Perturbative Analysis of the Neutron Point Kinetics Equations with and without Temperature Feedback Effects by Polynomial Approach Method

Fernanda Tumelero¹; Claudio Zen Petersen¹

¹ Universidade Federal de Pelotas (UFPel)

doi:10.20906/CPS/COB-2015-0498

Resumo

In this paper, we report a perturbative analysis of the Neutron Point Kinetics Equations with and without temperature feedback effects by Polynomial Approach Method. The idea of the method is to expand the neutron density, delayed neutron precursors concentration and temperature as a power series considering the reactivity as an arbitrary function of time in a short time span interval around an ordinary point. In the first interval one applies the initial conditions of the problem and the analytical continuation is used to determine the solutions of the next intervals. The objective of this analysis is to verify the stability of the method before perturbations included both in reactivity as in the initial condition to study the behavior of the linear and non-linear stiff differential equations. For the perturbation in reactivity, one considers different functions types: constant, ramp, quadratic, zig-zag, sinusoidal and pulsed source. Furthermore, one varies the time step size of the Polynomial Approach Method and performs an analysis of variance and one calculates the relative errors between the solutions with and without perturbation.

Palavras-chave: Perturbation Analysis; Neutron Point Kinetics Equations; Polynomial Approximation Method; Temperature Feedback