Numerical Investigation of the Aerodynamic Droplet Breakup at Mach Numbers Greater Than 1

Abstract

The present work examines numerically the breakup of water droplets exposed to gas flows at Mach numbers Ma>1, which resemble the ambient conditions encountered in the injection systems of supersonic combustion ramjet (scramjet) engines. A computational fluid dynamics (CFD) model is utilized that solves the compressible Navier-Stokes equations, the energy equation, and the mass conservation in volume fraction form [volume of fluid (VOF) method] along with two equations of state to model the density variations of the two phases. In addition, a coupled VOF/Lagrange model is employed to capture the appearance of microdroplets, which are smaller than the smallest grid cell. As a first step, a two-dimensional planar simulation (water column) is performed at conditions of Ma=1.47 in order to validate the numerical model; its results are compared against published experimental and numerical data. Good agreement is observed for the temporal evolution of droplet shape, the streamwise deformation, and the leading-edge displacement, as well as the shock wave reflection. Subsequently, the validated model is utilized to perform a three-dimensional (3D) simulation at Ma=1.23, which corresponds to the conditions of previous experimental studies, and its results are compared against the experimental data as well as the results from previous numerical studies, showing good agreement. Furthermore, surface instabilities are observed at the droplet surface initiated by interfacial instabilities due to the shearing effect and the interaction with the shock wave, pertaining to Kelvin-Helmholtz and Rayleigh-Taylor instabilities, despite the stabilizing contribution of surface tension; viscosity effects are found to play an insignificant role.