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.
Keywords: low Mach number flows, modelling of phase transition, analytical solutions, method of characteristics, positivity-preserving schemes
@article{M2AN_2014__48_6_1639_0,
author = {Bernard, Manuel and Dellacherie, St\'ephane and Faccanoni, Gloria and Grec, B\'er\'enice and Penel, Yohan},
title = {Study of a low {Mach} nuclear core model for two-phase flows with phase transition {I:} stiffened gas law},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {1639--1679},
year = {2014},
publisher = {EDP-Sciences},
volume = {48},
number = {6},
doi = {10.1051/m2an/2014015},
mrnumber = {3264368},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1051/m2an/2014015/}
}
TY - JOUR AU - Bernard, Manuel AU - Dellacherie, Stéphane AU - Faccanoni, Gloria AU - Grec, Bérénice AU - Penel, Yohan TI - Study of a low Mach nuclear core model for two-phase flows with phase transition I: stiffened gas law JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2014 SP - 1639 EP - 1679 VL - 48 IS - 6 PB - EDP-Sciences UR - http://geodesic.mathdoc.fr/articles/10.1051/m2an/2014015/ DO - 10.1051/m2an/2014015 LA - en ID - M2AN_2014__48_6_1639_0 ER -
%0 Journal Article %A Bernard, Manuel %A Dellacherie, Stéphane %A Faccanoni, Gloria %A Grec, Bérénice %A Penel, Yohan %T Study of a low Mach nuclear core model for two-phase flows with phase transition I: stiffened gas law %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2014 %P 1639-1679 %V 48 %N 6 %I EDP-Sciences %U http://geodesic.mathdoc.fr/articles/10.1051/m2an/2014015/ %R 10.1051/m2an/2014015 %G en %F M2AN_2014__48_6_1639_0
Bernard, Manuel; Dellacherie, Stéphane; Faccanoni, Gloria; Grec, Bérénice; Penel, Yohan. Study of a low Mach nuclear core model for two-phase flows with phase transition I: stiffened gas law. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 48 (2014) no. 6, pp. 1639-1679. doi: 10.1051/m2an/2014015
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