Wavenumber-Based Impedance Eduction with a Shear Grazing Flow

Abstract

While intrinsic by definition, the impedance measured by impedance eduction has been shown to depend on the direction of the incident waves relative to the mean flow. The purpose of the present work is to evaluate whether part of the observed differences could stem from a biased wavenumber definition made during the impedance eduction process.Comparisons are made between the results of impedance eductions with uniform flow and the Ingard-Myers boundary condition, with the 1D linearized Euler equations and with the 2D linearized Euler equations, i.e., in the cross section. Both numerical synthetic data and experimental data are used for the eduction of two sample liners, with bulk Mach numbers ranging from 0 to 0.3, and at frequencies ranging from 400 to 3000 Hz.Results show that for a rectangular cross-section duct, the knowledge of the 2D flow profile in the cross section is valuable for impedance eduction. Using only 1D flow profiles bias the educed impedance estimation.

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

“…In fact, for low Mach numbers and Helmholtz numbers, it is possible to show that ζ ≈ βM by comparing Eqs. ( 6) and (8), which is confirmed in Fig. 9.…”

“…However, Weng et al [4] concluded that viscosity is not able to account for the discrepancy between upstream and downstream and collapse the educed impedances onto one value per frequency, while Nark et al [7] found that small corrections to the mean flow velocity were sufficient to collapse the upstream and downstream educed impedances. More recently, Roncen et al [8] concluded that this inconsistency is still present even when considering a three-dimensional inviscid sheared flow profile and no-slip condition at the lined wall, suggesting the liner physics are still not fully captured. With this is mind, novel boundary conditions have been introduced in the past years by including an additional parameter to better describe the liner physics [9,10].…”

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

“…The difference in impedance when using upstream or downstream acoustic sources with both in-situ and impedance eduction techniques may arise from different reasons. In the case of impedance eduction, the flow is assumed as uniform, which may introduce a significant error especially for upstream acoustic propagation 40 i.e. when using a downstream acoustic source.…”

Design and optimization of acoustic liners with a shear grazing flow: OPAL software platform description

“…It basically consists in building an eigenvalue problem and solving it on arbitrary geometries, with or without flow and/or impedance boundary conditions. The generalized eigen problem is solved with an Arnoldi's method [21].…”