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AbstractAbstract

[en] In an attempt to better understand the influence of prompt and delayed neutrons on nuclear reactor dynamics, a continuous slowing down model based on Fermi age theory was developed several years ago. This model was easily incorporated into the one-group diffusion equation and provided a realistic physical picture of how delayed and prompt neutrons slow down and simultaneously diffuse throughout a medium. The model allows for different slowing down times for each delayed neutron group as well as for prompt neutrons and for spectral differences between the two typed of neutrons. Because of its generality, this model serves not only a a useful predictive tool to anticipate reactor transients, but also as an excellent educational tool to demonstrate the effect of delayed neutrons in reactor kinetics. However, because of numerical complications, the slowing down model could not be developed to its full potential. In particular, the major limitation was the inversion of the Laplace transform, which relied on a knowledge of the poles associated with the resulting transformed flux. For this reason, only one group of delayed neutrons and times longer than the slowing down times could be considered. As is shown, the new inversion procedure removes the short time limitation as well as allows for any number of delayed neutron groups. The inversion technique is versatile and is useful in teaching numerical methods in nuclear science

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American Nuclear Society annual meeting; San Diego, CA (USA); 12-16 Jun 1988; CONF-880601--

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Lapenta, G.; Ravetto, P.; Rostagno, M.M.

Politecnico di Torino (Italy)

Politecnico di Torino (Italy)

AbstractAbstract

[en] Recently, the problem of neutron transport in anisotropic media has received new attention in connection with safety studies of water reactors and design of gas-cooled systems. In situations presenting large voided regions, as the axial streaming is dominating with respect to the transverse one, the average properties of the homogenized material should physically account for such macroscopic anisotropy. Hence, it is suggested that cell calculations produce anisotropic average cross sections, e.g., axial (σ

_{A}) and transverse (σ_{T}) values. Since material anisotropy is due to leakage, as a first-step approximation, the medium can be considered isotropic with respect to scattering phenomena. Transport codes are currently being adapted to include anisotropic cross sections. An important aspect of code development is the validation of algorithms by analytical benchmarks. For that purpose, the present work is devoted to the fully analytical solution of transport problems in slab geometryPrimary Subject

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2000 Annual Meeting - American Nuclear Society; San Diego, CA (United States); 4-8 Jun 2000

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AbstractAbstract

[en] An approximate method to study the monokinetic linear transport equation is outlined, starting from its integral form, rather than the integro-differential one. The approximate solution may be deduced either analytically, in simple cases, or numerically by means of typical space discretization techniques, through a system of second-order differential equations, associated with proper boundary conditions. Both the system and the boundary conditions may be matched with the standard neutron diffusion multigroup ones, by means of a proper correspondence of the coefficients and of the unknowns. The slab and the radially-symmetric sphere are then analysed in detail. It is shown how, in the plane case, the present approximation is perfectly equivalent to the well-known discrete ordinate one. For curved geometries no such equivalence exists, and it is in these cases that the application of the method at hand looks promising, in order to avoid complications and numerical problems in practical applications. (author)

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Annals of Nuclear Energy (Oxford); ISSN 0306-4549; ; v. 9(3); p. 169-174

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Ravetto, P.

Research coordination meeting of the coordinated research project on analytical and experimental benchmark analyses of accelerator driven systems. Working material

Research coordination meeting of the coordinated research project on analytical and experimental benchmark analyses of accelerator driven systems. Working material

AbstractAbstract

No abstract available

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International Atomic Energy Agency, Technical Working Group on Fast Reactors, Vienna (Austria); 232 p; 2006; p. 90-99; Research coordination meeting of the coordinated research project on analytical and experimental benchmark analyses of accelerator driven systems; Minsk (Belarus); 5-9 Dec 2005; Also available on-line: http://www.iaea.org/inis/aws/fnss/fulltext/twgfr127.pdf; Published as PowerPoint presentation only

