Cálculo de função importância aplicado a problemas unidimensionais do transporte de nêutrons na formulação de ordenadas discretas (SN)

Abstract

When studying variations in nuclear reactor parameters, it is useful to calculate an importance function associated with an integral quantity (a measurable physical quantity). This integral quantity may be linear in the angular neutron flux, such as reactor core power or neutron absorption rate. The calculation of this importance function is realized using the adjoint formulation of neutron transport linear equation, which is obtained through mathematical definitions. Given the nature of the neutron transport equations, the adjoint formulation can be derived from the discretized balance equations written in matrix format or from the balance equation before making the appropriate discretizations. In the first case, the mathematical adjoint importance function is obtained and, in the second case, the physical adjoint importance function is obtained, which are not necessarily equivalent. Therefore, in this work, the importances functions, physical and mathematical, were calculated for one-dimensional fixed source problems, in the multigroups formulation of energy and isotropic scattering for multiplicative and nonmultiplicative medium. To solve these problems, the Discrete Ordinate (SN) formulation was used to discretize the angular variable and the Diamond Difference (DD) method was used to discretize the spatial variable. In this way, it was verified that when using these discretization methods, the importance functions are not equivalent, but there is a similarity relation between them. Furthermore, this relation arises automatically from the application of discretization methods in the calculation of the integral quantity, making it possible to use both, the physical importance function and the mathematical importance function, for your determination. This statement was verified for the calculation of reaction rates and obtained the same results, using both importances functions.