Study of a low Mach model for two-phase flows with phase transition II: tabulated equation of state

Abstract : In order to model the water flow in a nuclear reactor core, the authors carried out several studies coupling a low Mach model - named Low Mach Nuclear Core (LMNC) model - to the stiffened gas law for the equation of state. The LMNC model is derived from the compressible Navier-Stokes equations through an asymptotic expansion with respect to the Mach number commonly assumed to be small in this domain of application. This simplified system of equations provides qualitative results worth of interest under the stiffened gas hypothesis such as analytical solutions in dimension 1 and enables an easier numerical treatment in any dimension compared to the parent compressible model solved in the low Mach regime. Moreover, in the temperature and pressure regime of interest (namely high temperature and pressure situations), the stiffened gas law turns out to be inaccurate, which requires a new modelling of the equation of state. This is why this paper is devoted to the coupling of the LMNC model to an equation of state tuned by means of experimental values (NIST) for thermodynamic variables. The very point in this study consists in presenting an easy-to-implement procedure to fit tabulated values and derivatives satisfying positivity and monotonicity constraints for pure liquid and vapour phases. Modifications of previously published numerical schemes designed for a stiffened gas law are detailed in dimensions 1 and 2 to allow the use of a general equation of state. In the regime of interest and when the coolant is water, numerical results highlight the difference of tabulated equation of state with the stiffened gas law and also show that thermal conduction effects can be ignored.
Type de document :
Pré-publication, Document de travail
MAP5 2016-03. 2015
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Contributeur : Bérénice Grec <>
Soumis le : jeudi 12 mai 2016 - 17:15:35
Dernière modification le : jeudi 16 février 2017 - 01:07:29
Document(s) archivé(s) le : mercredi 16 novembre 2016 - 02:46:51


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  • HAL Id : hal-01111730, version 2



Stéphane Dellacherie, Gloria Faccanoni, Bérénice Grec, Yohan Penel. Study of a low Mach model for two-phase flows with phase transition II: tabulated equation of state. MAP5 2016-03. 2015. <hal-01111730v2>



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