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Direct numerical simulation of vortex synchronization due to small perturbations

Published online by Cambridge University Press:  26 August 2009

S. H. KIM ,
J. Y. PARK ,
N. PARK ,
J. H. BAE  and
J. Y. YOO
S. H. KIM
Affiliation:
School of Mechanical and Aerospace Engineering, Seoul National University, Seoul 151-744, Korea
J. Y. PARK
Affiliation:
Halla Climate Control Corporation, Daejeon 306-230, Korea
N. PARK
Affiliation:
Department of Aerospace Engineering and Mechanics, University of Minnesota, Minneapolis, MN 55455, USA
J. H. BAE
Affiliation:
Mechanical and Aerospace Engineering Department, University of California, Los Angeles, CA 90095-1597, USA
J. Y. YOO*
Affiliation:
School of Mechanical and Aerospace Engineering, Seoul National University, Seoul 151-744, Korea Institute of Advanced Machinery and Design, Seoul National University, Seoul 151-744, Korea
*
†Email address for correspondence: [email protected]
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Abstract

Direct numerical simulation (DNS) is performed to investigate the vortex synchronization phenomena in the wake behind a circular cylinder at the Reynolds numbers, Re = 220 (mode-A regime) and 360 (mode-B regime). To generate vortex synchronization, a sinusoidal streamwise velocity perturbation, the frequency of which is about twice the natural shedding frequency, is superimposed on the free stream velocity. At Re = 360, vortex synchronization occurs when the perturbation frequency is exactly twice the natural shedding frequency. However, at Re = 220, it does not occur when the same perturbation frequency condition is imposed. Instead, it occurs when the perturbation frequency is near twice the hypothetical two-dimensional laminar vortex shedding frequency as if there were no wake transition at Re = 220.

It is elucidated that, as a result of vortex synchronization, the trajectory of the Kármán vortices and the vortex structure are changed. The Kármán vortices are formed along the mean separating streamline slightly inside the mean wake bubble at Re = 220, but slightly outside at Re = 360. Thus, the Reynolds shear stress force has different contribution to the streamwise force balance of the mean wake bubble depending on the Reynolds numbers: its magnitude is negligible at Re = 220, compared to other force components, while it reverses its sign at Re = 360. More importantly, at Re = 220, the mode-A instability is suppressed into two-dimensional laminar flow with strong Kármań vortices. At Re = 360, the dominant instability mode changes from mode B to mode A.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 634 , 10 September 2009 , pp. 61 - 90
Copyright
Copyright © Cambridge University Press 2009

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