The acoustics of a lined duct with flow

A theory to calculate the sound propagation (including attenuation, reflection, radiation) through a three-sectioned cylindrical flow duct, modeling an aero-engine inlet is described. The flow is uniform apart from a thin boundary layer; two of the three sections are hard-walled, with an impedance-walled section in between. The modal amplitudes of the sound field in the duct are determined by an iterative technique allowing the modal expansions to include as many terms as required. The modal eigenvalues are found using a classification based on a distinction between acoustic modes and surface waves. Numerically, the main results are contour plots of constant attenuation, in the complex impedance plane. A dramatic effect of lining (via the occurrence of surface waves) on a sound field that is cut-off in a hard-walled duct is observed. The problems with a lining of constant impedance, and with a (necessarily variable) nonreflective impedance are considered. This problem is mainly relevant to an (acoustic) wind tunnel. It is shown that, for a given free field of the source, the solution describing this impedance distribution can be given analytically in closed form.