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Centrifugal instabilities during spin-down to rest in finite cylinders. Numerical experiments

Published online by Cambridge University Press:  20 April 2006

G. P. Neitzel  and
Stephen H. Davis
G. P. Neitzel
Affiliation:
Department of Mechanical and Energy Systems Engineering, Arizona State University, Tempe, Arizona 85281
Stephen H. Davis
Affiliation:
Department of Engineering Sciences and Applied Mathematics, Northwestern University, Evanston, Illinois 60201
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Abstract

A cylinder filled with a viscous, incompressible fluid is in an initial state of rigid-body rotation about its axis of symmetry. If the container is brought to rest impulsively, the resulting unsteady spin-down flow may be subject to sidewall instabilities due to an imbalance between centrifugal and pressure gradient forces. These instabilities are examined numerically using a finite-difference simulation to integrate the axisymmetric Navier–Stokes equations for a variety of aspect ratios and Reynolds numbers. The Taylor–Görtler vortex-wavelength spectrum, the torque and the angular momentum histories are calculated. Criteria for the onset time for instability and the spin-down time are given. The effects of the enhanced mixing due to instability on the spin-down characteristics and torque are discussed. The results are compared with experiment.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 102 , January 1981 , pp. 329 - 352
Copyright
© 1981 Cambridge University Press

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