A new approach for the optimal distribution of assemblies in a nuclear reactor

Abstract

The aim of this paper is to propose a new approach for optimizing the position of fuel assemblies in a nuclear reactor core. This is a control problem for the neutronic diffusion equation where the control acts on the coefficients of the equation. The goal is to minimize the power peak (i.e. the neutron flux must be as spatially uniform as possible) and maximize the reactivity (i.e. the efficiency of the reactor measured by the inverse of the first eigenvalue). Although this is truly a discrete optimization problem, our strategy is to embed it in a continuous one which is solved by the homogenization method. Then, the homogenized continuous solution is numerically projected on a discrete admissible distribution of assemblies.

Multi-phase structural optimizationviaa level set method

“…The Hadamard method of geometric shape optimization, as described in [21,27,36], was used, for example, in [26] for optimal composite design. The homogenization method [1,17,50] was the main tool in the multiphase problem studied in [3] for the optimal reloading of nuclear reactors (sequential laminates were shown to be optimal composite materials). In the framework of the SIMP (Solid Isotropic Material with Penalization) method, several interpolation schemes have been proposed for the mathematical formulation of the Hooke's tensor of the mixture [9,49,57].…”

Shape optimization of a Sodium Fast Reactor core

“…The equations of the continuous model are discretized with the finite element method on an initial mesh of 3.10 3 nodes. We have considered a domain ω whose dimensions are given in the table (2).…”

“…Those constraints would be chosen in order to take into account the size and the shape of the nuclear assemblies. This can be done either by adding some constraints directly in the algorithm or by performing a penalization method on the final shape (see [2]) .…”

“…The aim is to assess to what extent, such automatic way of improving the design could be positively employed. This kind of mathematical theory has already been investigated for optimizing the fuel reloading by the homogenization method (see [2]). We here restrict ourselves to the geometrical method.…”

“…Note that the application of our method leads to some designs whose interfaces can be parametrized by very smooth curves which can stand very far from realistic designs. We don't explain here the method that it would be possible to use for recovering an operational design but there exists several penalization methods (see [2]) that could be employed to this end.Résumé. On applique dans cet article une méthode d'optimisation géométrique dans le cadre de la conception d'un coeur de réacteur SFR (Sodium-cooled Fast Reactor, i.e.…”