Academic literature on the topic 'Stochastic neutronics'

Uncertainty Quantification (UQ) of numerical simulations is highly relevant in the study and design of complex systems. Among the various approaches available, Polynomial Chaos Expansion (PCE) analysis has recently attracted great interest. It belongs to nonintrusive spectral projection methods and consists of constructing system responses as polynomial functions of the stochastic inputs. The limited number of required model evaluations and the possibility to apply it to codes without any modification make this technique extremely attractive. In this work, we propose the use of PCE to perform UQ of complex, multi-physics models for liquid fueled reactors, addressing key design aspects of neutronics and thermal fluid dynamics. Our PCE approach uses Smolyak sparse grids designed to estimate the PCE coefficients. To test its potential, the PCE method was applied to a 2D problem representative of the Molten Salt Fast Reactor physics. An in-house multi-physics tool constitutes the reference model. The studied responses are the maximum temperature and the effective multiplication factor. Results, validated by comparison with the reference model on 103 Monte-Carlo sampled points, prove the effectiveness of our PCE approach in assessing uncertainties of complex coupled models.

We present a model of detectors operating with classical random fields and producing probabilities described by the formalism of quantum mechanics. The basic assumption of this measurement theory is that the probability of detection of field (= signal) is proportional to the power of this field. (Therefore we call this approach "power signal-field detection theory" – PFSDT.) Our approach has some similarities with stochastic electrodynamics. However, formalisms describing random fields – "quantum fluctuations" – are different. Moreover, our approach all particles are represented by random fields, e.g., electronic or neutronic field. Thus we have various types of "quantum fluctuations".

Asymptotic expressions for the bound state radial partial wave functions of three-body (nnc) halo nuclei with two loosely bound valence neutrons (n) are obtained in explicit form, when the relative distance between two neutrons (r) tends to infinity and the relative distance between the center of mass of core (c) and two neutrons (ρ) is too small or vice versa. These asymptotic expressions contain a factor that can strongly influence the asymptotic values of the three-body radial wave function in the vicinity of the hyperangle of φ~0 except 0 (r→∞ and ρ is too small except 0) or φ~π/2 except π/2 (ρ→∞ and r is too small except 0) in the configuration space. The derived asymptotic forms are applied to the analysis of the asymptotic behavior of the three-body (nnα) wave function for 6He nucleus obtained by other authors on the basis of multicluster stochastic variational method using the two forms of the αN-potential. The ranges of r (or ρ) from the asymptotical regions are determined for which the agreement between the calculated wave function and the asymptotics formulae is reached. Information about the values of the three-body asymptotic normalization factors is extracted.

Integral experiments in reactors or critical configurations claim to have very small experimental and technological uncertainties. Therefore these latter can be considered valuable experimental information in nuclear data evaluation. Because in the evaluation process the information is carried by model parameters, to perform a rigorous feedback on a nuclear model parameters p - for instance using a measured reactivity ρ-sensitivities S =∂ρ/ρ⁄∂p/p are needed. In usual integral feedbacks, sensitivity to multi-group cross sections are first obtained with deterministic code using perturbation theory. Then these multi-group cross section sensitivities are “convoluted” with parameter sensitivities in order to provide the sensitivity on nuclear model parameter. Recently stochastic approaches have been elaborated in order to obtain continuous cross-section sensitivities thus avoiding the multi-group discretization. In the present work we used the recent Iterated Fission Probability method of the TRIPOLI4 code [1] in order to obtain directly the sensitivity to nuclear physics parameters. We focus here on the sensitivity on resonance parameters and exemplified the method on the computation of sensitivities for 239Pu and 16O resonance parameters one the ICSBEP benchmark PST001. The underlying nuclear model describing resonant cross sections are based in the R-matrix formalism [2] that provides not only the interaction cross sections but also the angular distribution of the scattered neutrons i.e. differential cross sections. The method has thus been updated in order to compute parameter sensitives that include both contributions: cross section and angular distributions. This extension of the method was tested with exact perturbation of angular distribution and fission spectrum.

