The Inviscid Stability of Supersonic Flow Past Heated or Cooled Axisymmetric Bodies

The inviscid, linear, non-axisymmetric, temporal stability of the boundary layer associated with the supersonic flow past axisymmetric bodies with particular emphasis on long thin, straight circular cylinders, subject to heated or cooled wall conditions is investigated. The eigenvalue problem is computed in some detail for a particular Mach number or 3.8, revealing that the effect of curvature and the choice of wall conditions both have a significant effect on the stability of the flow. Both the asymptotic, large azimuthal wavenumber solution and the asymptotic, far downstream solution are obtained for the stability analysis and compared with numerical results. Additionally, asymptotic analyses valid for large radii of curvature with cooled-heated wall conditions, are presented. Important differences exist between the wall temperature conditions imposed in this paper and the adabatic wall conditions considered previously.