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Development of the wake behind a circular cylinder impulsively started into rotatory and rectilinear motion

Published online by Cambridge University Press:  26 April 2006

Yen-Ming Chen ,
Yuh-Roung Ou  and
Arne J. Pearlstein
Yen-Ming Chen
Affiliation:
NASA-Langley Research Center, Hampton, VA 23665, USA Present Address: General Electric Aircraft Engines, 1 Neumann Way, Cincinnati, OH 45215, USA.
Yuh-Roung Ou
Affiliation:
Institute for Computer Applications in Science and Engineering, NASA-Langley Research Center, Hampton, VA 23665, USA Present Address: Interdisciplinary Center for Applied Mathematics, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061, USA.
Arne J. Pearlstein
Affiliation:
Department of Mechanical and Industrial Engineering, University of Illinois at Urbana-Champaign, 1206 West Green Street, Urbana, IL 61801, USA
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Abstract

The temporal development of two-dimensional viscous incompressible flow generated by a circular cylinder impulsively started into steady rotatory and rectilinear motion at Re = 200 (based on the cylinder diameter 2a and the magnitude U of the rectilinear velocity) is studied computationally. We use an explicit finite-difference/pseudospectral technique and a new implementation of the Biot–Savart law to integrate a velocity/vorticity formulation of the Navier–Stokes equations. Results are presented for the four angular: rectilinear speed ratios α = Ωa/U (where Ω is the angular speed) considered experimentally by Coutanceau & Ménard (1985). For α ≤ 1, extension of the computations to dimensionless times larger than achieved either in the experimental work or in the computations of Badr & Dennis (1985) allows for a more complete discussion of the temporal development of the wake. Using the frame-invariant vorticity distribution, we discuss several aspects of the vortex kinematics and dynamics not revealed by the earlier work, in which vortex cores were identified from frame-dependent streamline and streamfunction information. Consideration of the flow in the absence of sidewalls confirms the artifactual nature of the trajectory of the first vortex reported by Coutanceau & Ménard for α = 3.25. For α greater than unity (the largest value considered by Badr & Dennis), our results indicate that at Re = 200 shedding of more than one vortex does indeed occur for α = 3.25 (and possibly for larger α), in contrast to the conclusion of Coutanceau & Ménard. Moreover, the shedding process is very different from that associated with the usual Kármán vortex street for α = 0. Specifically, consecutive vortices can be shed from one side of the cylinder and be of the same sense, in contrast to the non-rotating case, in which mirror-image vortices of opposite sense are shed alternately from opposite sides of the cylinder. The results are discussed in relation to the possibility of suppressing vortex shedding by open- or closed-loop control of the rotation rate.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 253 , August 1993 , pp. 449 - 484
Copyright
© 1993 Cambridge University Press

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