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AbstractAbstract

[en] The development of neutron physics and the transport equation is described, and the difference between dynamical nuclear systems and normal static nuclear reactors pointed out. The history of China's studies on nuclear constants and transport equation computation is reviewed, and some topics that need to be investigated in further detail are discussed. (authors)

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1 fig., 3 refs.

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Journal Article

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Wuli; ISSN 0379-4148; ; v. 38(12); p. 884-888

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Lathouwers, D., E-mail: D.Lathouwers@tudelft.nl

AbstractAbstract

[en] An adaption is presented to an earlier method for the prediction of time-eigenvalues of the neutron transport equation. Instead of using the full-parity first-order equation, the algorithm uses the even-parity formalism in the most expensive part of the computations resulting in a more economic method

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S0306-4549(06)00101-0; Copyright (c) 2006 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA)

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AbstractAbstract

[en] A quasi-static approach within the framework of neutron transport theory is used to develop a computational tool for the time-dependent analysis of nuclear systems. The determination of the shape function needed for the quasi- static scheme is obtained by the steady-state transport code Dragon. The kinetic model solves the system of ordinary differential equations for the amplitude function on a fast scale. The kinetic parameters are calculated by a coupling module that retrieves the shape from the output of the transport code and performs the required adjoint-weighted quadratures. When the update of the shape has to be carried out, the coupling module generates an appropriate input file for the transport code. Both the standard Improved Quasi-Static scheme and an innovative Predictor-Corrector algorithm are implemented. The results show the feasibility of both procedures and their effectiveness in terms of computational times and accuracy.

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21. International Conference on Transport Theory; Torino (Italy); Jul 2009

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Journal Article

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Conference

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Nuovo Cimento. C (Print); ISSN 2037-4909; ; v. 33(1); p. 13-20

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AbstractAbstract

[en] Our work considers spatially nonuniform states of particles, weakly interacting with a hydrodynamic medium. We developed a microscopic theory, describing such systems involving Bogolubov's reduced description method. It was shown that such systems have both kinetic and hydrodynamic stages of evolution. At the kinetic stage of evolution the one-particle distribution function is a reduced description parameter for particles, and, therefore, a medium is described by five hydrodynamic parameters (density, temperature, and velocity). The coupled system of equations of motion describing the system on the kinetic stage of evolution was obtained on the basis of Bogolubov's reduced description method. The transition from the kinetic to hydrodynamic stage of evolution for particles interacting with the medium was also studied within the reduced description method. It was shown that on the hydrodynamic stage the only description parameter of particles is their density, although the medium is still described by five hydrodynamic variables. Consequently, a coupled system of equations, which completely describe the evolution of the system under consideration on the hydrodynamic stage, including dissipation processes, was obtained. These equations were used to study the propagation of acoustic waves in our system. Also the influence of particles on relaxation processes was discussed. The obtained equations, for example, may be used to describe the neutrons propagating in a hydrodynamic medium without multiplication and capture.

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(c) 2009 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA)

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Fevotte, F.

CEA Saclay (DEN/DANS), 91 - Gif sur Yvette (France)

CEA Saclay (DEN/DANS), 91 - Gif sur Yvette (France)

AbstractAbstract

[en] At the various stages of a nuclear reactor's life, numerous studies are needed to guaranty the safety and efficiency of the design, analyse the fuel cycle, prepare the dismantlement, and so on. Due to the extreme difficulty to take extensive and accurate measurements in the reactor core, most of these studies are numerical simulations. The complete numerical simulation of a nuclear reactor involves many types of physics: neutronics, thermal hydraulics, materials, control engineering, Among these, the neutron transport simulation is one of the fundamental steps, since it allows computation - among other things - of various fundamental values such as the power density (used in thermal hydraulics computations) or fuel burn-up. The neutron transport simulation is based on the Boltzmann equation, which models the neutron population inside the reactor core. Among the various methods allowing its numerical solution, much interest has been devoted in the past few years to the Method of Characteristics in unstructured meshes (MOC), since it offers a good accuracy and operates in complicated geometries. The aim of this work is to propose improvements of the calculation scheme bound on the two dimensions MOC, in order to decrease the needed resources number. (A.L.B.)

Original Title

Techniques de tracage pour la methode des caracteristiques appliquee a la resolution de l'equation du transport des neutrons en domaines multi-dimensionnels

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Source

2008; 3 p; 8. scientific meeting of the Direction representative of the Nuclear activities of Saclay; 8. journee scientifique de la Direction Deleguee aux Activites Nucleaires de Saclay; Saclay (France); 11 Jun 2008

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Miscellaneous

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AbstractAbstract

[en] In typical lattice cells where a highly absorbing, small fuel element is embedded in the moderator, a large weakly absorbing medium, high-order transport methods become unnecessary. In this work we describe a hybrid discrete ordinates (S N) method for energy multigroup slab lattice calculations. This hybrid S N method combines the convenience of a low-order S N method in the moderator with a high-order S N method in the fuel. The idea is based on the fact that in weakly absorbing media whose physical size is several neutron mean free paths in extent, even the S

