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Specific objectives: Contribute with updated results to Ex I-3, computing uncertainties in k-eff, radial power distributions and peak factors; Compare nodal and pin-by-pin results; Evaluate the probability distribution of core parameters.

Through NURESAFE project, depth modifications were performed in the core simulator from the UPM COBAYA. COBAYA was recoded and integrated into NURESIM platform with all its capabilities. The last version of the code is COBAYA4. Moreover, a new coupling was developed with one of the last versions of the thermal-hydraulic code integrated into NURESIM platform, CTF. After all these depth changes, next step is COBAYA4 and coupling validation. The collaboration was carried out with North Carolina State University (NCSU), Reactor Dynamics and Fuel Modeling Group (RDFMG), to validate coupled system COBAYA4/CTF. RDFMG developed a coupling system MCNP6/CTF and it has been used as a reference solution to validate COBAYA4/CTF. A fuel assembly analysis was performed with both coupled systems. The fuel assembly comes from OECD/NEA UAM-LWR Benchmark. The results obtained from the two coupled systems have to be analyzed carefully. Two different neutronic codes compared were, Monte-Carlo and Neutronic Diffusion code. They use different neutronic solver. The two coupling are different, one is an external coupling and another an internal coupling. Moreover, the thermal-hydraulic models are little different, one is rod center and the other one is sub-channel center. Despite the internal differences, the two solutions are similar.

Revisión de las actividades desarrolladas en el marco del Acuerdo Específico de colaboración entre el Consejo de Seguridad Nuclear y la Universidad Politécnica de Madrid en el área de la propagación de incertidumbres en los cálculos neutrónicos. Ponencia invitada en la 48 Reunión Anual de la Sociedad Nuclear Alemana

Significant efforts are being devoted in order to boost R&D on advanced nuclear reactors due to their sustainability and improved safety characteristics. Numerous benchmarks, whose aim is to assess and improve the methodologies and computer codes used to calculate neutronic parameters and reactivity coefficients in SFRs, have been set up. Amongst them, as a contribution to the ESNII+ Project, a benchmark exercise evaluating the safety coefficients of an ASTRID-like reactor was performed. The objective of this work is to assess the safety coefficients of an ASTRID-like reactor in order to identify the capabilities and possible limitations of the methodologies, codes and nuclear data employed in the calculations. Furthermore, these results will be compared and validated against the results of other partners. The ASTRID-like core was modelled at operating conditions with the SCALE system and MCNP code, using ENDF/B-VII.0 and JEFF-3.1.1 libraries respectively. Core multiplication factor, power peaking factors, kinetic parameters, reactivity feedback coefficients and control system worth were calculated. Nine voiding scenarios were studied, confirming the negative reactivity effect from the total voiding of the core. A comparison between the participants in the benchmark was carried out, providing an evaluation of the performance of the current state-of-the art neutronic codes for Gen-IV SFR reactor safety analyses.

In order to evaluate the uncertainties in prediction of lattice-averaged parameters, input data of core neutronics codes, Exercise I-2 of the OECD benchmark for uncertainty anal-ysis in modeling (UAM) was proposed. This work aims to perform a sensitivity/uncertainty analysis of the BWR configurations defined in the benchmark for the purpose of Exercise I-2. Criticality calculations are done for a 7x7 BWR fresh fuel assembly at HFP in four configurations: single unrodded fuel assembly, rodded fuel assembly, assembly/reflector and assembly in a color-set. The SCALE6.1 code package is used to propagate cross section covariance data through lattice physics calculations to both k-effective and two-group assembly-homogenized cross sec-tions uncertainties. Computed sensitivities and uncertainties for all configurations are analyzed and compared. It was found that uncertainties are very similar for the four test-problems, showing that the influence of the assembly environment on uncertainty prediction is very small.

