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Bifurcation of swirl in liquid cones

Published online by Cambridge University Press:  26 April 2006

Vladimir Shtern  and
Antonio Barrero
Vladimir Shtern
Affiliation:
Department of Energy Engineering and Fluid Mechanics, University of Seville, E-41012 Seville, Spain
Antonio Barrero
Affiliation:
Department of Energy Engineering and Fluid Mechanics, University of Seville, E-41012 Seville, Spain
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Abstract

We show that rotation appears owing to bifurcation in primarily pure meridional steady motion of viscous incompressible fluid. This manifestation of the laminar axisymmetric 'swirl dynamo’ occurs in flows inside liquid conical menisci with the cone half-angle θc < 90°. The liquid flows towards the cone apex near the surface and moves away along the axis driven by (i) surface shear stresses (typical for electrosprays) or (ii) by body Lorentz forces (e.g. in the process of cathode eruption). When the motion intensity increases and passes a critical value, new swirling regimes appear resulting from the supercritical pitchfork bifurcation. This agrees with recent observations of swirl in Taylor cones. We find that when the swirl Reynolds number Γc reaches a threshold value, flow separation occurs and the meridional motion becomes two-cellular with inflows near both the surface and the axis, and an outflow near the cone θ = θs, 0 < θs < θc. In the limit of high Γc, the angular thickness of the near-surface cell tends to zero. In case (i) the swirl is concentrated near the surface while the motion inside the inner cell becomes purely meridional with the radial velocity being uniform. We also study the two-phase flow of a liquid inside and a gas outside the meniscus. Flow separation occurs in both media and then swirl is concentrated near the interface. In case (ii) we reveal another interesting effect: a cascade of flow separations near the axis. As the driving forces increase, meridional motion becomes multi-cellular although very slow in comparison with swirl. To cover all ranges of parameters we combine numerical calculations and asymptotic analyses.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 300 , 10 October 1995 , pp. 169 - 205
Copyright
© 1995 Cambridge University Press

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