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Formation mechanism of hairpin vortices in the wake of a truncated square cylinder in a duct

Published online by Cambridge University Press:  19 March 2010

VINCENT DOUSSET  and
ALBAN POTHÉRAT
VINCENT DOUSSET*
Affiliation:
Applied Mathematics Research Centre, Faculty of Engineering and Computing, Coventry University, Priory Street, Coventry CV1 5FB, UK
ALBAN POTHÉRAT
Affiliation:
Applied Mathematics Research Centre, Faculty of Engineering and Computing, Coventry University, Priory Street, Coventry CV1 5FB, UK
*
†Email address for correspondence: [email protected]
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Abstract

We investigate the laminar shedding of hairpin vortices in the wake of a truncated square cylinder placed in a duct, for Reynolds numbers around the critical threshold of the onset of vortex shedding. We single out the formation mechanism of the hairpin vortices by means of a detailed analysis of the flow patterns in the steady regime. We show that unlike in previous studies of similar structures, the dynamics of the hairpin vortices are entwined with that of the counter-rotating pair of streamwise vortices, which we found to be generated in the bottom part of the near wake (these are usually referred to as ‘base vortices’). In particular, once the hairpin structure is released, the base vortices attach to it, forming its legs, so these are streamwise, and not spanwise as previously observed in unconfined wakes or behind cylinders of lower aspect ratios. We also single out a trail of Ω-shaped vortices, generated between successive hairpin vortices through a mechanism that is analogous to that active in near-wall turbulence. Finally, we show how the dynamics of the structures we identified determine the evolution of the drag coefficients and Strouhal numbers when the Reynolds number varies.

JFM classification

Wakes/Jets: Shear layers Vortex Flows: Vortex shedding Wakes/Jets: Wakes
Type
Papers
Information
Journal of Fluid Mechanics , Volume 653 , 25 June 2010 , pp. 519 - 536
Copyright
Copyright © Cambridge University Press 2010

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References

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Dousset and Potherat supplementary movie

Movie 1. Animation exhibiting the shedding of regular harpin vortices at $Re=200$. Isocontours of vorticity: blue and red colours depict the lateral free shear layers, cyan and yellow the streamwise vortices and green the free shear layer stretching from the cylinder upper face. The formation mechanism of the hairpin vortices is the following: under their mutual interaction, the streamwise vortices lift up the tail of the top free shear layer, which turns unstable and shed. Two secondary streamwise vortices appear upstream the primary ones and wrap around the latter. The subsequent pairing between both primary and secondary streamwise vortices eventually causes the symmetric shedding of structures from both lateral free shear layers. The hairpin vortex is then formed and carried downstream by the free stream. Its legs are the extensions of the primary streamwise vortices. Three shedding periods are shown in this movie.

Download Dousset and Potherat supplementary movie(Video)
Video 1.7 MB