Victor Dykin

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 Greens function technique. The forward Greens 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 Greens 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.

Simulation of in-core neutron noise measurements for axial void profile reconstruction in boiling water reactors

This paper reports on the development and application of a method of emulating bubbly flow by generating bubbles with random sampling methods. The purpose of the modeling is that by using the simulated random two phase flow as input, one can generate “synthetic” neutron noise signals by convoluting the input with a simplified neuronic transfer function, on which the possibility of reconstructing the axial void profile from in-core neutron noise measurements can be studied by standard spectral noise analysis methods. The long term goal of this work is to elaborate methods of neutron noise analysis, by which the local void fraction in a boiling water reactor can be determined by measurements. In this preliminary stage, two methods for the reconstruction of the axial void and the velocity profiles are discussed. The first method is based on the break frequency of the neutron auto-power spectrum, whereas the second method only utilizes the information in the transit time of the void fluctuations between axial pairs of neutron detectors. A clear and monotonic relationship between the chosen observables and the two-phase flow properties was found, but an accurate determination of the void fraction requires further development and testing of the various unfolding alternatives.

The role of the eigenvalue separation in reactor dynamics and neutron noise theory

ABSTRACT The concept of eigenvalue separation (ES) was introduced in the past for the characterisation of the space-time kinetics of reactor transients, and the stability properties of large loosely coupled cores. However, most of the investigations reported so far concern the determination of the ES itself either from static calculations, or from measurements of the flux tilt or neutron noise cross-correlations. Conclusions on system behaviour were only drawn from the properties of the static eigenfunctions, comparing non-perturbed and perturbed systems, without explicitly solving the time- or frequency-dependent problem. In this paper, we explore the role of the ES on the neutronic response of a critical core to small stochastic perturbations (neutron noise); in particular, the spatial and frequency characteristics of the arising neutron noise as a function of the ES, as well as the spatial structure of the perturbation. It is shown that for systems with small ES and non-uniform perturbations, point kinetics will not dominate even for very low frequencies. The results lend some further insight into the origin and properties of the various types of boiling water reactor instabilities.

The Molten Salt Reactor Point-Kinetic Component of Neutron Noise in Two-Group Diffusion Theory

Abstract The derivation of the point-kinetic component of the neutron noise in two-group diffusion theory in molten salt reactors (MSRs), based on different techniques, is discussed. First, the point-kinetic component is calculated by projecting the corresponding full space-frequency–dependent solution onto the static adjoint. Then, following the standard procedure in reactor physics, the point-kinetic solution is determined by solving the linearized point-kinetic equations. Both results are thereafter analyzed and compared quantitatively. Such a comparison clearly indicates that the solution obtained by the conventional derivation, i.e., from the point-kinetic equations, significantly differs from the exact one and is not able to reproduce certain features of the latter. Similar discrepancies between the two methods were also pointed out and confirmed earlier in one-group MSR calculations.

Kinetics, dynamics, and neutron noise in stationary MSRs

Abstract This chapter discusses the statics, kinetics, and dynamics of molten salt reactors in a simple model that allows analytical solutions. Due to this, and the introduction of some further limiting cases, the chapter offers substantial insight into and understanding of the physics and the neutronic behavior of molten salt systems with circulating fuel. After a discussion of the properties of the model and the limiting cases for the static equations, a treatment of space–time transients is introduced, and some limiting cases are solved explicitly. Thereafter the kinetic and dynamic response of the reactor is derived by calculating the space–frequency-dependent neutron fluctuations (neutron noise) induced by small stationary perturbations of the system parameters. The validity of the point kinetic approximation and the calculation of the point kinetic component of the noise are discussed. Finally, the neutron noise induced by various perturbations propagating with the circulating fuel is calculated and discussed.

Development of a point-kinetic verification scheme for nuclear reactor applications

In this paper, a new method that can be used for checking the proper implementation of time- or frequency-dependent neutron transport models and for verifying their ability to recover some basic reactor physics properties is proposed. This method makes use of the application of a stationary perturbation to the system at a given frequency and extraction of the point-kinetic component of the system response. Even for strongly heterogeneous systems for which an analytical solution does not exist, the point-kinetic component follows, as a function of frequency, a simple analytical form. The comparison between the extracted point-kinetic component and its expected analytical form provides an opportunity to verify and validate neutron transport solvers. The proposed method is tested on two diffusion-based codes, one working in the time domain and the other working in the frequency domain. As long as the applied perturbation has a non-zero reactivity effect, it is demonstrated that the method can be successfully applied to verify and validate time- or frequency-dependent neutron transport solvers. Although the method is demonstrated in the present paper in a diffusion theory framework, higher order neutron transport methods could be verified based on the same principles.