Acoustic streaming generated by standing waves in narrow channels

Abstract

Considerable attention has been devoted to acoustic streaming following the initial investigation by Rayleigh. A standing wave in a channel generates acoustic streaming in the form of inner and outer vortices that circulate in opposite directions. The outer vortex is the streaming pattern described by Rayleigh. The inner vortex is generated within the viscous boundary layer and has comparable thickness. Because boundary layer thickness is typically an exceedingly small fraction of channel width, the inner vortex is normally disregarded in relation to the Rayleigh streaming. However, channel widths in stacks used in thermoacoustic engines are comparable to boundary layer thickness. As channel width decreases, the relative thickness, of the inner vortex increases as that of the outer vortex decreases, and when channel width is comparable to the boundary layer thickness, the inner vortex dominates the flow field. Previous studies of inner streaming vortices have focused mainly on the problem of a cylinder oscillating in an infinite fluid. Acoustic streaming in narrow channels is studied here analytically and numerically. An analytical solution is derived in the quadratic approximation. Fully nonlinear numerical results are obtained from a 2-D code recently developed for thermoacoustic engines. Analytical and numerical results are in good agreement. [Work supported by ONR.]