Instability of Taylor Vortex and Nonaxisymmetric Modes in Flow Between Rotating Porous Cylinders

Abstract

A numerical solution of linear differential equations governing the instability of Taylor vortex and nonaxisymmetric modes inflow between rotating porous cylinders is present. Solutions take into account the presence of a radial flow between the two rotating cylinders. The critical Reynolds number and corresponding critical axial and azimuthal wavenumber are shown for different values of radius ratio, ratio of angular velocities of the inner and outer cylinders. The results show that not only the critical Reynolds number but the oscillatory onset mode of nonaxisymmetric disturbances can be altered when a radial flow is superimposed on the circular Couette flow. The weak inward flow has a destablizing effect for wide-gap, corotating system of positive and large μ (ratio of angular velocities ω1 and ω2 ) and the weak outward flow has a destablizing effect for small gap, co-rotating system and all counter-rotating system. The most unstable mode of instability depends not only on the angular speed ratio of both cylinders but also the strength of radial flow.