A simulation-derived surrogate model for the vaporization rate of aluminum droplets heated by a passing shock wave

Abstract

The vaporization rate of aluminum droplets in shocked flows plays a crucial role in determining the energy release rate during the combustion of the aluminized energetic materials. In this paper, the physics of the vaporization of aluminum droplets in shocked flows is numerically investigated. Surrogate models for the temporally averaged Sherwood number and Nusselt number, cast as functions of shock Mach number and Reynolds number, are developed from the simulation-based data. The results show that the Sherwood number and the Nusselt number of the droplet increase monotonically with the Reynolds number. On the other hand, the Sherwood number and the Nusselt number exhibit non-monotonic behavior with increasing shock Mach number due to the transition of the post-shock flow from subsonic to the supersonic speeds as the shock Mach number is increased from 1.1 to 3.5. In contrast with available models in the literature that are commonly used in process scale computations of aluminum droplet vaporization, the current models for the Sherwood number and the Nusselt number are applicable over a wide range of the Reynolds number and the Mach number and will be useful in the macro-scale multi-phase simulations of the combustion of aluminumized energetic materials in high-speed flows.