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.
Highlights
The safety of a nuclear power plant is an extremely relevant topic in reactor physics
Inside the reactor core, there must be an equilibrium in the neutron balance, referring to the loss and gain of neutrons, ensuring control in the chain reaction for energy generation.It is in this sense that researchers in the area have invested in studies through models and mathematical methods that describe accurately, quickly and reliably the physical situation of the problem, important for decision making and operational control of a nuclear power plant. athematical models in nuclear reactor physics must take into account all aspects, variables and possible modifications in the reactor structure by internal and external agents, influencing the nuclear reaction and, the final analysis in the overall reactor behavior
The results are presented for the model with temperature feedback and, subsequently, for the model coupled to the effects of the main neutron absorbers poisons
Summary
The safety of a nuclear power plant is an extremely relevant topic in reactor physics. The most complete physico-mathematical model, when time-dependent and considering delayed neutrons [1], which determines the neutron population is known as the Neutron Transport equation. This model becomes impossible to solve when considering in its composition angular, energy, spatial and temporal variation in the equations. Even so, according to the literature, other models have been ensuring the simulation of the transient behavior of nuclear reactors, important for reactor control These models can be obtained through the Kinetics equations, which can be divided into the equations of the Neutron Point Kinetics (NPKE) and the equations of the Neutron Spatial Kinetics (NSKE). The model employed is that of Neutron Point Kinetics considering temperature effects and, subsequently, neutron absorbers poisons
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