Search

In a previous publication, a 2-D reactor model was introduced which contained a partially inserted thin absorber. Both the static flux, as well as the noise induced by the vertical oscillations of the rod were calculated by analytical methods. In this paper the validity of certain reactor kinetic approximations of the dynamical problem are investigated in the same reactor model. The induced noise is calculated in the adiabatic and in the plateau frequency approximation and compared with the exact solution. The significance of these two approximations is that they can be applied with existing core calculation codes either directly, or with minor modifications.

In conceptual and model studies of neutron noise and diagnostics, and even in most practical applications, simple homogeneous reactor models have been used so far, in which closed form analytical solutions are possible. In this paper a less trivial, axially non-homogeneous reactor model is used. In this model both the static flux and the noise equations can still be solved by analytical methods. The model consists of a 2-D homogeneous rectangular core in which a δ-function (Feinberg-Galanin) control rod is inserted partially. Solution of both the static flux and the dynamic equations (the latter corresponding to a rod manoeuvring experiment in which the rod is moved up and down periodically) can be given by two different analytical methodologies. Both are calculated and discussed in the paper. This model will be used later in concrete diagnostic applications as well as in studies of reactor kinetic approximations.

Diagnostics of core-barrel motion, and notably that of beam mode vibrations, has been usually performed by two distinct concepts. One strategy is to perform a qualitative analysis in the time domain, using descriptors such as vibration trajectory, probability distributions etc. This approach is rather realistic in the sense that it allows for general anisotropic pendular vibrations. The other strategy is to use frequency analysis with the goal of quantifying certain vibration properties. However, this second approach could so far handle only isotropic and unidirectional vibrations. In this paper we propose a unification of these two approaches by introducing a model by which general anisotropic vibrations can be quantified in the frequency domain. However, when separating the noise components prior to the frequency analysis, we suggest the use of symmetry properties of the noise in the time domain, based on reactor physics assumptions, as opposed to the earlier methods that use statistical independence of the components. Due to the unified approach, a combination of time and frequency domain analysis methods can be used for presentation and maximum information extraction.

Separation of various flux oscillation modes in boiling water reactor (BWR) noise measurements, based on flux factorization techniques (i.e., using orthogonality relations via integrals over the whole core), have been attempted in the past but without much success. One such example is the attempt made in 1990 in connection with the measurements in the Swedish Ringhals Unit 1 (Ringhals-1) BWR where both global (fundamental-mode) and regional (first-azimuthal-mode) oscillations were observed. Shown here is the reason for the failure of the earlier separation methods, that is, the presence of the local component of the noise with its known axial correlation properties. This component has been ignored in all BWR instability work so far. Further because of the approximation of the factorization integral by a finite sum, cross-correlations between all detectors will appear in the autocorrelation of the factorized detector signals. Taking into account the properties of both the noise structure and the approximate factorization, elaboration of factorization-based flux decomposition is possible. A phenomenological BWR noise model is used here in support of the decomposition technique. The model is also used to explain the success or failure ofprevious methods. The general factorization method proposed is demonstrated in various examples using the Ringhals-1 measurement data. In particular, the global and regional decay ratios are determined in a consistent way that is more general than the alternative methods used so far.

In two previous papers the neutron noise, induced by small vibrations of a strong absorber, was treated (Pazsit 1984, 1988). In these, two different rod models and corresponding different linearization procedures were used. The first, called the Feinberg-Galanin-Williams (FGW) model, uses a δ-function approximation of both the static and the vibrating rod. This model corresponds to preserving the static boundary condition (logarithmic derivative) at the surface of the moving rod. The second, a perturbative approach called the ϵd model, starts with a finite absorber and represents the vibration by two stationary absorbing layers with strengths fluctuating in opposite phase. It was found that these two models lead to differing results, indicating a contradiction. In this paper we show that the reason for this contradiction is that the previous results based on the ϵd model are in error. The error is due to the fact that the effect of the static rod was neglected in the Green's function. The correct ϵd result is calculated here in both one and two dimensions and is shown to be equivalent to the FGW results. This serves also as a confirmation of the two-dimensional FGW result which had earlier been derived only by heuristic arguments.