La nécessité de simulations précises d’un réacteur nucléaire et spécialement dans des cas de cœurs et de configurations de combustible complexes, a imposé un usage accru de Codes Neutroniques Stochastiques (CNS). De plus, une demande a émergé pour des CNS à capacité inhérente d’estimation en continu de la variation de la composition isotopique du cœur ainsi qu’à couplage thermo-hydraulique optimisé. Des capacités supplémentaires sont exigées pour ces codes au vu de leur utilisation pour l’étude de nouveaux concepts de réacteur comme les Réacteurs Conduits par Accélérateur (RCA). Plus précisément, le réacteur hybride comprenant un réacteur nucléaire conventionnel et un accélérateur, nécessite l’analyse des deux composantes (réacteur – accélérateur) par un outil capable de couvrir le spectre énergétique neutronique extrêmement étendu qui caractérise ce système hybride.Ce travail présente les principales caractéristiques et capacités du nouveau CNS ANET (Advanced Neutronics with Evolution and Thermal hydraulic feedback) développé en collaboration du NCSR Demokritos (Grèce) avec CNRS/IDRIS et UPMC (France) et couvrant autant que possible les exigences exposées ci-dessus. ANET est basé sur la version ouverte du code PHE GEANT3.21 et est destiné à effectuer des analyses de cœurs de réacteurs conventionnels de génération II et III ainsi que des RCA. ANET est construit avec la capacité inhérentea) d’effectuer des calculs d’évolution du combustibleb) de simuler le processus de spallation dans le cas des RCAtout en tenant compte de la thermo-hydraulique du système.La version actuelle d’ANET utilise les trois estimateurs standard Monte Carlo pour le calcul du facteur de multiplication neutronique effectif (keff), soit l’estimateur de collision, celui d’absorption et celui de longueur de trace. Pour ce qui est du calcul du débit de fluence neutronique et des taux de réaction, les estimateurs de collision et de longueur de trace sont implémentés dans ANET suivant la procédure standard Monte Carlo. Pour ce qui concerne les calculs d’évolution (par exemple la consommation du combustible), une approche purement stochastique est implémentée dans ANET. A noter que la procédure usuelle consiste à coupler le code neutronique stochastique avec un code déterministe qui calcule la consommation du combustible. Pour les besoins d’analyse des RCA, le module INCL/ABLA a été incorporé dans ANET de façon à ce que le processus de spallation soit simulé par le code. La capacité d’ANET de simuler des configurations classiques a été démontrée en utilisant des résultats de mesures et des simulations de vérification effectuées en utilisant d’autres codes bien établis, ainsi qu’il est montré par la suite.Des données provenant de plusieurs installations et des analyses de problèmes-type internationaux ont été utilisés pour vérifier et valider les capacités d’ANET.Pour conclure, les résultats obtenus lors des comparaisons avec des mesures ou avec des simulations effectuées en utilisant d’autres codes neutroniques stochastiques ou déterministes, montrent qu’ANET possède la capacité de calculer correctement d’importants paramètres de systèmes critiques ou sous-critiques. Par ailleurs, l’application préliminaire d’ANET à des problèmes dépendant du temps fournit des résultats encourageants. ANET produit des estimations de consommation de combustible raisonnables, compte tenu que des incertitudes dans ce domaine sont souvent de l’ordre de 20% ou plus. Finalement, les performances du code dans le cas de KUCA montrent qu’ANET peut analyser des RCA de façon satisfaisante
The necessity for precise simulations of a nuclear reactor especially in case of complex core and fuel configurations has imposed the increasing use of Monte Carlo (MC) neutronics codes. Besides, a demand of additional stochastic codes’ inherent capabilities has emerged regarding mainly the simulation of the temporal variations in the core isotopic composition as well as the incorporation of the T-H feedback. In addition to the above, the design of innovative nuclear reactor concepts, such as the Accelerator Driven System (ADSs), imposed extra requirements of simulation capabilities. More specifically, the combination of an accelerator and a nuclear reactor in the ADS requires the simulation of both subsystems for an integrated system analysis. Therefore a need arises for more advanced simulation tools, able to cover the broad neutrons energy spectrum involved in these systems.This work presents the main features and capabilities of the new MC neutronics code ANET (Advanced Neutronics with Evolution and Thermal hydraulic feedback), being developed in NCSR Demokritos (Greece) in cooperation with CNRS/IDRIS and UPMC (France) and intending to meet as effectively as possible the above described modelling requirements. ANET is based on the open-source version of the HEP code