Application of the Chebyshev polynomial (TN and UN) approximation to reflected slab geometry in the neutron transport equation and computation of critical half thicknesses
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A. Bülbül
Abstract
The transport of one-speed neutrons has been studied in isotropically scattering slab using ultraspherical polynomial approximation whose sub-cases are spherical harmonics approximation and Chebyshev polynomial approximation of first and second kind with reflective boundaries. An integral equation for the total flux has been derived and solved numerically for different values of c and reflection coefficients. In the solution, Marshak type vacuum boundary conditions were used. The critical thicknesses obtained by the Chebyshev polynomial method are in good agreement with literature values. Computations were made by using the TN, UN and PN approximations for comparison.
Kurzfassung
Anwendung der Tschebyscheff-Polynom-Approximation (TN und UN) auf reflektierende Stabgeometrie in der Neutronentransportgleichung und Berechnung kritischer Halbwertsdicken. Der Transport von Ein-Gruppen-Neutronen wurde bei isotroper Streuung in Stabgeometrie untersucht mit Hilfe ultraspärischer Polynom Approximation, die klassische polynomiellen Folgen, wie sphärische harmonische Approximation und Tschebyscheff-Polynom-Approximation erster und zweiter Ordnung mit reflektierenden Randbedingungen vereinheitlicht. Eine Integralgleichung für den gesamten Strahlungsfluss wurde hergeleitet und numerisch gelöst für verschiedene Werte von c und Reflektionskoeffizienten. Für den Lösungsweg wurden Vakuum-Randbedingungen vom Marshak-Typ verwendet. Die mit Hilfe der Tschebyscheff-Polynom-Approximation erhaltenen kritischer Halbwertsdicken stimmen gut mit Werten aus der Literatur überein. Zum Vergleich wurden Berechnungen mit TN, UN and PN Approximationen durchgeführt.
References
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© 2010, Carl Hanser Verlag, München
Artikel in diesem Heft
- Contents/Inhalt
- Contents
- Summaries/Kurzfassungen
- Summaries
- Technical Contributions/Fachbeiträge
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- Neutronic and burn-up calculations of heterogeneous Thorium/Uranium fuel in pressurized water reactors
- Research on pitting corrosion of steam generator heat transfer tubes based on acoustic emission
- Application of the Chebyshev polynomial (TN and UN) approximation to reflected slab geometry in the neutron transport equation and computation of critical half thicknesses
- UN approximation to critical slab problem for one-speed neutrons with isotropic, forward and backward scattering
- The albedo problem for pure-quadratic anisotropic scattering with İnönü scattering
- Technical Notes/Technische Mitteilungen
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Artikel in diesem Heft
- Contents/Inhalt
- Contents
- Summaries/Kurzfassungen
- Summaries
- Technical Contributions/Fachbeiträge
- Integrated online condition monitoring system for nuclear power plants
- Performance analysis of 233U for fixed bed nuclear reactors
- 3D thermal hydraulic simulation of the hot channel of a typical material testing reactor under normal operation conditions
- Analysis of the processes in the target cooling system of the W7-X fusion experiment
- Nuclear model calculation on charged particle induced reactions to produce 85Sr for diagnostic and endotherapy
- Neutronic and burn-up calculations of heterogeneous Thorium/Uranium fuel in pressurized water reactors
- Research on pitting corrosion of steam generator heat transfer tubes based on acoustic emission
- Application of the Chebyshev polynomial (TN and UN) approximation to reflected slab geometry in the neutron transport equation and computation of critical half thicknesses
- UN approximation to critical slab problem for one-speed neutrons with isotropic, forward and backward scattering
- The albedo problem for pure-quadratic anisotropic scattering with İnönü scattering
- Technical Notes/Technische Mitteilungen
- Targetry of Y2O3 on a copper substrate for the non-carrier-added 89Zr production via 89Y(p, n)89Zr reaction
