New Numerical Procedure for Impedance Eduction in Ducts Containing Mean Flow

Abstract

A new impedance eduction method is presented and validated against a benchmark method, and the effects of measurement uncertainty errors on the impedances educedwith this newmethod are assessed.Unique features of the newmethod include the following: 1) the upstream and downstream boundary conditions contain higher-order duct modes, 2) the impedance spectra of unique nonuniform test liners on opposite walls may be educed simultaneously, and 3) the measured data for the impedance eduction are acquired only at the source and duct termination planes. The validation exercise is performedwith a rigid-wall insert and a conventional liner over a range of frequencies and flowMach numbers in the NASALangleyResearchCenter’s grazing flow impedance tube. The primary conclusions of the study are that the impedance spectra of the rigid-wall insert and the conventional liner that were educed from the newmethod are in very good agreement with those that were educed by using the benchmarkmethod. However, the effects of measurement uncertainty on the educed impedance are greater at the lower frequencies and the higher Mach numbers for the newmethod. All indications are that this occurs because the newmethod 1) uses significantly less data to perform the impedance eduction than the benchmark and 2) is currently based on a rather crude approximation to the measured pressure gradient, which is more sensitive to the refractive effects of the boundary layer than the measured lower-wall pressure that is required in the benchmark method.