Measurements of Natural Frequency and Damping Constant of Single Steam Bubble Oscillating in Water

Abstract

The natural frequency fn and damping constant δ of a bubble in liquid have been determined by observing the resonance of the bubble to forced oscillation. The bubble was retained under a rigid plate horizontal disk, and the oscillation was applied by underwater speaker. The applied frequency f was kept constant while letting the bubble increase its volume and vary its radius R. Bubble resonance was detected by observing wrinkles appearing on the bubble due to surface waves. Resonance curves relating the amplitude of bubble radius variation to the intensity of applied oscillation is derived theoretically. Good agreement was seen between the data obtained from experiment and the theoretically derived resonance curves at test to the validity of the method proposed of determining fn and δ from bubble resonance. The values of δ and of the resonant bubble radius Ro of large steam bubbles (8.5 mm>R>11.5 mm) in water were determined at f =270, 290 and 358 Hz. The results support the assumption that for large bubbles the value of fn is little influenced by the exchange of mass between liquid and gaseous phases through evaporation and condensation accompanying bubble pressure oscillation. On the other hand, δ is found to be one order of magnitude higher than calculated for steam bubbles without taking into evaporation and condensation the interphase exchange of mass. The effect brought on δ by the interphase mass exchange can be taken into account by adding a new constant δpn to the terms constituting the total damping constant.