Lattice Boltzmann simulation of solid-liquid phase change with nonlinear density variation

Solid-liquid phase change problems have been extensively investigated by the lattice Boltzmann (LB) method in the past two decades, and the usual Boussinesq approximation with the assumption that the fluid density linearly varies with the temperature is widely applied. However, the actual variation of the fluid density with the temperature could be very complex for the phase change material near its solidus and liquidus temperatures. In this work, a double-distribution-function LB model is adopted to simulate the melting and solidification processes in a square cavity. The buoyancy force is directly calculated via the fluid density determined by temperature rather than the usual volume expansivity and temperature difference, and thus the present LB model can handle the nonlinear variation of the fluid density. Four different density variations (i.e., linear expansion, convex expansion, concave expansion, and water) are considered. The simulation results show that the convex and concave expansion variations can be roughly approximated by the linear expansion variation for both the melting and solidification processes. Due to the anomalous expansion over the temperature range of 0-4.0293 degrees C, the water variation cannot be approximated by the linear expansion variation, unless the involved temperature range is relatively large. The density variation determines the structure and strength of natural convection, thereby significantly affecting the melting and solidification processes. Published under an exclusive license by AIP Publishing.