Application of the homogeneous relaxation model for flash boiling under sub-atmospheric pressures

• Flashing two-phase flow in a nozzle at sub-atmospheric pressure is simulated. • HRM model is used to study low-pressure and low-temperature flash evaporation. • Model captures pressure undershoots, vapor generation, and void fraction trends. • Higher inlet pressure shortens flash delay, while higher temperature extends it. Flashing two-phase flows under sub-atmospheric outlet conditions in a converging–diverging nozzle are investigated using the Homogeneous Relaxation Model (HRM) within a two-phase mixture flow framework. The main objectives of this study are to conduct an in-depth investigation of low-temperature, low-pressure flash evaporation, which is essential in flash-based wastewater purification and power generation systems that utilize low-grade waste heat as an energy source, and to support the improvement of a proof-of-concept experimental setup currently being established in our laboratory through the findings of this study. The numerical results demonstrate that the mathematical model accurately reproduces pressure and void fraction distributions reported in the literature. It also captures key flashing features—including pressure undershoots, vapor generation delays, and pressure recovery—through the relaxation-time formulation. The results indicate that flashing flow in a converging–diverging nozzle is characterized by a sharp pressure drop near the throat, followed by rapid vapor generation and partial pressure recovery in the diverging section. This behaviour is primarily governed by nozzle geometry and the large disparity in specific volumes between the liquid and vapor phases. Vapor generation increases markedly at higher inlet pressures and temperatures, driven by the greater availability of superheat energy. The simulations further reveal that the mass flow rate is highly sensitive to inlet conditions: elevated inlet temperatures intensify vapor generation and consequently reduce mass flow rate, whereas achieving both high vapor production and high mass flow rates requires sufficiently high inlet pressures. The model also predicts shorter flash-delay distances at higher pressures, indicating an earlier onset of phase change, while longer delays occur at elevated temperatures due to increased metastability. Additionally, pressure undershoots become more pronounced with higher inlet temperatures, whereas their dependence on inlet pressure is negligible. It is found that, under fixed inlet conditions, lower sub-atmospheric back pressures enhance steam generation and promote pressure recovery after the nozzle throat, while simultaneously reducing the mass flow rate and the magnitude of pressure undershoots.