Stability of nonparallel developing flow in an annulus

Abstract

Abstract The linear spatial stability of the developing flow in a concentric annulus, incorporating all nonparallel effects, is described. The disturbance is assumed to be axisymmetric. The velocity profile in the developing flow region is obtained by an implicit finite-difference scheme. The method of multiple scales is used to account for the nonparallel effects. The fourth order Runge-Kutta method is used for integration along with a selective application of the Gram-Schmidt orthonormalization technique for circumventing the parasitic error-growth problem. It is found that the growth rate of the disturbance stream function yields the minimum critical Reynolds number. The critical Reynolds number versus the axial location curves exhibit a minimum and the location of this minimum shifts downstream as the diameter ratio reduces. At a given axial location the critical Reynolds number generally decreases with the diameter ratio. The difference between the critical Reynolds number evaluated from the parallel flow theory and that based on the growth rate of the disturbance stream function varies with the diameter ratio and decreases as the flow develops.