Rigid-Body Approximations to Turbulent Motion in a Liquid-Filled, Precessing, Spherical Cavity

[+] Author and Article Information
J. P. Vanyo

Department of Mechanical Engineering, University of California, Santa Barbara, Santa Barbara, Calif.

P. W. Likins

School of Engineering and Applied Science, University of California, Los Angeles, Los Angeles, Calif.

J. Appl. Mech 39(1), 18-24 (Mar 01, 1972) (7 pages) doi:10.1115/1.3422610 History: Received October 21, 1970; Online July 12, 2010


Rigid-body approximations for turbulent motion in a liquid-filled, spinning and precessing, spherical cavity are presented. The first model assumes the turbulent liquid to spin and precess as a rigid solid sphere coupled to the cavity wall by a thin layer of massless viscous liquid. The second model replaces the layer of massless viscous liquid by a series of n concentric rigid spherical shells. The number and thickness of the shells can be varied so that the interior sphere varies from a negligible diameter to nearly the diameter of the cavity. Although these models do not provide solutions of the fluid equations of motion, they yield steady-state energy dissipation rates that compare favorably with existing experimental data associated with turbulent flow in such a cavity. The models also duplicate several other important features of rotating fluid flow theory. In particular, the motions of the concentric shells exhibit characteristics associated with a classic Ekman layer structure.

Copyright © 1972 by ASME
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