Startseite Technik Half-space albedo problem with modified FN method for linear and quadratic anisotropic scattering
Artikel
Lizenziert
Nicht lizenziert Erfordert eine Authentifizierung

Half-space albedo problem with modified FN method for linear and quadratic anisotropic scattering

  • R. G. Türeci EMAIL logo und D. Türeci
Veröffentlicht/Copyright: 28. Februar 2022
Veröffentlichen auch Sie bei De Gruyter Brill

Abstract

One speed, time independent and homogeneous medium neutron transport equation can be solved with the anisotropic scattering which includes both the linear anisotropic and the quadratic anisotropic scattering properties. Having solved Case’s eigenfunctions and the orthogonality relations among these eigenfunctions, some neutron transport problems such as albedo problem can be calculated as numerically by using numerical or semi-analytic methods. In this study the half-space albedo problem is investigated by using the modified FN method.

Abstract

Die zeitunabhängige Eingruppen-Neutronentransportgleichung kann gelöst werden mit Hilfe der modifizierten FN-Methode für lineare und quadratische anisotrope Streuung. Nach Lösung der Case-Eigenfunktionen und der Orthogonalitätsrelationen zwischen diesen Eigenfunktionen, können einige Neutronentransportprobleme wie z.B. das Albedoproblem berechnet werden mit Hilfe numerischer oder semi-analytischer Methoden. In diesem Beitrag wird das Halbraum-Albedoproblem mit Hilfe der modifizierten F N-Methode näher untersucht.

References

1 Case, K. M., Zweifel, P. F.: Linear Transport Theory. Massachusetts: Addition-Wesley (1967)Suche in Google Scholar

2 Mika, J.: Neutron transport with anisotropic scattering. Nuclear Science and Engineering. 11(1961) 415, DOI:10.13182/NSE61-110.13182/NSE61-1Suche in Google Scholar

3 McCormick, N. J., Kusˇcˇer, I.: Half-space neutron transport with linearly anisotropic scattering. Journal of Mathematical Physics 6 (1965) 1939, DOI:10.1063/1.170474410.1063/1.1704744Suche in Google Scholar

4 Protopopescu, V., Sjöstrand, N. G.: On the solution of the dispersion equation for monoenergetic neutron transport with linearly anisotropic scattering. Progress in Nuclear Energy 7 (1981) 47, DOI:10.1016/0149-1970(81)90059-710.1016/0149-1970(81)90059-7Suche in Google Scholar

5 Siewert, C. E.; Benoist, P.: The FN Method in Neutron-Transport Theory, Part I: Theory and Applications. Nuclear Science and Engineering 69 (1979) 156, DOI:10.13182/NSE79-110.13182/NSE79-1Suche in Google Scholar

6 Grandjean, P.; Siewert, C. E.: The FN method in neutron transport theory Part II: applications and numerical results. Nuclear Science and Engineering 69 (1979) 16110.13182/NSE79-A20608Suche in Google Scholar

7 Kas¸kas¸, A., Tezcan, C.: The F-N method for anisotropic scattering in neutron transport theory: The half-space problems. J. Quant. Spectrosc. Rad. Transfer 55 (1) (1996) 41, DOI:10.1016/0022-4073(95)00143-310.1016/0022-4073(95)00143-3Suche in Google Scholar

8 Kavenoky, A.: The CN Method of Solving the Transport Equation: Application to Plane Geometry. Nuclear Science and Engineering 65 (1978) 20910.13182/NSE78-A27152Suche in Google Scholar

9 Erdog˘an, F., Güleçyüz, M. Ç., Kas¸kas¸, A., Tezcan, C.: Solution of the C-N equations using singular eigenfunctions and applications. Ann Nucl Energy 23 (6) (1996) 533, DOI:10.1016/0306-4549(95)00053-410.1016/0306-4549(95)00053-4Suche in Google Scholar

10 Tezcan, C., Güleçyüz, M. Ç., Erdog˘an, F.:A new approach of solving the third form of the transport equation in plane geometry: Half-space albedo-problem. J. Quant. Spectrosc. Rad. Transfer 55 (2) (1996) 251, DOI:10.1016/0022-4073(95)00147-610.1016/0022-4073(95)00147-6Suche in Google Scholar

11 Güleçyüz, M. Ç., Kas¸kas¸, A., Tezcan, C.: The singular eigenfunction analysis of the third form transport equation using half-range orthogonality relations:The Half-Space Problems. J. Quant. Spectrosc. Rad. Transfer 70 (1) (2001) 55, DOI:10.1016/S0022-4073(00)00119-910.1016/S0022-4073(00)00119-9Suche in Google Scholar

12 Protopopescu, V., Sjöstrand, N. G.: On the solution of the dispersion equation for monoenergetic neutron transport with quadratically anisotropic Scattering. CHT-RF-36, Chalmers University, Sweden (1981), PMid:6803333Suche in Google Scholar

13 Türeci, R. G., Türeci, D.: Time dependent albedo problem for quadratic anisotropic scattering. Kerntechnik 72 1–2 (2007) 5910.3139/124.100319Suche in Google Scholar

14 Türeci, R. G.; Güleçyüz, M. Ç.: The slab albedo and criticality problem fort he quadratic scattering kernel with the HN method. Kerntechnik 73 4 (2008) 17110.3139/124.100564Suche in Google Scholar

15 Türeci, R. G.: The albedo problem for püre-quadratic anisotropic scattering withI˙nönü scattering. Kerntechnik 75 (5) (2010) 292, DOI:10.3139/124.11008610.3139/124.110086Suche in Google Scholar

16 Türeci, D., Türeci, R. G., Teg˘men, A.; Güleçyüz, M. Ç.: Solving the constant source problem fort he quadratic anisotropic scattering kernel using the modified FN method. Kerntechnik 77(1) (2012) 60Suche in Google Scholar

17 Case, K. M.; de Hoffmann, F.; Placzek, G.: Introduction to the Theory of Neutron Diffusion. Los Alamos, New Mexico (1953)Suche in Google Scholar

18 Tezcan, C.; Kas¸kas¸, A.; Güleçyüz, M. Ç.: The H-N method for solving linear transport equation: Theory and applications. J. Quant. Spectrosc. Rad. Transfer 78 (2) (2003) 243–254, DOI:10.1016/S0022-4073(02)00224-810.1016/S0022-4073(02)00224-8Suche in Google Scholar

19 Tezcan, C., Güleçyüz, M. Ç., Türeci, R. G.; Kas¸kas¸, A.: The HN method for half-space albedo and constant source problem for isotropic and anisotropic scattering kernels. J. Quant. Spectrosc. Rad. Transfer 103 (2007) 611, DOI:10.1016/j.jqsrt.2006.08.01210.1016/j.jqsrt.2006.08.012Suche in Google Scholar

20 Tezcan, C., Güleçyüz, M. Ç., Türeci, R. G., Kas¸kas¸, A.: The H-N method for half space Albedo and constant source problems for isotropic scattering kernels J. Quant. Spectrosc. Rad. Transfer 103(3) (2007) 611–619, DOI:10.1016/j.jqsrt.2006.08.01210.1016/j.jqsrt.2006.08.012Suche in Google Scholar

Received: 2016-05-23
Published Online: 2022-02-28

© 2017 Carl Hanser Verlag GmbH & Co. KG

Heruntergeladen am 14.12.2025 von https://www.degruyterbrill.com/document/doi/10.3139/124.110641/pdf?lang=de
Button zum nach oben scrollen