Asymptotically Reduced Model for a Proton Exchange Membrane Fuel Cell Stack: Automated Model Generation and Verification

A proton exchange membrane fuel cell (PEMFC) stack can comprise a large number of cells and coolant plates; the former, in turn, contain further functional layers and groups. The large number of transport phenomena that occur at differing length scales throughout the stack pose a challenging problem for mathematical modeling. In this context, we present a "bottom-up" approach to overcome the difficulties in the mathematical modeling of a PEMFC stack; in short, a fast and memory-efficient reduced model for a single PEMFC derived earlier is coupled to a model for heat and charge transfer in a coolant plate to form a numerical building block, which can be replicated to form a virtual stack having the required number of cells. This procedure is automated to avoid the time-consuming task of manually creating the stack, as well as to remove the possibility of human error during the setup phase. The automated, reduced stack model is verified for a 10-cell stack with the full set of equations; good agreement is found when perturbations between cells are "small." We then study the computational efficiency of the reduced model for stacks comprising up to 400 cells: A typical run for a 10-cell and a 100-cell stack takes around 20 s and 3-4 min and requires 0.6 and 1.2 GB of random access memory, respectively. Finally, extensions to include the effects of perturbed flow, additional physics, external manifolds, and other types of flow fields are discussed. (C) 2010 The Electrochemical Society. [DOI: 10.1149/1.3384864] All rights reserved.