Phase-field-based lattice Boltzmann modeling of large-density-ratio two-phase flows

TL;DR

This paper introduces a simple, accurate lattice Boltzmann model capable of simulating large-density-ratio two-phase flows with high numerical accuracy and low spurious velocities, validated through various benchmark problems and droplet impact simulations.

Contribution

A novel LB model combining Allen-Cahn and Navier-Stokes equations with a new forcing function, improving accuracy and simplicity for large-density-ratio two-phase flow simulations.

Findings

Achieves small spurious velocities in simulations.

Good agreement with analytical and experimental results.

Successfully reproduces droplet splashing phenomena.

Abstract

In this paper, we present a simple and accurate lattice Boltzmann (LB) model for immiscible two-phase flows, which is able to deal with large density contrasts. This model utilizes two LB equations, one of which is used to solve the conservative Allen-Cahn equation, and the other is adopted to solve the incompressible Navier-Stokes equations. A novel forcing distribution function is elaborately designed in the LB equation for the Navier-Stokes equations, which make it much simpler than the existing LB models. In addition, the proposed model can achieve superior numerical accuracy compared with previous Allen-Cahn type of LB models. Several benchmark two-phase problems, including static droplet, layered Poiseuille flow, and Spinodal decomposition are simulated to validate the present LB model. It is found that the present model can achieve relatively small spurious velocities in the LB community, and the obtained numerical results also show good agreement with the analytical solutions or some available results. At last, we use the present model to investigate the droplet impact on a thin liquid film with a large density ratio of 1000 and the Reynolds number ranging from 20 to 500. The fascinating phenomenon of droplet splashing is successfully reproduced by the present model and the numerically predicted spreading radius exhibits to obey the power law reported in the literature.