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Two procedures of acoustic liner impedance eduction with account of the impedance variability

The paper considers two impedance eduction procedures of an acoustic liner typical for lining aircraft engine ducts. Usually applied approaches to liner impedance eduction consider it to be a constant along the liner sample, whereas at high levels of sound pressure inherent in the operating conditions of the aircraft engine, the impedance changes as a sound pressure changes. Including this effect into impedance eduction procedure will make it possible to increase the accuracy of determining the acoustic liner impedance. The first procedure is based on the description of the impedance variability along the liner as a function of the cubic spline. Its coefficients are determined from the optimization problem so as to ensure a minimum discrepancy between the computed and experimental values of the acoustic pressure at specified points in the grazing incidence impedance tube. The second procedure at the beginning describes the impedance distribution as a linear function of the acoustic pressure. Then, when minimizing the residual functional, an iterative procedure is performed at each optimization step, which solves a system of nonlinear algebraic equations to calculate acoustic pressure values. As a result, the coefficients of the impedance linear dependence are adjusted. Obtained results have shown that both proposed procedures lead to a decrease in the residual functional and in some cases it can be reduced by more than 2 times. The procedures adequately respond to pressure changes along the sample: the distance between the impedance peaks is close to the sound pressure halfwavelength at the frequency in question; for that part of the liner sample where the sound pressure level noticeable decreases the educed impedance is constant. This corresponds well to the ideas about the physics of the resonant acoustic liner operation at high and low sound pressure levels.