Observations on Impedance Eduction in a Grazing Flow Duct Facility


This paper focuses on details of impedance eduction based on grazing flow duct testing. In this indirect approach the impedance of a sample of acoustic material, imbedded in one wall of the duct, is deduced (educed) from measurements of the acoustic field in the duct and comparison with a theoretical model of the acoustic field in the duct. The theoretical model is adjusted with a systematic variation of impedance to search for and achieve the best match of measurement and prediction. For measurement 0 ≤M ≤0.4 accuracy the mean flow is limited to approximately, and to a maximum frequency dependent on the duct geometry and grazing flow Mach number. The goal of the eduction procedure reported here is to provide a research quality capability to determine the impedance of samples of uniform normally reacting acoustic liners designed for turbo-fan engine inlet and by-pass ducts. Additional goals include relatively low cost of instrumentation and rapid turnaround of testing and data post-processing. Instrumentation includes only two microphones, one fixed reference microphone and one traversing microphone. The measured acoustic field is defined by FFT processing at multiple dwell points of the traversing microphone on the duct wall opposite to the lining sample to produce an acoustic transfer function. A finite element propagation code is used for theoretical prediction of the acoustic transfer function. Specific details addressed here include a unique implementation of the finite element method for the convected wave equation tailored for the duct geometry and frequency range. The propagation model allows the duct termination plane to be represented by measured acoustic pressure or by a separately educed termination impedance. Comparisons are made of educed impedance spectra obtained with the two termination choices and it is found that the best quality impedance spectra are obtained with the termination impedance boundary condition. A supporting analysis is provided to define the range of frequency and duct grazing flow Mach number for which the principal limitation of plane wave propagation can be achieved consistent with the placement of source and termination microphones. A refinement of the eduction process is the introduction of a two level search with an initial iteration based on a fixed effective duct Mach number accounting for the duct flow profile and a final iteration that allows effective Mach number to vary to produce improved iteration error. Multiple examples of educed impedance spectra for single and two degree of freedom liners representative of current designs document the quality that can be achieved, as well as limitations.


Mechanical and Aerospace Engineering

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Article - Conference proceedings

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Publication Date

01 Jan 2022