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Yıl 2020, Cilt 3, Sayı 2, 98 - 108, 31.12.2020

Öz

Kaynakça

  • 1. Sahni, D. C., and Sjöstrand, N. G. Criticality and time eigenvalues in one-speed neutron transport.Prog. Nucl. Energy, 1990,23(3):241–289.
  • 2. Glasstone, B. S., George I. Nuclear ReactorTheory,1970, 68–74.
  • 3. Sahni, D. C. Dependence of the time eigenvalue of linear transport operator on the system size and other parameters -an application of the Perron-Erobenius theorem.Transp. Theory Stat. Phys., 1991, 20(5):483–498.
  • 4. Sahni, D. C., Dahl, B., and Sjöstrand, N. G. Behaviour of criticality eigenvalues of one-speed transport operator with linearly anisotropic scattering.Ann. Nucl. Energy, 1997, 24(2):135–145.
  • 5. Sahni, D. C., Garis, N. S., and Sjöstrand, N. G. Spectrum of one-speed Neutron transport operator with reflective boundary conditions in slab geometry.Transp. Theory Stat. Phys.,1995, 24(4):629–656.
  • 6. Sahni, D. C., Dahl, E. B., and Sjöstrand, N. J. Real criticality eigenvalues of the one-speed linear transport operator. Transp. Theory Stat. Phys., 1995, 24(9):1295–1317.
  • 7. Case, K. M., Zweifel, P. F., and Pomraning, G. C. Linear Transport Theory.Phys. Today, 1968.
  • 8. Duderstadt J, Martin W and Aronson R. Transport Theory. Physics Today,1982, (35):65-66.
  • 9. Mika, J. R. Neutron Transport with Anisotropic Scattering.Nucl. Sci. Eng.1961, 11:415–427.
  • 10. Williams M.Computational methods of neutron transport. Annals of Nuclear Energy,1985 (12)101.
  • 11. Case K. M. and Zweifel P. F.Linear Transport Theory. 1967.
  • 12. Davison, B. and Sykes, J. B. Neutron Transport Theory.Zeitschrift fur Naturforsch.-Sect. A J. Phys. Sci., 1957.
  • 13. Yaşa, F., Anli, F., and Güngör, S. Eigenvalue spectrum with chebyshev polynomial approximation of the transport equation in slab geometry.J. Quant. Spectrosc. Radiat. Transf., 2006, 97(1):51–57.
  • 14. Anli, F., Güngör, S., Yaşa, F., and Öztürk, H. TN approximation to reflected slab and computation of the critical half thicknesses.J. Quant. Spectrosc. Radiat. Transf., 2006,101(1):135-140.
  • 15. Hama Rashid, P. A. Investigation of the solution by using PN method of transport equation for triplet anısotropıc scatterıng. M. Thesis,2013.
  • 16. Yildiz,C., Variation of the critical slab thickness with the degree of strongly anisotropic scattering in one-speed neutron transport theory.Ann. Nucl. Energy, 1998, 25(8):529-540.
  • 17. Türeci, R. G.Solving the criticality problem with the reflected boundary condition for the triplet anisotropic scattering with the modified FN method.Kerntechnik, 2015,80(6):583–592.

CRITICAL SIZE OF A SLAB REACTOR WITH NEUTRON TRANSPORT THEORY OF THE TRIPLET ANISOTROPIC SCATTERING

Yıl 2020, Cilt 3, Sayı 2, 98 - 108, 31.12.2020

Öz

Critical thickness for one-group energy neutrons are determined for the triplet anisotropic-scattering in plane geometry by using Legendre polynomials of PN method, and Chebyshev polynomials of first type, TN method. Triplet anisotropic scattering is the fourth term of the scattering function. The neutron flux moments in the neutron transport equation comprises the eigenfunction of the neutron flux. By solving the eigenfunctions, the eigenvalues are obtained from Chebyshev polynomial solution. The resultant neutron flux equation composes of the eigenfunction, Chebyshev polynomial term and the number of secondary neutrons “c”. The solution of the eigenvalues gives imaginary root for c is smaller than one. So in this study we study with bigger than one c values. The critical size of the system is found by the Mark boundary condition. The critical size is calculated for different scattering types. The relations are presented in the following tables. It is seen that our results are compatible with the existing literature.

