Higher order TN approximation for the neutron diffusion problem in a slab reactor
-
H. Öztürk
and
B. Durmaz
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
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Articles in the same Issue
- Frontmatter
- Large eddy fire simulation applications from nuclear industry
- Characterization of polystyrene and polyacrylic based polymeric materials exposed to oxidative degradation
- Thorium-based CANDU qualification as plutonium burner
- Higher order TN approximation for the neutron diffusion problem in a slab reactor
- A Monte Carlo study on burnup treatment in sodium-cooled reactor with Th fuel
- Neutronics and both analytical and numerical solutions for the rod centered subchannel thermal-hydraulic model
Articles in the same Issue
- Frontmatter
- Large eddy fire simulation applications from nuclear industry
- Characterization of polystyrene and polyacrylic based polymeric materials exposed to oxidative degradation
- Thorium-based CANDU qualification as plutonium burner
- Higher order TN approximation for the neutron diffusion problem in a slab reactor
- A Monte Carlo study on burnup treatment in sodium-cooled reactor with Th fuel
- Neutronics and both analytical and numerical solutions for the rod centered subchannel thermal-hydraulic model
