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Modelling of confined vortex rings

Published online by Cambridge University Press:  05 June 2015

Ionut Danaila ,
Felix Kaplanski  and
Sergei Sazhin
Ionut Danaila
Affiliation:
Laboratoire de Mathématiques Raphaël Salem, Université de Rouen, F-76801, Saint-Étienne-du-Rouvray, France
Felix Kaplanski
Affiliation:
Laboratory of Multiphase Media Physics, Tallinn University of Technology, Akad. tee 15A, Tallinn 12618, Estonia
Sergei Sazhin*
Affiliation:
Sir Harry Ricardo Laboratories, School of Computing, Engineering and Mathematics, University of Brighton, Brighton BN2 4GJ, UK
*
†Email address for correspondence: S.Sazhin@brighton.ac.uk
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Abstract

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.

JFM classification

Mathematical Foundations: General fluid mechanics Vortex Flows: Vortex dynamics Vortex Flows: Vortex Flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 774 , 10 July 2015 , pp. 267 - 297
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© 2015 Cambridge University Press 

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