원자로 동특성 해석을 위한 확률 모델 개발

Abstract

To predict the space-time dependent behavior of a nuclear reactor, the conventional space-dependent kinetics equations are widely used for treating the spatial variables. However, the solutions of such deterministic space-dependent kinetics equations, which give only the mean values of the neutron population and the delayed neutron precursor concentrations, do not offer sufficient insight into the actual dynamic processes within a reactor, where the interacting populations vary randomly with space and time. It is also noted that at high power levels, the random behavior of a reactor is negligible but at low power levels, such as at start-up, random fluctuations in population dynamics can be significant. To mathematically describe the evolution of the state of a nuclear reactor using a set of stochastic kinetics equations, the forward stochastic model (FSM) in stochastic kinetics theory is devised through the concept of reactor transition probability and its probability generating function as the spatial domain of a reactor is partitioned into a number of space cells. Nevertheless, the FSM equations for the mean value of neutron and precursor distribution are deterministic-like. Furthermore, the numerical treatment of the FSM equations for the means, variances, and covariances is quite complicated and time-consuming. In the present study, a generalized stochastic model (called the stochastic space-dependent kinetics model or SSKM) based on the FSM and the It� stochastic differential equations was newly developed for the analysis of monoenergetic space-time nuclear reactor kinetics in one dimension. First, the FSM equations for determining the mean values of neutron and delayed-neutron precursor populations were considered as the deterministic ones without taking into account their variances and covariances. Second, the system of interest was randomized again in the light of the It� stochastic differential equations in order to derive the SSKM. The proposed model (SSKM), which can be considered as a generalization of the stochastic point-kinetics equations, was then validated by testing against analog Monte Carlo calculations for cases of slab reactors. The comparative results showed that the SSKM agrees well within about 5% with the Monte Carlo method. Also, the SSKM was confirmed to provide a fast calculation method in comparison with the Monte Carlo computations. Finally, an additional numerical investigation was conducted using the SSKM in order to observe the random fluctuations in population dynamics under various reactor transients. The numerical results, which appear plausible on a physical basis, demonstrate that the behavior of the stochastic neutron and precursor distributions within a reactor can be explicitly induced by using the SSKM. Thus, it is realized that the SSKM can be applied to reactor transient and safety analysis with possibility of predicting the trends in variances of the interacting populations in advance.