Abstract
Liquid–vapor flows exhibiting phase transition, including phase creation in single-phase flows, are of high interest in mathematics, as well as in the engineering sciences. In two preceding articles the authors showed on the one hand the capability of the isothermal Euler equations to describe such phenomena (Hantke and Thein, arXiv, 2017, arXiv:1703.09431). On the other hand they proved the nonexistence of certain phase creation phenomena in flows governed by the full system of Euler equations, see Hantke and Thein, Quart. Appl. Math. 2015, 73, 575–591. In this note, the authors close the gap for two-phase flows by showing that the two-phase flows considered are not possible when the flow is governed by the full Euler equations, together with the regular Rankine-Hugoniot conditions. The arguments rely on the fact that for (regular) fluids, the differences of the entropy and the enthalpy between the liquid and the vapor phase of a single substance have a strict sign below the critical point.
Highlights
Describing the dynamics of multiphase flows, flows including phase transition, is a challenging topic in mathematics and other sciences dealing with fluid dynamics, see [1]
This work dealt with the adiabatic Euler Equations (1a)–(1c), together with the classical
We considered the case of two adjacent phases of a single substance, and modeled the phase boundary as a sharp interface
Summary
Describing the dynamics of multiphase flows, flows including phase transition, is a challenging topic in mathematics and other sciences dealing with fluid dynamics, see [1]. For the modeling of phase transitions equations derived using averaging or homogenization techniques are often used—see, for instance, Zein et al [2]. For the system of isothermal Euler equations equipped with a kinetic relation, exact solutions for Riemann problems were constructed by Hantke et al [4,5]. Existence and uniqueness of the solution was proven These results include single-phase flows exhibiting phase creation, such as cavitation. Another hyperbolic and conservative system that may be considered are the full Euler equations. This work generalizes the results of Hantke et al [6] for two-phase flows modeled using a single set of Euler equations, together with a kinetic relation.
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