Abstract

Bifurcation of Acoustic Streaming Induced by a Standing Wave in a Two-Dimensional Rectangular Box

T.Yano, S.Fujikawa, M.Mizuno (Department of Mechanical Science, Hokkaido University, Sapporo, Japan)

e-mail: yano@mech-me.eng.hokudai.ac.jp

The large amplitude standing wave excited in a resonator induces acoustic streaming of Rayleigh type outside the acoustic boundary layer on the wall of the resonator. For the case that the resonator is a two-dimensional rectangular box, the streaming motion with large Reynolds number is examined numerically. The two-dimensional incompressible Navier-Stokes equations with no external force are used as the governing equations for the streaming velocity, which is defined by a time-averaged mass flux density vector. The steady velocity component at the outer edge of the acoustic boundary layer, which induces Rayleigh type streaming, is employed as the boundary condition for the Navier-Stokes equations. By using a finite-difference method, the bifurcation of steady acoustic streaming is clarified. The result shows that at a critical Reynolds number, the classical symmetric steady flow becomes unstable and a pair of stable steady flows emerges, the flow patterns of which are mirror images of each other. The critical Reynolds number and the resulting flow patterns are dependent upon the aspect ratio of the box and the mode of the standing wave.

Section : 7