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Hysteresis in vortex-induced vibrations: critical blockage and effect of m*

Published online by Cambridge University Press:  03 February 2011

T. K. PRASANTH ,
V. PREMCHANDRAN  and
SANJAY MITTAL
T. K. PRASANTH
Affiliation:
Department of Aerospace Engineering, Indian Institute of Technology Kanpur, UP 208 016, India
V. PREMCHANDRAN
Affiliation:
Department of Aerospace Engineering, Indian Institute of Technology Kanpur, UP 208 016, India
SANJAY MITTAL*
Affiliation:
Department of Aerospace Engineering, Indian Institute of Technology Kanpur, UP 208 016, India
*
†Email address for correspondence: [email protected]
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Abstract

The hysteretic behaviour of a freely vibrating cylinder, near the low-Reynolds-number end of synchronization/lock-in, in the laminar regime is investigated. Computations are carried out using a stabilized finite-element method. The flow remains two-dimensional in this Reynolds number regime. This is verified via comparison of two- and three-dimensional computations. The cylinder is free to undergo crossflow as well as in-line vibrations. The combined effect of mass ratio (1 ≤ m* ≤ 100) and blockage (0.25% ≤ B ≤ 12.5%) is studied in detail. The existence of a critical mass ratio (m*cr = 10.11), below which hysteresis disappears for an unbounded flow situation, is identified. For higher mass ratio the hysteretic behaviour is observed for all blockage. However, the hysteresis loop width is found to vary with B; its variation with m* and B is studied. The concept of critical blockage Bcr is introduced. For B ≤ Bcr the response of the cylinder is virtually the same as that in an unbounded flow domain. The variation of Bcr with m* is investigated. Furthermore, Bcr is found to vary non-monotonically with m* for m* ≤ m*cr and is almost constant for m* ≥ 20. The effect of damping, as well as restricting the cylinder to undergo transverse vibrations only, on the hysteresis behaviour is studied. The transverse-only motion leads to a larger hysteresis loop width compared with the transverse and the in-line motion of the cylinder. An attempt is made to explain this by comparing the results from forced vibrations.

JFM classification

Vortex Flows: Vortex shedding Wakes/Jets: Vortex streets
Type
Papers
Information
Journal of Fluid Mechanics , Volume 671 , 25 March 2011 , pp. 207 - 225
Copyright
Copyright © Cambridge University Press 2011

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