Hydrodynamic stability of Taylor–Dean flow between rotating porous cylinders with radial flow

Abstract

A linear stability analysis has been implemented for the Taylor–Dean flow between porous concentric rotating cylinders when radial flow is present. The stability equations with respect to both axisymmetric and nonaxisymmetric disturbances are derived and solved by a direct numerical procedure. Both types of radial flows, inward and outward flows, are considered. A parametric study covering wide ranges of α, the radial Reynolds number based on the radial velocity at the inner cylinder and inner radius, and β, a parameter characterizing the ratio of average pumping velocity due to azimuthal Poiseuille flow and rotation velocity due to inner cylinder rotation, is conducted for the situation of practical interest where the outer cylinder is stationary and the inner cylinder is rotating. The area where the onset mode is nonaxisymmetric is shown in the plane (β,α). A critical curve is discovered that the most stable state always occurs at the point on this curve for an assigned value of α. Moreover, a discontinuity of the critical axial wavenumber happens when the parameters α or β cross this curve. The critical mode transition of the onset of instability is demonstrated in detail and results for the variations of the critical Taylor number and axial wavenumber are presented. It is found that the superimposed radial flow may produce a stabilizing or destabilizing effect depending heavily on the value of β related to the basic state.