The sound-producing oscillations of round underexpanded jets impinging on normal plates

Abstract

The results of acoustical and optical experiments in which ‘‘moderately’’ underexpanded sonic round jets impinge on flat plates normal to the jet axis are presented and analyzed. Periodic unstable oscillations of the jet flow, with the resultant radiation of sound of discrete frequencies, occur over a wide variation of control parameters, namely, pressure ratio, plate size, and spacing of the plate from the jet nozzle. For ‘‘small’’ plates, the principal oscillations with λ/D about 4 (λ=acoustic wavelength, D=nozzle diameter) occur when the standoff shock wave lies in a pressure recovery region of the periodic cellular structure of the choked jet and is, therefore, highly unstable; then the oscillations have key characteristics in common with the high-harmonic excitation of Hartmann’s acoustic air-jet generator. An analogous feedback mechanism in the standoff zone is suggested in which pressure waves reflected from the plate trigger the motion of the unstable shock wave. For ‘‘large’’ plates, acoustic feedback to the nozzle occurs, and the principal tones have λ/D about 2 with frequencies nearly independent of pressure ratio (velocity) and plate size. They exhibit the sawtooth characteristic familiar in similar situations (edge tone, hole tone, and for subsonic jets interacting with flat plates), there being at least seven stages, frequently with frequency jumps between them. A feedback mechanism is suggested, and a formula for the frequency of oscillation is derived, the form of which is consistent with experimental data. Secondary tones also occur, at least some of those of higher frequency (λ/D≊1) appearing to be extensions of the large-plate principal tones, but those of lower frequency, while of the precisely same character, presumably are from a differing instability mode. The characteristics of these principal and secondary tones provide the means of analysis of the limited existing pertinent literature. Several sets of data can be classified into the small- and large-plate classes for ‘‘moderate’’ and ‘‘high’’ degrees of underexpansion. For ‘‘very highly’’ underexpanded jets, the mechanism for small and large plates appears to merge, and, correspondingly, there is no longer the distinction between the phenomena for small and large plates as pertains at lower pressure ratios.