Flash evaporation Riemann problem: formulation and its exact solution

Flash evaporation, a liquid-to-gas phase transition phenomenon in real fluids, is prevalent in aerospace propulsion systems. To elucidate the wave structures of flash evaporation in the equilibrium limit and provide theoretical benchmarks for computational fluid dynamics simulations, this paper formalises the flash evaporation Riemann problem (FeRP) characterised by the expansion branch crossing the saturation line, within the framework of homogeneous equilibrium and vapour–liquid equilibrium assumptions. An exact solution framework that analytically resolves all thermodynamic derivatives of equilibrium two-phase fluids is established for arbitrary two-parameter equations of state. By evaluating the Landau fundamental derivative, the non-classical wave structures arising in the FeRP are analysed, for which a stable iterative solution strategy incorporating the Chapman–Jouguet condition as an outer constraint is proposed. Furthermore, the FeRP framework is extended to the Riemann problem (RP) with a given thermodynamic non-equilibrium speed of sound, enabling a comprehensive evaluation of how this non-equilibrium closure affects the RP solution. Results indicate that such a non-equilibrium model alters the definition of the two-phase mixture entropy in the Euler equations, introducing a different isentropic path characterised by non-physical entropy decrease and density lag relative to the equilibrium path. Consequently, as the given speed of sound shifts from the complete equilibrium limit towards Wood’s mechanical equilibrium, the intermediate pressure, velocity and vaporisation extent in the RP solution decrease.