No abstract

In this work, the Neutron Point Kinetics equations are solved for six groups of delayed neutron precursors and different types of ramp reactivity, considering the temperature effects by the Rosenbrock’s method, to verify the methodology. Furthermore, the classical model is solved by inserting the effects of the main neutron poisons, considering constant reactivity for a group of precursors. The simulation consists of inserting a negative constant reactivity, simulating a reactor in its shutdown phase. Then, positive constant reactivity is inserted, simulating power resumption in a reactor already poisoned, to analyzing the final behavior of the neutron density. The simulation achieved its goal of simulating the behavior of the neutron poisons, so that the graphs make physical sense as expected. Therefore, it was found that the proposed method overcame the stiffness of the Neutron Point Kinetics model, and also solved a nonlinear problem by the inclusion of temperature and neutron poisons in the system.

Os autores apresentam uma abordagem semi-analítica para obter soluções para as equações da cinética pontual de nêutrons. A reatividade dependente do tempo é aproximada por aproximação constante por partes em tempo discretizado, e o sistema de equações diferenciais é resolvido por um fator de integração. O termo de fonte externa na solução possui uma integral, que é resolvida numericamente pela interpolação de polinômios de Lagrange e uma fórmula simples de quadratura. Mesmo que a fonte externa apresente não linearidade nas equações, a metodologia é apropriada. A metodologia proposta é utilizada em casos de referência padrão e seus resultados são comparados com os da literatura.

In this paper, the solution of the  Neutron Point Kinetics model is presented, adding the effects of temperature and absorbers poisons within a historical and technical context to simulate the preliminary characteristics of the Chernobyl accident. The Point Kinetics model was able to extract physical information consistent with what was expected to predict the reactor situation until the accident. It was also possible to verify, given the results, that the Rosenbrock method was able to overcome the degree of stiffness of the ODE system, besides solving a non-linear problem. Thus, this study has contributed to highlighting the importance of temperature effects and especially absorbers poisons in the final power behavior, extremely relevant for decision making in the operation and safety of a nuclear power plant.