Analytical Shock Jump Formulae for Cryogenic Homogeneous Two-Phase Nozzle Flow

Choked flux rates and shock jump relations were calculated both analytically and computationally for a converging-diverging nozzle. High inlet stagnation pressure with a maximum of 6.45MPa was applied to the cryogenic vapor-liquid nitrogen flow. The total inlet-to-static exit pressure ratio range was between 3.5 and 15.3. The analytical shock jump expressions, which were derived, are exact extensions of the Rankine-Hugoniot single-phase gas dynamic relations. Accordingly, a consistent agreement was obtained between analytical and computational pressure, Mach number and void fraction shock jumps. The numerical mass flux values were also successfully compared with experimental data and two separate analytical results, both obtained from a modified Henry-Fauske model and a homogeneous mass flux equation.