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Steady compressible vortex flows: the hollow-core vortex array

Published online by Cambridge University Press:  26 April 2006

K. Ardalan ,
D. I. Meiron  and
D. I. Pullin
K. Ardalan
Affiliation:
Applied Mathematics, California Institute of Technology, Pasadena, CA 91125, USA
D. I. Meiron
Affiliation:
Applied Mathematics, California Institute of Technology, Pasadena, CA 91125, USA
D. I. Pullin
Affiliation:
Graduate Aeronautical Laboratories, California Institute of Technology, Pasadena, CA 91125, USA
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Abstract

We examine the effects of compressiblity on the structure of a single row of hollowcore, constant-pressure vortices. The problem is formulated and solved in the hodograph plane. The transformation from the physical plane to the hodograph plane results in a linear problem that is solved numerically. The numerical solution is checked via a Rayleigh-Janzen expansion. It is observed that for an appropriate choice of the parameters M∞ = q∞/c∞, and the speed ratio, a = q∞/qv, where qv is the speed on the vortex boundary, transonic shock-free flow exists. Also, for a given fixed speed ratio, a, the vortices shrink in size and get closer as the Mach number at infinity, M∞, is increased. In the limit of an evacuated vortex core, we find that all such solutions exhibit cuspidal behaviour corresponding to the onset of limit lines.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 301 , 25 October 1995 , pp. 1 - 17
Copyright
© 1995 Cambridge University Press

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