ABSTRACT INTRODUCTION

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1 Geometrical analysis of Gas Diffusion Layer in a Direct Methanol Fuel Cell Low H.W., and Birgersson E. Engineering Science Programme National University of Singapore 10 Kent Ridge Road, Singapore ABSTRACT Modeling of gas diffusion layer in direct methanol fuel cell has been done extensively to improve the performance of fuel cell. Gas diffusion layer can be modeled as a combination of square pores in a space where fluid can permeate through it. In this paper, the significance of geometry in influencing permeability of the gas diffusion layer is studied. A fundamental model of gas diffusion layer is constructed to study the permeability. Systematic deformation is performed on the model and the permeability measured. It is shown that the geometry configuration, depending on the arrangement, has an impact on the permeability of gas diffusion layer. INTRODUCTION Alternative clean energy generations have emerged as solutions to conventional energy generation. Clean energy can be generated by wind, solar, ocean, thermal, and etc. One of the promising clean energy technologies is fuel cell technology. In fuel cell, oxidation and reaction at anode and cathode respectively will generate an overvoltage across the anode and cathode. The overvoltage will produce current when connected to external load. Depending on the type of fuel cells, the overvoltage and the current produced will be different, and they will be used for different purposes. Direct Methanol Fuel Cells (DFMC) has advantages over other fuel cells in certain areas. As compared to Protein Membrane Exchange Fuel Cell (PEMFC), DMFC uses methanol directly as fuel without conversion into Hydrogen. It is easily refillable and available at relatively low cost. There is also a significant decrease in hydrogen storage cost. One of the main challenges facing DMFC is the slow anode and cathode reaction time as compared to PEMFC, causing low overvoltage and current density as compared to PEMFC [1]. Therefore, DMFC can only be used for low power supply devices where high energy density is required, such as calculator. The overall chemical reaction of DMFC is 6 6 Gas diffusion layer (GDL) in the fuel cell is a complex fibrous 3D structure with variable wettability. In transport phenomenon, gas diffuses through GDL from flow channel to catalyst. Properties of GDL affects the amount of water in the catalyst layer and membrane. [2] GDL will remove fluid to prevent localized flooding. It also keeps some fluid on surface to maintain conductivity. Flooding in fuel cell will cause blockage of electrochemical activity while insufficient water will hinder electron transfer. GDL can influence current flow and subsequently the overvoltage of the cell. Therefore, optimization and characterization of GDL is crucial in improving the performance and efficiency of fuel cell. Due to the complexity of GDL, a scaled down version of 2D pore network modelling is modelled to study the geometrical effects on permeability [3]. Figure 1 shows the GDL under SEM.

2 In this paper, the pore network geometrical contribution on modelling and the accuracy of 2D modelling of GDL based on the proposed geometrical structure are studied. The permeability of the models is compared with the experimental value for verification and justification of 2D pore network model. (a) (b) Figure 1: SEM Micrograph of GDL materials in present study, with magnification, (a) 100x, (b) 1000x [4] Nomenclature ( Velocity vector (Pa) Fluid pressure ( External force Q Volumetric flux P (Pa) Linear pressure L (m) Diffusion Length K Intrinsic permeability Gravitational constant Fluid dynamic viscosity (Pa) Pressure at point x=l (Pa) Pressure at point x=0 Porosity,,(m) Relative coordinate of the pore, (m) Default coordinate of the fibre Reynolds number Density of fluid (m) representative grain diameter for the porous medium Fluid viscosity Fluid density Table 1: List of nomenclature used SIMULATION AND GOVERNING EQUATIONS The flow of methanol inside the model is governed by incompressible Navier-Stokes equation and equation of continuity at steady states. 0

3 Darcy s law is derived as an expression of conversation of momentum, and also through derivation from Navier-Stokes equation via homogenization. It is also analogous to Fourier s law in the field of heat conduction, or Fick s law in diffusion. It is given by Where P P P P L The equation relating velocity and permeability is given by: P P The boundary conditions are set as 0 and. Darcy s law assumes that pressure difference ( P) over a distance, L, must exist for the fluid to flow, and fluid will flow from high pressure towards low pressure. It also assumes discharge rate (Q) to increase proportionally with pressure difference. For this law to be valid, the Reynolds number should be less than one to have laminar flow. For methanol, it is known that 792, , and for GDL Toray 090, 10, as long as , there should be laminar flow within the layer and satisfied Darcy s Law. CONSTRUCTION OF PORE NETWORK The pore network model is constructed based on Toray 090 due to its common commercial usage. The physical properties are listed in table 1 [4]. Property Toray 090 Thickness () 290 Total porosity Fiber diameter () 9 in x direction ( 1510 in y direction ( 1510 in z direction ( The model can be constructed as a combination of square pores on a plane with pore size following Weibull cumulative distribution [5]. Topological study of Toray 090 shows that pore networks are aligned in z direction.

