Numerical and semi-analytical solution of a transient during the start-up of a slab reactor with circulating fuel at zero power

Abstract

We have developed semi-analytical solutions for a space–time dependent transient during start-up of a circulating fuel reactor with finite flow velocity. The simpler case of infinite flow velocity is also analytically treated. Via comparisons with our in-house 1D multigroup diffusion code which solves time-dependent problems of circulating fuel reactors, we have verified both the numerical and semi-analytical solutions. The highly oscillatory temporal dependence of the flux and the precursor density require the use of high precision arithmetic for Laplace inversion in the semi-analytical solution. The effect of arithmetic precision on the accuracy of the semi-analytical solution is also investigated. The semi-analytical solutions provide a tool for the verification of numerical methods developed for the transient neutronic analysis of circulating fuel reactors.