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

TN-Approximation höherer Ordnung des Neutronendiffusionsproblem in einer Platte
H. Öztürk and B. Durmaz
From the journal Kerntechnik

Abstract

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.

Abstract

Zur Berechnung der Diffusionslängen monoenergetischer Neutronen in einer homogenen Platte werden erstmals Näherungen höherer Ordnung der Tscheby-scheff-Polynome erster Art (TN) verwendet. In dieser Methode werden die Diffusionslängen der Neutronen mit verschiedenen Werten des c, der Anzahl der sekundären Neutronen pro Kollision, berechnet. Zunächst wird die traditionelle Legendre-Polynom-Näherung (PN) und dann die vorliegende TN-Methode separat verwendet. Die numerischen Ergebnisse für die Diffusionslängen sind in den Tabellen bis zu einer Ordnung von N = 9 aufgeführt. Auch ein kurzer Vergleich der Ergebnisse der vorliegenden Methode mit Daten aus der Literatur wird durchgeführt. Die Vorteile der neuen Methode lassen sich leicht an der guten Übereinstimmung mit den in den Vergleichstabellen angegebenen Ergebnissen ablesen und zeigen sich auch in der leichten Handhabung der vorgestellten Gleichungen. Für viele der c-Werte sind die mit der TN-Methode erzielten Ergebnisse besser als die mit der PN-Methode berechneten Daten.

References

1 Aspelund, O.: On a new method for solving the (Boltzmann) equation in neutron transport theory. PICG 16 (1958) 530 Search in Google Scholar

2 Conkie,W. R.: Polynomial approximations in neutron transport theory. Nucl. Sci. Eng. 6 (1959) 260, DOI:10.13182/NSE59-A28841 Search in Google Scholar

3 Yabushita, S.: Tschebyscheff polynomials approximation method of the neutron transport equation. J. Math. Phys. 2 (1961) 543, DOI:10.1063/1.1703739 Search in Google Scholar

4 Anlı, F.; Yaşa, F.; Güngör, S.; Öztürk, H. TN approximation to neutron transport equation and application to critical slab problem. J. Quant. Spectrosc. Radiat. Transfer 101 (2006) 129, DOI:10.1016/j.jqsrt.2005.11.010 Search in Google Scholar

5 Öztürk, H.; Anli, F.; Güngör, S. TN method for the critical thickness of one-speed neutrons in a slab for forward and backward scattering. J. Quant. Spectrosc. Radiat. Transfer, 105 (2007) 211, DOI:10.1016/j.jqsrt.2006.12.002 Search in Google Scholar

6 Öztürk, H.; Anli, F.; Güngör, S.: Application of the ФN method to the reflected critical slab problem for one-speed neutrons with forward and backward scattering. Kerntechnik 72/1–2 (2007) 74, DOI:10.3139/124.100321 Search in Google Scholar

7 Öztürk, H.; Güngör, S. TN approximation on the critical size of time-dependent, one-speed and one-dimensional neutron transport problem with anisotropic scattering. Ann. Nucl. Energy 36 (2009) 575, DOI:10.1016/j.anucene.2009.01.012 Search in Google Scholar

8 Öztürk, H. TN approximation for the critical size of one-speed neutrons in a slab with anisotropic scattering. Kerntechnik 78 (2013) 241, DOI:10.3139/124.110350 Search in Google Scholar

9 Öztürk, H.: The effect of strongly anisotropic scattering on the critical size of a slab in one-speed neutron transport theory: Modified ФN method. Ann. Nucl. Energy 65 (2014) 24, DOI:10.1016/j.anucene.2013.10.021 Search in Google Scholar

10 Öztürk, H.; Yapar, A. Ş.: Alternative scattering kernels for the first estimates of a reactor: diffusion length. Nucl. Sci. Tech. 29 (2018) 37, DOI:10.1007/s41365-018-0380-6 Search in Google Scholar

11 Bell, G. I.; Glasstone, S.: Nuclear reactor theory. New York, VNR Company, 1972 Search in Google Scholar

12 Case, K. M.; Zweifel, P. F.: Linear Transport Theory. 1st edn. Addison-Wesley Publishing Company, 1967 Search in Google Scholar

13 Arfken, G.: Mathematical methods for physicists. London, Academic Press, Inc., 1985 Search in Google Scholar

Received: 2021-02-15
Published Online: 2021-08-18
Published in Print: 2021-08-31

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