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A Conventional Phase Function with the Chebyshev Polynomials of Second Kind for the Criticality Problem in Transport Theory

Yıl 2017, Cilt: 7 Sayı: 2, 121 - 132, 04.01.2018

Öz

The
criticality calculations for one-speed neutrons in a finite homogenous slab are
done using the conventional Henyey-Greenstein (HG) phase function in transport theory.
After defining the phase function in transport equation, the neutron angular
flux is expanded in terms of the Chebyshev polynomials of second kind (UN method). Then, the
critical half-thicknesses of the slab are calculated for various values of the
scattering parameters. The numerical results obtained from the present method
are given in the tables together with the ones obtained using an alternative
phase function (Anlı-Güngör, AG) for comparison.

Kaynakça

  • Davison, B., Neutron Transport Theory, Oxford University Press, London, 1958.
  • Case, K. M., Zweifel, P. F., Linear Transport Theory, Addison-Wesley Publishing Company, 1967.
  • Bell, G. I., Glasstone, S., Nuclear Reactor Theory, VNR Company, New York, 1972.
  • Sahni, D. C., Sjöstrand, N. G., Garis, N. S., Criticality and time eigenvalues for one-speed neutrons in a slab with forward and backward scattering, J. Phys. D: Appl. Phys., 25, 1381-1389, 1992.
  • Henyey, L. G., Greenstein, J. L., Diffuse radiation in the galaxy, Astrophys. J., 93, 70-83, 1941.
  • Reynolds, L. O., McCormick, N. J., Approximate two parameter phase function for light scattering, J. Op. Soc. Am., 70, 1206-1212, 1980.
  • Williams, M. M. R., A synthetic scattering kernel for particle transport in absorbing media with anisotropic scattering, J. Phys. D: Appl. Phys., 11, 2455-2463, 1978.
  • Liu, P., A new phase function approximating to Mie scattering for radiative transport equations, Phys. Med. Biol., 39, 1025-1036, 1994.
  • Öztürk, H., The reflected critical slab problem for one-speed neutrons with strongly anisotropic scattering, Kerntechnik, 73, 66-74, 2008.
  • Öztürk, H., Anlı, F., Güngör, S., Application of the UN method to the reflected critical slab problem for one-speed neutrons with forward and backward scattering, Kerntechnik, 72, 74-76, 2007.
  • Öztürk, H., Anlı, F., Diffusion approximation for certain scattering parameters of the Anli-Güngör phase function, Kerntechnik, 77, 381-384, 2012.
  • Öztürk, H., Application of the Henyey-Greenstein and Anlı-Güngör phase functions for the solution of the neutron transport equation with Legendre polynomials: Reflected critical slab problem, Kerntechnik, 78, 447-453, 2013.
  • Anlı, F., Yaşa, F., Güngör, S., General eigenvalue spectrum in a one-dimensional slab geometry transport equation, Nucl. Sci. Eng., 150, 72-77, 2005.
  • Arfken, G., Mathematical Methods for Physicists, Academic Press, Inc., London, 1985.
  • Lee, C. E., Dias, M. P., Analytical solutions to the moment transport equations-I; one-group one-region slab and sphere criticality, Ann. Nucl. Energy, 11, 515-530, 1984.
  • Öztürk, H., Ege, Ö., An application of the alternative phase function with the second kind of Chebyshev polynomials: The criticality problem in transport theory (submitted to Kerntechnik).
  • Yıldız, C., Variation of the critical slab thickness with the degree of strongly anisotropic scattering in one-speed neutron transport theory, Ann. Nucl. Energy, 25, 529-540, 1998.
  • Sahni, D. C., Sjöstrand, N. G., Non-monotonic variation of the criticality factor with the degree of anisotropy in one-speed neutron transport, Transp. Theory Statist. Phys., 20, 339-349, 1991.

Transport Teoride Kritiklik Problemi için İkinci Tip Chebyshev Polinomları ile Konvansiyonel Bir Faz Fonksiyonu

Yıl 2017, Cilt: 7 Sayı: 2, 121 - 132, 04.01.2018

Öz

Transport
teoride konvansiyonel Henyey-Greenstein (HG) faz fonksiyonu kullanılarak sonlu
homojen bir dilimdeki nötronlar için kritiklik hesaplamaları yapılmıştır. Transport denkleminde faz fonksiyonu tanımlandıktan
sonra, açısal nötron akısı ikinci tip Chebyshev polinomları cinsinden seriye
açılmıştır (
UN metodu). Daha sonra, saçılma parametrelerinin farklı
değerleri için dilimin yarı-kalınlıkları hesaplanmıştır. Mevcut metotla elde
edilen nümerik sonuçlar, alternatif faz fonksiyonu
(Anlı-Güngör, AG) kullanılarak
elde edilen sonuçlar ile karşılaştırma yapmak için tablolarda verilmiştir.

