Abstract
The material composition of nuclear fuel changes
constantly due to nuclides transforming
to other nuclides via neutroninduced 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 halflives 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.
Original language  English 

Qualification  Doctor Degree 
Awarding Institution 

Supervisors/Advisors 

Award date  24 May 2013 
Place of Publication  Espoo 
Publisher  
Print ISBNs  9789513879990 
Electronic ISBNs  9789513880002 
Publication status  Published  2013 
MoE publication type  G5 Doctoral dissertation (article) 
Keywords
 burnup equations
 Chebyshev rational approximation
 CRAM
 matrix exponential
 sensitivity analysis
 uncertainty analysis
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Pusa, M. (2013). Numerical methods for nuclear fuel burnup calculations: Dissertation. VTT Technical Research Centre of Finland. http://www.vtt.fi/inf/pdf/science/2013/S32.pdf