Validation of an Inverse Semi-Analytical Technique to Educe Liner Impedance

In this paper, the acoustic impedance of a liner is educed by a novel semi-analytical inverse technique. The liner sample is placed flush with the solid walls in a rectangular duct with grazing flow. The technique uses complex acoustic pressure measured at four positions at the wall of the duct, upstream and downstream of the lined section, and educes the impedance with a mode-matching method. Previous studies neglected grazing flow nonuniformity and the pressure discontinuity that appears at the liner-wall boundary caused by the discontinuity of the acoustic particle velocity into the wall. In the present paper, the mode-matching formulation is rederived in terms of pressure instead of velocity potential which is found to be more numerically stable. Moreover, the proposed methodology is validated with benchmark data from an experiment performed by NASA. First, the ability of the code to reproduce the pressure field for a given impedance is tested. Second, the ability to educe the correct impedance for a given pressure distribution is tested. The results of the mode-matching code are in very good agreement with the experimental data. The effect of shear flow is investigated and it can be concluded that the assumption of uniform flow is appropriate for the chosen liner, duct size, and frequency range of interest.