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Accurate and reliable tools for sensitivity analysis and uncertainty quantification are needed to estimate the uncertainties in reactor key parameters (keff, βeff, Λeff, safety coefficients, …) and to identify possible nuclear data weaknesses. A Sensitivity and Uncertainty Methodology for MONte carlo codes (SUMMON) has been developed to calculate the sensitivities of the criticality safety parameters as well as their uncertainties due to uncertainties in nuclear data, addressing limitations of existing tools. The methodology is currently based on the use of the KSEN card of MCNP6 code to perform the eigenvalue sensitivity calculations, although any Monte Carlo code that can provide sensitivity coefficients can be used. The sensitivity coefficients of a reactivity response are calculated using the eigenvalue definition of reactivity, which is equivalent to applying the Equivalent Generalized Perturbation Theory. Moreover, the effective delayed neutron fraction sensitivity coefficients are derived from Bretscher’s approximation, whereas the sensitivity coefficients of the effective neutron generation time are obtained using the 1/v insertion method and the Equivalent Generalized Perturbation Theory. Uncertainties are propagated using the “Sandwich Rule” of the “Propagation of Moments” method employing state-of-the-art covariance libraries. The implementation in SUMMON of Bretscher’s approximation and the 1/v insertion method has been validated using integral experiments from ICSBEP and IRPhE databases, while the methods for calculating the sensitivity coefficients have been verified against consolidated codes, such as SCALE, SUSD3D, SERPENT and XSUSA and good agreement has been obtained.

Sodium-cooled Fast Reactors and Lead-cooled Fast Reactors have been selected by the Sustainable Nuclear Energy Technology Platform as technologies that can meet future European energy needs. To achieve the requested level of safety for these reactor technologies and to minimize the increase in the costs due to additional safety measures, accurate and reliable nuclear data are necessary. The objective of this work has been to analyse and improve the nuclear data required for the development, safety assessment and licensing of SFRs and LFRs, reducing the uncertainties in the reactor integral responses due to the uncertainties in nuclear data, in order to reach the target accuracies defined by researchers, industry and regulators. To that end, target accuracy and data assimilation analyses have been performed to identify nuclear data weaknesses and to reduce the uncertainties of integral safety-related parameters due to neutron induced nuclear data. As a result of this work, nuclear data needs for advanced SFRs and LFRs have been identified, improvements of existing nuclear data libraries have been suggested, nuclear data have been adjusted and uncertainties in reactor integral parameters have been reduced, meeting target accuracies after adjustment.

Monte Carlo neutron transport codes can be used for high-fidelity predictions of the performance of nuclear systems. However, validation against experiments is required in order to establish the credibility in the results and identify the inaccuracies due to the used calculation scheme and associated databases. The International Handbook of Evaluated Criticality Safety Benchmark Experiments (ICSBEP) contains criticality safety benchmarks derived from experiments that have been performed at various nuclear critical facilities around the world and are very valuable for validation purposes. The main objective of this work is the identification and modelling of experimental benchmarks included at ICSBEP in support of the validation of Monte Carlo neutron transport calculations when applied to fast systems, and in particular, KENO-VI and associated AMPX-formatted continuous-energy libraries from SCALE package. In such systems, the predicted k-eff values can be very sensitive to the treatment of nuclear data in the Unresolved Resonance Region (URR). Consequently, benchmarks with intermediate and fast spectra are identified and modelled with KENO-VI. Then, calculated results with and without probability tables in the URR are compared with each other in order to identify the most sensitive configurations to the URR. As a result of the proposed study, recommendations are given about the benchmarks that should be modelled and analysed to qualify the processed continuous-energy libraries before their use in Monte Carlo transport codes for practical fast reactor applications.

The ESFR-SMART project is the latest iteration of research into the behaviour of acommercial-size SFR core throughout its lifetime. As part of this project the ESFR corehas been modelled by a range of different reactor physics simulation codes at its end ofcycle state, and the important safety relevant parameters evaluated. These parameters arefound to agree well between the different codes, giving good confidence in the results.A detailed mapping of the local sodium void worth is also performed due to the problemsassociated with the positive void coefficient seen in large SFR designs. The local voidworth maps show that the use of zone-wise coefficients replicates the important reactivityfeedbacks to a high degree, indicating their suitability for use in SFR simulations.

