Laboratory measurements of the 1st and 2nd moments of propagation through bubbles in a flow

Abstract

The classic theory describing the change in soundspeed and attenuation for waves propagating in bubbly fluids (i.e., the 1st moment of the multiple scattering solution) can be viewed as a statement about the average pressure observed over all possible configurations of bubble position and size. The 2nd moment can also be predicted using the multiple scattering formulation, and both moments can be found independent of any knowledge of the fluid dynamic conditions controlling the mixing of bubbles. Characteristics of the fluid dynamics do appear in the time scales associated with this mixing, however, and this should be reflected in the time scales associated with convergence to the 1st and 2nd moments. This was explored by conducting propagation experiments in a tank filled with bubble-laden water that was subjected to varying flow conditions. Frequency dependent attenuation measurements were made and inverted for the bubble size distribution so that predictions of the 2nd moment could be compared to the observed quantities. High ping rates and long data records were used to observe the flow-dependent time scales associated with the measurements. The results of these experiments will be presented and discussed. [Work supported by ONR Code 321US. First author supported by a National Defense Science and Engineering Graduate Fellowhip.]