Analysis and prediction of shock formation in acoustic energy transfer systems

TL;DR

This paper develops an analytical method to predict shock formation distances in nonlinear acoustic wave propagation, improving efficiency and accuracy for acoustic energy transfer system design.

Contribution

It introduces a novel asymptotic and renormalization-based analytical approach for predicting shock formation in acoustic waves, validated against simulations and experiments.

Findings

Accurately predicts shock formation distance based on excitation amplitude.

Provides a faster alternative to traditional numerical simulations.

Validated with finite element simulations and experimental data.

Abstract

Losses associated with nonlinear wave propagation and exhibited by acoustic wave distortion and shock formation compromise the efficiency of contactless acoustic energy transfer systems. As such, predicting the shock formation distance and its dependence on the amplitude of the excitation is essential for their efficiency, design and operation. We present an analytical approach capable of predicting the shock formation distance of acoustic waves generated by a baffled disk with arbitrary deformation in a weakly viscous fluid medium. The loss-less Westervelt equation, used to model the nonlinear wave propagation, is asymptotically expanded based on the amplitude of the excitation. Because the solutions of the first- and second-order equations decay at different rates, we implement the method of renormalization and introduce a coordinate transformation to identify and eliminate the secular terms. The approach yields two partial differential equations that can be solved to predict the formation distance either analytically or numerically much faster than time-domain numerical simulations. The analysis and results are validated with solutions obtained from a nonlinear finite element simulation and previous experimental measurements.