Liquid-vapor flows in heated ducts: Reference solutions

Analytical one-dimensional steady state solutions in a heated duct of constant area are determined for two-phase liquid-gas and liquid-vapor mixtures. First, the exact solution for single-phase flow is recalled in the different flow regimes (subsonic and supersonic) for given inflow conditions. These solutions are extended in the context of duct connected to an upstream tank and to a downstream pressure outflow condition. Then, reference solutions for various two-phase flow models are developed for compressible two-phase flows. They are applied in the context of ideal gas and stiffened gas equation of state for liquid-gas and liquid-vapor flows. These solutions corresponds to limit situations of partial equilibrium among the phases. The first limit situation corresponds to a two-phase flow model where both phases evolve in mechanical equilibrium only. The second one corresponds to a two-phase model where the phases evolve in both mechanical and thermal equilibria. The last one corresponds to a model describing a liquid-vapor mixture in thermodynamical equilibrium. The three limit situations are compared to show the impact given the choice of one or another equilibrium on fluid state and in particular on mass flow rate in the duct.