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.

Scale-Resolving Simulation of Shock-Induced Aerobreakup of Water Droplet

“…Apparently, the predicted droplet displacement slightly increases with the numerical resolution, according to what was recently found in Ref. [13]. The accuracy of the prediction improved with increasing the resolution while approaching the reference data.…”

“…can be assumed as the internal length-scale of the turbulence model, and the dissipation term in Equation ( 6) can be thus rewritten as D k = ρk 3/2 /l RANS t . This unsteady SST-RANS model was already successfully applied for the computational evaluation of liquid droplet aerobreakup in recent studies [12,13], where it was demonstrated to provide mean flow results with engineering accuracy and low computational complexity.…”

“…Bounded second-order central differencing was used for the momentum and energy equations, while second-order upwind discretization was employed for the model equations and the continuity equation. As for the FV-based approximation of the latter, the compressive scheme, which is a second-order reconstruction scheme based on the gradient limiter, was applied for the advection term in (13).…”

“…In the framework of applied science research, according to recent findings, e.g., Refs. [12,13], unsteady Reynolds-averaged Navier-Stokes (RANS) modeling represents a viable alternative for the computational evaluation of the aerobreakup phenomenon, with engineering accuracy and at moderate computational cost. However, classical RANS solutions are known to lack spectral content, even for adequate spatial and temporal resolutions.…”