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Montagnini, B.; Ravetto, P., E-mail: piero.ravetto@polito.it

AbstractAbstract

[en] For a restricted, but not trivial, class of neutron diffusing systems, namely those in which the total cross section is everywhere constant ('constant sigma', or Cσ systems), the one-velocity, isotropic scattering transport equation in general 3D geometry can be transformed without any approximations into a second order integrodifferential equation that is formally identical to an energy-dependent diffusion equation. The latter equation, which can also be considered as the limit of the SP

_{2N-1}(or A_{N}) system of equations as N→∞, allows for a further transformation into a boundary integral form. If the Cσ system is made of homogeneous regions (each one with its own value of the scattering cross section), the Green function, or fundamental solution, to be used in each region can be worked out explicitly and is shown to involve a bilinear expansion in terms of the Case eigenfunctions. Such a structure is mirrored by the structure of the solution of the transport problem, which can also be given the form of a (regionwise) superposition of these eigenfunctionsPrimary Subject

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S0306454903002810; Copyright (c) 2003 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA)

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Landeyro, P.A.; Ravetto, P.; Silvani, V.

International conference on future nuclear systems. Challenge towards second nuclear era with advanced fuel cycles. Proceedings

International conference on future nuclear systems. Challenge towards second nuclear era with advanced fuel cycles. Proceedings

AbstractAbstract

[en] Some aspects connected to the relationship between the subcriticality margin and the safety of an accelerator-driven system for the burning of actinides are discussed. A subcritical system with fluid fuel is considered. The limits of simplified models such as point kinetics, which has been mainly developed for conventional critical reactor, is addressed. Therefore, a full multigroup spatial diffusion model is developed and numerically solved. Some power transients are presented, to evidence the role of the subcriticality margin. The implications of delayed emission is discussed and some results for a consistent β

_{eff}evaluation are presented. This activity is carried out in the framework of the European Community contract: F141-CT95-0012, Impact of the Accelerator-Driven Technologies on the Nuclear Reactor Safety. (author)Primary Subject

Source

Power Reactor and Nuclear Fuel Development Corp., Tokyo (Japan); Japan Atomic Energy Research Inst., Tokyo (Japan); 1588 p; 1997; p. 566-569; Atomic Energy Society of Japan; Tokyo (Japan); Global '97: International conference on future nuclear systems; Yokohama (Japan); 5-10 Oct 1997

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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] 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] Analytical solutions of nonstationary equations of neutron transport theory in A-n, S-2n approximations applicable for testing computer programs used to study safety problems are presented. For plane geometry with periodical boundary conditions certain numerical results obtained by one-velocity theory in the assumption of isotropic neutron scattering are given. The results explain visually transport effects related to the finite velocity of neutron propagation in space from a local pulsed sources. Balance equations are solved by the expansion into a series over eigen functions of the Helmholtz equation in combination with use of the Laplace transformation for time variable. The analytical solution under consideration can be used as a model one to study specificity of spatial transient processes

Original Title

Nekotorye analiticheskie resheniya nestatsionarnykh uravnenij perenosa nejtronov A-n-, S-2n-metodami

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Dulla, S.; Ravetto, P.; Rostagno, M.M., E-mail: piero.ravetto@polito.it

AbstractAbstract

[en] The quasi-static method for the neutron kinetics of nuclear reactors is generalized for application to neutron multiplying systems fueled by a fluid multiplying material, typically a mixture of fissile molten salts. The method is derived by the application of factorization formulae for both the neutron density and the delayed precursor concentrations and the projection of the balance equations upon a weighting function. A physically meaningful weight can be assumed as the solution of the adjoint model, which is constructed for the situation considered, including delayed neutrons. The quasi-static scheme is then applied to calculations of some transients for a typical configuration of a molten-salt reactor, in a multigroup diffusion model with a one-dimensional slug-flow velocity field. The physical features associated to the motion of the fissile material are highlighted

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S0306454904000982; Copyright (c) 2004 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA)

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