Transport calculations of the multiplicity moments for cylinders

In a previous paper by P\ue1zsit and P\ue1l [“Multiplicity Theory Beyond the Point Model,” Ann. Nucl. Energy, Vol. 154 (2021)], a general transport theory calculation of the factorial moments of the number of neutrons emitted spontaneously from a sample was elaborated. In contrast to the original derivations by Hage and Cifarelli [“On the Factorial Moments of the Neutron Multiplicity Distribution of Fission Cascades,” Nucl. Instrum. Meth. Phys. Res. A, Vol. 236 (1985)] and B\uf6hnel [“The Effect of Multiplication on the Quantitative Determination of Spontaneously Fissioning Isotopes by Neutron Correlation Analysis,” Nucl. Sci. Eng., Vol. 90 (1985)], also referred to as the point model, in the transport model the spatial and angular dependence of the internal fission chain is taken into account with a one-speed transport theory treatment. Quantitative results were given for a spherical item, and the bias of the point model regarding the estimation of the fission rate as compared to the more exact space-dependent model was estimated as a function of the size of the sphere and the α factor.In the present paper the formalism and the quantitative work are extended to the treatment of items with cylindrical shapes, which are more relevant in many practical applications. Results are presented for both square cylinders (D=H) and for tall (H/D>1) and flat (H/D<1) cylinders. This way the differences between the cylinder and the sphere on one hand and those between the various cylinder shapes on the other hand can be estimated. The results show that the bias depends on the geometry of the cylinder quite moderately, but similarly to the case of the sphere, the bias of the point model is quite significant for larger item sizes and α values, and it is nonconservative (underestimates the fissile mass) as well

Qualitative and quantitative investigation of the propagation noise in various reactor systems

The space-dependent neutron noise, induced by propagating perturbations (propagation noise for short) is investigated in a one-dimensional homogeneous model of various reactor systems. By using two-group theory, the noise in both the fast and the thermal group is calculated. The purpose is to investigate the dependence of the properties of the space-dependent fast and thermal propagation noise on the static neutron spectrum as well as on the presence of the fluctuations of several cross sections. The motivation for this study arose in connection with recent work on neutron noise in molten salt reactors (MSR) with propagating fuel of various compositions. Some new features of the induced noise were observed, but it was not clear whether these were due to the propagating perturbation alone, or to the propagation of the fuel and hence that of the delayed neutron precursors. The present study serves to clarify the significance of the spectral properties of the different cores through calculating the propagation noise in four different reactor systems, as well as considering the influence of the perturbation of the various cross sections. By comparing the results with those obtained in MSR, the effect of the moving fuel on the propagation noise is clarified. It is shown that in fast systems the noise in the fast group is much larger than in the thermal group and hence can gain diagnostic importance. It is also shown that the coexistence of several cross section fluctuations leads to qualitatively and quantitatively new characteristics of the noise, hence it is important to model the effect of e.g. temperature fluctuations of the coolant in a proper way. (C) 2013 Elsevier Ltd. All rights reserved

Space-Dependent Calculation of the Multiplicity Moments for Shells With the Inclusion of Scattering

In recent work, we extended the methodology of multiplicity counting in nuclear safeguards by elaborating the one-speed stochastic transport theory of the calculation of the so-called multiplicity moments, i.e., the factorial moments of the number of neutrons emitted from a fissile item, following a source event from an internal neutron source [spontaneous fission and ((Formula presented.)) reactions]. Calculations were made for solid spheres and cylinders, with the source being homogeneously distributed within the item. Recent measurements of the Rocky Flats Shells during the Measurement of Uranium Subcritical and Critical (MUSIC) campaign conducted by Los Alamos National Laboratory and assisted by the University of Michigan inspired us to extend the model to spherical shell geometry with a point source in the middle of the central cavity. Comparison of the calculated results with the experimental ones indicated that accounting for fission as the only neutron reaction (the standard procedure in the point model, adapted also in our work so far) was not sufficient for reaching good agreement with measurements. The model was therefore extended to include elastic scattering into the one-speed formalism, whereas the effect of inelastic scattering was accounted for in an empirical way. After these extensions, good agreement was found between the calculated and the measured values. The paper describes the extension of the theory and provides concrete quantitative results