GEANT3.21 and is targeting to the creation of an enhanced computational tool in the field of reactor analysis, capable of simulating both GEN II/III reactors and ADSs. ANET is structured with inherent capability of (a) performing burnup calculations and (b) simulating the spallation process in the ADS analysis, while taking T-H feedback into account.The current ANET version utilizes the three standard Monte Carlo estimators for the neutron multiplication factor (keff) calculation, i.e. the collision estimator, the absorption estimator and the track-length estimator. Regarding the simulation of neutron fluence and reaction rates, the collision and the track-length estimators are implemented in ANET following the standard Monte Carlo procedure. For the burnup calculations ANET attempts to apply a pure Monte Carlo approach, adopting the typical procedure followed in stochastic codes. With respect to code improvements for the ADS analysis, so far ANET has incorporated the INCL/ABLA code so that the spallation process can be inherently simulated. The ANET reliability in typical computations was tested using observational data and parallel simulations by different codes as described in the following chapters.Various installations and international benchmarks were considered suitable for the verification and validation of all the previously mentioned features incorporated in the new code ANET. The obtained results are compared with experimental data from the nuclear infrastructures and with computations performed by well-established stochastic or deterministic neutronics codes and show satisfactory agreement with both measurements and independent computations, verifying thus ANET’s ability to successfully simulate important parameters of critical and subcritical systems. Also, the preliminary ANET application for dynamic analysis is encouraging since it indicates the code capability to inherently provide a reasonable prediction for the core inventory evolution taking into account the uncertainties of the order of 20% and even higher that are traditionally expected in core inventory evolution calculations. Lastly, the code performance in the KUCA case was found satisfactory demonstrating thus inherent capability of analyzing ADSs

L’un des principaux objectifs de la physique des réacteurs nucléaires est de caractériser la répartition aléatoire de la population de neutrons au sein d’un réacteur. Les fluctuations de cette population sont liées à la nature stochastique des interactions des neutrons avec les noyaux fissiles du milieu : diffusion, capture stérile, ou encore émission de plusieurs neutrons lors de la fission d’un noyau. L’ensemble de ces mécanismes physiques confère une structure aléatoire branchante à la trajectoire des neutrons, alors modélisée par des marches aléatoires. Avec environs 10⁸ neutrons par centimètre cube dans un réacteur de type REP à pleine puissance en conditions stationnaires, les grandeurs physiques du système (flux, taux de réaction, énergie déposée) sont, en première approximation, bien représentées par leurs valeurs moyennes respectives. Ces observables physiques moyennes obéissent alors à l’équation de transport linéaire de Boltzmann. Au cours de ma thèse, je me suis penchée sur deux aspects du transport qui ne sont pas décrits par cette équation, et pour lesquels je me suis appuyée sur des outils issus de la théorie des marches aléatoires. Tout d’abord, grâce au formalisme de Feynman-Kac, j’ai étudié les fluctuations statistiques de la population de neutrons, et plus particulièrement le phénomène de « clustering neutronique », qui a été mis en évidence numériquement pour de faibles densités de neutrons (typiquement un réacteur au démarrage). Je me suis ensuite intéressée à différentes propriétés de la statistique d’occupation des neutrons effectuant un transport anormal (càd non-exponentiel). Ce type de transport permet de modéliser le transport dans des matériaux fortement hétérogènes et désordonnés, tel que les réacteurs à lit de boulets. L’un des aspects novateurs de ce travail est la prise en compte de la présence de bords. En effet, bien que les systèmes réels soient de taille finie, la plupart des résultats théoriques pré-existants sur ces thématiques ont été obtenus sur des systèmes de taille infinie
