Alternative scattering kernels for the first estimates of a reactor: diffusion length

Öztürk, Hakan; Yapar, Ayça Şimşek

doi:10.1007/s41365-018-0380-6

Cited by 3 publications

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References 17 publications

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“…This method has been used successfully before and it can be applied to other problems of the transport theory (Conkie, 1959;Yabushita, 1961;Aspelund, 1958). In the following years, UN method was successfully applied to problems of the transport theory (Öztürk, 2008;2012;Öztürk and Yapar, 2018). Therefore in this study, the first order approximation (U1 method) in which the neutron angular flux is expanded in terms of the Chebyshev polynomials of second kind was performed for the calculation of the extrapolated end-points z0 in a slab for various values of the c (the mean number of secondary neutrons per collision).…”

Section: Introductionmentioning

confidence: 99%

A Study on the Solution of the Extrapolation Distance Problem Using U1 Method

AKSU

Öztürk

2021

Osmaniye Korkut Ata Üniversitesi Fen Edebiyat Fakültesi Dergisi

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The neutron transport equation for one-speed neutrons in a homogeneous slab was solved for the solution of the extrapolation distance problem. In the solution algorithm of the problem first the traditional P1 method in which the neutron angular flux was expanded in terms of the Legendre polynomials and then the U1 method in which the neutron angular flux was expanded in terms of the Chebyshev polynomials of second kind were used. While it is possible to find the solution of the problem obtained by P1 method in literature, U1 method was first applied to this problem and an analytical expression was obtained as the main goal of this study. Finally, numerical results for the extrapolation distances were calculated using both methods and they were given in the tables together with the exact results for comparison. Although the results obtained in this study could be evaluated as not to be in a very good accordance with the results already presented in the literature; this should be realised as these calculations were carried out using only the lowest order approximations of the polynomial expansion techniques. Then it is clear that more convenient results with the literature may be obtained in case applying higher-order aproximations.However, it is important to underline that the U1 method was first pplied to the problem and an analytical expression for the extrapolation distance was derived explicitly.

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Section: Introductionmentioning

confidence: 99%

A Study on the Solution of the Extrapolation Distance Problem Using U1 Method

AKSU

Öztürk

2021

Osmaniye Korkut Ata Üniversitesi Fen Edebiyat Fakültesi Dergisi

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Higher Order U_N Method for the Solution of the Neutron Diffusion Problem

Öztürk

Tuğralı

2022

Journal of Computational and Theoretical Transport

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Higher order T_N approximation for the neutron diffusion problem in a slab reactor

Öztürk

Durmaz

2021

Kerntechnik

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Higher order approximations of the Chebyshev polynomials of first kind (TN) are used for the first time in calculation of the diffusion lengths of monoenergetic neutrons in a homogeneous slab. In the method, the diffusion lengths of the neutrons are calculated using various values of the c, the number of secondary neutrons per collision. First, the traditional Legendre polynomials (PN) approximation and then the present TN method are used separately. The numerical results for the diffusion lengths are tabulated in the tables up to an order of N = 9. A brief comparison is also done between the results obtained from the present method and the ones in literature. The advantages of the present method can easily be observed from the good accordance between results given in the tables for comparison and its easily executable equations. For many of the c values, the results obtained from TN method are better than the results obtained from PN method.

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Alternative scattering kernels for the first estimates of a reactor: diffusion length

Cited by 3 publications

References 17 publications

A Study on the Solution of the Extrapolation Distance Problem Using U1 Method

A Study on the Solution of the Extrapolation Distance Problem Using U1 Method

Higher Order U_N Method for the Solution of the Neutron Diffusion Problem

Higher order T_N approximation for the neutron diffusion problem in a slab reactor

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Alternative scattering kernels for the first estimates of a reactor: diffusion length

Cited by 3 publications

References 17 publications

A Study on the Solution of the Extrapolation Distance Problem Using U1 Method

A Study on the Solution of the Extrapolation Distance Problem Using U1 Method

Higher Order UN Method for the Solution of the Neutron Diffusion Problem

Higher order TN approximation for the neutron diffusion problem in a slab reactor

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Product

Resources

About

Higher Order U_N Method for the Solution of the Neutron Diffusion Problem

Higher order T_N approximation for the neutron diffusion problem in a slab reactor