Comparative Studies of Time-stepping Schemes for the Treatment of the Darcy Drag Term of the Momentum Equation

Abstract

A numerical comparison of time-stepping schemes for the solution of the conservation equations of mass and momentum of polymer electrolyte fuel cells (PEFCs) is presented. Darcy drag force is the dominating term for the fluid flow inside the gas diffusion layer (GDL). Permeability of the GDL is usually very small. Convergence of continuity is a major problem for the fluid flow through the GDL, and the situation becomes critical in lower-permeability cases. To overcome this kind of severe situation, an implicit scheme is used to obtain not only faster convergence but also a more accurate continuity condition. Explicit, implicit and semi-implicit treatment of the Darcy drag term is considered, and the schemes are compared for various physical parameters of the GDL, e.g., the Darcy number and the porosity parameter, by one dimensional numerical simulation. Influence of strict convergence on the secondary flow effect and on the pressure loss is described and the superiority of implicit scheme is confirmed for three-dimensional numerical simulation of PEFC channel flow.