BWR stability and bifurcation analysis using a novel reduced order model and the system code RAMONA

Boiling water reactor (BWR) stability analysis is usually carried out using large system codes. However, because of the large computational efforts required, such codes cannot in practice be employed for the detailed investigation of the complete manifold of solutions of the nonlinear differential equations describing the BWR system. In this context, reduced order models, containing a minimum number of system equations describing the most important physical phenomena, become necessary to provide deeper insight into the physical mechanisms underlying the different instability phenomena observed in BWRs, e.g. in-phase and out-of-phase power oscillations. A novel analytical, reduced order model has been currently developed to simulate the different types of instabilities encountered in heated channels and BWRs, viz. density wave oscillations (DWOs), as well as in-phase and out-of-phase oscillations in the reactor core. The complete model comprises three main parts: spatial lambda- mode neutron kinetics with the fundamental and first azimuthal modes, fuel heat conduction dynamics, and core thermal- hydraulics based on a drift flux model representation of the two-phase flow. Stability and semi-analytical bifurcation analysis is carried out for a purely thermal-hydraulic system (heated channel), as well as for a complete BWR (represented via two-channel nuclear-coupled thermal-hydraulics), using the current reduced order model in conjunction with the bifurcation code BIFDD. The impact of the drift flux parameters on the stability boundary (SB) and nature of bifurcation has thereby been investigated. Results show that both sub- and supercritical Hopf bifurcations are encountered along the stability boundary. Using a drift flux model instead of a homogeneous equilibrium model for the two-phase flow is found to have significant effects on the SB, as well as on the nature of Hopf bifurcation. For independent confirmation of the results of the semi- analytical bifurcation analyses, as well as to evaluate the system behaviour in regions away from the stability boundary, numerical integration has been carried out of the set of ordinary differential equations (ODEs) involved in each case. With each of the two channels of the currently developed BWR reduced order model representing half of the reactor core, it has been possible to apply it to the investigatio n of out-of-phase instability phenomena as well. First, the stability limits for in-phase and out-of-phase BWR oscillation modes for a generic case are determined in parameter space. An in-depth investigation is then performed of the properties of the elements of the eigenvectors associated with these two oscillation modes. Results show that analysing the properties of the eigenvectors can provide full information as regards the corresponding oscillation mode (in-phase or out-of-phase) without solving the set of system ODEs. In addition, such analysis conclusively shows that in-phase and out-of-phase oscillation modes in a BWR are whole-system mechanisms and not just limited to the excitation of the fundamental and first azimuthal modes of the neutron flux. In parallel to the generic studies with the reduced order model, a detailed local bifurcation analysis has been performed at two representative operational points for the Leibstadt and Ringhals-1 BWR nuclear power plants using the complex system code RAMONA. The goal in this analysis is to demonstrate how the system solution (behaviour) can, in some situations, vary in a significant manner when a certain parameter, e.g. the mass flow rate, is changed by small amounts. First, a correspondence hypothesis is proposed, underlining the unique relationship for BWRs between a stable (unstable) limit cycle solution and the occurrence of a supercritical (subcritical) Hopf bifurcation. The RAMONA analysis carried out clearly shows that stability and bifurcation analysis expertise using reduced order models is indeed very important for the understanding and appropriate interpretation of certain complicated nonlinear phenomena that are sometimes observed in simulations using system codes. Thus, the present investigations have revealed, for the first time, the occurrence of a subcritical Hopf bifurcation during BWR stability analysis using a system code. Such a study is thereby shown to allow the determination and characterisation of local stability boundaries within the exclusion area of a BWR's power-flow map. Finally, in order to assess the applicability (as well as limitations) of the currently developed reduced order in a more quantitative manner, it has been applied to the analysis of a specific Leibstadt operational point. Comparison of the results obtained with those of RAMONA show that, although the current reduced order model could adequately predict certain characteristics, it was not able to correctly predict some others because of the highly simplified reactor core geometry, the uncertainties in evaluating the design and operating parameters, as also the limitations of the feedback reactivity model employed. The main conclusion to be drawn in this context is that, although reduced order models do indeed allow an in-depth understanding of the complex processes determining BWR stability (through the possibility of conducting fast and detailed semi-analytical bifurcation analysis), they need to be considered as complementary tools to complex system codes, and not as alternatives

Modelling and simulations of reactor neutron noise induced by mechanical vibrations

Mechanical vibrations of core internals are among the main perturbations that induce oscillations in the neutron flux field, also known as neutron noise. In this work, different simulation models for the study of the influence of the mechanical vibrations of fuel assemblies on the neutron flux in the reactor core have been discussed. These methodologies employ the diffusion approximation, with or without a previous homogenization model, to simulate the neutron noise in the time or the frequency domain. The diffusion-based approach is expected to be less accurate in the vicinity of the vibrating fuel assemblies, but correct when considering distances larger than a few diffusion lengths away from the perturbation. All methodologies provide consistent results and can reproduce typical features of the neutron noise induced by mechanical vibrations of core components. First, FEMFFUSION can perform simulations in both the time and frequency domains. Second, CORE SIM + can be used to study various neutron noise scenarios in realistic three-dimensional reactor configurations. The third methodology is centred on using commercial codes as CASMO-5, SIMULATE-3 and SIMULATE-3K. This methodology allows time domain simulations of the neutron noise induced by different neutron noise sources in a nuclear reactor. Finally, a model for time-dependent geometry is implemented for the code system ATHLET/QUABOX-CUBBOX employing a cross-section-based approach for encoding water gap width variations at the reflector

