Effects of cross sections tables generation and optimization on rod ejection transient analyses

Best estimate analysis of rod ejection transients requires 3D kinetics core simulators. If they use cross sections libraries compiled in multidimensional tables,interpolation errors – originated when the core simulator computes the cross sections from the table values – are a source of uncertainty in k-effective calculations that should be accounted for. Those errors depend on the grid covering the domain of state variables and can be easily reduced, in contrast with other sources of uncertainties such as the ones due to nuclear data, by choosing an optimized grid distribution. The present paper assesses the impact of the grid structure on a PWR rod ejection transient analysis using the coupled neutron-kinetics/thermal-hydraulicsCOBAYA3/COBRA-TF system. Forthispurpose, the OECD/NEA PWR MOX/UO2 core transient benchmark has been chosen, as material compositions and geometries are available, allowing the use of lattice codes to generate libraries with different grid structures. Since a complete nodal cross-section library is also provided as part of the benchmark specifications, the effects of the library generation on transient behavior are also analyzed.Results showed large discrepancies when using the benchmark library and own-generated libraries when compared with benchmark participants’ solutions. The origin of the discrepancies was found to lie in the nodal cross sections provided in the benchmark.

Application of the Boundary Method to the determination of the properties of the beam cross-sections

Using the 3-D equations of linear elasticity and the asylllptotic expansion methods in terms of powers of the beam cross-section area as small parameter different beam theories can be obtained, according to the last term kept in the expansion. If it is used only the first two terms of the asymptotic expansion the classical beam theories can be recovered without resort to any "a priori" additional hypotheses. Moreover, some small corrections and extensions of the classical beam theories can be found and also there exists the possibility to use the asymptotic general beam theory as a basis procedure for a straightforward derivation of the stiffness matrix and the equivalent nodal forces of the beam. In order to obtain the above results a set of functions and constants only dependent on the cross-section of the beam it has to be computed them as solutions of different 2-D laplacian boundary value problems over the beam cross section domain. In this paper two main numerical procedures to solve these boundary value pf'oblems have been discussed, namely the Boundary Element Method (BEM) and the Finite Element Method (FEM). Results for some regular and geometrically simple cross-sections are presented and compared with ones computed analytically. Extensions to other arbitrary cross-sections are illustrated.

Shear stress distribution on beam cross-sections under shear loading

In this work, some results obtained by Trabucho and Viaño for the shear stress distribution in beam cross sections using asymptotic expansions of the three-dimensional elasticity equations are compared with those calculated by the classical formulae of the Strength of Materials. We use beams with rectangular and circular cross section to compare the degree of accuracy reached by each method.

Steps Ahead in the Few-Group CRoss-Section Library Generation at the Pin Level

There exists an interest in performing pin-by-pin calculations coupled with thermal hydraulics so as to improve the accuracy of nuclear reactor analysis. In the framework of the EU NURISP project, INRNE and UPM have generated an experimental version of a few group diffusion cross sections library with discontinuity factors intended for VVER analysis at the pin level with the COBAYA3 code. The transport code APOLLO2 was used to perform the branching calculations. As a first proof of principle the library was created for fresh fuel and covers almost the full parameter space of steady state and transient conditions. The main objective is to test the calculation schemes and post-processing procedures, including multi-pin branching calculations. Two library options are being studied: one based on linear table interpolation and another one using a functional fitting of the cross sections. The libraries generated with APOLLO2 have been tested with the pin-by-pin diffusion model in COBAYA3 including discontinuity factors; first comparing 2D results against the APOLLO2 reference solutions and afterwards using the libraries to compute a 3D assembly problem coupled with a simplified thermal-hydraulic model.

