Modelling of liquid oxygen nozzle flows under subcritical and supercritical pressure conditions. (October 2021) - Lyras, T.; Karathanassis, I.K.; Kyriazis, N.; Koukouvinis, P.; Gavaises, M.
Highlights: Numerical framework for wall-bounded flashing flow of cryogenic liquids proposed. Evaluation of pressure- and density-based solvers with different thermodynamics closures. Introduction of universal methodology suitable for sub- and supercritical conditions. Elucidation of flow-expansion dynamics in different regimes. DES for capturing instabilities induced by transition from super- to subsonic flow. Abstract: The two-phase flow of liquid oxygen in a converging-diverging nozzle has been numerically predicted at conditions resembling those that prevail in the lower-stage boosters of rocket engines realising lift off, as well as in the respective upper stages operating in sub-atmospheric pressures. A comparative evaluation of the predictive capability of a pressure and a density-based solver with various approaches regarding the imposed phase-change rate and thermodynamics closure have been performed. The departure from thermodynamic equilibrium during phase-change has been taken into account via implementation of a bubble-dynamics model employing the Hertz-Knudsen equation in the pressure based solver, whereas thermodynamic equilibrium is adopted in the density-based solver. Tabulated data for the variation of the fluid thermodynamic properties have been derived by the Helmholtz Equation of State (EoS) in a modelling approach universal for both the sub- and supercritical states. This approach has been comparatively assessed in the sub-critical regime against the bubble-dynamics-based model including different EoS for the liquid/vapour phases and against a different tabulated approach based on the NIST dataset for supercritical injection. In terms of flow physics, more severe flow expansion in the diverging part of the nozzle has been detected for subcritical pressures, leading to supersonic flow velocities and significant cooling of the fluid mixture. Complementary Detached Eddy Simulations (DES) have provided detailed insight on the complex expansion phenomena and flow instabilities manifesting on the divergent part of the nozzle for subcritical-injection conditions. The comparison of the numerical predictions against available experimental data and analytical solutions demonstrates the suitability of the employed methodologies in describing the evolution of the cryogenic oxygen flow expansion and phase-change.