Three-dimensional numerical simulation of solid oxide fuel cell cathode based on lattice Boltzmann method with sub-grid scale models

In the present study, three-dimensional numerical simulations are carried out to predict the electrochemical characteristics of solid oxide fuel cell (SOFC) cathodes based on a coupled method using sub-grid scale (SGS) model in a lattice Boltzmann method (LBM). Lattice Boltzmann method is used to solve the governing equations. In each coarse computational grid, local gas diffusivities, ion and electron conductivities are obtained by directly solving diffusion equations using the original fine sub-grid scale information. Two types of SGS models are introduced in this study, i.e. isotropic and anisotropic local diffusivities and conductivities. Proposed SGS local diffusivities and conductivities can maintain detailed information of the original fine microstructure even when coarser grid is used in the calculation. In the anisotropic SGS model, weighted summation of particle distribution function is applied in the LBM to maintain the invariances of local concentrations and potentials. From the tortuosity factor and overpotential calculation results, it is concluded that the proposed SGS models can drastically improve the computational accuracy without costing additional calculation time. Moreover, SGS model considering geometric anisotropies inside the calculation grid presents more precise results than the isotropic SGS model.