On a low Mach nuclear core model

Abstract

We propose to formally derive a low Mach number model adapted to the modeling of a water nuclear core (e.g. of PWR- or BWR-type) in the forced convection regime or in the natural convection regime by filtering out the acoustic waves in the compressible Navier-Stokes system. Then, we propose a monodimensional stationary analytical solution with regular and singular charge loss when the equation of state is a stiffened gas equation. Moreover, we show that this solution may not be admissible from a physical or a mathematical point of view for a particular choice of the mass flux and we study the consistency between this solution and the solution obtained from a Boussinesq approximation. Let us underline that the modeling of the nuclear core is simplified in this paper. For example, the flow is a single-phase flow and we do not model neither the porosity nor the turbulence. Nevertheless, it will be possible to enrich the modeling in the future.