Lattice Boltzmann Simulation of Incompressible Transport Phenomena in Macroscopic Solidification Processes

Abstract

A lattice Boltzmann (LB) simulation strategy is proposed for the incompressible transport phenomena occurring during macroscopic solidification of pure substances. The proposed model is derived by coupling a passive scalar-based thermal LB model with the classical enthalpy–porosity technique for solid–liquid phase-transition problems. The underlying hydrodynamics are monitored by a conventional single-particle density distribution function (DF) through a kinetic equation, whereas the thermal field is obtained from another kinetic equation which is governed by a separate temperature DF. The phase-changing aspects are incorporated into the LB model by inserting appropriate source terms in the respective kinetic equations through the most formal technique following the extended Boltzmann equations along with an appropriate enthalpy updating scheme. The proposed model is validated extensively with one- and two-dimensional solidification problems for which analytical and numerical results are available in the literature, and finally, it is used for solving a benchmark problem, the Bridgman crystal growth in a square crucible.

Notes

Note: The percent error is calculated using |φ − φ _z |/φ, where φ _z is based on 80 × 80 lattices.