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Solutions of the Navier-Stokes equations for vortex breakdown

Published online by Cambridge University Press:  29 March 2006

W. J. Grabowski  and
S. A. Berger
W. J. Grabowski
Affiliation:
Flow Research Inc., Los Angeles, California 90045
S. A. Berger
Affiliation:
Department of Mechanical Engineering, University of California, Berkeley
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Abstract

A numerical investigation of vortex breakdown has been undertaken in an attempt to understand its properties, and the mechanisms responsible for it. Solutions of the full steady axisymmetric Navier—Stokes equations for breakdown in an unconfined viscous vortex have been obtained for core Reynolds numbers up to 200, for a two-parameter family of assumed upstream velocity distributions. Diffusion and convection of vorticity away from the vortex core, and the strong coupling between the circumferential and axial velocity fields in highly-swirling flows, are shown to lead to stagnation and reversal of the axial flow near the axis. The various theories of vortex breakdown are considered in light of the present numerical solutions.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 75 , Issue 3 , 11 June 1976 , pp. 525 - 544
Copyright
© 1976 Cambridge University Press

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