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

Modal seismic analysis of a nuclear power plant control panel and comparison with SAP 4

The application of NASTRAN to seismic analysis by considering the example of a nuclear power plant control panel was considered. A modal analysis of a three-dimensional model of the panel, consisting of beam and quadri-lateral membrane elements, is performed. Using the results of this analysis and a typical response spectrum of an earthquake, the seismic response of the structure is obtained. ALTERs required to the program in order to compute the maximum modal responses as well as the resultant response are given. The results are compared with those obtained by using the SAP IV computer program

Numerical simulation of long and slender cylinders vibrating in axial flow applied to the Myrrha reactor

Flow induced vibrations are an important concern in the design of nuclear reactors. One of the possible designs of the 4th generation nuclear reactors is a lead-cooled fast reactor of which MYYRHA is a prototype. The combination of high liquid density, flow velocity, low pitch-to-diameter ratio and the absence of grid spacers makes this design prone to flow induced vibrations. Although most vibrations are induced by cross flow, axial flow around this slender structure could also induce vibrations. In order to gain insight in the possible vibrations (either induced by cross flow, axial flow or an external excitation) this study examines the change of eigenmodes and frequencies of a bare rod due to the lead-bismuth flow. To do so partitioned simulations of the fluid structure interaction are performed in which the structure is initially perturbed according to an in-air eigenmode

Industrial implementation of intelligent system techniques for nuclear power plant condition monitoring

As the nuclear power plants within the UK age, there is an increased requirement for condition monitoring to ensure that the plants are still be able to operate safely. This paper describes the novel application of Intelligent Systems (IS) techniques to provide decision support to the condition monitoring of Nuclear Power Plant (NPP) reactor cores within the UK. The resulting system, BETA (British Energy Trace Analysis) is deployed within the UK’s nuclear operator and provides automated decision support for the analysis of refuelling data, a lead indicator of the health of AGR (Advanced Gas-cooled Reactor) nuclear power plant cores. The key contribution of this work is the improvement of existing manual, labour-intensive analysis through the application of IS techniques to provide decision support to NPP reactor core condition monitoring. This enables an existing source of condition monitoring data to be analysed in a rapid and repeatable manner, providing additional information relating to core health on a more regular basis than routine inspection data allows. The application of IS techniques addresses two issues with the existing manual interpretation of the data, namely the limited availability of expertise and the variability of assessment between different experts. Decision support is provided by four applications of intelligent systems techniques. Two instances of a rule-based expert system are deployed, the first to automatically identify key features within the refuelling data and the second to classify specific types of anomaly. Clustering techniques are applied to support the definition of benchmark behaviour, which is used to detect the presence of anomalies within the refuelling data. Finally data mining techniques are used to track the evolution of the normal benchmark behaviour over time. This results in a system that not only provides support for analysing new refuelling events but also provides the platform to allow future events to be analysed. The BETA system has been deployed within the nuclear operator in the UK and is used at both the engineering offices and on station to support the analysis of refuelling events from two AGR stations, with a view to expanding it to the rest of the fleet in the near future

Tungsten nuclear rocket, phase II, part 1 Final report, Jan. 16 - Jun. 15, 1966

Critical experiments and nuclear analyses of tungsten water moderated nuclear rocket reacto

Development of 3-D Neutronic Kinetic Model and Control for CANDU Reactors

The development of a three dimensional (3-D) neutronic kinetic modeling process aiming at control system design for CANadian Deuterium Uranium (CANDU) reactors is carried out in this thesis using a modal synthesis method. In this method, the reactor space-time neutron flux is synthesized by a time-weighted series of precalculated neutron flux modes. These modes are eigenfunctions of the governing neutron diffusion equation at reference steady-state operating conditions. The xenon effect has also been considered. A special attention has been paid to compare the performance of the developed 3-D model with that of a traditional coupled point kinetic model. The 3-D reactor model is implemented by MATLAB/SIMULINK software environment. A nondimensionalized SIMULINK representation of the reactor model is established. The performance of the developed 3-D reactor neutronic kinetic model is then evaluated in a closed-loop environment with the help of a CANDU reactor regulating system (RRS) simulation platform. The dynamic behavior of the reactor model in a practical load-following mode has also been examined. The accuracy of the model has been validated against actual plant measurements under transient conditions. Through the analysis and simulation studies, it has convincingly demonstrated that the developed 3-D reactor model has significant advantages over the traditional coupled point kinetic model in terms of the improved accuracy and the higher resolution in modeling the reactor internal flux behaviors. Furthermore, using Graphic User Interface (GUI) techniques a user-friendly software package for the RRS simulation platform is developed. Based on the 3-D reactor model and identified deficiencies of existing RRS’ functions, an advanced 3-D reactor power distribution control is proposed and investigated. Linearization of the reactor model is performed and the performance of the linearized reactor model is evaluated in a closed-loop RRS environment. Using the feedback control law, a newly designed control strategy tries to suppress the effects of high order neutron flux modes and to emphasize behaviors of the dominant mode – the fundamental flux distribution adopted by the nominal design. Thereby, the 3-D power distribution shape during transients is optimally maintained closer to the nominal design shape than by the traditional RRS. The benefits of 3-D power distribution include not only the improved economical operation, but also improved safety as the uncertainties and the uneven power distribution are reduced. These have been confirmed by extensive simulation studies to Regional Overpower Protection (ROP) detectors’ flux transients during load following processes

