Numerical analysis of nonlinear axisymmetrical acoustic resonators

Abstract

High-power ultrasonic applications in industrial processing are based on nonlinear effects produced by finiteamplitude pressure variations. The knowledge of the nonlinear pressure distribution inside resonant cavities is essential for the development of practical applications. Some one-dimensional numerical models exist, which have shown the important dependence of pressure values and distribution, first, on the nonlinear distorsion and nonlinear attenuation, and second, on the geometry of the resonator. In this framework, we propose a finite-difference algorithm able to simulate linear standing waves and strongly nonlinear quasi-standing waves inside axisymmetrical rigid-walled resonators for homogeneous absorbing fluids. A fully nonlinear 3-D wave equation valid for axisymmetrical systems is written in Lagrangian coordinates. All calculations are performed in the time domain, giving all the harmonic components of the wave by only one resolution step, and allowing the possibility of using any time function excitation signal.

Influence of Surface Active Solute on Ultrasonic Waveform Distortion in Liquid Containing Air Bubbles

“…The curve has a steeper gradient for positive pressures and a broadened minimum for negative pressures. This is similar to the numerical results reported by Vanhille and Campos-Pozuelo at 200 kHz . In Figure b (1 mM SDS), very little distortion is seen in the waveform, even at high power.…”

“…To the best of our knowledge, there has been only one theoretical study by Vanhille and Campos-Pozuelo on the distortion of pressure waveforms in a standing wave which contains bubbles. However, that study dealt only with the pressure waveform in an air−water system and not with a system containing any surface active solutes.…”