Reduction-consistent axisymmetric lattice Boltzmann equation method for [formula omitted]-phase fluids

Abstract

We develop a reduction-consistent axisymmetric lattice Boltzmann equation method (LBE) for hydrodynamics and interface capturing among N (N≥ 2) immiscible fluids with large density and viscosity contrasts. In present work, the chemical potential form of interface force among N immiscible fluids is incorporated to the axisymmetric hydrodynamic equations, and the reduction-consistent axisymmetric conservative Allen–Cahn equation (ACACE) is developed for interface capturing of N (N≥ 2) immiscible fluids, then we propose a simple ACACE LBE for interface capturing, which has reduction-consistent property, and the axisymmetric hydrodynamic equations are solved by another LBE. Some axisymmetric benchmark multiphase problems are carried out to validate present LBE including stationary compound droplet, break up of compound liquid thread and compound droplet splashing on a thin liquid film, numerical results show that the predictions by present LBE agree well with the theoretical solutions/other numerical and available experimental results.