Comparative study of droplet growth models for non-equilibrium condensation with temperature-dependent thermophysical coupling

Non-equilibrium condensation is a complex multiphase phenomenon involving vapor–liquid phase change, droplet nucleation, and growth under high-speed flow conditions. Accurate modeling of interfacial transport processes is essential for predicting droplet size distributions, liquid volume fractions, and momentum exchange between gas and liquid phases. However, conventional models typically assume a constant gas-phase specific heat capacity ($C_p$) and neglect the contribution of the liquid phase, leading to systematic errors in energy conservation and thermophysical property representation. This study presents a thermodynamically consistent condensation modeling framework that incorporates temperature-dependent $C_p$ values for both vapor and liquid phases. The coupling of thermophysical properties is achieved through species transport equations, enabling dynamic updates of mixture properties during simulation. The framework is used to evaluate seven representative droplet growth models under two canonical configurations: a supersonic nozzle and a turbine blade cascade. Including the temperature-dependent liquid-phase $C_p$ reduces the predicted outlet liquid mass fraction and droplet radius by 2.69 % and 3.59 %, respectively, mitigating the overestimation of condensation intensity in conventional approaches. Among the models, the Gyarmathy and Hill formulations exhibit the highest accuracy, yielding mean relative errors below 0.65 % for pressure and 7 % for droplet radius. In contrast, the Hertz–Knudsen model significantly overpredicts growth due to its neglect of interfacial thermal resistance. Despite microscale discrepancies, all models converge to a final liquid mass fraction of 6-7 %, indicating a balance between nucleation and growth. This framework improves thermodynamic consistency and predictive accuracy in condensation modeling, supporting energy systems where phase-change prediction is critical.