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Aspect ratio-dependent hysteresis response of a heavy inverted flag

Published online by Cambridge University Press:  13 May 2022

Oluwafemi Ojo Open the ORCID record for Oluwafemi Ojo [Opens in a new window] ,
Yu-Cheng Wang ,
Alper Erturk Open the ORCID record for Alper Erturk [Opens in a new window]  and
Kourosh Shoele Open the ORCID record for Kourosh Shoele [Opens in a new window]
Oluwafemi Ojo
Affiliation:
Department of Mechanical Engineering, Joint College of Engineering, Florida A&M University-Florida State University, Tallahassee, FL 32310, USA
Yu-Cheng Wang
Affiliation:
G.W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA 30332, USA
Alper Erturk
Affiliation:
G.W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA 30332, USA
Kourosh Shoele*
Affiliation:
Department of Mechanical Engineering, Joint College of Engineering, Florida A&M University-Florida State University, Tallahassee, FL 32310, USA
*
†Email address for correspondence: kshoele@eng.famu.fsu.edu
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Abstract

The bistable fluttering response of heavy inverted flags with different aspect ratios ($AR$) is investigated to determine how the vortical structures affect the intermittent vibration response of the flag. A heavy inverted flag in a uniform flow may exhibit several response modes; amongst them are three major modes that occur over an extended velocity range: stationary, large-scale periodic oscillation and one-sided deflected modes. Significant hysteretic bistability is observed at the transition between these modes for all $AR$, which is notably different from the conventional flag vibration with a fixed leading edge and free trailing edge where no hysteresis is observed at the lower $AR$ limit ($AR<1$). The difference is associated with the distinct roles of vortices around the flag. Experiments with flags made of spring steel are conducted in a wind tunnel, where the flow speed is steadily increased and later decreased to obtain different oscillatory modes of the heavy inverted flags. The experimental results are used to validate the numerical model of the same problem. It is found that different critical velocities exist for increasing and decreasing flow velocities, and there is a sustained hysteresis for all $AR$ controlled by the initiation threshold and growth of the leading-edge and side-edge vortices. The effect of the vortices in the bistable oscillation regime is quantified by formulating a modal force partitioning approach. It is shown that $AR$ can significantly alter the static and dynamic vortex interaction with the flexible plate, thereby changing the flag's hysteresis behaviour and bistable response.

JFM classification

Aerodynamics: Flow-structure interactions Nonlinear Dynamical Systems: Bifurcation
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 942 , 10 July 2022 , A4
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Copyright
© The Author(s), 2022. Published by Cambridge University Press

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