Lattice Boltzmann solver for multi-phase flows: Application to high Weber and Reynolds numbers

TL;DR

This paper introduces a novel lattice Boltzmann algorithm capable of accurately simulating high Weber and Reynolds number multi-phase flows, validated through complex 2D and 3D flow phenomena including droplet impact and splashing.

Contribution

The study develops a new lattice Boltzmann solver combining a decoupled phase-field formulation and cumulants-based collision operator for high Weber and Reynolds number regimes.

Findings

Successfully simulates Rayleigh-Taylor instability in 2D and 3D

Accurately models droplet impact on liquid sheets

Captures fingering instabilities and breakup consistent with experiments

Abstract

The lattice Boltzmann method, now widely used for a variety of applications, has also been extended to model multi-phase flows through different formulations. While already applied to many different configurations in the low Weber and Reynolds number regimes, applications to higher Weber/Reynolds numbers or larger density/viscosity ratios are still the topic of active research. In this study, through a combination of the decoupled phase-field formulation -- conservative Allen-Cahn equation -- and a cumulants-based collision operator for a low-Mach pressure-based flow solver, we present an algorithm that can be used for higher Reynolds/Weber numbers. The algorithm is validated through a variety of test-cases, starting with the Rayleigh-Taylor instability both in 2-D and 3-D, followed by the impact of a droplet on a liquid sheet. In all simulations, the solver is shown to correctly capture the dynamics of the flow and match reference results very well. As the final test-case, the solver is used to model droplet splashing on a thin liquid sheet in 3-D with a density ratio of 1000 and kinematic viscosity ratio of 15 -- matching the water/air system -- at We=8000 and Re=1000. The results show that the solver correctly captures the fingering instabilities at the crown rim and their subsequent breakup, in agreement with experimental and numerical observations reported in the literature.