DOI QR코드

DOI QR Code

Using the Monte Carlo method to solve the half-space and slab albedo problems with Inönü and Anlı-Güngör strongly anisotropic scattering functions

  • Bahram R. Maleki (Department of Nuclear Engineering, Hacettepe University)
  • 투고 : 2022.08.21
  • 심사 : 2022.09.22
  • 발행 : 2023.01.25

초록

Different types of deterministic solution methods were used to solve neutron transport equations corresponding to half-space and slab albedo problems. In these types of solution methods, in addition to the error of the numerical solutions, the obtained results contain truncation and discretization errors. In the present work, a non-analog Monte Carlo method is provided to simulate the half-space and slab albedo problems with Inönü and Anlı-Güngör strongly anisotropic scattering functions. For each scattering function, the sampling method of the direction of the scattered neutrons is presented. The effects of different beams with different angular dependencies and the effects of different scattering parameters on the reflection probability are investigated using the developed Monte Carlo method. The validity of the Monte Carlo method is also confirmed through the comparison with the published data.

키워드

과제정보

The author thanks Professor Mehmet Tombakoglu for his valuable suggestions and helpful discussions.

참고문헌

  1. J.J. Duderstadt, L.J. Hamilton, Nuclear Reactor Analysis, Wiley, 1976.
  2. W. Stacey, Nuclear reactor physics, comp. rev. and enl 2 (2007).
  3. M. Hanus, Mathematical Modeling of Neutron Transport, PhD thesis, PhD thesis, University of West Bohemia, 2014.
  4. Y. Wu, Neutronics of Advanced Nuclear Systems, Springer, 2019.
  5. A.J. Hoffman, A Time-dependent Method of Characteristics Formulation with Time Derivative Propagation, PhD thesis, University of Michigan, 2013.
  6. A.K. Prinja, E.W. Larsen, General principles of neutron transport, in: Handbook of Nuclear Engineering, Springer, 2010, 427-542.
  7. A. Yilmazer, M. Tombakoglu, Unified treatment of the p (λ) n approximation to solve the reflected slab criticality problem with strong anisotropy, Kerntechnik 73 (5-6) (2008) 260-268. https://doi.org/10.3139/124.100474
  8. A. Yilmazer, Solution of one-speed neutron transport equation for strongly anisotropic scattering by tn approximation: slab criticality problem, Annals of Nuclear Energy 34 (9) (2007) 743-751. https://doi.org/10.1016/j.anucene.2007.03.010
  9. D. Sahni, N. Sjostrand, Time eigenvalue spectrum for one-speed neutron transport in spheres with strong forward-backward scattering, Annals of Nuclear Energy 26 (4) (1999) 347-358. https://doi.org/10.1016/S0306-4549(98)00072-3
  10. J. Wang, W.R. Martin, B.S. Collins, Code verification of mpact using ganapol critical rod benchmark, in: EPJ Web of Conferences, 247, EDP Sciences, 2021, 10027.
  11. N.G. Sjoestrand, Accurate critical slab calculations for various degrees of anisotropy and for different reflection coefficients, Kerntechnik 75 (1-2) (2010) 58-59. https://doi.org/10.3139/124.110062
  12. C. Tezcan, Third form of the transport equation for extremely anisotropic scattering kernel, Journal of quantitative spectroscopy and radiative transfer 55 (1) (1996) 33-40. https://doi.org/10.1016/0022-4073(95)00142-5
  13. C. Yildiz, Variation of the critical slab thickness with the degree of strongly anisotropic scattering in one-speed neutron transport theory, Annals of Nuclear Energy 25 (8) (1998) 529-540. https://doi.org/10.1016/S0306-4549(97)00114-X
  14. H. Ozturk, The effect of strongly anisotropic scattering on the critical size of a slab in one-speed neutron transport theory: modified un method, Annals of nuclear energy 65 (2014) 24-29. https://doi.org/10.1016/j.anucene.2013.10.021
  15. C. Yildiz, Variation of the albedo and the transmission factor with forward and backward scattering in neutron transport theory-the fn method, Annals of Nuclear Energy 27 (9) (2000) 831-840. https://doi.org/10.1016/S0306-4549(00)00002-5
  16. C. Yildiz, Calculation of the albedo and transmission in a slab with a specified isotropic scattering using the fn method, Journal of Quantitative Spectroscopy and Radiative Transfer 70 (1) (2001) 37-45. https://doi.org/10.1016/S0022-4073(00)00115-1
  17. A.A. Hendi, A. Elghazaly, The solution of the neutron transport equation in a slab with anisotropic scattering, Journal of Quantitative Spectroscopy and Radiative Transfer 84 (3) (2004) 339-347. https://doi.org/10.1016/S0022-4073(03)00188-2
  18. R. Tureci, Half-space albedo problem for inonu, linear and quadratic anisotropic scattering, Nuclear Engineering and Technology 52 (4) (2020) 700-707. https://doi.org/10.1016/j.net.2019.10.008
  19. M. Kocmen, A. Tegmen, D. Tureci, M. Gulecyuz, R. Tureci, Albedo and constant source problems for extremely anisotropic scattering, Kerntechnik 78 (3) (2013) 245-249. https://doi.org/10.3139/124.110355
  20. A. Kaskas, C. Tezcan, The fn method for anisotropic scattering in neutron transport theory: the half-space problems, Journal of Quantitative Spectroscopy and Radiative Transfer 55 (1) (1996) 41-46. https://doi.org/10.1016/0022-4073(95)00143-3
  21. R.G. McClarren, Calculating time eigenvalues of the neutron transport equation with dynamic mode decomposition, Nuclear Science and Engineering 193 (8) (2019) 854-867. https://doi.org/10.1080/00295639.2018.1565014
  22. D.C. Sahni, R.G. Tureci, A.Z. Bozkir, Partial range completeness of case eigenfunctions and numerical solution of singular integral equations of particle transport problems, Journal of Computational and Theoretical Transport 49 (7) (2020) 349-367. https://doi.org/10.1080/23324309.2020.1819329
  23. A.Z. Bozkir, R.G. Tureci, D.C. Sahni, Half-space albedo problem for the anligungor scattering function, Kerntechnik 87 (2) (2022) 237-248. https://doi.org/10.1515/kern-2021-1028
  24. A.F. Bielajew, Fundamentals of the Monte Carlo Method for Neutral and Charged Particle Transport, 1, The University of Michigan, 2001.
  25. E. Inonu, A theorem on anisotropic scattering, Transport theory and statistical physics 3 (2-3) (1973) 137-146. https://doi.org/10.1080/00411457308205276
  26. B. Rashidian Maleki, A non-analog Monte Carlo simulation method for slab albedo problem with linear-anisotropic scattering, ALKU Fen Bilimleri Dergisi 3 (1) (2021) 1-13. https://doi.org/10.46740/alku.825400
  27. S.K. Bose, Numerical Methods of Mathematics Implemented in Fortran, Springer, 2019.
  28. H. Koklu, O. Ozer, Critical thickness problem for tetra-anisotropic scattering in the reflected reactor system, Pramana 95 (4) (2021) 1-11. https://doi.org/10.1007/s12043-020-02034-4
  29. W.H. Press, S.A. Teukolsky, W.T. Vetterling, B.P. Flannery, Numerical Recipes in Fortran 77, i, 2003.