Design of optimum acoustic treatment for rectangular ducts with flow

A design optimization technique for acoustic treatment in rectangular ducts with uniform mean flow is presented. The technique is based on the acoustic wave solution in terms of series of characteristic duct modes. The analysis allows multiple axial treatment sections along the length of the duct and requires a known modal characterization of the sound source. Conditions of acoustic pressure and acoustic velocity continuity are used to match modal solutions at planes of impedance discontinuity in the duct. Experimental techniques for obtaining this modal characterization are presented. Using duct modes measured at the source plane, the optimization technique is exercised to design an optimized single element liner in a case without mean flow, and optimized single and dual element liners in cases with mean flow. The validity of the program for predicting noise suppression is demonstrated by comparing analytical predictions with measured data for several (non-optimum) cases. Application to treatment design in turbomachinery exhaust ducts is considered.