Learning Centre

Numerical methods for nuclear fuel burnup calculations

 |  Login

Show simple item record

dc.contributor Aalto-yliopisto fi
dc.contributor Aalto University en
dc.contributor.advisor Leppänen, Jaakko, Dr., VTT Technical Research Centre of Finland
dc.contributor.author Pusa, Maria
dc.date.accessioned 2013-05-14T09:00:27Z
dc.date.available 2013-05-14T09:00:27Z
dc.date.issued 2013
dc.identifier.isbn 978-951-38-8000-2 (electronic)
dc.identifier.isbn 978-951-38-7999-0 (printed)
dc.identifier.issn 2242-1203 (electronic)
dc.identifier.issn 2242-119X (printed)
dc.identifier.issn 2242-119X (ISSN-L)
dc.identifier.uri https://aaltodoc.aalto.fi/handle/123456789/10159
dc.description.abstract The material composition of nuclear fuel changes constantly due to nuclides transforming to other nuclides via neutron-induced transmutation reactions and spontaneous radioactive decay. The objective of burnup calculations is to simulate these changes over time. This thesis considers two essential topics of burnup calculations: the numerical solution of burnup equations based on computing the burnup matrix exponential, and the uncertainty analysis of neutron transport criticality equation based on perturbation theory. The burnup equations govern the changes in nuclide concentrations over time. They form a system of first order differential equations that can be formally solved by computing the matrix exponential of the burnup matrix. Due to the dramatic variation in the half-lives of different nuclides, the system is extremely stiff and the problem is complicated by vast variations in the time steps used in burnup calculations. In this thesis, the mathematical properties of burnup matrices are studied. It is deduced that their eigenvalues are generally confined to a region near the negative real axis. Rational approximations that are accurate near the negative real axis, and the Chebyshev rational approximation method (CRAM) in particular, are proposed as a novel method for solving the burnup equations. The results suggest that the proposed approach is capable of providing a robust and accurate solution to the burnup equations with a very short computation time. When a mathematical model contains uncertain parameters, this uncertainty is propagated to responses dependent on the model. This thesis studies the propagation of neutron interaction data uncertainty through the criticality equation on a fuel assembly level. The considered approach is based on perturbation theory, which allows computing the sensitivity profiles of a response with respect to any number of parameters in an efficient manner by solving an adjoint system in addition to the original forward problem. The uncertainty related to these parameters can then be propagated deterministically to the response by linearizing the response. en
dc.format.extent 92 + app. 82
dc.format.mimetype application/pdf
dc.language.iso en en
dc.publisher Aalto University en
dc.publisher Aalto-yliopisto fi
dc.relation.ispartofseries VTT Science en
dc.relation.ispartofseries 32
dc.relation.haspart [Publication 1]: M. Pusa and J. Leppänen, “Computing the matrix exponential in burnup calculations”, Nucl. Sci. Eng., 164, 2, 140–150 (2010).
dc.relation.haspart [Publication 2]: M. Pusa, “Rational approximations to the matrix exponential in burnup calculations”, Nucl. Sci. Eng., 169, 2, 155–167 (2011).
dc.relation.haspart [Publication 3]: M. Pusa, “Correction to partial fraction decomposition coefficients for Chebyshev rational approximation on the negative real axis”, arXiv:1206.2880v1[math.NA] (2012).
dc.relation.haspart [Publication 4]: M. Pusa and J. Leppänen, “Solving linear systems with sparse Gaussian elimination in the Chebyshev rational approximation method (CRAM)”, accepted for publication in Nucl. Sci. Eng. (Nov 2013).
dc.relation.haspart [Publication 5]: M. Pusa, “Incorporating sensitivity and uncertainty analysis to a lattice physics code with application to CASMO-4”, Ann. Nucl. Energy, 40, 1, 153–162 (2012).
dc.relation.haspart [Publication 6]: M. Pusa, “Perturbation-theory-based sensitivity and uncertainty analysis with CASMO-4”, Sci. Technol. Nucl. Install., 2012, 157029 (2012).
dc.subject.other Energy en
dc.subject.other Physics en
dc.title Numerical methods for nuclear fuel burnup calculations en
dc.type G5 Artikkeliväitöskirja fi
dc.contributor.school Perustieteiden korkeakoulu fi
dc.contributor.school School of Science en
dc.contributor.department Matematiikan ja systeemianalyysin laitos fi
dc.contributor.department Department of Mathematics and Systems Analysis en
dc.subject.keyword burnup equations en
dc.subject.keyword Chebyshev rational approximation en
dc.subject.keyword CRAM en
dc.subject.keyword matrix exponential en
dc.subject.keyword sensitivity analysis en
dc.subject.keyword uncertainty analysis en
dc.identifier.urn URN:ISBN:978-951-38-8000-2
dc.type.dcmitype text en
dc.type.ontasot Doctoral dissertation (article-based) en
dc.type.ontasot Väitöskirja (artikkeli) fi
dc.contributor.supervisor Nevanlinna, Olavi, Prof., Aalto University, Finland
dc.opn Munthe-Kaas, Antonella Zanna, Prof., University of Bergen, Norway
dc.rev Kodeli, Ivan, Dr., Jožef Stefan Institute, Slovenia
dc.rev Tuomela, Jukka, Prof., University of Eastern Finland

Files in this item

This item appears in the following Collection(s)

Show simple item record

Search archive

Advanced Search

article-iconSubmit a publication