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Stability of Taylor–Dean flow in a small gap between rotating cylinders

Published online by Cambridge University Press:  26 April 2006

Falin Chen  and
M. H. Chang
Falin Chen
Affiliation:
Institute of Applied Mechanics, National Taiwan University, Taipei, Taiwan 10764, ROC
M. H. Chang
Affiliation:
Institute of Applied Mechanics, National Taiwan University, Taipei, Taiwan 10764, ROC
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Abstract

A linear stability analysis has been implemented for Taylor–Dean flow. a viscous flow between rotating concentric cylinders with a pressure gradient acting in the azimuthal direction. The analysis is made under the assumption that the gap spacing between the cylinders is small compared to the mean radius (small-gap approximation). A parametric study covering wide ranges of μ. the ratio of angular velocity of the outer cylinder to that of inner cylinder. and β. a parameter characterizing the ratio of representative pumping and rotation velocities is conducted. For − 1 [les ] μ < 1, results show that non-axisymmetric instability modes prevail in a wide range of β. The most stable state is found to occur within − 3.9 < β < − 3.6 for μ < 0.3 and at − β ≈ 1.59μ + 3.5 for μ > 0.3. The most stable state is always accompanied by a shortest critical axial wavelength. Instability modes with different azimuthal wavenumber have similar stability characteristics because the basic state is either close to or at the most stable situation. This similarity is absent from either Taylor or Dean flow.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 243 , October 1992 , pp. 443 - 455
Copyright
© 1992 Cambridge University Press

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