Impedance Eduction with an Extended Search Procedure


This paper documents the application of a finite element model for the specific purpose of impedance eduction by an inverse method in a flow duct facility with an upper Mach number capability of approximately M = 0.5 and an upper frequency limit for plane wave propagation of approximately 3000 Hz. The acoustic field is not limited locally to plane wave propagation, but away from any non-uniformity in duct geometry or acoustic treatment non-planar propagation is cut-off and the acoustic field approaches uniformity. Source conditions and termination conditions are therefore represented by a plane wave mode. The physical duct for which results are presented is uniform with square cross section with acoustic treatment inserted on one wall. The duct model is two dimensional based on the assumption of no variation of the acoustic field across the width dimension between hard walls. Duct geometry is arbitrary in the height dimension with the upper wall lined and the lower wall lined or unlined depending on the case. Applications presented deal only with a uniform duct test facility, though the model is general enough to include a curved duct test facility. Impedance eduction from experimental data is based on an iterative process in which impedance of a sample lining is assumed and the acoustic field is predicted with the finite element code. A search algorithm is used to find the best fit of the predicted acoustic field with the measured acoustic field. In this investigation additional degrees of freedom are introduced in the search process so that lining impedance, termination impedance, and duct Mach number are varied to produce the best fit with the measured acoustic field. With Mach number as a degree of freedom, substantially improved data fitting is achieved as compared to the use of an a priori assumption of effective Mach number presumed to account for real flow effects. In this paper details of the finite element method implemented are referred to the literature, but a complete development of the correct termination impedance used as a natural boundary condition is provided. Published NASA Langley Research Center Grazing Incidence Tube data is used in benchmark examples. Data from the Spirit AeroSystems flow duct facility is used to emphasize the quality of results achieved.

Meeting Name

15th AIAA/CEAS Aeroacoustics Conference (2009: May 11-13, Miami, FL)


Mechanical and Aerospace Engineering

Keywords and Phrases

Finite Element Model; Flow Duct Facility; Impedance Eduction; Inverse Method

Document Type

Article - Conference proceedings

Document Version


File Type





© 2009 American Institute of Aeronautics and Astronautics (AIAA), All rights reserved.

Publication Date

13 May 2009

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