Time-domain simulation of acoustic wave scattering and internal propagation from gas bubbles of various shapes

Abstract

Acoustic scattering and resonances resulting from plane waves incident upon a gas bubble are simulated using a time-domain simulation based on numerical solutions. The time histories of scattering pressure and velocity, both outside and inside the bubble, are obtained simultaneously from an immersed-boundary method allowing for the investigation of both exterior and interior fields with complex geometries. The acoustic resonances of the bubble are investigated for various bubble sizes, shapes and inner gas parameters, and these are compared to the partial wave scattering solutions for spherical bubbles. Agreement is shown with the analytical solutions in the linear acoustic limit. The linear resonance frequency increases with the bubble’s inner background pressure and independent of the incident wave amplitude or frequency. In addition to scattering outside of the bubble, acoustic propagation inside the interior gas is investigated with respect to the monopole resonance. A significant advantage is that this time-domain simulation combined with the immersed-boundary method can be readily adapted for various shapes of bubbles. The scattering and resonance behaviors are compared with the approximate analytical results using the shape factor method. The simulation can be extended to less studied shapes relevant to underwater and physical acoustics applications such as “pancake-shaped” bubbles.