Keywords: electrode design, proton exchange membrane fuel cell, catalyst layer, finite elements, sensitivity analysis, gradient-based optimization.

The potential of fuel cells as a clean and efficient energy conversion technology have long been recognized. They have a high theoretical efficiency, and, unlike batteries, they can produce electricity continuously as long as supplied with a fuel. When fuelled by hydrogen, the only by-products of a fuel cell are water and heat. Proton exchange membrane (PEM) fuel cells are the leading type of fuel cell to replace internal combustion engines in transportation applications and rechargeable batteries in portable applications. PEM fuel cells are, however, still in early development stages and require significant improvements in performance, durability and cost. The combination of new and optimized materials, improved product development, novel architectures, more efficient transport processes, and design optimization and integration are expected to lead to major gains in these areas. Advanced computational models [1]) coupled with optimization techniques offer the prospect of systematic simulation, design and optimization of fuel cell systems and could greatly assist in the effective integration of novel design concepts, materials and operating strategies, as well as allowing reduced reliance on hardware prototyping and shorter development cycles.The catalyst layer in a proton exchange membrane fuel cell (PEMFC) is a critical component from the viewpoint of both cost and performance. It is in these layers that the electrochemical reaction occurs, and therefore they are responsible for enhancing reaction rates and reducing activation losses. Due to their relatively low operating temperature, platinum is the catalyst of choice in PEM fuel cells. Most experimental and modelling work to date to optimize catalyst layer compositions has been done using either trial-and-error or parametric studies in conjunction with graphical methods. These approaches are valid if the number of design variables is small, however, for larger numbers of design variables (e.g. point loading distribution, porosity and Nafion volume fraction) a multivariable numerical optimization analysis should be used. In this study, we develop and demonstrate a gradient-based framework that allows systematic multivariable optimization of fuel cell catalyst layers. A two-dimensional, single-phase catalyst layer model is first obtained that properly accounts for solid and electrolyte phase potential and water and oxygen concentration in the catalyst layer. This model results in a set of nonlinear partial differential equations that is solved using an adaptive finite element method. The implementation of the model involved the development of a computer code using an object-oriented programming language, i.e. C++, and the solution of the system using the objects provided by the deal.II finite element library [2]. The resulting model is capable of obtaining measures of performance of the catalyst layer such as current density and overpotential for any combination of catalyst layer design parameters. This model was described in detail and validated in [3].Having developed and validated a computational model accounting for all salient transport phenomena, we use the direct method to analytically derive the sensitivity equations of the current density produced at the catalyst layer with respect to the desired design parameters. The design parameters in this paper are catalyst layer composition parameters such as the volume fraction of Nafion and the catalyst mass loading. These sensitivity equations are also solved using a finite element formulation and are validated by comparing them to the numerical gradients obtained using forward differences with several step sizes. This study is not only useful for the validation of the analytical sensitivities but also to estimate the error produced by using numerical sensitivities instead of analytical sensitivities. Finally, the optimization framework is completed by coupling the described model and sensitivity equations to a gradient-based optimization algorithm. Using this framework, numerical optimization of a PEM catalyst layer was performed efficiently and reliably and a catalyst layer composition was obtained that maximizes the produced current density. The optimal catalyst layer results obtained in more than a 30% increase on the current density with respect to a current catalyst layer design.

1

B.R. Sivertsen and N. Djilali. Cfd based modelling of proton exchange membrane fuel cells.
Journal of Power Sources, 141(1):65-78, February 2005. doi:10.1016/j.jpowsour.2004.08.054

2

W. Bangerth, R. Hartmann, and G. Kanschat. deal.II Differential Equations Analysis Library, Technical Reference.

3

M. Secanell, B. Carnes, A. Suleman, and N. Djilali. A PEM fuel cell cathode model for gradient-based optimization. In III European Conference on Computational Mechanics. ECCOMAS, June 3-5 2006. doi:10.1007/1-4020-5370-3_730

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