Preparing Exercise I-3: Optimization of cross-section tables using sensitivity coefficients in COBAYA3

There exists an interest in performing full core pin-by-pin computations for present nuclear reactors. In such type of problems the use of a transport approximation like the diffusion equation requires the introduction of correction parameters. Interface discontinuity factors can improve the diffusion solution to nearly reproduce a transport solution. Nevertheless, calculating accurate pin-by-pin IDF requires the knowledge of the heterogeneous neutron flux distribution, which depends on the boundary conditions of the pin-cell as well as the local variables along the nuclear reactor operation. As a consequence, it is impractical to compute them for each possible configuration. An alternative to generate accurate pin-by-pin interface discontinuity factors is to calculate reference values using zero-net-current boundary conditions and to synthesize afterwards their dependencies on the main neighborhood variables. In such way the factors can be accurately computed during fine-mesh diffusion calculations by correcting the reference values as a function of the actual environment of the pin-cell in the core. In this paper we propose a parameterization of the pin-by-pin interface discontinuity factors allowing the implementation of a cross sections library able to treat the neighborhood effect. First results are presented for typical PWR configurations.

In this paper the extension of the multigroup nodal diffusion code ANDES, based on the Analytic Coarse Mesh Finite Difference (ACMFD) method, from Cartesian to hexagonal geometry is presented, as well as its coupling with the thermal–hydraulic (TH) code COBRA-IIIc for hexagonal core analysis. In extending the ACMFD method to hexagonal assemblies, triangular-Z nodes are used. In the radial plane, a direct transverse integration procedure is applied along the three directions that are orthogonal to the triangle interfaces. The triangular nodalization avoids the singularities, that appear when applying transverse integration to hexagonal nodes, and allows the advantage of the mesh subdivision capabilities implicit within that geometry. As for the thermal–hydraulics, the extension of the coupling scheme to hexagonal geometry has been performed with the capability to model the core using either assembly-wise channels (hexagonal mesh) or a higher refinement with six channels per fuel assembly (triangular mesh). Achieving this level of TH mesh refinement with COBRA-IIIc code provides a better estimation of the in-core 3D flow distribution, improving the TH core modelling. The neutronics and thermal–hydraulics coupled code, ANDES/COBRA-IIIc, previously verified in Cartesian geometry core analysis, can also be applied now to full three-dimensional VVER core problems, as well as to other thermal and fast hexagonal core designs. Verification results are provided, corresponding to the different cases of the OECD/NEA-NSC VVER-1000 Coolant Transient Benchmarks.

This paper summarizes the work being performed at the Department of Nuclear Engineering (www.din.upm.es) of the Universidad Politécnica de Madrid to improve the education and training of future Spanish nuclear engineers according to the Bologna rules. We present two main efforts introduced in our programme: i) the understanding of the current computational methodologies/codes starting from the nuclear data processing, then the lattice and core calculations codes, and finally the power plant simulators, ii) the development of practical teaching-learning experiences with an Interactive Graphical Simulator of a real nuclear power plant.

Neutron kinetics has been implemented in the 3D nodal solver ANDES, which has been coupled to the core thermal-hydraulics (TH) code COBRA-III for core transient analysis. The purpose of this work is, first, to discuss and test the ability of the kinetics solver ANDES to model transients; and second, by means of a systematic analysis, including alternate kinetics schemes, time step size, nodal size, neutron energy groups and spectrum, to serve as a basis for the development of more accurate and efficient neutronics/thermal-hydraulics tools for general transient simulations. The PWR MOX/UO2 transient benchmark provided by the OECD/NEA and US NRC was selected for these goals. The obtained ANDES/COBRA-III results were consistent with other solutions to the benchmark; the differences in the TH feedback led to slight differences in the core power evolution, whereas very good agreements were found in the other requested parameters. The performed systematic analysis highlighted the optimum kinetics iterative scheme, and showed that neutronics spatial discretization effects have stronger influence than time discretization effects, in the semi-implicit scheme adopted, on the numerical solution. On the other hand, the number of energy groups has an important influence on the transient evolution, whereas the assumption of using the prompt neutron spectrum for delayed neutrons is acceptable as it leads to small relative errors.