Core physics and safety analysis of Generation-IV Sodium Fast Reactors using existing and newly developed computational tools

El futuro de la energía nuclear de fisión dependerá, entre otros factores, de la capacidad que las nuevas tecnologías demuestren para solventar los principales retos a largo plazo que se plantean. Los principales retos se pueden resumir en los siguientes aspectos: la capacidad de proporcionar una solución final, segura y fiable a los residuos radiactivos; así como dar solución a la limitación de recursos naturales necesarios para alimentar los reactores nucleares; y por último, una mejora robusta en la seguridad de las centrales que en definitiva evite cualquier daño potencial tanto en la población como en el medio ambiente como consecuencia de cualquier escenario imaginable o más allá de lo imaginable. Siguiendo estas motivaciones, la Generación IV de reactores nucleares surge con el compromiso de proporcionar electricidad de forma sostenible, segura, económica y evitando la proliferación de material fisible. Entre los sistemas conceptuales que se consideran para la Gen IV, los reactores rápidos destacan por su capacidad potencial de transmutar actínidos a la vez que permiten una utilización óptima de los recursos naturales. Entre los refrigerantes que se plantean, el sodio parece una de las soluciones más prometedoras. Como consecuencia, esta tesis surgió dentro del marco del proyecto europeo CP-ESFR con el principal objetivo de evaluar la física de núcleo y seguridad de los reactores rápidos refrigerados por sodio, al tiempo que se desarrollaron herramientas apropiadas para dichos análisis. Efectivamente, en una primera parte de la tesis, se abarca el estudio de la física del núcleo de un reactor rápido representativo, incluyendo el análisis detallado de la capacidad de transmutar actínidos minoritarios. Como resultado de dichos análisis, se publicó un artículo en la revista Annals of Nuclear Energy [96]. Por otra parte, a través de un análisis de un hipotético escenario nuclear español, se evalúo la disponibilidad de recursos naturales necesarios en el caso particular de España para alimentar una flota específica de reactores rápidos, siguiendo varios escenarios de demanda, y teniendo en cuenta la capacidad de reproducción de plutonio que tienen estos sistemas. Como resultado de este trabajo también surgió una publicación en otra revista científica de prestigio internacional como es Energy Conversion and Management [97]. Con objeto de realizar esos y otros análisis, se desarrollaron diversos modelos del núcleo del ESFR siguiendo varias configuraciones, y para diferentes códigos. Por otro lado, con objeto de poder realizar análisis de seguridad de reactores rápidos, son necesarias herramientas multidimensionales de alta fidelidad específicas para reactores rápidos. Dichas herramientas deben integrar fenómenos relacionados con la neutrónica y con la termo-hidráulica, entre otros, mediante una aproximación multi-física. Siguiendo este objetivo, se evalúo el código de difusión neutrónica ANDES para su aplicación a reactores rápidos. ANDES es un código de resolución nodal que se encuentra implementado dentro del sistema COBAYA3 y está basado en el método ACMFD. Por lo tanto, el método ACMFD fue sometido a una revisión en profundidad para evaluar su aptitud para la aplicación a reactores rápidos. Durante ese proceso, se identificaron determinadas limitaciones que se discutirán a lo largo de este trabajo, junto con los desarrollos que se han elaborado e implementado para la resolución de dichas dificultades. Por otra parte, se desarrolló satisfactoriamente el acomplamiento del código neutrónico ANDES con un código termo-hidráulico de subcanales llamado SUBCHANFLOW, desarrollado recientemente en el KIT. Como conclusión de esta parte, todos los desarrollos implementados son evaluados y verificados. En paralelo con esos desarrollos, se calcularon para el núcleo del ESFR las secciones eficaces en multigrupos homogeneizadas a nivel nodal, así como otros parámetros neutrónicos, mediante los códigos ERANOS, primero, y SERPENT, después. Dichos parámetros se utilizaron más adelante para realizar cálculos estacionarios con ANDES. Además, como consecuencia de la contribución de la UPM al paquete de seguridad del proyecto CP-ESFR, se calcularon mediante el código SERPENT los parámetros de cinética puntual que se necesitan introducir en los típicos códigos termo-hidráulicos de planta, para estudios de seguridad. En concreto, dichos parámetros sirvieron para el análisis del impacto que tienen los actínidos minoritarios en el comportamiento de transitorios. Concluyendo, la tesis presenta una aproximación sistemática y multidisciplinar aplicada al análisis de seguridad y comportamiento neutrónico de los reactores rápidos de sodio de la Gen-IV, usando herramientas de cálculo existentes y recién desarrolladas ad' hoc para tal aplicación. Se ha empleado una cantidad importante de tiempo en identificar limitaciones de los métodos nodales analíticos en su aplicación en multigrupos a reactores rápidos, y se proponen interesantes soluciones para abordarlas. ABSTRACT The future of nuclear reactors will depend, among other aspects, on the capability to solve the long-term challenges linked to this technology. These are the capability to provide a definite, safe and reliable solution to the nuclear wastes; the limitation of natural resources, needed to fuel the reactors; and last but not least, the improved safety, which would avoid any potential damage on the public and or environment as a consequence of any imaginable and beyond imaginable circumstance. Following these motivations, the IV Generation of nuclear reactors arises, with the aim to provide sustainable, safe, economic and proliferationresistant electricity. Among the systems considered for the Gen IV, fast reactors have a representative role thanks to their potential capacity to transmute actinides together with the optimal usage of natural resources, being the sodium fast reactors the most promising concept. As a consequence, this thesis was born in the framework of the CP-ESFR project with the generic aim of evaluating the core physics and safety of sodium fast reactors, as well as the development of the approppriated tools to perform such analyses. Indeed, in a first part of this thesis work, the main core physics of the representative sodium fast reactor are assessed, including a detailed analysis of the capability to transmute minor actinides. A part of the results obtained have been published in Annals of Nuclear Energy [96]. Moreover, by means of the analysis of a hypothetical Spanish nuclear scenario, the availability of natural resources required to deploy an specific fleet of fast reactor is assessed, taking into account the breeding properties of such systems. This work also led to a publication in Energy Conversion and Management [97]. In order to perform those and other analyses, several models of the ESFR core were created for different codes. On the other hand, in order to perform safety studies of sodium fast reactors, high fidelity multidimensional analysis tools for sodium fast reactors are required. Such tools should integrate neutronic and thermal-hydraulic phenomena in a multi-physics approach. Following this motivation, the neutron diffusion code ANDES is assessed for sodium fast reactor applications. ANDES is the nodal solver implemented inside the multigroup pin-by-pin diffusion COBAYA3 code, and is based on the analytical method ACMFD. Thus, the ACMFD was verified for SFR applications and while doing so, some limitations were encountered, which are discussed through this work. In order to solve those, some new developments are proposed and implemented in ANDES. Moreover, the code was satisfactorily coupled with the thermal-hydraulic code SUBCHANFLOW, recently developed at KIT. Finally, the different implementations are verified. In addition to those developments, the node homogenized multigroup cross sections and other neutron parameters were obtained for the ESFR core using ERANOS and SERPENT codes, and employed afterwards by ANDES to perform steady state calculations. Moreover, as a result of the UPM contribution to the safety package of the CP-ESFR project, the point kinetic parameters required by the typical plant thermal-hydraulic codes were computed for the ESFR core using SERPENT, which final aim was the assessment of the impact of minor actinides in transient behaviour. All in all, the thesis provides a systematic and multi-purpose approach applied to the assessment of safety and performance parameters of Generation-IV SFR, using existing and newly developed analytical tools. An important amount of time was employed in identifying the limitations that the analytical nodal diffusion methods present when applied to fast reactors following a multigroup approach, and interesting solutions are proposed in order to overcome them.

