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Liquid oxygen (LOX) constitutes a popular propellant used in multistage rockets for space launch vehicles. It is characterised as a cryogenic liquid as it remains in this state at temperatures below 90K. Depending on the specific rocket-engine design and its location at the tandem stage configuration, the delivery of LOX to mix with the main fuel can be realised at either supercritical (lower-stages) or subcritical (upper stages) pressure conditions. The present study demonstrates the applicability and accuracy of different numerical approaches with regards to capturing phase-change of LOX in both sub- and supercritical regimes in a converging-diverging nozzle layout. Hydrodynamic-instability effects have been taken into account through URANS simulations and DES. At subcritical pressures, phase change manifests itself through bubble nucleation. The rapid pressure drop in the nozzle throat is probable to lead to bulk liquid vaporisation, a process commonly termed as flash boiling. The phase-change rate between the compressible liquid/vapour phases for flash boiling conditions has been predicted employing a relation derived from the kinetic theory of gases (Hertz-Knudsen equation), also including an empirical term to describe potential departure from thermodynamic equilibrium conditions. The numerical predictions were compared against experimental data available in the open literature and their accuracy was verified. On the contrary, for supercritical conditions, no interface emerges and the fluid density exhibits a smooth variation with pressure. Real fluid thermodynamics in this case have been implemented through properties (pressure, temperature or speed of sound) tables derived by the NIST dataset and the numerical predictions have been compared against a benchmark solution derived using the Helmholtz energy Equation of State. The comparative investigation has demonstrated that the two-phase jet expansion dynamics exhibit much more profound features in the subcritical-pressure regime compared to supercritical expansion. Depending on the inlet/outlet pressure ratio, or, in other words, the degree of superheat, a complex pattern of shock cells with a clear Mach disk sets in at the nozzle diverging part, a topology completely absent for supercritical pressures. It can be postulated that the two-phase expansion dynamics resemble those of a supersonic gas jet. DES has verified that the flow transition from supersonic to subsonic velocities at the edges of shock cells induces instabilities responsible for the formation of a transient secondary-flow pattern downstream the location of the Mach disk.
