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The formation of vortex rings in a strongly forced round jet

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Abstract

The periodic formation of vortex rings in the developing region of a round jet subjected to high-amplitude acoustic forcing is investigated with High-Speed Particle Image Velocimetry. Harmonic velocity oscillations ranging from 20 to 120% of the mean exit velocity of the jet was achieved at several forcing frequencies determined by the acoustic response of the system. The time-resolved history of the formation process and circulation of the vortex rings are evaluated as a function of the forcing conditions. Overall, high-amplitude forcing causes the shear layers of the jet to breakup into a train of large-scale vortex rings, which share many of the features of starting jets. Features of the jet breakup such as the roll-up location and vortex size were found to be both amplitude and frequency dependent. A limiting time-scale of t/T ≈ 0.33 based on the normalized forcing period was found to restrict the growth of a vortex ring in terms of its circulation for any given arrangement of jet forcing conditions. In sinusoidally forced jets, this time-scale corresponds to a kinematic constraint where the translational velocity of the vortex ring exceeds the shear layer velocity that imposes pinch-off. This kinematic constraint results from the change in sign in the jet acceleration between t = 0 and t = 0.33T. However, some vortex rings were observed to pinch-off before t = 0.33T suggesting that they had acquired their maximum circulation. By invoking the slug model approximations and defining the slug parameters based on the experimentally obtained time- and length-scales, an analytical model based on the slug and ring energies revealed that the formation number for a sinusoidally forced jet is L/D ≈ 4 in agreement with the results of Gharib et al. (J Fluid Mech 360:121–140, 1998).

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Acknowledgments

Dr James Dawson is indebted to Dr Tim Nickels for his many suggestions and helpful discussions on vortex rings related problems, he will be sorely missed. Dr James Dawson is supported by EPSRC under the Advanced Research Fellowship scheme.

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  1. Department of Engineering, University of Cambridge, Trumpington Street, Cambridge, CB2 1PZ, UK

    E. Aydemir, N. A. Worth & J. R. Dawson

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  1. E. Aydemir
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  2. N. A. Worth
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  3. J. R. Dawson
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Correspondence to J. R. Dawson.

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Aydemir, E., Worth, N.A. & Dawson, J.R. The formation of vortex rings in a strongly forced round jet. Exp Fluids 52, 729–742 (2012). https://doi.org/10.1007/s00348-011-1110-6

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  • DOI: https://doi.org/10.1007/s00348-011-1110-6

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