Westinghouse Electric Sweden AB’s three-dimensional reactor core simulation program POLCA uses a large number of tables containing various fuel dependent data, such as cross sections, pin power maps with power distribution etc. POLCA uses quadratic and linear interpolation to extract the values needed for the simulation. However, finding the correct values to interpolate between takes time. This master thesis describes a method of compacting the tables by removing values, in order to shorten the needed simulation time. This is done so that no significant accuracy is lost in the interpolations. The method also finds deviant values and replaces these with new, interpolated values. The thesis shows that approximately 90 % of all values can be removed without losing significant accuracy. These results are however heavily dependent on the choice of accuracy loss criterion; a lower allowance for accuracy loss lowers the amount of values which can be removed sharply.

<div>This dissertation is devoted to developing a first-of-a-kind uncertainty characterization framework (UCF) providing comprehensive, efficient and scientifically defendable methodologies for uncertainty characterization (UC) in best-estimate (BE) reactor physics simulations. The UCF is designed with primary application to CANDU neutronics calculations, but could also be applied to other thermal-spectrum reactor systems. The overarching goal of the UCF is to propagate and prioritize all sources of uncertainties, including those originating from nuclear data uncertainties, modeling assumptions, and other approximations, in order to reliably use the results of BE simulations in the various aspects of reactor design, operation, and safety. The scope of this UCF is to propagate nuclear data uncertainties from the multi-group format, representing the input to lattice physics calculations, to the few-group format, representing the input to nodal diffusion-based core simulators and quantify the uncertainties in reactor core attributes.</div><div>The main contribution of this dissertation addresses two major challenges in current uncertainty analysis approaches. The first is the feasibility of the UCF due to the complex nature of nuclear reactor simulation and computational burden of conventional uncertainty quantification (UQ) methods. The second goal is to assess the impact of other sources of uncertainties that are typically ignored in the course of propagating nuclear data uncertainties, such as various modeling assumptions and approximations.</div>To deal with the first challenge, this thesis work proposes an integrated UC process employing a number of approaches and algorithms, including the physics-guided coverage mapping (PCM) method in support of model validation, and the reduced order modeling (ROM) techniques as well as the sensitivity analysis (SA) on uncertainty sources, to reduce the dimensionality of uncertainty space at each interface of neutronics calculations. In addition to the efficient techniques to reduce the computational cost, the UCF aims to accomplish four primary functions in uncertainty analysis of neutronics simulations. The first function is to identify all sources of uncertainties, including nuclear data uncertainties, modeling assumptions, numerical approximations and technological parameter uncertainties. Second, the proposed UC process will be able to propagate the identified uncertainties to the responses of interest in core simulation and provide uncertainty quantifications (UQ) analysis for these core attributes. Third, the propagated uncertainties will be mapped to a wide range of reactor core operation conditions. Finally, the fourth function is to prioritize the identified uncertainty sources, i.e., to generate a priority identification and ranking table (PIRT) which sorts the major sources of uncertainties according to the impact on the core attributes’ uncertainties. In the proposed implementation, the nuclear data uncertainties are first propagated from multi-group level through lattice physics calculation to generate few-group parameters uncertainties, described using a vector of mean values and a covariance matrix. Employing an ROM-based compression of the covariance matrix, the few-group uncertainties are then propagated through downstream core simulation in a computationally efficient manner.<div>To explore on the impact of uncertainty sources except for nuclear data uncertainties on the UC process, a number of approximations and assumptions are investigated in this thesis, e.g., modeling assumptions such as resonance treatment, energy group structure, etc., and assumptions associated with the uncertainty analysis itself, e.g., linearity assumption, level of ROM reduction and associated number of degrees of freedom employed. These approximations and assumptions have been employed in the literature of neutronic uncertainty analysis yet without formal verifications. The major argument here is that these assumptions may introduce another source of uncertainty whose magnitude needs to be quantified in tandem with nuclear data uncertainties. In order to assess whether modeling uncertainties have an impact on parameter uncertainties, this dissertation proposes a process to evaluate the influence of various modeling assumptions and approximations and to investigate the interactions between the two major uncertainty sources. To explore this endeavor, the impact of a number of modeling assumptions on core attributes uncertainties is quantified.</div><div>The proposed UC process has first applied to a BWR application, in order to test the uncertainty propagation and prioritization process with the ROM implementation in a wide range of core conditions. Finally, a comprehensive uncertainty library for CANDU uncertainty analysis with NESTLE-C as core simulator is generated compressed uncertainty sources from the proposed UCF. The modeling uncertainties as well as their impact on the parameter uncertainty propagation process are investigated on the CANDU application with the uncertainty library.</div>

