Sharp-interface calculations of the vaporization rate of reacting aluminum droplets in shocked flows

•The numerical study of aluminum droplet combustion shows a transition from diffusion-limited combustion to kinetically limited combustion at high Mach numbers.•A surrogate model for the Sherwood number of the reacting aluminum droplets is developed from the simulation data.•A multi-fidelity approach for developing the surrogate model is demonstrated to reduce the computation cost of model development. The vaporization rate of reacting aluminum droplets in high-speed flows plays a crucial role in determining the energy released during the combustion of aluminized solid propellants and explosives. This work develops a model for the vaporization rate of burning aluminum droplets in shocked flows using data from high-resolution simulations. A levelset-based sharp-interface method is used to resolve the dynamics at the droplet-air interface. Several reactive calculations of shock-droplet interaction are performed in the parameter space of Mach number (1.1 - 3.5) and Reynolds number (100 – 1000) to understand the influence of local flow parameters on the flame structure around the reacting aluminum droplet. The results show a transition from diffusion limited to kinetically limited combustion of the aluminum droplets when the Mach number is increased and the droplet size or the Reynolds number is decreased. The transition from diffusion-limited combustion to kinetically limited combustion is found to significantly affect the flame dynamics and vaporization rate of the reacting droplets. Therefore, empirical models for the vaporization rate of droplets, developed for diffusion limited combustion regimes, do not represent the kinetically limited combustion in high Mach number conditions. A new model for the Sherwood number spanning diffusion and kinetically limited regimes of the reacting aluminum droplets is developed using an economical multi-fidelity surrogate modeling technique. The current model for the Sherwood number for reacting aluminum droplets will be useful in predicting the energy released from the combustion of aluminized energetic materials in shocked flows. Although the current method is developed in the context of aluminum droplet combustion, it can be extended to develop surrogate models of Sherwood number for general liquid fuel droplets in compressible flows.