POWER-SERIES SOLUTIONS OF THE REACTOR KINETICS EQUATIONS

Accurate solutions of the reactor kinetics equations in a lumped model with time-varying reactivity have been obtained using a spreadsheet o n a personal computer (PC)/workstation from a straightforward power se ries recurrence relation. These have been shown to converge readily ov er time steps of similar to 1/3 s in models of a thermal reactor. Solu tions over such macrosteps can readily be extended to durations of int erest (similar to 100 s). Examples are given for both a ramp reactivit y input and an oscillating reactivity. This latter shows in a direct f ashion 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 fas t reactors. It is concluded that accurate calculations of thermal and fast reactor transients, obtained analytically with considerable diffi culty, are readily available to the student on a PC.