3 results
A model for confined vortex rings with elliptical-core vorticity distribution
- Ionut Danaila, Felix Kaplanski, Sergei S. Sazhin
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- Journal:
- Journal of Fluid Mechanics / Volume 811 / 25 January 2017
- Published online by Cambridge University Press:
- 07 December 2016, pp. 67-94
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We present a new model for an axisymmetric vortex ring confined in a tube. The model takes into account the elliptical (elongated) shape of the vortex ring core and thus extends our previous model (Danaila et al. J. Fluid Mech., vol. 774, 2015, pp. 267–297) derived for vortex rings with quasi-circular cores. The new model offers a more accurate description of the deformation of the vortex ring core, induced by the lateral wall, and a better approximation of the translational velocity of the vortex ring, compared with the previous model. The main ingredients of the model are the following: the description of the vorticity distribution in the vortex ring is based on the previous model of unconfined elliptical-core vortex rings (Kaplanski et al. Phys. Fluids, vol. 24, 2012, 033101); Brasseur’s approach (Brasseur, NASA Tech. Rep. JIAA TR-26, 1979) is then applied to derive a wall-induced correction for the Stokes streamfunction of the confined vortex ring flow. We derive closed formulae for the flow streamfunction and vorticity distributions. An asymptotic expression for the long-time evolution of the drift velocity of the vortex ring as a function of the ellipticity parameter is also derived. The predictions of the model are shown to be in agreement with direct numerical simulations of confined vortex rings generated by a piston–cylinder mechanism. The predictions of the model support the recently suggested heuristic relation (Krieg & Mohseni Trans. ASME J. Fluids Engng, vol. 135, 2013, 124501) between the energy and circulation of vortex rings with converging radial velocity. A new procedure for fitting experimental and numerical data with the predictions of the model is described. This opens the way for applying the model to realistic confined vortex rings in various applications including those in internal combustion engines.
Modelling of confined vortex rings
- Ionut Danaila, Felix Kaplanski, Sergei Sazhin
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- Journal:
- Journal of Fluid Mechanics / Volume 774 / 10 July 2015
- Published online by Cambridge University Press:
- 05 June 2015, pp. 267-297
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This paper is focused on the investigation of vortex rings evolving in a tube. A new theoretical model for a confined axisymmetric vortex ring is developed. The predictions of this model are shown to be in agreement with available experimental data and numerical simulations. The model combines the viscous vortex ring model, developed by Kaplanski & Rudi (Phys. Fluids, vol. 17, 2005, 087101), with Brasseur’s (PhD thesis, Stanford University) approach to deriving a wall-induced streamfunction correction. Using the power-law assumption for the time variation of the viscous length of the vortex ring, the time variations of the main integral characteristics, circulation, kinetic energy and translational velocity are obtained. Direct numerical simulation (DNS) is used to test the range of applicability of the model and to investigate new physical features of confined vortex rings recently reported in the experimental study by Stewart et al. (Exp. Fluids, vol. 53, 2012, pp. 163–171). The model is shown to lead to a very good approximation of the spatial distribution of the Stokes streamfunction, obtained by DNS. The vortex signature and the time evolution of the energy of the vortex are also accurately predicted by the model. A procedure for fitting the model with realistic vortex rings, obtained by DNS, is suggested. This opens the way to using the model for practical engineering applications.
A generalized vortex ring model
- FELIX KAPLANSKI, SERGEI S SAZHIN, YASUHIDE FUKUMOTO, STEVEN BEGG, MORGAN HEIKAL
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- Journal:
- Journal of Fluid Mechanics / Volume 622 / 10 March 2009
- Published online by Cambridge University Press:
- 10 March 2009, pp. 233-258
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A conventional laminar vortex ring model is generalized by assuming that the time dependence of the vortex ring thickness ℓ is given by the relation ℓ = atb, where a is a positive number and 1/4 ≤ b ≤ 1/2. In the case in which , 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 ℓℓ′. This generalization is performed both in the case of a fixed vortex ring radius R0 and increasing vortex ring radius. In the latter case, the so-called second Saffman's formula is modified. In the case of fixed R0, 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.