G. Verdú

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.

Aplication of Hopf bifurcation theory and variational methods to the study of limit cycles in boiling water reactors

Abstract In this paper we analyze the limit cycles which arise in Boiling Water Reactor using Hopf bifurcation theory and variational methods. We prove that we can apply the central manifold method to this kind of system in order to reduce the dimension of the state space. This systematic reduction is performed for the BWR dynamical system and it is obtained a reduced two dimensional one which contains all the information about the bifurcation. We have also introduced in this paper the parameter which define from a nonlinear point of view, the limit cycle stability. Finally the calculation of the limit cycle period is performed by variational and Hopf bifurcation methods, the agreement between both methods is excellent.

Turbulent vapor condensation with noncondensable gases in vertical tubes

This paper develops a theory for turbulent vapor condensation in vertical tubes when non-condensable gases are present. The local heat transfer coefficient is calculated and the results are compared with experimental data. Approximate methods to calculate the condensate film thickness with good precision are developed without need to iterate to solve the transcendental equation which obeys the film thickness. A comparison of the theory predictions with some experimental data resulted in a good agreement.

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.

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.

Treatment of 137Cs liquid wastes by reverse osmosis. Part I. Preliminary tests

Abstract As a consequence of an accidental fusion of a 137Cs source in a steel production factory, 40 m3 of radioactive liquids were generated in the plant decontamination process. This radioactive liquid waste was treated by a reverse osmosis plant, managing to declassify more than 36 m3. The remaining 4 m3 were treated by evaporation reducing the final volume to less than 1 m3. Prior to the waste treatment at the steel factory, preliminary tests were done in order to determine reverse osmosis membrane performance with 137Cs effluents. The influence ofgamma and electron irradiation on structure and transport properties of reverse osmosis membranes was studied; and reverse osmosis performance with a 137Cs-contaminated liquid obtained from contaminated ashes was assessed. The aim of this paper is to describe and show the results of these preliminary tests.

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.

Monte carlo simulation of the compton scattering technique applied to characterize diagnostic x-ray spectra.

The quality control of x-ray tubes for medical radiodiagnostic services is very important for such devices. Therefore, the development of new procedures to characterize the x-ray primary beam is highly interesting in order to obtain an accurate assessment of the actual photon spectrum. The Compton scattering technique is very useful to determine x-ray spectra (in the 10-150 kVp range), avoiding a pile-up effect in the detector since a large room is not usually available to apply other techniques. In this work, this process has been simulated using a Monte Carlo code, MCNP 4C. Some geometrical models have been developed and different techniques have been studied in order to improve statistics and accuracy in the acquisition of Pulse Height Distribution (PHD). The effect of both the collimation of the primary beam and the scattering angle of the spectrometer has been analyzed. Results obtained using simulation models have been compared with experimental measurements.