Neutron Noise Simulator Research Articles

Development of High-Speed Neutron Noise Simulator based on High order Nodal Expansion Method for Hexagonal Geometry in Frequency-Domain

Development of High-Speed Neutron Noise Simulator based on High order Nodal Expansion Method for Hexagonal Geometry in Frequency-Domain

A comprehensive analysis of thermal–hydraulic signatures in neutron noise of WWER-type reactors

The neutron noise phenomenon, occurring in all types of nuclear reactors, provides valuable insights into the dynamic behavior of these reactors. In this work, a well-justified approach for modeling neutron noise induced by thermal–hydraulic sources in a hexagonal reactor core is presented in detail. These sources encompass fluctuations in key features of the inlet coolant, including flow rate, temperature, and boric acid concentration. Our proposed approach touches on various aspects of the distribution of thermal–hydraulic parameters among coolant loops, accounting for both uniform and non-uniform distributions. The latter allows for the asymmetric and asynchronous distribution of their fluctuating component among the coolant loops. To manage such complexity, it becomes imperative to determine the contribution of each fuel assembly based on each coolant loop. To achieve this, CFD simulations are conducted for the downcomer and lower plenum of the reactor pressure vessel. These simulations provide essential data to establish the coolant mixing matrix, which accounts for non-uniform distributions. The obtained mixing matrix is subsequently integrated into our neutron noise simulator, DYNOSIM, ensuring the faithful reproduction of neutron noise. Our study comprehensively analyzes both uniform and non-uniform scenarios. The radial and axial distributions of neutron noise amplitude and phase are examined for these scenarios. Their qualitative verifications are conducted by prior works in this field. Furthermore, we compare one of the uniform scenarios with reference results obtained using a frequency domain simulator. Notably, our CFD simulation results closely match the experimental data. Our findings demonstrate the effectiveness and efficiency of this methodology in modeling and understanding neutron noise in hexagonal reactor cores.

Modeling and simulation of neutron noise triggered by fuel assembly vibrations in 3D hexagonal geometry

Neutron noise is a natural phenomenon in nuclear reactors. Hence, its investigation plays a significant role in nuclear reactor physics and safety-related issues. While neutron noise could have various origins, the proposed work focuses on those induced by fuel assembly vibration in hexagonal cores. To this aim, a 3D neutron noise simulator has been developed based on the multi-point kinetics equations for a hexagonal geometry coupled with the expanded multi-nodal approach as a thermal-hydraulic model. Employing these models, the neutron noise was analyzed in the time domain to provide the advantage of modeling non-linearities. This simulator is capable of simultaneous simulation of vibrating fuel assemblies with various vibrational characteristics, in particular, mode. It features the capability of neutron noise modeling at both the nuclear data generation level and the level of the neutronic calculations. The validity of the model is demonstrated by a transient accident and a noise problem. The outcomes are compared to reference data, showing good agreement. Then, to further study noise responses, several scenarios encircling various vibrating fuel assemblies in different situations are simulated. These experiments prove the appropriate performance of the proposed simulator for modeling and analyzing neutron noise in hexagonal cores.

Development of SD-HACNEM neutron noise simulator based on high order nodal expansion method for rectangular geometry

In this study, the SD-HACNEM (Sharif Dynamic - High order Average Current Nodal Expansion Method) neutron noise simulator in two energy groups using a second-order flux expansion method for two-dimensional rectangular X Y-geometry has been developed. In the first step, the calculations were performed for the steady state and results of ACNEM (Average Current Nodal Expansion Method) and HACNEM (High order Average Current Nodal Expansion Method) were examined and compared. To solve the problem, the power iteration algorithm has been used to calculate the distribution of neutron flux and neutron multiplication factor by considering the coarse-mesh (each fuel assembly one node). To validate the steady state calculations, the results were compared with the western nuclear reactor BIBLIS-2D (reference model). In the next step, dynamic calculations were performed in the frequency domain. For this purpose, after discretizing the neutron noise equations by the high-order average current nodal expansion method (NEM), a neutron noise source of absorber with variable strength was simulated. The results were verified by performing simulation at zero frequency and adjoint calculations. Then, the distribution of neutron noise for Inadvertent Loading and Operation of a Fuel Assembly in an Improper Position (ILOFAIP) is obtained. The numerical results showed that the use of HACNEM compared with ACNEM, without reducing the size of the meshes in neutron noise simulation, presented more accurate.

