Fundamentals of 3-D Neutron Kinetics and Current Status

This lecture includes the following topics: 1) A summary of the cell and lattice calculations used to generate the neutron reaction data for neutron kinetics, including the spectral and burn up calculations of LWR cells and fuel assembly lattices, and the main nodal kinetics parameters: mean neutron generation time and delayed neutron fraction; 2) the features of the advanced nodal methods for 3-D LWR core physics, including the treatment of partially inserted control rods, fuel assembly grids, fuel burn up and xenon and samarium transients, and ex core detector responses, that are essential for core surveillance, axial offset control and operating transient analysis; 3) the advanced nodal methods for 3-D LWR core neutron kinetics (best estimate safety analysis, real time simulation); and 4) example applications to 3-D neutron kinetics problems in transient analysis of PWR cores, including model, benchmark and operational transients without, or with simple, thermal-hydraulics feedback

Basis for Coupled 3-D Neutronics-Thermal-Hydraulics

The purpose of this seminar is first to discuss the basis of the coupling between 3-D Neutron- Kinetics and Thermal-Hydraulics codes, including the control and 3-D variables to interchange, the transform of the 3-D NK and TH core nodalizations, and the schemes for temporal coupling and time-step control. As representative examples of the NK-TH core coupling, we discuss first the integration of a 3-D NK nodal code with a TH subchannel code, for detailed transient core analysis; and second the coupling of 3-D NK nodal codes with TH system codes, for general transient and safety analysis. In chapter 2, we analyze several prototype model transients in PWR, where large 3-D core asymmetries are found and the NK-TH coupling is quite significant, including loss-of-flow and symmetric and asymmetric core cooling, considering the effects on the responses of the excore detectors. In chapter 3, we discuss the analysis of an increase-of-flow transient actually occurred in an operating PWR and the comparison with the measured data. In chapter 4, we summarize the phenomena and results of the calculations of the NEA/NSC Benchmark on the main steam line break (MSLB) transient in a PWR. Finally, we will discuss the state-of-the-art issues in LWR coupled NK-TH 3-D transient analysis and ongoing and planned computational developments

Development of an Analytic Nodal Diffusion Solver in Multigroups for 3D Reactor Cores with Rectangular or Hexagonal Assemblies.

More accurate modelling of physical phenomena involved in present and future nuclear reactors requires a multi-scale and multi-physics approach. This challenge can be accomplished by the coupling of best-estimate core-physics, thermal-hydraulics and multi-physics solvers. In order to make viable that coupling, the current trends in reactor simulations are along the development of a new generation of tools based on user-friendly, modular, easily linkable, faster and more accurate codes to be integrated in common platforms. These premises are in the origin of the NURESIM Integrated Project within the 6th European Framework Program, which is envisaged to provide the initial step towards a Common European Standard Software Platform for nuclear reactors simulations. In the frame of this project and to reach the above-mentioned goals, a 3-D multigroup nodal solver for neutron diffusion calculations called ANDES (Analytic Nodal Diffusion Equation Solver) has been developed and tested in-depth in this Thesis. ANDES solves the steady-state and time-dependent neutron diffusion equation in threedimensions and any number of energy groups, utilizing the Analytic Coarse-Mesh Finite-Difference (ACMFD) scheme to yield the nodal coupling equations. It can be applied to both Cartesian and triangular-Z geometries, so that simulations of LWR as well as VVER, HTR and fast reactors can be performed. The solver has been implemented in a fully encapsulated way, enabling it as a module to be readily integrated in other codes and platforms. In fact, it 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. Verification of performance has shown that ANDES is a code with high order definition for whole core realistic nodal simulations. In this paper, the methodology developed and involved in ANDES is presented

Análisis de la transmutación de Actínidos Minoritarios en un reactor rápido de sodio con modelo de carga homogéneo mediante el código MCNPX-CINDER

El reactor rápido refrigerado por sodio (SFR) constituye uno de los conceptos más prometedores de los seis considerados en la Generación IV de reactores nucleares, encontrándose actualmente en fase de investigación. En este marco surge el proyecto europeo CP ESFR (Collaborative Project for an European Sodium Fast Reactor) cuya finalidad es analizar los diversos desafíos y oportunidades que el desarrollo de este tipo de reactores plantea, ya sea en términos de seguridad, tecnología de sodio, capacidades transmutadoras, etc

Transient analysis in the 3D nodal kinetics and thermal-hydraulics ANDES/COBRA coupled system

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

Whole Core Pin-by-Pin Coupled Neutronic-Thermal-hydraulic Steady state and Transient Calculations using COBAYA3 code