Kaynakça

  • 1. Sahni, D. C., and Sjöstrand, N. G. Criticality and time eigenvalues in one-speed neutron transport.Prog. Nucl. Energy, 1990,23(3):241–289.
  • 2. Glasstone, B. S., George I. Nuclear ReactorTheory,1970, 68–74.
  • 3. Sahni, D. C. Dependence of the time eigenvalue of linear transport operator on the system size and other parameters -an application of the Perron-Erobenius theorem.Transp. Theory Stat. Phys., 1991, 20(5):483–498.
  • 4. Sahni, D. C., Dahl, B., and Sjöstrand, N. G. Behaviour of criticality eigenvalues of one-speed transport operator with linearly anisotropic scattering.Ann. Nucl. Energy, 1997, 24(2):135–145.
  • 5. Sahni, D. C., Garis, N. S., and Sjöstrand, N. G. Spectrum of one-speed Neutron transport operator with reflective boundary conditions in slab geometry.Transp. Theory Stat. Phys.,1995, 24(4):629–656.
  • 6. Sahni, D. C., Dahl, E. B., and Sjöstrand, N. J. Real criticality eigenvalues of the one-speed linear transport operator. Transp. Theory Stat. Phys., 1995, 24(9):1295–1317.
  • 7. Case, K. M., Zweifel, P. F., and Pomraning, G. C. Linear Transport Theory.Phys. Today, 1968.
  • 8. Duderstadt J, Martin W and Aronson R. Transport Theory. Physics Today,1982, (35):65-66.
  • 9. Mika, J. R. Neutron Transport with Anisotropic Scattering.Nucl. Sci. Eng.1961, 11:415–427.
  • 10. Williams M.Computational methods of neutron transport. Annals of Nuclear Energy,1985 (12)101.
  • 11. Case K. M. and Zweifel P. F.Linear Transport Theory. 1967.
  • 12. Davison, B. and Sykes, J. B. Neutron Transport Theory.Zeitschrift fur Naturforsch.-Sect. A J. Phys. Sci., 1957.
  • 13. Yaşa, F., Anli, F., and Güngör, S. Eigenvalue spectrum with chebyshev polynomial approximation of the transport equation in slab geometry.J. Quant. Spectrosc. Radiat. Transf., 2006, 97(1):51–57.
  • 14. Anli, F., Güngör, S., Yaşa, F., and Öztürk, H. TN approximation to reflected slab and computation of the critical half thicknesses.J. Quant. Spectrosc. Radiat. Transf., 2006,101(1):135-140.
  • 15. Hama Rashid, P. A. Investigation of the solution by using PN method of transport equation for triplet anısotropıc scatterıng. M. Thesis,2013.
  • 16. Yildiz,C., Variation of the critical slab thickness with the degree of strongly anisotropic scattering in one-speed neutron transport theory.Ann. Nucl. Energy, 1998, 25(8):529-540.
  • 17. Türeci, R. G.Solving the criticality problem with the reflected boundary condition for the triplet anisotropic scattering with the modified FN method.Kerntechnik, 2015,80(6):583–592.

Ayrıntılar

Birincil Dil İngilizce
Konular Mühendislik
Bölüm Articles
Yazarlar

Halide KOKLU> (Sorumlu Yazar)
GAZİANTEP ÜNİVERSİTESİ, MÜHENDİSLİK FAKÜLTESİ, FİZİK MÜHENDİSLİĞİ BÖLÜMÜ, FİZİK MÜHENDİSLİĞİ PR. (İNGİLİZCE)
0000-0003-1787-6693
Türkiye


Okan OZER>
GAZİANTEP ÜNİVERSİTESİ, MÜHENDİSLİK FAKÜLTESİ, FİZİK MÜHENDİSLİĞİ BÖLÜMÜ, FİZİK MÜHENDİSLİĞİ PR. (İNGİLİZCE)
Türkiye