The safety level of Sodium Fast Reactors is directly related with the sodium void reactivity. A low-void effect design has been proposed within the Horizon2020 ESFR-SMART project thanks to the introduction of a sodium plenum above the active core. In order to assess the impact of this core conception on transient analysis, a map with the spatial distribution of sodium void worth can be computed and fed into a point-kinetics-based transient code. Due to the spatial correlations between neighboring zones, the global effect of voiding two different axial or radial regions is not necessarily the sum of both individual contributions. Neglecting those correlations in the void worth map and consequently in the transient analysis may lead to an unrealistic prediction of the transient sequences. In this work, a method based on sensitivity analysis and similarity assessment is proposed for predicting those correlations. The method proved to be able to establish correlations between axial slices of a sub-assembly and was checked against realistic sodium void propagation patterns.

This paper assesses the impact of the homogenization level (nodal or pin-by-pin) on the uncertainties predicted by core simulators, highlighting the need of calculations at pin level for a reliable estimate of uncertainties in hot channel factors. In order to perform the analysis, two methodologies for nuclear data uncertainty quantification in stand-alone neutronics calculations have been implemented in the core simulator COBAYA. The first one is based on first-order perturbation theory and allows sensitivity/uncertainty analysis in the multiplication factor. The second one is based on random sampling and allows the uncertainty propagation in all responses computed by the code. Both methodologies are used in conjunction with SCALE system, which provides the capabilities to propagate the nuclear data uncertainties into the few-group constants required for the diffusion calculations. These methodologies are validated using a simplified pin-cell and a fuel assembly, and then applied to a full 3D core in the context of the OECD/NEA UAM benchmark (Uncertainty Analysis in Best-Estimate Modeling for Design, Operation and Safety Analysis of LWRs).

At UPM, in-depth modifications of the core simulator COBAYA, able to perform neutronics diffusion calculations at both nodal and pin-by-pin levels, have been accomplished during the 7th Framework EURATOM NURESAFE project. The main goal was to upgrade its integration in the European Platform for Nuclear Reactor Safety Simulation in order to facilitate the coupling with any other code of the platform for multi-physics analysis, focusing also on the code legibility and maintainability. An external and flexible coupling with the thermal-hydraulics code COBRA-TF was designed. As a result, COBAYA4/COBRA-TF allows multiscale coupled calculations, enabling both nodal and pin-by-pin neutronics resolutions using both assembly-based channels and pin-based subchannels at the thermal-hydraulics domain. Flexible mapping schemes also in axial direction can be defined. The coupled system was applied to a Main Steam Line Break transient benchmark. Pin-by-pin 3D simulations using one thermal-hydraulic channel per assembly were carried out in a reasonable computing time, and results compared to nodal solutions demonstrating the multiscale coupling capability for full core transients. Pin-by-pin calculations using thermal-hydraulics subchannels will be performed in a near future to assess the role that a very detailed mapping can play to predict realistic local parameters. While in asymmetric transients the effect can be important, it is expected that in symmetric transients assembly-based thermal-hydraulics channels can provide accurate pin-by-pin solutions in execution times suitable for routine analysis. The performed work will bring the ability to explore in an easy way multiscale effects on safety transient evaluations and give recommendations for the neutronics/thermal-hydraulics mapping depending on the application.

International audience; Within the NURESAFE project, a main steam line break benchmark has been defined and solved by codes integrated into the European code platform NURESIM. The paper describes the results of the calculations for this benchmark. Six different solutions using different codes and code systems are provided for the comparison. The quantitative differences in the results are dominated by the differences in the secondary system parameters during the depressurization. The source of these differences comes mainly from the application of different models for the two-phase leak flow available in the system codes. The use of two different thermal hydraulic system codes influences the results more than expected when the benchmark was created. The codes integrated into the NURESIM platform showed their applicability to a challenging transient like a main steam line break. © 2017 Elsevier B.V.

