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On the origin of the secondary vortex street

Published online by Cambridge University Press:  24 September 2012

Bhaskar Kumar  and
Sanjay Mittal
Bhaskar Kumar
Affiliation:
Department of Mechanical Engineering, Indian Institute of Technology Hyderabad, AP 502205, India
Sanjay Mittal*
Affiliation:
Department of Aerospace Engineering, Indian Institute of Technology Kanpur, UP 208 016, India
*
†Email address for correspondence: smittal@iitk.ac.in
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Abstract

The origin of the secondary vortex street, observed in the far wake in the flow past a circular cylinder, is investigated. The Reynolds number, based on the diameter of the cylinder, is 150. The von Kármán vortex street, which originates in the near wake, decays exponentially downstream of the cylinder. Beyond the region of decay, a broad band of frequencies are selectively amplified, leading to the formation of a secondary vortex street consisting of packets of large-scale vortex structures. The streamwise location of the onset of the instability, frequency of the generation of packets and their convection speed are estimated via direct numerical simulation (DNS). Global linear stability analysis of the time-averaged flow reveals the presence of unstable convective modes that travel at almost the same speed and have a structure similar to the packet-like disturbances as observed in the DNS. Sensitivity analysis of the global convective modes to structural perturbations is carried out to locate the region of the wake that is most significant in generating the modes responsible for the appearance of the secondary vortex street. This information is utilized to control the flow. By placing a ‘slip’ splitter plate along the wake centre line, in the overlap region of the direct and the adjoint modes, the oscillations in the far wake are significantly reduced, though the oscillations related to the primary vortex shedding in the near wake are not. It is also found that suppression of the primary vortex shedding leads to annihilation of the secondary vortex street as well. Linear stability analysis of the steady-state flow does not yield any modes that can explain the appearance of the secondary vortex street. The steady and time-averaged wake profiles, for the flow, are compared to bring out the differences in the two. The effect of free-stream oscillations on the evolution of the secondary vortex street is investigated. By reducing the amplitude of inlet excitation, a gradual transition from ordered shedding in the far wake to the appearance of a broad-band spectrum of frequencies, as in the unforced wake, is observed. All the computations have been carried out using a stabilized finite element method.

JFM classification

Instability: Absolute/convective instability Flow Control: Instability control Wakes/Jets: Vortex streets
Type
Papers
Information
Journal of Fluid Mechanics , Volume 711 , 25 November 2012 , pp. 641 - 666
Copyright
Copyright © Cambridge University Press 2012

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