A general formulation for a mathematical PEM fuel cell model

A general formulation for a comprehensive fuel cell model, based on the conservation principle is presented. The model formulation includes the electro-chemical reactions, proton migration, and the mass transport of the gaseous reactants and liquid water. Additionally, the model formulation can be applied to all regions of the PEM fuel cell: the bipolar plates, gas flow channels, electrode backing, catalyst, and polymer electrolyte layers. The model considers the PEM fuel cell to be composed of three phases: reactant gas, liquid water, and solid. These three phases can co-exist within the gas flow channels, electrode backing, catalyst, and polymer electrolyte layers. The conservation of mass, momentum, species, and energy are applied to each phase, with the technique of volume averaging being used to incorporate the interactions between the phases as interfacial source terms. In order to avoid problems arising from phase discontinuities, the gas and liquid phases are considered as a mixture. The momentum interactions between the fluid and solid phases are modeled by the Darcy-Forchheimer term. The electro-oxidation of H-2 and CO, the reduction of O-2, and the heterogeneous oxidation of H-2 and CO are considered in the catalyst layers. Due to the small pore size of the polymer electrolyte layer, the generalized Stefan-Maxwell equations, with the polymer considered as a diffusing species, are used to describe species transport. One consequence of considering the gas and liquid phases as a mixture is that expressions for the velocity of the individual phases relative to the mixture must be developed. In the gas flow channels, the flow is assumed homogeneous, while the Darcy and Schlogl equations are used to describe liquid water transport in the electrode backing and polymer electrolyte layers. Thus, two sets of equations, one for the mixture and another for the solid phase, can be developed to describe the processes occurring within a PEM fuel cell. These equations are in a conservative form, and can be solved using computational fluid dynamic techniques. (c) 2004 Elsevier B.V. All rights reserved.