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Sphere–wall collisions: vortex dynamics and stability

Published online by Cambridge University Press:  07 March 2007

MARK C. THOMPSON ,
THOMAS LEWEKE  and
KERRY HOURIGAN
MARK C. THOMPSON
Affiliation:
Fluids Laboratory for Aeronautical and Industrial Research (FLAIR), Department of Mechanical Engineering, PO Box 31, Monash University, Melbourne, Victoria 3800, Australia
THOMAS LEWEKE
Affiliation:
Institut de Recherche sur les Phénomènes Hors Équilibre (IRPHE), UMR 6594 CNRS/Universités Aix-Marseille I & II, 49, rue Frédéric Joliot-Curie, B.P. 146, F-13384 Marseille Cedex 13, France
KERRY HOURIGAN
Affiliation:
Fluids Laboratory for Aeronautical and Industrial Research (FLAIR), Department of Mechanical Engineering, PO Box 31, Monash University, Melbourne, Victoria 3800, Australia
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Abstract

For moderate Reynolds numbers, a sphere colliding with a wall in the normal direction will lead to a trailing recirculating wake, threading over the sphere after impact and developing into a complex vortex-ring system as it interacts with vorticity generated at the wall. The primary vortex ring, consisting of the vorticity from the wake of the sphere prior to impact, persists and convects, relatively slowly, outwards away from the sphere owing to the motion induced from its image. The outward motion is arrested only a short distance from the axis because of the strong interaction with the secondary vorticity. In this paper, the structure and evolution of this combined vortex system, consisting of a strong compact primary vortex ring surrounded by and interacting with the secondary vorticity, is quantified through a combined experimental and numerical study. The Reynolds-number range investigated is (100 < Re < 2000). At Reynolds numbers higher than about 1000, a non-axisymmetric instability develops, leading to rapid distortion of the ring system. The growth of the instability does not continue indefinitely, because of the dissipative nature of the flow system; it appears to reach a peak when the wake vorticity first forms a clean primary vortex ring. A comparison of the wavelength, growth rate and perturbation fields predicted from both linear stability theory and direct simulations, together with theoretical predictions, indicates that the dominant physical mechanism for the observed non-axisymmetric instability is centrifugal in nature. The maximum growth occurs at the edge of the primary vortex core, where the vorticity changes sign. Notably, this is a physical mechanism different from that proposed previously to explain the development of the three-dimensional flow of an isolated vortex ring striking a wall.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 575 , March 2007 , pp. 121 - 148
Copyright
Copyright © Cambridge University Press 2007

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