Modal content of noise generated by a coaxial jet in a pipe

The problem investigated was that of noise generated by air flow through a coaxial obstruction in a long, straight pipe of inside diameter, D = 97 mm. Downstream modal pressure spectra in the 200–6000 Hz frequency range were measured by a new technique 1] for orifices and nozzles of diameter d where $\text{0·03 ? (}\text{d}\text{D}\text{) ? 0·52}$. The Mach numbers of the flow through the restrictions ranged from 0·15 to choked conditions. The shape of the modal frequency spectrum was found to be determined by the frequency ratio $\text{f}{}_{\mathrm{r}}\text{=}\text{He}\text{St}\text{=}\text{U}{}_{\mathrm{i}}\text{D}\text{a}{}_0\text{d}$, where U_i is the jet velocity and a₀ is the speed of sound in the gas downstream of the restriction. This parameter is the ratio of two non-dimensional frequencies: namely, He, which controls acoustic propagation inside circular ducts, and St, which scales the jet noise spectrum shape. At low f_r(<3) the higher modes dominate the noise spectrum above their cut-off frequencies, while for higher f_r all modes are approximately of equal amplitude. The nature of large scale turbulence structures in the region of the jet near the nozzle exit may be used to explain these phenomena. The measured modal pressure spectra were converted to modal power spectra and integrated over the frequency range 200–6000 Hz. The acoustic efficiency levels (acoustic power normalized by jet kinetic energy flow), when plotted vs. jet Mach number, depend strongly on the ratio of restriction diameter to pipe diameter ($\text{d}\text{D}$). Dividing the efficiency levels by the area ratio, $\text{(}\text{d}\text{D}\text{)}{}^2$, correlated the results over a moderate range of ($\text{d}\text{D}$).