A CFD Model for the Evaporation of Sub-Micron Droplet Sprays Across Normal Shocks

The rapid evaporation of liquid droplets across a normal shock wave is a phenomenon of critical importance in advanced propulsion and clean energy systems, such as NH3 supersonic separation. The conventional Spalding d2-law is commonly used to model such phenomena, but it is not suitable for predicting the complete vaporization of sub-micron droplets, particularly as evaporation approaches the free-molecular regime. To address this issue, this paper introduces a novel time-dependent one-dimensional CFD model, which is used to analyze the shock structure, the non-equilibrium heat and mass transfer between the liquid and gas phases, and the evolution of the droplets’ size through the shock. The model describes the evaporation of NH3 sub-micron droplet sprays across a stationary normal shock for various fractions of the liquid phase. The Gyarmathy evaporation model is utilized to accurately account for the transition from diffusion-governed to free-molecular regimes, alongside a new two-phase Rankine–Hugoniot shock jump formulation. The study reveals the influence of a steady normal shock on the physical structure of a droplet-laden flow, including the existence of an initial droplet size swelling through the shock, and quantifies the subsequent complete evaporation of the suspended droplets. The maximum swelling throughout the shock is up to 17%, which corresponds to the case with 8% liquid phase mass fraction in the flow. The model provides acceptable accuracy in calculating the two-phase parameters in high-speed flows and can be extended for modeling more complex, multidimensional detonation and propulsion systems.