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On impedance conditions for circular multiperforated acoustic liners

Schmidt, Kersten and Semin, Adrien and Thöns-Zueva, Anastasia and Bake, Friedrich :
On impedance conditions for circular multiperforated acoustic liners.
In: Journal of Mathematics in Industry, 8 ISSN 2190-5983
[Article], (2018)

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Item Type: Article
Title: On impedance conditions for circular multiperforated acoustic liners
Language: English
Abstract:

Background The acoustic damping in gas turbines and aero-engines relies to a great extent on acoustic liners that consists of a cavity and a perforated face sheet. The prediction of the impedance of the liners by direct numerical simulation is nowadays not feasible due to the hundreds to thousands repetitions of tiny holes. We introduce a procedure to numerically obtain the Rayleigh conductivity for acoustic liners for viscous gases at rest, and with it define the acoustic impedance of the perforated sheet.

Results The proposed method decouples the effects that are dominant on different scales: (a) viscous and incompressible flow at the scale of one hole, (b) inviscid and incompressible flow at the scale of the hole pattern, and (c) inviscid and compressible flow at the scale of the wave-length. With the method of matched asymptotic expansions we couple the different scales and eventually obtain effective impedance conditions on the macroscopic scale. For this the effective Rayleigh conductivity results by numerical solution of an instationary Stokes problem in frequency domain around one hole with prescribed pressure at infinite distance to the aperture. It depends on hole shape, frequency, mean density and viscosity divided by the area of the periodicity cell. This enables us to estimate dissipation losses and transmission properties, that we compare with acoustic measurements in a duct acoustic test rig with a circular cross-section by the German Aerospace Center in Berlin.

Conclusions A precise and reasonable definition of an effective Rayleigh conductivity at the scale of one hole is proposed and impedance conditions for the macroscopic pressure or velocity are derived in a systematic procedure. The comparison with experiments show that the derived impedance conditions give a good prediction of the dissipation losses.

Journal or Publication Title: Journal of Mathematics in Industry
Volume: 8
Classification DDC: 500 Naturwissenschaften und Mathematik > 510 Mathematik
Divisions: 04 Department of Mathematics > Numerical Analysis and Scientific Computing
Date Deposited: 12 Jul 2019 12:55
Last Modified: 12 Nov 2019 13:49
DOI: 10.1186/s13362-018-0057-0
URN: urn:nbn:de:tuda-tuprints-88595
URI: https://tuprints.ulb.tu-darmstadt.de/id/eprint/8859
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