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Large-Scale Optimization of Polymer Electrolyte Membrane Fuel Cells

*geometry optimization*, which focuses on finding the optimum channel configuration and overall cell dimensions; and (2)

*microstructure optimization*, which focuses on finding the optimum distributions of the porosity, catalyst, and electrolyte that maximize the power density of the cell [1]. The number of design parameters in each of the above problems is relatively large, which makes the design of PEMFCs a difficult mathematical problem. For instance, let us consider problem (2): if we assume that the fuel cell is discretized using a 3-D finite element discretization with 10

^{6}nodes, the design variables consist of the mesh-point values of the porosity, catalyst concentration, and electrolyte density at each mesh point. Hence, the number of design variables is 3 ×10

^{6}, which make the design of PEMFC a large-scale optimization problem. Usually, such large optimization problems are solved on parallel computer clusters, with a large number of concurrent processors.

In this presentation we focus on the large-scale design of the microstructure of the PEMFC by developing a gradient-based method for the computation of the optimum (mathematically exact) distributions of the porosity, catalyst, and electrolyte that maximize the power density of the cell. It should be noted that traditional heuristic techniques such as genetic algorithms, swarm-optimization or other evolutionary algorithms are inappropriate for the large-scale optimization of PEMFCs. Indeed, the number of optimization variables in non-heuristic techniques in of the order or 5-10 variables, which is a few orders of magnitude smaller than the total number of design variables in PEMFCs. Since the computation time of heuristic techniques increases approximately exponentially with the number of design variables, the total optimization time of heuristic techniques becomes unpractical in large-scale optimization problems.

The technique presented in this work is based on evaluating the sensitivity functions of the cell voltage and discharge current and applying a gradient-based maximization method to optimize the PEMFC. The sensitivity functions are computed efficiently using an adjoint space approach suitable for large-scale systems that can be simulated using 2-D or 3-D finite element models. The computational cost required to compute the sensitivity functions is relatively small since our technique requires solving only one sparse system of linear equations instead of performing multiple device simulations. For this reason, the numerical algorithm presented in this work can be implemented on single processor computers even in the case of 3-D finite element problems.

Using the proposed algorithm we are able to predict the optimum distribution of platinum particles and electrolyte inside the catalyst layers, as well as the optimum porosity profile that maximizes the power density of the cell. The optimum distributions and porosity profiles depends on the positions of landings and openings, and on the geometry and dimensions of the layers. In agreement with existing experimental data, we obtain that the catalyst density should be distributed non-uniformly inside the cell in order to increase the power density of the cell (see figure). In the case of the porosity profile it is more efficient to increase the porosity towards the gas diffusion layer side in order to increase the flow of the oxygen and water vapors. In the case of the electrolyte distribution in the catalyst layers it is more efficient to increase the fraction of the electrolyte towards the membrane in order to decrease the ohmic losses of the protons.

Finally, it should be noted that our numerical algorithm can also show how the optimum distributions of the catalyst, porosity and electrolyte vary with the discharge conditions. The results describe the complete profiles of the optimal catalyst and porosity by providing the full distribution of optimum locations and concentration of platinum particles in the catalyst layer, as well as the “ideal” porosity distribution of the PEMFC under the specified operating conditions. More details about the technique, the numerical implementation, and the final optimized structures will be presented at the conference.

**References**

[1] M. Secanell, J. Wishart, and P. Dobson, "Computational design and optimization of fuel cells and fuel cell systems: A review," Journal of Power Sources, vol. 196, pp. 3690-3704, 2011.

[2] P. Andrei, G. Mixon, M. Mehta, and V. Bevara, "Design of the catalyst layers in PEMFCs using an adjoint sensitivity analysis approach," 227^{th} ECS Meeting, Chicago, IL, 2015.