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Influence of aspect ratio on the dynamics of a freely moving circular disk

Published online by Cambridge University Press:  02 June 2010

A. R. SHENOY  and
C. KLEINSTREUER
A. R. SHENOY*
Affiliation:
Department of Mathematics, University of North Carolina at Chapel Hill, Chapel Hill, NC 27599-3250, USA
C. KLEINSTREUER
Affiliation:
Department of Mechanical and Aerospace Engineering, North Carolina State University, Raleigh, NC 27695-7910, USA
*
†Email address for correspondence: akshenoy@yahoo.com
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Abstract

The influence of aspect ratio (χ = diameter/thickness) on the vortex shedding behaviour of fixed, and freely moving, circular disk has been investigated numerically. The aspect ratio significantly changes the structure of the vortices shed from the disk, thus altering the fluid induced forces. Disks of χ = 2 and 4 were selected, and by choosing Re = 240 periodic behaviour was observed for both the ‘fixed’ and ‘freely’ moving disks. First, the vortex structures shed from a ‘fixed’ circular disk of χ = 2 and 4 were computed for Re = 240. This was followed by a computation of their trajectories falling ‘freely’ under the action of gravity at Re = 240. For the ‘fixed’ disk of χ = 2, periodic shedding of one-sided hairpin-shaped vortex loops was observed. The flow field had a spatial planar symmetry and the vortices were shed from the same location, resulting in an asymmetric lateral force on the disk. The Strouhal number (St), calculated using the fluctuation in the axial velocity in the far-wake, was 0.122. This vortex shedding behaviour is referred to as the ‘single-sided’ vortex shedding mode. For the ‘fixed’ disk of χ = 4, periodic shedding of hairpin-shaped vortex loops was observed from the diametrically opposite location of the disk. The flow field had a spatial planar symmetry, and also a spatio-temporal one, with respect to a plane orthogonal to the spatial symmetry plane. The shed vortices induced a symmetric lateral force on the disk with a zero mean. The computed Strouhal number, was equal 0.122, same as that for χ = 2. This vortex shedding behaviour is referred as the ‘double-sided’ vortex shedding mode. For the ‘freely falling’ disk of χ = 2, an oscillatory motion was observed in a plane with a 83° phase lag between the lateral and angular velocity. The Strouhal number (Stb), calculated using the oscillation frequency of the ‘freely’ falling disk was equal to 0.116, which is comparable to the St of the fixed disk. For a ‘freely falling’ disk of χ = 4, oscillatory motion was observed in a plane with a 21° phase lag between the lateral and angular velocity. The Strouhal number (Stb) was equal to 0.171, which differs from the St observed in the wake of the fixed disk.

JFM classification

Aerodynamics: Flow-structure interactions Vortex Flows: Vortex shedding
Type
Papers
Information
Journal of Fluid Mechanics , Volume 653 , 25 June 2010 , pp. 463 - 487
Copyright
Copyright © Cambridge University Press 2010

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Shenoy and Kleinstreuer supplementary movie

Movie 1. Single-sided vortex shedding observed behind a disk of aspect ratio=2 at Re=240 (free-stream oriented along the positive z-direction).

Download Shenoy and Kleinstreuer supplementary movie(Video)
Video 4.6 MB

Shenoy and Kleinstreuer supplementary movie

Movie 2. Double-sided vortex shedding observed behind a disk of aspect ratio=4 at Re=240 (free-stream oriented along the positive z-direction).

Download Shenoy and Kleinstreuer supplementary movie(Video)
Video 3.4 MB

Shenoy and Kleinstreuer supplementary movie

Movie 3. Single-sided vortex shedding observed behind a disk of aspect ratio=2 at Re=240 using azimuthal vorticity contours on the symmetry plane (free-stream oriented along the positive z-direction).

Download Shenoy and Kleinstreuer supplementary movie(Video)
Video 2.7 MB

Shenoy and Kleinstreuer supplementary movie

Movie 4. Double-sided vortex shedding observed behind a disk of aspect ratio=4 at Re=240 using azimuthal vorticity contours on the symmetry plane (free-stream oriented along the positive z-direction).

Download Shenoy and Kleinstreuer supplementary movie(Video)
Video 2.1 MB

Shenoy and Kleinstreuer supplementary movie

Movie 5. Vortex structures behind a freely falling disk, along the negative z-direction, of aspect ratio=2 at Re=240 .

Download Shenoy and Kleinstreuer supplementary movie(Video)
Video 1.1 MB

Shenoy and Kleinstreuer supplementary movie

Movie 6. Vortex structures behind a freely falling disk, along the negative z-direction, of aspect ratio=4 at Re=240.

Download Shenoy and Kleinstreuer supplementary movie(Video)
Video 1.5 MB