Propagation of Cross-Section Uncertainties in Criticality Calculations in the Framework of UAM-Phase I Using MCNPX-2.7e and SCALE-6.1

In the framework of the OECD/NEA project on Benchmark for Uncertainty Analysis in Modeling (UAM) for Design, Operation, and Safety Analysis of LWRs, several approaches and codes are being used to deal with the exercises proposed in Phase I, “Specifications and Support Data for Neutronics Cases.” At UPM, our research group treats these exercises with sensitivity calculations and the “sandwich formula” to propagate cross-section uncertainties. Two different codes are employed to calculate the sensitivity coefficients of to cross sections in criticality calculations: MCNPX-2.7e and SCALE-6.1. The former uses the Differential Operator Technique and the latter uses the Adjoint-Weighted Technique. In this paper, the main results for exercise I-2 “Lattice Physics” are presented for the criticality calculations of PWR. These criticality calculations are done for a TMI fuel assembly at four different states: HZP-Unrodded, HZP-Rodded, HFP-Unrodded, and HFP-Rodded. The results of the two different codes above are presented and compared. The comparison proves a good agreement between SCALE-6.1 and MCNPX-2.7e in uncertainty that comes from the sensitivity coefficients calculated by both codes. Differences are found when the sensitivity profiles are analysed, but they do not lead to differences in the uncertainty.

Radiative properties for warm and hot dense matter

We will present calculations of opacities for matter under LTE conditions. Opacities are needed in radiation transport codes to study processes like Inertial Confinement Fusion and plasma amplifiers in X-ray secondary sources. For the calculations we use the code BiGBART, with either a hydrogenic approximation with j-splitting or self-consistent data generated with the atomic physics code FAC. We calculate the atomic structure, oscillator strengths, radiative transition energies, including UTA computations, and photoionization cross-sections. A DCA model determines the configurations considered in the computation of the opacities. The opacities obtained with these two models are compared with experimental measurements.

Propagation of Nuclear Data Uncertainties in Transmutation Calculations Using ACAB Code

The assessment of the accuracy of parameters related to the reactor core performance (e.g., ke) and f el cycle (e.g., isotopic evolution/transmutation) due to the uncertainties in the basic nuclear data (ND) is a critical issue. Different error propagation techniques (adjoint/forward sensitivity analysis procedures and/or Monte Carlo technique) can be used to address by computational simulation the systematic propagation of uncertainties on the final parameters. To perform this uncertainty assessment, the ENDF covariance les (variance/correlation in energy and cross- reactions-isotopes correlations) are required. In this paper, we assess the impact of ND uncertainties on the isotopic prediction for a conceptual design of a modular European Facility for Industrial Transmutation (EFIT) for a discharge burnup of 150 GWd/tHM. The complete set of uncertainty data for cross sections (EAF2007/UN, SCALE6.0/COVA-44G), radioactive decay and fission yield data (JEFF-3.1.1) are processed and used in ACAB code.

Kinetics of color center formation in silica irradiated with swift heavy ions: Thresholding and formation efficiency

We have determined the cross-section σ for color center generation under single Br ion impacts on amorphous SiO2. The evolution of the cross-sections, σ(E) and σ(Se), show an initial flat stage that we associate to atomic collision mechanisms. Above a certain threshold value (Se > 2 keV/nm), roughly coinciding with that reported for the onset of macroscopic disorder (compaction), σ shows a marked increase due to electronic processes. In this regime, a energetic cost of around 7.5 keV is necessary to create a non bridging oxygen hole center-E′ (NBOHC/E′) pair, whatever the input energy. The data appear consistent with a non-radiative decay of self-trapped excitons.

Review of the C-nat(n,gamma) cross section and criticality calculations of the graphite moderated reactor BR1

A review of the experimental data for natC(n,c) and 12C(n,c) was made to identify the origin of the natC capture cross sections included in evaluated data libraries and to clarify differences observed in neutronic calculations for graphite moderated reactors using different libraries. The performance of the JEFF-3.1.2 and ENDF/B-VII.1 libraries was verified by comparing results of criticality calculations with experimental results obtained for the BR1 reactor. This reactor is an air-cooled reactor with graphite as moderator and is located at the Belgian Nuclear Research Centre SCK-CEN in Mol (Belgium). The results of this study confirm conclusions drawn from neutronic calculations of the High Temperature Engineering Test Reactor (HTTR) in Japan. Furthermore, both BR1 and HTTR calculations support the capture cross section of 12C at thermal energy which is recommended by Firestone and Révay. Additional criticality calculations were carried out in order to illustrate that the natC thermal capture cross section is important for systems with a large amount of graphite. The present study shows that only the evaluation carried out for JENDL-4.0 reflects the current status of the experimental data.

