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In the pursuit of enhanced engine performance and reduced emissions, the design of liquid-fueled propulsion systems is shifting towards much higher combustor pressures, surpassing the nominal critical pressure of the fuel and air. This trend leads to the adoption of supercritical conditions, wherein the liquid fuel is injected into the ambient air at supercritical pressure and temperature, causing the fuel temperature to exceed its nominal critical point. This transition from a liquid-like to a gas-like behavior, known as "transcritical behavior," is a crucial aspect governing the operation of modern high-pressure propulsion and energy conversion systems. In these systems, the primary liquid jet breakup and the subsequent break-up of the resulting droplets into smaller droplets, namely secondary breakup, significantly impact mixing and combustion processes. Despite its importance, there has been a limited focus on droplet breakup at supercritical conditions, particularly at higher flow speeds relevant to high-speed liquid-fuel propulsion systems. Surface tension effects are often neglected in the simulation of transcritical flow, assuming surface tension vanishes beyond the critical point, while recent experiments and molecular dynamics simulations suggest that surface tension effects persist at transcritical conditions. To gain insight into the effects of surface tension on transcritical flows, we have developed a fully compressible multiphaseDirect Numerical Simulation (DNS) approach that accounts for decaying surface effects. The diffuse interface method is employed to represent transcritical interfaces, accounting for surface tension effects calculated using molecular dynamics simulations. This approach is employed to investigate the behavior of subcritical n-dodecane droplets in a supercritical nitrogen environment interacting with a shockwave, aiming to identify the governing breakup regimes at transcritical conditions. The development of quantitative measures enables the generalization of droplet breakup modes for transcritical droplets. The insights gained from this study contribute to advancing the understanding of transcritical liquid breakup, providing valuable knowledge for designing and optimizing high-speed propulsion systems 

The phase transition from subcritical to supercritical conditions, referred to as transcritical behavior, significantly impacts the evaporation and fuel–air mixing in high-pressure liquid-fuel propulsion systems. Transcritical behavior is characterized as a transition from classical two-phase evaporation to a single-phase gas-like diffusion regime as surface tension and latent heat of vaporization reduce. However, the interfacial behavior represented by the surface tension coefficient and evaporation rate during this transition which are crucial inputs for Computational Fluid Dynamics (CFD) simulations of practical transcritical fuel spray is still missing. This study aims at developing new evaporation rate and surface tension models for transcritical n-dodecane droplets using molecular dynamics (MD) simulations irrespective of the droplet size. As MD simulations are primarily limited to the nanoscale, the new models can bridge the gap between MD and continuum simulations and enable the direct application of these findings to microscopic droplets. A new characteristic timescale, i.e., “undroplet time,” is defined which marks the transition from classical two-phase evaporation to single-phase gas-like diffusion behavior. The undroplet time indicates the onset of droplet core disintegration and penetration of nitrogen molecules into the droplet, which occurs after the vanishment of the surface tension. By normalizing the time with respect to the undroplet time, the rate of surface tension decay, evaporation rate, and the rate of droplet mass depletion become independent of the droplet size. Calculation of pairwise correlation coefficients for the entire MD results shows that both surface tension coefficient and evaporation rate are strongly correlated with the background temperature, while pressure and droplet size play a less significant role past the critical point. Therefore, new models for surface tension coefficient and evaporation rate spanning from sub- to supercritical conditions are developed as a function of background pressure and temperature, which can be used in continuum simulations. The identified phase change behavior based on the undroplet time shows a good agreement with the phase change regime maps obtained using microscale experiments and nanoscale MD predictions.