An heuristic model for droplet phase change in supersonic flows*

Traditional liquid carbon-based fuels possess low heat capacity and latent heat of evaporation, enabling rapid heating and evaporation. In conditions where compression work and heat transfer are dominant, such as in supersonic flows, the external layer of the droplet can quickly reach a critical state and be advected away, significantly accelerating the phase transition beyond the traditional thermal/diffusive process. This study presents a heuristic model designed to predict droplet phase change in supersonic flows, addressing the intricate interaction between high-speed gas dynamics and liquid phase transformations. The model integrates fundamental principles from thermodynamics and trans-critical states to estimate evaporation rates and droplet size evolution in supersonic environments. By simplifying the complex physics involved, the model provides a practical approach for understanding droplet behavior under extreme aerodynamic conditions. Key features of the model include considerations of shockwave-induced pressure and temperature variations, droplet deformation, and the effects of the trans-critical state. Validation against experimental data and computational fluid dynamics simulations demonstrates that the heuristic model accurately captures the essential trends in droplet evaporation time scales, offering valuable insights for integration with Eulerian-Lagrangian CFD simulations.