On the prediction of sound attenuation in acoustically lined circular ducts

A prediction method for sound attenuation in acoustically lined circular ducts of uniform cross section containing radially sheared fluid flow is developed. The flow is regarded as consisting of a core of uniform flow surrounded by a thin layer near the duct wall in which the flow is sheared. The method is based on the solutions (acoustic modes) of an eigenfunction derived from the governing wave equation and the boundary conditions. Sound attenuation is computed by assuming equal distribution of the acoustic energy among the propagating acoustic modes at the reference plane. Amplitudes of modes reflected from the duct termination are considered negligible. To test the method, predictions are compared with measured data from circular section flow duct absorber test facilities and from liner tests in the intake duct of the RB 211 turbofan engine. The agreement between the measured and the predicted attenuation spectra is very good when sound propagation is upstream. In the downstream propagation case, equal modal energies lead to slight over prediction of sound attenuation at higher frequencies. An empirical solution to this problem is found by restricting the computation to the modes of the first four circumferential orders. A numerical technique is developed which uses only a fraction of the modal solutions to compute attenuations without loss of accuracy, thus considerably saving computing time and costs. A detailed study is carried out to highlight the effects on modal and total attenuations of changes in the values of the principal parameters and a number of design guidelines are deduced. Procedures for the prediction of sound attenuation in engine ducts are discussed and an approach to design the most effective liners is suggested. A comprehensive set of computer programs is developed to assist the Noise Engineer in the predictions and design optimisations of acoustic liners in project engines.