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.

sensitivity analysis

Nuclear best estimate codes

uncertainty analysis


Augusto Hernandéz Solís

Chalmers, Chemical and Biological Engineering, Nuclear Chemistry

In recent years, it has been recognized by the nuclear community that if useful conclusions are to be obtained from BE codes, these should be supplemented by a quantitative uncertainty analysis. In this thesis, uncertainty and sensitivity analysis is performed on neutronic and thermal‐hydraulic calculations of LWRs. A statistical approach is employed, where the non‐deterministic treatment of a physical model that induces a stochastic nature on the code outputs is based on a sampling methodology. The preferred sampling strategy for the current study corresponds to the quasi‐random Latin Hypercube Sampling (LHS). This technique allows a much better coverage of the input uncertainties than simple random sampling (SRS) because it densely stratifies across the range of each input probability distribution. This is one of the first works that employs LHS to sample the input uncertain space, and then relies on the concept of non‐parametric tolerance intervals for the code output uncertainty assessment for both neutronic and thermal‐hydraulic calculations. It is shown at the different stages in the modeling of LWRs that LHS offers the possibility to assess more realistic non‐parametric tolerance limits than SRS, because code non‐linearities are much better handled when the input space is covered in an efficient way.

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Doktorsavhandlingar vid Chalmers tekniska högskola. Ny serie

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