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Flow of an incompressible fluid in a partially filled, rapidly rotating cylinder with a differentially rotating endcap

Published online by Cambridge University Press:  20 April 2006

M. A. Shadday ,
R. J. Ribando  and
J. J. Kauzlarich
M. A. Shadday
Affiliation:
Department of Mechanical and Aerospace Engineering, Research Laboratories for the Engineering Sciences, School of Engineering and Applied Science, University of Virginia, Charlottesville, Virginia 22901 Present address: Department of Mechanical Engineering, University of South Carolina, Columbia, South Carolina.
R. J. Ribando
Affiliation:
Department of Mechanical and Aerospace Engineering, Research Laboratories for the Engineering Sciences, School of Engineering and Applied Science, University of Virginia, Charlottesville, Virginia 22901
J. J. Kauzlarich
Affiliation:
Department of Mechanical and Aerospace Engineering, Research Laboratories for the Engineering Sciences, School of Engineering and Applied Science, University of Virginia, Charlottesville, Virginia 22901
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Abstract

The flow in a partially filled, strongly rotating cylinder with a differentially rotating endcap was studied both experimentally and numerically. The cylindrical container was mounted with a vertical axis of rotation, partially filled with an incompressible fluid, and rotated at a sufficiently high angular velocity that the fluid formed a film of essentially uniform thickness on the sidewall of the container. An axial circulation in this fluid film was induced by the differential rotation of one of the container endcaps. A laser-Doppler velocimeter was used to measure the axial and azimuthal velocity components. The experimental results were compared with a finite-difference model of the flow, and the agreement between the two was good. Boundary layers of thickness proportional to E1/3, where E = ν/ΩL2 is the Ekman number, are found both at the lateral wall and at the vertical free surface. The existence of an E1/3 boundary layer along the free surface is due to the invariant structure of the E½ Ekman layers on the horizontal surfaces with respect to a free surface. The radial transport in the Ekman layers of a partially filled rotating cylinder is essentially the same as that in a completely filled container. The axial transport, which in a completely filled container would have occurred in the volume now occupied by an empty core, is instead confined to a thin boundary layer along the free surface.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 130 , May 1983 , pp. 203 - 218
Copyright
© 1983 Cambridge University Press

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