Spatially-varying impedance model for locally reacting acoustic liners at a high sound intensity

Abstract

This paper is concerned with spatially-varying acoustic liner impedance in aeroacoustic ducts, in the presence of a high sound pressure level. It is shown that impedance discontinuity is a leading order parameter in the definition of the impedance variation. A large impedance discontinuity yields a high normal velocity variation, leading to significant nonlinear effects. An iterative numerical strategy is proposed to predict the spatiallyvarying acoustic impedance over a liner. A Bayesian inference process is coupled with a surrogate model to validate the model with measurements of the acoustic velocity fields above a liner at a high sound intensity, obtained using laser Doppler velocimetry.

Generic and broadband non-linear time domain impedance boundary condition

“…Contrary to what was expected from Ref. [60], the real part of the spatially-varying impedance does not display a much higher value in the case of M2 where the linear resistance is very low. The difference in behaviour remains unexplained, and is here not attributed to the presence of viscosity in the NS equations, since similar results were obtained with the Euler equations.…”

“…After this limit, the resistance becomes too high and the attenuation decreases, as in the case of M1. The second reason behind this nonphysical change is rooted in our last work [60] on the topic, where we used an iterative method in the frequency domain to tackle the non-linear behavior of the impedance. One of the conclusions of that work was that for a given α NL , less resistive liners would display an increased variation of the impedance across their surface, because the impedance discontinuities would be more marked at the wall-liner junctions, inducing a higher normal velocity close to the discontinuity.…”

A comparison of in situ and impedance eduction experimental techniques for acoustic liners with grazing flow and high sound pressure level

“…26 The SPL for the microphones used for the KT algorithm during the Sample B measurements with 145 dB are presented in Figure 14. One alternative to address this decay along the axis is to consider an impedance model embedded within the eduction technique, so the impedance spatial variation may be considered, similar as has been applied recently by Roncen et al 27 Other phenomena related to the SPL is observed in the Sample A results. The acoustic sources were not capable of reaching the target 145 dB at the facesheet at higher frequencies, although the incident SPL increased considerably.…”

“…26 The SPL for the microphones used for the KT algorithm during the Sample B measurements with 145 dB are presented in Figure 14. One alternative to address this decay along the axis is to consider an impedance model embedded within the eduction technique, so the impedance spatial variation may be considered, similar as has been applied recently by Roncen et al 27

Figure 14.SPL at microphones opposite to the wall. Sample B, no-flow condition and 145°dB at liner facesheet.

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