| Issue |
ESAIM: M2AN
Volume 53, Number 1, January–February 2019
|
|
|---|---|---|
| Page(s) | 63 - 84 | |
| DOI | https://doi.org/10.1051/m2an/2018044 | |
| Published online | 02 April 2019 | |
Research Article
A thermodynamically consistent model of a liquid-vapor fluid with a gas
Laboratoire de Mathématiques Jean Leray, Université de Nantes & CNRS UMR 6629, BP 92208, 44322 Nantes Cedex 3, France
* Corresponding author: helene.mathis@univ-nantes.fr
Received:
12
October
2017
Accepted:
29
June
2018
This work is devoted to the consistent modeling of a three-phase mixture of a gas, a liquid and its vapor. Since the gas and the vapor are miscible, the mixture is subjected to a non-symmetric constraint on the volume. Adopting the Gibbs formalism, the study of the extensive equilibrium entropy of the system allows to recover the Dalton’s law between the two gaseous phases. In addition, we distinguish whether phase transition occurs or not between the liquid and its vapor. The thermodynamical equilibria are described both in extensive and intensive variables. In the latter case, we focus on the geometrical properties of equilibrium entropy. The consistent characterization of the thermodynamics of the three-phase mixture is used to introduce two Homogeneous Equilibrium Models (HEM) depending on mass transfer is taking into account or not. Hyperbolicity is investigated while analyzing the entropy structure of the systems. Finally we propose two Homogeneous Relaxation Models (HRM) for the three-phase mixtures with and without phase transition. Supplementary equations on mass, volume and energy fractions are considered with appropriate source terms which model the relaxation towards the thermodynamical equilibrium, in agreement with entropy growth criterion.
Mathematics Subject Classification: 76T30 / 80A10 / 35Q79
Key words: Multiphase flows / entropy / thermodynamics of equilibrium / phase transition / homogeneous equilibrium model / hyperbolicity / homogeneous relaxation model
© The authors. Published by EDP Sciences, SMAI 2019
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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