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Intrinsic features of flow-induced stability of a square cylinder

Published online by Cambridge University Press:  24 July 2024

Cuiting Lin Open the ORCID record for Cuiting Lin [Opens in a new window]  and
Md. Mahbub Alam Open the ORCID record for Md. Mahbub Alam [Opens in a new window]
Cuiting Lin
Affiliation:
Center for Turbulence Control, Harbin Institute of Technology (Shenzhen), Shenzhen 518055, China
Md. Mahbub Alam*
Affiliation:
Center for Turbulence Control, Harbin Institute of Technology (Shenzhen), Shenzhen 518055, China
*
†Email address for correspondence: [email protected], [email protected]
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Abstract

Vortex-induced vibrations and galloping of an elastically mounted square cylinder are investigated for cylinder mass ratio m* = 2–50, damping ratio ζ = 0–1.0, mass-damping ratio m*ζ = 0–50 and flow reduced velocity Ur = 1–80. We home in on the effects of m*, ζ, m*ζ, $({m^\ast } + m_{a\textrm{0}}^\ast )\zeta$ and $({m^\ast } + m_{ae}^\ast )\zeta$ on the critical reduced velocity Urc marking the onset of galloping, where $m_{a\textrm{0}}^\ast $ is the quiescent-fluid added mass ratio and $m_{ae}^\ast $ is the effective added mass ratio. Vibration responses, forces, vibration frequencies and added mass ratios are studied and discussed. The different branches of vortex-induced vibrations have different dependencies of $m_{ae}^\ast $ on Ur. The $m_{ae}^\ast $ in the initial branch is positive and drops rapidly with Ur, but that in the lower branch is negative and declines gently. In the galloping regime, $m_{ae}^\ast $ jumps from negative to positive at the onset of galloping, declining slightly with increasing Ur. Our results and prediction equations show that when ζ = 0, Urc is independent of m* for m* ≥ 5, albeit slightly higher for m* = 3. The latter is ascribed to mode competition. When ζ > 0, Urc linearly increases with increasing ζ. Detailed analysis substantiates that m*ζ or $({m^\ast } + m_{a\textrm{0}}^\ast )\zeta$ does not serve as the unique criterion to predict the galloping occurrence. Here, we propose a new combined mass-damping parameter $({m^\ast } + m_{ae}^\ast )\zeta$ in the relationship between galloping onsets and structural properties, which successfully scales all data of Urc at different m* and ζ values.

JFM classification

Vortex Flows: Vortex shedding
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 988 , 10 June 2024 , A50
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Copyright
© The Author(s), 2024. Published by Cambridge University Press

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