Straightforward impedance eduction method for non-grazing incidence wave with multiple modes

The control of modern aeroengine noise poses great challenge to the design of acoustic liners, due to the existence of multiple higher-order modes over a very wide frequency range in acoustic nacelles. In order to meet the pressing demand, the straightforward impedance eduction method is further developed such that it can be applied to more general acoustic environment where there are both plane mode and higher-order modes incident upon a test liner. A novelty of the present method is using a diagonally mounted microphone array on the opposite wall of the test liner in a flow duct, thus the measured wall sound pressure simultaneously contains the information of the modes in both the axial and transverse directions. Then, the employment of Prony's method enables the realization of the full modal decomposition to the acoustic field in the flow duct. Numerical experiments simulating acoustic fields with a finite element model are conducted to investigate and validate the feasibility of the present method for both a small-scale and a large-scale flow ducts. Two ceramic tubular liners and a perforated liner are tested as specimens, whose impedance values to be educed are known a priori by means of existing impedance models. Random perturbation is added into the acoustic field data to simulate realistic noisy acoustic environments. The results show that the present method can educe the imposed impedance with a good accuracy when the liner specimens are subjected to the sound field composing of multiple incident modes including several transverse modes in both ducts. The frequency scope of the impedance eduction is considerably extended when compared with the methods restricted by the assumption of plane incident mode, with the upper frequency reaching up to 6.0 kHz and 5.0 kHz for the ducts, respectively. A parametric study indicates that the accuracy of impedance eduction can be promoted by increasing the signal-to-noise ratio and the number of microphones.