Teşekkür The manuscript was presented in TICMET19 conference.
Yayımlanma Tarihi 31 Aralık 2020
Yayınlandığı Sayı Yıl 2020, Cilt 3, Sayı 2

Kaynak Göster

Bibtex @araştırma makalesi { tijmet710273, journal = {The International Journal of Materials and Engineering Technology}, eissn = {2667-4033}, address = {tijmet.info@gmail.com}, publisher = {Necip Fazıl YILMAZ}, year = {2020}, volume = {3}, number = {2}, pages = {98 - 108}, title = {CRITICAL SIZE OF A SLAB REACTOR WITH NEUTRON TRANSPORT THEORY OF THE TRIPLET ANISOTROPIC SCATTERING}, key = {cite}, author = {Koklu, Halide and Ozer, Okan} }
APA Koklu, H. & Ozer, O. (2020). CRITICAL SIZE OF A SLAB REACTOR WITH NEUTRON TRANSPORT THEORY OF THE TRIPLET ANISOTROPIC SCATTERING . The International Journal of Materials and Engineering Technology , 3 (2) , 98-108 . Retrieved from https://dergipark.org.tr/tr/pub/tijmet/issue/56425/710273
MLA Koklu, H. , Ozer, O. "CRITICAL SIZE OF A SLAB REACTOR WITH NEUTRON TRANSPORT THEORY OF THE TRIPLET ANISOTROPIC SCATTERING" . The International Journal of Materials and Engineering Technology 3 (2020 ): 98-108 <https://dergipark.org.tr/tr/pub/tijmet/issue/56425/710273>
Chicago Koklu, H. , Ozer, O. "CRITICAL SIZE OF A SLAB REACTOR WITH NEUTRON TRANSPORT THEORY OF THE TRIPLET ANISOTROPIC SCATTERING". The International Journal of Materials and Engineering Technology 3 (2020 ): 98-108
RIS TY - JOUR T1 - CRITICAL SIZE OF A SLAB REACTOR WITH NEUTRON TRANSPORT THEORY OF THE TRIPLET ANISOTROPIC SCATTERING AU - HalideKoklu, OkanOzer Y1 - 2020 PY - 2020 N1 - DO - T2 - The International Journal of Materials and Engineering Technology JF - Journal JO - JOR SP - 98 EP - 108 VL - 3 IS - 2 SN - -2667-4033 M3 - UR - Y2 - 2020 ER -
EndNote %0 The International Journal of Materials and Engineering Technology CRITICAL SIZE OF A SLAB REACTOR WITH NEUTRON TRANSPORT THEORY OF THE TRIPLET ANISOTROPIC SCATTERING %A Halide Koklu , Okan Ozer %T CRITICAL SIZE OF A SLAB REACTOR WITH NEUTRON TRANSPORT THEORY OF THE TRIPLET ANISOTROPIC SCATTERING %D 2020 %J The International Journal of Materials and Engineering Technology %P -2667-4033 %V 3 %N 2 %R %U
ISNAD Koklu, Halide , Ozer, Okan . "CRITICAL SIZE OF A SLAB REACTOR WITH NEUTRON TRANSPORT THEORY OF THE TRIPLET ANISOTROPIC SCATTERING". The International Journal of Materials and Engineering Technology 3 / 2 (Aralık 2020): 98-108 .
AMA Koklu H. , Ozer O. CRITICAL SIZE OF A SLAB REACTOR WITH NEUTRON TRANSPORT THEORY OF THE TRIPLET ANISOTROPIC SCATTERING. TIJMET. 2020; 3(2): 98-108.
Vancouver Koklu H. , Ozer O. CRITICAL SIZE OF A SLAB REACTOR WITH NEUTRON TRANSPORT THEORY OF THE TRIPLET ANISOTROPIC SCATTERING. The International Journal of Materials and Engineering Technology. 2020; 3(2): 98-108.
IEEE H. Koklu ve O. Ozer , "CRITICAL SIZE OF A SLAB REACTOR WITH NEUTRON TRANSPORT THEORY OF THE TRIPLET ANISOTROPIC SCATTERING", The International Journal of Materials and Engineering Technology, c. 3, sayı. 2, ss. 98-108, Ara. 2020