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Effect of an internal nonlinear rotational dissipative element on vortex shedding and vortex-induced vibration of a sprung circular cylinder

Published online by Cambridge University Press:  31 August 2017

Ravi Kumar R. Tumkur Open the ORCID record for Ravi Kumar R. Tumkur [Opens in a new window] ,
Arne J. Pearlstein ,
Arif Masud ,
Oleg V. Gendelman ,
Antoine B. Blanchard ,
Lawrence A. Bergman  and
Alexander F. Vakakis
Ravi Kumar R. Tumkur*
Affiliation:
Department of Aerospace Engineering, University of Illinois at Urbana-Champaign, IL 61801, USA
Arne J. Pearlstein
Affiliation:
Department of Mechanical Science and Engineering, University of Illinois at Urbana-Champaign, IL 61801, USA
Arif Masud
Affiliation:
Department of Civil and Environmental Engineering, University of Illinois at Urbana-Champaign, IL 61801, USA
Oleg V. Gendelman
Affiliation:
Faculty of Mechanical Engineering, Technion-Israel Institute of Technology, Haifa 3200003, Israel
Antoine B. Blanchard
Affiliation:
Department of Aerospace Engineering, University of Illinois at Urbana-Champaign, IL 61801, USA
Lawrence A. Bergman
Affiliation:
Department of Aerospace Engineering, University of Illinois at Urbana-Champaign, IL 61801, USA
Alexander F. Vakakis
Affiliation:
Department of Mechanical Science and Engineering, University of Illinois at Urbana-Champaign, IL 61801, USA
*
†Email address for correspondence: tumkur.ravikumar@gmail.com
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Abstract

We computationally investigate coupling of a nonlinear rotational dissipative element to a sprung circular cylinder allowed to undergo transverse vortex-induced vibration (VIV) in an incompressible flow. The dissipative element is a‘nonlinear energy sink’ (NES), consisting of a mass rotating at fixed radius about the cylinder axis and a linear viscous damper that dissipates energy from the motion of the rotating mass. We consider the Reynolds number range $20\leqslant Re\leqslant 120$ , with $Re$ based on cylinder diameter and free-stream velocity, and the cylinder restricted to rectilinear motion transverse to the mean flow. Interaction of this NES with the flow is mediated by the cylinder, whose rectilinear motion is mechanically linked to rotational motion of the NES mass through nonlinear inertial coupling. The rotational NES provides significant ‘passive’ suppression of VIV. Beyond suppression however, the rotational NES gives rise to a range of qualitatively new behaviours not found in transverse VIV of a sprung cylinder without an NES, or one with a ‘rectilinear NES’, considered previously. Specifically, the NES can either stabilize or destabilize the steady, symmetric, motionless-cylinder solution and can induce conditions under which suppression of VIV (and concomitant reduction in lift and drag) is accompanied by a greatly elongated region of attached vorticity in the wake, as well as conditions in which the cylinder motion and flow are temporally chaotic at relatively low $Re$ .

JFM classification

Nonlinear Dynamical Systems: Chaos Vortex Flows: Vortex shedding

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Papers
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Journal of Fluid Mechanics , Volume 828 , 10 October 2017 , pp. 196 - 235
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© 2017 Cambridge University Press 

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