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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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[en] Conventional finite-element solutions of the even-parity transport equation for systems with voids treat the void as a region of low absorption. This treatment tends to give physically-unacceptable solutions to void problems as the void cross-section tends to zero. An explanation for the effect is proposed. Biased finite elements are used in two ways to obtain physically-acceptable solutions for the void regions. Two new methods are described and tested. The iterative method synthesizes finite-element solution using a sequence of problems with constant absorptions in the void regions. The sequence is terminated when the fluxes in the void regions become steady. The extrapolation method obtains a best approximation to the void solution by combining two or more independent biased trial functions in an optimum way. The extrapolation method is further subdivided into elementary and nodal or multiparameter extrapolation. The relevant theory of both the iteration and extrapolation methods is given. Several 2-D test problems using the above methods have been investigated. Results are compared with those obtained with other numerical methods and almost analytical results of the point kernel method for voids surrounded by purely absorbing media. (author)

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[en] In one-speed, time-independent, neutron transport theory, the Fsub(N) method is used for the FBIS (forward-backward-isotropic scattering) model to reinvestigate the behaviour of the critical size in plane and spherical geometries. For the FIS (forward-isotropic scattering) model the numerical results are compared with previously obtained variational results and it is shown that they are in agreement. For the BIS (backward-isotropic scattering) model exact results are obtained and compared with the first-order approximate results obtained using the method of elementary solutions. (author)

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[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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[en] The monoenergetic integral transport equation for a multilayer slab geometry has been solved by Legendre expansion method. The method utilizes an expansion of the neutron flux over entire multilayer slab geometry in Legendre polynomials of the position co-ordinate (Single Expansion Method - SEM). This formulation is an extension of Carlvik's (1968) method for a homogeneous slab. Earlier (Raghav, 1984) the expansion of the neutron flux was done in each layer in Legendre polynomials of the position co-ordinate (Multi Expansion Method - MEM). The aim in this paper is to compare both the approaches of SEM and MEM. A few multilayer slab systems with vacuum boundary conditions have been selected for this purpose and Ksub(eff), the effective multiplication factor of the system, has been compared. SEM requires the evaluation of the integrals where the limits are not -1 to + 1 (as they are in MEM and where analytical expressions can be derived), in these cases we have derived recurrence relations (which are described in the Appendix) to evaluate such integrals. (author)

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[en] An explicit expression is obtained for the neutron flux in the one-speed backward-forward scattering model in a general homogeneous convex medium. The method can be extended to energy-dependent problems via the multigroup procedure. (author)

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Technical notes.

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[en] Recent progress in the development of coarse-mesh nodal methods for the numerical solution of the neutron diffusion and transport equations is reviewed. In contrast with earlier nodal simulators, more recent nodal diffusion methods are characterized by the systematic derivation of spatial coupling relationships that are entirely consistent with the multigroup diffusion equation. These relationships most often are derived by developing approximations to the one-dimensional equations obtained by integrating the multidimensional diffusion equation over directions transverse to each coordinate axis. Both polynomial and analytic approaches to the solution of the transverse-integrated equations are discussed, and the Cartesian-geometry polynomial approach is derived in a manner which motivates the extension of this formulation to the solution of the diffusion equation in hexagonal geometry. Iterative procedures developed for the solution of the nodal equations are discussed briefly, and numerical comparisons for representative three-dimensional benchmark problems are given. The application of similar ideas to the neutron transport equation has led to the development of coarse-mesh transport schemes that combine nodal spatial approximations with angular representations based on either the standard discrete-ordinate approximation or double Psub(n) expansions of the angular dependence of the fluxes on the surfaces of the nodes. The former methods yield improved difference approximations to the multidimensional discrete-ordinates equations, while the latter approach leads to equations similar to those obtained in interface-current nodal-diffusion formulations. The relative efficiencies of these two approaches are discussed, and directions for future work are indicated. (author)

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[en] From the stochastic transport theory with delayed neutrons, the Boltzmann transport equation with delayed neutrons for the average flux emerges in a natural way without recourse to any approximation. From this theory a general expression is obtained for the Feynman Y-function when delayed neutrons are included. The single mode approximation for the particular case of a subcritical assembly is developed, and it is shown that Y-function reduces to the familiar expression quoted in many books, when delayed neutrons are not considered, and spatial and source effects are not included. (author)

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[en] This paper reports the results of our investigations on the neutron-noise transmission characteristics of non-multiplying media using transport theory. The study has been carried out systematically by first considering the infinite medium case for monoenergetic neutrons and then extending it to the finite media, multigroup and anisotropic scattering cases. The results are particularly related with the problems and prospects of the neutron-noise studies by excore detectors in fast reactors and would be particularly useful in developing the technology of malfunction detection by neutron-noise methods. (author)

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Reactor noise - SMORN V: 5. specialists meeting on reactor noise; Munich (Germany, F.R.); 12-16 Oct 1987

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[en] A simple extension of the discrete ordinates method for solving the transport equation with quadrilateral meshes in X-Y and R-Z geometry is described. Numerical results of some benchmark problems are presented for showing the adequacy of the modified scheme. (author)

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