Nuclear Data Uncertainty Propagation to Reactivity Coefficients of a Sodium Fast Reactor

The assessment of the uncertainty levels on the design and safety parameters for the innovative European Sodium Fast Reactor (ESFR) is mandatory. Some of these relevant safety quantities are the Doppler and void reactivity coefficients, whose uncertainties are quantified. Besides, the nuclear reaction data where an improvement will certainly benefit the design accuracy are identified. This work has been performed with the SCALE 6.1 codes suite and its multigroups cross sections library based on ENDF/B-VII.0 evaluation.

Impact of Nuclear Data Uncertainties on Advanced Fuel Cycles and Their Irradiated Fuel - A comparison between Libraries

The uncertainties on the isotopic composition throughout the burnup due to the nuclear data uncertainties are analysed. The different sources of uncertainties: decay data, fission yield and cross sections; are propagated individually, and their effect assessed. Two applications are studied: EFIT (an ADS-like reactor) and ESFR (Sodium Fast Reactor). The impact of the uncertainties on cross sections provided by the EAF-2010, SCALE6.1 and COMMARA-2.0 libraries are compared. These Uncertainty Quantification (UQ) studies have been carried out with a Monte Carlo sampling approach implemented in the depletion/activation code ACAB. Such implementation has been improved to overcome depletion/activation problems with variations of the neutron spectrum.

Development of a methodology for nuclear data uncertainty propagation on isotopic evolution calculations for advanced nuclear systems

