A REGULARIZED PHASE-FIELD LATTICE BOLTZMANN MODEL FOR TWO-PHASE FLOWS

At present, the lattice Boltzmann (LB) model based on the phase field theory has been widely applied in gas-liquid two-phase flow problems. In order to improve the numerical stability of the existing phase field LB models, a new regularized phase-field lattice Boltzmann model (RLBM) is proposed for simulating gas-liquid two-phase flows with large density ratio and high viscosity ratio in this work. The proposed model consists of two core modules, namely interface tracking and flow field solver, where the interface is governed by the conservating Allen-Cahn (A-C) phase-field equation, and the flow field is governed by the incompressible Navier-Stokes (N-S) equations. Firstly, two regularized lattice Boltzmann equations (LBE) have been constructed to obtain flow field and phase field information, respectively. Unlike the standard single-relation-time (SRT) model, a non-equilibrium pre-collision function, which is only related to the macroscopic variables, have been introduced into the collision term of the evolution equation in the proposed model. It has been confirmed that this model can accurately recover to the macroscopic flow field and phase filed governing equations by the multi-scale Chapman-Enskog (C-E) analysis. Furthermore, to verify the effectiveness of the present model, four typical two-phase flow cases were simulated in this paper, including static droplet, Rayleigh-Taylor (R-T) instability problems, bubble rising and a single droplet impacting on the liquid film. The obtained numerical results of these typical examples demonstrate that the proposed model can accurately simulate gas-liquid two-phase flow problems under large density ratio, high viscosity ratio and high Reynolds number. More importantly, compared to the traditional phase field SRT model, which could cause non-convergence issues at low mobility ( \theta _M < 2.0 \times 10^ - 2 ), it has been found that the model proposed in this paper exhibits better stability in simulating complex two-phase flow with low mobility ( \theta _M = 1.0 \times 10^ - 6) , and can more accurately characterize interface flow and capture interface morphology.