Study of a low Mach nuclear core model for single-phase flows

Manuel Bernard (1) , Stéphane Dellacherie (2) , Gloria Faccanoni (3) , Bérénice Grec (4) , Olivier Lafitte (5) , Tan Trung Nguyen (6) , Yohan Penel (7)

1 Inria Lille - Nord Europe
2 CEA-DES (ex-DEN) - CEA-Direction des Energies (ex-Direction de l'Energie Nucléaire)
3 IMATH - Institut de Mathématiques de Toulon - EA 2134
4 MAP5 - UMR 8145 - Mathématiques Appliquées Paris 5
5 LAGA - Laboratoire Analyse, Géométrie et Applications
6 LATP - Laboratoire d'Analyse, Topologie, Probabilités
7 SIMPAF - SImulations and Modeling for PArticles and Fluids

This paper deals with the modelling of the coolant (water) in a nuclear reactor core. This study is based on a monophasic low Mach number model (LMNC model) coupled to the stiffened gas law for a single-phase flow. Some analytical steady and unsteady solutions are presented for the 1D case. We then introduce a numerical scheme to simulate the 1D model in order to assess its relevance. Finally, we carry out a normal mode perturbation analysis in order to approximate 2D solutions around the 1D steady solutions.

Domaines: Analyse numérique [math.NA]; Equations aux dérivées partielles [math.AP]

Manuel Bernard, Stéphane Dellacherie, Gloria Faccanoni, Bérénice Grec, Olivier Lafitte, et al.. Study of a low Mach nuclear core model for single-phase flows. ESAIM: Proceedings, 2012, 38, pp.118-134. ⟨10.1051/proc/201238007⟩. ⟨hal-00662978⟩