Kaynakça

  • Davison, B., Neutron Transport Theory, Oxford University Press, London, 1958.
  • Case, K. M., Zweifel, P. F., Linear Transport Theory, Addison-Wesley Publishing Company, 1967.
  • Bell, G. I., Glasstone, S., Nuclear Reactor Theory, VNR Company, New York, 1972.
  • Sahni, D. C., Sjöstrand, N. G., Garis, N. S., Criticality and time eigenvalues for one-speed neutrons in a slab with forward and backward scattering, J. Phys. D: Appl. Phys., 25, 1381-1389, 1992.
  • Henyey, L. G., Greenstein, J. L., Diffuse radiation in the galaxy, Astrophys. J., 93, 70-83, 1941.
  • Reynolds, L. O., McCormick, N. J., Approximate two parameter phase function for light scattering, J. Op. Soc. Am., 70, 1206-1212, 1980.
  • Williams, M. M. R., A synthetic scattering kernel for particle transport in absorbing media with anisotropic scattering, J. Phys. D: Appl. Phys., 11, 2455-2463, 1978.
  • Liu, P., A new phase function approximating to Mie scattering for radiative transport equations, Phys. Med. Biol., 39, 1025-1036, 1994.
  • Öztürk, H., The reflected critical slab problem for one-speed neutrons with strongly anisotropic scattering, Kerntechnik, 73, 66-74, 2008.
  • Öztürk, H., Anlı, F., Güngör, S., Application of the UN method to the reflected critical slab problem for one-speed neutrons with forward and backward scattering, Kerntechnik, 72, 74-76, 2007.
  • Öztürk, H., Anlı, F., Diffusion approximation for certain scattering parameters of the Anli-Güngör phase function, Kerntechnik, 77, 381-384, 2012.
  • Öztürk, H., Application of the Henyey-Greenstein and Anlı-Güngör phase functions for the solution of the neutron transport equation with Legendre polynomials: Reflected critical slab problem, Kerntechnik, 78, 447-453, 2013.
  • Anlı, F., Yaşa, F., Güngör, S., General eigenvalue spectrum in a one-dimensional slab geometry transport equation, Nucl. Sci. Eng., 150, 72-77, 2005.
  • Arfken, G., Mathematical Methods for Physicists, Academic Press, Inc., London, 1985.
  • Lee, C. E., Dias, M. P., Analytical solutions to the moment transport equations-I; one-group one-region slab and sphere criticality, Ann. Nucl. Energy, 11, 515-530, 1984.
  • Öztürk, H., Ege, Ö., An application of the alternative phase function with the second kind of Chebyshev polynomials: The criticality problem in transport theory (submitted to Kerntechnik).
  • Yıldız, C., Variation of the critical slab thickness with the degree of strongly anisotropic scattering in one-speed neutron transport theory, Ann. Nucl. Energy, 25, 529-540, 1998.
  • Sahni, D. C., Sjöstrand, N. G., Non-monotonic variation of the criticality factor with the degree of anisotropy in one-speed neutron transport, Transp. Theory Statist. Phys., 20, 339-349, 1991.
Toplam 18 adet kaynakça vardır.

Ayrıntılar

Konular Mühendislik
Bölüm Matematik
Yazarlar

Hakan Öztürk

Yayımlanma Tarihi 4 Ocak 2018
Gönderilme Tarihi 12 Eylül 2017
Kabul Tarihi 12 Aralık 2017
Yayımlandığı Sayı Yıl 2017 Cilt: 7 Sayı: 2

Kaynak Göster

APA Öztürk, H. (2018). A Conventional Phase Function with the Chebyshev Polynomials of Second Kind for the Criticality Problem in Transport Theory. Adıyaman University Journal of Science, 7(2), 121-132.
AMA Öztürk H. A Conventional Phase Function with the Chebyshev Polynomials of Second Kind for the Criticality Problem in Transport Theory. ADYU J SCI. Ocak 2018;7(2):121-132.
Chicago Öztürk, Hakan. “A Conventional Phase Function With the Chebyshev Polynomials of Second Kind for the Criticality Problem in Transport Theory”. Adıyaman University Journal of Science 7, sy. 2 (Ocak 2018): 121-32.
EndNote Öztürk H (01 Ocak 2018) A Conventional Phase Function with the Chebyshev Polynomials of Second Kind for the Criticality Problem in Transport Theory. Adıyaman University Journal of Science 7 2 121–132.
IEEE H. Öztürk, “A Conventional Phase Function with the Chebyshev Polynomials of Second Kind for the Criticality Problem in Transport Theory”, ADYU J SCI, c. 7, sy. 2, ss. 121–132, 2018.
ISNAD Öztürk, Hakan. “A Conventional Phase Function With the Chebyshev Polynomials of Second Kind for the Criticality Problem in Transport Theory”. Adıyaman University Journal of Science 7/2 (Ocak 2018), 121-132.
JAMA Öztürk H. A Conventional Phase Function with the Chebyshev Polynomials of Second Kind for the Criticality Problem in Transport Theory. ADYU J SCI. 2018;7:121–132.
MLA Öztürk, Hakan. “A Conventional Phase Function With the Chebyshev Polynomials of Second Kind for the Criticality Problem in Transport Theory”. Adıyaman University Journal of Science, c. 7, sy. 2, 2018, ss. 121-32.
Vancouver Öztürk H. A Conventional Phase Function with the Chebyshev Polynomials of Second Kind for the Criticality Problem in Transport Theory. ADYU J SCI. 2018;7(2):121-32.

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