Spatial Stability of Concentric Annular Flow

Abstract

Spatial stability of fully-developed axial flow in a concentric annulus to infinitesimal, axisymmetric as well as non-axisymmetric disturbances is investigated. The solution employs a selective application of the Gram-Schmidt orthonormalization procedure in order to control the parasitic error during numerical integration. Results presented in the form of neutral stability curves for several values of the diameter ratio and angular wavenunaber show that the flow is, more unstable to non-axisymmetric disturbances than to the axisymmetric ones. The sequence for the values of angular wavenumber in order of increasing critical Reynolds number depends on the diameter ratio of the annulus. As the angular wavenumber increases, the phase velocity of the neutral disturbances approaches a constant, about 1/4th of the maximum velocity of axial flow through the annulus. The results match, in the limit, with those for the plane-Poiseuille flow.