An Energy Assessment for Liquids in a Filled Precessing Spherical Cavity

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Abstract
Experimental results and analytical approximations for energy dissipation due to liquids in a filled precessing spherical cavity are presented. The range of physical parameters include kinematic viscosities from 1 to 1000 centistokes, half coning angles from 5/8 to 10 deg, precession speeds from 0.15 to 200 rpm, and spin speeds (relative to the precessing frame) of from 7.5–900 rpm. These parameters and the associated energy dissipation rates, as low as 10−4 watts, place the results in the region of direct applicability to spinning satellite stability problems. A dimensionless parameter related to an Ekman number is used to correlate energy dissipation rates with laminar, intermediate, and fully turbulent flows. The reduced data are integrated with data from other sources and used to develop equations in dimensionless form for the experimental and analytical results. The results, while not defining details of fluid motion, place experimental bounds on the integrated shear stress at the cavity wall for analytical models.

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