Acoustic Streaming Induced by Wall Oscillations of a Plane Rectangular Resonator

We consider the flow of a viscous compressible gas in a closed rectangular resonator induced by harmonic oscillations of its boundary on the first resonance frequency. The method of successive approximations is used to study the two-dimensional acoustic streaming in a resonator of arbitrary width. The existence of an acoustic streaming in the form of four Rayleigh vortices and four Schlichting vortices is revealed. The similarity between the acoustic streamings occurring in the cases of horizontal harmonic oscillations of an enclosure and oscillations of a resonator wall is shown, which indicates a weak influence of the means of standing wave generation on the acoustic streaming pattern. It is found that as the channel width decreases, the Schlichting vortex dimensions increase compared with those of Rayleigh vortices. When the channel width is less than six thicknesses of the acoustic boundary layer, the Rayleigh vortices disappear and only the Schlichting vortices remain. It is established that in the case of an oscillating enclosure the centers of the Rayleigh and Schlichting vortices lie in the same cross-section, while in the case of the resonator with an oscillating boundary the centers of the Schlichting vortices are displaced toward the vertical walls.

Automated summary

This study investigates the flow of a viscous compressible gas in a closed rectangular resonator induced by harmonic oscillations of its boundary, revealing the existence of four Rayleigh vortices and four Schlichting vortices. The results show that as the channel width decreases, the dimensions of Schlichting vortices increase while Rayleigh vortices disappear. The influence of different means of standing wave generation on the acoustic streaming pattern is found to be weak.