The prompt supercritical process of a nuclear reactor with temperature feedback and initial power as well as heat transfer with a big step reactivity (ρ0>β) is analyzed in this paper. Considering the effect of heat transfer on temperature of the reactor, a new model is set up. For any initial power, the variations of output power and reactivity with time are obtained by numerical method. The effects of the big inserted step reactivity and initial power on the prompt supercritical process are analyzed and discussed. It was found that the effect of heat transfer on the output power and reactivity can be neglected under any initial power, and the output power obtained by the adiabatic model is basically in accordance with that by the model of this paper, and the analytical solution can be adopted. The results provide a theoretical base for safety analysis and operation management of a power reactor.
The continuous indication of the neutron density and its rate of change are important for the safe startup and operation of reactors. The best way to achieve this is to obtain analytical solutions of the neutron kinetics equations because none of the developed numerical methods can well satisfy the need for real-time or even super-time computation for the safe startup and operation of reactors in practice. In this paper, an accurate analytical solution of point kinetics equations with one-group delayed neutrons and an extraneous neutron source is proposed to calculate the change in neutron density, where the whole process from the subcritical stage to critical and supercritical stages is considered for step reactivity insertions. The accurate analytical solution can also be used as a benchmark of all numerical methods employed to solve stiff neutron kinetics equations.
