Home Solving the criticality problem with the reflected boundary condition for the triplet anisotropic scattering with the modified FN method
Article
Licensed
Unlicensed Requires Authentication

Solving the criticality problem with the reflected boundary condition for the triplet anisotropic scattering with the modified FN method

  • R. G. Türeci
Published/Copyright: December 12, 2015
Become an author with De Gruyter Brill
Submit Manuscript Author Information
Kerntechnik
From the journal Kerntechnik Volume 80 Issue 6

Abstract

One speed, time independent neutron transport equation in slab geometry can be solved with the triplet anisotropic scattering for the criticality problem with the reflected boundary condition. The value of the critical slab thickness is investigated numerically by using the Modified FN (HN) method. Case's eigenfunctions, normalization relation and orthogonality relations must be derived for this scattering in order to use the Modified FN method. Some selected values, which can be calculated from the criticality equation, can be tabulated. Also the term which comes from the Poincaré-Bertrand formula may be added to the orthogonality formula of the continuum eigenfunction.

Kurzfassung

Die Ein-Gruppen, zeitabhängige Neutronen-Transportgleichung in Stabgeometrie kann mit der anisotropen Triplett-Streuung für das Kritikalitätsproblem mit reflektierter Randbedingung gelöst werden. Der Wert der kritischen Stabdicke wurde numerisch untersucht mit Hilfe der modifizierten FN (HN) Methode. Case-Eigenfunktionen, Normalisierungsbeziehung und Orthogonalitätsrelationen müssen für diese Streuung abgeleitet werden, um die modifizierte FN (HN) Methode anwenden zu können. Einige aus der Kritikalitätsgleichung berechnete ausgewählte Werte können in tabellarischer Form dargestellt werden. Der aus der Poincaré-Bertrand Formel stammende Term kann zur Orthogonalitätsformel der Kontinuum-Eigenfunktion hinzugefügt werden.

* e-mail:

References

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

2 Mika, J.: Neutron transport with anisotropic scattering. Nuclear Science and Engineering.11 (1961) 41510.13182/NSE61-1Search in Google Scholar

3 Atalay, M. A.: The reflected slab and sphere criticality problem with anisotropic scattering in one-speed neutron transport theory. Progress in Nuclear Energy31 (1997) 229–25210.1016/0149-1970(95)00094-1Search in Google Scholar

4 Atalay, M. A.: Milne problem for linearly anisotropic scattering and a specularly reflecting boundary. Annals of Nuclear Energy27 (2000) 1483–150410.1016/S0306-4549(00)00011-6Search in Google Scholar

5 Siewert, C. E.; Benoist, P.: The FN Method in Neutron-Transport Theory, Part I: Theory and Applications. Nuclear Science and Engineering69 (1979) 156–16010.13182/NSE79-1Search 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 Engineering69 (1979) 16110.13182/NSE79-A20608Search in Google Scholar

7 Güleçyüz, M. Ç., Tezcan, C.: The F-N method anisotropic scattering in neutron transport theory: The critical slab problem. J.Quant. Spectrosc. Rad. Transfer56 (2) (1996) 30910.1016/0022-4073(96)00057-XSearch in Google Scholar

8 Kaşkaş, A.; Tezcan, C.: The F-N method for anisotropic scattering in neutron transport theory: The half-space problems. J.Quant. Spectrosc. Rad. Transfer55 (1) (1996) 4110.1016/0022-4073(95)00143-3Search in Google Scholar

9 Kavenoky, A.: The CN Method of Solving the Transport Equation: Application to Plane Geometry. Nuclear Science and Engineering65 (1978) 20910.13182/NSE78-A27152Search in Google Scholar

10 Erdoğan, F.; Güleçyüz, M. Ç.; Kaşkaş,A.; Tezcan, C.: Solition of the C-N equationsSearch in Google Scholar

11 Kaşkaş,A.; Güleçyüz,M. Ç.; Tezcan, C.: The slab albedo problem using singular eigenfunctions and the third form of the transport equation. Ann Nucl Energy.23 (17) (1996) 137110.1016/0306-4549(95)00118-2Search in Google Scholar

12 Tezcan, C.; Güleçyüz, M. Ç.; Erdoğan, F.: A new approach of solving the third form of the transport equation in plane geometry: Half-space albedo-problem. J.Quant. Spectrosc. Rad. Transfer55 (2) (1996) 25110.1016/0022-4073(95)00147-6Search in Google Scholar