Neutron noise simulator based on the boundary element method (BEM)

The purpose of the present study is to develop the neutron diffusion solver and neutron noise simulator based on the Boundary Element Method (BEM). The 2-D, 2-G neutron/adjoint diffusion equation and corresponding neutron/adjoint noise equation were solved using the mentioned method. The developed neutron static and noise simulator based on the finite element method gives accurate results when the more number of the elements is used. The motivation of the present research is to use the boundary element method to reduce the computational cost. The boundary element method attempts to use the givenboundary conditionsto fit boundary values into the integral equation, rather than values throughout the space defined by a partial differential equation.The results of static calculation were then benchmarked against the valid data for BIBLIS-2D and IAEA-2D benchmark problems. The neutron noise calculation due to the absorber of variable strength neutron noise source was performed using BEM and the Green's function technique. The adjoint of noise equation was also solved using the same method applied to the forward calculation. Comparison of the calculated neutron noise at zero frequency with the results of static calculation, utilizing the result of adjoint noise calculation and qualitative comparison with similar reported results are three different procedures to validate the neutron noise calculation.The analysis of the results obtained from the BEM shows that the boundary element method alone, or coupled with the finite element method, is ideally suited for the static and neutron noise calculation from both the accuracy and efficiency viewpoints.

A FINITE ELEMENT METHOD FOR NEUTRON NOISE ANALYSIS IN HEXAGONAL REACTORS

The early detection of anomalies through the analysis of the neutron noise recorded by incore and ex-core instrumentation gives the possibility to take proper actions before such problems lead to safety concerns or impact plant availability. The study of the neutron fluctuations permits to detect and differentiate anomalies depending on their type and possibly to characterize and localize such anomalies. This method is non-intrusive and does not require any external perturbation of the system. To effectively use the neutron noise for reactor diagnostics it is essential to accurately model the effects of the anomalies on the neutron field. This paper deals with the development and validation of a neutron noise simulator for reactors with different geometries. The neutron noise is obtained by solving the frequency-domain two-group neutron diffusion equation in the first order approximation. In order to solve this partial differential equation a code based on a high order finite element method is developed. The novelty of this simulator resides on the possibility of dealing with rectangular meshes in any kind of geometry, thus allowing for complex domains and any location of the perturbation. The finite element method also permits automatic refinements in the cell size (h-adaptability) and in its polynomial degree (p-adaptability) that lead to a fast convergence. In order to show the possibilities of the neutron noise simulator developed a perturbation in a hexagonal two-dimensional reactor is investigated in this paper.

High accurate three-dimensional neutron noise simulator based on GFEM with unstructured hexahedral elements

Abstract The purpose of the present study is to develop the 3D static and noise simulator based on Galerkin Finite Element Method (GFEM) using the unstructured hexahedral elements. The 3D, 2G neutron diffusion and noise equations are discretized using the unstructured hexahedral by considering the linear approximation of the shape function in each element. The validation of the static calculation is performed via comparison between calculated results and reported data for the VVER-1000 benchmark problem. A sensitivity analysis of the calculation to the element type (unstructured hexahedral or tetrahedron elements) is done. Finally, the neutron noise calculation is performed for the neutron noise source of type of variable strength using the Green function technique. It is shown that the error reduction in the static calculation is considerable when the unstructured tetrahedron elements are replaced with the hexahedral ones. Since the neutron flux distribution and neutron multiplication factor are appeared in the neutron noise equation, the more accurate calculation of these parameters leads to obtaining the neutron noise distribution with high accuracy. The investigation of the changes of the neutron noise distribution in axial direction of the reactor core shows that the 3D neutron noise analysis is required instead of 2D.

Neutron noise modelling for nuclear reactor diagnostics

This paper presents the development of a neutron noise simulator for fine-mesh applications.The neutron noise of power nuclear reactors deals with the fluctuations of the neutron flux that are induced by fluctuations or oscillations of the reactor properties, i.e. displacement of core components, temperature or density variations, etc. Since the appearance of these perturbations can be problematic for the operation of nuclear reactors, it is desirable to be able to analyze their possible effects. The comparison between the modelling of such perturbations and possible measurements also gives the possibility to determine the driving perturbation in an operating nuclear reactor. One modelling approach is to solve numerically the neutron noise diffusion equation. This paper presents CORE SIM+, an under-development numerical tool oriented to neutron noise problems that require the fine-mesh spatial discretization of the reactor core.

Neutron noise simulation using ACNEM in the hexagonal geometry

In the present study, the development of a neutron noise simulator, DYN-ACNEM, using the Average Current Nodal Expansion Method (ACNEM) in 2-G, 2-D hexagonal geometries is reported. In first stage, the static neutron calculation is performed. The neutron/adjoint flux distribution and corresponding eigen-values are calculated using the algorithm developed based on power iteration method by considering the coarse meshes. The results of the static calculation are validated against the well-known IAEA-2D benchmark problem. In the second stage, the dynamic calculation is performed in the frequency domain in which the dimension of the variable space of the noise equations is lower than the time dependent equations. Induced neutron/adjoint noise distribution due to the neutron noise source of type absorber of variable strength is calculated as well. Two different methods are used to validate the neutron noise calculation. The Inadvertent Loading and Operation of a Fuel Assembly in an Improper Position (ILOFAIP) as an important neutron noise source is investigated using ACNEM in this study.

