Numerical analysis of nonlinear axisymmetrical acoustic resonators

High-power ultrasonic applications in industrial processing are based on nonlinear effects produced by finite-amplitude 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 distortion 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 3D 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.