. J. Hydrogen Energy 2010, 35, [13] K. Jiao and X. Li, Fuel Cells 2010, 10, 351. [14] K. Jiao, I. E. Alaefour and X. Li, Fuel 2011, 90, 568. [15] T. E. Springer, I. D. Raistrick, J. Eletrochem. Soc. 1989, 136, [16] F. Barbir, PEM Fuel Cells Theory and Practice, Elsevier Academic Press, London, United Kingdom, [17] D. M. Bernardi, M. W. Verbrugge, AICHE J. 1991, 37, WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim FUEL CELLS 00, 0000, No. 0, 1 11

11 [18] T. E. Springer, M. S. Wilson, S. J. Gottesfeld, J. Electrochem. Soc. 1993, 138, [19] K. Broka, P. Ekdunge, J. Appl. Electrochem. 1997, 27, 281. [20] M. Eikerling, A. A. Kornyshev, J. Electroanal. Chem. 1998, 453, 89. [21] S. Srinivasan, H. D. Hurwitz, O. M. Bockris, J. Chem. Phys. 1967, 46, [22] Y. Bultel, P. Ozil, R. Durand, Electrochem. Acta 1998, 432, [23] E. Robalinho, Ph.D. Thesis, Universidade de São Paulo, São Paulo, Brasil, [24] E. Robalinho, E. F. Cunha, A. B. Andrade, M. L. M. Bejarano, M. Linardi, E. Cekinski, Proc. COMSOL Conference [25] E. F. Cunha, E. Robalinho, A. B. Andrade, M. L. M. Bejarano, E. Cekinski, M. Linardi, Proc. 2nd European Fuel Cell Technol. and Appl. Conference 2007, 255. [26] J. Lobato, P. Canizares, M. A. Rodrigo, F. J. Pinar, E. Mena, D. Úbeda, Int. J. Hydrogen Energy 2010, 35, [27] N. H. Jalani, M. Ramanib, K. Ohlsson, S. Buelte, G. Pacifico, R. Pollard, R. Staudt, R. Datta J. Power Sources 2006, 160, [28] M. Mamlouk, K. Scott Int. J. Hydrogen Energy 2010, 35, 784. [29] Z. Liu, J. S. Wainright, M. H. Litt, R. F. Savinell Electrochim. Acta 2006, 51, [30] L. Qingfeng, H. A. Hjuler, N. J. Bjerrum Electrochim. Acta 2000, 45, [31] J. Lobato, P. Canizares, M. A. Rodrigo, J. J. Linares, F. J. Pinar, Int. J. Hydrogen Energy 2003, 35, [32] K. Kwon, T. Y. Kim, D. Y. Yoo, S.-G. Hong, J. O. Park, J. Power Sources 2009, 188, 463. FUEL CELLS 00, 0000, No. 0, WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim 11