Study of a low Mach nuclear core model for two-phase flows with phase transition I: stiffened gas law

Bernard, Manuel; Dellacherie, Stéphane; Faccanoni, Gloria; Grec, Bérénice; Penel, Yohan

ESAIM: Mathematical Modelling and Numerical Analysis , Tome 48 (2014) no. 6, pp. 1639-1679.

In this paper, we are interested in modelling the flow of the coolant (water) in a nuclear reactor core. To this end, we use a monodimensional low Mach number model supplemented with the stiffened gas law. We take into account potential phase transitions by a single equation of state which describes both pure and mixture phases. In some particular cases, we give analytical steady and/or unsteady solutions which provide qualitative information about the flow. In the second part of the paper, we introduce two variants of a numerical scheme based on the method of characteristics to simulate this model. We study and verify numerically the properties of these schemes. We finally present numerical simulations of a loss of flow accident (LOFA) induced by a coolant pump trip event.

Classification : 35Q35, 35Q79, 65M25, 76T10
Mots clés : low Mach number flows, modelling of phase transition, analytical solutions, method of characteristics, positivity-preserving schemes

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