Spectral Mass Gauging of Unsettled Liquid with Acoustic Waves

Propellant mass gauging is one of the key technologies required to enable the next step in NASA's space exploration program. At present, there is no reliable method to accurately measure the amount of unsettled liquid propellant of an unknown configuration in a propellant tank in micro- or zero gravity. We propose a new approach to use sound waves to probe the resonance frequencies of the two-phase liquid-gas mixture and take advantage of the mathematical properties of the high frequency spectral asymptotics to determine the volume fraction of the tank filled with liquid. We report the current progress in exploring the feasibility of this approach, both experimental and theoretical. Excitation and detection procedures using solenoids for excitation and both hydrophones and accelerometers for detection have been developed. A 3% uncertainty for mass-gauging was demonstrated for a 200-liter tank partially filled with water for various unsettled configurations, such as tilts and artificial ullages. A new theoretical formula for the counting function associated with axially symmetric modes was derived. Scaling analysis of the approach has been performed to predict an adequate performance for in-space applications.