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The inviscid stability of supersonic flow past a sharp cone

Abstract

In this paper we consider the laminar boundary layer which forms on a sharp cone in a supersonic freestream, where lateral curvature plays a key role in the physics of the problem.

This flow is then analysed from the point of view of linear, temporal, inviscid stability. Indeed, the basic, nonaxisymmetric disturbance equations are derived for general flows of this class, and a so-called “triply generalized” inflexion condition is found for the existence of “subsonic” neutral modes of instability. This condition is analogous to the well-known generalized inflexion condition found in planar flows, although in the present case the condition depends on both axial and azimuthal wave numbers.

Extensive numerical results are presented for the stability problem at a freestream Mach number of 3.8, for a range of streamwise locations. These results reveal that a new mode of instability may occur, peculiar to flows of this type involving lateral curvature. This mode occurs at small wave numbers, but under certain circumstances may in fact be the most unstable (and hence important) mode.

Additionally, asymptotic analyses valid close to the tip of the cone and far downstream from the cone are presented, and these give a partial (asymptotic) description of this additional mode of instability.

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Additional information

This research was supported by the National Aeronautics and Space Administration under NASA Contract No. NASI-18605 where one of the authors (P.W.D.) was in residence at the Institute for Computer Applications in Science and Engineering (ICASE), NASA Langley Research Centre, Hampton, VA 23665, U.S.A. S.J.S. was in the receipt of a Northern Ireland Education Department studentship. A number of computations were carried out at the University of Manchester Computer Centre, with computer time provided under S.E.R.C. Grant No. GR/E/25702 and by the University of Manchester.

Communicated by Philip Hall

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Duck, P.W., Shaw, S.J. The inviscid stability of supersonic flow past a sharp cone. Theoret. Comput. Fluid Dynamics 2, 139–163 (1990). https://doi.org/10.1007/BF00271601

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Keywords

  • Boundary Layer
  • Mach Number
  • Supersonic Flow
  • Laminar Boundary Layer
  • Small Wave