One of the key goals of nuclear reactor physics is to determine the distribution of the neutron population within a reactor core. This population indeed fluctuates due to the stochastic nature of the interactions of the neutrons with the nuclei of the surrounding medium: scattering, emission of neutrons from fission events and capture by nuclear absorption. Due to these physical mechanisms, the stochastic process performed by neutrons is a branching random walk. For most applications, the neutron population considered is very large, and all physical observables related to its behaviour, such as the heat production due to fissions, are well characterised by their average values. Generally, these mean quantities are governed by the classical neutron transport equation, called linear Boltzmann equation. During my PhD, using tools from branching random walks and anomalous diffusion, I have tackled two aspects of neutron transport that cannot be approached by the linear Boltzmann equation. First, thanks to the Feynman-Kac backward formalism, I have characterised the phenomenon of “neutron clustering” that has been highlighted for low-density configuration of neutrons and results from strong fluctuations in space and time of the neutron population. Then, I focused on several properties of anomalous (non-exponential) transport, that can model neutron transport in strongly heterogeneous and disordered media, such as pebble-bed reactors. One of the novel aspects of this work is that problems are treated in the presence of boundaries. Indeed, even though real systems are finite (confined geometries), most of previously existing results were obtained for infinite systems

Des milieux hétérogènes et désordonnés émergent dans plusieurs applications de la science et de l'ingénierie nucléaires, en particulier en ce qui concerne la propagation des neutrons et des photons. Les exemples sont très répandus et concernent par exemple la double hétérogénéité des éléments combustibles dans les réacteurs à lit de boulets ou l'évaluation de la probabilité de re-criticité suite aux arrangements aléatoires du combusitble résultant d'accidents graves. Dans cette thèse, nous étudierons le transport linéaire de particules dans des milieux aléatoires. Dans la première partie, nous nous concentrerons sur quelques modèles mathématiques qui peuvent être utilisés pour la description de matériaux aléatoires. Une attention particulière sera accordée aux tessellations stochastiques, où un domaine est partitionné en polyèdres convexes en échantillonnant des hyperplans aléatoires selon une probabilité donnée. Les inclusions stochastiques de sphères dans une matrice seront également brièvement introduites. Un code informatique sera développé afin de construire explicitement de telles géométries par des méthodes de Monte Carlo. Dans la deuxième partie, nous évaluerons ensuite les caractéristiques générales du transport de particules dans des milieux aléatoires. Pour ce faire, nous allons considérer quelques benchmarks assez simples pour permettre une compréhension approfondie des effets des géométries aléatoires sur les trajectoires de particules tout en conservant les propriétés clés du transport linéaire. Les calculs de transport seront réalisés en utilisant le code de transport de particules Monte Carlo Tripoli4, développé au SERMA. Les cas de modèles de désordre quenched et annealed seront considérés séparément. Dans le premier, un ensemble de géométries sera généré en utilisant notre code, et le problème de transport sera résolu pour chaque configuration: des moyennes d'ensemble seront alors prises pour les observables d'intérêt. Dans le second cas, un modèle de transport efficace capable de reproduire les effets du désordre dans une seule réalisation sera étudié. Les approximations des modèles annealed seront élucidées, et des améliorations significatives seront proposées
Heterogeneous and disordered media emerges in several applications in nuclear science and engineering, especially in relation to neutron and photon propagation. Examples are widespread and concern for instance the double-heterogeneity of the fuel elements in pebble-bed reactors, or the assessment of re-criticality probability due to the random arrangement of fuel resulting from severe accidents. In this Thesis, we will investigate linear particle transport in random media. In the first part, we will focus on some mathematical models that can be used for the description of random media. Special emphasis will be given to stochastic tessellations, where a domain is partitioned into convex polyhedra by sampling random hyperplanes according to a given probability. Stochastic inclusions of spheres into a matrix will be also briefly introduced. A computer code will be developed in order to explicitly construct such geometries by Monte Carlo methods. In the second part, we will then assess the general features of particle transport within random media. For this purpose, we will consider some benchmark problems that are simple enough so as to allow for a thorough understanding of the effects of the random geometries on particle trajectories and yet retain the key properties of linear transport. Transport calculations will be realized by using the Monte Carlo particle transport code Tripoli4, developed at SERMA. The cases of quenched and annealed disorder models will be separately considered. In the former, an ensemble of geometries will be generated by using our computer code, and the transport problem will be solved for each configuration: ensemble averages will then be taken for the observables of interest. In the latter, effective transport model capable of reproducing the effects of disorder in a single realization will be investigated. The approximations of the annealed disorder models will be elucidated, and significant ameliorations will be proposed

