Failure of the Ingard–Myers boundary condition for a lined duct: An experimental investigation

Abstract

This paper deals with experimental investigation of the lined wall boundary condition in flow duct applications such as aircraft engine systems or automobile mufflers. A first experiment, based on a microphone array located in the liner test section, is carried out in order to extract the axial wavenumbers with the help of an "high-accurate" singular value decomposition Prony-like algorithm. The experimental axial wavenumbers are then used to provide the lined wall impedance for both downstream and upstream acoustic propagation by means of a straightforward impedance education method involving the classical Ingard-Myers boundary condition. The results show that the Ingard-Myers boundary condition fails to predict with accuracy the acoustic behavior in a lined duct with flow. An effective lined wall impedance, valid whatever the direction of acoustic propagation, can be suitably found from experimental axial wavenumbers and a modified version of the Ingard-Myers condition with the form inspired from a previous theoretical study [Aurégan et al., J. Acoust. Soc. Am. 109, 59-64 (2001)]. In a second experiment, the scattering matrix of the liner test section is measured and is then compared to the predicted scattering matrix using the multimodal approach and the lined wall impedances previously deduced. A large discrepancy is observed between the measured and the predicted scattering coefficients that confirms the poor accuracy provided from the Ingard-Myers boundary condition widely used in lined duct applications.

A wave expansion method for acoustic propagation in lined flow ducts

“…Thirdly, and perhaps most likely, this disagreement at lower frequencies is consistent with the type of failure of the Myers boundary condition discussed in Ref. [24], where the model impedance values were found to be dependent on the direction of propagation. Therefore, waves reflected back upstream see a different impedance.…”

“…It has also been shown that the Myers model fails to result in a single impedance value for wave propagation downstream and upstream in a lined duct when the acoustic boundary layer is not much smaller that the mean flow boundary layer thickness, i.e. at low frequencies [24]. This finding does not negate the use of the model altogether but rather it limits its applicability.…”

Evaluation of Wall Boundary Conditions for Impedance Eduction Using a Dual-Source Method

“…11 In their paper, Renou and Auregan used Prony's method 12 to educe the impedance of a conventional liner using the Ingard-Myers boundary condition under the assumptions of uniform flow. They educed different impedances for an upstream and downstream source, although the incident sound pressure level and the mean flow Mach number were held constant for both sources.…”

“…They educed different impedances for an upstream and downstream source, although the incident sound pressure level and the mean flow Mach number were held constant for both sources. Because the liner impedance should not be dependent on whether the source is upstream or downstream, 11 it was concluded that "the Ingard-Myers boundary condition fails to predict with accuracy the acoustic behavior in a lined duct with flow." They presented results for a conventional liner achieved at a single flow speed to support this conclusion.…”

The Effect of Boundary Layers on Bulk Reacting Liners at Low Mach Number Flows

“…Myers' condition is easily implemented due to its simplicity and the minimum of information needed of the boundary layer geometry etc. However, the condition has been proven to fail to describe the influence of the flow above the surface, in for example 15 .…”