In this work we develop and demonstrate the analytic coarse-mesh finite difference (ACMFD) method for multigroup - with any number of groups - and multidimensional diffusion calculations of eigenvalue and external source problems. The first step in this method is to reduce the coupled system of the G multigroup diffusion equations, inside any homogenized region (or node) of any size, to the G independent modal equations in the real or complex eigenspace of the G × G multigroup matrix. The mathematical and numerical analysis of this step is discussed for several reactor media and number of groups. As a second step, we discuss the analytical solutions in the general (complex) modal eigenspace for one-dimensional plane geometry, deriving the generalized Chao's relation among the surface fluxes and the net currents, at a given interface, and the node-average fluxes, essential in the ACMFD method. We also introduce here the treatment of heterogeneous nodes, through modal interface flux discontinuity factors, and show the analytical and numerical application to core-reflector problems, for a single infinite reflector and for reflectors with two layers of different materials. Then, we address the general multidimensional case, with rectangular X-Y-Z geometry considered, showing the equivalency of the methods of transverse integration and incomplete expansion of the multidimensional fluxes, in the real or complex modal eigenspace of the multigroup matrix. A nonlinear iteration scheme is implemented to solve the multigroup multidimensional nodal problem, which has shown a fast and robust convergence in proof-of-principle numerical applications to realistic pressurized water reactor cores, with heterogeneous fuel assemblies and reflectors.

The purpose of this paper is first to discuss the methods developed in our three-dimensional pressurized water reactor core dynamics code SIMTRAN and its coupling to the system code RELAP-5 for general transient and safety analysis. Then, we summarize its demonstration application to the Nuclear Energy Agency (NEA)/ Organization for Economic Cooperation and Development (OECD) Benchmark on Main Steam Line Break (MSLB), co-sponsored by the U.S. Nuclear Regulatory Commission (NRC) and other regulatory institutions. In particular, our work has been supported by the Spanish “Consejo de Seguridad Nuclear” (CSN) under a CSN research project. Our results for the steady states and the guided-core transients, proposed as exercise 2 of the MSLB benchmark, show small deviations from the mean results of all participants, especially in core average parameters. For the full-coupled core-plant transients, exercise 3, a detailed comparison with the University of Purdue–NRC results using PARCS/RELAP-5, shows quite good agreement in both integral and local parameters, especially for the more extreme return-to-power scenario.

In order to take into account in a more effective and accurate way the intranodal heterogeneities in coarse-mesh finite-difference (CMFD) methods, a new equivalent parameter generation methodology has been developed and tested. This methodology accounts for the dependence of the nodal homogeneized two-group cross sections and nodal coupling factors, with interface flux discontinuity (IFD) factors that account for heterogeneities on the flux-spectrum and burnup intranodal distributions as well as on neighbor effects. The methodology has been implemented in an analytic CMFD method, rigorously obtained for homogeneous nodes with transverse leakage and generalized now for heterogeneous nodes by including IFD heterogeneity factors. When intranodal mesh node heterogeneity vanishes, the heterogeneous solution tends to the analytic homogeneous nodal solution. On the other hand, when intranodal heterogeneity increases, a high accuracy is maintained since the linear and nonlinear feedbacks on equivalent parameters have been shown to be as a very effective way of accounting for heterogeneity effects in two-group multidimensional coarse-mesh diffusion calculations.

