Induced Neutron Noise Research Articles

Understanding the neutron noise induced by fuel assembly vibrations in linear theory

This paper investigates the underlying physical mechanisms involved in the monochromatic vibrations of fuel assemblies and their effects on the induced neutron noise throughout the core of nuclear reactors, in the framework of simplified benchmark configurations. Any vibrating fuel pin introduces noise sources at the frequency of vibrations, as well as at higher harmonics, the first one being the most significant of those. Depending on the harmonics considered, the position of the vibrating fuel pin, the size of the core and its macroscopic cross-sections, different noise responses are observed within the reactor core. Through the lens of a decomposition of the neutron noise into its point-kinetics component and its deviation from it, the spectrum of noise responses is explained and related to the spatial distribution of the amplitude and phase of the noise sources at the considered frequencies. At the frequency of vibration, possible out-of-phase behaviour of the induced neutron noise can be partially or totally shadowed by the in-phase point-kinetics component, the only exception being for central vibrations in symmetrical systems. At the frequency of the first higher harmonics, the structure of the induced neutron noise is more involved. Nevertheless, due to the compensation of the individual responses associated to the different components of the noise source at that frequency, point-kinetics has a significant contribution. The results of this work sheds new light on the complex spatial pattern of the neutron noise computed by realistic core simulators in case of vibrations of fuel assemblies.

Design and Simulation of Gamma Spectrometry Experiments in the CROCUS Reactor

Gamma rays in nuclear reactors, arising either from fission or decay processes, significantly contribute to the heating and dose of the reactor components. Zero power research reactors offer the possibility to measure gamma rays in a purely neutronic environment, allowing for validation experiments of computed spectra, dose estimates, reactor noise and prompt to delayed gamma ratios. This data then contributes to models, code validation and photo atomic nuclear data evaluation. In order to contribute to aforementioned experimental data, gamma detection capabilities are being added to the CROCUS reactor facility. The CROCUS reactor is a two-zone, uranium-fueled light water moderated facility operated by the Laboratory for Reactor Physics and Systems Behaviour (LRS) at the Swiss Federal Institute of Technology Lausanne (EPFL). With a maximum power of 100W, it is a zero power reactor used for teaching and research, most recently for intrinsic and induced neutron noise studies. For future gamma detection applications in the CROCUS reactor, an array of four detectors - two large 5”x10” Bismuth Germanate (BGO) and two smaller Cerium Bromide (CeBr3) scintillators - was acquired. The BGO detectors are to be arbitrarily positioned in the core reflector and out of the vessel for measurements at arbitrary distances. The CeBr3 detectors on the other hand are small enough to be set in the guide tubes of the control rods for in-core measurements. We present a study of the neutron and gamma flux in the core and reflector using the MCNP 6.2 and Serpent 2 Monte Carlo codes for coupled neutron and photon transport criticality calculations. More specifically, we investigate and compare predicted spectra as well as reactivity worth of different envisioned experimental setups. We further predict pulse height spectra as well as doses to the crystals with and without cadmium shielding to estimate allowable reactor powers with respect to detector radiation hardness. The results serve as basis for calibration and aid in the design and regulatory approval of the experiments.