El Reactor Rapido refrigerado por Plomo (LFR) es una de las tres tecnologias seleccionadas por la Plataforma Tecnologica de Energia Nuclear Sostenible que pueden satisfacer las futuras necesidades energeticas europeas. Investigadores e industria estan 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 diseno del reactor, la operacion y la evaluacion de la seguridad. En el diseno de reactores nucleares, las incertidumbres provienen principalmente de las propiedades de los materiales, las tolerancias de fabricacion, las condiciones operativas, las herramientas de simulacion y los datos nucleares. De hecho, la incertidumbre en los datos nucleares es una de las fuentes mas importantes de incertidumbre en el diseno del reactor y en las simulaciones de la fisica del reactor y, en el pasado, se han obtenido sistematicamente importantes diferencias entre las incertidumbres y las precisiones objetivo. Es necesario cumplir con la precision objetivo no solo para lograr el nivel de seguridad requerido para esta tecnologia, sino tambien 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 evaluacion de seguridad y el licenciamiento de los reactores LFR, reduciendo las incertidumbres en los parametros 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 parametros de seguridad clave del reactor (factor de multiplicacion neutronico, keff, fraccion efectiva de neutrones diferidos, beff, tiempo efectivo de generacion de neutrones, Leff, coeficientes de reactividad, ...) e identificar posibles debilidades en los datos nucleares. Existen herramientas para calcular la incertidumbre de un parametro 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 isotopos y canales de reaccion a incluir en el analisis; uso de datos nucleares en estructura de multigrupos; uso de una libreria de datos nucleares especifica y/o una matriz de covarianza especifica; y la limitacion en la complejidad del sistema a analizar debido al numero requerido de simulaciones. Por lo tanto, en este trabajo, se ha desarrollado una Metodologia de Sensibilidad e Incertidumbre para codigos de MONtecarlo (SUMMON). SUMMON es una herramienta concebida para realizar analisis automatizados completos de sensibilidad e incertidumbre de los parametros de reactividad (para seguridad) mas relevantes de disenos de reactores desde el punto de vista neutronico, es decir, keff, beff, Leff y los coeficientes de reactividad, utilizando librerias de datos nucleares y covarianzas de ultima generacion. SUMMON se ha validado utilizando experimentos integrales del ICSBEP (International Handbook of Evaluated Criticality Safety Benchmark Experiments) y se ha verificado exhaustivamente con codigos consolidados como SCALE, SUSD3D y SERPENT. Se ha encontrado un buen acuerdo entre los codigos. Una vez SUMMON fue desarrollado, se llevaron a cabo analisis preliminares para el diseno de MYRRHA (Multi-purpose hYbrid Research Reactor for High-tech Applications), un reactor rapido refrigerado con plomo-bismuto. Primero, se utilizo la libreria de datos nucleares ENDF/B-VII.0 para identificar los datos nucleares mas importantes para las reacciones inducidas por neutrones en los calculos de criticidad de los LFR. Posteriormente, la libreria JEFF-3.3T1, version beta en ese momento de la nueva version de la libreria de datos nucleares evaluada en Europa, se analizo utilizando los mejores conjuntos de datos experimentales dependientes de la energia disponibles. El bismuto y el plomo, identificados en los analisis anteriores como isotopos 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 region 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 version final de dicha libreria de datos nucleares. A continuacion, se realizaron analisis de sensibilidad e incertidumbre con las librerias de datos nucleares JEFF-3.3 y ENDF/B-VIII.0 mediante SUMMON para estimar las incertidumbres en los parametros de criticidad de MYRRHA. Si bien se observo un buen acuerdo en las incertidumbres totales producidas por ambas librerias, las diferencias en las evaluaciones y la inexistencia de correlaciones y evaluaciones de covarianzas hicieron que los contribuyentes a la incertidumbre total difirieran. Ademas, las precisiones objetivo de diseno para algunos parametros de seguridad, como el factor de multiplicacion neutronica, se excedieron en mas del doble para las evaluaciones de datos nucleares consideradas. Con el fin de proporcionar datos nucleares ajustados, no solo capaces de predecir las propiedades del reactor dentro de la precision objetivo de diseno, sino tambien estadisticamente coherentes con los diversos experimentos diferenciales, se desarrollo el modulo de Asimilacion de Datos Con summoN (DAWN). DAWN se basa en la combinacion de datos de covarianza experimentales y experimentos integrales junto con tecnicas avanzadas de ajuste estadistico (minimos cuadrados generalizados). DAWN ha sido verificado utilizando el metodo TMC (Total MonteCarlo) para diferentes experimentos integrales. Finalmente, DAWN se uso para realizar una asimilacion de los principales contribuyentes a la incertidumbre mediante el uso de datos nucleares de JEFF-3.3 a priori y experimentos de masa critica disponibles publicamente en el ICSBEP. La consistencia del ajuste se verifico con datos experimentales diferenciales y se encontro un buen acuerdo. Se obtuvo una reduccion significativa en la incertidumbre utilizando los experimentos mas representativos de MYRRHA, debido a la reduccion en la incertidumbre de los contribuyentes principales y la presencia a posteriori de fuertes correlaciones cruzadas entre isotopos y reacciones que no existian a priori. Los resultados muestran que se puede lograr una reduccion de casi 300 pcm realizando una asimilacion con el experimento mas sensible al mayor contribuyente a la incertidumbre. Esto demuestra que la combinacion de datos de covarianza experimental y experimentos integrales junto con la tecnica de minimos cuadrados generalizados puede proporcionar datos nucleares ajustados capaces de predecir las propiedades del reactor con menor incertidumbre, coherentes con los datos diferenciales.

