Abstract
This study investigated by an analytical method the flow that develops in the gap between concentric rotating cylinders when the Taylor number Ta exceeds the first critical value. Concentric cylinders rotating at the speed ratio μ=0 are investigated over the radius ratio range 0.20≤η≤0.95. This range includes configurations characterised by a larger annular gap width d than classical journal bearing test cases and by a Taylor number beyond the first critical Taylor number at which Taylor vortices develop. The analysis focuses on determining the parameters for the direct transition from axisymmetric Couette flow to wavy Taylor vortex flow. The results show a marked change in trend as the radius ratio η reduces below 0.49 and 0.63 for the azimuthal wave-numbers m=2 and 3 respectively. The axial wavenumber increases so that the resulting wavy Taylor vortex flow is characterised by vortex structures elongated in the radial direction, with a meridional cross-section that is significantly elliptical. The linear stability analysis of the perturbation equations suggests this instability pattern is neutrally stable. Whereas a direct transition from axisymmetric Couette flow is not necessarily the only route for the onset of wavy Taylor vortex flow, the significant difference between the predicted pattern at large gap widths and classical wavy Taylor vortex flow merits further investigation.
Highlights
The flow in the gap between concentric independently rotating cylinders has attracted great attention over the years
This leads to a new secondary steady flow state, the axisymmetric Taylor vortex flow, which is characterised by the formation of regularly spaced vortices spanning the gap between the inner cylinder and the outer cylinder in the axial direction
The new numerical solutions of the perturbation equations are compared in Fig. 2 and in Fig. 3 with the results reported by Roberts [32], by Schwarz et al [15], and by Kruger et al [22], for different values of η over the range 0.75 ≤ η ≤ 0.95, at μ = 0
Summary
The flow in the gap between concentric independently rotating cylinders has attracted great attention over the years This dates back to 1888 and 1890, when Mallock [1] and Couette [2] conducted independent experiments using concentric rotating cylinders. Taylor’s experiment [3] showed that, when the angular velocity of the inner cylinder is increased above a certain threshold, the steady and axisymmetric Couette flow becomes unstable. From the time Taylor [3] first established the threshold at which the axisymmetric Couette flow becomes unstable, further investigations have been conducted both experimentally and analytically to determine the onset of this rotational instability in terms of the first critical Taylor number Tac
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