El Reactor Rápido refrigerado por Plomo (LFR) es una de las tres tecnologías seleccionadas por la Plataforma Tecnológica de Energía Nuclear Sostenible que pueden satisfacer las futuras necesidades energéticas europeas. Investigadores e industria están realizando importantes esfuerzos para superar los principales inconvenientes del despliegue industrial de los LFR, que son la falta de experiencia operacional y el impacto de las incertidumbres en el diseño del reactor, la operación y la evaluación de la seguridad. En el diseño de reactores nucleares, las incertidumbres provienen principalmente de las propiedades de los materiales, las tolerancias de fabricación, las condiciones operativas, las herramientas de simulación y los datos nucleares. De hecho, la incertidumbre en los datos nucleares es una de las fuentes más importantes de incertidumbre en el diseño del reactor y en las simulaciones de la física del reactor y, en el pasado, se han obtenido sistemáticamente importantes diferencias entre las incertidumbres y las precisiones objetivo. Es necesario cumplir con la precisión objetivo no sólo para lograr el nivel de seguridad requerido para esta tecnología, sino también para minimizar el aumento de los costes debido a medidas de seguridad adicionales. Con esos antecedentes, el objetivo principal de este trabajo ha sido analizar y mejorar los datos nucleares necesarios para el desarrollo, la evaluación de seguridad y el licenciamiento de los reactores LFR, reduciendo las incertidumbres en los parámetros de reactividad (para seguridad) debido a las incertidumbres en los datos nucleares, con el fin de alcanzar las precisiones objetivo definidas por investigadores, industria y reguladores. Herramientas de sensibilidad e incertidumbre precisas y con alta fiabilidad son necesarias para estimar las incertidumbres en parámetros de seguridad clave del reactor (factor de multiplicación neutrónico, keff, fracción efectiva de neutrones diferidos, eff, tiempo efectivo de generación de neutrones, , coeficientes de reactividad, ...) e identificar posibles debilidades en los datos nucleares. Existen herramientas para calcular la incertidumbre de un parámetro del reactor debida a las incertidumbres en los datos nucleares. Sin embargo, estas herramientas poseen varias limitaciones, como carecer de capacidades de procesamiento en paralelo; necesidad de que el usuario seleccione los isótopos y canales de reacción a incluir en el análisis; uso de datos nucleares en estructura de multigrupos; uso de una librería de datos nucleares específica y/o una matriz de covarianza específica; y la limitación en la complejidad del sistema a analizar debido al número requerido de simulaciones. Por lo tanto, en este trabajo, se ha desarrollado una Metodología de Sensibilidad e Incertidumbre para códigos de MONtecarlo (SUMMON). SUMMON es una herramienta concebida para realizar análisis automatizados completos de sensibilidad e incertidumbre de los parámetros de reactividad (para seguridad) más relevantes de diseños de reactores desde el punto de vista neutrónico, es decir, keff, eff, eff y los coeficientes de reactividad, utilizando librerías de datos nucleares y covarianzas de última generación. SUMMON se ha validado utilizando experimentos integrales del ICSBEP (International Handbook of Evaluated Criticality Safety Benchmark Experiments) y se ha verificado exhaustivamente con códigos consolidados como SCALE, SUSD3D y SERPENT. Se ha encontrado un buen acuerdo entre los códigos. Una vez SUMMON fue desarrollado, se llevaron a cabo análisis preliminares para el diseño de MYRRHA (Multi-purpose hYbrid Research Reactor for High-tech Applications), un reactor rápido refrigerado con plomo-bismuto. Primero, se utilizó la librería de datos nucleares ENDF/B-VII.0 para identificar los datos nucleares más importantes para las reacciones inducidas por neutrones en los cálculos de criticidad de los LFR. Posteriormente, la librería JEFF-3.3T1, versión beta en ese momento de la nueva versión de la librería de datos nucleares evaluada en Europa, se analizó utilizando los mejores conjuntos de datos experimentales dependientes de la energía disponibles. El bismuto y el plomo, identificados en los análisis anteriores como isótopos clave, fueron seleccionados como los principales objetos de estudio para la mejora de los datos nucleares, ya que son de vital importancia y no fueron cubiertos en el proyecto piloto CIELO. Se encontraron problemas en la región de resonancias