This PhD study, developed at Universitat Politècnica de València (UPV), aims to cover the first phase of the benchmark released by the expert group on Uncertainty Analysis in Modeling (UAM-LWR). The main contribution to the benchmark, made by the thesis' author, is the development of a MATLAB program requested by the benchmark organizers. This is used to generate neutronic libraries to distribute among the benchmark participants. The UAM benchmark pretends to determine the uncertainty introduced by coupled multi-physics and multi-scale LWR analysis codes. The benchmark is subdivided into three phases: 1. Neutronic phase: obtain collapsed and homogenized problem-dependent cross sections and criticality analyses. 2. Core phase: standalone thermohydraulic and neutronic codes. 3. System phase: coupled thermohydraulic and neutronic code. In this thesis the objectives of the first phase are covered. Specifically, a methodology is developed to propagate the uncertainty of cross sections and other neutronic parameters through a lattice physics code and core simulator. An Uncertainty and Sensitivity (U&S) analysis is performed over the cross sections contained in the ENDF/B-VII nuclear library. Their uncertainty is propagated through the lattice physics code SCALE6.2.1, including the collapse and homogenization phase, up to the generation of problem-dependent neutronic libraries. Afterward, the uncertainty contained in these libraries can be further propagated through a core simulator, in this study PARCSv3.2. The module SAMPLER -available in the latest release of SCALE- and DAKOTA 6.3 statistical tool are used for the U&S analysis. As a part of this process, a methodology to obtain neutronic libraries in NEMTAB format -to be used in a core simulator- is also developed. A code-to-code comparison with CASMO-4 is used as a verification. The whole methodology is tested using a Boiling Water Reactor (BWR) reactor type. Nevertheless, there is not any concern or limitation regarding its use in any other type of nuclear reactor. The Gesellschaft für Anlagen und Reaktorsicherheit (GRS) stochastic methodology for uncertainty quantification is used. This methodology makes use of the high-fidelity model and nonparametric sampling to propagate the uncertainty. As a result, the number of samples (determined using the revised Wilks' formula) does not depend on the number of input parameters but only on the desired confidence and uncertainty of output parameters. Moreover, the output Probability Distribution Functions (PDFs) are not subject to normality. The main disadvantage is that each input parameter must have a pre-defined PDF. If possible, input PDFs are defined using information found in the related literature. Otherwise, the uncertainty definition is based on expert judgment. A second scenario is used to propagate the uncertainty of different thermohydraulic parameters through the coupled code TRACE5.0p3/PARCSv3.0. In this case, a PWR reactor type is used and a transient control rod drop occurrence is simulated. As a new feature, the core is modeled chan-by-chan following a fully 3D discretization. No other study is found using a detailed 3D core. This U&S analysis also makes use of the GRS methodology and DAKOTA 6.3.
Este trabajo de doctorado, desarrollado en la Universitat Politècnica de València (UPV), tiene como objetivo cubrir la primera fase del benchmark presentado por el grupo de expertos Uncertainty Analysis in Modeling (UAM-LWR). La principal contribución al benchmark, por parte del autor de esta tesis, es el desarrollo de un programa de MATLAB solicitado por los organizadores del benchmark, el cual se usa para generar librerías neutrónicas a distribuir entre los participantes del benchmark. El benchmark del UAM pretende determinar la incertidumbre introducida por los códigos multifísicos y multiescala acoplados de análisis de reactores de agua ligera. El citado benchmark se divide en tres fases: 1. Fase neutrónica: obtener los parámetros neutrónicos y secciones eficaces del problema específico colapsados y homogenizados, además del análisis de criticidad. 2. Fase de núcleo: análisis termo-hidráulico y neutrónico por separado. 