Design of solid oxide fuel cell (SOFC) channel layout using the topology optimization method with a design variable propagation approach

This paper presents a novel numerical framework for designing solid oxide fuel cell (SOFC) channel layouts using the topology optimization (TO) method. The proposed design approach combines a 2D optimization problem with a fully coupled 3D multiphysics modeling procedure based on the Finite Element Method (FEM). The main idea is to propagate the design variable from the 2D design space to the 3D modeling space by solving a partial differential equation with the prescribed Dirichlet boundary condition. This propagated variable is then used to propose appropriate material model interpolations and, therefore, to define design-dependent effective properties that allow us to solve the TO-based design problem. Thus, the complexity of the optimization problem is reduced while keeping a numerical model robust enough to represent the behavior of the fuel cell in operation and all the processes involved. The governing equations for momentum conservation, mass transfer, electrochemical kinetics, and ionic and electronic charge transport are solved in three dimensions using the FEM. The optimization problem is formulated to improve the SOFC performance by maximizing the average current density, subject to a maximum length-scale constraint to define the channel width. Sensitivities are calculated using the adjoint method with automatic differentiation, and the optimization problem is solved using an iterative gradient-based interior point algorithm. The results show optimized topologies with different channel widths, whose performances are compared to usual planar SOFC flow fields found in the literature, such as parallel serpentine and traditional parallel layouts. Optimized solutions present more uniform flow and current density distributions, combined with lower pressure drops, which are essential to improve the overall system efficiency and durability.