resueltas en las evaluaciones del plomo y el bismuto en JEFF-3.3T1 y se dieron recomendaciones al proyecto JEFF, que se adoptaron en la versión final de dicha librería de datos nucleares. A continuación, se realizaron análisis de sensibilidad e incertidumbre con las librerías de datos nucleares JEFF-3.3 y ENDF/B-VIII.0 mediante SUMMON para estimar las incertidumbres en los parámetros de criticidad de MYRRHA. Si bien se observó un buen acuerdo en las incertidumbres totales producidas por ambas librerías, las diferencias en las evaluaciones y la inexistencia de correlaciones y evaluaciones de covarianzas hicieron que los contribuyentes a la incertidumbre total difirieran. Además, las precisiones objetivo de diseño para algunos parámetros de seguridad, como el factor de multiplicación neutrónica, se excedieron en más del doble para las evaluaciones de datos nucleares consideradas. Con el fin de proporcionar datos nucleares ajustados, no sólo capaces de predecir las propiedades del reactor dentro de la precisión objetivo de diseño, sino también estadísticamente coherentes con los diversos experimentos diferenciales, se desarrolló el módulo de Asimilación de Datos Con summoN (DAWN). DAWN se basa en la combinación de datos de covarianza experimentales y experimentos integrales junto con técnicas avanzadas de ajuste estadístico (mínimos cuadrados generalizados). DAWN ha sido verificado utilizando el método TMC (Total Monte Carlo) para diferentes experimentos integrales. Finalmente, DAWN se usó para realizar una asimilación de los principales contribuyentes a la incertidumbre mediante el uso de datos nucleares de JEFF-3.3 a priori y experimentos de masa crítica disponibles públicamente en el ICSBEP. La consistencia del ajuste se verificó con datos experimentales diferenciales y se encontró un buen acuerdo. Se obtuvo una reducción significativa en la incertidumbre utilizando los experimentos más representativos de MYRRHA, debido a la reducción en la incertidumbre de los contribuyentes principales y la presencia a posteriori de fuertes correlaciones cruzadas entre isótopos y reacciones que no existían a priori. Los resultados muestran que se puede lograr una reducción de casi 300 pcm realizando una asimilación con el experimento más sensible al mayor contribuyente a la incertidumbre. Esto demuestra que la combinación de datos de covarianza experimental y experimentos integrales junto con la técnica de mínimos cuadrados generalizados puede proporcionar datos nucleares ajustados capaces de predecir las propiedades del reactor con menor incertidumbre, coherentes con los datos diferenciales. ----------ABSTRACT---------- The Lead-cooled Fast Reactor (LFR) is one of the three technologies selected by the Sustainable Nuclear Energy Technology Platform that can meet future European energy needs. Significant efforts are being made by researchers and industry to overcome the main drawbacks for the industrial deployment of LFR, which are the lack of operational experience and the impact of uncertainties in the reactor design, operation and safety assessment. In nuclear reactor design the uncertainties mainly come from material properties, fabrication tolerances, operative conditions, simulation tools and nuclear data. Indeed, the uncertainty in nuclear data is one of the most important sources of uncertainty in reactor design and reactor physics simulations, and significant gaps between the uncertainties and the target accuracies have been systematically shown in the past. Meeting the target accuracy is required not only to achieve the requested level of safety for this technology, but also to minimize the increase in the costs due to additional security measures. With that background, the main objective of this work has been to analyse and improve the nuclear data required for the development, safety assessment and licensing of LFR reactors, reducing the uncertainties in the criticality safety parameters due to the uncertainties in nuclear data, in order to reach the target accuracies defined by researchers, industry and regulators. To estimate the uncertainties in reactor key parameters (effective neutron multiplication factor, keff, effective delayed neutron fraction, βeff, effective neutron generation time, eff, safety coefficients, …) and to identify possible nuclear data weaknesses, accurate and reliable tools for sensitivity analysis and uncertainty quantification are needed. Tools able to calculate the uncertainty of a response