Stability of the boundary layer on a spinning blunt-nosed cylinder

A linear stability analysis has been carried out by the authors (Kao, K.H., and Chow, C.Y., 'Stability Analyses of Boundary Layer on a Semi-Infinite Circular Cylinder With and Without Spin,' AIAA Paper 90-0116, 1990) for an incompressible laminar boundary layer along a semi-infinite cylinder of constant radius aligned with an external flow, with and without a constant angular speed about its axis. The influences of transverse curvature and spin motion are shown to have stabilizing and destabilizing effects, respectively. That work is extended here to consider a more realistic cylindrical body with a blunt nose, which generates an axial pressure gradient in the boundary layer. A numerical procedure is described to examine the stability of the boundary layer along a Rankine half-body generated by superposition of a point source and a uniform flow. Boundary-layer profiles and their neutral stability curves are obtained by the application of an implicit method and the Chebyshev collocation spectral method, respectively. From stability diagrams obtained herein for the cylinder with and without spin, the critical Reynolds number and the position on the cylinder at which onset of instability occurs can be determined.