Development of three-dimensional capabilities for modelling stationary fluctuations in nuclear reactor cores

Abstract

This paper presents the development of a numerical tool meant at modelling the effect of stationary fluctuations in nuclear cores for systems cooled with either liquid water or boiling water. The originating fluctuations are defined for the variables describing the boundary conditions of the system, i.e. inlet velocity, inlet enthalpy, and outlet pressure. The tool then determines in the frequency domain the three-dimensional distributions within the core of the corresponding fluctuations in neutron flux, coolant density, coolant velocity, coolant enthalpy, and fuel temperature. The tool is thus based on the simultaneous modelling of neutron transport, fluid dynamics, and heat transfer in a truly integrated and fully coupled manner. The modelling of neutron transport relies on the two-group diffusion approximation and a spatial discretization based on finite differences. The modelling of fluid dynamics is performed using the Homogeneous Equilibrium Model, with a void fraction correction based on a pre-computed distribution of the static slip ratio (when two-phase flow conditions are encountered). Heat conduction in the fuel pins is also accounted for, and the heat transfer between the fuel pins and the coolant is modelled also using a pre-computed distribution of the heat transfer coefficient. The spatial discretization of the fluid dynamic and heat transfer problems is carried out using finite volumes. The tool, currently entirely Matlab based, requires minimal input data, mostly in form of the three-dimensional distributions of the macroscopic cross-sections and their relative dependence on coolant density and fuel temperature, the point-kinetic parameters of the core, as well as the three-dimensional distribution of the slip ratio (in case of two-phase flow conditions) and of the heat transfer coefficient. Such data can be provided by any static core simulator that thus needs to be run prior to using the present tool. In addition to briefly summarizing the different test cases used to verify the code, the paper also presents the results of simulations performed for a typical Pressurized Water Reactor and for a typical Boiling Water Reactor, as illustrations of the capabilities of the tool.