A Monte Carlo-based Bayesian inference model is applied to the prediction of reactor operation parameters of a PWR nuclear power plant. In this non-perturbative framework, high-dimensional covariance information describing the uncertainty of microscopic nuclear data is combined with measured reactor operation data in order to provide statistically sound, well founded uncertainty estimates of integral parameters, such as the boron letdown curve and the burnup-dependent reactor power distribution. The performance of this methodology is assessed in a blind test approach, where we use measurements of a given reactor cycle to improve the prediction of the subsequent cycle. As it turns out, the resulting improvement of the prediction quality is impressive. In particular, the prediction uncertainty of the boron letdown curve, which is of utmost importance for the planning of the reactor cycle length, can be reduced by one order of magnitude by including the boron concentration measurement information of the previous cycle in the analysis. Additionally, we present first results of non-perturbative nuclear-data updating and show that predictions obtained with the updated libraries are consistent with those induced by Bayesian inference applied directly to the integral observables., Comment: 10 pages, 11 figures

This paper summarizes the nodal level results from the VVER MSLB core simulation in the NURESAFE EU project. The main objective is to implement and verify new developments in the models and couplings of 3D core simulators for cores with hexagonal fuel assemblies. Recent versions of the COBAYA and DYN3D core physics codes, and the FLICA4 and CTF thermal-hydraulic codes were tested standalone and coupled through standardized coupling functions in the Salome platform. The MSLB core transient was analyzed in coupled code simulation of a core boundary condition problem derived from the OECD VVER MSLB benchmark. The impact of node sub-division and different core mixing models, as well as the effects of CFD computed core inlet thermal-hydraulic boundary conditions on the core dynamics were explored.

