A complementary Doppler Broadening formalism and its impact on nuclear reactor simulation
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R. Dagan
Abstract
The Boltzmann Transport equation is the governing formalism upon which simulations of nuclear reactors are performed, in particular when strong absorption or anisotropic scattering are significant. On the left (loss) hand side of the balance equation one finds the absorption and the scattering cross section Σa(E′), Σs(E′) respectively. Those cross sections are energy and temperature dependent i.e. Doppler Broadened. The scattering cross section appears explicitly again on the right (production) hand side of the equation in its differential form ∫∫0∞Σ(E → E′); Ω → Ω′)dE dΩ. However, this term is commonly evaluated at 0 K and it does not account for the existing resonances which are the underlying characteristic for Doppler Broadening. Evidently one gets an inherent inconsistency between the integral and differential scattering cross section within the transport solver codes. In this study this missing Doppler Broadened formalism for the differential scattering cross section is introduced in its stochastic and deterministic form. The impact on core criticality is shown to be up to 600 pcm and the change in the nuclides' inventory significant, in particular the 239PU content can be changed by several percents.
Kurzfassung
Die grundlegende Gleichung der Neutronenphysik ist die Boltzmann-Transportgleichung. Falls in einer Kernreaktorsimulation starke Absorption oder anisotrope Streuung beschrieben werden soll, wird auf eine Näherung dieser Gleichung zurückgegriffen. Der Absoptions- und der Streuwirkungsquerschnitt treten implizit auf der linken Seite der Gleichung als integrale Verlustterme auf. Sie sind energie- und temperaturabhängig, d.h. Doppler verbreitert. Der Streuwirkungsquerschnitt tritt explizit in seiner differenziellen Form auf der rechten Seite der Boltzmanngleichung als Produktionsterm auf. Hier jedoch findet die Dopplerverbreiterung in der Regel nicht statt, d.h. die Temperaturabhängigkeit sowie die Existenz der Resonanzen bleiben unberücksichtigt. In dieser Studie wird der Doppler verbreiterte Streukern vorgestellt, sowie nach seiner Implementierung in einem stochastischen Transportcode dessen Einfluss auf Kenngrößen der Reaktorphysik diskutiert. Es wird gezeigt, dass sich dieses Verfahren mit bis zu 600 pcm in der Kritikalität im Vergleich zum Standardverfahren auswirkt. Darüber hinaus ändert sich das Nuklidinventar deutlich, insbesondere die erbrütete Menge 239Pu.
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© 2011, Carl Hanser Verlag, München
Artikel in diesem Heft
- Contents/Inhalt
- Contents
- Summaries/Kurzfassungen
- Summaries
- Editorial
- Plant behaviour and coupling with reactor physics
- Technical Contributions/Fachbeiträge
- Multi-scale coupled code systems: from coarse-mesh to high-fidelity LWR core calculations
- Development of multi-physics code systems based on the reactor dynamics code DYN3D
- Development of the coupled 3D neutron kinetics/thermal-hydraulics code DYN3D-HTR for the simulation of transients in block-type HTGR
- Influence of nuclear data uncertainties on reactor core calculations
- Analysis of reactor lattice and core parameters in view of nuclear data modifications
- A complementary Doppler Broadening formalism and its impact on nuclear reactor simulation
- Experiences with the coupled code system S3R/RELAP5-3D in training simulators
- BWR transient analysis with the coupled code system S3K/RELAP5
- The development and assessment of TRACE model for Lungmen ABWR
Artikel in diesem Heft
- Contents/Inhalt
- Contents
- Summaries/Kurzfassungen
- Summaries
- Editorial
- Plant behaviour and coupling with reactor physics
- Technical Contributions/Fachbeiträge
- Multi-scale coupled code systems: from coarse-mesh to high-fidelity LWR core calculations
- Development of multi-physics code systems based on the reactor dynamics code DYN3D
- Development of the coupled 3D neutron kinetics/thermal-hydraulics code DYN3D-HTR for the simulation of transients in block-type HTGR
- Influence of nuclear data uncertainties on reactor core calculations
- Analysis of reactor lattice and core parameters in view of nuclear data modifications
- A complementary Doppler Broadening formalism and its impact on nuclear reactor simulation
- Experiences with the coupled code system S3R/RELAP5-3D in training simulators
- BWR transient analysis with the coupled code system S3K/RELAP5
- The development and assessment of TRACE model for Lungmen ABWR
