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

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

Modeling noise experiments performed at AKR-2 and CROCUS zero-power reactors

CORTEX is a EU H2020 project (2017-2021) devoted to the analysis of ’reactor neutron noise’ in nuclear reactors, i.e. the small fluctuations occurring around the stationary state due to external or internal disturbances in the core. One important aspect of CORTEX is the development of neutron noise simulation codes capable of modeling the spatial variations of the noise distribution in a reactor. In this paper we illustrate the validation activities concerning the comparison of the simulation results obtained by several noise simulation codes with respect to experimental data produced at the zero-power reactors AKR-2 (operated at TUD, Germany) and CROCUS (operated at EPFL, Switzerland). Both research reactors are modeled in the time and frequency domains, using transport or diffusion theory. Overall, the noise simulators managed to capture the main features of the neutron noise behavior observed in the experimental campaigns carried out in CROCUS and AKR-2, even though computational biases exist close to the region where the noise-inducing mechanical vibration was located (the so-called ”noise source”). In some of the experiments, it was possible to observe the spatial variation of the relative neutron noise, even relatively far from the noise source. This was achieved through reduced uncertainties using long measurements, the installation of numerous, robust and efficient detectors at a variety of positions in the near vicinity or inside the core, as well as new post-processing methods. For the numerical simulation tools, modeling the spatial variations of the neutron noise behavior in zero-power research reactors is an extremely challenging problem, because of the small magnitude of the noise field; and because deviations from a point-kinetics behavior are most visible in portions of the core that are especially difficult to be precisely represented by simulation codes, such as experimental channels. Nonetheless the limitations of the simulation tools reported in the paper were not an issue for the CORTEX project, as most of the computational biases are found close to the noise source

Analysis of the neutron noise induced by fuel assembly vibrations

The investigation of neutron noise is key to several applications in nuclear reactor physics, such as the detection of control rod or assembly vibrations and the diagnostic of coolant speed and void fraction. In this paper we will elucidate some aspects of the noise equations in the Fourier domain, for the case of periodic fuel rod vibrations with frequency\ua0ω0\ua0in a small symmetrical system in which the perturbation is centrally located. We will in particular focus on the double frequency effect, i.e., the emergence of a noise component at\ua02ω0\ua0(possibly stronger than the one at the fundamental frequency\ua0ω0). Our analysis will be carried out without truncating the noise source at the first order and in the context of a non-perturbative approach (i.e., without resorting to linearization). For this purpose, we will select a simple benchmark configuration that is amenable to accurate reference solutions obtained by solving the exact time-dependent transport equations. The analysis carried out in this work suggests that the non-perturbative noise equations are mandatory in order to properly discriminate the possible emergence of double frequency effects in neutron noise, especially in view of comparing simulation results to experimental data

On the simulation of neutron noise induced by vibrations of fuel pins in a fuel assembly

Vibrations of fuel assemblies are an important issue in the safe operation of nuclear reactors, because they can challenge the integrity of the fuel with potential for radioactive releases. Reactor neutron noise-based techniques for monitoring vibrations are valuable for core diagnostic since they are not intrusive and make use of ordinary neutron flux measurements from ex-core and in-core detectors. The application of these techniques involves the solution of inverse problems that require numerical simulations capable of estimating the reactor neutron noise, given a model of the vibrations. For this purpose, several novel reactor neutron noise solvers have been developed in the CORTEX project using either Monte Carlo or deterministic methods, such as the discrete ordinates method, the method of characteristics, and the diffusion approximation. In the current work, these solvers have been scrutinized by computing the neutron noise induced by vibrations of one or multiple fuel pins in a simplified UOX fuel assembly benchmark, via proper variations of macroscopic neutron cross sections. The comparison of these neutron noise solutions obtained from the different methods shows novel insights into the simulation of neutron noise induced by mechanical vibrations, such as the challenges posed by the Monte Carlo method, the impact of the angular discretization on the application of the discrete ordinates method, and the accuracy of the diffusion approximation assessed via the higher-order neutron transport methods