A sensitivity and uncertainty analysis was carried out to estimate the uncertainty in the neutron multiplication factor k eff and to identify the most important nuclear data for neutron induced reactions for criticality calculations of the latest MYRRHA designs. Sensitivity profiles, i.e. sensitivity to the nuclear data as a function of incoming neutron energy, were derived for both a critical and sub-critical core. They were calculated using codes that are based on different methodologies including stochastic and deterministic calculations (i.e. SCALE, MCNP and XSUN). The neutron induced nuclear data sensitivity analysis outlined the following quantities to be of special importance for the MYRRHA reactor concept: 239 Pu(n,γ) both in resonance and fast energy region, (n,f) fast, χ and ν fast; 238 U(n,n′) fast, (n,γ) resonance and fast, (n,n) resonance and fast; 240 Pu ν fast; 238 Pu(n,f) both resonance and fast; 56 Fe(n,γ) both resonance and fast. Differences of less than 4% between codes were obtained for these quantities, with few exceptions ( 238 Pu(n,f), 238 U(n,n) and 56 Fe(n,γ) reactions). Nuclear data covariance matrices of different libraries (SCALE-6, COMMARA-2 and JENDL-4.0m) were used to derive the uncertainty in k eff based on the calculated sensitivities. This study reveals that the largest contributions to k eff uncertainty result from the uncertainty in the average prompt neutron fission multiplicity of 239 Pu, in the 238 U inelastic scattering cross section and 239 Pu fission cross section, using the covariances from SCALE-6, COMMARA-2 and JENDL-4.0m, respectively.

International audience; The impact of the current nuclear data library covariances such as in ENDF/B-VII.1, JEFF-3.2, JENDL-4.0, SCALE and TENDL, for relevant current reactors is presented in this work. The uncertainties due to nuclear data are calculated for existing PWR and BWR fuel assemblies (with burn-up up to 40 GWd/tHM, followed by 10 years of cooling time) and for a simplified PWR full core model (without burn-up) for quantities such as k∞ , macroscopic cross sections, pin power or isotope inventory. In this work, the method of propagation of uncertainties is based on random sampling of nuclear data, either from covariance files or directly from basic parameters. Additionally, possible biases on calculated quantities are investigated such as the self-shielding treatment. Different calculation schemes are used, based on CASMO, SCALE, DRAGON, MCNP or FISPACT-II, thus simulating real-life assignments for technical-support organizations. The outcome of such a study is a comparison of uncertainties with two consequences. One: although this study is not expected to lead to similar results between the involved calculation schemes, it provides an insight on what can happen when calculating uncertainties and allows to give some perspectives on the range of validity on these uncertainties. Two: it allows to dress a picture of the state of the knowledge as of today, using existing nuclear data library covariances and current methods.

The MYRRHA (Multi-purpose hYbrid Research Reactor for High-tech Applications) concept is a flexible experimental lead-bismuth cooled and mixed-oxide (MOX) fueled fast spectrum facility designed to operate both in sub-critical (accelerator driven) and critical modes. One of the key issues for the safe operation of the reactor is the uncertainty assessment during the design works. The main objective of the European project CHANDA (solving CHAllenges in Nuclear DAta) Work Package 10 is to improve MYRRHA relevant nuclear data in order to reduce the reactor parameter uncertainties derived from them. In order to achieve this goal, several tasks have been undertaken. First, a sensitivity study of MYRRHA integral parameters, such as energy dependent cross sections, fission spectra and neutron multiplicities, to nuclear data has been conducted resulting in a list of MYRRHA relevant quantities (nuclides and reactions). On the second task, an analysis of the existing experimental data and evaluations for the quantities included in the list has been carried out. In this framework, the impact on the multiplication factor of quantities from different nuclear data libraries for different nuclides, reactions and energy regions has been investigated on the MYRRHA MOX critical core model. As the next step, new experiments and evaluations will be performed in order to improve existing nuclear data libraries.

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-hydraulics COBAYA3/COBRA-TF system. For this purpose, the OECD/NEA PWR MOX/UO 2 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.

