Unified treatment of the P(λ)n approximation to solve the reflected slab criticality problem with strong anisotropy
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A. Yılmazer
Abstract
Ultraspherical polynomial P(λ)n approximations are used in reflected slab criticality calculations for strongly anisotropic scattering. A unique formulation is developed for reflected slab criticality conditions whose special cases are spherical harmonics approximations, Chebyshev polynomial approximations of first and second kind. It is shown in the calculations that all ultraspherical polynomial approximations are equivalent regarding the convergence of the solution of one-speed neutron transport equation for various degrees of anisotropy and cross section parameters. Although some ultraspherical polynomials approximations converge in the mean as the order of approximation is increased and some converge uniformly, they all converge to the same critical thickness which implies their equi-convergence. It is also demonstrated that the first order approximation P(λ)1 would give the exact critical thickness for a certain value of the parameter λ.
Kurzfassung
Ultrasphärische P(λ)n Polynom Approximationen werden verwendet bei Kritikalitätsberechnungen mit reflektierenden Randbedingungen für streng anisotrope Streuung. Eine einheitliche Formulierung wurde entwickelt für Kritikalitätsberechnungen mit reflektierenden Randbedingungen, deren Spezialfälle sphärisch harmonische Approximationen sind, Tschebyscheff-Polynom-Approximationen der ersten und zweiten Art. Es wird in den Berechnungen gezeigt, dass alle ultrasphärischen Polynom-Approximationen äquivalent sind in Bezug auf die Konvergenz der Lösung der Eingruppen-Neutronentransportgleichung für verschiedene Anisotropiegrade und Wirkungsquerschnittparameter. Obwohl einige ultrasphärische Polynom-Approximationen im Mittel konvergieren bei steigender Approximationsordnung und einige gleichförmig konvergieren, konvergieren alle zur gleichen kritischen Dicke, die ihre Equikonvergenz mit einbeziehen. Es wird auch gezeigt, dass die P(λ)1 Approximation erster Ordnung für einen bestimmten Wert des Parameters λ die exakte kritische Dicke ergeben würde.
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© 2008, Carl Hanser Verlag, München
Artikel in diesem Heft
- Contents/Inhalt
- Contents
- Summaries/Kurzfassungen
- Summaries
- Technical Contributions/Fachbeiträge
- Development and validation of the pressure surge computer code DYVRO mod. 3
- Simulation model of a nuclear power plant turbine
- Study on the thermal-hydraulics characteristics of a boiling two-phase natural circulation loop with nanofluids
- The effect of combination of different materials on neutron absorption in a nuclear research reactor spent fuel pool
- Re-evaluation of the criticality experiments of the “Otto Hahn Nuclear Ship” reactor
- Potential advantages and disadvantages of sequentially building small nuclear units instead of a large nuclear plant
- Radiological consequences of potential sabotage attack to storage casks on the ISFSI site
- Unified treatment of the P(λ)n approximation to solve the reflected slab criticality problem with strong anisotropy
- A comparative study on classical polynomial approximations to the transport equation in spherical media albedo problems
- Solution of half space and slab albedo problems for linearly anisotropic scattering with the modified FN method
- Study of the effect of anisotropic scattering on the critical slab problem in neutron transport theory using Chebyshev polynomials
Artikel in diesem Heft
- Contents/Inhalt
- Contents
- Summaries/Kurzfassungen
- Summaries
- Technical Contributions/Fachbeiträge
- Development and validation of the pressure surge computer code DYVRO mod. 3
- Simulation model of a nuclear power plant turbine
- Study on the thermal-hydraulics characteristics of a boiling two-phase natural circulation loop with nanofluids
- The effect of combination of different materials on neutron absorption in a nuclear research reactor spent fuel pool
- Re-evaluation of the criticality experiments of the “Otto Hahn Nuclear Ship” reactor
- Potential advantages and disadvantages of sequentially building small nuclear units instead of a large nuclear plant
- Radiological consequences of potential sabotage attack to storage casks on the ISFSI site
- Unified treatment of the P(λ)n approximation to solve the reflected slab criticality problem with strong anisotropy
- A comparative study on classical polynomial approximations to the transport equation in spherical media albedo problems
- Solution of half space and slab albedo problems for linearly anisotropic scattering with the modified FN method
- Study of the effect of anisotropic scattering on the critical slab problem in neutron transport theory using Chebyshev polynomials
