Self-excited depth-mode resonance for a wall-mounted cavity in turbulent flow

Abstract

Experimental and theoretical results are presented for a wall-mounted cavity in turbulent flow, oscillating at Helmholtz or depth-mode resonance, where the mouth dimensions are small compared with acoustic wavelength. A new, computerized, hot-wire method was employed to investigate the oscillating flow field in the cavity mouth. Measured wavelength of the interface wave agrees well with predictions of Michalke, using an equivalent laminar flow model based on the oscillating mean velocity profile. By means of a forward transfer function derived from the theoretical interface wave model and a backward transfer function derived from organ-pipe theory, a root locus solution of the frequency lock-in problem has been obtained. Predicted frequencies and sound pressure amplitudes are in good agreement with experimental values at the lower modes. Both resonant and off-resonant oscillation was investigated. For resonant oscillation, the streamwise slot width is required to be M−1/4 times the disturbance wavelength, where M is an integer. For situations in which the equations are applicable, the method can be used to predict design parameters for nonoscillating wall cavities in moving vessels.