_{2}method (P_{1}approximation), leads to an accurate result. We use special fuel-moderator interface conditions and the Laplace transform (LTS_{N}) analytical numerical method to calculate the two-energy group neutron flux distributions and the thermal disadvantage factor. We present numerical results for a range of typical model problems.Primary Subject

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21. International Conference on Transport Theory; Torino (Italy); Jul 2009

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Journal Article

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Nuovo Cimento. C (Print); ISSN 2037-4909; ; v. 33(1); p. 231-238

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Chabod, Sebastien P., E-mail: sebastien.chabod@lpsc.in2p3.fr

AbstractAbstract

[en] We report the formulation of the number of elastic scatterings required to slow down a neutron. By establishing its analytical expression, we show that this number displays a discontinuity and an oscillatory transient that progressively dampens when the neutron energy decreases. This result does not apply to neutrons with energies lower than a few eV, as we restrict our study to scatterings on free stationary nuclei.

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S0375-9601(10)01235-1; Available from http://dx.doi.org/10.1016/j.physleta.2010.09.036; Copyright (c) 2010 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA)

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Santandrea, S.; Mosca, P.

American Nuclear Society, 555 North Kensington Avenue, La Grange Park, IL 60526 (United States)

American Nuclear Society, 555 North Kensington Avenue, La Grange Park, IL 60526 (United States)

AbstractAbstract

[en] In this paper we present a new numerical scheme for the Method Of Characteristic (MOC) in unstructured geometries for the neutron transport equation. The MOC has become a familiar tool for transport calculations in reactor physics [1], and its use will probably increase in the future. One of the major drawbacks of the MOC is the difficulty to implement higher-order integration schemes to improve spatial convergence. We present here a higher-order schemes for the MOC. We define a conservative and linear characteristic scheme based on linear interpolation on the surface's values of the collisions sources. We have called it Conservative Linear Surface (CLS) scheme in contrast to a preceding non conservative version. Results comparisons of the well-known Stepanek benchmark show CLS faster convergence over the standard step characteristic scheme. A generalization of the synthetic DP

_{N}acceleration scheme provides an efficient method to accelerate the internal transport iterations. (authors)Primary Subject

Source

2006; 10 p; American Nuclear Society - ANS; La Grange Park (United States); PHYSOR-2006: American Nuclear Society's Topical Meeting on Reactor Physics - Advances in Nuclear Analysis and Simulation; Vancouver, BC (Canada); 10-14 Sep 2006; ISBN 0-89448-697-7; ; Country of input: France; 7 refs.

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AbstractAbstract

[en] A stochastic neutron transport theory, in which we consider the probability P

_{N}(r, t, uΩ) that the neutron densities N_{i}(i=l, 2, ..., n) emerge in the phase space point (r, u_{i}Ω_{i}) at time t respectively, was given by means of the probability theory, and a set of non-linear integral-differential equations for the probability generating functions F_{n}(r, t, uΩ, S) was derived. The equation for one-order moment ∂F_{1}/∂S_{1}under some approximation is just the Boltzmann equation for the average neutron number. One-velocity neutron stochastic theory with isotropic scatting was applied to a point model. An approximate solution for the generating function and the equations for moments of the probability distribution and their solutions were derived. It is shown that in a supercritical system, at t→∞, the probability appearing finite neutrons is zero, P_{N}=0 (0< N<∞), in other words, the system has no or infinite neutrons. A formula for standard deviation shows that the fluctuation of neutron number in the near critical (0<λ<< 1) system should be paid our attention when the fluctuation of initial neutron number ξ_{0}is larger and the initial neutron average number (N_{0})-bar is not large enough, or neutron source Q is weaker. (authors)Primary Subject

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3 refs.

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Journal Article

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Atomic Energy Science and Technology; ISSN 1000-6931; ; v. 42(12); p. 1057-1063

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Yunzhao, Li; Hongchun, Wu; Liangzhi, Cao; Qichang, Chen

American Nuclear Society, Inc., 555 N. Kensington Avenue, La Grange Park, Illinois 60526 (United States)

American Nuclear Society, Inc., 555 N. Kensington Avenue, La Grange Park, Illinois 60526 (United States)

AbstractAbstract

[en] In this triangular nodal-SP3 method, neutron transport equation is transformed by employing an isotropic SP3 method into two coupled equations that are both in the same mathematic form with diffusion equation, and then a triangular nodal method is proposed to solve the two coupled equations. In the triangular nodal method, adjacent nodes are coupled through partial currents. Since transverse integral technique which is widely used in regular nodal method can not be used in triangular geometry because of mathematical singularity, a nodal response matrix between incoming and outgoing currents is obtained by expanding detailed nodal flux distribution into a sum of exponential functions. Numerical results demonstrate that k

_{eff}and power distribution agree well with other codes, and the triangular nodal-SP3 method appears faster. (authors)Primary Subject

Source

2010; 11 p; American Nuclear Society - ANS; La Grange Park, Illinois (United States); PHYSOR 2010: Advances in Reactor physics to Power the Nuclear Renaissance; Pittsburgh, PA (United States); 9-14 May 2010; ISBN 978-0-89448-079-9; ; Country of input: France; 15 refs.

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