A discrete ordinates operator for the diffuse transmission of a mixed neutron beam through a multilayered medium
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M. P. de Abreu
Abstract
In this article the transport model and inductive approach reported in a recent work have been extended, and a discrete ordinates operator for the diffuse transmission of a mixed neutron beam through a multilayered medium is derived. At first, a mathematical description of the mixed beam transport problem that we are concerned with is given. The resulting mathematical problem is, according to Chandrasekhar, decomposed into uncollided and diffuse problems. After treating the uncollided problem analytically, a discrete ordinates formulation of the diffuse problem is considered. A set of spatially discretised equations that are free from spatial truncation error is then introduced. Finally, a discrete ordinates operator that replaces the entire multilayered medium in diffuse neutron transmission computations is derived inductively. To the best of our knowledge, such an operator has never been reported previously in neutron transport literature. Numerical results for a four-layer medium are presented to illustrate the computational merit of a computer code based on our diffuse transmission operator.
Kurzfassung
In diesem Beitrag wird das Transportmodell und der induktive Ansatz einer vorangegangenen Arbeit erweitert. Ein diskrete Ordinaten Operator für die diffuse Transmission eines gemischten Neutronenstrahls durch ein mehrschichtiges Medium wird hergeleitet. Zunächst wird das hier behandelte Transportproblem gemischter Neutronenstrahlen mathematisch beschrieben. Das sich daraus ergebende mathematische Problem zerfällt nach Chandrasekhar in einen Anteil vor dem ersten Stoß des Neutrons und in einen diffusen Anteil. Nach der analytischen Behandlung des Anteils vor dem ersten Stoß, wird eine Formulierung des diffusen Anteils nach der Methode der diskreten Ordinaten betrachtet. Es wird eine Reihe von räumlich diskretisierten Gleichungen eingeführt, die unabhängig sind von räumlichen Abbruchfehlern. Schließlich wird ein diskrete Ordinaten Operator induktiv hergeleitet, der das gesamte mehrschichtiges Medium ersetzt. Nach unserem Wissen wurde über einen solchen Operator in der Neutronentransportliteratur bisher nichts berichtet. Numerische Ergebnisse für ein 4-Schichten Medium werden vorgestellt, um die Vorteile eines Rechencodes auf der Basis unseres Operators für die diffuse Transmission zu erläutern.
References
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© 2010, Carl Hanser Verlag, München
Artikel in diesem Heft
- Contents/Inhalt
- Contents
- Summaries/Kurzfassungen
- Summaries
- Technical Contributions/Fachbeiträge
- Adaptation of the FEMAXI-6 code and RBMK fuel rods model testing employing the best estimate approach
- In-reactor measurements of fuel centerline temperature variation during power change
- Pertinence of tests used for conformity assessments of fire resistance of nuclear power plant components – opinion of several institutions in Europe
- Analysis of the instability of OTSG of movable nuclear power devices by using the multivariable frequency domain method
- Steady state thermal hydraulic calculations for MTR plate-type research reactors
- Production cross sections of medical 110,111In radionuclides
- Nuclear level density parameters of some largely deformed nuclei of medical radionuclides in low-lying collective excitation modes
- A discrete ordinates operator for the diffuse transmission of a mixed neutron beam through a multilayered medium
- Kritikalitätssicherheit der Endlagerung ausgedienter Kernbrennstoffe
- Technical Notes/Technische Mitteilungen
- Methods for thin foil thickness determination by using alpha spectroscopy
Artikel in diesem Heft
- Contents/Inhalt
- Contents
- Summaries/Kurzfassungen
- Summaries
- Technical Contributions/Fachbeiträge
- Adaptation of the FEMAXI-6 code and RBMK fuel rods model testing employing the best estimate approach
- In-reactor measurements of fuel centerline temperature variation during power change
- Pertinence of tests used for conformity assessments of fire resistance of nuclear power plant components – opinion of several institutions in Europe
- Analysis of the instability of OTSG of movable nuclear power devices by using the multivariable frequency domain method
- Steady state thermal hydraulic calculations for MTR plate-type research reactors
- Production cross sections of medical 110,111In radionuclides
- Nuclear level density parameters of some largely deformed nuclei of medical radionuclides in low-lying collective excitation modes
- A discrete ordinates operator for the diffuse transmission of a mixed neutron beam through a multilayered medium
- Kritikalitätssicherheit der Endlagerung ausgedienter Kernbrennstoffe
- Technical Notes/Technische Mitteilungen
- Methods for thin foil thickness determination by using alpha spectroscopy
