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.
Rigid-Body Approximations to Turbulent Motion in a Liquid-Filled, Precessing, Spherical Cavity
Vanyo, J. P., and Likins, P. W. (March 1, 1972). "Rigid-Body Approximations to Turbulent Motion in a Liquid-Filled, Precessing, Spherical Cavity." ASME. J. Appl. Mech. March 1972; 39(1): 18–24. https://doi.org/10.1115/1.3422610
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