On the use of a stress–impedance model to describe sound propagation in a lined duct with grazing flow

Abstract

With flow, the acoustic effect of a locally reacting lined wall cannot be described by a single quantity independent of the incident wave, such as a wall impedance. At least two quantities, intrinsic to the liner and to the flow, are required to describe the effect of the lined wall regardless of the incident wave. In addition to the impedance, the unsteady tangential force exerted by the wall on the flow has to be taken into account. This force is due either to viscous effects or to the unsteady transfer of axial momentum from the flow into the lined wall. This paper describes a stress-impedance model, where the two variables used are the impedance and the friction factor that links the pressure to a tangential stress at the wall. The use of a wall stress helps to better understand the mechanisms of momentum transfer between the flow and the wall in the vicinity of an acoustic treatment.

Wavenumber-Based Impedance Eduction with a Shear Grazing Flow

“…It is also shown that a correlation exists between the remaining impedance mismatch and the uncertainties obtained via the Bayesian inference eduction, showing that the two quantities might relate to the same phenomenon (larger uncertainties when the liner is not absorbent). Another possibility is the presence of unmodeled physics of the impedance boundary condition, which is still an ongoing research topic [42,43]. However, the present work shows that the refinement of physics modeling will require accounting for the experimental uncertainties in impedance eduction.…”

Flow–acoustic resonance in a cavity covered by a perforated plate

“…At the entrance of each hole a resistive sheet with R = 0.0175 has been added, which accounts for the thermo-viscous effects. This value has been empirically chosen so that, in § 4, both unstable and stable global modes can be obtained by slightly adjusting R. Such a resistance can also mitigate the convergence problem of the calculations, which is caused by the discontinuity of df /dy at y = 1 (Dai & Aurégan 2016, 2018. It has been shown that sound can be amplified by this non-local liner at certain frequencies (Dai & Aurégan 2019).…”

“…However, it should be noted that such an impedance model can lead to inaccuracy in describing wave propagation in a flow duct, especially when the flow velocity is high (Dai & Aurégan 2016;Aurégan 2018). For this reason, only a qualitative comparison can be made between the discrete and homogenized models, and a quantitative agreement requires a more precise homogenization of a perforated plate with flow.…”

“…Liners are effective in mitigating noise emissions from flow ducts such as aero-engine nacelles. A detailed description of sound absorption in a lined flow duct (Tam et al 2014;Zhang & Bodony 2016) and an accurate boundary condition on the lined wall (Khamis & Brambley 2016Aurégan 2018;Masson et al 2018;Mathews et al 2018) have been the subject of recent studies. On the other hand, a liner with a grazing flow can also act as a sound amplifier (Brandes & Ronneberger 1995;Ronneberger & Jüschke 2007;Aurégan & Leroux 2008;Marx et al 2010;Marx & Aurégan 2013;Dai & Aurégan 2018), or a 'singer' (Tam et al 2014).…”

“…Sketches of (a) flow-acoustic coupling along a cavity-backed perforated plate in a flow duct and (b) hole-by-hole calculation of wave scattering. (Dai & Aurégan 2016, 2018. First, a complete description of the problem is presented, where the linear flow-acoustic coupling near the perforated plate is modelled hole by hole.…”