Una apropiada evaluación de los márgenes de seguridad de una instalación nuclear, por ejemplo, una central nuclear, tiene en cuenta todas las incertidumbres que afectan a los cálculos de diseño, funcionanmiento y respuesta ante accidentes de dicha instalación. Una fuente de incertidumbre son los datos nucleares, que afectan a los cálculos neutrónicos, de quemado de combustible o activación de materiales. Estos cálculos permiten la evaluación de las funciones respuesta esenciales para el funcionamiento correcto durante operación, y también durante accidente. Ejemplos de esas respuestas son el factor de multiplicación neutrónica o el calor residual después del disparo del reactor. Por tanto, es necesario evaluar el impacto de dichas incertidumbres en estos cálculos. Para poder realizar los cálculos de propagación de incertidumbres, es necesario implementar metodologías que sean capaces de evaluar el impacto de las incertidumbres de estos datos nucleares. Pero también es necesario conocer los datos de incertidumbres disponibles para ser capaces de manejarlos. Actualmente, se están invirtiendo grandes esfuerzos en mejorar la capacidad de analizar, manejar y producir datos de incertidumbres, en especial para isótopos importantes en reactores avanzados. A su vez, nuevos programas/códigos están siendo desarrollados e implementados para poder usar dichos datos y analizar su impacto. Todos estos puntos son parte de los objetivos del proyecto europeo ANDES, el cual ha dado el marco de trabajo para el desarrollo de esta tesis doctoral. Por tanto, primero se ha llevado a cabo una revisión del estado del arte de los datos nucleares y sus incertidumbres, centrándose en los tres tipos de datos: de decaimiento, de rendimientos de fisión y de secciones eficaces. A su vez, se ha realizado una revisión del estado del arte de las metodologías para la propagación de incertidumbre de estos datos nucleares. Dentro del Departamento de Ingeniería Nuclear (DIN) se propuso una metodología para la propagación de incertidumbres en cálculos de evolución isotópica, el Método Híbrido. Esta metodología se ha tomado como punto de partida para esta tesis, implementando y desarrollando dicha metodología, así como extendiendo sus capacidades. Se han analizado sus ventajas, inconvenientes y limitaciones. El Método Híbrido se utiliza en conjunto con el código de evolución isotópica ACAB, y se basa en el muestreo por Monte Carlo de los datos nucleares con incertidumbre. En esta metodología, se presentan diferentes aproximaciones según la estructura de grupos de energía de las secciones eficaces: en un grupo, en un grupo con muestreo correlacionado y en multigrupos. Se han desarrollado diferentes secuencias para usar distintas librerías de datos nucleares almacenadas en diferentes formatos: ENDF-6 (para las librerías evaluadas), COVERX (para las librerías en multigrupos de SCALE) y EAF (para las librerías de activación). Gracias a la revisión del estado del arte de los datos nucleares de los rendimientos de fisión se ha identificado la falta de una información sobre sus incertidumbres, en concreto, de matrices de covarianza completas. Además, visto el renovado interés por parte de la comunidad internacional, a través del grupo de trabajo internacional de cooperación para evaluación de datos nucleares (WPEC) dedicado a la evaluación de las necesidades de mejora de datos nucleares mediante el subgrupo 37 (SG37), se ha llevado a cabo una revisión de las metodologías para generar datos de covarianza. Se ha seleccionando la actualización Bayesiana/GLS para su implementación, y de esta forma, dar una respuesta a dicha falta de matrices completas para rendimientos de fisión. Una vez que el Método Híbrido ha sido implementado, desarrollado y extendido, junto con la capacidad de generar matrices de covarianza completas para los rendimientos de fisión, se han estudiado diferentes aplicaciones nucleares. Primero, se estudia el calor residual tras un pulso de fisión, debido a su importancia para cualquier evento después de la parada/disparo del reactor. Además, se trata de un ejercicio claro para ver la importancia de las incertidumbres de datos de decaimiento y de rendimientos de fisión junto con las nuevas matrices completas de covarianza. Se han estudiado dos ciclos de combustible de reactores avanzados: el de la instalación europea para transmutación industrial (EFIT) y el del reactor rápido de sodio europeo (ESFR), en los cuales se han analizado el impacto de las incertidumbres de los datos nucleares en la composición isotópica, calor residual y radiotoxicidad. Se han utilizado diferentes librerías de datos nucleares en los estudios antreriores, comparando de esta forma el impacto de sus incertidumbres. A su vez, mediante dichos estudios, se han comparando las distintas