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NONSYMMETRIC BRANCHING OF FLUID FLOWS IN 3D VESSELS

Part of: Incompressible viscous fluids

Published online by Cambridge University Press:  08 June 2018

N. C. OVENDEN Open the ORCID record for N. C. OVENDEN [Opens in a new window]  and
F. T. SMITH Open the ORCID record for F. T. SMITH [Opens in a new window]
N. C. OVENDEN*
Affiliation:
Department of Mathematics, University College London, Gower St, London WC1E 6BT, UK email n.ovenden@ucl.ac.uk, f.smith@ucl.ac.uk
F. T. SMITH
Affiliation:
Department of Mathematics, University College London, Gower St, London WC1E 6BT, UK email n.ovenden@ucl.ac.uk, f.smith@ucl.ac.uk
*
✉n.ovenden@ucl.ac.uk
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Abstract

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Nonsymmetric branching flow through a three-dimensional (3D) vessel is considered at medium-to-high flow rates. The branching is from one mother vessel to two or more daughter vessels downstream, with laminar steady or unsteady conditions assumed. The inherent 3D nonsymmetry is due to the branching shapes themselves, or the differences in the end pressures in the daughter vessels, or the incident velocity profiles in the mother. Computations based on lattice-Boltzmann methodology are described first. A subsequent analysis focuses on small 3D disturbances and increased Reynolds numbers. This reduces the 3D problem to a two-dimensional one at the outer wall in all pressure-driven cases. As well as having broader implications for feeding into a network of vessels, the findings enable predictions of how much swirling motion in the cross-plane is generated in a daughter vessel downstream of a 3D branch junction, and the significant alterations provoked locally in the shear stresses and pressures at the walls. Nonuniform incident wall-shear and unsteady effects are examined. A universal asymptotic form is found for the flux change into each daughter vessel in a 3D branching of arbitrary cross-section with a thin divider.

Keywords

branchingnonsymmetry

MSC classification

Primary: 76D09: Viscous-inviscid interaction
Type
Research Article
Information
The ANZIAM Journal , Volume 59 , Issue 4 , April 2018 , pp. 533 - 561
Copyright
© 2018 Australian Mathematical Society 

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