Integration methods for the time dependent neutron diffusion equation and other approximations of the neutron transport equation

[ES] Uno de los objetivos más importantes en el análisis de la seguridad en el campo de la ingeniería nuclear es el cálculo, rápido y preciso, de la evolución de la potencia dentro del núcleo del reactor. La distribución de los neutrones se puede describir a través de la ecuación de transporte de Boltzmann. La solución de esta ecuación no puede obtenerse de manera sencilla para reactores realistas, y es por ello que se tienen que considerar aproximaciones numéricas. En primer lugar, esta tesis se centra en obtener la solución para varios problemas estáticos asociados con la ecuación de difusión neutrónica: los modos lambda, los modos gamma y los modos alpha. Para la discretización espacial se ha utilizado un método de elementos finitos de alto orden. Diversas características de cada problema espectral se analizan y se comparan en diferentes reactores. Después, se investigan varios métodos de cálculo para problemas de autovalores y estrategias para calcular los problemas algebraicos obtenidos a partir de la discretización espacial. La mayoría de los trabajos destinados a la resolución de la ecuación de difusión neutrónica están diseñados para la aproximación de dos grupos de energía, sin considerar dispersión de neutrones del grupo térmico al grupo rápido. La principal ventaja de la metodología que se propone es que no depende de la geometría del reactor, del tipo de problema de autovalores ni del número de grupos de energía del problema. Tras esto, se obtiene la solución de las ecuaciones estacionarias de armónicos esféricos. La implementación de estas ecuaciones tiene dos principales diferencias respecto a la ecuación de difusión neutrónica. Primero, la discretización espacial se realiza a nivel de pin. Por tanto, se estudian diferentes tipos de mallas. Segundo, el número de grupos de energía es, generalmente, mayor que dos. De este modo, se desarrollan estrategias a bloques para optimizar el cálculo de los problemas algebraicos asociados. Finalmente, se implementa un método modal actualizado para integrar la ecuación de difusión neutrónica dependiente del tiempo. Se presentan y comparan los métodos modales basados en desarrollos en función de los diferentes modos espaciales para varios tipos de transitorios. Además, también se desarrolla un control de paso de tiempo adaptativo, que evita la actualización de los modos de una manera fija y adapta el paso de tiempo en función de varias estimaciones del error.[CA] Un dels objectius més importants per a l'anàlisi de la seguretat en el camp de l'enginyeria nuclear és el càlcul, ràpid i precís, de l'evolució de la potència dins del nucli d'un reactor. La distribució dels neutrons pot modelar-se mitjançant l'equació del transport de Boltzmann. La solució d'aquesta equació per a un reactor realístic no pot obtenir's de manera senzilla. És per això que han de considerar-se aproximacions numèriques. En primer lloc, la tesi se centra en l'obtenció de la solució per a diversos problemes estàtics associats amb l'equació de difusió neutrònica: els modes lambda, els modes gamma i els modes alpha. Per a la discretització espacial s'ha utilitzat un mètode d'elements finits d'alt ordre. Algunes de les característiques dels problemes espectrals s'analitzaran i es compararan per a diferents reactors. Tanmateix, diversos solucionadors de problemes d'autovalors i estratègies es desenvolupen per a calcular els problemes obtinguts de la discretització espacial. La majoria dels treballs per a resoldre l'equació de difusió neutrònica estan dissenyats per a l'aproximació de dos grups d'energia i sense considerar dispersió de neutrons del grup tèrmic al grup ràpid. El principal avantatge de la metodologia exposada és que no depèn de la geometria del reactor, del tipus de problema d'autovalors ni del nombre de grups d'energia del problema. Seguidament, s'obté la solució de les equacions estacionàries d'harmònics esfèrics. La implementació d'aquestes equacions té dues principals diferències respecte a l'equació de difusió. Primer, la discretització espacial es realitza a nivell de pin a partir de l'estudi de diferents malles. Segon, el nombre de grups d'energia és, generalment, major que dos. D'aquesta forma, es desenvolupen estratègies a blocs per a optimitzar el càlcul dels problemes algebraics associats. Finalment, s'implementa un mètode modal amb actualitzacions dels modes per a integrar l'equació de difusió neutrònica dependent del temps. Es presenten i es comparen els mètodes modals basats en l'expansió dels diferents modes espacials per a diversos tipus de transitoris. A més a més, un control de pas de temps adaptatiu es desenvolupa, evitant l'actualització dels modes d'una manera fixa i adaptant el pas de temps en funció de vàries estimacions de l'error.[EN] One of the most important targets in nuclear safety analyses is the fast and accurate computation of the power evolution inside of the reactor core. The distribution of neutrons can be described by the neutron transport Boltzmann equation. The solution of this equation for realistic nuclear reactors is not straightforward, and therefore, numerical approximations must be considered. First, the thesis is focused on the attainment of the solution for several steady-state problems associated with neutron diffusion problem: the $\lambda$-modes, the $\gamma$-modes and the $\alpha$-modes problems. A high order finite element method is used for the spatial discretization. Several characteristics of each type of spectral problem are compared and analyzed on different reactors. Thereafter, several eigenvalue solvers and strategies are investigated to compute efficiently the algebraic eigenvalue problems obtained from the discretization. Most works devoted to solve the neutron diffusion equation are made for the approximation of two energy groups and without considering up-scattering. The main property of the proposed methodologies is that they depend on neither the reactor geometry, the type of eigenvalue problem nor the number of energy groups. After that, the solution of the steady-state simplified spherical harmonics equations is obtained. The implementation of these equations has two main differences with respect to the neutron diffusion. First, the spatial discretization is made at level of pin. Thus, different meshes are studied. Second, the number of energy groups is commonly bigger than two. Therefore, block strategies are developed to optimize the computation of the algebraic eigenvalue problems associated. Finally, an updated modal method is implemented to integrate the time-dependent neutron diffusion equation. Modal methods based on the expansion of the different spatial modes are presented and compared in several types of transients. Moreover, an adaptive time-step control is developed that avoids setting the time-step with a fixed value and it is adapted according to several error estimations.Carreño Sánchez, AM. (2020). Integration methods for the time dependent neutron diffusion equation and other approximations of the neutron transport equation [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/144771TESI

