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Dynamics and stability of a vortex ring impacting a solid boundary

Published online by Cambridge University Press:  26 April 2006

J. D. Swearingen ,
J. D. Crouch  and
R. A. Handler
J. D. Swearingen
Affiliation:
Naval Research Laboratory, Washington, DC 20375, USA Present address: Mechanical Engineering Department, The University of Kansas, Lawrence, KS 66045, USA
J. D. Crouch
Affiliation:
Naval Research Laboratory, Washington, DC 20375, USA Present address: Boeing Commercial Airplane Group, PO Box 3707, MS 7H-90, Seattle, WA 98124-2207, USA
R. A. Handler
Affiliation:
Naval Research Laboratory, Washington, DC 20375, USA
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Abstract

Direct numerical simulations were used to study the dynamics of a vortex ring impacting a wall at normal incidence. The boundary layer formed as the ring approaches the wall undergoes separation and roll-up to form a secondary vortex ring. The secondary ring can develop azimuthal instabilities which grow rapidly owing to vortex stretching and tilting in the presence of the mean strain field generated by the primary vortex ring. The stability of the secondary ring was investigated through complementary numerical experiments and stability analysis. Both perturbed and unperturbed evolutions of the secondary ring were simulated at a Reynolds number of about 645, based on the initial primary-ring propagation velocity and ring diameter. The linear evolution of the secondary vortex-ring instability was modelled analytically by making use of a quasi-steady approximation. This allowed a localized stability analysis following Widnall & Sullivan's (1973) earlier treatment of an isolated vortex ring. Amplitude evolution and growth-rate predictions from this analysis are in good agreement with the simulation results. The analysis shows that the secondary vortex ring is unstable to long-wavelength perturbations, even though an isolated ring having similar characteristics would be stable.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 297 , 25 August 1995 , pp. 1 - 28
Copyright
© 1995 Cambridge University Press

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