Performing three-dimensional pin-by-pin full core calculations based on an improved solution of the multi-group diffusion equation is an affordable option nowadays to compute accurate local safety parameters for light water reactors. Since a transport approximation is solved, appropriate correction factors, such as interface discontinuity factors, are required to nearly reproduce the fully heterogeneous transport solution. Calculating exact pin-by-pin discontinuity factors 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; however, inaccurate correction factors are one major source of error in core analysis when using multi-group diffusion theory. An alternative to generate accurate pin-by-pin interface discontinuity factors is to build a functional-fitting that allows incorporating the environment dependence in the computed values. This paper suggests a methodology to consider the neighborhood effect based on the Analytic Coarse-Mesh Finite Difference method for the multi-group diffusion equation. It has been applied to both definitions of interface discontinuity factors, the one based on the Generalized Equivalence Theory and the one based on Black-Box Homogenization, and for different few energy groups structures. Conclusions are drawn over the optimal functional-fitting and demonstrative results are obtained with the multi-group pin-by-pin diffusion code COBAYA3 for representative PWR configurations.

In this paper, we assess the impact of activation cross-section uncertainties on relevant fuel cycle parameters for a conceptual design of a modular European Facility for Industrial Transmutation (EFIT) with a “double strata” fuel cycle. Next, the nuclear data requirements are evaluated so that the parameters can meet the assigned design target accuracies. Different discharge burn-up levels are considered: a low burn-up, corresponding to the equilibrium cycle, and a high burn-up level, simulating the effects on the fuel of the multi-recycling scenario. In order to perform this study, we propose a methodology in two steps. Firstly, we compute the uncertainties on the system parameters by using a Monte Carlo simulation, as it is considered the most reliable approach to address this problem. Secondly, the analysis of the results is performed by a sensitivity technique, in order to identify the relevant reaction channels and prioritize the data improvement needs. Cross-section uncertainties are taken from the EAF-2007/UN library since it includes data for all the actinides potentially present in the irradiated fuel. Relevant uncertainties in some of the fuel cycle parameters have been obtained, and we conclude with recommendations for future nuclear data measurement programs, beyond the specific results obtained with the present nuclear data files and the limited available covariance information. A comparison with the uncertainty and accuracy analysis recently published by the WPEC-Subgroup26 of the OECD using BOLNA covariance matrices is performed. Despite the differences in the transmuter reactor used for the analysis, some conclusions obtained by Subgroup26 are qualitatively corroborated, and improvements for additional cross sections are suggested.

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.

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 A— 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.

A comprehensive transmutation study has been performed for steels considered in the selection of structural materials for magnetic and inertial fusion reactors for the international fusion materials irradiation facility (IFMIF) neutron irradiation environment, as well as in the international thermonuclear experimental reactor (ITER) and a fusion demonstration reactor (DEMO) for comparison purposes. An element by element transmutation approach is used in the study, addressing the generation of: (1) H and He and (2) solid transmutants. The IEAF 2001 activation library and the activation code ACAB were applied in the IFMIF transmutation analysis, after proving the applicability of ACAB for transmutation calculations in intermediate energy systems.

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.

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.

Engineering of innovative reactor concepts requires computational tools capable of producing results with a high level of accuracy. These results are affected by different sources of uncertainty such as the ones coming from nuclear data. The assessment of the uncertainty levels on the design and safety parameters is mandatory. The uncertainty quantification applied here is based on the adjoint sensitivity analysis, where the sensitivities of design values to nuclear data are employed together with the nuclear data uncertainties to propagate these uncertainties to the design parameters. The European Sodium Fast Reactor (ESFR) is the innovative reactor model considered here, designed in the framework of a EURATOM Collaborative Project. Some of the relevant safety quantities linked to it are Doppler and void reactivity coefficients, whose uncertainties are quantified. Also the identification of the nuclear reaction data where an improvement will certainly benefit the design accuracy is performed. 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.

