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Stability of symmetric vortices in two dimensions and over three-dimensional slender conical bodies

Published online by Cambridge University Press:  30 April 2003

JINSHENG CAI ,
FENG LIU  and
SHIJUN LUO
JINSHENG CAI
Affiliation:
Department of Mechanical and Aerospace Engineering, University of California, Irvine, CA 92697-3975, USA
FENG LIU
Affiliation:
Department of Mechanical and Aerospace Engineering, University of California, Irvine, CA 92697-3975, USA
SHIJUN LUO
Affiliation:
Department of Aircraft Engineering, Northwestern Polytechnical University, Xi'an, China
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Abstract

A general stability condition for vortices in a two-dimensional incompressible inviscid flow field is presented. This condition is first applied to analyse the stability of symmetric vortices behind elliptic cylinders and circular cylinders with a splitter plate at the rear stagnation point. The effect of the size of the splitter plate on the stability of the vortices is studied. It is also shown that no stable symmetric vortices exist behind two-dimensional bodies based on the stability condition. The two-dimensional stability condition is then extended to analyse the absolute (temporal) stability of a symmetric vortex pair over three-dimensional slender conical bodies. The three-dimensional problem is reduced to a vortex stability problem for a pair of vortices in two dimensions by using the conical flow assumption, classical slender-body theory, and postulated separation positions. The bodies considered include circular cones and highly swept flat-plate wings with and without vertical fins, and elliptic cones of various eccentricities. There exists an intermediate cone with a finite thickness ratio between the circular cone and the flat-plate delta wing for which the symmetric vortices change from being unstable to being stable at a given angle of attack. The effects of the fin height and the separation position on the stability of the vortices are studied. Results agree well with known experimental observations.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 480 , 10 April 2003 , pp. 65 - 94
Copyright
© 2003 Cambridge University Press

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