aproximaciones del Método Híbrido y otras metodologías para la porpagación de incertidumbres de datos nucleares: Total Monte Carlo (TMC), desarrollada en NRG por A.J. Koning y D. Rochman, y NUDUNA, desarrollada en AREVA GmbH por O. Buss y A. Hoefer. Estas comparaciones demostrarán las ventajas del Método Híbrido, además de revelar sus limitaciones y su rango de aplicación. ABSTRACT For an adequate assessment of safety margins of nuclear facilities, e.g. nuclear power plants, it is necessary to consider all possible uncertainties that affect their design, performance and possible accidents. Nuclear data are a source of uncertainty that are involved in neutronics, fuel depletion and activation calculations. These calculations can predict critical response functions during operation and in the event of accident, such as decay heat and neutron multiplication factor. Thus, the impact of nuclear data uncertainties on these response functions needs to be addressed for a proper evaluation of the safety margins. Methodologies for performing uncertainty propagation calculations need to be implemented in order to analyse the impact of nuclear data uncertainties. Nevertheless, it is necessary to understand the current status of nuclear data and their uncertainties, in order to be able to handle this type of data. Great eórts are underway to enhance the European capability to analyse/process/produce covariance data, especially for isotopes which are of importance for advanced reactors. At the same time, new methodologies/codes are being developed and implemented for using and evaluating the impact of uncertainty data. These were the objectives of the European ANDES (Accurate Nuclear Data for nuclear Energy Sustainability) project, which provided a framework for the development of this PhD Thesis. Accordingly, first a review of the state-of-the-art of nuclear data and their uncertainties is conducted, focusing on the three kinds of data: decay, fission yields and cross sections. A review of the current methodologies for propagating nuclear data uncertainties is also performed. The Nuclear Engineering Department of UPM has proposed a methodology for propagating uncertainties in depletion calculations, the Hybrid Method, which has been taken as the starting point of this thesis. This methodology has been implemented, developed and extended, and its advantages, drawbacks and limitations have been analysed. It is used in conjunction with the ACAB depletion code, and is based on Monte Carlo sampling of variables with uncertainties. Different approaches are presented depending on cross section energy-structure: one-group, one-group with correlated sampling and multi-group. Differences and applicability criteria are presented. Sequences have been developed for using different nuclear data libraries in different storing-formats: ENDF-6 (for evaluated libraries) and COVERX (for multi-group libraries of SCALE), as well as EAF format (for activation libraries). A revision of the state-of-the-art of fission yield data shows inconsistencies in uncertainty data, specifically with regard to complete covariance matrices. Furthermore, the international community has expressed a renewed interest in the issue through the Working Party on International Nuclear Data Evaluation Co-operation (WPEC) with the Subgroup (SG37), which is dedicated to assessing the need to have complete nuclear data. This gives rise to this review of the state-of-the-art of methodologies for generating covariance data for fission yields. Bayesian/generalised least square (GLS) updating sequence has been selected and implemented to answer to this need. Once the Hybrid Method has been implemented, developed and extended, along with fission yield covariance generation capability, different applications are studied. The Fission Pulse Decay Heat problem is tackled first because of its importance during events after shutdown and because it is a clean exercise for showing the impact and importance of decay and fission yield data uncertainties in conjunction with the new covariance data. Two fuel cycles of advanced reactors are studied: the European Facility for Industrial Transmutation (EFIT) and the European Sodium Fast Reactor (ESFR), and response function uncertainties such as isotopic composition, decay heat and radiotoxicity are addressed. Different nuclear data libraries are used and compared. These applications serve as frameworks for comparing the different approaches of the Hybrid Method, and also for comparing with other methodologies: Total Monte Carlo (TMC), developed at NRG by A.J. Koning and D. Rochman, and NUDUNA, developed at AREVA GmbH by O. Buss and A. Hoefer. These comparisons reveal the advantages, limitations and the range of application of the Hybrid Method.

