Axisymmetric lattice Boltzmann simulation of the heat-exchanger method-based sapphire crystal growth

Abstract

The crystal-growth process in a heat-exchanger method (HEM)-based system was simulated using the lattice Boltzmann technique. The two-dimensional enthalpy-based lattice Boltzmann model was extended to treat the axisymmetric solid-liquid phase change problems. The proposed model demonstrates high accuracy over a large range of Biot and Stefan numbers and exhibits superiority over the first-order perturbation method, especially, in cases involving large Stefan numbers. Macroscopic crystal-growth simulations primarily focus on flow patterns in the melt and heat-transfer processes inside the crucible. Effects of dimensionless convective boundaries and Rayleigh numbers (Ra) on transport phenomena and the crystal/melt interface have also been discussed. It was observed that a decrease in the superheating temperature causes an increase in crystal fraction and decline in convection intensity. The area of the cooling zone mainly influences crystal growth rate during the initial stages of the process. In the later stages, however, the Biot number corresponding to the heating boundary assumes a more significant role. At low Rayleigh numbers, heat transfer via conduction is dominant in the melt. With increase in Ra values, melt convection tends to strengthen, thereby tending to deform the isothermal lines and phase interface.