PREDICTION OF LOW-FREQUENCY TONES PRODUCED BY FLOW THROUGH A DUCT WITH A GAP

A method is presented for predicting the frequencies of tones produced by high Reynolds number, subsonic flow through a duct with a gap. An inviscid, linear model of the fluid motion is developed in which the shear layer delimiting the jet formed between the inlet and exit of the duct gap is modelled as a vortex sheet. The linear analysis is used to calculate the Rayleigh conductivity parameter which is then analyzed to find the frequency dependence of the shear layer behavior. The calculations for the case when an external load is applied across the shear layer have been carried out for Strouhal numbers from 0 to 10, Mach numbers from 0·001 to 0·5, and a gap length-to-diameter ratio of 0·5 to 2·0. The resonant frequencies have been calculated for Mach numbers ranging from 0·001 to 0·8 at a length-to-diameter ratio of 1·0. The results for the forced motion in the low Mach number limit compare well with previous incompressible predictions for flow past wall apertures. The resonant frequency predictions have been validated at the Mach number of 0·52 through comparison with experimental data.