Experimentally testing impedance boundary conditions for acoustic liners with flow: Beyond upstream and downstream

Abstract

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Design of a single degree of freedom acoustic liner for a fan noise test rig

“…The key idea of impedance eduction methods is to compare the measured acoustic field to the numerical one with a given initial impedance guess, for instance an impedance prediction given the liner geometry, and from that iterate the liner impedance until both fields converge. The mode-matching method has been selected over the Finite Element Method 33 and other similar numerical techniques due to its reduced computational cost and high accuracy, 34 which are essential characteristics for inverse methods.…”

“…[35][36][37][38] Although similar in nature, each of these works adopt different assumptions and solution strategies. The procedure here described follows the same approach from Spillere et al, 34 and for that reason details are omitted for brevity.…”

“…In general, the choice of matching condition is of little importance in the context of impedance eduction, provided some guidelines for the cost function are followed. 34 Substitution of equations (21a) and (21b) into equations (23a) and (23b) lead to a system of 2N equations at each interface. Inputs are the plane wave amplitudes A � 1 propagating towards the liner sample, which can be determined from an over-determined plane wave decomposition upstream and downstream to the lined section.…”

“…The use of alternative boundary conditions that take into account boundary layer effects are also not sufficient to remove this discrepancy in two-dimensional models. 34 Given the typical duct dimensions of liner test rigs, duct propagation models for impedance eduction should include the three-dimensional flow profile. Regarding the in-situ impedance, it is difficult to determine the local boundary layer characteristics at the liner leading and trailing edges, and whether this change would be sufficient to cause the observed differences in resistance.…”

Acoustic-induced velocity in a multi-orifice acoustic liner grazed by a turbulent boundary layer

“…However, these modifications are not able yet to explain some experimental contradictions, such as the dependence of the acoustic impedance on the relative direction between the convecting flow and the acoustic waves [8,9]. It has been recently proven that this is caused by inaccurate modelling of the boundary conditions [10].…”