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Three-dimensional mode selection of the flow past a rotating and inline oscillating cylinder

Published online by Cambridge University Press:  19 September 2018

David Lo Jacono Open the ORCID record for David Lo Jacono [Opens in a new window] ,
Rémi Bourguet Open the ORCID record for Rémi Bourguet [Opens in a new window] ,
Mark C. Thompson  and
Justin S. Leontini
David Lo Jacono*
Affiliation:
Institut de Mécanique des Fluides de Toulouse (IMFT), Université de Toulouse, CNRS, Toulouse, France Fluids Laboratory for Aeronautical and Industrial Research (FLAIR), Department of Mechanical and Aerospace Engineering, Monash University, Melbourne, Victoria 3800, Australia
Rémi Bourguet
Affiliation:
Institut de Mécanique des Fluides de Toulouse (IMFT), Université de Toulouse, CNRS, Toulouse, France
Mark C. Thompson
Affiliation:
Fluids Laboratory for Aeronautical and Industrial Research (FLAIR), Department of Mechanical and Aerospace Engineering, Monash University, Melbourne, Victoria 3800, Australia
Justin S. Leontini
Affiliation:
Swinburne University of Technology, Hawthorn, Victoria, 3122, Australia
*
†Email address for correspondence: [email protected]
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Abstract

This paper studies the transition to three-dimensional flow in the wake of a cylinder immersed in a free stream, where the cylinder is externally forced to continuously rotate about its axis and to linearly oscillate in the streamwise direction. Floquet stability analysis is used to assess the stability of the nominal two-dimensional flows at a Reynolds number $Re=100$ and rotation rate $\unicode[STIX]{x1D6FC}=\unicode[STIX]{x1D714}D/U=3$ to three-dimensional perturbations, as a function of the amplitude and frequency of the linear oscillations. Two modes of instability are found, distinguished by their spatial structure, temporal behaviour and apparent mechanism. The first mode has a shorter wavelength in the spanwise direction and appears to be linked to a centrifugal instability in the layer of fluid near the rotating body. The second mode has a longer wavelength and is linked to an instability of the vortex cores in the wake that is subharmonic, leading to a period doubling. Either mode can be stable while the other is unstable, depending primarily on the frequency of the oscillation of the cylinder. This indicates that either mode can control the transition to a three-dimensional flow. The results are compared to the fully three-dimensional simulation results of a rotating cylinder elastically mounted and free to oscillate in the streamwise direction from Bourguet & Lo Jacono (J. Fluid Mech., vol. 781, 2015, pp. 127–165), and appear to be able to explain the surprising switching of the observed spanwise wavelength in that flow as a change in the dominant mode, and therefore mechanism, of instability.

JFM classification

Instability: Instability Wakes/Jets: Wakes
Type
JFM Rapids
Information
Journal of Fluid Mechanics , Volume 855 , 25 November 2018 , R3
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Copyright
© 2018 Cambridge University Press 

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