Adaptive time-step control for modal methods to integrate the neutron diffusion equation

[EN] The solution of the time-dependent neutron diffusion equation can be approximated using quasi-static methods that factorise the neutronic flux as the product of a time dependent function times a shape function that depends both on space and time. A generalization of this technique is the updated modal method. This strategy assumes that the neutron flux can be decomposed into a sum of amplitudes multiplied by some shape functions. These functions, known as modes, come from the solution of the eigenvalue problems associated with the static neutron diffusion equation that are being updated along the transient. In previous works, the time step used to update the modes is set to a fixed value and this implies the need of using small time-steps to obtain accurate results and, consequently, a high computational cost. In this work, we propose the use of an adaptive control time-step that reduces automatically the time-step when the algorithm detects large errors and increases this value when it is not necessary to use small steps. Several strategies to compute the modes updating time step are proposed and their performance is tested for different transients in benchmark reactors with rectangular and hexagonal geometry.This work has been partially supported by Spanish Ministerio de Economia y Competitividad under projects ENE2017-89029-P and MTM2017-85669-P and financed with the help of a Primeros Proyectos de Investigacion (PAID-06-18) from Vicerrectorado de Investigacion, Innovacion y Transferencia of the Universitat Politecnica de Valencia.Carreño, A.; Vidal-Ferràndiz, A.; Ginestar Peiro, D.; Verdú Martín, GJ. (2021). Adaptive time-step control for modal methods to integrate the neutron diffusion equation. Nuclear Engineering and Technology. 53(2):399-413. https://doi.org/10.1016/j.net.2020.07.004S39941353

Index to NASA Tech Briefs, January - June 1967

Technological innovations for January-June 1967, abstracts and subject inde