Numerical Modeling of PEM Fuel Cells Under Partially Hydrated Membrane Conditions

In proton-exchange membrane fuel cells it is particularly important to maintain appropriate water content and temperature in the electrolyte membrane. The water balance depends on the coupling between diffusion of water, pressure variation, and the electro-osmotic drag in the membrane. In this paper we apply conservation laws for water and current, in conjunction with an empirical relationship between electro-osmotic drag and water content, to obtain a transport equation for water molar concentration and to derive a new equation for the electric potential that strictly accounts for variable water content and is more accurate than the conventionally used Laplace’s equation. The model is coupled with a computational fluid dynamics model that includes the porous gas diffusion electrodes and the reactant flow channels. The resulting coupled model accounts for multi-species diffusion (Stefan-Maxwell equation); first-order reaction kinetics (Butler-Volmer equation); proton transport (Nernst-Planck equation); and water transport in the membrane (Schlo¨gl equation). Numerical simulations for a two-dimensional cell are performed over nominal current densities ranging from $i=0.4$ to $i=1.2 A/cm2.$ The relationship between humidification and the membrane potential loss is investigated, and the impact and importance of two-dimensionality, temperature, and pressure nonuniformities are analyzed and discussed.