Optimization of multidimensional cross-section tables for few-group core calculations

Multigroup diffusion codes for three dimensional LWR core analysis use as input data pre-generated homogenized few group cross sections and discontinuity factors for certain combinations of state variables, such as temperatures or densities. The simplest way of compiling those data are tabulated libraries, where a grid covering the domain of state variables is defined and the homogenized cross sections are computed at the grid points. Then, during the core calculation, an interpolation algorithm is used to compute the cross sections from the table values. Since interpolation errors depend on the distance between the grid points, a determined refinement of the mesh is required to reach a target accuracy, which could lead to large data storage volume and a large number of lattice transport calculations. In this paper, a simple and effective procedure to optimize the distribution of grid points for tabulated libraries is presented. Optimality is considered in the sense of building a non-uniform point distribution with the minimum number of grid points for each state variable satisfying a given target accuracy in k-effective. The procedure consists of determining the sensitivity coefficients of k-effective to cross sections using perturbation theory; and estimating the interpolation errors committed with different mesh steps for each state variable. These results allow evaluating the influence of interpolation errors of each cross section on k-effective for any combination of state variables, and estimating the optimal distance between grid points.

Uncertainty methods inactivation and inventory calculations

For a number of important nuclides, complete activation data libraries with covariance data will be produced, so that uncertainty propagation in fuel cycle codes (in this case ACAB,FISPIN, ...) can be developed and tested. Eventually, fuel inventory codes should be able to handle the complete set of uncertainty data, i.e. those of nuclear reactions (cross sections, etc.), radioactive decay and fission yield data. For this, capabilities will be developed both to produce covariance data and to propagate the uncertainties through the inventory calculations.