Numerical optimization of proton exchange membrane fuel cell cathodes

A fuel cell gradient-based optimization framework based on adaptive mesh refinement and analytical sensitivities is presented. The proposed approach allows for efficient and reliable multivariable optimization of fuel cell designs. A two-dimensional single-phase cathode electrode model that accounts for voltage losses across the electrolyte and solid phases and water and oxygen concentrations is implemented using an adaptive finite element formulation. Using this model, a multivariable optimization problem is formulated in order to maximize the current density at a given electrode voltage with respect to electrode composition parameters, and the optimization problem is solved using a gradient-based optimization algorithm. In order to solve the optimization problem effectively using gradient-based optimization algorithms, the analytical sensitivity equations of the model with respect to the design variables are obtained. This approach reduces the necessary computational time to obtain the gradients and improves significantly their accuracy when compared to gradients obtained using numerical sensitivities. Optimization results show a substantial increase in the fuel cell performance achieved by increasing platinum loading and reaching a Nafion mass fraction around 20-30 wt.% in the catalyst layer.