Modelling of liquid oxygen and nitrogen injection under flashing conditions

The present numerical investigation of two-phase flashing flows examines the injection of liquid oxygen and liquid nitrogen into near-vacuum conditions prevailing in the upper-stage boosters of rocket engines. The predictive capability of a pressure-based solver and a density-based solver, each employing distinct approaches related to the imposed phase-change rate and thermodynamics closure, has been comparatively evaluated. Regarding the pressure-based solver, the departure from thermodynamic equilibrium during phase-change has been taken into account via the implementation of a bubble-dynamics model employing the Hertz-Knudsen equation. In contrast, the density-based solver relies on the adoption of thermodynamic equilibrium while real-fluid thermodynamic properties are assumed by loading tabulated values to the solver. Each thermodynamic property value was calculated in advance by solving the Helmholtz Equation of State (EoS) for a wide range of density and internal energy conditions. Numerical findings have been compared against experimental data available in the literature. The comparison demonstrates the capability of both methodologies in capturing the evolution of cryogenic flashing flow expansion, phase-change, and spray formation. The salient features identified in the numerical results, i.e., the expansion sphere immediately downstream of the injector exit, the bell-shaped topology of the spray, as well as the dependency of the spray cone angle on superheat, are in agreement with experimental measurements. Especially the density-based approach has been proven highly accurate with respect to the steady expanding flow described by a level of superheat in the range of 3 to 245, while also being independent of any parameter tuning.