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Technical Briefs

On Approximating the Translational Velocity of Vortex Rings

[+] Author and Article Information
Michael Krieg

Department of Mechanical and Aerospace Engineering,
University of Florida,
Gainesville, FL 32611

Kamran Mohseni

Department of Mechanical and Aerospace Engineering,
Department of Computer and Electrical Engineering,
Institute for Networked Autonomous Systems,
University of Florida, Gainesville, FL 32611
e-mail: mohseni@ufl.edu

1Corresponding author.

Contributed by the Fluids Engineering Division of ASME for publication in the Journal of Fluids Engineering. Manuscript received December 17, 2012; final manuscript received August 13, 2013; published online September 19, 2013. Assoc. Editor: Peter Vorobieff.

J. Fluids Eng 135(12), 124501 (Sep 19, 2013) (6 pages) Paper No: FE-12-1636; doi: 10.1115/1.4025287 History: Received December 17, 2012; Revised August 13, 2013

A method is presented whereby the translational velocity of a vortex ring can be approximated from the total circulation, impulse, and kinetic energy of the vortex system. Assuming a uniform vorticity density, these bulk quantities define a unique stable vortex ring configuration, and the translational velocity can be inferred from this configuration and the system scaling. Here, the accuracy of this approximation is presented for vortex rings formed from starting jets, and the translational velocity is also characterized as it relates to the driving parameters. The translational velocity is well approximated for a wide range of experimentally generated vortex rings. It is observed that starting jets with a converging radial velocity create vortex rings with a significantly higher translational velocity. The converging radial velocity was observed to increase translational velocity by as much as 30% over parallel jet flows with identical volume flux and nozzle diameter, but the exact increase is specific to the nozzle arrangement and driving conditions.

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References

Figures

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Fig. 1

Layout of a typical vortex ring created from a starting jet and coordinate system of the problem

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Fig. 2

Dimensionless energy and circulation for the Norbury family of vortices [17] are shown (a) with respect to mean core radius ɛ and (b) with respect to each other

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Fig. 3

Conceptual diagram of the layout of different nozzles used to generate various jet flows for this experiment

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Fig. 4

Testing environment; (a) schematic diagram and (b) actual layout. Tank is approximately 1 m × 1.3 m × 2.4 m.

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Fig. 5

Vortex ring translational velocity and piston velocity versus formation time, t*, for (a) case 1, (b) case 3, (c) case 2, and (d) case 4, as summarized in Table 1

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