PARCS vs CORE SIM neutron noise simulations

In a nuclear reactor, even operating at full power and steady-state conditions, fluctuations are detected in the recording of any process parameter. These fluctuations (also called noise) could be of various origins, such as, turbulence, mechanical vibrations, coolant boiling, etc. The monitoring and complete comprehension of those parameters should thus allow detecting, using existing instrumentation and without introducing any external perturbation to the system, possible anomalies before they have any inadvertent effect on plant safety and availability.In order to reproduce and study the induced neutron noise in a nuclear reactor core, it is compulsory to develop suitable tools. Existing time-domain codes were originally not developed for this type of calculations. Modifications of those codes and the development of an associated intricate methodology are necessary for enabling noise calculations. This involves, in some cases, changes in the source code and the development of new auxiliary tools to ensure accurate reproductions of the core behavior under the existence of a neutron noise source.In the proposed work, the time-domain neutron diffusion code PARCS is used to model the effect of stationary perturbations representative of given neutron noise sources. In order to validate the feasibility of the time-dependent methodology thus developed, comparisons with the results of simulations performed in the frequency domain, using the CORE SIM tool, developed at Chalmers University of Technology, are performed.The development of a few test cases based on a real reactor model are undertaken as the basis for such comparisons and a methodology aimed at assessing the time-domain simulations versus the frequency-domain simulations is established. It is demonstrated that PARCS, although not primarily developed for neutron noise calculations, can reproduce neutron noise patterns for reasonable frequencies. However, it is also observed that unphysical results are occasionally obtained.

3D convolutional and recurrent neural networks for reactor perturbation unfolding and anomaly detection

With Europe's ageing fleet of nuclear reactors operating closer to their safety limits, the monitoring of such reactors through complex models has become of great interest to maintain a high level of availability and safety. Therefore, we propose an extended Deep Learning framework as part of the CORTEX Horizon 2020 EU project for the unfolding of reactor transfer functions from induced neutron noise sources. The unfolding allows for the identification and localisation of reactor core perturbation sources from neutron detector readings in Pressurised Water Reactors. A 3D Convolutional Neural Network (3D-CNN) and Long Short-Term Memory (LSTM) Recurrent Neural Network (RNN) have been presented, each to study the signals presented in frequency and time domain respectively. The proposed approach achieves state-of-the-art results with the classification of perturbation type in the frequency domain reaching 99.89% accuracy and localisation of the classified perturbation source being regressed to 0.2902 Mean Absolute Error (MAE).

On a various soft computing algorithms for reconstruction of the neutron noise source in the nuclear reactor cores

This paper presents a comparative study of various soft computing algorithms for reconstruction of neutron noise sources in the nuclear reactor cores. To this end, the computational code for reconstruction of neutron noise source is developed based on the Adaptive Neuro-Fuzzy Inference System (ANFIS), Decision Tree (DT), Radial Basis Function (RBF) and Support Vector Machine (SVM) algorithms. Neutron noise source reconstruction process using the developed computational code consists of three stages of training, testing and validation. The information of neutron noise sources and induced neutron noise distributions are used as output and input data of training stage, respectively. As input data, both the real and imaginary parts of numerical value of the neutron noise in the detector are used. In the present study, the neutron noise source of absorber of variable strength type is only considered. The neutron noise distributions in the detectors due to 2000 randomly generated neutron noise sources are calculated using the developed computational code based on Galerkin Finite Element Method (GFEM). As output data, the strength, frequency of occurrence and location (X and Y coordinates) of the considered neutron noise sources are used. The VVER-1000 reactor core is considered as the benchmarking problem for validation of performed simulation using developed computational code. All specifications of neutron noise source including strength, frequency and location of the neutron noise source are reconstructed with high accuracy. Finally, a sensitivity analysis of results to the number of active detectors in the reactor core is performed. A comparative study of the performance of different developed algorithms represents Decision Tree as the most appropriate one for reconstruction of the neutron noise source in the nuclear reactor cores.

Investigation of the ex-core noise induced by fuel assembly vibrations in the Ringhals-3 PWR

