Transmission of Sound in Ducts with Thin Shear Layers—Convergence to the Uniform Flow Case

Eversman, Walter; Beckemeyer, Roy J.

doi:10.1121/1.1913082

Cited by 111 publications

(86 citation statements)

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“…The reason for this decision appears to be based on the work of Eversman and Beckemeyer 7 in which it was demonstrated that in the limiting case as the boundary layer thickness tends to zero, the boundary condition reduces to that of continuity of particle displacement. Thus, for at least a brief period in history, the question of the proper wall impedance boundary condition to be used for a mean flow model with slip seems to have been resolved.…”

Section: Introductionmentioning

confidence: 99%

Evaluation of Wall Boundary Conditions for Impedance Eduction Using a Dual-Source Method

Watson

Jones

2012

18th AIAA/CEAS Aeroacoustics Conference (33rd AIAA Aeroacoustics Conference)

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The accuracy of the Ingard-Myers boundary condition and a recently proposed modified Ingard-Myers boundary condition is evaluated for use in impedance eduction under the assumption of uniform mean flow. The evaluation is performed at three centerline Mach numbers, using data acquired in a grazing flow impedance tube, using both upstream and downstream propagating sound sources, and on a database of test liners for which the expected behavior of the impedance spectra is known. The test liners are a hard-wall insert consisting of 12.6 mm thick aluminum, a linear liner without a facesheet consisting of a number of small diameter but long cylindrical channels embedded in a ceramic material, and two conventional nonlinear liners consisting of a perforated facesheet bonded to a honeycomb core. The study is restricted to a frequency range for which only plane waves are cut on in the hard-wall sections of the flow impedance tube. The metrics used to evaluate each boundary condition are 1) how well it educes the same impedance for upstream and downstream propagating sources, and 2) how well it predicts the expected behavior of the impedance spectra over the Mach number range. The primary conclusions of the study are that the same impedance is educed for upstream and downstream propagating sources except at the highest Mach number, that an effective impedance based on both the upstream and downstream measurements is more accurate than an impedance based on the upstream or downstream data alone, and that the Ingard-Myers boundary condition with an effective impedance produces results similar to that achieved with the modified Ingard-Myers boundary condition. Subscripts: D,U = a downstream source and an upstream source quantity e, s = an exit plane and a source plane quantity FEM, Meas = a finite element computed and a measured quantity J = lower wall microphone counter (J = 1, 2, 3 . . . nwall)

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Section: Introductionmentioning

confidence: 99%

Evaluation of Wall Boundary Conditions for Impedance Eduction Using a Dual-Source Method

Watson

Jones

2012

18th AIAA/CEAS Aeroacoustics Conference (33rd AIAA Aeroacoustics Conference)

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“…Equation (11) boundary condition, with ∂v ′ /∂t on the right hand side of (11) given by either boundary condition (5) or (9). This may be contrasted against the direct method written in the same form,…”

Section: Using Characteristics To Apply the Boundary Conditionmentioning

confidence: 99%

“…For flat surfaces where (n ·∇u 0 )·n ≡ 0, equation (1) was shown by Eversman and Beckemeyer [9] and Tester [10] to be the correct limit of an infinitely thin inviscid boundary layer.…”

Section: Introductionmentioning

confidence: 99%

Time-domain implementation of an impedance boundary condition with boundary layer correction

Gabard

2016

Journal of Computational Physics

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A time-domain boundary condition is derived that accounts for the acoustic impedance of a thin boundary layer over an impedance boundary, based on the asymptotic frequency-domain boundary condition of Brambley [ , AIAA J. 49(6), pp. 1272[ -1282. A finite-difference reference implementation of this condition is presented and carefully validated against both an analytic solution and a discrete dispersion analysis for a simple test case. The discrete dispersion analysis enables the distinction between real physical instabilities and artificial numerical instabilities. The cause of the latter is suggested to be a combination of the real physical instabilities present and the aliasing and artificial zero group velocity of finite-difference schemes. It is suggested that these are general properties of any numerical discretization of an unstable system. Existing numerical filters are found to be inadequate to remove these artificial instabilities as they have a too wide pass band. The properties of numerical filters required to address this issue are discussed and a number of selective filters are presented that may prove useful in general. These filters are capable of removing only the artificial numerical instabilities, allowing the reference implementation to correctly reproduce the stability properties of the analytic solution.

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“…This condition assumes an infinitely thin boundary layer, and effectively uses a vortex sheet model where the continuity of pressure and normal displacement is applied [16,39,15]. In the limit of an infinitely small source (w → 0) the present test case is equivalent to the benchmark problem proposed in reference [8] and for which a complete analytical solution has been made available.…”

Section: Problem Descriptionmentioning

confidence: 99%

A full discrete dispersion analysis of time-domain simulations of acoustic liners with flow

Gabard

2014

Journal of Computational Physics

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The effect of flow over an acoustic liner is generally described by the Myers impedance condition. The use of this impedance condition in time-domain numerical simulations has been plagued by stability issues, and various ad hoc techniques based on artificial damping or filtering have been used to stabilise the solution. The theoretical issue leading to the ill-posedness of this impedance condition in the time domain is now well understood. For computational models, some trends have been identified, but no detailed investigation of the cause of the instabilities in numerical simulations has been undertaken to date. This paper presents a dispersion analysis of the complete numerical model, based on finite-difference approximations, for a twodimensional model of a uniform flow above an impedance surface. It provides insight into the properties of the instability in the numerical model and clarifies the parameters that influence its presence. The dispersion analysis is also used to give useful information about the accuracy of the acoustic solution.Comparison between the dispersion analysis and numerical simulations shows that the instability associated with the Myers condition can be identified in the numerical model, but its properties differ significantly from that of the continuous model. The unbounded growth of the instability in the continuous model is not present in the numerical model due to the wavenumber aliasing inherent to numerical approximations. Instead, the numerical instability includes a wavenumber component behaving as an absolute instability. The trend previously reported that the instability is more likely to appear with fine grids is explained. While the instability in the numerical model is heavily dependent on the spatial resolution, it is well resolved in time and is not sensitive to the time step. In addition filtering techniques to stabilise the solutions are considered and it is found that, while they can reduce the instability in some cases, they do not represent a systematic or robust solution in general.

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Transmission of Sound in Ducts with Thin Shear Layers—Convergence to the Uniform Flow Case

Cited by 111 publications

References 0 publications

Evaluation of Wall Boundary Conditions for Impedance Eduction Using a Dual-Source Method

Evaluation of Wall Boundary Conditions for Impedance Eduction Using a Dual-Source Method

Time-domain implementation of an impedance boundary condition with boundary layer correction

A full discrete dispersion analysis of time-domain simulations of acoustic liners with flow

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