The albedo problem for pure-quadratic anisotropic scattering with İnönü scattering
-
R. G. Türeci
Abstract
In this study the half-space albedo problem has been investigated for highly anisotropic scattering. For this highly anisotropic scattering the İnönü scattering has been added to the pure-quadratic anisotropic scattering. The general solution of the one-speed neutron transport equation can be written as linear combination of the solutions which involve these scatterings. Hence, Case's eigenfunctions and the related semi-analytical methods can be used to get the albedo calculations. Some selected numerical data have been tabulated. To compare these results with the İnönü scattering values the linear interpolation technique has been used. Successful results have been achieved.
Kurzfassung
In der vorliegenden Arbeit wurde das Halbraum-Albedo-Problem für hoch anisotrope Streuung untersucht. Für diese hoch anisotrope Streuung wurde die İnönü Streuung zu der reinquadratischen anisotropen Streuung dazu gerechnet. Die allgemeine Lösung der Ein-Gruppen-Neutronentransportgleichung kann als lineare Kombination von Gleichungen beschrieben werden, die diese Streuungen enthält. Deshalb können die Case Eigenfunktionen und die entsprechenden semi-analytischen Verfahren für die Albedo-Berechnungen verwendet werden. Einige ausgewählte numerische Daten wurden in tabellarischer Form dargestellt. Um diese Ergebnisse mit Werten der İnönü Streuung vergleichen zu können, wurden lineare Interpolationsverfahren verwendet. Die Ergebnisse zeigen eine gute Übereinstimmung.
References
1 Case, K. M., Zweifel, P. F.: Linear Transport Theory. Massachusetts: Addison-Wesly (1967)Suche in Google Scholar
2 Mika, J.: Neutron transport with anisotropic scattering. Nucl. Sci. Eng.11 (1961) 415Suche in Google Scholar
3 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)10.1016/0149-1970(81)90059-7Suche 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 Energy7 (1) (1981) 47–5810.1016/0149-1970(81)90059-7Suche in Google Scholar
5 McCormickN.J.: One-speed neutron transport problems in plane geometry. Thesis, University of Michigan, USA (1965)Suche in Google Scholar
6 Türeci, R. G.; Türeci, D.: Time-dependent albedo problem for quadratic anisotropic scattering. KERNTECHNIK72 (1–2) (2007) 59–65Suche in Google Scholar
7 Türeci, R. G.; Güleçyüz, M. Ç.: The slab albedo and criticality problem fot the quadratic scattering kernel with HN method. KERNTECHNIK73 (4) (2008) 171–175Suche in Google Scholar
8 Tezcan, C.; Kaşkaş, A.; Güleçyü, M. Ç.: The HN method for solving linear transport equation: theory and applicationsJQSRT78 (2003) 243–25410.1016/S0022-4073(02)00224-8Suche in Google Scholar
9 İnönü, E.: Transp. Theory Stat Phys3 (1973) 10710.1080/00411457308205275Suche in Google Scholar
10 Sahni, D. C.; Sjöstrand, N. G.: One-speed neutron transport in reflected spheres. Annl. Nucl Energy24 (14) (1997) 1157–117010.1016/S0306-4549(97)00028-5Suche in Google Scholar
11 Siewert, C. E.; Devaux, C.: The effect of forward and backward scattering on the law of darkeing for the Milne problem and the spherical albedo. JQSRT20 (1978) 29–33Suche in Google Scholar
12 Tezcan, C.: J. Math Phys32 (1) (1991) 31010.1063/1.529089Suche in Google Scholar
13 Kaşkaş, A.; Tezcan, C.: The FN method for anisotropic scattering in neutron transport theory: the half space problems. JQSRT55 (1) (1996) 41–46Suche in Google Scholar
14 Tezcan, C.: Third form of the transport equation for extremely anisotropic scattering kernel. JQSRT55 (1) (1996) 33–40Suche in Google Scholar
15 Güleçyüz, M. Ç.; Kaşkaş, A.; Tezcan, C.: Slab Albedo problem for anisotropic scattering using singular eigenfunction solution on the CN equationsJQSRT61 (3) (1998) 329–338Suche in Google Scholar
16 Sahni, D. C.; Sjöstrand, N. G.: Time eigenvalues spectrum for one speed neutron transport in spheres with strong forward-bacward scattering. Ann. Nucl. Energy26 (1999) 347–358Suche in Google Scholar
