Slowing of vortex rings by development of Kelvin waves

Hershberger, Robert E.; Bolster, Diogo; Donnelly, Russell J.

doi:10.1103/physreve.82.036309

Cited by 7 publications

(8 citation statements)

References 23 publications

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“…The drag force on the vortex ring is F d = C d qpD VR aV 2 , where the hydrodynamic drag coefficient, C d , incorporates the dependence on the confinement ratio (the ratio of the diameter of the vortex ring to the diameter of confinement domain, D VR /D), represented by the unknown function g D VR D À Á . This suggested drag force on the vortex ring has the similar functional form but a different prefactor to the drag force proposed by Hershberger et al (2010) and Sullivan et al (2008)…”

Section: Methodsmentioning

confidence: 78%

The decay of confined vortex rings

et al. 2012

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Vortex rings are produced during the ejection of fluid through a nozzle or orifice, which occurs in a wide range of biological conditions such as blood flow through the valves of the heart or through arterial constrictions. Confined vortex ring dynamics, such as these, have not been previously studied despite their occurrence within the biological flow conditions mentioned. In this work, we investigate laminar vortex rings using particle image velocimetry and develop a new semi-empirical model for the evolution of vortex ring circulation subject to confinement. Here we introduce a decay parameter b which exponentially grows with increasing vortex ring confinement ratio, the ratio of the vortex ring diameter (D VR ) to the confinement diameter (D), with the relationship b ¼ 4:38 expð9:5D VR =DÞ; resulting in a corresponding increase in the rate of vortex ring circulation decay. This work enables the prediction of circulation decay rate based on confinement, which is important to understanding naturally occurring confined vortex ring dynamics.

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Section: Methodsmentioning

confidence: 78%

The decay of confined vortex rings

et al. 2012

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“…Once impressed on the sharp pin (5), the balloon burst and a vortex ring bubble was produced; a hypodermic needle with outer diameter of 0.4 mm was chosen as the pin. Similar to Hershberger et al (2010), all the experimental data were obtained photographically. Three cameras (6-8) with speed of 60 f.p.s.…”

Section: The Experimentsmentioning

confidence: 99%

“…According to the literature (e.g. Walker et al 1987;Sullivan et al 2008;Hershberger, Bolster & Donnelly 2010;Gan, Dawson & Nickels 2012) the common technique for the generation of a vortex ring bubble is the rapid ejection of fluid into a water tank through an orifice exit. In other words, the initial source of energy is kinetic, whereas the vortex ring bubbles studied herein are powered by the potential energy initially stored in the underwater balloons.…”

Section: Introductionmentioning

confidence: 99%

A balloon bursting underwater

2015

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A buoyant vortex ring produced by an underwater bursting balloon was studied experimentally. The effect of dimensionless surface tension on characteristics including rise velocity, rate of expansion, circulation, trajectory, and lifetime of the vortex ring bubble was investigated. Results showed reasonable agreement with the literature on vortex rings produced by conventional approaches. It was observed that as the dimensionless surface tension increased, the rise velocity, the circulation and consequently the stability of the vortex ring bubble increased; however, the rate of expansion tends toward constant values. A semi-analytical model is proposed by modifying the drag-based model presented by Sullivan et al. (J. Fluid Mech., vol. 609, 2008, pp. 319-347) to make it applicable to buoyant vortex rings. The modified model suggests that the vortex ring expansion is essentially due to the buoyancy force. An expression is also derived for the circulation in terms of the initial volume of the balloon and the depth at which the balloon bursts.

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“…We have taken many photographs of vortex rings with equipment Krutzsch could not even dream of having (e.g. [10,11]). Ours are no better, and often perhaps inferior.…”

mentioning

confidence: 99%

“…Krutzsch used some clever tricks such as dropping a mirror behind a ring so that it can be photographed in motion. We recently employed this very technique to produce the pictures published in [11]. When reading the paper, the amount of work, patience and effort on Krutzsch's part to obtain these high quality images and data is evident.…”

mentioning

confidence: 99%

An appreciation of the 1939 paper “On an experimentally observed phenomenon on vortex rings ...” by Carl‐Heinz Krutzsch

2011

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Why then do we feel that this paper, now over 70 years old, is still worth reading? The first thing we notice, of course, is the subject matter. Vortex rings have been a subject of great fascination to fluid dynamicists for a very long time, dating back to Reynolds in 1876 [1] or even earlier to Rogers in 1858 [2], the founder of MIT. This initial interest is in part due to Lord Kelvin's idea that such rings were a model of atoms [3] (at the time Lord Kelvin was Sir William Thomson). Like many subjects in fluid mechanics, it is one where interest in the community has been up and down, but it is one in which there has always been interest. They are visually stunning phenomena, which can capture even lay peoples' interest. From a scientific perspective they pose many interesting and theoretically challenging questions. This paper was perhaps the first to study wave motion on the vortex core and to attempt to describe the initial roll-up of the fluid exiting the gun.A quick search in recent literature highlights the importance of vortex rings in the natural and manufactured world, ranging from fish swimming [4] and inter-fish communication [5] to insect flight [6] to manufactured jet propulsion [7] or robotics problems [8]. The beauty, complexity and universality of vortex rings is perhaps best summarized in the oft-quoted words of the late Phillip Saffman (1981) [9]: "One particular motion exemplifies the whole range of problems of vortex motion and is also a commonly known phenomenon, namely the vortex ring... Their formation is a problem of vortex sheet dynamics, the steady state is a problem of existence, their duration is a problem of stability, and if there are several we have a problem of vortex interactions."The second thing we would like to highlight from the Krutzsch paper is the exceptionally fine quality of the photographs. As with any good scientific paper, the high quality images convey much of the information in the article, which we believe gave rise to its interest by the scientific community despite any challenges *

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Slowing of vortex rings by development of Kelvin waves

Cited by 7 publications

References 23 publications

The decay of confined vortex rings

The decay of confined vortex rings

A balloon bursting underwater

An appreciation of the 1939 paper “On an experimentally observed phenomenon on vortex rings ...” by Carl‐Heinz Krutzsch

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