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Vortex rings in radially confined domains

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Abstract

The dynamics of vortex rings generated within confined domains are relevant to important hydrodynamic processes such as flow past heart valves or severe arterial constrictions. However, despite their importance, these flows have not received much attention to date. This study examines the development and evolution of radially confined vortex rings. Time-resolved digital particle image velocimetry was used to investigate two levels of radial confinement and a range of vortex ring strengths. We found that for severely confined vortex rings, the formation time and peak circulation values were unaffected for L/D 0 < 4 cases and slightly affected for larger L/D 0 cases. After pinch-off, circulation decay was observed with an approximately constant normalized circulation decay rate. We found that with increasing circulation strength, the nondimensional time delay between the pinch-off and the onset of circulation decay reduced due to an increased vortex ring diameter within the confinement domain and a reduction in the necessary time for the surface induced and core vorticity regions to interact. This study uncovers the dynamics of radially confined vortex rings and show that the nondimensional rate of circulation decay is dependent on the vortex ring confinement ratio (ratio of the vortex ring orifice diameter to the diameter of the outer cylinder), and the time delay between the vortex pinch-off and the onset of circulation is dependent on the vortex ring circulation strength.

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Abbreviations

a :

Vortex core radius

D :

Diameter of the confinement domain

D 0 :

Diameter of the piston cylinder

D VR :

Vortex ring core-to-core diameter

FN:

Formation number

L :

Length of the piston travel

P :

Velocity program factor

Re :

Reynolds number

Re J :

Modified Reynolds number

T*:

Nondimensional formation time

W*:

Normalized vorticity

Γ:

Circulation

Γ0 :

Peak circulation

ν:

Kinematic viscosity

ω:

Vorticity

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Acknowledgments

The authors would like to thank John J. Charonko and Casandra L. Niebel for their help with this work. This work was partially supported by a National Science Foundation Graduate Research Fellowship as well as National Science Foundation Grant (0547434). Any opinions, findings, conclusions, or recommendations expressed in this publication are those of the authors and do not necessarily reflect the views of the National Science Foundation.

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  1. Department of Mechanical Engineering, Virginia Tech, 114U Randolph Hall, Blacksburg, VA, 24061, USA

    Kelley C. Stewart & Pavlos P. Vlachos

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  1. Kelley C. Stewart
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  2. Pavlos P. Vlachos
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Correspondence to Pavlos P. Vlachos.

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Stewart, K.C., Vlachos, P.P. Vortex rings in radially confined domains. Exp Fluids 53, 1033–1044 (2012). https://doi.org/10.1007/s00348-012-1343-z

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