due to uncertainties in nuclear data are available. However they possess several limitations such as no parallel processing capabilities; user selection of isotope and reaction channels to be included in the analysis; use of multi-group nuclear data; use of specific nuclear data library and/or specific covariance matrix; and limited complexity of the system under analysis due to the required number of simulations. Hence, in the framework of this work, a Sensitivity and Uncertainty Methodology for MONte carlo codes (SUMMON) has been developed. SUMMON is a tool conceived to perform complete automated sensitivity and uncertainty analyses of the most relevant criticality safety parameters of detailed complex reactor designs from the neutronic point of view, i.e., keff, eff, eff and reactivity coefficients, using state-of-the-art nuclear data libraries and covariances. SUMMON has been validated using integral experiments from the International Handbook of Evaluated Criticality Safety Benchmark Experiments (ICSBEP) and extensively verified against consolidated codes such as SCALE, SUSD3D and SERPENT. Good agreement between codes has been found. Once SUMMON was developed, preliminary analyses were carried out for MYRRHA (Multi-purpose hYbrid Research Reactor for High-tech Applications) lead-bismuth cooled fast reactor design. First, the ENDF/B-VII.0 nuclear data library was used, in order to identify the most important nuclear data for neutron induced reactions for criticality safety calculations of LFRs. Then, the recently released JEFF-3.3T1 library, the beta proposal at the time for the next version of the European evaluated nuclear data library, was analysed using the best documented energy dependent experimental data sets available. Bismuth and lead, identified in the previous analyses as key isotopes, were chosen as the main objects of study for improvement of nuclear data since they are of vital importance and were not covered in the CIELO pilot project. Problems were found in the resolved resonance region of JEFF-3.3T1 bismuth and lead evaluations and recommendations were given to the JEFF project, which were adopted in the release version of the library. Next, sensitivity and uncertainty analyses using the state-of-the-art JEFF-3.3 and ENDF/B-VIII.0 nuclear data libraries were performed with SUMMON to estimate the uncertainties in the criticality safety parameters of MYRRHA. While good agreement was observed in the total uncertainties yielded by both libraries, differences in evaluations, missing correlations and missing covariance evaluations, caused the contributors to the total uncertainty to differ. Furthermore, the design target accuracies for some criticality safety parameters, such as the effective neutron multiplication factor, still exceeded by more than a factor of two for the considered modern nuclear data evaluations. In order to provide adjusted nuclear data, not only capable of predicting reactor properties within the target design accuracy, but also statistically consistent with the various differential measurements, the Data Assimilation With summoN (DAWN) module was developed. DAWN is based on the combination of experimental covariance data and integral experiments together with advanced statistical adjustment techniques (Generalised Least Squares). DAWN has been verified against the Total Monte Carlo (TMC) method for several integral experiments. Finally, DAWN was used to perform an assimilation on the main contributors to the uncertainty using JEFF-3.3 nuclear data as a prior and publicly available critical mass experiments from the ICSBEP. The consistency of the nuclear data adjustment was checked against differential experimental data and good agreement was found. A significant reduction in uncertainty was obtained using the experiments most representative of MYRRHA, due to the reduction in the uncertainty of the major contributors and to the presence a posteriori of strong cross-correlations between isotopes and reactions that did not exist a priori. Results show that a reduction of nearly 300 pcm can be achieved performing an assimilation with the most sensitive experiment to the major contributor to the uncertainty. It proves that the combination of experimental covariance data and integral experiments together with Generalised Least Squares technique, can provide adjusted nuclear data capable of predicting reactor properties with lower uncertainty and consistent with differential data.