Ringhals Diagnostics and Monitoring, Final Research Report 2012-2014

This report gives an account of the work performed by the Department of Nuclear Engineering, Chalmers, in the frame of research collaboration with Ringhals, Vattenfall AB, contract No. 630217-031. The contract constitutes a 3-year co-operative research work concerning diagnostics and monitoring of the BWR and PWR units. The work in thecontract has been performed between January 1st 2012, and December 31st, 2014. During this period, we have worked with four main items as follows:1. Development and application of the analysis method of core barrel vibrations, developed in the previous Stages, to three ex-core measurements performed during several cycles in R2, R3 and R4. What regards R2, this was the first attempt to analyze ex-core measurements taken at BOC, MOC and EOC, with the new curve-fitting procedure;2. Investigation of the ultra-low frequency oscillations in reactor power in R4;3. Development of the theory and simulations in order to determine the void content in R1 from the analysis of in-core measurements;4. Evaluation of the measurements made in R1 with the use of 4 LPRMs and one TIP detector, for testing the velocity and void fraction profile reconstruction methods.This work was performed at the Department of Nuclear Engineering, Chalmers University of Technology by Victor Dykin, Cristina Montalvo (visitor from the TechnicalUniversity of Madrid), Imre P\ue1zsit (project co-ordinator) and Henrik Nyl\ue9n, who was also the contact person at Ringhals

Development of a new method to determine the axial void velocity profile in BWRs from measurements of the in-core neutron noise

Determination of the local void fraction in BWRs from in-core neutron noise measurements requires the knowledge of the axial velocity of the void. The purpose of this paper is to revisit the problem of determining the axial void velocity profile from the transit times of the void between axially placed detectors, determined from in-core neutron noise measurements. In order to determine a realistic velocity profile which shows an inflection point and hence has to be at least a third order polynomial, one needs four transit times and hence five in-core detectors at various axial elevations, whereas the standard instrumentation usually consists only of four in-core detectors. Attempts to determine a fourth transit time by adding a TIP detector to the existing four LPRMs and cross-correlate it with any of the LPRMs have been unsuccessful so far. In this paper we thus propose another approach, where the TIP detector is only used for the determination of the axial position of the onset of boiling. By this approach it is sufficient to use only three transit times. Moreover, with another parametrisation of the velocity profile, it is possible to reconstruct the velocity profile even without knowing the onset point of boiling, in which case the TIP is not needed, although at the expense of a less flexible modelling of the velocity profile. In the paper the principles are presented, and the strategy is demonstrated by concrete examples, with a comparison of the performance of the two different ways of modelling the velocity profile. The method is tested also on velocity profiles supplied by system codes, as well as on transit times from neutron noise measurements

Ringhals Diagnostics and Monitoring, Annual Research Report 2015

This report gives an account of the work performed by the Division of Subatomic and Plasma Physics (former Division of Nuclear Engineering), Chalmers, in the frame of a research collaboration with Ringhals, Vattenfall AB, contract No. 630217-031. The contract constitutes a 1-year co-operative research work concerning diagnostics and monitoring of the BWR and PWR units. The work in the contract has been performed between January 1st 2015, and December 31st, 2015. During this period, we have worked with five main items as follows:1. Development of the mode separation model with an extension to describe 3-D core barrel vibrations;2. Analysis of new ex-core measurements, taken in R-4 after power uprate;3. Investigation of the correctness of the hypothesis that the reactivity component extracted from the ex-core detector signals can be due to fuel assembly vibrations with CORE SIM;4. A basic study in neutron noise theory which could provide some indirect support for the determination of the void fraction from neutron noise measurements;5. A preliminary study of the possibility of modelling 3-dimensional fuel assembly vibrations in a realistic PWR system with the CORE SIM simulator.This work was performed at the Nuclear Engineering Group of the Division of Subatomic and Plasma Physics, Chalmers University of Technology by Victor Dykin (project co-ordinator), Cristina Montalvo (visitor from the Technical University of Madrid), Hoai-Nam Tran (research collaborator from Duy Tan University), Imre P\ue1zsit and Henrik Nyl\ue9n, who was also the contact person at Ringhals

The Effect of Different Perturbations on the Stability Analysis of Light Water Reactors

