Phase-Field-Based LBM Analysis of KHI and RTI in Wide Ranges of Density Ratio, Viscosity Ratio, and Reynolds Number

Abstract

Numerous studies have elaborated the dominated roles of Kelvin-Helmholtz instability (KHI) and Rayleigh-Taylor instability (RTI) in the liquid sheet breakup and primary atomization. As for applications in aeronautics, the liquid-gas mixing generally occurs at the challenging conditions of a large density ratio and high Reynolds number. Hence, the evaluation of KHI and RTI under such challenging conditions will have great significance in better understanding the destabilizing mechanism of the liquid layer. To this end, a lattice Boltzmann multiple-relaxation-time (MRT) two-phase model, based on the conservative Allen-Cahn equation, is reconstructed for the present study. Preliminarily, the numerical stability and accuracy of this MRT model are tested by Laplace’s law under a large density ratio and high Reynolds number, including the sensitivity study to the values of mobility. Afterward, KHI and RTI are investigated in wide ranges of the Reynolds number, density ratio, and viscosity ratio. Numerical results indicate that the enhanced viscous force of light fluid with an increasing viscosity ratio notably suppresses the roll-ups of heavy fluid in KHI and RTI. As for the density ratio, it generally shows negative impacts on fluid-mixing in KHI and spike-spiraling in RTI. However, when the density ratio and the Reynolds number both arrive at high levels, the Kelvin-Helmholtz wavelets aroused by a dominated inertia force of heavy fluid trigger severe interface disintegration. The above results once more demonstrate the excellent ability of the present model in dealing with challenging conditions. Besides, the morphological characteristics of KHI and RTI at a high Reynolds number and large density ratio also greatly support the typical interface breakup mechanism observed in primary atomization.