Modelling and simulation of liquid-vapor phase transition in compressible flows based on thermodynamical equilibrium∗
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2 DEN/DANS/DM2S/SFME/LETR, Commissariat à l’Énergie Atomique Saclay, 91191 Gif-sur-Yvette, France
3 Conseiller Scientifique du DM2S – Commissariat à l’Énergie Atomique Saclay, 91191 Gif-sur-Yvette, France
4 CMAP, École Polytechnique, CNRS, 91128 Palaiseau, France
Revised: 13 July 2011
In the present work we investigate the numerical simulation of liquid-vapor phase change in compressible flows. Each phase is modeled as a compressible fluid equipped with its own equation of state (EOS). We suppose that inter-phase equilibrium processes in the medium operate at a short time-scale compared to the other physical phenomena such as convection or thermal diffusion. This assumption provides an implicit definition of an equilibrium EOS for the two-phase medium. Within this framework, mass transfer is the result of local and instantaneous equilibria between both phases. The overall model is strictly hyperbolic. We examine properties of the equilibrium EOS and we propose a discretization strategy based on a finite-volume relaxation method. This method allows to cope with the implicit definition of the equilibrium EOS, even when the model involves complex EOS’s for the pure phases. We present two-dimensional numerical simulations that shows that the model is able to reproduce mechanism such as phase disappearance and nucleation.
Mathematics Subject Classification: 76T10 / 76N10 / 65M08
Key words: Compressible flows / two-phase flows / hyperbolic systems / phase change / relaxation method
This work has been achieved within the framework of the NEPTUNE project, financially supported by CEA (Commissariat à l’Énergie Atomique), EDF (Électricité de France), IRSN (Institut de Radioprotection et de Sûreté Nucléaire) and AREVA-NP. The authors thank the CEA for its financial support. Grégoire Allaire is a member of the DEFI project at INRIA Saclay Ile-de-France and is partially supported by the Chair “Mathematical modeling and numerical simulation”, F-EADS – École Polytechnique – INRIA.
© EDP Sciences, SMAI, 2012