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[en] Highlights: •A modified α − k power iteration method is presented for computing the time-eigenvalue. •It is not required to provide the initial values of α for the modified method. •Computational experiences validate the validity and efficiency of the new method. -- Abstract: A modified α − k power iteration method is presented for the prediction of time-eigenvalue(α) of the neutron transport equation. By developing a direct relationship between K-eigenvalue and α-eigenvalue, a new formula is introduced to estimate the value of α. Compared with the conventional method, it is not required to provide the initial values of α for the modified method. Since it is always difficult to guess the suitable initial values, the modified method is more convenient for solving time-eigenvalue problems. Computational experiences show that the accuracy of the modified method is the same as the conventional method.
[en] Nuclear reactor physics deals with the solution of the neutron transport equation, for which several numerical methods and resulting calculation codes exist. Using parallel programming to multiply the resources available to these codes, it is possible to increase their computational power, thus improving their modelling capabilities. This work focuses on the optimization of neutron transport algorithms by means of parallel programming techniques. For cell calculations, the collision probabilities and heterogeneous response (HRM) methods are considered, including the associated multigroup scheme, as implemented in INVAP’s cell calculation code, CONDOR. The diffusion method in a finite difference formulation, used in CITVAP for core calculations, is optimized as well. The parallel methods obtained are implemented in OpenMP, an application for parallel programming in shared memory computers. (author)
[es]La física de reactores está basada en la resolución de la ecuación de transporte de neutrones, para la cual existen diversos esquemas numéricos y códigos de cálculo que los implementan. La programación en paralelo permite aumentar la velocidad de estos códigos mediante la utilización de múltiples unidades de procesamiento, mejorando la capacidad de modelado. En este trabajo se estudió la paralelización de distintos algoritmos asociados a la ecuación de transporte. Para la etapa de cálculos de celda fueron considerados los métodos de probabilidades de colisión y de respuesta heterogénea (HRM), incluyendo el esquema multigrupo asociado, y su implementación en el código CONDOR, desarrollado en INVAP. El método de difusión en diferencias finitas implementado en el código CITVAP fue analizado para los cálculos de núcleo. La programación de los algoritmos desarrollados se realizó en OpenMP, una herramienta de procesamiento en paralelo en el modelo de memoria compartida. (author)
[en] The method of characteristics (MOC) is one of the main methods for solving reactor neutron transport equation currently. A transport theory code based on the method of characteristics and an OpenMP parallel version of the method of characteristics calculation code were developed. OpenMP is a parallel programming model with shared memory architectures, using Fork-Join parallel execution mode, which is suitable for SMP shared memory multi-processor systems and multi-core processors architecture. The code was verified and validated by different benchmarks. The numerical results demonstrate that the code can give excellent accuracy for both the neutron effective multiplication factor and relative neutron flux (normalized cell power) distribution for neutron transport problem. The use of OpenMP can obtain good acceleration effect, making the calculation time significantly reduced. (authors)
[en] Sodium-cooled nuclear reactors offer interesting perspectives in terms of uranium resources economy and radioactive waste management. In order to meet modern safety standards, though, increasingly complex core concepts have been proposed for this technology.Hence, the first objective of this thesis is the identification of the main physical phenomena that need to be taken into account when modeling the neutronic behavior of a heterogeneous nuclear core in a fast neutron spectrum. The second objective is the development of appropriate calculation schemes in the APOLLO3 code, developed at CEA. After a brief reminder of neutronic calculation theory and methods, this document presents a critical analysis of the neutronic calculation schemes available in APOLLO3 for sodium-cooled applications. This analysis highlights the necessity to model, during the cross section preparation phase, angular modes of the neutron flux that are representative of the core geometrical configuration. To meet this need in axially heterogeneous geometries, a 2D/1D approximation to the 3D neutron transport equation is derived and implemented in APOLLO3. In particular, it is shown that this approximation allows to consistently represent axial angular modes of the flux in 2D calculation domains. Besides, a new traverse model is proposed for the core/reflector radial interface, as well as an innovative control rod calculation method. The combination of these methods allows to define a unique, and numerically validated, reference calculation scheme in APOLLO3, suitable for the calculation of a wide range of complex sodium-cooled nuclear cores. (author)