The effect of cycle burnup on the ex-core detector noise at the frequency of the pendular core barrel vibrations in the Ringhals-3 PWR core was investigated using a neutron noise simulator. The purpose of the investigations was to confirm or disprove a hypothesis raised by Sweeney et al. (1985) that fuel assembly vibrations could affect the ex-core detector noise and cause the corresponding peak in the auto power spectral density (APSD) to increase during the cycle due to the effects of fuel burnup, the change of boron concentration, flux redistribution etc. Numerical calculations were performed by modelling the vibrations of fuel assemblies at different locations in the core and calculating the induced neutron noise at three burnup steps. The APSD of the ex-core detector noise was evaluated with the assumption of vibrations either along a straight-line or along a random two-dimensional trajectory, with two different representations of the cross section perturbations caused by the vibrations. The results show the obvious effect of in-core fuel vibrations on the ex-core detector noise, but the monotonic increase of the APSD does not occur for all fuel elements, vibration types and cross section perturbation models. Such an increase of the of APSD occurs predominantly for peripheral assemblies with one of the perturbation models. However, assuming simultaneous vibrations of a number of fuel assemblies uniformly distributed over the core with random vibrations and the more realistic perturbation model, the effect of the peripheral assemblies will dominate and hence the surmised monotonic increase of the amplitude of the ex-core neutron noise during the cycle can be confirmed.

Propagation noise calculations in VVER-type reactor core

Neutron noise induced by propagating disturbances in VVER-type reactor core is addressed in this paper. The spatial discretization of the governing equations is based on the box-scheme finite difference method for triangular-z geometry. Using the derived equations, a 3-D 2-group neutron noise simulator (called TRIDYN-3) is developed for hexagonal-structured reactor core, by which the discrete form of both the forward and adjoint reactor dynamic transfer functions (in the frequency domain) can be calculated. In addition, both types of noise sources, namely point-like and traveling perturbations, can be modeled by TRIDYN-3. The results are then benchmarked in different cases. Considering the noise source as propagating perturbations of the macroscopic absorption cross sections, the induced neutron noise is calculated throughout the reactor core. For the first time, adjoint approach is applied and examined for modeling moving noise sources. Moreover, the space- and frequency-dependence of the propagation noise are investigated in this paper.

Calculation of the Neutron Noise Induced by Periodic Deformations of a Large Sodium-Cooled Fast Reactor Core

The subject of this paper is the calculation of the neutron noise induced by small-amplitude stationary radial variations of the core size (core expansion/compaction, also called core flowering) of a large sodium-cooled fast reactor. The calculations were performed on a realistic model of the European Sodium Fast Reactor (ESFR) core with a thermal output of 3600 MW(thermal), using a multigroup neutron noise simulator. The multigroup cross sections and their fluctuations that represent the core geometry changes for the neutron noise calculations were generated by the code ERANOS. The space and energy dependences of the noise source represented by the core expansion/compaction and the induced neutron noise are calculated and discussed.

Analytical investigation of the properties of the neutron noise induced by vibrating absorber and fuel rods

Abstract Analytical solution methods for the neutron noise in a one-dimensional multi-region system in two-group theory, which have so far been based on the adjoint function technique, are extended here to using the forward Green's function technique. The forward Green's functions were calculated analytically for a noise source in a core surrounded by reflector regions at both sides. It is shown that with symbolic computation methods, the forward Green's function can be used for the calculation of the space- and frequency-dependent noise in the first order approximation for arbitrary noise sources which have an analytical representation. The properties of the induced neutron noise were investigated for vibrations of both absorbers and fuel assemblies, with two representations of the noise sources: a point-like source which corresponds to the vibrations of a fuel rod, and a finite width source which corresponds to vibrations of a fuel assembly. The contributions of the components induced by the fluctuations of the various types of macroscopic cross sections in the total noise are also discussed and the information content of the noise in the fast group is explored for the identification of fuel assembly vibrations.

Development of a 2-D 2-group neutron noise simulator for hexagonal geometries

In this paper, the development of a neutron noise simulator for hexagonal-structured reactor cores using both the forward and the adjoint methods is reported. The spatial discretisation of both 2-D 2-group static and dynamic equations is based on a developed box-scheme finite difference method for hexagonal mesh boxes. Using the power iteration method for the static calculations, the 2-group neutron flux and its adjoint with the corresponding eigenvalues are obtained by the developed static simulator. The results are then benchmarked against the well-known CITATION computer code. The dynamic calculations are performed in the frequency domain which leads to discarding of the time discretisation. Then, the developed 2-D 2-group neutron noise simulator calculates both the discretised forward and the adjoint reactor transfer function between a point source and its induced neutron noise, by assuming the neutron noise source as an “absorber of variable strength” type. The neutron noise induced by a “vibrating absorber” type of noise source may also be modeled using the calculated transfer function. The viability of the simulator is verified for different benchmark cases.

