Enthalpy-based immersed boundary-lattice Boltzmann model for solid-liquid phase change in porous media under local thermal non-equilibrium condition

Heat transfer enhancement structures are adopted to improve the performance of latent heat thermal energy storage (LHTES) systems, such as metallic porous matrix, multi-tube, and fin. The metallic porous matrix and complex geometries of the structures bring difficulties to the numerical studies of the solid-liquid phase transition in the enhanced LHTES system. In this work, an enthalpy-based immersed boundary (IB)-lattice Boltzmann (LB) model is proposed for solid-liquid phase change problems in porous media under the local thermal non-equilibrium (LTNE) condition. In this model, to reduce the numerical diffusion across the solid-liquid interface, a two-relaxation-time (TRT)-LB model is developed to obtain the temperature field of phase change material (PCM). Two single-relaxation-time (SRT)-LB equations (LBEs) are employed for the velocity field of the liquid PCM and the temperature field of the porous matrix, respectively. The partially saturated method is used for the non-slip boundary condition on the moving solid-liquid interface. Different discrete source term schemes are employed for source terms induced by surface heat transfer and IB. Based on the source term treatment, the multi-direct-forcing IB-LB method is employed for the implementation of velocity, enthalpy and temperature boundary conditions on the complex boundary. The proposed model is verified by four cases: one-dimensional conduction melting under the LTNE condition, natural convection in a metallic porous matrix-filled cavity, conduction melting in an annulus filled with metallic porous matrix, and constrained melting in an isothermal circular cylinder without porous media. As an example of application, a metallic porous matrix-enhanced LHTES system with different multi-tube arrangements at different Rayleigh numbers (Ra) and porosities is investigated.