Numerical Simulation of Water Solidification in a Square Cavity Using Lattice Boltzmann Method

In this paper, we numerically investigated two-dimensional water freezing phenomena in a square cavity. Because of the temperature difference between vertical heated walls, natural convection occurs in the domain, simulated with the Boussinesq approximation's help. The Prandtl number of ۷.۰ is used for water. The main governing equations of the problem, momentum, and energy equations, are solved using the Lattice Boltzmann method. We verify our code with natural convection cases without solidification. Moreover, the results of this study are compared against the prior CFD solvers for a square cavity. The Rayleigh number is varied between ۲۵,۰۰۰ and ۲,۵۰۰,۰۰۰. In this way, we can analyze the effect of the Rayleigh number on the ice formation during the solidification process. The results demonstrate that by increasing the Rayleigh number, natural convection and the rate of heat transfer increase in the domain, which leads to the decrease in the thickness of the formed ice.

Keywords:

Lattice Boltzmann Method (LBM) , Natural Convection , Heat Transfer , Solidification , Computational Fluid Dynamics (CFD)