Shock Propagation and Attenuation in Bubbly Liquids: Modeling Wave Propagation Using a Nonlinear Equation-of-State
Final technical rept. 1 Jun 96-31 May 99
BOSTON UNIV MA DEPT OF AEROSPACE AND MECHANICAL ENGINEERING
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Bubbly media play a significant role in underwater acoustics, medical ultrasound and in industrial systems where gas-liquid flows are present. The focus of our research has been to develop a continuum model for bubbly mixtures that can be used to model physical phenomena in these areas. The key to the continuum model is a nonlinear, non-equilibrium equation of state EOS that relates pressure to the mixture density and the number density number of bubbles per unit volume and their first two material time derivatives. The derivation of the EOS is presented here and a number of traveling wave solutions obtained using this nonlinear EOS are discussed. To develop an accurate model, two important damping mechanisms for the medium had to be incorporated heat transfer and relative motion between the gas and liquid phases. To quantify the importance of heat transfer, an analysis of single-bubble radial oscillations was completed in this work, and a Pade approximation for the thermal damping was derived from the linearized gas dynamics equations. A second important damping mechanism arises from relative motion between the gas bubbles and the liquid. The quantitative effects of relative motion on the damping of waves in bubbly liquids has also been examined and is described here.
- Fluid Mechanics