4 Figure 2: General geometrical properties of pore network [6] The pore network model is constructed to determine the permeability of the model by varying the displacement deviation factor (DDF). The porosity is for all models constructed. To investigate the DDF, a model is constructed with linearly aligned idealized pore network. The pore network is slowly displaced from the original position and the displacements measured. The following equation is used to compute DDF: For simplification, the model is constructed with constant porosity of It is assumed that the pore size does not change with applied pressure and velocity of fluid. At 20 0 C, methanol has the following properties: 0.52mPa 792 The following model is constructed as the default model, where further modifications are done relative to this model. y z x 20 Figure 3: basic model for simulation

5 RESULTS AND DISCUSSION For convenience of calculation, DDF is measured in number of units displaced, with each displacement unit fixed at 1 micron. The following relationship is obtained. The respective permeability is compared with the research papers [7,8]. 3 models have been constructed to determine the displacement-permeability relationship. Table 2 shows the models constructed with descriptions. Model A Model B Model C Comparison model This model is constructed with 15 random displacements along the x and y axis. For each simulation, every 15 random displacements are performed on top of the previous 15 displacements. The cumulative effects of the pore displacement on permeability are displaced in figure 4. The next model is constructed on sequential pore displacement, up to a certain number of pores. A pore is displaced at any point in time. The effect of pore displacement is measured for different pores. After that, the effect of cumulative pore displacement on permeability is calculated. This model is constructed with large number of relative movements of pore network. Certain number (9/12/16) of pores is displaced towards the same direction and magnitude at the same time. This is a comparison of two extreme conditions. A default model (DDF=0) and a modified model with extreme pore displacement (DDF=max) are constructed. Table 2: Models constructed and descriptions (m 2 ) 6.600E-12 Model A 6.400E E E E E DDF/10-8 (m 2 ) Figure 4: simulation results for model A 20 From this result, it is obvious that the cummulative impact will affect the permeability of the model. The significant drop in permeability after the first 15 displacements has affected the subsequent models. The subsequent 15 displacements deviate from the first 15 displacmenets by 2.5%, which is less significant as compared to the first deviatin from default model. (m 2 ) 6.520E E E E E E-12 Model B DDF/10 8 (m 2 ) Figure 5: Simulation of model B 20

6 The small geometrical deviation may affect local velocity field. However, it does not seem to have significant impact on overall velocity field. Therefore, it may not affect the overall permeability significantly. (m 2 ) 6.600E E E E E-12 Model C DDF/10 8 (m 2 ) Figure 6: Simulation of model C 20 The overall simultaneous relative movements of certain number of pores might produce averaging effect which does not influence the permeability significantly. It is obvious that one model configuration will affect the permeability of the next model configuration. From these results, it is observed that increasing number of displacement units will generally reduce the permeability, depending on the geometrical structure of the model. The deviation of permeability is affected by the extent of pore deviation. The following table summarizes the deviation of permeability from the higher bound value for each of the models. Model Relative deviation A 12.3% B 0.6% C 5.3% The comparison model is constructed to compare the two extreme cases of simulation. Model number Default model 6.50x10-12 High obstructions model 5.362x10-12 Relative deviation: 17.5% a b Figure 7: Comparison of (a) default model, and (b) high obstructions model

7 With this significant relative deviation, we can see that the geometrical distribution of pore network will affect the permeability of the gas diffusion layer. The reduction of permeability shows that the complex geometrical structure in figure 7b reduces the overall velocity, therefore reducing the permeability of the medium. CONCLUSION The permeability of the gas diffusion layer, when modeled with COMSOL, is found to be affected by the geometry of the pore network. The assumption with average pore size of 10 micron, laminar flow, and square pore size has produced measureable results in defining the influence of pore network distribution in material permeability. The maximum possible deviation of permeability from the default model, assuming even pore network distribution, is found to be 17.5%. Depending on the geometrical distribution of pore network, the permeability is found to be decreasing with increasing pore network displacement. This shows the significance of pore network geometry distribution in modeling as it affects the fluid velocity in the medium. ACKNOWLEDGEMENTS I would like to thank Prof Erik Birgersson who have been guiding me along the way to completing this project. REFERENCES [1] J. Larminie & A. Dicks, Fuel Cell Systems Explained 2 nd Edition. UK: Wiley [2] K. Tetsuya, F. Toru, M. Koji, An approach to modeling two-phrase transport in the gas diffusion layer of a proton exchange membrane fuel cell. J. Power Sources, 175 (2008) [3] J. Larminie & A. Dicks, Fuel Cell Systems Explained 2 nd Edition. UK: Wiley [4] J. T. Gostick, M. A. Ioannidis, M. W. Fowler, & M. D. Pritzker. Pore Network modeling of bifrous gas diffusion layers for polymer electrolyte membrane fuel cells. J. Power Sources, 173 (2007) [5] J. T. Gostick, M. A. Ioannidis, M. W. Fowler, & M. D. Pritzker. Pore Network modeling of bifrous gas diffusion layers for polymer electrolyte membrane fuel cells. J. Power Sources, 173 (2007) [6] J. T. Gostick, M. A. Ioannidis, M. W. Fowler, & M. D. Pritzker. Pore Network modeling of bifrous gas diffusion layers for polymer electrolyte membrane fuel cells. J. Power Sources, 173 (2007) [7] T. Zhang. Analysis of the Gas Diffusion Layer in a PEM Fuel Cell. [8] K. Tetsuya, F. Toru, M. Koji, An approach to modeling two-phrase transport in the gas diffusion layer of a proton exchange membrane fuel cell. J. Power Sources, 175 (2008)