Vortex Rings

Lim, T. T.; Nickels, T. B.

doi:10.1007/978-94-011-0249-0_4

Cited by 134 publications

(102 citation statements)

References 72 publications

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“…Finally, one ring was approximated by the set of 12,100 vector vorticity particles. At first we tried to reproduce the leap-frogging ("vortex game") phenomenon [7,11,14]. When two co-axial vortex rings are made to travel in the same direction the velocity field induced by the second ring will cause the first ring to contract and accelerate.…”

Section: Numerical Resultsmentioning

confidence: 99%

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Vorticity Particle Method for Simulation of 3D Flow

Kudela

Regucki

2004

Computational Science - ICCS 2004

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Abstract. The vortex-in-cell method for three-dimensional, viscous flow was presented. A viscous splitting algorithm was used. Initially the Euler inviscid equation was solved. Following that, the viscous effect was taken into account by the solution of the diffusion equation. The diffusion equation was then solved by the particle strength exchange (PSE) method. Validation of the method was tested by simulation of the leapfrogging phenomenon for two vortex rings moving along a common axis of symmetry and the reconnection phenomenon of two colliding vortex rings for viscous flow.

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Section: Numerical Resultsmentioning

confidence: 99%

“…In this case we assume that the flow is inviscid. It is known that the "vortex game" is relatively difficult to repeat experimentally [7]. This is due to the fact that it is very sensitive in regard to the initial positions of the rings and their parameters.…”

Section: Numerical Resultsmentioning

confidence: 99%

Vorticity Particle Method for Simulation of 3D Flow

Kudela

Regucki

2004

Computational Science - ICCS 2004

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“…Shariff & Leonard 1992;Lim & Nickels 1995). In the case of classical vortex rings generated in liquids (e.g.…”

Section: Theory Versus Experimentsmentioning

confidence: 99%

“…The importance of vortex rings was emphasized by Saffman (1992) who wrote, 'This commonly known phenomenon exemplifies the whole range of problems of vortex motion'. The properties of the vortex rings have been studied for over a century both theoretically and experimentally (Helmholtz 1858;Lamb 1932;Phillips 1956;Norbury 1973;Kambe & Oshima 1975;Saffman 1992;Shariff & Leonard 1992;Lim & Nickels 1995). Recent developments on the modelling side include Stanaway, Cantwell & Spalart (1988), Rott & Cantwell (1993a, b), Mohseni & Gharib (1998), Kaplanski & Rudi (1999, 2005, Fukumoto & Moffatt (2000), Shusser & Gharib (2000), Mohseni (2001Mohseni ( , 2006, Linden & Turner (2001) and Fukumoto & Kaplanski (2008).…”

Section: Introductionmentioning

confidence: 99%

A generalized vortex ring model

et al. 2009

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A conventional laminar vortex ring model is generalized by assuming that the time dependence of the vortex ring thickness is given by the relation = a t b , where a is a positive number and 1/4 6 b 6 1/2. In the case in which a = √ 2ν, where ν is the laminar kinematic viscosity, and b = 1/2, the predictions of the generalized model are identical with the predictions of the conventional laminar model. In the case of b = 1/4 some of its predictions are similar to the turbulent vortex ring models, assuming that the time-dependent effective turbulent viscosity ν * is equal to . This generalization is performed both in the case of a fixed vortex ring radius R 0 and increasing vortex ring radius. In the latter case, the so-called second Saffman's formula is modified. In the case of fixed R 0 , the predicted vorticity distribution for short times shows a close agreement with a Gaussian form for all b and compares favourably with available experimental data. The time evolution of the location of the region of maximal vorticity and the region in which the velocity of the fluid in the frame of reference moving with the vortex ring centroid is equal to zero is analysed. It is noted that the locations of both regions depend upon b, the latter region being always further away from the vortex axis than the first one. It is shown that the axial velocities of the fluid in the first region are always greater than the axial velocities in the second region. Both velocities depend strongly upon b. Although the radial component of velocity in both of these regions is equal to zero, the location of both of these regions changes with time. This leads to the introduction of an effective radial velocity component; the latter case depends upon b. The predictions of the model are compared with the results of experimental measurements of vortex ring parameters reported in the literature.

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“…Because the vortex ring remained attached to the shear layer, the rear boundary of the ring was not easily distinguishable. However, isolated laminar vortex rings are known from How visualisation experiments to exhibit high degrees of fore-aft symmetry (Lim & Nickels 1995). Therefore, we reflected the contour shapes obtained for the front half of the vortex about the core centreline, and constructed the symmetric core shown in figure 1 0. A comparison of the distributions of~ and w along the centreline of the vortex core in the experimental and model vortex rings is shown in figure 11 .…”

Section: The Construction Of Piecewise-linear Models For Axisymmetricmentioning

confidence: 99%

Nested contour dynamics models for axisymmetric vortex rings and vortex wakes

O’Farrell

Dabiri

2014

J. Fluid Mech.

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Inviscid models for vortex rings and dipoles are constructed using nested patches of vorticity. These models constitute more rcalislic approximations to experimcncal vortex rings and dipoles than the single-contour models of Norbury and Pierrehumbert, and nested contour dynamics algorithms allow their simulation with low computational cost. In two dimensions, nested-contour models for the analytical Lamb dipole are constructed. In the axisymmetric case, a family of models for vortex rings generated by a piston-cylinder apparatus at different stroke ratios is constructed from experimental data. The perturbation response of this family is considered by the introduction of a small region of vorticity at the rear of the vortex, which mimics the addition of circulation to a growing vortex ring by a feeding shear layer. Model vortex rings are found to either accept the additional circu lation or shed vorticity into a tail, depending on the perturbation size. A change in the behaviour of the model vortex rings is identified at a stroke ratio of three, when it is found that the maximum relative perturbation size vortex rings can accept becomes approximately constant. We hypothesise that this change in response is related to p inch-off, and that pinch-off might be understood and predicted based on the perturbation responses of model vortex rings. In particu lar, we suggest that a perturbation response-based framework can be useful in understanding vortex formation in biological flows.

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Vortex Rings

Cited by 134 publications

References 72 publications

Vorticity Particle Method for Simulation of 3D Flow

Vorticity Particle Method for Simulation of 3D Flow

A generalized vortex ring model

Nested contour dynamics models for axisymmetric vortex rings and vortex wakes

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