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Flow-induced motions of flexible plates: fluttering, twisting and orbital modes

Published online by Cambridge University Press:  07 February 2019

Yaqing Jin ,
Jin-Tae Kim ,
Shifeng Fu  and
Leonardo P. Chamorro Open the ORCID record for Leonardo P. Chamorro [Opens in a new window]
Yaqing Jin
Affiliation:
Mechanical Science and Engineering Department, University of Illinois, Urbana, IL 61801, USA
Jin-Tae Kim
Affiliation:
Mechanical Science and Engineering Department, University of Illinois, Urbana, IL 61801, USA
Shifeng Fu
Affiliation:
Mechanical Science and Engineering Department, University of Illinois, Urbana, IL 61801, USA College of Water Conservancy and Hydropower Engineering, Hohai University, Nanjing 210024, China
Leonardo P. Chamorro*
Affiliation:
Mechanical Science and Engineering Department, University of Illinois, Urbana, IL 61801, USA Civil and Environmental Engineering Department, University of Illinois, Urbana, IL 61801, USA Aerospace Engineering Department, University of Illinois, Urbana, IL 61801, USA
*
†Email address for correspondence: lpchamo@illinois.edu
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Abstract

The unsteady dynamics of wall-mounted flexible plates under inclined flows was fundamentally described using theoretical arguments and experiments under various Cauchy numbers $Ca=\unicode[STIX]{x1D70C}_{f}bL^{3}U_{0}^{2}/(EI)\in [7,81]$ (where $\unicode[STIX]{x1D70C}_{f}$ is the fluid density, $b$ and $L$ are the plate width and length, $U_{0}$ is the incoming velocity, $E$ is Young’s modulus and $I$ is the second moment of the area) and inclination angles $\unicode[STIX]{x1D6FC}$. Three-dimensional particle tracking velocimetry and a high-resolution force sensor were used to characterize the evolution of the plate dynamics and aerodynamic force. We show the existence of three distinctive, dominant modes of tip oscillations, which are modulated by the structure dynamic and flow instability. The first mode is characterized by small-amplitude, planar fluttering-like motions occurring under a critical Cauchy number, $Ca=Ca_{c}$. Past this condition, the motions are dominated by the second mode consisting of unsteady twisting superimposed onto the fluttering patterns. The onset of this mode is characterized by a sharp increase of the force fluctuation intensity. At sufficiently high $Ca$ and $\unicode[STIX]{x1D6FC}$, the plate may undergo a third mode given by large-scale tip orbits about the mean bending. Using the equation of motion and first-order approximations, we propose a formulation to estimate $Ca_{c}$ as a function of $\unicode[STIX]{x1D6FC}$; it exhibits solid agreement with experiments.

Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 864 , 10 April 2019 , pp. 273 - 285
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Copyright
© 2019 Cambridge University Press 

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Jin et al. supplementary movie 1

Raw video illustrating small-amplitude fluttering. This sample movie is played 8x slower.

Download Jin et al. supplementary movie 1(Video)
Video 2.9 MB

Jin et al. supplementary movie 2

Raw video illustrating twisting oscillations. This sample movie is played 8x slower.

Download Jin et al. supplementary movie 2(Video)
Video 2.9 MB

Jin et al. supplementary movie 3

Raw video illustrating large-scale orbital motions. This sample movie is played 8x slower.

Download Jin et al. supplementary movie 3(Video)
Video 2.9 MB