Neutron noise analysis techniques are studied and developed, with primary useof determining the stability of Boiling Water Reactors (BWRs). In particular, the role ofa specific perturbation prevailing in Light Water Reactors, the propagating densityperturbation, in the stability of BWRs and on the noise field of LWRs in general, isinvestigated by considering three topics.In the first topics, we investigate how the neutronic response of the reactor, usuallydescribed as a second order system driven by a white noise driving force, is affected bya non-white driving force. This latter arises from the reactivity effect of the propagatingdensity perturbations. The investigation is performed by using spectral and correlationanalysis. Propagating perturbations with different velocities are analyzed. We investigatehow the accuracy of the determination of the so-called decay ratio (DR) of the system,based on the assumption of white noise driving force, deteriorateswith deviations from the white noise character of the driving force.In the second topics, the space dependence of the neutron noise, induced bypropagating density perturbations, represented through the perturbation ofthe absorption, is determined and discussed. A full analytical solution was obtainedby the use of the Green\u27s function technique. The solution was analyzed for differentfrequencies and different system sizes. An interesting new interference effectbetween the point-kinetic and space-dependent components of the induced noise wasdiscovered and interpreted in physical terms.In the last topics, a non-linear stability analysis of a BWR is performed,using so called Reduced Order Model (ROM) techniques. A ROM is usually constructedby reducing the full set of 3D space-time dependent neutron-kinetics,thermal-hydraulics and heat transfer equations to time-dependent ones, byconsidering space dependence in a lumped parameter model (one or two discrete channels).The main novelty of our work is to treat thespace dependence by four heated channels. This extension makes itpossible to account for the effect of three neutronic modes: fundamental, firstand second azimuthal ones. The Forsmark-1 instability event in 1996/1997was chosen to be investigated by the ROM developed in this work. The reactor response was determinedfor various operational points to identify the stable/unstable reactorbehavior. The suitability of using the DR as the stability parameter in case of non-linear oscillationsis also being investigated

Noise Applications in Light Water Reactors with Traveling Perturbations

Neutron noise induced by perturbations traveling with the coolant of light water reactors (LWRs) is investigated. Different methods to simulate the effect of propagating perturbations are considered. The studies are performed in both open- and closed-loop systems and summarized in three chapters.In the first chapter, the space-dependence of the neutron noise due to propagating perturbations calculated in one-group theory and one dimension in a pressurized water reactor (PWR) is investigated. A full analytical solution, obtained by the use of Green\u27s function technique, is analyzed for different frequencies and different system sizes. An interesting new interference effect between the point-kinetic and space-dependent components of the induced noise isdiscovered and interpreted in physical terms. A similar investigation is performed in two-group theory for four reactor systems with different neutron spectra. The goal is to investigate the dependence of the properties of the induced neutron noise on the neutron spectrum. The presence of the fluctuations of several cross sections is also analyzed and resulted in qualitatively and quantitatively new characteristics of the induced noise. Further, a simple numerical Monte Carlo-based model to simulate the boiling process in a boiling water reactor (BWR) heated channel, is constructed. The output of the model is then used to estimate the local component of the neutron noise induced by density fluctuations in the coolant numerically convoluting it with proper transfer functions.In the second chapter, a four-heated channel reduced order model (ROM), accounting for the first three neutronic modes, is constructed to study both global and regional instabilities. Some additional modifications compared with the earlier-developed models are performed to improve the consistency of the model. It is shown that the ROM is capable to reproduce the main features of core-wide instabilities. Moreover, it is proven that the inclusion of both azimuthal modes brings some importance for the correct identification of stability boundaries. The ROM is also extended to simulate the effect of local instabilities, such as the Forsmark-1 instability event of 1996/1997. A good qualitative agreement with real measurements is found.In the last chapter, a number of the applications of the noise diagnostics based on the foregoing calculations are discussed. The case when the neutronic response of the reactor is affected bya non-white driving force (propagating perturbation) is studied. It is also investigated how the accuracy of the determination of the so-called decay ratio (DR) of the system, based on the assumption of a white noise driving force, deteriorates with deviations from the white noise character of the driving force. Furthermore, the earlier developed ROM is applied to analyze what stability indicators other than the DR can be used to describe the stability of the system. As a candidate, the coupling reactivity coefficients are chosen and their dependence on the DR is investigated. It is shown that such a dependence deviates form the conventional one, presumably caused by the inherent inertia of the system. Finally, two techniques, one based on the break-frequency of auto power spectral density (APSD) of the neutron noise and another on the transit times of propagating void fluctuations are discussed for reconstructing the axial void profile from the Monte-Carlo simulated neutron noise. It is shown that both methods provide promising results

Using neutron noise to determine void fraction

A long-known dependence of neutron noise phenomena on void fraction has become the basis of a useful online monitoring technique that backs up computational models and improves operations. Calculations have shown good agreement with simulated data; calculations with real data are expected later this year

Using neutron noise to determine void fraction

A long-known dependence of neutron noise phenomena on void fraction has become the basis of a useful online monitoring technique that backs up computational models and improves operations. Calculations have shown good agreement with simulated data; calculations with real data are expected later this year