Adjoint Method for the Optimization of the Catalyst Distribution in Proton Exchange Membrane Fuel Cells

Abstract

In this article we present an adjoint method for the optimization of the catalyst distribution in proton exchange membrane fuel cells (PEMFCs). By using the theory of functional analysis we derive analytical equations for the sensitivity functions of the cell voltage with respect to the catalyst distribution in a very general framework, independent on the transport model used to simulate the PEMFC. Then we present an efficient numerical algorithm to calculate the sensitivity functions using the adjoint method. The adjoint method has the advantage that it can be applied to the optimization of systems with a large (>104) number of optimization variables that are computed simultaneously and independently to maximize the objective function. Finally, we apply the method to the optimization of 2-D platinum distribution in PEMFCs. We show that the optimum platinum distribution varies with the operating conditions, position of landings and openings, cell geometry, and dimensions of the catalyst layers. The method presented in this work can be naturally extended to the optimization of other 2-D and 3-D field variables such as the porosity of catalyst and gas diffusion layers, particle size distribution, or microstructure of the cell.