Tradicionalmente, los análisis de seguridad de las plantas nucleares se han realizado usando métodos e hipótesis pesimistas, forzando que los resultados sean conservadores. En los últimos años, y gracias a la mejora en la precisión de las herramientas computacionales, se ha empezado a considerar el uso de simulaciones realistas para dichos análisis de seguridad. Sin embargo, estas predicciones realistas deben ser complementadas con una rigurosa cuantificación del impacto de las incertidumbres en los parámetros de entrada sobra las respuestas de interés. Estos nuevos métodos se conocen como BEPU (del inglés “best-estimate plus uncertainties”). Conscientes de la importancia del papel de las incertidumbres, el Comité de Ciencia Nuclear de la OECD/NEA lanzó el programa “OECD Benchmark for Uncertainty Analysis in Best Estimate Modeling for Design, Operation and Safety Analysis of LWRs”, que es un ejercicio internacional con el objetivo de desarrollar métodos de cuantificación de incertidumbres para reactores de agua ligera. Esta tesis ha sido realizada en el marco del citado proyecto UAM, con el objetivo de desarrollar técnicas de análisis de sensibilidad y cuantificación de incertidumbre de aplicación a simulaciones de núcleo completo usando las herramientas de la Universidad Politécnica de Madrid (COBAYA4 y SEANAP), convirtiéndolas en herramientas BEPU. La fuente de incertidumbre podrá ser cualquier parámetro de entrada al código: datos nucleares así como parámetros tecnológicos, termohidráulicos y termomecánicos. Como respuesta de interés se tomará cualquier parámetro calculado por los códigos, como por ejemplo reactividad o distribución de potencia. El primer sistema, SEANAP, es un completo conjunto de herramientas para la simulación de reactores de agua a presión, que cubre todos los pasos, desde la recarga hasta las simulaciones del núcleo, y que ha demostrado muy buen acuerdo entre los valores calculados y los medidos en varias centrales nucleares españolas. La metodología de análisis de incertidumbre implementada en el sistema se basa en muestreo aleatorio de los parámetros de entrada. Además, y gracias a una colaboración con AREVA GmbH, se ha implementado una técnica de asimilación de datos de forma que se puede incluir información de medidas de ciclos pasados para mejorar las predicciones de los ciclos siguientes. Se incluye la aplicación de este sistema al diseño de un ciclo de un núcleo de agua a presión. El segundo sistema se basa en COBAYA4, evolución del simulador de núcleo incluido en SEANAP. Las características más relevantes de COBAYA4 son: i) su capacidad de realizar simulaciones en multigrupos y multiescala (nodal y pin-by-pin); ii) su flexibilidad para funcionar con distintos códigos lattice; iii) su capacidad para realizar simulaciones multifísica por medio de su acoplamiento con códigos termohidráulicos, lo que permite usar diferentes resoluciones en los dominios neutrónico y termohidráulico. Se usa SCALE/NEWT como código lattice, y COBRA-TF como código termohidráulico, por lo que el sistema completo es conocido como SCALE/COBAYA4/COBRA-TF. En este segundo sistema se ha implementado una técnica de análisis de sensibilidad basada en el cálculo del flujo adjunto para obtener los coeficientes de sensibilidad de la keff respecto de las secciones eficaces macroscópicas. Para el análisis de incertidumbre se han implementado dos metodologías. La primera es determinista y usa los coeficientes de sensibilidad anteriores aplicándolos en la Regla del sandwich junto con la matriz de covarianzas de los parámetros homogeneizados y en pocos grupos de energía, obteniendo la incertidumbre en la respuesta (keff ). Dicha matriz de covarianzas se puede generar gracias a las capacidades para cuantificación de incertidumbre disponibles en el sistema SCALE6.2, elegido como código lattice para COBAYA4. La segunda metodología de análisis de incertidumbre está basada en muestreo aleatorio de los parámetros de entrada: datos nucleares usando la secuencia SAMPLER de SCALE, y parámetros tecnológicos, termohidráuilicos y termomecánicos usando otras herramientas de muestreo como DAKOTA. Se incluyen tres aplicaciones de este segundo sistema: i) propagación de incertidumbres en datos nucleares aplicado a cálculos puramente neutrónicos de núcleo completo usando SCALE y COBAYA4; ii) propagación de incertidumbres tecnológicas, termohidráulicas y termomecánicas en cálculos acoplados usando COBAYA4 y COBRA-TF; iii) propagación de incertidumbres en datos nucleares a las secciones eficaces homogeneizadas en pocos grupos de energía durante el quemado del combustible usando SCALE. Agrupando todos