Mathematical and computational models of nuclear reactor start-up physics and operations
File(s)
Author(s)
Gordon, Travis
Type
Thesis
Abstract
This thesis presents the stochastic and deterministic point-kinetic analyses associated with low neutron source nuclear reactor start-up and start-up accidents. Nuclear reactor kinetics in the absence of strong neutron sources is inherently stochastic. Firstly, the accuracy and computational efficiency of five models capable of simulating stochastic neutron kinetics are numerically compared. The merits of the Pál-Bell equations are highlighted against the forward probability balance equations, forward generating function equations, analogue Monte-Carlo, and Itô-calculus approaches. An overview of nuclear reactor start-up physics and the methods required to model the associated neutron kinetics is presented. The relationship between neutron source, neutron detectors, reactivity control mechanisms, approach to delayed-critical, and potential accident scenarios is explained. This thesis focuses on calculating the probability of a rogue stochastic transient during a nuclear reactor start-up accident. The numerical analysis required to ensure the accurate computation of the safety
probability is presented with a particular focus on very low neutron source strengths and very large ramp rates. The accuracy and computational efficiency of a new approximate method of calculating the maturity time is numerically compared against the conventional method. The new method does not require solving for the neutron population variance, is shown to be numerically accurate, and offers time savings of 90%. A new sub-critical wait-time experiment that can be performed using current zero power nuclear reactors while adhering to strict regulations is presented for the purposes of validating stochastic nuclear reactor codes such as CALLISTO-SPK. The Pál-Bell equations are not able to accommodate changes in the macroscopic neutron cross-sections arising from temperature and void changes or other physical processes. This thesis uses an Itô-calculus approach to investigate the consequence of not modelling feedback mechanisms within the Pál-Bell equations.
probability is presented with a particular focus on very low neutron source strengths and very large ramp rates. The accuracy and computational efficiency of a new approximate method of calculating the maturity time is numerically compared against the conventional method. The new method does not require solving for the neutron population variance, is shown to be numerically accurate, and offers time savings of 90%. A new sub-critical wait-time experiment that can be performed using current zero power nuclear reactors while adhering to strict regulations is presented for the purposes of validating stochastic nuclear reactor codes such as CALLISTO-SPK. The Pál-Bell equations are not able to accommodate changes in the macroscopic neutron cross-sections arising from temperature and void changes or other physical processes. This thesis uses an Itô-calculus approach to investigate the consequence of not modelling feedback mechanisms within the Pál-Bell equations.
Version
Open Access
Date Issued
2023-09-14
Date Awarded
01/12/2024
License URL
Advisor
Eaton, Matthew
Cooling, Christopher
McCoy, Emma
Haigh, Peter
Copestake, Alan
Sponsor
Engineering and Physical Sciences Research Council
Rolls-Royce Group plc
Grant Number
EP/R513052/1
Publisher Department
Mechanical Engineering
Publisher Institution
Imperial College London
Qualification Level
Doctoral
Qualification Name
Doctor of Philosophy (PhD)