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Flash evaporation Riemann problem: formulation and its exact solution
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DOI：10.1017/jfm.2026.11752.png)
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Abstract
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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.
Keywords:
condensation/evaporation
gas dynamics
multiphase flow
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3.9
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2.0W
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9.4W
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