13 Tezcan, C.; Kaşkaş,A.; Güleçyüz,M. Ç.: The singular eigenfunctions method: The Milne problem for isotropic and extremely anisotropic scattering. J.Quant. Spectrosc. Rad. Transfer62 (1) (1999) 4910.1016/S0022-4073(98)00040-5Search in Google Scholar

14 Güleçyüz,M. Ç.; Kaşkaş,A.; Tezcan, C.: Slab albedo problem for anisotropic scattering using singualr eigenfunction solution of the C-N equations. J.Quant. Spectrosc. Rad. Transfer61 (3) (1999) 32910.1016/S0022-4073(97)00241-0Search in Google Scholar

15 Kaşkaş,A.; Tezcan, C.; Güleçyüz,M. Ç.: The solution of the third form transport equation using singular eigenfunctions: The slab and the sphere criticality problems. J.Quant. Spectrosc. Rad. Transfer66 (6) (2000) 51910.1016/S0022-4073(99)00180-6Search in Google Scholar

16 Güleçyüz,M. Ç.; Kaşkaş,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. Transfer70 (1) (2001) 5510.1016/S0022-4073(00)00119-9Search in Google Scholar

17 Türeci, R. G.; Güleçyüz,M. Ç.; Kaşkaş,A.; Tezcan, C.: The singular eigenfunction method: the critical slab problem for linearly anisotropic scattering. Kerntechnik70 (2005) 32210.3139/124.100250Search in Google Scholar

18 Tezcan, C.; Kaşkaş,A.; Güleçyüz,M. Ç.: The H-Ν method for solving linear transport equation: Theory and applications. J.Quant. Spectrosc. Rad. Transfer78 (2) (2003) 243–25410.1016/S0022-4073(02)00224-8Search in Google Scholar

19 Tezcan, C.; Kaşkaş,A.; Güleçyüz,M. Ç.: The HN method for solving linear transport equation: theory and applications. J.Quant. Spectrosc. Rad. Transfer (2003) 7824310.1016/S0022-4073(02)00224-8Search in Google Scholar

20 Türeci, R. G.; Güleçyüz,M. Ç.; Kaşkaş,A.; Tezcan, C.: Application of the HN method to the critical slab problem for reflecting boundary conditions. J.Quant. Spectrosc. Rad. Transfer (2004) 8849910.1016/j.jqsrt.2004.04.001Search in Google Scholar

21 Türeci, R. G.; Güleçyüz,M. Ç.; Kaşkaş,A.; Tezcan, C.: Application of teh H-N method to the critical slab problem for reflecting boundary conditions. J.Quant. Spectrosc. Rad. Transfer (2004) 88 (4): 499–51710.1016/j.jqsrt.2004.04.001Search in Google Scholar

22 Güleçyüz, M. Ç.; Türeci, R. G.; Tezcan, C.: The critical slab problem for linearly anisotropic scattering and reflecting boundary conditions with the H-N method. Kerntechnik71 (2006) 14910.3139/124.100288Search in Google Scholar

23 Tezcan, C.; Güleçyüz,M. Ç.; Türeci, R. G.; Kaşkaş,A.: The HN method for half-space albedo and constant source problem for isotropic and anisotropic scattering kernels. J. Quant. Spectrosc. Rad. Transfer103 (2007) 61110.1016/j.jqsrt.2006.08.012Search in Google Scholar

24 Türeci, R. G.; Türeci,D.: Time dependent albedo problem for quadratic anisotropic scattering. Kerntechnik721–2 (2007) 5910.3139/124.100319Search in Google Scholar

25 Türeci, R. G.; Güleçyüz,M. Ç.; Tezcan, C.: H-N solutions of the time dependent linear neutron transport equation for a slab and a sphere. Kerntechnik72 (2007) 6610.3139/124.100320Search in Google Scholar

26 Tezcan, C.: Extension of the H-N method for solving radiation transfer problems in plane for general anisotropic scattering. Kerntechnik72 (2007) 287–28910.3139/124.100357Search in Google Scholar

27 Türeci, G, Gülecyüz,M. Ç.; Tezcan, C.: H-N solutions of the time dependent linear neutron transport equation for a slab and a sphere. Kerntechnik72 (2007) 66–7310.3139/124.100320Search in Google Scholar

