Eventos Anais de eventos
ENCIT 2016
16th Brazilian Congress of Thermal Sciences and Engineering
PERTURBATIVE ANALYSIS OF THE STEADY STATE MULTI-GROUP MULTI-LAYER NEUTRON DIFFUSION EQUATION IN CARTESIAN GEOMETRY BY FICTITIOUS BORDERS POWER METHOD
Submission Author:
Rodrigo Zanette , RS
Co-Authors:
Claudio Zen Petersen, Welton Menezes
Presenter: Rodrigo Zanette
doi://10.26678/ABCM.ENCIT2016.CIT2016-0020
Abstract
In this paper presents a perturbative analysis in the solution of one-dimensional steady state multi-layer multi-group neutron diffusion equation in cartesian geometry by Fictitious Borders Power Method. The equation is solved applying the iterative power method that consists in solve the neutron diffusion equation for each iteration in which the source term is always updated by neutron flux on the previous iteration. This iterative process of source is held until a determined stop criterion for the convergence of the solution. For each new iteration is added new terms which becomes very laborious. To overcome this problem is proposed the reconstruction of the neutron flux by polynomial interpolation. The solution remains in a standard form for all iterations. However, when modeled for large dimensions, in the interpolation arise Vandermonde's arrays which are almost singulars. To eliminate this singularity the domain is subdivided in R fictitious regions and solved the neutron diffusion equation for each region. The arbitrary constants arising from solution of the homogeneous problem are found applying boundary conditions, flux and current density continuity in the interfaces. To analyze the sensitivity of the nuclear parameters in the convergence and behavior of the solution is introduced a perturbation in each parameter of same magnitude order using a random fluctuation multiplied by a constant. The results obtained are compared with benchmark results present in the literature.
Keywords
neutron diffusion equation, power method, fictitious borders, perturbative analysis, neutron diffusion equation, power method, fictitious borders, perturbative analysis
