Feedback mechanism of low-speed edgetones

Abstract

A feedback mechanism of low-speed edgetones is analyzed by using the jet edge interaction model in which reaction of the edge is regarded as an array of dipoles. From the jet-edge interation 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 tip to a peak value around a quarter wavelength downstream, which may be regarded as an 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, the phase factorp is found to be in the range, −1/2<p<0, in the phase criterion of the form,h/A+h/λ=n+p, where h is the stand-off distance.A and λ the wavelengths of downstream and upstream respectively, andn the stage number. From the existing experimental data the phase factor is estimated on the basis that the convection wavelength is dependent only upon the mean jet velocity and the frequency, but not upon the stage number. The experimental values are in the same range of the theoretical estimation indicating that the phase factor is not a universal constant but varies in the range, −1/2<p<0, depending on the nozzle-edge configuration and the flow condition.