Slab Geometride Lineer Anizotropik Nötron Transport Denklemine İkinci Tip Chebyshev Polinom Yaklaşımı

Abstract

Tek boyutlu dilim geometride, tek hızlı ve lineer anizotropik saçılmalı durumda nötron transport denklemi değişkenlere ayırma yöntemi kullanılarak çözülmüştür. Konuma bağlı kısım eksponansiyel bir fonksiyon, açıya bağlı kısım ise Legendre veya Chebyshev Polinomları olarak seçilmiştir. Chebyshev Polinomlarının II. tipi kullanıldığından UN yaklaşımı olarak adlandırıldı. Bu diferansiyel eşitliklerin çözümü için hem PN hem de UN yönteminde eksponansiyel bir fonksiyon önerilmiştir. Önerilen fonksiyon diferansiyel eşitliklerde kullanılarak öz değerlerinin hesaplanabileceği birbirine bağlı analitik denklemler elde edilmiştir. Bu analitik denklemler çözülmüş c0 ve c1’in (çarpışma başına ortaya çıkan nötron sayıları) farklı değerler için (0 ≤ c1 < 2: c0=0, c0=0.25, c0 =0.50, c0 =0.75, c0 =0.99) ν öz değerleri hesaplanmış ve karşılaştırma yapmak için tablolar sunulmuştur

Keywords

• Slab geometri,nötron transport denklemi,Chebyshev polinomlar

Second Type Chebyshev Polynomial Approximation to Linearly Anisotropic Neutron Transport Equation in Slab Geometry

Abstract

In one-dimensional slab geometry, the neutron transport equation was solved in one-speed and linearly anisotropic scattering by implementing the method of separation of variables. The part which depended on the position selected as an exponential function on the other hand the part that was relied upon the angle was chosen as Legendre polynomials or Chebyshev polynomials. The approximation we used is called as UN method because in the method second type Chebyshev polynomials were used. To solve these differential equations, an exponential function was suggested in both PN and UN method. By using the suggested function in differential equations, analytical equations in which ν eigenvalues can be calculated were obtained. These analytical equations were solved and ν eigenvalues calculated for different values (0≤c <2: c =0, c0 =0.25, c0 =0.50, c0=0.75, c =0.99) of c0 and c (where c is the number of secondary neutrons per collision) and the results were presented in the same tables for comparison

Keywords

• Slab geometry, neutron transport equation, Chebyshev polynomials

References

1. Yaşa F., 2002. Solution with green spectral function method of transport equations in spherical geometry, PhD Thesis., Cukurova University, Adana, 62 p.
2. Bell W.W., 1967. Special Functions for Scientists and Engineer, D. Van Nostrand Company Ltd., London, 270 p.
3. Arfken G., 1970. Mathematical Methods for Physics, 2ed, Academic Press Inc., New York, 815 p.
4. Conkie W. R., 1959. Polynomial approximations in neutron transport theory, Nuclear Science and Engineering, 6: 260-266.
5. Arfken G.B., Weber H.J., 1995. Mathematical methods for physicists, Academic Press, London, 4th Edition, 1028 p.
6. Bell G. I., Glasstone S., 1970. Nuclear Reactor Theory, Van Nostrand Reinhold Company, United States of America, 619 p.
7. Muhammet Karataşlı e-mail: [e-mail]
8. Tahsin Özer e-mail: [e-mail]

9. Ahmet Varinlioğlu e-mail: [e-mail]