Analysis methods for the determination of possible unseated fuel assemblies in BWRs

This paper describes noise-based methods, the purpose of which is to determine whether the core of a Boiling Water Reactor (BWR) contains unseated fuel assembly(ies) or not. The characteristic feature of an unseated fuel assembly is to render the corresponding fuel channel thermal-hydraulically unstable since some of the coolant bypasses the fuel channel. The induced neutron noise has a strong space-dependence due to the localized character of the perturbation. Several techniques relying on the analysis of the spatial structure of the in-core neutron noise can thus be used to determine whether the induced neutron noise might correspond to unseated fuel assembly(ies). These techniques rely on time-domain and frequency-domain analysis. This paper presents in all cases expected spatial signatures determined from calculations, and compares these theoretical findings to two practical examples, where noise measurements were carried out: a local instability event, and a global oscillation coexisting with a regional oscillation.

Identification and localization of absorbers of variable strength in nuclear reactors

This paper investigates the possibility of localising a noise source of the type “absorber of variable strength” (or reactor oscillator) from as few as five neutron detectors evenly distributed throughout the core of a commercial nuclear reactor. The novelty of this investigation lies with the fact that the calculations are performed for a realistic 2-D heterogeneous reactor in the 2-group diffusion approximation, via the prior determination of the corresponding reactor transfer function. It is first demonstrated that the response of such a reactor to a localized perturbation deviates significantly from point-kinetics. The space-dependence of the induced neutron noise thus carries enough information about the location of the noise source, which makes it possible to determine its position from a few detector readings. The identification of the type of noise source is easily performed from the in-phase behaviour of the induced neutron noise. Different unfolding techniques are finally tested. All these techniques rely on the use of the reactor transfer function. One of these techniques is based on the comparison between the actual measured neutron noise and the neutron noise calculated for every possible location of the noise source. This technique is very reliable and almost insensitive to the contamination of the detector signals by background noise, but also extremely CPU consuming. Another technique, based on the piece-wise inversion of the reactor transfer function and requiring little CPU effort, was developed. Although this technique is much less reliable when background noise is present, this technique is useful to indicate a region of the reactor where a noise source is likely to be located.

Development of a 2-D 2-group neutron noise simulator

In this paper, the development of a so-called neutron noise simulator is reported. This simulator calculates both the direct and the adjoint reactor transfer function between a stationary noise source and its induced neutron noise for any 2-dimensional heterogeneous critical system. The main advantage of this neutron noise simulator is that any realistic core can be modelled, since the simulator is designed to rely on a set of material constants corresponding to the actual reactor operating conditions. The calculations are performed in the 2-group diffusion approximation and in the frequency domain. The spatial discretisation is carried out with respect to the finite difference scheme. The noise source, expressed as an “absorber of variable strength” type, is defined directly from the fluctuations of the macroscopic cross-sections and can be spatially distributed over the core or concentrated in a few discrete nodes. If the noise source is a point-source, the simulator actually estimates the 2-dimensional 2-group discretised Green's function of the system. From the calculated Green's function, the neutron noise induced by a “vibrating absorber” type of noise source can also be determined. Different benchmark cases show that this neutron noise simulator works satisfactorily.

