Simulation of Corner Solidification in a Cavity Using the Lattice Boltzmann Method

Abstract

This study investigates corner solidification in a closed cavity in which the left and bottom walls are kept at a temperature lower than its initial temperature. The liquid material in the cavity initially lies at its phase transition temperature and, due to cold boundary conditions at the left–bottom walls, solidification starts. The simulation of corner solidification was performed using a kinetic-based lattice Boltzmann method (LBM), and the tracking of the solid–liquid interface was captured through the evaluation of time. The present investigation addresses the effect of natural convection over conduction across a wide range of higher Rayleigh numbers, from 106 to 108. The total-enthalpy-based lattice Boltzmann method (ELBM) was used to observe the thermal profiles in the entire cavity with a two-phase interface. The isotherms reveal the relative dominance of natural convection over conduction, and the pattern of interface reveals the effective growth of the solidified layer in the cavity. To quantify the uniformity of cooling, a coefficient of variation (COV) for the thermal field was calculated in the effective solidified zone at a wide range of Ra. The results show that the value of COV increases with Ra and reduces with time. The thermal instability in the flow field is also quantified through FFT analyses.