A STUDY OF THE DAMPING AND STABILITY OF A PULSATING SPHERICAL BUBBLE IN A FLOWING FLUID.
NAVY MINE DEFENSE LAB PANAMA CITY FLA
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Previous studies have dealt with radiation, thermal, and viscous damping of pulsating spherical bubbles in a fluid. The purpose of the present study has been to investigate theoretically the additional effect, if any, of directional motion upon damping for a pulsating spherical bubble in a flowing fluid. To do this, the r-component of the vector Navier-Stokes equation for viscous, incompressible flow is coupled to the stream functions for flow around small, intermediate and large bubble sizes. The resulting second order nonlinear differential equations are then solved by a linearization technique to obtain approximate solutions. Graphs of the damping or growth constants for the various bubble sizes and hydrodynamic models are presented. Theoretical results are compared to the available experimental data in the acoustics literature for the particular case of an air bubble in water. The results of this theoretical study show that the radial viscous damping term has the same form for all bubble sizes, and the term arising from directional motion is a function of fluid velocity, angular position, reciprocal bubble equilibrium radius and reciprocal resonant frequency. The most important conclusion is that this latter term can predict bubble breakup for large bubbles. Author
- Fluid Mechanics