17 Ganapol, B. d.; Kornreich, D. E.: The Green's function method for the monoenergetic transport equation with forward/backward/isotropic scattering. Anl Nucl Energy23 (4/5) (1996) 301–320Suche in Google Scholar
18 Yıldız, C.: Variation of the critical slab thickness with the degree of strongly anisotropic scattering in one-speed neutron transport theory. Ann. Nucl. Energy25 (8) (1998) 529–540Suche in Google Scholar
19 Yıldız, C.: Influence of anisotropic scattering on the size of time-dependent systems in monoenergetic neutron transport J Phys D: Appl. Phys.33 (1999) 317–325Suche in Google Scholar
20 Yıldız, C.: PN solutions of the time-dependent neutron transport equation with anisotropic scattering in a homogeneous sphere J Phys D: Appl. Phys.33 (2000) 704–710Suche in Google Scholar
21 Yıldız, C.: The spherical harmonics method for anisotropic scattering in neutron transport theory: the critical sphere problem JQSRT71 (2001) 25–37Suche in Google Scholar
22 Yıldız, C.: The FN solution of the time-dependent neutron transport equation for a sphere with forward scatteringJQSRT74 (2002) 521–529Suche in Google Scholar
23 Tezcan, C.; Güleçyüz, M. Ç.; Türeci, R. G.; Kaşkaş, A.: The HN method for half-space albedo and constant source problems for isotropic and anisotropic scattering kernels. JQSRT103 (2007) 611–61910.1016/j.jqsrt.2006.08.012Suche in Google Scholar
© 2010, Carl Hanser Verlag, München
Artikel in diesem Heft
- Contents/Inhalt
- Contents
- Summaries/Kurzfassungen
- Summaries
- Technical Contributions/Fachbeiträge
- Integrated online condition monitoring system for nuclear power plants
- Performance analysis of 233U for fixed bed nuclear reactors
- 3D thermal hydraulic simulation of the hot channel of a typical material testing reactor under normal operation conditions
- Analysis of the processes in the target cooling system of the W7-X fusion experiment
- Nuclear model calculation on charged particle induced reactions to produce 85Sr for diagnostic and endotherapy
- Neutronic and burn-up calculations of heterogeneous Thorium/Uranium fuel in pressurized water reactors
- Research on pitting corrosion of steam generator heat transfer tubes based on acoustic emission
- Application of the Chebyshev polynomial (TN and UN) approximation to reflected slab geometry in the neutron transport equation and computation of critical half thicknesses
- UN approximation to critical slab problem for one-speed neutrons with isotropic, forward and backward scattering
- The albedo problem for pure-quadratic anisotropic scattering with İnönü scattering
- Technical Notes/Technische Mitteilungen
- Targetry of Y2O3 on a copper substrate for the non-carrier-added 89Zr production via 89Y(p, n)89Zr reaction
Artikel in diesem Heft
- Contents/Inhalt
- Contents
- Summaries/Kurzfassungen
- Summaries
- Technical Contributions/Fachbeiträge
- Integrated online condition monitoring system for nuclear power plants
- Performance analysis of 233U for fixed bed nuclear reactors
- 3D thermal hydraulic simulation of the hot channel of a typical material testing reactor under normal operation conditions
- Analysis of the processes in the target cooling system of the W7-X fusion experiment
- Nuclear model calculation on charged particle induced reactions to produce 85Sr for diagnostic and endotherapy
- Neutronic and burn-up calculations of heterogeneous Thorium/Uranium fuel in pressurized water reactors
- Research on pitting corrosion of steam generator heat transfer tubes based on acoustic emission
- Application of the Chebyshev polynomial (TN and UN) approximation to reflected slab geometry in the neutron transport equation and computation of critical half thicknesses
- UN approximation to critical slab problem for one-speed neutrons with isotropic, forward and backward scattering
- The albedo problem for pure-quadratic anisotropic scattering with İnönü scattering
- Technical Notes/Technische Mitteilungen
- Targetry of Y2O3 on a copper substrate for the non-carrier-added 89Zr production via 89Y(p, n)89Zr reaction