los desarrollos, esta tesis proporciona un marco para análisis BEPU de reactores de agua a presión usando simuladores de núcleo. ----------ABSTRACT---------- Traditionally, safety analyses of nuclear power plants were carried out using pessimistic methods and hypotheses, forcing the results to be conservative. In recent years, and thanks to the increased accuracy in computational tools, realistic simulations are being considered for application in safety analysis. However, the realistic or best-estimate predictions must be complemented with a rigorous quantification of the impact of the input parameters uncertainties on the responses of interest. These approaches are named best-estimate plus uncertainty (BEPU) methods. Aware of the importance of the role of uncertainties, the OECD/NEA Nuclear Science Committee launched the “OECD Benchmark for Uncertainty Analysis in Best Estimate Modeling for Design, Operation and Safety Analysis of LWRs”. This is an international exercise with the aim of developing uncertainty quantification methods for light water reactors simulations. This thesis has been done in the framework of the mentioned UAM Benchmark, with the main objective of implementing sensitivity analysis and uncertainty quantification techniques in the core simulators developed at Universidad Politécnica de Madrid (COBAYA4 and SEANAP), converting those best-estimate approaches in BEPU methodologies. The source of the uncertainties can be any input parameter to the codes: nuclear data as well as technological, thermalhydraulics and thermomechanics parameters; and the response of interest will be any parameter calculated by the codes: reactivities, power distributions, among others. The first system, SEANAP, is a complete set of tools for the simulation of PWR, covering all steps from refueling to core simulations, which has demonstrated a good agreement between calculated and measured values in several Spanish nuclear power plants. The uncertainty analysis methodology implemented in the system is based on random sampling of the input parameters. In addition, and thanks to a collaboration with AREVA GmbH, a data assimilation technique has been also implemented to include measurements of past cycles in order to improve the predictions of the subsequent cycles. The application of this system to the design of a cycle of a PWR core is included. The second system is based on COBAYA4, evolution of the core simulator included in SEANAP. The most relevant features of COBAYA4 are: i) its ability to perform multigroup and multiscale (nodal and pin-by-pin) simulations; ii) its flexibility to work with different lattice physics codes; iii) its capability to deal with multiphysics problems through its coupling to thermalhydraulics codes, allowing different resolutions in the neutronics and thermalhydraulics domains. SCALE/NEWT is used as lattice code, and COBRA-TF as thermalhydraulics solver, so the whole system is referred to as SCALE/COBAYA4/COBRA-TF. In this second system one sensitivity analysis and two uncertainty quantification techniques have been implemented. The sensitivity analysis uses an adjoint sensitivity procedure to calculate the sensitivity coefficients of the response keff to the few-group macroscopic cross sections. The first uncertainty quantification technique is deterministic and uses those sensitivity coefficients in the Sandwich Rule together with the covariance matrix of the few-group homogenized constants to obtain the uncertainty in the response (keff ). That covariance matrix can be generated thanks to the uncertainty quantification capabilities of SCALE6.2, chosen as upstream code for COBAYA4, so that the few-group cross-sections can be provided with their covariance matrices. The second uncertainty analysis methodology is based on random sampling of the input parameters: nuclear data using the SAMPLER sequence from SCALE; technological, thermalhydraulics, and thermomechanics parameters using other sampling tools like DAKOTA. Three applications of this second system are included: i) propagation of nuclear data uncertainties in standalone neutronics calculations to full core results, using SCALE and COBAYA4; ii) propagation of technological, thermalhydraulics and thermomechanics uncertainties in coupled calculations using COBAYA4 and COBRATF; iii) propagation of nuclear data uncertainties on the few-group homogenized cross sections along burnup using SCALE. All in all, this thesis provides an uncertainty quantification framework for the BEPU analysis of pressurized water reactors using core simulators.

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.