Deep learning techniques for in-core perturbation identification and localization of time-series nuclear plant measurements

The research conducted has been made possible through funding from the Euratom research and training programme 2014-2018 under grant agreement No 754316 for the “CORe Monitoring Techniques And EXperimental Validation And Demonstration (CORTEX)” Horizon 2020 project, 2017-2021.Peer reviewedPublisher PD

Towards a Deep Unified Framework for Nuclear Reactor Perturbation Analysis

In this paper, we take the first steps towards a novel unified framework for the analysis of perturbations in both the Time and Frequency domains. The identification of type and source of such perturbations is fundamental for monitoring reactor cores and guarantee safety while running at nominal conditions. A 3D Convolutional Neural Network (3D-CNN) was employed to analyse perturbations happening in the frequency domain, such as an absorber of variable strength or propagating perturbation. Recurrent neural networks (RNN), specifically Long Short-Term Memory (LSTM) networks were used to study signal sequences related to perturbations induced in the time domain, including the vibrations of fuel assemblies and the fluctuations of thermal-hydraulic parameters at the inlet of the reactor coolant loops. 512 dimensional representations were extracted from the 3D-CNN and LSTM architectures, and used as input to a fused multi-sigmoid classification layer to recognise the perturbation type. If the perturbation is in the frequency domain, a separate fully-connected layer utilises said representations to regress the coordinates of its source. The results showed that the perturbation type can be recognised with high accuracy in all cases, and frequency domain scenario sources can be localised with high precision

Results of the application and demonstration calculations

CORTEX - Research and Innovation Action (RIA) This project has received funding from the European Union's Horizon 2020 research and innovation programme under grant agreement No 754316.Publisher PD

Uncertainties for Swiss LWR spent nuclear fuels due to nuclear data

This paper presents a study of the impact of the nuclear data (cross sections, neutron emission and spectra) on different quantities for spent nuclear fuels (SNF) from Swiss power plants: activities, decay heat, neutron and gamma sources and isotopic vectors. Realistic irradiation histories are considered using validated core follow-up models based on CASMO and SIMULATE. Two Pressurized and one Boiling Water Reactors (PWR and BWR) are considered over a large number of operated cycles. All the assemblies at the end of the cycles are studied, being reloaded or finally discharged, allowing spanning over a large range of exposure (from 4 to 60 MWd/kgU for ≃9200 assembly-cycles). Both UO2 and MOX fuels were used during the reactor cycles, with enrichments from 1.9 to 4.7% for the UO2 and 2.2 to 5.8% Pu for the MOX. The SNF characteristics presented in this paper are calculated with the SNF code. The calculated uncertainties, based on the ENDF/B-VII.1 library are obtained using a simple Monte Carlo sampling method. It is demonstrated that the impact of nuclear data is relatively important (e.g. up to 17% for the decay heat), showing the necessity to consider them for safety analysis of the SNF handling and disposal

Analysis of simulated signals from neutron detectors in PWR reactors when mechanical and themohydraulic perturbations are applied.

KWU-PWR plants have shown a high neutron noise level which has caused operational problems. The region of interest is below 1 Hz, so thermal-hydraulic oscillations seem to be a cause of this high level. In the last years, the neutron noise has increased when the fuel elements design has changed. This may indicate that there is a relationship between the spectral characteristics of the neutron detector signals and the fuel elements behavior. In order to advance in understanding these phenomena, the S3K software has been used to simulate both mechanical and thermal-hydraulic perturbations. The simulated neutron detector signals were analyzed and compared with plant data

Neutron noise analysis of simulated mechanical and thermal-hydraulic perturbations in a PWR core

KWU pre-Konvoi PWRs (SIEMENS design) are commonly exhibiting high neutron noise levels which canlead to costly operational issues (i.e. activation of SCRAM system, operation of unrated core power, etc.).The frequency region of interest of neutron noise is below 1 Hz, which is the typical frequency range ofthermal-hydraulic phenomena. This feature seems to indicate that, coolant flow and temperature oscil-lations can have a key impact on neutron noise phenomena. Moreover, an increasing neutron noise trend(in term of normalized root mean square) was recently observed in many KWU-PWRs. This increasingtrend has been speculated to be correlated with the introduction of a new fuel design type in theKWU-PWRs. This fact indicates that there should be some correlation between neutron noise spectralcharacteristics and fuel assemblies’ performance. In order to advance in understanding this phenomenon,the transient nodal code SIMULATE-3K (S3K) has been used to simulate mechanical vibrations of fuelassemblies and thermal-hydraulic fluctuations of the core inlet flow and temperature. The simulatedneutron detectors responses are analysed with noise analysis techniques and compared to real plant data.This analysis indicates that the cross-feedback between the mechanical and thermal-hydraulic distur-bances complicate the identification of the origin of the perturbation source. The simulated results indi-cate that the neutron noise spectral characteristics can be associated separately to different causes. In thissense, the results of this work seem to indicate that the spectral features of the neutron noise are a con-sequence of both mechanical perturbations and thermal-hydraulic fluctuations