Stability of developing flow in an annulus. I - Axisymmetric disturbances

The spatial stability of a developing axial flow in a concentric annulus against infinitesimal axisymmetric disturbances is described. The mainflow velocity field is determined by a finite difference technique, and the eigenvalue problem is solved using the fourth order Runge-Kutta method and the Gram-Schmidt orthonormalization technique. For an axisymmetric disturbance, the developing axial flow in a concentric annulus is found to possess two spatially unstable modes, the Outer Wall Mode (OWM) and the Inner Wall Mode (IWM), which behave differently as the annulus diameter ratio is varied. While in the near entry region the OWM is more unstable than the IWM for all diameter ratios except those close to unity, the fully developed flow has only one unstable mode (IWM) for all diameter ratios. At a given axial location in the inlet region and with a decreasing diameter ratio, the critical Reynolds number decreases and the critical frequency increases for the OWM, while the critical Reynolds number increases and the critical frequency decreases for the IWM.