Point flux nodal expansion scheme applied to the neutron noise analysis of the nuclear reactor core

In this paper, a neutron noise simulator based on the point flux nodal expansion method (PFNEM) for nuclear reactor cores with rectangular geometry is developed. The point flux scheme is a kind of nodal expansion method (NEM) which is based on keeping balance of neutrons in every node and has been proved very efficient for LWR analysis. The method can be applied to mesh volumes as coarse as the reactor subassemblies to speed up calculations. In this work, the PFNEM is implemented for spatial discretization of neutron diffusion equation in the frequency domain in order to obtain the neutron noise, fluctuation of neutron flux around its mean value. The fluctuations of the absorption macroscopic cross sections in both fast and thermal energy groups are assumed as the neutron noise source. The adjoint noise analysis is also carried out to validate forward noise calculation results. Three test problems including 2-region slab reactor, 2D TWIGL seed-blanket reactor and 2D LRA BWR are assessed for evaluating the noise results. In addition, an adopted iterative scheme is also presented for the solution of neutron noise equations. Altogether, static and dynamic calculations results demonstrate the good accuracy of proposed approach.

Development of 3D neutron noise simulator based on GFEM with unstructured tetrahedron elements

In the present study, the neutron noise, i.e. the stationary fluctuation of the neutron flux around its mean value is calculated based on the 2G, 3D neutron diffusion theory. To this end, the static neutron calculation is performed at the first stage. The spatial discretization of the neutron diffusion equation is performed based on linear approximation of Galerkin Finite Element Method (GFEM) using unstructured tetrahedron elements. Using power iteration method, neutron flux and corresponding eigen-value are obtained. The results are then benchmarked against the valid results for VVER-1000 (3D) benchmark problem. In the second stage, the neutron noise equation is solved using GFEM and Green’s function method for the absorber of variable strength noise source. Two procedures are used to validate the performed neutron noise calculation. The calculated neutron noise distributions are displayed in the different axial layers in the reactor core and its variation in axial direction is investigated. The main novelty of the present paper is the solution of the neutron noise equations in the three dimensional geometries using unstructured tetrahedron elements.

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.

Properties of Neutron Noise Induced by Localized Perturbations in an SFR

Investigation of the properties of neutron noise induced by localized perturbations in a sodium-cooled fast reactor has been performed using a multigroup neutron noise simulator. Three representations of the noise source associated with the perturbations of absorption, fission, and scattering cross sections, respectively, were assumed to be located at the first fuel ring around the central assembly. The energy- and space-dependent noise, that is, the amplitude and the phase, was calculated in a wide range of frequencies, for example, 0.1–100 Hz. The results show that in the important energy range (>1.0 keV) where the noise amplitude is significant the phase is almost constant with energy at the calculated frequencies despite the source types. At low frequencies, the variation of the phase is negligibly small at a large distance from the source. The perturbation in several fast groups has a significant contribution and dominates the amplitude and the phase of the induced noise.

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.

Development of a multi-group neutron noise simulator for fast reactors

The paper presents the development of a neutron noise simulator for fast reactors based on diffusion theory with multi-energy groups. The noise sources are modelled via small stationary fluctuations of macroscopic cross sections, and the induced first order noise is solved fully in the frequency domain. The tool is expected to be applicable for monitoring of fast reactor cores and also for other reactor types with hexagonal fuel assemblies. Some numerical calculations of the neutron noise induced by localized perturbations in a sodium-cooled fast reactor are demonstrated.

A multi-group neutron noise simulator for fast reactors

A neutron noise simulator has been developed for fast reactors based on diffusion theory with multi-energy groups and several groups of delayed neutron precursors. The tool is expected to be applicable for core monitoring of fast reactors and also for other reactor types with hexagonal fuel assemblies. The noise sources are modeled through small stationary fluctuations of macroscopic cross sections, and the induced first order noise is solved fully in the frequency domain. Numerical algorithms are implemented for solving both the static and noise equations using finite differences for spatial discretization, where a hexagonal assembly is radially divided into finer triangular meshes. A coarse mesh finite difference (CMFD) acceleration has been used for accelerating the convergence of both the static and noise calculations. Numerical calculations have been performed for the ESFR core with 33 energy groups and 8 groups of delayed neutron precursors using the cross section data generated by the ERANOS code. The results of the static state have been compared with those obtained using ERANOS. The results show an adequate agreement between the two calculations. Noise calculations for the ESFR core have also been performed and demonstrated with an assumption of the perturbation of the absorption cross section located at the central fuel ring.

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.

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.