Ultrasonic flow meter for propellant on-orbit gauging based on folded multi-tone phase measurement: Model analysis

Ultrasonic flow meter which provides non-invasive no-moving-parts construction is one of the fasted-growing technologies in flow gauging. Based on the general elasticity theory, this paper investigates sound wave propagation in elastic solid, as well as the mathematical description of ultrasonic transducer with the help of electric-acoustic analysis. Moreover, wave phenomenon in moving fluid is introduced and a general solution of wave propagation in cylindrical bounded pipeline is obtained based on the perturbation theory. Furthermore, a mathematical modeling of the ultrasonic flow meter is established in the uniform fluid velocity profile using continuous wave and a novel solution based on modified multi-tone phase measurement is investigated with the advantage of cancellation of impact of complex cylindrical waveguide in different modes which is widely available in pulse-wave-based measurement application. In the end, phase lock loop (PLL) is introduced and analyzed in the signal processing of noise attenuation and phase shift tracking.