On Sound Radiation from an Open-Ended Non-Uniformly Lined Cylindrical Nozzle

The paper considers the radiation of sound out of a cylindrical duct with non-uniformly lined walls. The consideration of a flanged nozzle reduces the problem to the radiation of sound from a disk at the nozzle exit plane to an observer in the far-field. The turbulent and irregular shear layer issuing from the nozzle lip of the unflanged nozzle changes the directivity and spectrum, as discussed in several references. The sound field in the nozzle exit plane consists of cylindrical waves with complex radial, and hence axial wavenumbers, due to a circumferentially non-uniform wall impedance. The modes in the duct are related to the modes in the far-field, allowing a comparison of different duct linings: uniform or circumferentially non-uniform, the latter with a smaller or larger degree of variation. It is concluded that a non-uniformly lined wall, with circumferential impedance variations of 30% has an observable difference in the sound radiated outside the duct to the far-field. The effect of the circumferentially non-uniform impedance of the duct wall on the far-field depends on the acoustic mode, and can be either moderate attenuation or slight amplification.