28 Tezcan, C.; Güleçyüz,M. Ç.; Türeci, R. G.; Kaşkaş,A.: The H-N method for half space Albedo and constant source problems for isotropic scattering kernels. J.Quant. Spectrosc. Rad. Transfer103 (2007) 611–61910.1016/j.jqsrt.2006.08.012Search in Google Scholar

29 Bülbül,A.; Kara, A.; Anli, F.: Application of the TN method to critical slab problem for one-speed neutrons with forward and backward scattering and efficiency of reflection coefficient. Kerntechnik75 (2010) 377–38010.3139/124.110117Search in Google Scholar

30 KaraA.; AnlıF.: Effects on criticality of selected scattering phase functions in neutron transport equation using the Chebyshev approximation. Kerntechnik78 (2013) 233–23710.3139/124.110287Search in Google Scholar

31 Türeci, R. G.: The Albedo problem for pure-triplet scattering. Kerntechnik72 (5–6) (2007) 29010.3139/124.100358Search in Google Scholar

32 CaseK.M.; de HoffmannF.; PlaczekG.: Introduction to the Theory of Neutron Diffusion. Los Alamos, New Mexico (1953)Search in Google Scholar

Received: 2015-07-30
Published Online: 2015-12-12
Published in Print: 2015-12-17

© 2015, Carl Hanser Verlag, München

Articles in the same Issue

  1. Contents/Inhalt
  2. Contents
  3. Summaries/Kurzfassungen
  4. Summaries
  5. Technical Contributions/Fachbeiträge
  6. Considering the uncertainties in empirical correlations for vertical countercurrent flow limitation (CCFL) with TRACE
  7. 3RIP trip startup test simulation of TRACE/PARCS model for Lungmen ABWR under different power and flow conditions
  8. Development of a new analytic function expansion nodal code, HexDANM, for solving the neutron diffusion equation in hexagonal-Z geometry
  9. Laser cleaning of steam generator tubing based on acoustic emission technology
  10. Axial enrichment profile in advance nuclear energy power plant at supercritical-pressures
  11. Analysis of the small break loss of coolant accident in the VVER-1000/V446 reactor
  12. Thermal hydraulic analysis of reactivity accidents in MTR research reactors using RELAP5
  13. Depletion of Gadolinium burnable poison in a PWR assembly with high burnup fuel
  14. Nuclear model calculations on cyclotron production of 51Cr
  15. Radiotracer application for characterization of nuclear grade anion exchange resins Tulsion A-23 and Dowex SBR LC
  16. Solving the criticality problem with the reflected boundary condition for the triplet anisotropic scattering with the modified FN method
https://doi.org/10.3139/124.110563

Articles in the same Issue

  1. Contents/Inhalt
  2. Contents
  3. Summaries/Kurzfassungen
  4. Summaries
  5. Technical Contributions/Fachbeiträge
  6. Considering the uncertainties in empirical correlations for vertical countercurrent flow limitation (CCFL) with TRACE
  7. 3RIP trip startup test simulation of TRACE/PARCS model for Lungmen ABWR under different power and flow conditions
  8. Development of a new analytic function expansion nodal code, HexDANM, for solving the neutron diffusion equation in hexagonal-Z geometry
  9. Laser cleaning of steam generator tubing based on acoustic emission technology
  10. Axial enrichment profile in advance nuclear energy power plant at supercritical-pressures
  11. Analysis of the small break loss of coolant accident in the VVER-1000/V446 reactor
  12. Thermal hydraulic analysis of reactivity accidents in MTR research reactors using RELAP5
  13. Depletion of Gadolinium burnable poison in a PWR assembly with high burnup fuel
  14. Nuclear model calculations on cyclotron production of 51Cr
  15. Radiotracer application for characterization of nuclear grade anion exchange resins Tulsion A-23 and Dowex SBR LC
  16. Solving the criticality problem with the reflected boundary condition for the triplet anisotropic scattering with the modified FN method
Sign up now to receive a 20% welcome discount
Institutional Access
How does access work?
Have an idea on how to improve our website?
Please write us.
© 2025 De Gruyter Brill
Downloaded on 3.10.2025 from https://www.degruyterbrill.com/document/doi/10.3139/124.110563/html
Scroll to top button