Random fluctuations in nuclear reactors : stochastic point kinetics equations with two-energy groups

Abstract

ABSTRACT: Dynamics of a nuclear reactor is described on the basis of the mean values of the neutronnucleus interactions. The Point Kinetics equations model uses these values to describe the time evolution of the neutron population in homogeneous reactors. Significant random fluctuations of the neutron population are observed at the reactor startup and shutdown, caused by the statistical nature of the system and due to unexpected events, such as sub-cooled boiling, pressure fluctuations, and mechanical vibrations of control and fuel rods, among others. The Point kinetics equations cannot describe these fluctuations due to their deterministic nature. An adequate description of the reactor dynamics is achieved through stochastic models, such as the stochastic Point Kinetics equations, which provides accurate information on the mean values and standard deviations of the neutron populations. However, this model considers mono-energetic neutrons, which is far from reality. In addition, the realizations of the stochastic process do not adequately describe the reactor dynamics. The aim of this study is adding physical rigor to the stochastic model of the Point Kinetics equations by discriminating in energy the neutron population, which determines the probability of interaction with atomic nuclei; and to propose a solution to the problem of the stochastic realizations of the related process. The outcome is a stochastic model with realizations in agreement with reality, and predictions of both the mean values and the standard deviations, which turns out to be in good agreement with experimental and simulated data reported previously. These comparisons show that our stochastic model accurately describes the random behavior of the neutron population in a homogeneous nuclear reactor. Finally, it is worth mentioning that, as result of the research work of this Master program, the next two publications are being prepared (see Appendix A for details): 1. Theta Method Applied to Two-Energy Groups Point Kinetics Equations. 2. Stochastic Point Reactor Kinetics Equations with Two-Energy Groups.