Why condensation by compression in pure water vapor cannot occur in an approach based on Euler equations

Abstract

Abstract. Phase transitions are in the focus of the modeling of multiphase flows. A large number of models is available to describe such processes. We consider several different two phase models that are based on the Euler equations of compressible fluid flows and which take into account phase transitions between a liquid phase and its vapor. Especially we consider the flow of liquid water and water vapor. We give a mathematical proof, that all these models are not able to describe the process of condensation by compression. This behavior is in agreement with observations in experiments, that simulate adiabatic flows, and shows that the Euler equations give a fairly good description of the process. The mathematical proof is valid for the official standard IAPWS-IF97 for water and for any other good equation of state. Also the opposite case of expanding the liquid phase will be discussed.

On the Impossibility of First-Order Phase Transitions in Systems Modeled by the Full Euler Equations

“…In this work, we want to show what is responsible for this deficiency. 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. A more detailed remark is given in Section 4 .…”

“…[ 4 , 16 ]. We want to emphasize that the previous results generalize the statements given in [ 6 ] in the case where a single set of equations, together with a kinetic relation, is used to describe the two-phase flow.…”

“…In [ 6 ], we discussed the cases of nucleation and cavitation for all models based on the Euler equations, including Baer–Nunziato-type models. There, the mass transfer due to the phase transition is modeled by the source terms.…”

“…Secondly, here we directly used the Rankine–Hugoniot conditions to yield a contradiction, instead of comparing the slopes of the saturation curve with a shock curve, respectively. Thirdly, it is not restricted to water as in [ 6 ], where we have used the IAPWS-IF97 EOS [ 13 ]. The present results are valid for any given substance where entropy, enthalpy, and density of the liquid and the vapor phase are related, as in Section 3 .…”

A general existence result for isothermal two-phase flows with phase transition

“…Additionally we can treat nucleation an cavitation. In view of the work by Hantke, T. [10] the last point has to be emphasized. To our knowledge this is the most general result concerning Riemann problems for isothermal two phase flows.…”