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The inviscid axisymmetric stability of the supersonic flow along a circular cylinder

Published online by Cambridge University Press:  26 April 2006

Peter W. Duck
Peter W. Duck
Affiliation:
Department of Mathematics, University of Manchester, Manchester M13 9PL, UK
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Abstract

The supersonic flow past a thin straight circular cylinder is investigated. The associated boundary-layer flow (i.e. the velocity and temperature field) is computed; the asymptotic, far downstream solution is obtained, and compared with the full numerical results.

The inviscid, linear, axisymmetric (temporal) stability of this boundary layer is also studied. A so-called ‘doubly generalized’ inflexion condition is derived, which is a condition for the existence of so-called ‘subsonic’ neutral modes. The eigenvalue problem (for the complex wavespeed) is computed for two free-stream Mach numbers (2.8 and 3.8), and this reveals that curvature has a profound effect on the stability of the flow. The first unstable inviscid mode is seen to disappear rapidly as curvature is introduced, whilst the second (and generally the most important) mode suffers a substantially reduced amplification rate.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 214 , May 1990 , pp. 611 - 637
Copyright
© 1990 Cambridge University Press

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