Flash evaporation Riemann Problem: Formulation and its Exact Solution

TL;DR

This paper formulates and solves the Flash evaporation Riemann problem analytically, providing insights into complex two-phase flow behaviors in aerospace applications and evaluating the implications of different thermodynamic models.

Contribution

It introduces an exact analytical solution framework for the FeRP with arbitrary equations of state, analyzing non-classical wave structures and thermodynamic effects of models like Wood's.

Findings

Wood's model alters the mixture entropy and introduces a density lag effect.

The exact solution captures complex wave structures in two-phase flows.

Wood's model underestimates vaporization and intermediate pressures.

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.