Three-dimensional multiple-relaxation-time lattice Boltzmann models for single-phase and solid-liquid phase-change heat transfer in porous media at the REV scale

In this paper, three-dimensional (3D) multiple-relaxation-time (MRT) lattice Boltzmann (LB) models are developed for single-phase and solid-liquid phase-change heat transfer in porous media at the representative elementary volume (REV) scale. These models are developed in the framework of the double-distribution-function (DDF) approach: the flow field is solved by an isothermal MRT-LB model with the D3Q15 or D3Q19 lattice based on the generalized non-Darcy model, while the temperature field is solved by a thermal MRT-LB model with the D3Q7 lattice. In the 3D DDF-MRT model for solid-liquid phase-change heat transfer in porous media, the enthalpy method is employed to capture the solid-liquid phase interface in an implicit manner. Mesoscopically, the effective enthalpy is defined as the basic evolution variable of the enthalpy-based MRT-LB model, and as a result, the temperature and liquid-fraction fields can be solved without iteration procedure. The practicability and accuracy of the proposed models are demonstrated by numerical simulations of several 3D single-phase and solid-liquid phase-change heat transfer problems in porous media at the REV scale. It is shown that the 3D DDF-MRT models for convection heat transfer in porous media are second-order accurate in space. In addition, the influences of Darcy number and porosity on the melting (solidification) processes of 3D melting (solidification) with convection in a cubical porous cavity are investigated by the enthalpy-based DDF-MRT model.