Fast Numerical Simulation of Two-Phase Transport Model in the Cathode of a Polymer Electrolyte Fuel Cell

In this paper, we apply streamline-diffusion and Galerkin-least-squares fi- nite element methods for 2D steady-state two-phase model in the cathode of polymer electrolyte fuel cell (PEFC) that contains a gas channel and a gas diffusion layer (GDL). This two-phase PEFC model is typically modeled by a modified Navier-Stokes equa- tion for the mass and momentum, with Darcy's drag as an additional source term in momentum for flows through GDL, and a discontinuous and degenerate convection- diffusion equation for water concentration. Based on the mixed finite element method for the modified Navier-Stokes equation and standard finite element method for wa- ter equation, we design streamline-diffusion and Galerkin-least-squares to overcome the dominant convection arising from the gas channel. Meanwhile, we employ Kirch- hoff transformation to deal with the discontinuous and degenerate diffusivity in water concentration. Numerical experiments demonstrate that our finite element methods, together with these numerical techniques, are able to get accurate physical solutions with fast convergence.

[1]  Vaughan R Voller,et al.  TREATMENT OF DISCONTINUOUS THERMAL CONDUCTIVITY IN CONTROL-VOLUME SOLUTIONS OF PHASE-CHANGE PROBLEMS , 1993 .

[2]  Chaoyang Wang,et al.  Two-Phase Modeling and Flooding Prediction of Polymer Electrolyte Fuel Cells , 2005 .

[3]  Vishwanath Prasad,et al.  Experimental verification of Darcy-Brinkman-Forchheimer flow model for natural convection in porous media , 1991 .

[4]  Todd Arbogast,et al.  A Nonlinear Mixed Finite Eelement Method for a Degenerate Parabolic Equation Arising in Flow in Porous Media , 1996 .

[5]  P. Pinsky,et al.  A galerkin least-squares finite element method for the two-dimensional Helmholtz equation , 1995 .

[6]  Chao-Yang Wang,et al.  Two-Phase Transport in Proton Exchange Membrane Fuel Cells , 1999, Heat Transfer: Volume 1.

[7]  N. Phan-Thien,et al.  Galerkin/least-square finite-element methods for steady viscoelastic flows , 1999 .

[8]  Jinchao Xu,et al.  A domain decomposition method for two-phase transport model in the cathode of a polymer electrolyte fuel cell , 2009, J. Comput. Phys..

[9]  P. Saffman.  On the Boundary Condition at the Surface of a Porous Medium , 1971 .

[10]  Carol S. Woodward,et al.  Analysis of Expanded Mixed Finite Element Methods for a Nonlinear Parabolic Equation Modeling Flow into Variably Saturated Porous Media , 2000, SIAM J. Numer. Anal..

[11]  M. E. Rose,et al.  Numerical methods for flows through porous media. I , 1983 .

[12]  Vaughan R Voller,et al.  Numerical treatment of rapidly changing and discontinuous conductivities , 2001 .

[13]  Hans-Görg Roos,et al.  The streamline-diffusion method for a convection-diffusion problem with a point source , 2003 .

[14]  T. Hughes,et al.  Convergence analyses of Galerkin least-squares methods for symmetric advective-diffusive forms of the Stokes and incompressible Navier-Stokes equations , 1993 .

[15]  D. Joseph,et al.  Boundary conditions at a naturally permeable wall , 1967, Journal of Fluid Mechanics.

[16]  D. Arnold.  Mixed finite element methods for elliptic problems , 1990 .

[17]  Z. H. Wang,et al.  Two-phase flow and transport in the air cathode of proton exchange membrane fuel cells , 2000 .

[18]  J. Crank.  Free and moving boundary problems , 1984 .

[19]  Chao-Yang Wang,et al.  Fundamental Models for Fuel Cell Engineering , 2004 .

[20]  Jinchao Xu,et al.  A Combined Finite Element-Upwind Finite Volume Method for Liquid-Feed Direct Methanol Fuel Cell Simulations , 2008 .

[21]  Tong Kang,et al.  Some A Posteriori Error Estimates of the Finite-Difference Streamline-Diffusion Method for Convection-Dominated Diffusion Equations , 2001, Adv. Comput. Math..

[22]  Koichi Niijima,et al.  Pointwise error estimates for a streamline diffusion finite element scheme , 1989 .

[23]  Xiaoping,et al.  UNIFORMLY-STABLE FINITE ELEMENT METHODS FOR DARCY-STOKES-BRINKMAN MODELS , 2008 .

[24]  Tayfan E. Tezduyar,et al.  Stabilized Finite Element Formulations for Incompressible Flow Computations , 1991 .

[25]  Stephan Luckhaus,et al.  Quasilinear elliptic-parabolic differential equations , 1983 .

[26]  A. Quarteroni,et al.  Numerical Approximation of Partial Differential Equations , 2008 .

[27]  A. H. Schatz,et al.  Crosswind Smear and Pointwise Errors in Streamline Diffusion Finite Element Methods , 1987 .

[28]  M. Chipot.  Finite Element Methods for Elliptic Problems , 2000 .

[29]  Willi Jäger,et al.  On The Interface Boundary Condition of Beavers, Joseph, and Saffman , 2000, SIAM J. Appl. Math..

[30]  Lutz Tobiska,et al.  The SDFEM for a Convection-Diffusion Problem with a Boundary Layer: Optimal Error Analysis and Enhancement of Accuracy , 2003, SIAM J. Numer. Anal..

[31]  Chao-Yang Wang,et al.  Multiphase flow and heat transfer in porous media , 1997 .