Application of the UN method to the reflected critical slab problem for one-speed neutrons with forward and backward scattering
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H. Öztürk
Abstract
The UN method is used to solve the critical slab problem for reflecting boundary conditions in one-speed neutron transport theory. The isotropic scattering kernel with the combination of forward and backward scattering is chosen for the neutrons in a uniform finite slab. It is shown that the method converges rapidly with easily executable equations. The presented numerical results are compared with the results available in the literature.
Kurzfassung
Das Kritikalitätsproblem in der Eingruppen-Neutronentransporttheorie wird mit Hilfe der UN-Methode in ebener Geometrie mit Reflektorrandbedingungen gelöst. Zur Beschreibung der Neutronenstreuung in einer endlichen homogenen Platte wurde ein isotroper Streukern gewählt, der Vorwärts- und Rückwärtsstreuung kombiniert. Es wird gezeigt, dass diese auf leicht auszuführenden Gleichungen basierende Methode schnell konvergiert. Die vorgestellten numerischen Ergebnisse werden verglichen mit den in der Literatur verfügbaren Daten.
References
1Davison, B.: Neutron transport theory. London, Oxford University Press, 1958Search in Google Scholar
2Bell, G. I.; Glasstone, S.: Nuclear reactor theory. New York, VNR Company, 1972Search in Google Scholar
3Arfken, G.: Mathematical methods for physicists. London, Academic Press, Inc., 1985Search in Google Scholar
4Aspelund, O.: On a new method for solving the (Boltzmann) equation in neutron transport theory. PICG16 (1958) 530Search in Google Scholar
5Conkie, W. R.: Polynomial approximations in neutron transport theory. Nucl. Sci. Eng.6 (1959) 260Search in Google Scholar
6Yabushita, S.: Tschebyscheff polynomials approximation method of the neutron transport equation. J. Math. Phys.2 (1961) 543Search in Google Scholar
7Carlson, B.; Bell, G.: Proc. 2nd U.N. Int. Conf. Peaceful Uses of Atomic Energy, United Nations, New York16 (1958) 535Search in Google Scholar
8Siewert, C. E.; Williams, M. M. R.: The effect of anisotropic scattering on the critical slab problem in neutron transport theory using a synthetic kernel. J. Phys. D: Appl. Phys.10 (1977) 2031Search in Google Scholar
9Lee, C. E.; Dias, M. P.: Analytical solutions to the moment transport equations-I; one-group one-region slab and sphere criticality. Ann Nucl Energy11 (1984) 515Search in Google Scholar
10Aranson, R.: Critical problems for bare and reflected slabs and spheres. Nucl. Sci. Eng.86 (1984) 150Search in Google Scholar
11Sahni, D. C.; Sjöstrand, N. G.; Garis, N. S.: Criticality and time eigenvalues for one-speed neutrons in a slab with forward and backward scattering. J. Phys. D: Appl. Phys.25 (1992) 1381Search in Google Scholar
12Atalay, M. A.: The reflected slab and sphere criticality problem with anisotropic scattering in one-speed neutron transport theory. Prog. Nucl. Energy31 (1997) 229Search in Google Scholar
13Yasa, F.; Anli, F.; Güngör, S.: Eigenvalue spectrum with Chebyshev polynomial approximation of the transport equation in slab geometry. J. Quant. Spectrosc. Radiat. Transfer97 (2006) 5110.1016/j.jqsrt.2004.12.017Search in Google Scholar
14Anli, F.; Yasa, F.; Güngör, S.; Öztürk, H.: TN approximation to neutron transport equation and application to critical slab problem. J. Quant. Spectrosc. Radiat. Transfer101 (2006) 12910.1016/j.jqsrt.2005.11.010Search in Google Scholar
15Anli, F.; Yasa, F.; Güngör, S.; Öztürk, H.: TN approximation to reflected slab and computation of the critical half thickness. J. Quant. Spectrosc. Radiat. Transfer101 (2006) 13510.1016/j.jqsrt.2005.11.011Search in Google Scholar
© 2007, Carl Hanser Verlag, München
Articles in the same Issue
- Contents/Inhalt
- Contents
- Summaries/Kurzfassungen
- Summaries
- Technical Contributions/Fachbeiträge
- Wavelet techniques for the determination of the decay ratio in boiling water reactors
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- Calculation of the pin power distribution for a thorium reactor assembly and benchmarking
- Comparative assessment of methods for the reactivity measurement in subcritical systems by pulsed experiments
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- Prediction of the onset of flow instability in the ETRR-2 research reactor under loss of flow accident
- Time-dependent albedo problem for quadratic anisotropic scattering
- HN solutions of the time dependent linear neutron transport equation for a slab and a sphere
- Application of the UN method to the reflected critical slab problem for one-speed neutrons with forward and backward scattering
- The effects of different expansions of the exit distribution on the extrapolation length for linearly anisotropic scattering
- Technical Note
- Shadowing the earth from Lagrange Point L1
Articles in the same Issue
- Contents/Inhalt
- Contents
- Summaries/Kurzfassungen
- Summaries
- Technical Contributions/Fachbeiträge
- Wavelet techniques for the determination of the decay ratio in boiling water reactors
- Analytical and experimental investigations of shear stress in rod bundles with irregular cells
- Incineration of weapon grade plutoniumin a (DT) fusion driven hybrid reactor using various coolants
- Calculation of the pin power distribution for a thorium reactor assembly and benchmarking
- Comparative assessment of methods for the reactivity measurement in subcritical systems by pulsed experiments
- Thermal-hydraulic modeling of reactivity accidents in MTR reactors
- Prediction of the onset of flow instability in the ETRR-2 research reactor under loss of flow accident
- Time-dependent albedo problem for quadratic anisotropic scattering
- HN solutions of the time dependent linear neutron transport equation for a slab and a sphere
- Application of the UN method to the reflected critical slab problem for one-speed neutrons with forward and backward scattering
- The effects of different expansions of the exit distribution on the extrapolation length for linearly anisotropic scattering
- Technical Note
- Shadowing the earth from Lagrange Point L1
