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Modelling and simulation of liquid-vapor phase transition incompressible flows based on thermodynamical equilibrium∗

Published online by Cambridge University Press:  13 February 2012

Gloria Faccanoni ,
Samuel Kokh  and
Grégoire Allaire
Gloria Faccanoni
Affiliation:
IMATH – Université du Sud Toulon-Var, Avenue de l’Université, 83957 La Garde, France. [email protected]
Samuel Kokh
Affiliation:
DEN/DANS/DM2S/SFME/LETR, Commissariat à l’Énergie Atomique Saclay, 91191 Gif-sur-Yvette, France; [email protected]
Grégoire Allaire
Affiliation:
Conseiller Scientifique du DM2S – Commissariat à l’Énergie Atomique Saclay, 91191 Gif-sur-Yvette, France CMAP, École Polytechnique, CNRS, 91128 Palaiseau, France; [email protected]
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Abstract

In the present work we investigate the numerical simulation of liquid-vapor phase changein compressible flows. Each phase is modeled as a compressible fluid equipped with its ownequation of state (EOS). We suppose that inter-phase equilibrium processes in the mediumoperate at a short time-scale compared to the other physical phenomena such as convectionor thermal diffusion. This assumption provides an implicit definition of an equilibriumEOS for the two-phase medium. Within this framework, mass transfer is the result of localand instantaneous equilibria between both phases. The overall model is strictlyhyperbolic. We examine properties of the equilibrium EOS and we propose a discretizationstrategy based on a finite-volume relaxation method. This method allows to cope with theimplicit definition of the equilibrium EOS, even when the model involves complex EOS’s forthe pure phases. We present two-dimensional numerical simulations that shows that themodel is able to reproduce mechanism such as phase disappearance and nucleation.

Keywords

Compressible flowstwo-phase flowshyperbolic systemsphase changerelaxation method
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 46 , Issue 5 , September 2012 , pp. 1029 - 1054
Copyright
© EDP Sciences, SMAI, 2012

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