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Stability of Taylor–Couette flow with oscillatory radial throughflow

Published online by Cambridge University Press:  19 December 2024

Cheng-Cheng Wang ,
Peng Gao Open the ORCID record for Peng Gao [Opens in a new window]  and
Xi-Yun Lu Open the ORCID record for Xi-Yun Lu [Opens in a new window]
Cheng-Cheng Wang
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei, Anhui 230026, PR China
Peng Gao*
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei, Anhui 230026, PR China
Xi-Yun Lu
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei, Anhui 230026, PR China
*
†Email address for correspondence: [email protected]
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Abstract

The stability of Taylor–Couette flow modulated by oscillatory wall suction/blowing is investigated using Floquet linear stability analysis. The growth rate and stability mode are obtained by numerical calculation and asymptotic expansion. By calculating the effect of wall suction/blowing on the critical mode of steady Taylor–Couette flow, it is found that for most suction/blowing parameters, the maximum disturbance growth rate of the critical mode decreases and the flow becomes more stable. Only in a very small parameter region, wall suction/blowing increases the maximum disturbance growth rate of the critical mode, resulting in flow instability when the gap between the cylinders is large. The asymptotic results for small suction/blowing amplitudes indicate that the change of flow instability is mainly due to the steady correction of the basic flow induced by the modulation. A parametric study of the critical inner Reynolds number and the associated critical wavenumber is performed. It is found that the flow is stabilized by the modulation for most of the parameter ranges considered. For a wide gap between the cylinders, it is possible for the system to be mildly destabilized by weak suction/blowing.

JFM classification

Flow Control: Instability control Instability: Shear-flow instability
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 1001 , 25 December 2024 , A57
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Copyright
© The Author(s), 2024. Published by Cambridge University Press

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