An evaluation of a 3D free-energy-based lattice Boltzmann model for multiphase flows with large density ratio

Abstract

In this paper, the 3D Navier-Stokes (N-S) equation and Cahn-Hilliard (C-H) equations were solved using a free-energy-based lattice Boltzmann (LB) model. In this model, a LB equation with a D3Q19 velocity model is used to recover continuity and N-S equations while another LB equation with D3Q7 velocity model for solving C-H equation (Int. J. Numer. Meth. Fluids, 2008; 56:1653-1671) is applied to solve the 3D C-H equation. To avoid the excessive use of computational resources, a moving reference frame is adopted to allow long-time simulation of a bubble rising. How to handle the inlet/outlet and moving-wall boundary conditions are suggested. These boundary conditions are simple and easy for implementation. This model's performance on two-phase flows was investigated and the mass conservation of this model was evaluated. The model is validated by its application to simulate the 3D air bubble rising in viscous liquid (density ratio is 1000). Good agreement was obtained between the present numerical results and experimental results when Re is small. However, for high-Re cases, the mass conservation seems not so good as the low-Re case. © 2009 John Wiley & Sons, Ltd.