Zero-G Propellant Gauging Utilizing Radio Frequency Techniques in a Spherical Resonator

The resonant properties of a spherical cavity are described as a means of gauging liquid propellants in a zero-gravity field. The configuration of a liquid propellant in a partially filled spherical cavity have been shown to be such that a spherical vapor bubble exists in the center of the cavity. Spherical wave functions are developed and the boundary conditions applied to give an analytical expression for the cavity resonant frequency as a function of volumetric propellant loading. An aluminum scale-model, two inches in diameter, spherical cavity was constructed and loaded with varying dielectric shells to verify the mathematical predictions. Close agreement, within several percent, was obtained for three different dielectric constants, 2.5, 5, and 10.