Study on the Interface Instability of a Shock Wave–Sub-Millimeter Liquid Droplet Interface and a Numerical Investigation of Its Breakup

Abstract

This study investigated the influence of instability on the interaction between sub-millimeter liquid droplets and shock waves. Experiments were conducted using 0.42 mm diameter droplets with varying shock wave Mach numbers. The investigation quantified the effects of Weber numbers and initial diameters on the development of Rayleigh–Taylor and Kelvin–Helmholtz instabilities at the shock wave–sub-millimeter liquid droplet interface. Three-dimensional numerical simulations were performed to investigate the deformation and breakup behaviors of sub-millimeter liquid droplets under the impact of a shock wave with a Mach number of 2.12. The post-shock gas flow environment in this condition was in a supersonic state. The simulations utilized the volume-of-fluid method to model the gas–liquid interface, employed unsteady Reynolds-averaged Navier–Stokes methods to simulate turbulence, and incorporated grid gradient adaptive technology to enhance computational efficiency. The results revealed that by increasing the Weber number or decreasing the initial diameter, both the growth rate and the wavenumber extremum of the Rayleigh–Taylor and Kelvin–Helmholtz instability waves increased. The variation in the K–H instability’s growth rate extremum increasing Weber number surpassed that of the R–T’s instability. This indicated that both the R–T and K–H waves on sub-millimeter liquid droplets tended to exhibit increased growth rates and reduced scales. Moreover, as the Weber number increased, the K–H instability became dominant in the aerodynamic fragmentation. The numerical simulations showed good qualitative agreement with the experimental data, affirming the viability of numerical methods for addressing such challenges. The evolution of the sub-millimeter liquid droplets was marked by two primary stages, flattening and shear stripping, signifying that the K–H instability-driven SIE mechanism governed the aerodynamic breakup in the supersonic post-shock airflow.