名古屋大学博士学位論文 学位の種類:博士(工学) 学位授与年月日:平成19年9月28日

Dans le cadre des études de neutronique menées pour réacteurs de GEN-IV, les nouveaux outils de calcul des cœurs de réacteur sont implémentés dans l’ensemble du code APOLLO3® pour la partie déterministe. Ces méthodes de calculs s’appuient sur des données nucléaires discrétisée en énergie (appelées multi-groupes et généralement produites par des codes déterministes eux aussi) et doivent être validées et qualifiées par rapport à des calculs basés sur la méthode de référence Monte-Carlo. L’objectif de cette thèse est de mettre au point une technique alternative de production des propriétés nucléaires multi-groupes par un code de Monte-Carlo (TRIPOLI-4®). Dans un premier temps, après avoir réalisé des tests sur les fonctionnalités existantes de l’homogénéisation et de la condensation avec des précisions meilleures accessibles aujourd’hui, des incohérences sont mises en évidence. De nouveaux estimateurs de paramètres multi-groupes ont été développés et validés pour le code TRIPOLI-4®à l’aide de ce code lui-même, puisqu’il dispose de la possibilité d’utiliser ses propres productions de données multi-groupes dans un calcul de cœur. Ensuite, la prise en compte de l’anisotropie de la diffusion nécessaire pour un bon traitement de l’anisotropie introduite par des fuites des neutrons a été étudiée. Une technique de correction de la diagonale de la matrice de la section efficace de transfert par diffusion à l’ordre P1 (nommée technique IGSC et basée sur une évaluation du courant des neutrons par une technique introduite par Todorova) est développée. Une amélioration de la technique IGSC dans la situation où les propriétés matérielles du réacteur changent drastiquement en espace est apportée. La solution est basée sur l’utilisation d’un nouveau courant qui est projeté sur l’axe X et plus représentatif dans la nouvelle situation que celui utilisant les approximations de Todorova, mais valable seulement en géométrie 1D. A la fin, un modèle de fuite B1 homogène est implémenté dans le code TRIPOLI-4® afin de produire des sections efficaces multi-groupes avec un spectre critique calculé avec l’approximation du mode fondamental. Ce modèle de fuite est analysé et validé rigoureusement en comparant avec les autres codes : Serpent et ECCO ; ainsi qu’avec un cas analytique.L’ensemble de ces développements dans TRIPOLI-4® permet de produire des sections efficaces multi-groupes qui peuvent être utilisées dans le code de calcul de cœur SNATCH de la plateforme PARIS. Ce dernier utilise la théorie du transport qui est indispensable pour la nouvelle filière à neutrons rapides. Les principales conclusions sont : -Le code de réseau en Monte-Carlo est une voie intéressante (surtout pour éviter les difficultés de l’autoprotection, de l’anisotropie limitée à un certain ordre du développement en polynômes de Legendre, du traitement des géométries exactes 3D), pour valider les codes déterministes comme ECCO ou APOLLO3® ou pour produire des données pour les codes déterministes ou Monte-Carlo multi-groupes.-Les résultats obtenus pour le moment avec les données produites par TRIPOLI-4® sont comparables mais n’ont pas encore vraiment montré d’avantage par rapport à ceux obtenus avec des données issues de codes déterministes tel qu’ECCO. / In the framework of the Generation IV reactors neutronic research, new core calculation tools are implemented in the code system APOLLO3® for the deterministic part. These calculation methods are based on the discretization concept of nuclear energy data (named multi-group and are generally produced by deterministic codes) and should be validated and qualified with respect to some Monte-Carlo reference calculations. This thesis aims to develop an alternative technique of producing multi-group nuclear properties by a Monte-Carlo code (TRIPOLI-4®).At first, after having tested the existing homogenization and condensation functionalities with better precision obtained nowadays, some inconsistencies are revealed. Several new multi-group parameters estimators are developed and validated for TRIPOLI-4® code with the aid of itself, since it has the possibility to use the multi-group constants in a core calculation.Secondly, the scattering anisotropy effect which is necessary for handling neutron leakage case is studied. A correction technique concerning the diagonal line of the first order moment of the scattering matrix is proposed. This is named the IGSC technique and is based on the usage of an approximate current which is introduced by Todorova. An improvement of this IGSC technique is then presented for the geometries which hold an important heterogeneity property. This improvement uses a more accurate current quantity which is the projection on the abscissa X. The later current can represent the real situation better but is limited to 1D geometries.Finally, a B1 leakage model is implemented in the TRIPOLI-4® code for generating multi-group cross sections with a fundamental mode based critical spectrum. This leakage model is analyzed and validated rigorously by the comparison with other codes: Serpent and ECCO, as well as an analytical case.The whole development work introduced in TRIPLI-4® code allows producing multi-group constants which can then be used in the core calculation solver SNATCH in the PARIS code platform. The latter uses the transport theory which is indispensable for the new generation fast reactors analysis. The principal conclusions are as follows:-The Monte-Carlo assembly calculation code is an interesting way (in the sense of avoiding the difficulties in the self-shielding calculation, the limited order development of anisotropy parameters, the exact 3D geometries) to validate the deterministic codes like ECCO or APOLLO3® and to produce the multi-group constants for deterministic or Monte-Carlo multi-group calculation codes. -The results obtained for the moment with the multi-group constants calculated by TRIPOLI-4 code are comparable with those produced from ECCO, but did not show remarkable advantages.