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A Modification to the Kirchhoff Conditions at a Bifurcation and Loss Coefficients
Linköping University, Department of Mathematics, Computational Mathematics. Linköping University, Faculty of Science & Engineering.ORCID iD: 0000-0002-2681-8965
Linköping University, Department of Management and Engineering, Applied Thermodynamics and Fluid Mechanics. Linköping University, Faculty of Science & Engineering. Linköping University, Center for Medical Image Science and Visualization (CMIV).ORCID iD: 0000-0001-5526-2399
Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
St Petersburg State University, Russia; St Petersburg State Polytech University, Russia.
2018 (English)Report (Other academic)
Abstract [en]

One dimensional models for fluid flow in tubes are frequently used tomodel complex systems, such as the arterial tree where a large numberof vessels are linked together at bifurcations. At the junctions transmission conditions are needed. One popular option is the classic Kirchhoffconditions which means conservation of mass at the bifurcation andprescribes a continuous pressure at the joint.

In reality the boundary layer phenomena predicts fast local changesto both velocity and pressure inside the bifurcation. Thus it is not appropriate for a one dimensional model to assume a continuous pressure. In this work we present a modification to the classic Kirchhoff condi-tions, with a symmetric pressure drop matrix, that is more suitable forone dimensional flow models. An asymptotic analysis, that has beencarried out previously shows that the new transmission conditions hasen exponentially small error.

The modified transmission conditions take the geometry of the bifurcation into account and can treat two outlets differently. The conditions can also be written in a form that is suitable for implementationin a finite difference solver. Also, by appropriate choice of the pressuredrop matrix we show that the new transmission conditions can producehead loss coefficients similar to experimentally obtained ones.

Place, publisher, year, edition, pages
2018. , p. 11
Series
LiTH-MAT-R, ISSN 0348-2960 ; 2018:5
National Category
Mathematics
Identifiers
URN: urn:nbn:se:liu:diva-147718ISRN: LiTH-MAT-R--2018/05--SEOAI: oai:DiVA.org:liu-147718DiVA, id: diva2:1204214
Available from: 2018-05-07 Created: 2018-05-07 Last updated: 2018-05-07Bibliographically approved

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Berntsson, FredrikKarlsson, MattsKozlov, Vladimir

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Computational MathematicsFaculty of Science & EngineeringApplied Thermodynamics and Fluid MechanicsCenter for Medical Image Science and Visualization (CMIV)Mathematics and Applied Mathematics
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