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Flow between time-periodically co-rotating cylinders

Published online by Cambridge University Press:  25 October 1999

PATRICIA ERN  and
JOSÉ EDUARDO WESFREID
PATRICIA ERN
Affiliation:
Laboratoire de Physique et Mécanique des Milieux Hétérogènes, UMR CNRS 7636, Ecole Supérieure de Physique et Chimie Industrielles de Paris – ESPCI, 10, rue Vauquelin, 75231 Paris cedex 05, France Present address: Institut de Mécanique des Fluides, UMR CNRS/INP-UPS 5502, Alléc du Professeur Camille Soula, 31400 Toulouse, France.
JOSÉ EDUARDO WESFREID
Affiliation:
Laboratoire de Physique et Mécanique des Milieux Hétérogènes, UMR CNRS 7636, Ecole Supérieure de Physique et Chimie Industrielles de Paris – ESPCI, 10, rue Vauquelin, 75231 Paris cedex 05, France
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Abstract

We consider oscillatory flows between concentric co-rotating cylinders at angular velocity Ω(t) = Ωm + Ωo cos ωt as a prototype to investigate the competing effects of centrifugal and Coriolis forces on the flow stability. We first study by flow visualization the effect of the mean rotation Ωm on the centrifugal destabilization due to the temporal modulation. We show that increasing the mean rotation first destabilizes and then restabilizes the flow. The instability of the purely azimuthal basic flow is then analysed by investigating the dynamics of the axial velocity component of the vortex structures. Velocity measurements performed in the rotating frame of the cylinders using ultrasound Doppler velocimetry show that secondary flow appears and disappears several times during a flow period. Based on a finite-gap expression for the basic flow, linear stability analysis is performed with a quasi-steady approach, providing the times of appearance and disappearance of secondary flow in a cycle as well as the effect on the instability threshold of the mean rotation. The theoretical and numerical results are in agreement with experimental results up to intermediate values of the frequency. Notably, the flow periodically undergoes restabilization at particular time intervals.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 397 , 25 October 1999 , pp. 73 - 98
Copyright
© 1999 Cambridge University Press

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