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AbstractAbstract

[en] The present paper concerns a proper statement and a new application of the so-called space asymptotic neutron transport theory in stationary reactor physics. In the first part we formulate the essential assumptions of space asymptotic transport, and briefly discuss how, to some extent, they can be physically justified for stationary problems. Some theoretical questions of primary interest, such as the solvability of the equation in the absence of external sources, i.e. the reactor criticality condition, the space-energy separability of the unique asymptotic solution, i.e. a quite general formulation of the so-called first fundamental theorem of reactor physics, are dealt with in some detail. The whole procedure is formulated within a multigroup scheme for the treatment of the energy variable. Afterwards, the results of asymptotic theory are used as a first guess to initialize an iterative procedure to numerically solve the integral transport equation. The numerical examples presented put into perspective how the use of all the information that can be achieved with little calculation effort from space asymptotic theory might noticeably enhance the convergence velocity of the procedure. The results also give a chance to comment upon the actual range of validity of the separability theorem and on some features of the transport equation eigenvalue computation, when dealing with reactor problems of practical interest. (author)

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AbstractAbstract

[en] Some possible generalised and physically meaningful formulations of the eigenvalue problem are discussed in some detail within the field of integral multigroup neutron transport. An alternative to the time eigenvalue, that takes into account the phenomena involved in delayed neutron emissions, is also introduced and interpreted. Such an eigenvalue concept gives much more information as far as the asymptotic time behaviour of a reactor is concerned. An iterative numerical procedure, in the frame of methods for the determination of lambda matrices latent roots, which is suitable to solve all proposed eigenvalue problems, is developed and applied. Its remarkable efficiency is shown, presenting some results for geometrically simple plane situations. (orig.)

[de]

Diese Arbeit beschaeftigt sich mit einigen verallgemeinerten, physikalisch sinnvollen Formulierungen des Eigenwertproblems im Rahmen der integralen Vielgruppen-Neutronentransporttheorie. Dabei wird eine Alternative zum Zeit-Eigenwert eingefuehrt und interpretiert, welche die Vorgaenge im Zusammenhang mit der Emission verzoegerter Neutronen zu beruecksichtigen gestattet. Dieses Eigenwertkonzept gibt mehr Informationen ueber das asymptotische Zeitverhalten des Reaktors. Zur Bestimmung der latenten Wurzeln von Lambda-Matrizen wurde ein numerisches Iterationsverfahren entwickelt und angewandt; es ist zur Loesung aller hier betrachteten Eigenwertprobleme geeignet. Einige Loesungen fuer einfache ebene Geometrien werden angegeben. An ihnen zeigt sich die Leistungsfaehigkeit des vorgeschlagenen Verfahrens. (orig.)Primary Subject

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Colombo, V.; Ravetto, P.

Proceedings of the 23rd intersociety energy conversion engineering conference

Proceedings of the 23rd intersociety energy conversion engineering conference

AbstractAbstract

[en] Critical calculations can constitute a good test for the comparisons of the performances of numerical methods to solve the neutron transport equation for multiplying systems. For some paradigmatic calculations, physically significant (collision and multiplication) eigenvalues can be compared with exact ones, when available. From such operations, a good insight into the capabilities of the numerical methods can be actually obtained. This work is devoted to present a selected set of comparisons of critical calculations in the one- and multi-energy-group cases. Results are obtained from iterative procedures applied to the integral form of the transport equation. The convergence rate enhancement that can be achieved by using spatially asymptotic guesses, in order to start the procedure, is also put into evidence in the multigroup cases. Higher order integration technique, referring to a Simpson-like integration rule, will be exploited and their performances highlighted

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Goswami, D.Y; Volume 1: Stirling engines, heat engines, thermoelectric power, thermal rejection systems, advanced cycles and systems, nuclear power, thermionic power; vp; 1988; p. 561-566; American Society of Mechanical Engineers; New York, NY (USA); 23. intersociety energy conversion engineering conference; Denver, CO (USA); 31 Jul - 5 Aug 1988; CONF-880702--

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AbstractAbstract

[en] A finite element methodology is employed to discretize the direction coordinate for transport problems in integro-differential form. It is shown that the method proposed can satisfactorily handle particle streaming phenomena and, especially, high order anisotropy of emissions from collisions. As a consequence, the method is applicable to many problems of neutron and photon transport (shielding and blanket problems, multiplying systems). The method can be formulated in a way suitable for handling by current discrete ordinate transport numerical algorithms. (author)

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Colombo, V.; Coppa, G.G.M.; Lapenta, G.; Ravetto, P.

The physics of reactors: operation, design and computation. Volume 3

The physics of reactors: operation, design and computation. Volume 3

AbstractAbstract

[en] A new numerical finite element technique for the angular discretization of the neutron transport equation is proposed, with special reference to two spatial dimension x-y systems. Its performance with respect to the mitigation of ray effects is discussed on physical grounds and on the basis of some test numerical calculations. It is shown how the methodology can efficiently cope with the problem of high order scattering anisotropy, where usual discrete ordinate frameworks can hardly be applied and usually give unsatisfactory results. The particular interest of the finite element scheme relies also in the fact that it produces a model that can be generally given a formal S

_{N}structure, which makes possible the use of already existing numerical proceduresPrimary Subject

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Societe Francaise d'Energie Nucleaire (SFEN), 75 - Paris (France); 475 p; 1990; p. II.10-II.19; Societe Francaise pour l'Energie Nucleaire; Paris (France); International Conference on the Physics of Reactors: Operation, Design and Computation; Marseille (France); 23-27 Apr 1990

