Skip to content
Licensed Unlicensed Requires Authentication Published by De Gruyter March 26, 2013

Neutron transport problems for extremely anisotropic scattering

Neutronentransportprobleme bei extrem anisotroper Streuung
  • A. Kaşkaş , M. Karahasanoğlu and M. Ç. Güleçyüz
From the journal Kerntechnik

Abstract

Half-space albedo, slab albedo and critical slab problems will be solved for extremely anisotropic scattering using the analytical expressions of the FN method with a different numerical approximation. The infinite medium Green's function for the anisotropic scattering case obtained in terms of the infinite medium Green's function for the isotropic scattering is used. The numerical results are compared with data available in the literature.

Kurzfassung

Half-space Albedo, Slab Albedo und Critical Slab Probleme werden für extrem anisotrope Streuung gelöst mit Hilfe der analytischen Ausdrücke der FN Methode mit einer anderen numerischen Näherung. Die Green's Funktion für unendliche Medien wird für den Fall anisotroper Streuung in Form der Green's Funktion für unendliche Medien für isotrope Streuung verwendet. Die numerischen Ergebnisse werden mit Daten aus der Literatur verglichen.


Corresponding Author: Kaşkaş. E-mail:

References

1Case, K. M.; De Hoffmann, F.; Placzek, G.: Introduction to the theory of neutron diffusion. Vol. 1, Los Alamos Scientific Laboratory, (1953)Search in Google Scholar

2Siewert, CE.; Benoist, P.: The FN method in neutron transport theory, Part I: Theory and applications. Nucl. Sci. Eng.69 (1979) 156Search in Google Scholar

3Grandjean, P.; SiewertC. E.: The FN method in neutron transport theory, Part II: applications and numerical Results. Nucl. Sci. Eng.69 (1979) 161Search in Google Scholar

4Case, K. M.; ZweifelP. F.: Linear Transport Theory. Addison-Wesley Publishing Company, (1967)Search in Google Scholar

5Benoist, P.; Kavenoky, A.: A new method of approximation of the Boltzmann equation. Nucl. Sci. Eng.32 (1968) 225Search in Google Scholar

6Kavenoky, A.: The CN method of solving the transport equation: application to plane geometry. Nucl. Sci. Eng.65 (1978) 209Search in Google Scholar

7Kavenoky, A.: Nucl. Sci. Eng.65 (1978) 514Search in Google Scholar

8Tezcan, C.; Kaşkaş, A.; Güleçyüz, M. Ç.: The HN method for solving linear transport equation: theory and application. J. Quant. Spectrosc. Radiat. Transfer78 (2003) 24310.1016/S0022-4073(02)00224-8Search in Google Scholar

9Kaşkaş, A.; Tezcan, C.: The FN method for anisotropic scattering in neutron transport theory: the half-space problems. J. Quant. Spectrosc. Radiat. Transfer55 (1996) 41Search in Google Scholar

10Erdoğan, F.; Güleçyüz, M. Ç.; Kaşkaş, A.; Tezcan, C.: Solution of the CN equations using singular eigenfunctions and applications. Annals of Nuclear Energy23 (1996) 533Search in Google Scholar

11Tezcan, C.: The third form of the transport equation for extremely anisotropic scattering kernel. J. Quant. Spectrosc. Radiat. Transfer55 (1996) 3310.1016/0022-4073(95)00142-5Search in Google Scholar

12Benoist, P.; Kharchaf, A.; Sanchez, R.: Multigroup CN method – I. Half-space albedo problem. Annals of Nuclear Energy23 (1996) 103310.1016/0306-4549(96)84660-3Search in Google Scholar

13Kharchaf, A.; Benoist, P.; Sanchez, R.: Multigroup CN method – II. Albedo and transmission for a slab. Annals of Nuclear Energy23 (1996) 104910.1016/0306-4549(95)00113-1Search in Google Scholar

14YıldızC.: Calculation of the albedo and transmission in a slab with a specified isotropic scattering using FN method. J. Quant. Spectrosc. Radiat. Transfer70 (2001) 3710.1016/S0022-4073(00)00115-1Search in Google Scholar

15Hendi, A. A.; Elghazaly, A.: The solution of the neutron transport equation in a slab with anisotropic scattering. J. Quant. Spectrosc. Radiat. Transfer84 (2004) 33910.1016/S0022-4073(03)00188-2Search in Google Scholar

16Güleçyüz, M.Ç., Kaşkaş, A., Tezcan, C.: Slab albedo problem for anisotropic scattering using singular eigenfunction solution of the CN equations. J. Quant. Spectrosc. Radiat. Transfer61 (1999) 32910.1016/S0022-4073(97)00241-0Search in Google Scholar

17YıldızC.: Variation of the albedo and the transmission factor with forward and backward scattering in neutron transport theory – The FN method. Annals of Nuclear Energy27 (2000) 83110.1016/S0306-4549(00)00002-5Search in Google Scholar

18TezcanC., YıldızC.: The criticality problems with the FN method for the FBIS model. Annals of Nuclear Energy13 (1986) 34510.1016/0306-4549(86)90091-5Search in Google Scholar

19GüleçyüzM. Ç. and TezcanC.: The FN method for anisotropic scattering in neutron transport theory: The critical slab problem. J. Quant. Spectrosc. Radiat. Transfer 56 (1996) 309Search in Google Scholar

20AtalayM. A.: The critical slab problem for reflecting boundary conditions in one-speed neutron transport theory. Annals of Nuclear Energy23 (1996) 18310.1016/0306-4549(95)00024-7Search in Google Scholar

21AtalayM. A.: The reflected slab and sphere criticality with anisotropic scattering in one speeed neutron transport theory. Progress in Nuclear Energy31 (1997) 22910.1016/0149-1970(95)00094-1Search in Google Scholar

22YıldızC.: Variation of the critical slab thickness with the degree of strongly anisotropic scattering in one-speed neutron transport theory. Annals of Nuclear Energy25 (1998) 52910.1016/S0306-4549(97)00114-XSearch in Google Scholar

23SiewertC. E.: The Critical Problem with High-Order Anisotropic Scattering, Annals of Nuclear Energy28 (2001) 82510.1016/S0306-4549(00)00090-6Search in Google Scholar

24CaldeiraA. D., GarciaR. D. M.: On criticality calculations in multislab geometry. Annals of Nuclear Energy28 (2001) 156310.1016/S0306-4549(00)00119-5Search in Google Scholar

25WilliamsM. M. R.: Critical conditions in an infinitely reflected, multiplying slab using two-group, integral transport theory. Annals of Nuclear Energy29 (2002) 19310.1016/S0306-4549(01)00031-7Search in Google Scholar

26TüreciR. G., GüleçyüzM. Ç., KaşkaşA., TezcanC.: Application of the HN method to the critical slab problem for reflecting boundary conditions. J. Quant. Spectrosc. Radiat. Transfer88 (2004) 49910.1016/j.jqsrt.2004.04.001Search in Google Scholar

27TezcanC.: The one-speed albedo and the slab albedo problem for the FBI kernel, Journal of Mathematical Physics, 32 (1) (1991) 310Search in Google Scholar

Received: 2006-6-19
Published Online: 2013-03-26
Published in Print: 2006-11-01

© 2006, Carl Hanser Verlag, München

Downloaded on 17.5.2024 from https://www.degruyter.com/document/doi/10.3139/124.100306/html
Scroll to top button