Minor actinides (MAs) transmutation is a main design objective of advanced nuclear systems such as generation IV Sodium Fast Reactors (SFRs). In advanced fuel cycles, MA contents in final high level waste packages are main contributors to short term heat production as well as to long-term radiotoxicity. Therefore, MA transmutation would have an impact on repository designs and would reduce the environment burden of nuclear energy. In order to predict such consequences Monte Carlo (MC) transport codes are used in reactor design tasks and they are important complements and references for routinely used deterministic computational tools. In this paper two promising Monte Carlo transport-coupled depletion codes, EVOLCODE and SERPENT, are used to examine the impact of MA burning strategies in a SFR core, 3600 MWth. The core concept proposal for MA loading in two configurations is the result of an optimization effort upon a preliminary reference design to reduce the reactivity insertion as a consequence of sodium voiding, one of the main concerns of this technology. The objective of this paper is double. Firstly, efficiencies of the two core configurations for MA transmutation are addressed and evaluated in terms of actinides mass changes and reactivity coefficients. Results are compared with those without MA loading. Secondly, a comparison of the two codes is provided. The discrepancies in the results are quantified and discussed.

The prediction of the tritium production is required for handling procedures of samples, safety & maintenance and licensing of the International Fusion Materials Irradiation Facility (IFMIF). A comparison of the evaluated tritium production cross-sections with available experimental data from the EXFOR data base has shown insufficient validation. And significant discrepancies in evaluated cross-section libraries, including lack of tritium production reactions for some important elements, were found. Here, we have addressed an uncertainty analysis to draw conclusions on the reliability of the tritium prediction under the potential impact of activation cross-section uncertainties. We conclude that there is not sufficient experimental validation of the evaluated tritium production cross-sections, especially for iron and sodium. Therefore a dedicated experimental validation program for those elements should be desirable.

A comprehensive study is performed in order to assess the pertinence of fission chambers coated with different fissile materials for high neutron flux detection. Three neutron scenarios are proposed to study the fast component of a high neutron flux: (i) high neutron flux with a significant thermal contribution such as BR2, (ii) DEMO magnetic fusion reactor, and (iii) IFMIF high flux test module. In this study, the inventory code ACAB is used to analyze the following questions: (i) impact of different deposits in fission chambers; (ii) effect of the irradiation time/burn-up on the concentration; (iii) impact of activation cross-section uncertainties on the composition of the deposit for all the range of burn-up/irradiation neutron fluences of interest. The complete set of nuclear data (decay, fission yield, activation cross-sections, and uncertainties) provided in the EAF2007 data library are used for this evaluation.

The present study is mainly aimed to provide the primary damage (displacements per atom, generation of solid transmutants and gas production rates) of structural materials irradiated in the high and medium flux test modules of the International Fusion Materials Irradiation Facility (IFMIF). We have investigated if the change of the composition during the irradiation time has effect on the prediction of the atomic displacements. The effect of the activation cross section uncertainties in the assessment of both solid transmutants and hydrogen and helium production is also analyzed. The results are provided element-by-element, so that the primary damage of any material irradiated in such neutron environments can be easily assessed; in this paper, we have predicted the primary damage of the low activation steel Eurofer.

In this work we address the development and implementation of the analytic coarse-mesh finite-difference (ACMFD) method in a nodal neutron diffusion solver called ANDES. The first version of the solver is implemented in any number of neutron energy groups, and in 3D Cartesian geometries; thus it mainly addresses PWR and BWR core simulations. The details about the generalization to multigroups and 3D, as well as the implementation of the method are given. The transverse integration procedure is the scheme chosen to extend the ACMFD formulation to multidimensional problems. The role of the transverse leakage treatment in the accuracy of the nodal solutions is analyzed in detail: the involved assumptions, the limitations of the method in terms of nodal width, the alternative approaches to implement the transverse leakage terms in nodal methods – implicit or explicit −, and the error assessment due to transverse integration. A new approach for solving the control rod “cusping” problem, based on the direct application of the ACMFD method, is also developed and implemented in ANDES. The solver architecture turns ANDES into an user-friendly, modular and easily linkable tool, as required to be integrated into common software platforms for multi-scale and multi-physics simulations. ANDES can be used either as a stand-alone nodal code or as a solver to accelerate the convergence of whole core pin-by-pin code systems. The verification and performance of the solver are demonstrated using both proof-of-principle test cases and well-referenced international benchmarks.

