Local Effects of Sheared Grazing Flow on Impedance Eduction

Impedance eduction is the preferred method for acoustic liner characterization under grazing flow conditions. The method usually assumes an uniform impedance for the whole lined wall. However, in situ local measurements suggest the liner impedance is influenced by the flow profile above the liner. Therefore, the liner impedance is expected to vary spatially due to the three-dimensional nature of the grazing flow profile inside dedicated test rigs. In this work, we study the impact on impedance eduction of failing to account for this local variation in liner impedance. A numerical synthesized experiment is used to investigate the uniform impedance assumption. The axial wavenumbers of a lined rectangular duct with sheared flow profile are obtained by solving the Pridmore-Brown Equation. The wavenumbers in the lined section are evaluated with both a variable wall impedance and with the wall impedance taken constant at an averaged value. The wavenumbers are then used to educe the lined wall impedance by means of the traditional straightforward impedance eduction method. Results suggest that the impact of assuming an uniform impedance at the lined wall are negligible, since both upstream and downstream wavenumbers evaluated for the different impedance assumptions almost perfectly match.