D. Ginestar

Time series analysis and forecasting techniques for municipal solid waste management

Successful planning and operation of a solid waste management system depends on municipal solid waste (MSW) generation process knowledge and on accurate predictions of solid waste quantities produced. Conventional analysis and prediction models are based on demographic and socioeconomic factors. However, this kind of analysis is related to mean generation data. Dynamic MSW generation analysis can be done using time series data of solid waste generated quantities. In this paper some tools for time series analysis and forecasting are proposed to study MSW generation. A prediction technique based on non-linear dynamics is proposed, comparing its performance with a seasonal AutoRegressive and Moving Average (sARIMA) methodology, dealing with short and medium term forecasting. Finally, a practical implementation consisting of the study of MSW time series of three cities in Spain and Greece is presented.

3D λ-modes of the neutron-diffusion equation

Abstract The paper deals with the calculation of the 3D harmonic lambda modes in a B.W.R. reactor. An algorithm to calculate the harmonic lambda modes corresponding to the steady state two-group 3D neutron-diffusion equation is presented. The algorithm uses subspace iteration method techniques combined with convergence acceleration based on variational principles. The methodology has been tested on two benchmark problems, and applied to obtain the 3D modes of the Cofrentes Nuclear Power Plant.

A nodal modal method for the neutron diffusion equation. Application to BWR instabilities analysis

Abstract Fast codes, capable of dealing with three-dimensional geometries, are needed to be able to simulate spatially complicated transients in a nuclear power reactor. In this paper, we propose a modal method to integrate the neutron diffusion equation in which the spatial part has been previously dicretized using a nodal collocation method. For the time integration of the resulting system of differential equations it is supposed that the solution can be expanded as a linear combination of the dominant Lambda modes associated with a static configuration of the reactor core and, using the eigenfunctions of the adjoint problem, a system of differential equations of lower dimension is obtained. This system is integrated using a variable time step implicit method. Furthermore, for realistic transients, it would be necessary to calculate a large amount of modes. To avoid this, the modal method has been implemented making use of an updating process for the modes at each certain time step. Five transients have been studied: a homogeneous reactor, a non-homogeneous reactor, the 3D Langenbuch reactor and two transients related with in-phase and out-of-phase oscillations of Leibstadt NPP. The obtained results have been compared with the ones provided by a method based on a one-step backward discretization formula.

The implicit restarted Arnoldi method, an efficient alternative to solve the neutron diffusion equation

Abstract To calculate the neutronic steady state of a nuclear power reactor core and its subcritical modes, it is necessary to solve a partial eigenvalue problem. In this paper, an implicit restarted Arnoldi method is presented as an advantageous alternative to classical methods as the Power Iteration method and the Subspace Iteration method. The efficiency of these methods, has been compared calculating the dominant Lambda modes of several configurations of the Three Mile Island reactor core.

On the regional oscillation phenomenon in BWR's.

Abstract In the last 20 years many papers have been devoted to the study of BWR stability phenomenon. While the physical mechanisms of global power oscillations are well-known, the regional power oscillation phenomenon is not understandable in all details. Our paper should be a contribution to the understanding of conditions under which regional power oscillations can be expected. With this aim we have analyzed, with the system code RAMONA3–12, some stability experiments which were conducted on the NPP Leibstadt. To test the ability of the monitoring system to cope with demanding operation situations, the power oscillations during the experiments were deliberately transformed from the in-phase into the out-of-phase mode, via changing some control rod positions. Hence, we have been able to study the “real world” of a BWR core in the regional oscillation mode. We focused our work on the analysis of the higher mode feedback reactivities (dynamical reactivities) and the calculation of some spatial indices. The feedback reactivities have been calculated with the code LAMBDA-REAC. From the results obtained we conclude that it is in the case of certain specific types of power distribution that a particular mode coupling mechanism can cause regional oscillations to occur.

Coupling of density wave oscillations in parallel channels with high order modal kinetics: application to BWR out of phase oscillations

Abstract In this paper, we study the behavior of a system formed by two parallel channels coupled to a multimodal kinetics. The first problem that arises is the calculation of the reactivity coefficients for the higher modes. This problem is solved by means of the introduction of distribution factors for a given reactor region which depend on the involved modes. We have also performed a detailed analysis of the different instability types which can be obtained from the model changing the boundary conditions and the feedback gains of the fundamental and first harmonic modes.

Non linear analysis of out of phase oscillations in boiling water reactors

Abstract Out of phase oscillations have been observed recently in many boiling water reactors during stability tests and also in start up conditions. Many authors have attempted to explain these regional oscillations, but the explanations given are not complete. In this paper, we develop a non linear phenomenological model that can explain, both in phase and out of phase oscillations. The neutronic loop has been described on the basis of an expansion in terms of A-modes. Furthermore, for a semiquantitative representation of the dynamics, reduced order model have been obtained reducing the number of regions, modes and energy groups considered in the problem. In this line, we propose a model that qualitatively explains the dynamic behavior of these oscillations verifying that in phase oscillations only appear when the azimuthal mode has not enough thermal-hydraulic feedback to overcome the eigenvalue separation and also, that it is possible that self-sustained out of phase oscillations arise due to the different thermal-hydraulic properties of the two reactor core lobes, if the modal reactivities have appropriate feedback gains.

High order backward discretization of the neutron diffusion equation

Abstract Fast codes capable of dealing with three-dimensional geometries, are needed to be able to simulate spatially complicated transients in a nuclear reactor. We propose a new discretization technique for the time integration of the neutron diffusion equation, based on the backward difference formulas for systems of stiff ordinary differential equations. This method needs to solve a system of linear equations for each integration step, and for this purpose, we have developed an iterative block algorithm combined with a variational acceleration technique. We tested the algorithm with two benchmark problems, and compared the results with those provided by other codes, concluding that the performance and overall agreement are very good.

A Transient Modal Analysis of a BWR Instability Event

To solve the time dependent neutron diffusion equation a modal method, based on the expansion of the neutronic flux in terms of the dominant Lambda modes of a static configuration of the reactor is presented. This method is used to analyse transients of a nuclear power reactor where an instability event can be developed. A simulation of a transient with the same conditions given for the case 9 of Ringhals stability benchmark has been analysed. It is shown that with these conditions an out of phase oscillation associated with the two first azimuthal modes can be developed. These results are corroborated using a power modal decomposition, using the local power distribution provided by RAMONA code. To complete the analysis, the modal feedback reactivities have been calculated to study the coupling mechanism among modes.

Nonrelativistic limit of supersymmetric theories

The superfield formulation of the nonrelativistic limit of supersymmetric theories is given using a precise group‐theoretical definition. The procedure is applied to the Wess–Zumino superfield Lagrangian and to supersymmetric QED.