3. Fase de sistema: análisis termo-hidráulico y neutrónico acoplados. En esta tesis se completan los principales objetivos de la primera fase. Concretamente, se desarrolla una metodología para propagar la incertidumbre de secciones eficaces y otros parámetros neutrónicos a través de un código lattice y un simulador de núcleo. Se lleva a cabo un análisis de incertidumbre y sensibilidad para las secciones eficaces contenidas en la librería neutrónica ENDF/B-VII. Su incertidumbre se propaga a través del código lattice SCALE6.2.1, incluyendo las fases de colapsación y homogenización, hasta llegar a la generación de una librería neutrónica específica del problema. Luego, la incertidumbre contenida en dicha librería puede continuar propagándose a través de un simulador de núcleo, para este estudio PARCSv3.2. Para el análisis de incertidumbre y sensibilidad se ha usado el módulo SAMPLER -disponible en la última versión de SCALE- y la herramienta estadística DAKOTA 6.3. Como parte de este proceso, también se ha desarrollado una metodología para obtener librerías neutrónicas en formato NEMTAB para ser usadas en simuladores de núcleo. Se ha realizado una comparación con el código CASMO-4 para obtener una verificación de la metodología completa. Esta se ha probado usando un reactor de agua en ebullición del tipo BWR. Sin embargo, no hay ninguna preocupación o limitación respecto a su uso con otro tipo de reactor nuclear. Para la cuantificación de la incertidumbre se usa la metodología estocástica Gesellschaft für Anlagen und Reaktorsicherheit (GRS). Esta metodología hace uso del modelo de alta fidelidad y un muestreo no paramétrico para propagar la incertidumbre. Como resultado, el número de muestras (determinado con la fórmula revisada de Wilks) no depende del número de parámetros de entrada, sólo depende del nivel de confianza e incertidumbre deseados de los parámetros de salida. Además, las funciones de distribución de probabilidad no están limitadas a normalidad. El principal inconveniente es que se ha de disponer de las distribuciones de probabilidad de cada parámetro de entrada. Si es posible, las distribuciones de probabilidad de entrada se definen usando información encontrada en la literatura relacionada. En caso contrario, la incertidumbre se define en base a la opinión de un experto. Se usa un segundo escenario para propagar la incertidumbre de diferentes parámetros termo-hidráulicos a través del código acoplado TRACE5.0p3/PARCSv3.0. En este caso, se utiliza un reactor tipo PWR para simular un transitorio de una caída de barra. Como nueva característica, el núcleo se modela elemento a elemento siguiendo una discretización totalmente en 3D. No se ha encontrado ningún otro estudio que use un núcleo tan detallado en 3D. También se usa la metodología GRS y el DAKOTA 6.3 para este análisis de incertidumbre y sensibilidad.
Aquest treball de doctorat, desenvolupat a la Universitat Politècnica de València (UPV), té com a objectiu cobrir la primera fase del benchmark presentat pel grup d'experts Uncertainty Analysis in Modeling (UAM-LWR). La principal contribució al benchmark, per part de l'autor d'aquesta tesi, es el desenvolupament d'un programa de MATLAB sol¿licitat pels organitzadors del benchmark, el qual s'utilitza per a generar llibreries neutròniques a distribuir entre els participants del benchmark. El benchmark del UAM pretén determinar la incertesa introduïda pels codis multifísics i multiescala acoblats d'anàlisi de reactors d'aigua lleugera. El citat benchmark es divideix en tres fases: 1. Fase neutrònica: obtenir els paràmetres neutrònics i seccions eficaces del problema específic, col¿lapsats i homogeneïtzats, a més de la anàlisi de criticitat. 2. Fase de nucli: anàlisi termo-hidràulica i neutrònica per separat. 3. Fase de sistema: anàlisi termo-hidràulica i neutrònica acoblats. En aquesta tesi es completen els principals objectius de la primera fase. Concretament, es desenvolupa una metodologia per propagar la incertesa de les seccions eficaces i altres paràmetres neutrònics a través d'un codi lattice i un simulador de nucli. Es porta a terme una anàlisi d'incertesa i sensibilitat per a les seccions eficaces contingudes en la llibreria neutrònica ENDF/B-VII. La seua incertesa es propaga a través del codi lattice SCALE6.2.1, incloent les fases per col¿lapsar i homogeneïtzar, fins aplegar a la generació d'una llibreria neutrònica específica del problema. Després, la incertesa continguda en la esmentada llibreria pot continuar propagant-se a través d'un simulador de nucli, per a aquest estudi PARCSv3.2. Per a l'anàlisi d'incertesa i sensibilitat s'ha utilitzat el mòdul SAMPLER -disponible a l'última versió de SCALE- i la ferramenta estadística DAKOTA 6.3. Com a part d'aquest procés, també es desenvolupa una metodologia per a obtenir llibreries neutròniques en format NEMTAB per ser utilitzades en simuladors de nucli. S'ha realitzat una comparació amb el codi CASMO-4 per obtenir una verificació de la metodologia completa. Aquesta s'ha provat utilitzant un reactor d'aigua en ebullició del tipus BWR. Tanmateix, no hi ha cap preocupació o limitació