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AbstractAbstract

[en] The determination of the space behavior of a plasma under an external time oscillating charge distribution is an important problem in fundamental plasma physics. Within the linearized collisionless Vlasov plasma model, the solution presents a great deal of difficulties, specially from a computational point of view. Several techniques (e.g. the methods of Gould, Derfler-Simonen and Buzzi) have been proposed; they all refer to the application of the space Fourier transform and then they have to tackle the hard problem of the inverse transform of 1/var-epsilon(k,iω), where E(k,iω) is the usual plasma dielectric constant. All these techniques turn out to be very complicate. In this paper an alternative procedure is proposed. It is based on an integro-differential equation. The integro-differential equation can be deduced directly from the Vlasov-Poisson model, without application of the Fourier transform. The equation is handled directly by means of numerical techniques employing spatial finite elements leading to a linear algebraic system of equations to be solved by simple iterative techniques. Physically significant results are presented and discussed. Also the possibility to extend the present procedure to more complicate plasma configurations is considered

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Anon; 200 p; ISBN 0-7803-0716-X; ; 1992; p. 84; IEEE Service Center; Piscataway, NJ (United States); 19. Institute of Electrical and Electronic Engineers (IEEE) international conference on plasma science; Tampa, FL (United States); 1-3 Jun 1992; Available from IEEE Service Center, 445 Hoes Lane, Piscataway, NJ 08854-4150 (United States)

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Colombo, V.; Coppa, G.G.M.; Melisurgo, V.; Ravetto, P.

Proceedings of the international conference on mathematics and computations, reactor physics, and environmental analyses. Volume 1 and 2

Proceedings of the international conference on mathematics and computations, reactor physics, and environmental analyses. Volume 1 and 2

AbstractAbstract

[en] Some modifications of the Diffusion Synthetic Acceleration (DSA) technique are proposed to face its loss of effectiveness when dealing with highly anisotropic scattering. A model case convergence analysis of the proposed techniques is performed; an extensive set of comparisons with results obtained by means of already assessed DSA modification techniques is reported for various scattering cross-section configurations. The importance of non asymptotic convergence velocity as a theoretical means to characterize and optimize different acceleration methods is also discussed

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Anon; 1629 p; 1995; p. 1352-1361; American Nuclear Society, Inc; La Grange Park, IL (United States); International conference on mathematics and computations, reactor physics, and environmental analyses; Portland, OR (United States); 30 Apr - 4 May 1995; American Nuclear Society, Inc., 555 N. Kensington Ave., La Grange Park, IL 60525 (United States)

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Colombo, V.; Coppa, G.; Ravetto, P.; Sumini, M.

Proceedings of the 1988 International Reactor Physics Conference. Volume 2

Proceedings of the 1988 International Reactor Physics Conference. Volume 2

AbstractAbstract

[en] A description of the theoretical foundations of the N

_{n}method in neutron transport theory is given, as a preliminary for further applications of the model to neutron two-dimensional x-y calculations. Different schemes for the discretization of the space second order system of equations that constitutes the approximation are presented. In particular, standard fine mesh finite differences and coarse mesh are considered. Also the possibility of application of the boundary elements methodology is investigated. A few test results are finally presented for some critical and source injected problemsPrimary Subject

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American Nuclear Society, La Grange Park, IL (USA); 504 p; 1988; p. II.135-II.144; American Nuclear Society; LaGrange Park, IL (USA); International reactor physics conference; Jackson Hole, WY (USA); 18-22 Sep 1988; CONF-880911--VOL.2; American Nuclear Society, 555 N. Kensington Ave., LaGrange Park, IL 60525

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AbstractAbstract

[en] An approximate determination of the critical eigenvalue of the neutron transport equation in integral form, within both the one speed and energy multigroup models, for a homogeneous medium, is achieved by means of a variational technique. The space asymptotic solutions for both the direct and adjoint problems are used as trial functions. A variational procedure is also developed and numerically exploited within the Fourier transformed domain, where noticeable theoretical features can be demonstrated. It is evidenced that excellent results can be obtained with little computational effort, and a set of critical calculations in plane geometry is presented and discussed. copyright 1988 Academic Press, Inc

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Bruna, G.; Cristofori, A.; Colombo, V.; Gandini, A.

International conference on the physics of reactors PHYSOR96, vol. 1

International conference on the physics of reactors PHYSOR96, vol. 1

AbstractAbstract

[en] The heuristically based generalized perturbation theory (HGPT), to first and higher order, applied to the neutron field of a reactor system, is discussed in relation to quasistatic problems. This methodology is of interest in reactor operation. In this application it may allow an on-line appraisal of the main physical 'observables' (i.e., quantities which can be directly measured by core neighbouring devices) of the reactor system when subject to alterations relevant to normal system exploitation, e.g., control rod movement, and/or soluble boron concentration changes to be introduced for compensating power level variations following electrical network demands. In a frame of a wide R and D program aimed at setting up a fast answering system for operator's support in PWR normal operation, a joint cooperation is underway among FRAMATOM, ENEA and University of Bologna for the development of an original application of the GPT methodology to PWR technology. The present paper, after describing the main features of the theory, in particular the fundamentals of the so called 'control variable option', emphasizes the general objectives of such a system. The results from a small scale investigation performed on a simplified PWR system corroborate the validity of the methodology proposed and allow to draw some preliminary conclusions on its industrial potentiality. (author)

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Japan Atomic Energy Research Inst., Tokyo (Japan); Power Reactor and Nuclear Fuel Development Corp., Tokyo (Japan); 615 p; Sep 1996; p. A/31-A/40; PHYSOR96: international conference on the physics of reactors 1996; Mito (Japan); 16-20 Sep 1996; Available from Atomic Energy Society of Japan

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