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The role of wake stiffness on the wake-induced vibration of the downstream cylinder of a tandem pair

Published online by Cambridge University Press:  08 February 2013

G. R. S. Assi ,
P. W. Bearman ,
B. S. Carmo ,
J. R. Meneghini ,
S. J. Sherwin  and
R. H. J. Willden
G. R. S. Assi
Affiliation:
Department of Naval Architecture and Ocean Engineering, University of São Paulo, São Paulo, 05508-030, Brazil
P. W. Bearman
Affiliation:
Department of Aeronautics, Imperial College, London SW7 2AZ, UK
B. S. Carmo
Affiliation:
Department of Mechanical Engineering, University of São Paulo, São Paulo, 05508-030, Brazil
J. R. Meneghini
Affiliation:
Department of Mechanical Engineering, University of São Paulo, São Paulo, 05508-030, Brazil
S. J. Sherwin
Affiliation:
Department of Aeronautics, Imperial College, London SW7 2AZ, UK
R. H. J. Willden
Affiliation:
Department of Engineering Science, University of Oxford, Oxford OX1 3PJ, UK
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Abstract

When a pair of tandem cylinders is immersed in a flow the downstream cylinder can be excited into wake-induced vibrations (WIV) due to the interaction with vortices coming from the upstream cylinder. Assi, Bearman & Meneghini (J. Fluid Mech., vol. 661, 2010, pp. 365–401) concluded that the WIV excitation mechanism has its origin in the unsteady vortex–structure interaction encountered by the cylinder as it oscillates across the wake. In the present paper we investigate how the cylinder responds to that excitation, characterising the amplitude and frequency of response and its dependency on other parameters of the system. We introduce the concept of wake stiffness, a fluid dynamic effect that can be associated, to a first approximation, with a linear spring with stiffness proportional to $\mathit{Re}$ and to the steady lift force occurring for staggered cylinders. By a series of experiments with a cylinder mounted on a base without springs we verify that such wake stiffness is not only strong enough to sustain oscillatory motion, but can also dominate over the structural stiffness of the system. We conclude that while unsteady vortex–structure interactions provide the energy input to sustain the vibrations, it is the wake stiffness phenomenon that defines the character of the WIV response.

JFM classification

Aerodynamics: Flow-structure interactions Wakes/Jets: Vortex streets Wakes/Jets: Wakes/Jets
Type
Papers
Information
Journal of Fluid Mechanics , Volume 718 , 10 March 2013 , pp. 210 - 245
Copyright
©2013 Cambridge University Press

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