Determination of large-size liner impedance based on numerical simulation of sound propagation in a duct with specified azimuthal modal structure

A study of determining impedance of a large-size sound-absorbing liner with azimuthal acoustic modes propagating in a duct was conducted on the basis of numerical simulation. The first stage of the study consisted in developing a method of impedance eduction on the basis of a simple cylinder model with microphones installed outside the sound-absorbing liner section. The full-scale experiment was replaced by numerical simulation of the propagation of a specified azimuthal noise structure in a cylindrical duct with known impedance wall (direct problem). As a result of solving the direct problem, the values of acoustic pressures are determined at those points where microphones are to be installed during the realization of the full-scale experiment. The results obtained are used to find the initial impedance value (inverse problem). The solution of the inverse problem using the procedure of minimizing the discrepancy between the acoustic pressures of the direct and inverse problems showed good accuracy of finding the impedance. It was also found that the accuracy of impedance eduction practically does not vary with the angle of installation of the linear array of microphones. The second stage of the study consisted in applying the developed approach to the model of a facility for testing large-size sound-absorbing liners. Acceptable accuracy of determining the impedance was achieved with certain quality of the finite element mesh. It has also been checked that, to save the computational time, for some acoustical modes acceptable accuracy of impedance eduction is possible in an axisymmetric statement. Thus, the possibility of using the proposed approach based on numerical simulation for the eduction of  sound-absorbing liner impedance was confirmed.