Numerical investigation of wall temperature effects on non-equilibrium condensation in supersonic nozzle using Eulerian-Eulerian model

Abstract Non-equilibrium condensation (NEC) commonly arises in various industrial applications, including steam turbines, supersonic nozzles, and aerospace propulsion systems. This phenomenon can significantly impair system efficiency and reliability by introducing abrupt phase transitions and associated energy losses. To mitigate its effects, several control methods have been proposed, among which surface heating stands out as a widely studied technique. In most existing research, surface heating has been implemented by applying a heat flux to the nozzle walls. In contrast, the present study investigates a different approach, wherein a constant-temperature wall is employed to introduce surface heating directly into the supersonic flow. The objective is to evaluate how this thermal boundary condition affects key two-phase flow parameters, including droplet size, condensed mass, nucleation rate, droplet growth rate, and liquid mass fraction (LMF). The numerical framework is validated using experimental data from the International Wet Steam Experimental Project (IWSEP) nozzle, ensuring the reliability of the predictions. Following validation, the study examines the influence of two wall temperatures – 400 °C and 800 °C – on nozzle performance and condensation behavior. Results indicate that heating the wall to 800 °C induces substantial changes in the internal flow structure and condensation characteristics. Specifically, the condensation shock shifts noticeably downstream, and both the peak nucleation rate and maximum LMF decrease sharply – by approximately 91 % and 6 %, respectively – compared to an adiabatic baseline. Additionally, the analysis reveals a clear relationship between wall temperature and mass flow rate. As the wall temperature increases, the mass flow rate decreases, with a reduction of about 3.86 % observed at 800 °C. Overall, these findings demonstrate that surface heating through wall temperature control offers an effective mechanism to influence and manage the behavior of NEC, with important implications for improving the efficiency and control of high-speed flow systems.