Stability of developing flow in an annulus. part II. Non-axisymmetric disturbances

Abstract

Abstract Spatial stability of the developing axial flow in a concentric annulus against infinitesimal axisymmetric disturbances is described. The mainflow velocity field is determined by means of a finite difference technique and the eigenvalue problem is solved using the fourth order Runge-Kutta method along with a selective application of the Gram-Schmidt orthonormalization technique. Two unstable modes, termed as outer and inner wall modes (OWM and IWM) are found to exist for this problem. These modes behave differently in the inlet region with respect to the annulus diameter ratio. For all diameter ratios except those close to unity the OWM is more unstable than the IWM in the near entry region. However, as the flow develops hydrodynamically, these modes reverse roles so that the fully developed axial flow in the annulus has only one unstable mode (the IWM) for all diameter ratios. Variation of critical Reynolds number, frequency and wavenumber for both the modes in the inlet region is displayed for a wide range of diameter ratios.