Application of a stream-function numerical approach to Rayleigh streaming

Abstract

In 1995 Kamakura et al. [J. Acoust. Soc. Am. 97 (5, Pt. 1), 2740–2746] showed how an incompressible, viscous fluid stream-function vorticity formulation could be applied to model the time dependent build up of acoustic streaming in and around the focal area of an ultrasonic transducer in water. They found excellent qualitative agreement between their numerical results and experimental findings available in the literature. The purpose of the present research is to apply this numerical method to the Rayleigh streaming encountered in resonator tubes of thermoacoustic devices. A new code has been written from scratch and benchmarked against the published results of Kamakura et al. with excellent agreement. An overview of both the algorithm and application method to the Rayleigh streaming problem briefly will be provided. Initial results and comparisons to recent analytical solutions will be given. While not as flexible as high-resolution computational fluid dynamics calculations on large parallel computers for the study of acoustic streaming, the present formulation is much faster and can run on a desktop machine. [Work supported by ONR.]