J.L. Muñoz-Cobo

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.

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.

Hilbert–Huang analysis of BWR neutron detector signals: application to DR calculation and to corrupted signal analysis

Abstract In this paper, we present an application of the empirical mode decomposition method [Proc. R. Soc. Lond. A 454 (1998) 903], to the stability analysis of BWR. The methodology developed in this paper decomposes the original time series data in intrinsic oscillation modes or IMFs. Then we compute for each IMF, its Hilbert amplitude spectrum and its Hilbert marginal spectrum. From the intrinsic mode related to BWR stability we have obtained by ordinary autoregressive methods the decay ratio value and the oscillation frequency. Also we have proven that the original signal can be reconstructed with seven IMFs and that this modes are mutually orthogonals.

Parallel channel instabilities in boiling water reactor systems: boundary conditions for out of phase oscillations

Abstract In this paper we study the boundary conditions during out of phase oscillations, in a system formed by two parallel channels coupled to multimodal neutron kinetics. The fact that the pressure drop can change with time, but remains the same in all the parallel channels, leads us to analytical integration of the time derivative term of the channel momentum equation, in order to get a dynamic equation for the inlet mass flux to each channel. From these inlet mass flux dynamic equations plus the appropriate boundary conditions, we have obtained the expression of the time dependent common pressure drop to all the channels. Finally the oscillations in the pressure drop and in the inlet mass flux to the channels have been investigated when out of phase oscillations take place.

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.

Subcritical reactivity monitoring in accelerator driven systems

Abstract In this paper, an absolute measurements technique for the subcriticality determination is presented. The development of accelerator driven systems (ADS) requires the development of methods to monitor and control the subcriticality of this kind of system, without interfering with its normal operation mode. This method is based on the stochastic neutron and photon transport theory that can be implemented by presently available neutron transport codes. As a by-product of the methodology a monitoring measurement technique has been developed and verified using two coupled Monte Carlo programs. The first one, LAHET, simulates the spallation collisions and the high energy transport and the other, MCNPDSP, is used to estimate the counting statistics from neutron ray counter in fissile system, and the transport for neutrons with energies less than 20 Mev. Through the analysis of the counter detectors it is possible to determine the kinetics parameters and the k eff value. We present two different ways to obtain these parameters using the accelerator or using a Cf-252 source. A good agreement between theory and simulations has been obtained with both sources.

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.

Heat transfer modeling in the vertical tubes of the passive containment cooling system of the simplified boiling water reactor

The long term containment cooling of GEs passive BWR design is based on a new safety system called PCCS (passive containment cooling system). Performance of this system relies on the pressure difference between the drywell and wetwell in case of an accident and on the condensation of steam moving downward inside vertical tubes fully submerged in a water pool initially at room temperature. In this paper a model based on the resolution of momentum equations of both phases, the application of the heat and mass transfer analogy, and the consideration of the presence of a noncondensable gas by diffusion theory in a boundary layer is presented. Assumptions and approximations taken resulted in new methods to estimate film thickness and heat transport from the gas to the interface. Influence of phenomena such as suction, flow development, film waviness, and droplet entrainment has been accounted for. Based on this formulation, a computer programme called HVTNC (heat transfer in vertical tubes with noncondensables) has been built up. HVTNC results have been compared to the experimental data available. Experimental trends have been reproduced. Heat transfer has been found to be severely degraded by the presence of noncondensables whereas high Reynolds numbers of gas flow have been seen to enhance shear stress and therefore, heat transmission. The average error of HVTNC is essentially located at regions where only a residual fraction of heat remains to be transferred, so that minor deviations can be anticipated in the overall heat transfer in the tube. Comparison of HVTNC to other models show a substantial gain of accuracy with respect to earlier models.

Modal influence of the detector location for the noise calculation of the ADS

Abstract The purpose of this paper is to investigate the space dependence of neutron noise in a source-driven subcritical system. The noise produced by the fluctuations of the source are measured from the cross spectrum between the source and a detector located inside the system using the methodology of Munoz-Cobo et al. (Munoz-Cobo, J.L., Rugama, Y., Valentine, T., Mihalczo, J., Perez, R., 2002. Annals of Nuclear Energy in press). The prompt neutron decay constant obtained from the source-detector cross spectrum is dependent on the detector location because of the influence of higher modes of the neutron flux. One group diffusion theory is used to determine the eigenvalues and eigenfunctions of the fundamental and higher modes. This analytical approximation will be used to explain the detector location effect through quantitative evaluation of a specific model. The analytical system subcriticality will be obtained from the eigenvalue equation in the static case at two different subcritical situations.