Linear reactor kinetics and neutron noise in systems with fluctuating boundaries

The general theory of linear reactor kinetics and that of the induced neutron noise is developed for systems with varying size, i.e. in which the position of the boundary fluctuates around a stationary value. The point kinetic and adiabatic approximations are defined by a generalisation of the flux factorisation, and the full solution of the general problem with an arbitrarily fluctuating boundary is given by the Green's function technique. The correctness of the general solution is proven both generally and also by considering the simple case of a 2-D cylindrical reactor with a fluctuating radius, in which case a direct compact solution is possible.

Control rod localisation with neural networks using a complex transfer function

Control rod vibrations in a PWR can be detected and localised by measurement and spatial unfolding of the induced neutron noise. Neutron noise based control rod localisation has been performed in the past both in a traditional way and by artificial neural networks (ANNs). In all previous work, the transfer function used was a simple and real valued function, based on the so-called power reactor approximation. A real valued transfer function means that the phase information contained in the signal propagation is neglected. In this work a more realistic, complex valued transfer function is used. The performance of the neural network based localisation technique is investigated by this complex transfer function. Several other questions of the application and optimization of ANNs in rod localisation are also addressed.

96/06041 Modelling of a vibrating reactor boundary and calculation of the induced neutron noise

Neutron spectrum analyses of spallation neutrons are conducted in the accelerator-driven system (ADS) facility at the Kyoto University Critical Assembly (KUCA). High-energy protons (100 MeV) obtained from the fixed field alternating gradient accelerator are injected onto a tungsten target, whereby the spallation neutrons are generated. For neutronic characteristics of spallation neutrons, the reaction rates and the continuous energy distribution of spallation neutrons are measured by the foil activation method and by an organic liquid scintillator, respectively. Numerical calculations are executed by MCNPX with JENDL/HE-2007 and ENDF/B-VI libraries to evaluate the reaction rates of activation foils (bismuth and indium) set at the target and the continuous energy distribution of spallation neutrons set in front of the target. For the reaction rates by the foil activation method, the C/E values between the experiments and the calculations are found around a relative difference of 10%, except for some reactions. For continuous energy distribution by the organic liquid scintillator, the spallation neutrons are observed up to 45 MeV. From these results, the neutron spectrum information on the spallation neutrons generated at the target are attained successfully in injecting 100 MeV protons onto the tungsten target.

Modelling of a vibrating reactor boundary and calculation of the induced neutron noise

Three different models of a moving (vibrating) reactor boundary in time-dependent diffusion theory are investigated. The models are: (a) a localized absorber of variable strength at the boundary (equivalent to a perturbational treatment); (b) a time-varying extrapolation length; (c) explicit treatment of the moving boundary with a new transformation technique. The induced neutron noise was calculated in first order of the perturbation parameter both exactly and in the adiabatic approximation. All three models lead to equivalent results, confirming the applicability of perturbation techniques in treating moving perturbations (e.g. vibrating control rods). Application of the adiabatic approximation in model (c) required the extension of the Henry formalism, i.e. the use of orthogonality relations expressed as integrals over the system, to cases with non-constant system volume. The incentives for investigating a time-varying boundary arose from problems related to vibrating control rods; however, the results have some general relevance for systems with a varying volume such as gaseous core or liquid fuel reactors.

Spatial noise-source reconstruction

The possibility of determining the spatial dependence of cross-section fluctuations (noise sources) from the measurement of the induced neutron noise at discrete spatial points is investigated. In contrast to the usual methods, no preliminary knowledge of the functional form of the space dependence of the noise source is assumed, instead the integral formula relating the cross-section fluctuations to the induced neutron noise is inverted in an approximative manner. Such a method has the advantage that it can be applied to various noise sources in a reactor, and the results on the spatial distribution of noise sources can be interpreted without expert knowledge, i.e. can be displayed directly to the operator. As an obvious consequence of the above-mentioned arbitrariness in the type of noise source, the precision of this type of reconstruction or unfolding procedure is lower than that of traditional methods. The dependence of the precision of the reconstruction method on the type of noise source, reactor size and of number of detectors used is investigated in numerical examples.