Flash evaporation Riemann Problem: Formulation and its Exact Solution

TL;DR

The study formalizes the Flash evaporation Riemann Problem (FeRP) under the Homogeneous Equilibrium Model and Vapor-Liquid Equilibrium, capturing depressurization-driven liquid–vapor transitions with an exact Newton-based solution framework for arbitrary two-parameter EoS. It derives a complete set of thermodynamic derivatives for single- and two-phase regimes and analyzes non-classical wave phenomena through the Landau derivative $\Gamma$, providing robust methods for rarefaction and composite waves with Chapman–Jouguet constraints. A parallel analysis of Wood's mechanical-equilibrium speed of sound reveals thermodynamic inconsistencies within the FeRP framework, including a density lag and non-physical entropy changes that underpredict intermediate pressure, velocity, and vaporization relative to full equilibrium. The findings, demonstrated on n-dodecane and related fluids, inform accurate Riemann-solution benchmarks for propulsion-relevant two-phase flows and offer open-source tooling for reproducibility and CFD validation.

Abstract

Flash evaporation, a liquid-to-gas phase transition phenomenon in real fluids, is prevalent in aerospace propulsion systems. To elucidate the physical mechanisms of such complex flows and provide theoretical benchmarks for Computational Fluid Dynamics simulations, this paper formalizes the Flash evaporation Riemann problem (FeRP) characterized by the expansion branch crossing the saturation line, within the framework of Homogeneous Equilibrium and Vapor-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 analyzed, for which a stable iterative solution strategy incorporating the Chapman-Jouguet condition as an outer constraint is proposed. Furthermore, an exact solution for the FeRP based on Wood's mechanical equilibrium speed of sound is developed, enabling a comprehensive evaluation of its thermodynamic implications. Results indicate that Wood's model alters the definition of the two-phase mixture entropy in the Euler equations, introducing an isentropic path characterized by a "density lag" effect and non-physical entropy decrease. Comparative analysis of the FeRP under typical scramjet fuel injection conditions reveals that, although Wood's model captures the general trend of the Riemann solution curve, it significantly underestimates intermediate pressure, velocity, and the extent of vaporization relative to the complete equilibrium model.

Figures (12)

• Figure 1: Phase diagram of n-dodecane
• Figure 2: Flash evaporation in propulsion system
• Figure 3: Thermodynamic Boundary and Phase Model of n-dodecane on the $P-\rho$ Plane
• Figure 4: Three types of solution curves for the flash RP, using the n-dodecane phase diagram as an example
• Figure 5: Landau derivative $\Gamma$ of n-dodecane