respecte del seu ús amb un altre tipus de reactor nuclear. Per a la quantificació de la incertesa s'utilitza la metodologia estocàstica Gesellschaft für Anlagen und Reaktorsicherheit (GRS). Aquesta metodologia fa ús del model d'alta fidelitat i un mostreig no paramètric per propagar la incertesa. Com a resultat, el nombre de mostres (determinat amb la fórmula revisada de Wilks) no depèn del nombre de paràmetres d'entrada, sols depèn del nivell de confiança i incertesa desitjats dels paràmetres d'eixida. A més, las funcions de distribució de probabilitat no estan limitades a la normalitat. El principal inconvenient és que s'ha de disposar de les distribucions de probabilitat de cada paràmetre d'entrada. Si és possible, les distribucions de probabilitat d'entrada es defineixen utilitzant informació trobada a la literatura relacionada. En cas contrari, la incertesa es defineix en base a l'opinió d'un expert. S'utilitza un segon escenari per propagar la incertesa de diferents paràmetres termo-hidràulics a través del codi acoblat TRACE5.0p3/PARCSv3.0. En aquest cas, s'utilitza un reactor tipus PWR per simular un transitori d'una caiguda de barra. Com a nova característica, cal assenyalar que el nucli es modela element a element seguint una discretizació totalment 3D. No s'ha trobat cap altre estudi que utilitze un nucli tan detallat en 3D. També s'utilitza la metodologia GRS i el DAKOTA 6.3 per a aquesta anàlisi d'incertesa i sensibilitat.¿
Mesado Melia, C. (2017). Uncertainty Quantification and Sensitivity Analysis for Cross Sections and Thermohydraulic Parameters in Lattice and Core Physics Codes. Methodology for Cross Section Library Generation and Application to PWR and BWR [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/86167
TESIS

AbstractCross-section uncertainties of Pb and Bi isotopes could consequently affect the precision of nuclear design calculations of preliminary analyses, before the actual operation of upcoming ADS, since Pb and Bi are composed partly of coolant material (lead-bismuth eutectic: LBE) in ADS facilities. The main characteristics of LBE in ADS are recognized as follows: chemically inactive; high boiling point mechanically; excellent neutron economy caused by large scattering cross sections. From the viewpoint of neutronics, LBE exerts considerable impact on nuclear design parameters for numerical simulations of neutron interactions of Pb and Bi isotopes. As a suitable way of investigating cross-section uncertainties, sample reactivity worth measurements in critical states are considered effective with the use of reference and test materials in a zero-power state, such as a critical assembly, because integral parameter information on cross sections of test materials can be acquired experimentally. For the required experimental study on Pb and Bi nuclear data uncertainties, the sample reactivity worth experiments are carried out at the KUCA core by the substitution of reference (aluminum) for test (Pb or Bi) materials, and numerical simulations are performed with stochastic and deterministic calculation codes together with major nuclear data libraries.

In recent years there has been an increasing demand from nuclear research, industry, safety, and regulation bodies for best estimate predictions of Light Water Reactors (LWR’s) performances to be provided with their confidence bounds. From a neutronic point of view, among the different sources of uncertainty the main challenge is represented by the one related to the accuracy of the nuclear data libraries used in the transport calculations. The assessment of nuclear data uncertainties and their impact on the main reactor parameters plays a fundamental role not only for criticality safety but also in burnup analyses. In facts, the accurate prediction of nuclear parameters in burnup calculations strongly affects the management of spent nuclear fuel, the core design, as well as the economy and safety of nuclear reactors. In this paper a study related to the impact of the nuclear data uncertainties on the evolution in time of the criticality and the nuclide concentrations in burnup calculations is presented. The analysis has been performed by using a statistical sampling methodology in which all the uncertain parameters are handled as random dependent variables by a sampling procedure. The probability distributions of the uncertain input parameters are used to generate random variations of these input quantities starting from a covariance library in a 56-group energy structure. Calculations have been performed by means of the SCALE 6.2.2 code and ENDF/B-VII.1 nuclear data. The method has been tested on a PWR pin cell model representative of the TMI-1 15 × 15 assembly as defined in an international benchmark exercise. In the first part of the paper the methodology and the neutronics modelling of the problem are presented.

