Wavenumber-Based Impedance Eduction with a Shear Grazing Flow

While intrinsic by definition, the impedance measured by impedance eduction has been shown to depend on the direction of the incident waves relative to the mean flow. The purpose of the present work is to evaluate whether part of the observed differences could stem from a biased wavenumber definition made during the impedance eduction process. Comparisons are made between the results of impedance eductions with uniform flow and the Ingard-Myers boundary condition, with the one-dimensional (1D) linearized Euler equations and with the two-dimensional (2D) linearized Euler equations, that is, in the cross section. Both numerical synthetic data and experimental data are used for the eduction of two sample liners, with bulk Mach numbers ranging from 0 to 0.3, and at frequencies ranging from 400 to 3000 Hz. Results show that, for a rectangular-cross-section duct, the knowledge of the 2D flow profile in the cross section is valuable for impedance eduction. Using only 1D flow profiles biases the educed impedance estimation.