An Adaptive Numerical Framework for the Electro‐Chemical Transport in Direct Internal Reforming Solid Oxide Fuel Cells (DIR‐SOFC)

ABSTRACT This work presents a discretization strategy based on the Continuous Galerkin (CG) formulation with a new Adaptative Mesh Refinement (AMR) strategy to simulate Direct Steam Internal Reforming Solid Oxide Fuel Cells (DIR‐SOFC). The governing equations used in the proposed methodology are based on Ohm's law for the electrochemical potentials at each conductive phase and the Dusty Gas Model (DGM) for species diffusion, assuming uniform and constant temperature and pressure. The reactions induced in the different regions of the domain (electrolyte, anode, and cathode) result in sharp variations of the solution on the different interfaces that need to be properly captured. Thus, to enhance the simulation accuracy and efficiency, a new AMR strategy is proposed, refining the mesh according to the error estimators of the potentials. Additionally, a novel iterative approach to accurately approximate the concentration polarization in the anode by employing the Bulter–Volmer equations is also presented for the Direct Internal Reforming (DIR). Finally, we present several examples to validate and assess the capabilities of this formulation and validate the numerical results with reference examples. Furthermore, a parametric analysis is conducted to investigate the impact of temperature and cell current on potentials, chemical composition, and fuel cell efficiency.