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

The analytic nodal diffusion solver ANDES in multigroups for 3D rectangular geometry: Development and performance analysis

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

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

On the Extension of the Analytic Nodal Diffusion Solver ANDES to Sodium Fast Reactors

Within the framework of the Collaborative Project for a European Sodium Fast Reactor, the reactor physics group at UPM is working on the extension of its in-house multi-scale advanced deterministic code COBAYA3 to Sodium Fast Reactors (SFR). COBAYA3 is a 3D multigroup neutron kinetics diffusion code that can be used either as a pin-by-pin code or as a stand-alone nodal code by using the analytic nodal diffusion solver ANDES. It is coupled with thermalhydraulics codes such as COBRA-TF and FLICA, allowing transient analysis of LWR at both fine-mesh and coarse-mesh scales. In order to enable also 3D pin-by-pin and nodal coupled NK-TH simulations of SFR, different developments are in progress. This paper presents the first steps towards the application of COBAYA3 to this type of reactors. ANDES solver, already extended to triangular-Z geometry, has been applied to fast reactor steady-state calculations. The required cross section libraries were generated with ERANOS code for several configurations. The limitations encountered in the application of the Analytic Coarse Mesh Finite Difference (ACMFD) method –implemented inside ANDES– to fast reactors are presented and the sensitivity of the method when using a high number of energy groups is studied. ANDES performance is assessed by comparison with the results provided by ERANOS, using a mini-core model in 33 energy groups. Furthermore, a benchmark from the NEA for a small 3D FBR in hexagonal-Z geometry and 4 energy groups is also employed to verify the behavior of the code with few energy groups

A proposed parameterization of interface discontinuity factors depending on neighborhood for pin-by-pin diffusion computations for LWR

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

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

Desarrollo de una herramienta de verificación para cálculos de difusión mediante COBAYA

El código COBAYA4 es un simulador de núcleo multi-escala que resuelve la ecuación de difusión 3D en multigrupos en geometría cartesiana y hexagonal[3]. Este código ha sido desarrollado en el Departamento de Ingeniería Nuclear desde los años 80[2] ampliando su alcance y funcionalidades de forma continua. Como parte de estos desarrollos es necesaria la verificación continua de que el código sigue teniendo al menos las mismas capacidades que tenía anteriormente. Además es necesario establecer casos de referencia que nos permitan confirmar que los resultados son comparables a los obtenidos con otros códigos con modelos de mayor precisión. El desarrollo de una herramienta informática que automatice la comparación de resultados con versiones anteriores del código y con resultados obtenidos mediante modelos de mayor precisión es crucial para implementar en el código nuevas funcionalidades. El trabajo aquí presentado ha consistido en la generación de la mencionada herramienta y del conjunto de casos de referencia que han constituido la matriz mencionada

Interface discontinuity factors in the modal eigenspace of the multigroup diffusion matrix

Interface discontinuity factors based on the Generalized Equivalence Theory are commonly used in nodal homogenized diffusion calculations so that diffusion average values approximate heterogeneous higher order solutions. In this paper, an additional form of interface correction factors is presented in the frame of the Analytic Coarse Mesh Finite Difference Method (ACMFD), based on a correction of the modal fluxes instead of the physical fluxes. In the ACMFD formulation, implemented in COBAYA3 code, the coupled multigroup diffusion equations inside a homogenized region are reduced to a set of uncoupled modal equations through diagonalization of the multigroup diffusion matrix. Then, physical fluxes are transformed into modal fluxes in the eigenspace of the diffusion matrix. It is possible to introduce interface flux discontinuity jumps as the difference of heterogeneous and homogeneous modal fluxes instead of introducing interface discontinuity factors as the ratio of heterogeneous and homogeneous physical fluxes. The formulation in the modal space has been implemented in COBAYA3 code and assessed by comparison with solutions using classical interface discontinuity factors in the physical spac

Efectos de generación y optimización de librerías de secciones eficaces en el análisis de transitorios en reactores PWR

Los análisis de los transitorios y situaciones accidentales de los reactores de agua ligera requieren el uso de simuladores y códigos a nivel de núcleo completo con modelos de cinética 3D. Normalmente estos códigos utilizan como datos de entrada librerías de secciones eficaces compiladas en tablas multidimensionales. En este caso, los errores de interpolación, originados a la hora de computar los valores de las secciones eficaces a partir de los puntos de la tabla, son una fuente de incertidumbre en el cálculo del parámetro k-efectiva y deben de tenerse en cuenta. Estos errores dependen de la estructura de la malla de puntos que cubre el dominio de variación de cada una de las variables termo-hidráulicas en las que se tabula la librería de secciones eficaces, y pueden ser minimizados con la elección de una malla adecuada, a diferencia de los errores debidos a los datos nucleares. En esta ponencia se evalúa el impacto que tiene una determinada malla sobre un transitorio en un reactor PWR consistente en la expulsión de una barra de control. Para ello se han usado los códigos neutrónico y termo-hidráulico acoplados COBAYA3/COBRA-TF. Con este objetivo se ha escogido el OECD/NEA PWR MOX/UO2 rod ejection transient benchmark ya que proporciona unas composiciones isotópicas y unas configuraciones geométricas definidas que permiten el empleo de códigos lattice para generar librerías propias. El código de transporte utilizado para ello ha sido el código APOLLO2.8. Así mismo, ya que se proporcionaba también una librería como parte de las especificaciones, los efectos debidos a la generación de éstas sobre la respuesta del transitorio son analizados. Los resultados muestran grandes discrepancias al emplear la librería del benchmark o las librerías propias comparándolas con las soluciones de otros participantes. El origen de estas discrepancias se halla en las secciones eficaces nodales proporcionadas en el benchmark

Coupled calculations COBAYA4/CTF for different MSLB scenarios in the frame of NURESAFE project

The new version of COBAYA diffusion code, COBAYA4, has been integrated into SALOME platform in order to enable the coupling with other thermal-hydraulics codes of the platform. Particularly, it has been coupled with CTF code, and the system COBAYA4-CTF is employed within NURESAFE project for the simulation of MSLB transient in two different reactors: PWR and VVER