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Free-surface Taylor vortices

Published online by Cambridge University Press:  26 April 2006

F. J. Wang  and
G. A. Domoto
F. J. Wang
Affiliation:
Department of Mechanical Engineering, Columbia University, New York, NY 10027, USA Present address: Xerox Corporation, Webster Research Center, Marking Physics Laboratory, 800 Phillips Road, 0114-23D, Webster, NY 14580, USA
G. A. Domoto
Affiliation:
Xerox Corporation, Webster Research Center, Mechanical Engineering Science Laboratory, 141 Webber Avenue, North Tarrytown, NY 10591, USA
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Abstract

The hydrodynamic instability of a viscous incompressible flow with a free surface is studied both numerically and experimentally. While the free-surface flow is basically two-dimensional at low Reynolds numbers, a three-dimensional secondary flow pattern similar to the Taylor vorticies between two concentric cylinders appears at higher rotational speeds. The secondary flow has periodic velocity components in the axial direction and is characterized by a distinct spatially periodic variation in surface height similar to a standing wave. A numerical method, using boundary-fitted coordinates and multigrid methods to solve the Navier–Stokes equations in primitive variables, is developed to treat two-dimensional free-surface flows. A similar numerical technique is applied to the linearized three-dimensional perturbation equations to treat the onset of secondary flows. Experimental measurements have been obtained using light sheet techniques to visualize the secondary flow near the free surface. Photographs of streak lines were taken and compared to the numerical calculations. It has been shown that the solution of the linearized equations contains most of the important features of the nonlinear secondary flows at Reynolds number higher than the critical value. The experimental results also show that the numerical method predicts well the onset of instability in terms of the critical wavenumber and Reynolds number.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 261 , 25 February 1994 , pp. 169 - 198
Copyright
© 1994 Cambridge University Press

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