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Vortex-induced vibrations of a long flexible cylinder in shear flow

Published online by Cambridge University Press:  27 April 2011

REMI BOURGUET ,
GEORGE E. KARNIADAKIS  and
MICHAEL S. TRIANTAFYLLOU
REMI BOURGUET*
Affiliation:
Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
GEORGE E. KARNIADAKIS
Affiliation:
Division of Applied Mathematics, Brown University, Providence, RI 02912, USA
MICHAEL S. TRIANTAFYLLOU
Affiliation:
Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
*
†Email address for correspondence: bourguet@mit.edu
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Abstract

We investigate the in-line and cross-flow vortex-induced vibrations of a long cylindrical tensioned beam, with length to diameter ratio L/D = 200, placed within a linearly sheared oncoming flow, using three-dimensional direct numerical simulation. The study is conducted at three Reynolds numbers, from 110 to 1100 based on maximum velocity, so as to include the transition to turbulence in the wake. The selected tension and bending stiffness lead to high-wavenumber vibrations, similar to those encountered in long ocean structures. The resulting vortex-induced vibrations consist of a mixture of standing and travelling wave patterns in both the in-line and cross-flow directions; the travelling wave component is preferentially oriented from high to low velocity regions. The in-line and cross-flow vibrations have a frequency ratio approximately equal to 2. Lock-in, the phenomenon of self-excited vibrations accompanied by synchronization between the vortex shedding and cross-flow vibration frequencies, occurs in the high-velocity region, extending across 30% or more of the beam length. The occurrence of lock-in disrupts the spanwise regularity of the cellular patterns observed in the wake of stationary cylinders in shear flow. The wake exhibits an oblique vortex shedding pattern, inclined in the direction of the travelling wave component of the cylinder vibrations. Vortex splittings occur between spanwise cells of constant vortex shedding frequency. The flow excites the cylinder under the lock-in condition with a preferential in-line versus cross-flow motion phase difference corresponding to counter-clockwise, figure-eight orbits; but it damps cylinder vibrations in the non-lock-in region. Both mono-frequency and multi-frequency responses may be excited. In the case of multi-frequency response and within the lock-in region, the wake can lock in to different frequencies at various spanwise locations; however, lock-in is a locally mono-frequency event, and hence the flow supplies energy to the structure mainly at the local lock-in frequency.

JFM classification

Vortex Flows: Vortex shedding Wakes/Jets: Vortex streets
Type
Papers
Information
Journal of Fluid Mechanics , Volume 677 , 25 June 2011 , pp. 342 - 382
Copyright
Copyright © Cambridge University Press 2011

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