Low-frequency oscillations of bubble plumes

Abstract

The collective oscillations of bubbles in a plume are believed responsible for the portion of the ocean noise spectrum that is roughly less than 1 kHz. The plume due to its dimensions and change in speed of sound from that of pure water acts as a resonating cavity. Since a plume may have a relatively complex shape, making it difficult to predict resonant frequencies, theoretical and experimental work is being carried out on simpler geometric models. The initial model has been created to predict the resonance of a cylindrical bubble cloud assuming a uniform void fraction throughout. The theory predicts an oscillatory pressure field described by Bessel functions [Jn( )] inside the cloud an an evanescent field described by modified Bessel functions [Kn( )] outside of it. Once the dimensions of the cloud are fixed, the only parameter that is varied is the void fraction. A relatively simple characteristic equation was obtained that was used to predict the resonant frequencies. Experimental work was carried out in a pool 3 m in diameter and 1 m deep. The cylindrical bubble cloud was created by passing compressed air through an annular array of hypodermic needles. Void fractions were altered by changing the flow rate to the bubble maker, and they were measured by determining the local speed of sound; the two are related by a simple expression if the frequency propagating through the cloud is less than the resonant frequency of the bubbles which compose it. Experimental measurements appear to verify the theoretical model. The model was then adapted to account for a gradient in the void fraction as a function of radius. The cloud was approximated to be four concentric cylinders with different void fractions. This is a more realistic model of a bubble plume in an ocean environment. The void fraction in each ring was estimated through the local speed of sound measurements. There was reasonable agreement between theory and experiment. [Work supported by ONR.]