Linear stability analysis of the flow between rotating cylinders of wide gap
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Abstract© 2018 The Authors 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.
CitationAdebayo, D., Al-Ameri, J., Tyukin, I. and Rona, A. (2018) Linear stability analysis of the flow between rotating cylinders of wide gap, European Journal of Mechanics, B/Fluids, 72(2018), pp. 567-575.
JournalEuropean Journal of Mechanics, B/Fluids
Description© 2018 The Authors. Published by Elsevier. This is an open access article available under a Creative Commons licence. The published version can be accessed at the following link on the publisher’s website: https://doi.org/10.1016/j.euromechflu.2018.07.002
SponsorsThis project has been supported by a Specific Targeted Research Project of the European Community’s Sixth Framework Programme under contract number NMP3-CT-2006-032669 (PROVAEN). The original acquisition of MATLAB software licenses was part-funded by EPSRC grant GR/N23745/01.
Except where otherwise noted, this item's license is described as https://creativecommons.org/licenses/by/4.0/