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Diffusion Approximation with Henyey-Greenstein Phase Function Using UN Method

Year 2015, Volume: 10 Issue: 2, 87 - 91, 22.11.2015

Abstract

U1 and P1 approximations are applied to one-dimensional neutron transport equation and HenyeyGreenstein phase function is used for calculating diffusion length. Numerical results obtained from U1 and P1 approximations are compared with each other for different collision parameters and t parameters. 

References

  • Lamarsh J.R., 1977. Introduction to Nuclear engineering, Addison-Wesley Company.
  • Stacey W.M., 2007. Nuclear reactor physics, Wiley-Vch Verlag GmbH & Co.KGaA, Weinheim.
  • Öztürk H., Bülbül A., Kara A., 2010. U1 approximation to neutron transport equation and calculation of the asymptotic relaxation length, Kerntechnik, 75: 375-376.
  • Öztürk H., Anli F., Güngör S., 2007. Application of the UN method to the reflected critical slab problem for one-speed neutrons with forward and backward scattering, Kerntechnik, 72: 74-76.
  • Bülbül, A, Ulutaş, M., Anli, F., 2008. Application of the UN approximation to the neutron transport equation in slab geometry, Kerntechnik, 73: 61-65.
  • Henyey L.G., Greenstein J.L., 1941. Diffuse radiation in the galaxy, Astrophysics Journal, 93: 70-83.
  • Kamiuto K., 1987. Study of the Henyey-Greenstein Approximation to scattering phase function, Journal of Quantitative Spectroscopy and Radiative Transfer, 37: 411-413.
  • Haltrin V.I., 2002. One-parameter two-term Henyey-Greenstein phase function for light scattering in seawater, Applied Optics, 41: 1022-1028.
  • Pomraning G.C., 1988. On the Henyey-Greenstein approximation to scattering phase functions, Journal of Quantitative Spectroscopy and Radiative Transfer, 39: 109-113.
  • Reynold L.O., McCormic N.J., 1980. Approximate two-parameter phase function for light scattering, Journal of the Optical Society of America, 70: 1206-1212.
  • Liu P., 1994. A new phase function approximating to Mie scattering for radiative transport equations, Physics in Medicine and Biology, 39: 1025-1036.
  • Bell G.I., Glasstone S., 1970. Nuclear reactor theory. New York, VNR Company, 619 p.
  • Arfken G., 1985. Mathematical methods for physicists, London, Academic Press, Inc., 985 p.
  • Ahmet Bülbül e-mail: ahmetbulbul@gmail.com
  • Hakan Öztürk e-mail: hakanozturk3@gmail.com

UN Metodu Kullanarak Henyey-Greenstein Faz Fonksiyonu ile Difüzyon Yaklaşımı

Year 2015, Volume: 10 Issue: 2, 87 - 91, 22.11.2015

Abstract

U1 ve P1 yaklaşımları tek boyutlu nötron transport denklemine uygulandı ve difüzyon uzunluğu hesabı için Henyey-Greenstein faz fonksiyonu kullanıldı. Farklı çarpışma parametreleri ve t parametresi için U1 ve P1 yaklaşımlarından elde edilen nümerik sonuçlar birbiri arasında kıyaslandı.

References

  • Lamarsh J.R., 1977. Introduction to Nuclear engineering, Addison-Wesley Company.
  • Stacey W.M., 2007. Nuclear reactor physics, Wiley-Vch Verlag GmbH & Co.KGaA, Weinheim.
  • Öztürk H., Bülbül A., Kara A., 2010. U1 approximation to neutron transport equation and calculation of the asymptotic relaxation length, Kerntechnik, 75: 375-376.
  • Öztürk H., Anli F., Güngör S., 2007. Application of the UN method to the reflected critical slab problem for one-speed neutrons with forward and backward scattering, Kerntechnik, 72: 74-76.
  • Bülbül, A, Ulutaş, M., Anli, F., 2008. Application of the UN approximation to the neutron transport equation in slab geometry, Kerntechnik, 73: 61-65.
  • Henyey L.G., Greenstein J.L., 1941. Diffuse radiation in the galaxy, Astrophysics Journal, 93: 70-83.
  • Kamiuto K., 1987. Study of the Henyey-Greenstein Approximation to scattering phase function, Journal of Quantitative Spectroscopy and Radiative Transfer, 37: 411-413.
  • Haltrin V.I., 2002. One-parameter two-term Henyey-Greenstein phase function for light scattering in seawater, Applied Optics, 41: 1022-1028.
  • Pomraning G.C., 1988. On the Henyey-Greenstein approximation to scattering phase functions, Journal of Quantitative Spectroscopy and Radiative Transfer, 39: 109-113.
  • Reynold L.O., McCormic N.J., 1980. Approximate two-parameter phase function for light scattering, Journal of the Optical Society of America, 70: 1206-1212.
  • Liu P., 1994. A new phase function approximating to Mie scattering for radiative transport equations, Physics in Medicine and Biology, 39: 1025-1036.
  • Bell G.I., Glasstone S., 1970. Nuclear reactor theory. New York, VNR Company, 619 p.
  • Arfken G., 1985. Mathematical methods for physicists, London, Academic Press, Inc., 985 p.
  • Ahmet Bülbül e-mail: ahmetbulbul@gmail.com
  • Hakan Öztürk e-mail: hakanozturk3@gmail.com
There are 15 citations in total.

Details

Primary Language English
Subjects Metrology, Applied and Industrial Physics
Journal Section Makaleler
Authors

Ayça Şimşek Yapar This is me

Ahmet Bülbül

Hakan Öztürk This is me

Publication Date November 22, 2015
Published in Issue Year 2015 Volume: 10 Issue: 2

Cite

IEEE A. Şimşek Yapar, A. Bülbül, and H. Öztürk, “Diffusion Approximation with Henyey-Greenstein Phase Function Using UN Method”, Süleyman Demirel University Faculty of Arts and Science Journal of Science, vol. 10, no. 2, pp. 87–91, 2015.