Lattice Boltzmann Simulation of High-Diffusivity Problems With Application to Energy Transport in a High-Temperature Solar Thermochemical Reactor

Abstract

We describe a general technique for rescaling the high-diffusivity convection diffusion equation (CDE) when it is simulated with the lattice Boltzmann equation (LBE) method. The macroscopic CDE is recovered from the kinetic-based LBE when the mean free path of the particles is much smaller than the lattice grid size. As the relaxation time and the mean free path are proportional to the diffusion coefficient of the CDE in LBE models, direct use of a large diffusion coefficient would lead to large numerical errors in LBE simulations. To improve accuracy, we rescale the CDE by choosing a large time scale and a moderate relaxation coefficient so that the characteristic Fourier number for the diffusion process remains the same. The rescaled LBE model is first validated with two numerical tests for which analytical solutions are available: the transient heat conduction in a semi-infinite solid and that inside a circle. The comparison between the LBE results and analytical solutions shows that the numerical errors are greatly reduced when the high diffusion coefficient is rescaled down. It is then applied in a diffusion-radiation coupled model to simulate the energy transport in a high-temperature solar thermochemical reactor for hydrogen production. Rescaling of the solar flux boundary conditions and the chemical reaction source terms due to the rescaling of the diffusion coefficient is also discussed and the simulation results will be used to optimize the cavity-reactor design.