Large Eddy Simulation of Flashing Cryogenic Liquid with a Compressible Volume of Fluid Solver
Jan Wilhelm Gärtner  1, *@  , Andreas Rees  2@  , Andreas Kronenburg  1@  , Joachim Sender  2@  , Michael Oschwald  2@  , Daniel Loureiro  1@  
1 : Institut für Technische Verbrennung, Universität Stuttgart
Herdweg 51 70174 Stuttgart Deutschland -  Germany
2 : Institute of Space Propulsion, German Aerospace Center (DLR)
Langer Grund 74239 Hardthausen -  Germany
* : Corresponding author

For the development of new upper orbit thrusters with cryogenic propellants, it is important to understand the dynamics of oxidizer and fuel injection at near vacuum conditions before ignition. Due to the low ambient pressure with respect to the saturation pressure at the injection temperature, the propellants enter a superheated state and evaporate rapidly. This process is called flash evaporation. To simulate such a flashing cryogenic jet a compressible multiphase solver is developed in OpenFOAM. The homogeneous relaxation model (HRM) is chosen to model the phase change. For solving this multiphase problem, a one-fluid approach which solves for the mixture properties and phase fraction is selected. For the equation of state, the open source library CoolProp is used to calculate density, enthalpy and the saturation conditions. Further, the numerical methods to solve and capture the supersonic multiphase flow with a Volume of Fluid (VoF) method is described. The transition from mechanical break up to fully flashing spray and the change from subsonic to supersonic flow is investigated in detail. The numerical results are validated with experiments conducted at DLR Lampoldshausen which provide shadowgraph images. As a first approximation to fuel-oxidizer mixing, cryogenic nitrogen jet experiments at the DLR test bench M3.3 in Lampoldshausen are made and numerically investigated with large eddy simulations. It is noted that the flashing jet becomes supersonic and forms a shock shortly after the nozzle exit. This occurs despite the velocity being lower than the sonic velocities associated with each individual pure phase.
The results show that the HRM model can predict the onset of the partial flashing flow, however fully flashing jet with 180 degree spray angle cannot be predicted with the HRM coefficients commonly used.

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