Numerical simulation of melting in porous media via a modified temperature-transforming model

A modified temperature-transforming model that considers the dependence of heat capacity on the fractions of a solid and a liquid in the mushy zone is employed to solve melting in porous media. Because natural convection only occurs in the liquid phase, the velocity of the phase change material in the solid region is set to zero by a ramped switch-off method. The convection in the liquid region is modeled using the Navier-Stokes equation with Darcy's term and Forchheimer's extension. The effect of natural convection is considered using the Boussinesq approximation. The results show that the temperature-transforming model with the heat capacity dependency are closer to experimental results with gallium as the temperature-transforming model and packed glass beads as the porous structure. The modified temperature-transforming model is then further used to study the melting of copper saturated in porous media and formed by sintered steel particles. The results show that melting is accelerated under a higher Rayleigh number, due to the stronger convection effect, and the melting is dominated by conduction for the case with a lower Darcy number.