A 2D model for shape optimization of solid oxide fuel cell cathodes

A topology optimization method is used to identify the optimal shape of the nano-composite cathode of a solid oxide fuel cell (SOFC). A simplified analysis model is used in computations aimed at reducing ohmic losses by optimizing the shape of the cathode to minimize resistance. The model of the SOFC is reduced to a periodic, 2D conduction problem with design-dependent ionic transfer boundary conditions. Special techniques are introduced to avoid physically inadmissible designs that would otherwise be allowed by the 2D model. Isoperimetric constraints on the perimeter and the amount of material are used in the problem. Numerical examples are provided to discuss the effect of material properties and the resource restrictions introduced by the constraints. The methodology discussed can be applied to similar problems involving design-dependent boundary conditions.