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

• Published in: Annals of nuclear energy Vol. 153; p. 108080
• Main Authors: Ozgener, Huseyin Atila, Ozgener, Bilge
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.04.2021
• Subjects: Circulating fuel reactors; high precision Laplace inversion; Semi-analytical solution; Start-up transient; Verification of numerical solution; Semi-analytical solution; Start-up transient; Verification of numerical solution; Circulating fuel reactors; high precision Laplace inversion
• ISSN: 0306-4549; 1873-2100
• DOI: 10.1016/j.anucene.2020.108080

•The start-up of a CFR from a critical no-flow state to a critical flow state is analyzed.•A one energy and one precursor group slab diffusion model with known flow velocity is used.•The transient is solved numerically by a diffusion code and analytically by the Laplace method.•Our analysis showed the existence of power oscillations with period equal to circulation time.•The numerical and semi-analytical solutions with enough precision arithmetic agree perfectly. 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.