Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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


Authors: Maren Hantke and Ferdinand Thein
Journal: Quart. Appl. Math. 73 (2015), 575-591
MSC (2010): Primary 35Q31, 82B26, 82C26, 80A22, 76B10
DOI: https://doi.org/10.1090/qam/1393
Published electronically: June 16, 2015
MathSciNet review: 3400760
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Abstract | References | Similar Articles | Additional Information

Abstract: Phase transitions are in the focus of the modeling of multiphase flows. A large number of models are available to describe such processes. We consider several different two phase models that are based on the Euler equations of compressible fluid flows and that 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.


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Additional Information

Maren Hantke
Affiliation: Institute for Analysis and Numerics, Otto-von-Guericke-University Magdeburg, PSF 4120, D–39016 Magdeburg, Germany
Address at time of publication: University of Leipzig, Mathematical Institute, PF 100920, D-04009 Leipzig, Germany
Email: maren.hantke@ovgu.de

Ferdinand Thein
Affiliation: Institute for Analysis and Numerics, Otto-von-Guericke-University Magdeburg, PSF 4120, D–39016 Magdeburg, Germany
Email: ferdinand.thein@ovgu.de

DOI: https://doi.org/10.1090/qam/1393
Received by editor(s): December 10, 2013
Published electronically: June 16, 2015
Additional Notes: The second author was supported by Landesgraduiertenstipendium Sachsen-Anhalt and is supported by the DFG grant HA 6471/2-1. The authors thankfully acknowledge the support.
Article copyright: © Copyright 2015 Brown University


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