Two-phase nozzle flow and the subcharacteristic condition

We consider nozzle flow models for two-phase flow with phase transfer. Such models are based on energy considerations applied to the frozen and equilibrium limits of the underlying relaxation models. In this paper, we provide an explicit link between the mass flow rate predicted by these models and the classical subcharacteristic condition of Chen, Levermore and Liu. In particular, we demonstrate that for sufficiently small pressure differences, the equilibrium nozzle model will predict a lower mass flow rate than the frozen model when the subcharacteristic condition is satisfied. An application to tank leakage of CO2 is presented, indicating that the frozen and equilibrium models provide significantly different predictions. This difference is comparable in magnitude to the modeling error introduced by applying simple ideal-gas/incompressible-liquid equations-of-state for CO2.