Nowadays, coupled 3D neutron-kinetics and thermal-hydraulic core calculations are performed by applying a radial average channel approach using a meshing of one quarter of assembly in the best case. This approach does not take into account the subchannels effects due to the averaging of the physical fields and the loose of heterogeneity in the thermal-hydraulic modelization. Therefore the models do not have enough resolution to predict those subchannels effects which are important for the fuel design safety margins, because it is in the local scale, where we can search the hottest pellet or the maximum heat flux. The UPM advanced multi-scale neutron-kinetics and thermal-hydraulics methodologies being implemented in COBAYA3 include domain decomposition by alternate core dissections for the local 3D fine-mesh scale problems (pin cells/subchannels) and an analytical nodal diffusion solver for the coarse mesh scale coupled with the thermal-hydraulic using a modelization of one channel per assembly or per quarter of assembly. In this work, we address the domain decomposition by the alternate core dissections methodology applied to solve coupled 3D neutronic/thermal-hydraulic (N-TH) problems at the fine-mesh scale. The N-TH coupling at the cell-subchannel scale allows the treatment of the effects of the detailed TH feedbacks on cross-sections, thus resulting in better estimates of the local safety margins at the pin level

The Analytic Coarse-Mesh Finite Difference Method for Multigroup and Multidimensional Diffusion Calculations

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

El código nodal analítico ANDES para difusión en geometría 3D y multi-grupos: Desarrollo y Resultados

La necesidad de métodos computacionales cada vez más exactos para la simulación de los fenómenos físicos presentes en los reactores nucleares actuales y futuros, requiere una aproximación multi-escala y multi-física. Este reto puede ser realizado mediante el acoplamiento de códigos best-estimate de neutrónica y termo-hidráulica. Con este objetivo, la tendencia actual en el campo de simulación de reactores es el desarrollo de una nueva generación de herramientas que sean fáciles de usar, modulares, intercambiables y de esta manera, integrables en plataformas comunes. Estas son las premisas que dieron lugar al proyecto integrado NURESIM dentro del 6º Programa Marco de la Unión Europea (Cacuci et al., 2006). En el marco de este proyecto se ha desarrollado y validado un código nodal de difusión tridimensional en multi-grupos llamado ANDES (Analytic Nodal Diffusion Equation Solver)(Lozano et al., 2007). El código ANDES resuelve la ecuación de difusión neutrónica en geometría Cartesiana (LWR) o geometría Triangular-Z (VVER, HTGR, SFR) en tres dimensiones y multigrupos de energía. Para ello utiliza el método Analítico en Malla Gruesa y Diferencias Finitas (ACMFD) (Aragonés et al., 2007) para obtener las ecuaciones de acoplamiento nodal. Esta metodología, originalmente introducida por Y.A. Chao (Chao, 1999, 2000) para la ecuación de difusión estacionaria ha sido extendida para la ecuación cinética (Lozano et al., 2008), lo que permite no sólo el cálculo de estados estacionarios, sino también de transitorios originados por un cambio en las condiciones neutrónicas o termohidráulicas. Para la simulación de transitorios, así como de estacionarios a potencia, se ha llevado a cabo el acoplamiento de ANDES con el código termohidráulico COBRA (Jiménez et al., 2007). Es destacable el gran esfuerzo realizado en dotar al código de una estructura que lo convierta en una herramienta fácilmente integrable, lo que ha permitido la integración del mismo en nuestro código 3D de celda COBAYA3 (Herrero et al., 2007), así como en la nueva plataforma DESCARTES (Calvin et al., 2005)

Methods and Results for the MSLB NEA Benchmark Using SIMTRAN and RELAP5

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

Development and Performance of the ANDES/COBRA-III Coupled System in Hexagonal-Z Geometry

In this paper, the extension of the nodal diffusion code ANDES, based on the ACMFD method, to hexagonal geometry is presented, as well as its coupling with the thermal-hydraulic (TH) code COBRA-IIIc/MIT-2 for such hexagonal problems. In extending the ACMFD method to hexagonal assemblies, triangular-Z nodes are used, taking advantage of the mesh refinement capabilities implicit within that geometry. The existing TH coupling for Cartesian geometry applications has also been extended to hexagonal problems, 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. Therefore, the work presented here introduces an improvement in the TH VVER core modelling, where in the best case scenario, just twenty axial layers and one channel per fuel assembly were used. As a result, the neutronic and thermal-hydraulics (N-TH) coupled code, ANDES/COBRA-IIIc, extensively verified in Cartesian geometry cores analysis, can also be applied to full threedimensional VVER core problems. Some verification results are provided, corresponding to 2nd exercises (HZP and HP steady states) of the OECD/NEA- VVER-1000 Coolant Transient benchmark and to the HZP and HFP steady states of the V1000CT2-EXT2 NURESIM benchmark