Thermal Lattice Boltzmann Model for Incompressible Flows through Porous Media

Abstract

In this paper, the lattice Boltzmann method (LBM) is applied to simulation of natural convection in porous media using Brinkman-Forchheimer equation. The Brinkman-Forchheimer equation is recovered from a kinetic equation for the density distribution function that has a forcing term and the equilibrium distribution function including the porosity. The temperature equation which neglects the compression work done by the pressure and the viscous heat dissipation is calculated by a kinetic equation for thermal energy distribution function. The velocity and temperature profiles of the LBM shows good agreement with those of the finite difference method (FDM) for the Poiseuille flow filled with a porous medium and with the analytical solutions for the porous plate problem. The stream lines and isothermal patterns show that the LB model is able to keep the same accuracy with the FDM. For various values of Darcy and Rayleigh numbers, and of porosities, the solutions of the LBM are compared with those of earlier studies. The numerical experiment shows excellent agreement for the Brinkman-extended Darcy model and for the Brinkman-Forchheimer model. This paper leads to the conclusion that the LBM can simulate natural convection in porous media in both Darcy and non-Darcy region at the representative elementary volume scale.