Under the cooperative effort of the Civil Nuclear Energy R&D Working Group within the framework of the U.S.-Japan bilateral, Argonne National Laboratory (ANL) and Japan Atomic Energy Agency (JAEA) have been performing benchmark study using Japan Sodium-cooled Fast Reactor (JSFR) design with metal fuel. In this benchmark study, core characteristic parameters at the beginning of cycle were evaluated by the best estimate deterministic and stochastic methodologies of ANL and JAEA. The results obtained by both institutions are agreed well with less than 200 pcm of discrepancy on the neutron multiplication factor, and less than 3% of discrepancy on the sodium void reactivity, Doppler reactivity, and control rod worth. The results by the stochastic and deterministic were compared in each party to investigate impacts of the deterministic approximation and to understand potential variations in the results due to different calculation methodologies employed. Impacts of the nuclear data libraries were also investigated using a sensitivity analysis methodology.

Nuclear reactor simulation is often based on multi-group cross-section libraries. The structure and resolution of these libraries have a strong influence on the accuracy and computational time; hence, number of groups and energy structure must be carefully considered. The relationship between group structures and how they impact generated cross-sections can be a critical parameter. Common energy boundaries shared among major group structures were identified and the relative kinship among those was reconstructed in an effort to build a family tree of major group structures. Stochastic code Serpent2 [1] was employed to generate cross-sections of selected isotopes at different reactor compositions and conditions, using the investigated energy group structures. The impact on their generation was quantified by spectral weighted deviation. The 35 major energy structures were divided into three basic families. The key parameters distinguishing them were their applicability to thermal or fast reactors and their applicability in neutronic or multiphysics investigations. A sensitivity threshold of the generated cross-sections over the group structure resolution was investigated. The aim was to identify a group structure with very low dependency on the actual reactor spectrum.

Research Centre Rez solves several safety related projects dealing with safety of Czech NPPs, some of which require fully functioning Three Dimensional (3D) model of the reactor core. While in a number of safety analysis of various accident scenarios it is sufficient to use one point reactor kinetics, there are selected types of accidents in which it is useful to model the space (3D) neutron kinetics, in particular control rod ejections, boron dilution scenarios, including transitions from design basis to beyond design basis accidents. This paper is focused to analyze the present model of the core of VVER1000/V320 reactor. Which is applicable for 3D modeling of neutron kinetics in selected design and beyond design basis accidents. The model is based on a cross-sections library created by SCALE 6.1.2/TRITON simulations. PARCS 3.2 code uses homogenized cross-sections libraries to calculate neutronic and other core parameters of the PWR reactors. Similar model is prepared with MCNP6 for comparison between deterministic (Pn spherical-harmonics method used in PARCS) and the stochastic (Monte Carlo) approach (used in MCNP6). Such comparison will serve as a demonstration of the capability of the PARCS code for VVER1000/V320 analyses.

In the framework of surveillance program dosimetry, the main parameter in the determination of the fracture toughness and the integrity of the reactor pressure vessel (RPV) is the fast neutron fluence on pressure vessel. Its calculated value is extrapolated using neutron transport codes from measured reaction rate value on dosimeters located on the core barrel. EDF R&D has developed a new 3D tool called EFLUVE3D based on the adjoint flux theory. This tool is able to reproduce on a given configuration the neutron flux, fast neutron fluence and reaction rate or dpa results of an exact Monte Carlo calculation with nearly the same accuracy. These EFLUVE3D calculations does the Source*Importance product which allows the calculation of the flux, the neutronic fluence (flux over 1MeV integrated on time) received at any point of the interface between the skin and the pressure vessel but also at the capsules of the pressurized water reactor vessels surveillance program and the dpa and reaction rates at different axial positions and different azimuthal positions of the vessel as well as at the surveillance capsules. Moreover, these calculations can be carried out monthly for each of the 58 reactors of the French current fleet in challenging time (less than 10mn for the total fluence and reaction rates calculations considering 14 different neutron sources of a classical power plant unit compared to more than 2 days for a classic Monte Carlo flux calculation at a given neutron source). The code needs as input: - for each reaction rate, the geometric importance matrix produced for a 3D pin by pin mesh on the basis of Green’s functions calculated by the Monte Carlo code TRIPOLI; - the neutron sources calculated on assemblies data (enrichment, position, fission fraction as a function of evolution), pin by pin power and irradiation. These last terms are based on local in-core activities measurements extrapolated to the whole core by use of the EDF core calculation scheme and a pin by pin power reconstruction methodology. This paper presents the fundamental principles of the code and its validation comparing its results to the direct Monte Carlo TRIPOLI results. Theses comparisons show a discrepancy of less than 0,5% between the two codes equivalent to the order of magnitude of the stochastic convergence of Monte Carlo results.