Power Series Solutions of the Reactor Kinetics Equations

Abstract

Accurate solutions of the reactor kinetics equations in a lumped model with time-varying reactivity have been obtained using a spreadsheet on a personal computer (PC)/workstation from a straightforward power series recurrence relation. These have been shown to converge readily over time steps of in models of a thermal reactor. Solutions over such macrosteps can readily be extended to durations of interest (∼100 s). Examples are given for both a ramp reactivity input and an oscillating reactivity. This latter shows in a direct fashion the first-order phase distortion and the second-order effect on power level that are generally associated with perturbation solutions that have to be taken to second order. The method applies also to fast reactors. It is concluded that accurate calculations of thermal and fast reactor transients, obtained analytically with considerable difficulty, are readily available to the student on a PC.