Measurement of Energy Dissipation in a Liquid-Filled, Precessing, Spherical Cavity

Abstract

Methods are described for the experimental measurement and analytical estimation of the losses of mechanical energy in a spinning and precessing spherical cavity filled with fluid. Test results are presented and correlated with analytical estimates based on two different mathematical models of the system. The experimental apparatus is a gimbaled mechanism which constrains a rigid body with a spherical cavity to spin about an axis through the cavity center at a constant rate ψ̇, while the spin axis cones about an inertially fixed axis at a constant rate φ̇ with a constant conical half angle θ. Measurements of current required by motors which maintain the constancy of ψ̇ and φ̇ provide a measure of the energy losses in the fluid in the steady state, after suitable dry test calibrations. Experimental results are presented for a 22-cm-dia cavity containing fluids of kinematic viscosities of 1 and 20 centistokes, with θ ranging from 5–30 deg, ψ̇ ranging from 60–1000 rpm, and φ̇ ranging from −400 to +600 rpm. Analytical approximations are developed on the basis of (a) a variation of the oscillating flat-plate solution, and (b) a rigid interior sphere of fluid idealization. The rigid sphere method gives energy dissipation rates that are generally valid over most of the important range of parameters, while the oscillating surface solution is generally an order of magnitude too low in its predictions of energy dissipation.