Calculation of the critical thickness for one-speed neutrons in a reflected slab with backward and forward scattering using modified TN method
-
H. Öztürk
and A. Bülbül
Abstract
The reflected critical slab problem is investigated in one-speed neutron transport theory for reflecting boundary conditions. The neutron angular flux is expanded in a series of first kind Chebyshev polynomials and isotropic, backward and forward scattering kernel is used as the scattering function. The critical sizes for one-speed neutrons in a uniform finite slab surrounded by identical reflectors from both sides are calculated for various values of the collision parameter, backward and forward scattering and reflection coefficient. Numerical values calculated for the critical slab are presented in the tables and are found to be in good agreement with literature values.
References
1 O.Aspelund: On a new method for solving the (Boltzmann) equation in neutron transport theory. PICG16 (1958) 530Search in Google Scholar
2 W. R.Conkie: Polynomial approximations in neutron transport theory. Nucl. Sci. Eng.6 (1959) 26010.13182/NSE59-A28841Search in Google Scholar
3 S.Yabushita: Tschebyscheff polynomials approximation method of the neutron transport equation. J. Math. Phys.2 (1961) 54310.1063/1.1703739Search in Google Scholar
4 F.Anli; F.Yasa; S.Güngör; H.Öztürk: 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
5 F.Anli; S.Güngör; F.Yasa; H.Öztürk: TN approximation to reflected slab and computation of the critical half thicknesses. J. Quant. Spectrosc. Radiat. Transfer101 (2006) 13510.1016/j.jqsrt.2005.11.011Search in Google Scholar
6 H.Öztürk; F.Anli; S.Güngör: TN method for the critical thickness of one-speed neutrons in a slab with forward and backward scattering. J. Quant. Spectros. Radiat. Trans.105 (2007) 21110.1016/j.jqsrt.2006.12.002Search in Google Scholar
7 H.Öztürk; F.Anli; S.Güngör: Application of the UN method to the reflected critical slab problem for one-speed neutrons with forward and backward scattering. Kerntechnik72/1–2 (2007) 7410.3139/124.100321Search in Google Scholar
8 H.Öztürk: The reflected critical slab problem for one-speed neutrons with strongly anisotropic scattering. Kerntechnik73/1–2 (2008) 6610.3139/124.100532Search in Google Scholar
9 A.Bülbül; H.Demir; F.Anlı; H.Öztürk: Application of the TN method to critical slab problem for one-speed neutrons with forward and backward scattering. Nucl. Eng. Design241 (2011) 145410.1016/j.nucengdes.2011.01.044Search in Google Scholar
10 B.Davison: Neutron transport theory. London, Oxford University Press, 195810.1063/1.3062414Search in Google Scholar
11 D. C.Sahni; N. G.Sjöstrand; N. S.Garis: Criticality and time eigenvalues for one-speed neutrons in a slab with forward and backward scattering. J. Phys. D: Appl. Phys.25 (1992) 138110.1088/0022-3727/25/10/001Search in Google Scholar
12 G.Arfken: Mathematical methods for physicists. London, Academic Press, Inc.: 198510.1119/1.1988084Search in Google Scholar
13 G. I.Bell; S.Glasstone: Nuclear reactor theory. New York, VNR Company, 1972Search in Google Scholar
14 M. A.Atalay: The reflected slab and sphere criticality problem with anisotropic scattering in one-speed neutron transport theory. Prog. Nucl. Energy31 (1997) 22910.1016/0149-1970(95)00094-1Search in Google Scholar
15 M. A.Atalay: Fourier mode analysis of reflected slab and sphere criticality. Prog. Nucl. Energy44 (2004) 25310.1016/S0149-1970(04)90013-3Search in Google Scholar
16 C. E.Lee; M. P.Dias: Analytical solutions to the moment transport equations-I; one-group one-region slab and sphere criticality. Ann. Nucl. Energy11 (1984) 51510.1016/0306-4549(84)90076-8Search in Google Scholar
17 H.Öztürk: Modified UN method for the reflected critical slab problem with forward and backward scattering. Kerntechnik76 (2011) 14210.3139/124.110126Search in Google Scholar
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Articles in the same Issue
- Contents/Inhalt
- Contents
- Summaries/Kurzfassungen
- Summaries
- Technical Contributions/Fachbeiträge
- Development of inflatable seals for the rotatable plugs of sodium cooled fast breeder reactors: a review – Part II: R&D necessities and development across the world
- Analysis of radwaste management alternatives during dismantling of Ignalina NPP systems with low level contamination
- Calculation of excitation functions for the production of Cu and Co medical isotopes
- Reliability assessment of the passive heat removal system of the VVER-1000 reactor at Kudankulam NPP
- Calculation of the neutronic behavior of minor actinides burning in a thermal research reactor using the MCNPX 2.6 code
- Steam drum level control studies of a natural circulation multi loop reactor
- Analyses in regulatory practice
- Technical Notes/Technische Mitteilungen
- Installation and measurement capacity of 3 × 592 GBq 241Am–Be neutron irradiation cell
- Calculation of the critical thickness for one-speed neutrons in a reflected slab with backward and forward scattering using modified TN method