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Three-dimensionality in the wake of a rapidly rotating cylinder in uniform flow

Published online by Cambridge University Press:  30 July 2013

A. Rao ,
J. S. Leontini ,
M. C. Thompson  and
K. Hourigan
A. Rao
Affiliation:
Fluids Laboratory for Aeronautical and Industrial Research (FLAIR), Department of Mechanical and Aerospace Engineering, Monash University, Melbourne, Victoria 3800, Australia
J. S. Leontini*
Affiliation:
Fluids Laboratory for Aeronautical and Industrial Research (FLAIR), Department of Mechanical and Aerospace Engineering, Monash University, Melbourne, Victoria 3800, Australia
M. C. Thompson
Affiliation:
Fluids Laboratory for Aeronautical and Industrial Research (FLAIR), Department of Mechanical and Aerospace Engineering, Monash University, Melbourne, Victoria 3800, Australia
K. Hourigan
Affiliation:
Fluids Laboratory for Aeronautical and Industrial Research (FLAIR), Department of Mechanical and Aerospace Engineering, Monash University, Melbourne, Victoria 3800, Australia Division of Biological Engineering, Monash University, Melbourne, Victoria 3800, Australia
*
†Email address for correspondence: [email protected]
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Abstract

The flow around an isolated cylinder spinning at high rotation rates in free stream is investigated. The existence of two steady two-dimensional states is confirmed, as is the existence of a secondary mode of vortex shedding. The stability of the two steady states to three-dimensional perturbations is established using linear stability analysis. At lower rotation rates on the first steady state, two three-dimensional modes are confirmed, and their structure and curves of marginal stability as a function of rotation rate and Reynolds number are determined. One mode (named mode $E$) appears consistent with a hyperbolic instability in the wake, while the second (named mode $F$) appears to be a centrifugal instability of the flow very close to the cylinder surface. At higher rotation rates on the second steady state, a single three-dimensional mode due to centrifugal instability (named mode ${F}^{\prime } $) is found. This mode becomes increasingly difficult to excite as the rotation rate is increased.

JFM classification

Instability: Parametric instability Vortex Flows: Vortex Flows Wakes/Jets: Wakes/Jets
Type
Papers
Information
Journal of Fluid Mechanics , Volume 730 , 10 September 2013 , pp. 379 - 391
Copyright
©2013 Cambridge University Press 

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