Uncertainty and sensitivity analysis applied to LWR neutronic and thermal-hydraulic calculations
Doctoral thesis, 2012
The deterministic modeling of LWRs begins with the computation of energy‐collapsed and homogenized
macroscopic cross‐sections by means of a lattice code. Once these parameters are functionalized as a function
of the reactor state variables and discretized in space, they are used as input variables by core simulators in
order to calculate the spatial distribution of the neutron flux and thus, the spatial distribution of the power.
Once the power is determined, the thermal‐hydraulic variables are updated, and the process repeated until
convergence. This thesis is divided in three different parts related to the possible neutronic and thermalhydraulic
modeling strategies. In the first part, microscopic cross‐section uncertainties based on two modern
nuclear data libraries such as JENDL‐4 and ENDF/B‐VII.1 were derived in multi‐group format. These were
propagated through lattice calculations in order to perform uncertainty analysis on the infinite neutron
multiplication factor (, and on two‐group homogenized macroscopic cross‐sections corresponding to a PWR
fuel segment. The aim is to compare the uncertainty assessment on and on the macroscopic cross‐sections
when the different nuclear libraries are employed. It was found that the computed uncertainties based on
JENDL‐4 are much higher than the computed uncertainties based on ENDF/B‐VII.1. A sensitivity analysis
showed that the multi‐group variances of the Uranium‐235 fission reaction based on JENDL‐4 are very high,
being this the main reason of the observed large discrepancies in the different uncertainty assessments.
In the second part of the thesis, two types of uncertainty analyses were performed on core simulations. The
first one corresponds to the forward approach of input uncertainty propagation, where the input uncertain
space formed by the nodal two‐group macroscopic cross sections and diffusion coefficients is sampled both
with SRS and LHS. The possible ranges of variation of such an input space are based on data from a depletion
calculation corresponding to the cycle 26 of the Swedish Ringhals‐1 BWR. The aim of this study is to compare
the efficiency of the uncertainty assessment performed on the nodal thermal flux when SRS and LHS are
employed. On the other hand, in the second type of uncertainty analysis presented in this chapter,
discrepancies between spatial measured and calculated fluxes in Ringhals‐1 are used to perform an inverse
uncertainty analysis on the spatial dependence of the different core parameters. This analysis is carried out
using Bayesian statistics, where, for a certain cycle, the frequency distributions of macroscopic cross‐sections
and diffusion coefficients at every assembly node are updated based on the error distribution of the spatial
thermal flux. Emphasis was made on performing uncertainty analysis as well on the coefficients of a nodal
cross‐section model. Although a very simple model was derived, the aim is to propose an uncertainty
assessment based on replicated sampling techniques such as the general bootstrap method.
Finally, in the third part of the thesis, uncertainty and sensitivity analyses were applied to thermal‐hydraulic
calculations. The objective is to show that when experimental data are available, uncertainty analysis can be
used in the validation process of a BE code. Quantitative limits based on a statistical theory were computed to
validate code thermal‐hydraulic features in predicting pressure drop, void fraction and critical heat flux based
on the macroscopic exercises of the OECD/NRC BWR Full‐Size Fine‐Mesh Bundle Test (BFBT) benchmark.
The present study performs a realistic analysis of nuclear reactors, particularly in the uncertainty prediction of
important neutronic and thermal‐hydraulic parameters of light water reactors.
Nuclear best estimate codes