Feedback mechanism of low-speed edgetones

Abstract

The feedback mechanism of low-speed edgetones is analyzed by using the jet–edge interaction model in which reaction of the edge is modeled by an array of dipoles. From the jet–edge interaction model the surface pressure of the edge and the upstream wave are estimated by assuming the downstream disturbance as a sinuously oscillating flow with a constant convection speed. The surface pressure distribution on the edge is found to increase from zero at the edge tip to a peak value around a quarter wavelength downstream, which may be regarded as the effective source point of the upstream-propagating sound wave. From the condition that the two wave trains should be phase-locked at the nozzle lip, p=−14 is obtained for low-speed edgetones in the phase criterion of the form, h/Λ+h/λ=n+p, where h is the stand-off distance, Λ and λ are the wavelengths of downstream and upstream, respectively, and n is the stage number. Based on the phase criterion, the ratio of the convection speed, Uc, to the jet speed, U0, is estimated from the experimental data for low-speed edgetones and found to be about Uc/U0=0.6 and to be almost independent of frequency. Finally, an approximate model for the frequency characteristics has been obtained in the form, St=(d/h)[(n−1/4)/(1/0.6+M0)], where d is the width of the two-dimensional nozzle, M0 the Mach number of the jet velocity, St is the Strouhal number, St=fd/U0, and f is the frequency. The present model is confirmed substantially in comparison with available experimental data.