Numerical Modeling and Validation of Supersonic Two-Phase Flow of CO2 in Converging-Diverging Nozzles

CO₂ is an attractive alternative to conventional refrigerants due to its low direct global warming effects. Unfortunately, CO₂ and many alternative refrigerants have lower thermodynamic performance resulting in larger indirect emissions. Effective use of ejectors to recover part of the lost expansion work, which occurs in throttling devices can close this performance gap and enable the use of CO₂. In an ejector, the pressure of the motive fluid is converted into momentum through a choked converging-diverging nozzle, which then entrains and raises the energy of a lower-momentum suction flow. In a two-phase ejector, the motive nozzle flow is complicated by non-equilibrium phase change affecting local sonic velocity and leading to various types of shockwaves, pseudo shocks, and expansion waves inside or outside the exit of the nozzle. Since the characteristics of the jet leaving the motive nozzle greatly affect the performance of the ejector, this paper focuses on the details of flow development and shockwave interaction within and just outside the nozzle. The analysis is based on a high-fidelity model that incorporates real-fluid properties of CO₂, local mass and energy transfer between phases, and a two-phase sonic velocity model in the presence of finite-rate phase change. The model has been validated against literature data for two-phase supersonic nozzles as well as overall ejector performance data. The results show that due to non-equilibrium effects and delayed phase change, the flow can choke well downstream of the minimum-area throat. Also, Mach number profiles show that, although phase change is at a maximum near the boundaries, the flow first becomes supersonic in the interior of the flow where sound speed is lowest. Shock waves occurring within the nozzle can interact with the boundary layer flow and result in a ‘shock train’ and a sequence of subsonic and supersonic flow observed previously in single-phase nozzles. In cases with lower nozzle back pressure, the flow continues to accelerate through the nozzle and the exit pressure adjusts in a series of supersonic expansion waves.