Rafael Miró

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.

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.

Cobalt Therapy Dosimetric Calculations Over a Voxelized Heterogeneous Phantom: Validation of Different Monte Carlo Models and Methodologies Against Experimental Data

The main goal of the present paper is to quantify, in homogeneous and heterogeneous phantoms, the differences between experimentally measured dose distributions inside it, and those calculated by the simulation of different transport models using the Monte Carlo computer code MCNP. This objective has been achieved simulating the electron and photon transport in a water phantom irradiated by a Theratron 780 (MDS Nordion) 60Co radiotherapy unit, which has been realistically modeled, considering field sizes from 5 cmtimes5 cm to 20 cmtimes20 cm. The source description and characteristics of the incident beam have been slightly modified in order to study the results variations of these models. Different methodologies have also been applied to speed up the calculations with the aim of applying MCNP efficiently in radiotherapy treatment planning

Singular system analysis of the Local Power Range Monitor (LPRM) readings of a Boiling Water Reactor (BWR) in an unstable event

Singular system analysis is a successful technique to separate oscillating components from a given signal. A methodology is proposed to apply this technique to the signals obtained from the LPRMs of a boiling water reactor core and extract the contributions of the in-phase oscillation and the out-of-phase oscillations from the LPRM readings during an unstable event. This methodology has been validated with synthetic signals and simulations of in-phase and out-of-phase oscillations of the Leibstadt reactor. Finally, one case of Ringhals I Stability Benchmark has been analysed.

Resolution of the Generalized Eigenvalue Problem in the Neutron Diffusion Equation Discretized by the Finite Volume Method

Numerical methods are usually required to solve the neutron diffusion equation applied to nuclear reactors due to its heterogeneous nature. The most popular numerical techniques are the Finite Difference Method (FDM), the Coarse Mesh Finite Difference Method (CFMD), the Nodal Expansion Method (NEM), and the Nodal Collocation Method (NCM), used virtually in all neutronic diffusion codes, which give accurate results in structured meshes. However, the application of these methods in unstructured meshes to deal with complex geometries is not straightforward and it may cause problems of stability and convergence of the solution. By contrast, the Finite Element Method (FEM) and the Finite Volume Method (FVM) are easily applied to unstructured meshes. On the one hand, the FEM can be accurate for smoothly varying functions. On the other hand, the FVM is typically used in the transport equations due to the conservation of the transported quantity within the volume. In this paper, the FVM algorithm implemented in the ARB Partial Differential Equations solver has been used to discretize the neutron diffusion equation to obtain the matrices of the generalized eigenvalue problem, which has been solved by means of the SLEPc library.

Considerations of MCNP Monte Carlo code to be used as a radiotherapy treatment planning tool

The present work has simulated the photon and electron transport in a Theratron 780reg (MDS Nordion) 60Co radiotherapy unit, using the Monte Carlo transport code, MCNP (Monte Carlo N-Particle). This project explains mainly the different methodologies carried out to speedup calculations in order to apply this code efficiently in radiotherapy treatment planning

Comparison of experimental 3D dose curves in a heterogeneous phantom with results obtained by MCNP5 simulation and those extracted from a commercial treatment planning system

Commercial planning systems used in radiotherapy treatments use determinist correlations to evaluate dose distribution around regions of interest. Estimated dose with this type of planners can be problematic, especially when analyzing heterogeneous zones. The present work is focused in quantifying the dose distribution in a heterogeneous medium irradiated by a 6 MeV photon beam emitted by an Elekta Precise Radiotherapy Unit head. Dose mapping inside the heterogeneous water phantom has been simulated with the photon and electron transport with Monte Carlo computer code MCNP5 and also, using a commercial treatment planning software in the same irradiation conditions. The calculated results were compared with experimental relative dose curves. This comparison shows that inside the heterogeneity region, the commercial algorithms are not able to predict the variation of dose in the heterogeneous zones with the same precision as MCNP5.

Two Techniques for the Analysis of the Local Power Range Monitors Readings under BWR Unstable Conditions

As an example of accidental situations in nuclear power plants, we consider the power oscillations that can occur in a boiling water reactor (BWR) nuclear power plant (NPP) under certain circumstances. An interesting problem is to study and characterize these instabilities analyzing the neutronic power signals obtained from the local power range monitors (LPRMs) installed in the reactor core. Several techniques exist to detect and classify the possible oscillations in a BWR. The power decomposition method and the singular system analysis methodology are reviewed and the performance of both techniques is compared analyzing points 9 and 10 of cycle 14 of the OECD Ringhals 1 stability benchmark