Shock formation distance—A design parameter for high power acoustic energy transfer systems

Abstract

An interesting consequence of the nonlinear propagation of a finite-amplitude acoustic wave is the formation of a discontinuity in the pressure or also known as shock formation. It is associated with the dissipation of energy that is proportional to the cube of jump in the discontinuity. Such a loss in energy is detrimental for acoustic energy transfer applications as it will compromise the energy transfer efficiency. As such, the knowledge of the shock formation distance (SFD) is essential for designing efficient high-power energy transfer systems. We present an analytical frequency domain approach capable of predicting the SFD in the acoustic pressure distribution generated by a baffled disk with a general transverse deformation in a weakly viscous fluid medium. The nonlinear wave propagation is modeled using the Westervelt equation and the approach is based on solving it using the method of renormalization. The approach can be implemented either analytically or numerically to predict the SFD much faster than the time-domain simulations. The numerical implementation also allows the flexibility of using this approach for any source configuration. [This work was supported by NSF Grant No. ECCS-1711139, which is gratefully acknowledged.]