Numerical stability of Monte Carlo neutron transport and isotopic depletion for nuclear reactor analysis

Coupling Monte Carlo neutron transport with isotopic depletion is known to produce non-physical results for large reactor geometries. This thesis begins with a survey of the stable methods used to avoid this and highlights some of their drawbacks. Chapter 2 introduces the known phenomenon of neutron clustering in Monte Carlo as a factor strongly contributing to previous reports of instability. It is shown that attempting to minimise clustering effects produces more stable burn-up calculations. Furthermore, accounting for clustering is shown to allow for the accurate simulation of xenon transients in simple systems which have been noted to pose a challenge for burn-up simulations. Finally, it is demonstrated that neutron clustering can also affect burn-up simulations substantially even when xenon equilibrium is enforced, namely by way of the previously hypothesised `gadolinium instabilities'. Chapter 3 begins by highlighting how implicit burn-up schemes may be viewed as root-finding schemes for a discrete map. It is shown that, for reasonably long time-steps, the corrector step of predictor-corrector schemes does not succeed in locating the root (or the stable solution) of this map. Hence, relaxation schemes are introduced; relaxation schemes have been applied to neutronics/depletion coupling previously in the form of the stochastic approximation, although this is relatively inefficient. The relaxation scheme proposed here uses a fixed relaxation factor (rather than the variable factor previously used) and demonstrates its improved stability and computational efficiency compared to the stochastic approximation. The same investigations are applied to a depletion problem where equilibrium xenon is enforced -- it is seen that this, too, can be unstable, but is resolvable through relaxation. Chapter 4 performs a Von Neumann stability analysis of a simple coupled neutron diffusion-depletion system. Extending a previous analysis, this chapter provides a justification for applying a relaxation to predictor-corrector schemes, shows the possibility of obtaining symmetric burn-up instabilities, and demonstrates that no neutronics-depletion coupling scheme, without relaxation, is assuredly more stable than another, depending on the depletion system in question. Finally, Chapter 5 summarises the findings, proposes an explanation regarding general cases of burn-up instability, and suggests future work.

Name dc:type.qualificationname

Doctor of Philosophy (PhD)

Level dc:type.qualificationlevel

Doctoral

Grantor dc:publisher.institution

University of Cambridge

Year dc:date.issued

2020

Author dc:creator

• Cosgrove, Paul

Advisor dc:contributor.advisor

• Shwageraus, Eugene

• Nuclear
• Monte Carlo
• Reactor
• Neutron transport
• Isotopic depletion

Licence

• https://apollo8-f-pro.lib.cam.ac.uk/bitstreams/ea3050b9-cb57-4823-aca8-f717685240b8/download
• https://www.rioxx.net/licenses/all-rights-reserved/

Language dc:language

eng

Author Identifier

0000-0003-2829-6299

OAI identifier oai:identifier

oai:www.repository.cam.ac.uk:1810/311429