A model for detonation-driven droplet combustion

The interaction between shock waves and liquid droplets is a critical phenomenon in a variety of high speed flow applications. Although experimental investigations have provided valuable insights, the development of a comprehensive physical framework describing droplet breakup and the subsequent liquid-to-gas phase transition under extreme thermodynamic conditions is still limited. This study introduces a heuristic model that estimates the droplet evaporation timescale based on global energy conservation, incorporating the effects of momentum coupling and droplet deformation. The model describes the phase change through a surface regression velocity, providing a dynamic, geometry-sensitive measure of mass transfer. Comparison with experimental data demonstrates excellent agreement in terms of droplet deformation, expansion, and acceleration, as well as the influence of transcritical thermodynamic behavior. This approach is applied to a constant-volume reactor containing a liquid fuel droplet under conditions representative of practical detonation engines. Evaporation makes the equivalence ratio vary within the prescribed volume, ranging from very lean to very rich conditions. During the initial stage, when phase change is governed by the regression of the stagnation plane, the mixture remains between lean and stoichiometric limits, resulting in a positive heat-release rate and a moderate increase in the ambient temperature. After the critical point is reached, trans- and super-critical evaporation rates dominate, leading to a substantial increase in mass and energy transfer. This rapid increase of the equivalence ratio and decrease of internal energy result in a negative net heat-release rate, accompanied by a rapid drop in temperature and pressure. Novelty and significance This study presents a novel heuristic framework to accurately predict the evaporation dynamics of liquid droplets subjected to shock waves under extreme thermodynamic conditions. Unlike conventional models that inadequately capture rapid nonlinear phenomena inherent to supersonic environments, this approach notably matches experimental observations of droplet deformation, acceleration, and thermodynamically complex transcritical behaviors. This advancement provides essential theoretical and computational foundations for improved modeling of droplet combustion in high speed, multiphase flow applications.