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


Type
Thesis
Change log
Authors
Abstract

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.

Description
Date
2020-04-27
Advisors
Shwageraus, Eugene
Keywords
Nuclear, Monte Carlo, Reactor, Neutron transport, Isotopic depletion
Qualification
Doctor of Philosophy (PhD)
Awarding Institution
University of Cambridge
Sponsorship
EPSRC (1818942)
EPSRC ICO-CDT