Two methodologies to propagate the uncertainties on the nuclide inventory in combined Monte Carlo-spectrum and burn-up calculations are presented, based on sensitivity/uncertainty and random sampling techniques (uncertainty Monte Carlo method). Both enable the assessment of the impact of uncertainties in the nuclear data as well as uncertainties due to the statistical nature of the Monte Carlo neutron transport calculation. The methodologies are implemented in our MCNP–ACAB system, which combines the neutron transport code MCNP-4C and the inventory code ACAB. A high burn-up benchmark problem is used to test the MCNP–ACAB performance in inventory predictions, with no uncertainties. A good agreement is found with the results of other participants. This benchmark problem is also used to assess the impact of nuclear data uncertainties and statistical flux errors in high burn-up applications. A detailed calculation is performed to evaluate the effect of cross-section uncertainties in the inventory prediction, taking into account the temporal evolution of the neutron flux level and spectrum. Very large uncertainties are found at the unusually high burn-up of this exercise (800 MWd/kgHM). To compare the impact of the statistical errors in the calculated flux with respect to the cross uncertainties, a simplified problem is considered, taking a constant neutron flux level and spectrum. It is shown that, provided that the flux statistical deviations in the Monte Carlo transport calculation do not exceed a given value, the effect of the flux errors in the calculated isotopic inventory are negligible (even at very high burn-up) compared to the effect of the large cross-section uncertainties available at present in the data files.

A comprehensive assessment on the eligibility of reduced activation (RA) steels as structural chamber material in Inertial Fusion Energy (IFE) thick-liquid concepts is performed. As far as alloying elements, it is shown that the activation of tungsten is a question to debate. Regarding impurity elements, it is analyzed if they could question the possibility of obtaining real RA steels for shallow land burial (SLB). The effect of the thickness of the liquid wall on the SLB response of alloying and impurity elements is computed. And above all, we have estimated the impact of cross section uncertainties when addressing the former questions, and we identify those to be improved. The necessary improvement of some tungsten and niobium cross sections is justified.

The primary damage behaviour of the low activation steel Eurofer was studied under irradiation in the high flux test module of IFMIF and in the first structural wall of the magnetic (ITER and DEMO) and inertial (HYLIFE-II and HAPL) fusion energy (MFE/IFE) reactors. We have calculated the damages, gas production rates and gas to dpa production ratio with ACAB code. The effect of activation cross section uncertainties in the assessment of hydrogen and helium production is also analysed.

In this work, a detailed assessment of the decay heat power for the commercial-size European sodium-cooled fast reactor (ESFR) at the end of its equilibrium cycle has been performed. The summation method has been used to compute very accurate spatial- and time-dependent decay heat by employing state-of-the-art coupled transport-depletion computational codes and nuclear data. This detailed map provides basic information for subsequent transient calculations of the ESFR. A comprehensive analysis of the decay heat has been carried out and interdependencies between decay heat and different parameters characterizing the core state prior to shutdowns, such as discharge burnup or type of fuel material, have been identified. That analysis has served as a basis to develop analytic functions to reconstruct the spatial-dependent decay heat power for the ESFR for cooling times within the first day after shutdown.

In the paper, the specification of a new neutronics benchmark for large sodium cooled fast reactor (SFR) core and results of modeling by different participants are presented. The neutronics benchmark describes the core of the French sodium cooled reactor Superphénix at its startup configuration, which in particular was used for experimental measurement of reactivity characteristics. The benchmark consists of the detailed heterogeneous core specification for neutronic analysis and the results of the reference solution. Different core geometries and thermal conditions from the cold “as fabricated” up to full power were considered. The reference Monte Carlo (MC) solution of serpent 2 includes data on multiplication factor, power distribution, axial and radial reaction rates distribution, reactivity coefficients and safety characteristics, control rods worth, kinetic data. The results of modeling with seven other solutions using deterministic and MC methods are also presented and compared to the reference solution. The comparisons results demonstrate appropriate agreement of evaluated characteristics. The neutronics results will be used in the second phase of the benchmark for the evaluation of transient behavior of the core.