[fr]Les reacteurs nucleaires refroidis au sodium offrent des perspectives interessantes pour la filiere nucleaire (utilisation optimale de l'uranium naturel, reduction de la radiotoxicite des dechets nucleaires). Cependant, la necessite d'elever le niveau de surete de ces reacteurs aux standards du XXIe siecle a conduit a des designs de coeurs tres heterogenes. Ainsi, les objectifs de la these sont l'identification des principaux phenomenes physiques devant etre pris en compte lors du calcul neutronique de coeurs heterogenes en spectre rapide, ainsi que le developpement de schemas de calcul adaptes dans le code APOLLO3 du CEA. Apres quelques rappels theoriques et methodologiques, ce document presente une analyse critique des schemas de calcul disponibles dans APOLLO3 pour les reacteurs refroidis au sodium. Cette analyse permet de mettre en evidence la necessite de simuler, des l'etape de preparation des sections efficaces, des modes angulaires du flux qui soient representatifs de la configuration geometrique du coeur. Pour repondre a ce besoin dans le cadre de geometries presentant une forte heterogeneite axiale, une approximation 2D/1D a l'equation du transport des neutrons 3D est developpee. Cette derniere permet de representer de maniere coherente, et a moindre cout, des effets d'anisotropie axiale dans des calculs 2D. Une nouvelle modelisation de type traverse de l'interface coeur/reflecteur est egalement proposee, ainsi qu'une methode de calcul innovante des barres de controle. Ces methodes permettent, in fine, de definir un schema de calcul de reference unique et valide numeriquement, adapte a la modelisation des coeurs de reacteurs refroidis au sodium. (l'auteur)
[en] We investigate transport theory for anisotropic transport of neutrons in finite medium or injected externally. When anisotropic transport is treated by the usual transport equation, on which reversibility of collisions is shown imposed, successive collisions always induce 'self-collision' or sham collision; the fact is unavoidable as long as statistical ensemble is constructed from the reductionistic mechanical-systems. Then, irreductionistic elements, or spatial cells containing assembly of free neutrons (and implicit medium nuclei) uniformly are introduced, from which alternative Liouville equation is constructed. Successive collisions are expressed by fusing three cells; for reviving mechanical law in the collisions the law of action and reaction is applied to between first fused-cell and third cell. Extended transport equation can thus describe the process of chaotically mixing anisotropic momentum, i.e., the well-known deep penetration. (author)
[en] The critical size of a finite homogenous slab is investigated for one-speed neutrons using the alternative phase function (AG, Anlı–Güngör) in place of the scattering function of the transport equation. First of all, the neutron angular flux expanded in terms of the Chebyshev polynomials of second kind (UN approximation) together with the AG phase function is applied to the transport equation to obtain a criticality condition for the system. Then, using various values of the scattering parameters, the numerical results for the critical half-thickness of the slab are calculated and they are tabulated in the tables together with the ones obtained from the conventional spherical harmonic (PN) method for comparison. They can be said to be in good accordance with each other.
[en] The solution of the Milne problem is studied by one-speed neutron transport equation in plane geometry with İnönü’s scattering kernel, which is known as a linear combination of the forward, backward and isotropic scattering kernel (FBIS kernel). The solution of the neutron transport equation with İnönü’s scattering kernel can be written in terms of the solution of the neutron transport equation for isotropic scattering case. The extrapolation distance is calculated with modified FN (or 𝐻N) method. The numerical values of the extrapolation distance are obtained depending on the secondary neutron numbers and anisotropy coefficients and compared with the available data in the literature values. (author)
[en] This project is dedicated to the development of the micro-depletion method in the chain of codes DRAGON/DONJON. A full-core calculation is usually a two-level computational scheme. Two different computational codes are required to perform such a calculation: a lattice code (DRAGON in our case) and a diffusion code (DONJON in our case). A lattice calculation is done to generate multi-parameter reactor databases. Theses tables are compatible with the diffusion code. We can use them to compute the fluxes over the reactor using a diffusion approximation. In this case, the fuel depletion in the core is realized by the computation of new burnups, thanks to the local power levels. The micro-depletion method is based on the numerical solution of the depletion equations, also called as the Bateman equations. In each bundle, isotopic concentrations are available to compute the reaction rates, and perform the depletion. At each burnup step, these concentrations are updated with the aid of a depletion equations solver. The main advantage of this method, in comparison to an interpolation computation, is the consideration of local effects. While solving the depletion equations, local reaction rates are used to find the new densities. When we interpolate the databases, only the burnup of the fuel is used to get new nuclear properties. However, some fission products are more dependent on the actual flux they are exposed to than on the energy released during the operation time of the core. This is the case for Xenon-135. Because of the huge absorption cross section of Xenon-135, this isotope plays an important role in the reactor behaviour. To investigate this problem, a module is written to compute the Xenon distribution in the DONJON code. This module is used in an interpolation calculation to correct the densities estimated by the database. A step-by-step approach is used in this document. The goal is to underline the main contribution by using micro-depletion method. Two Benchmarks are studied using a reference DRAGON calculation. Different power levels are tested to put emphasis on the consideration of local effects according to the two methods. We observe that the effective multiplication factor tends to be biased for low power macroscopic depletion calculations. Certain interpolated isotopic concentrations are biased because they correspond to nominal power concentrations. (author)