Acoustic resonances and sound scattering by a shear layer

Koutsoyannis, S. P.; Karamcheti, K.; Galant, David

doi:10.2514/6.1979-627

Cited by 9 publications

(22 citation statements)

References 1 publication

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“…The model involves an acoustic triple deck ( Figure 2) with: (i) acoustic-vortical waves of shear type [8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25] in the upper and lower boundary layers, each involving three non-plane wave modes 42,44 ; (ii) these are coupled to the upstream and downstream propagating plane waves convected by the uniform core flow. The eight wave amplitudes are determined from eight conditions: (i) two impedance boundary conditions at the lined walls; (ii) two sets of three matching conditions at the interfaces between the boundary layers and the core flow.…”

Section: Discussionmentioning

confidence: 99%

“…[1][2][3][4][5][6][7] The shear layers near the walls lead to the coupling of sound with vorticity significantly changing the properties of the acoustics waves. [8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25] In order to reduce noise, the nozzle walls often use liners that, if locally reacting, can be represented by an impedance distribution. [26][27][28][29][30][31][32][33][34][35][36][37][38][39][40][41] The bias flow out perforated liners can have a significant effect on sound in a boundary layer 42 even for small velocities.…”

Section: Introductionmentioning

confidence: 99%

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Sound propagation in a lined nozzle with shear and bias flows

Campos

Legendre²

2018

International Journal of Aeroacoustics

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In this study, the propagation of waves in a two-dimensional parallel-sided nozzle is considered allowing for the combination of: (a) distinct impedances of the upper and lower walls; (b) upper and lower boundary layers with different thicknesses with linear shear velocity profiles matched to a uniform core flow; and (c) a uniform cross-flow as a bias flow out of one and into the other porous acoustic liner. The model involves an "acoustic triple deck" consisting of third-order nonsinusoidal non-plane acoustic-shear waves in the upper and lower boundary layers coupled to convected plane sinusoidal acoustic waves in the uniform core flow. The acoustic modes are determined from a dispersion relation corresponding to the vanishing of an 8 Â 8 matrix determinant, and the waveforms are combinations of two acoustic and two sets of three acousticshear waves. The eigenvalues are calculated and the waveforms are plotted for a wide range of values of the four parameters of the problem, namely: (i/ii) the core and bias flow Mach numbers; (iii) the impedances at the two walls; and (iv) the thicknesses of the two boundary layers relative to each other and the core flow. It is shown that all three main physical phenomena considered in this model can have a significant effect on the wave field: (c) a bias or cross-flow even with small Mach number M 0 $0:03 À 0:06 relative to the mean flow Mach number M 1 $0:3 À 1:2 can modify the waveforms; (b) the possibly dissimilar impedances of the lined walls can absorb (or amplify) waves more or less depending on the reactance and inductance; (a) the exchange of the wave energy with the shear flow is also important, since for the same stream velocity, a thin boundary layer has higher vorticity, and lower vorticity corresponds to a thicker boundary layer. The combination of all these three effects (a-c) leads to a large set of different waveforms in the duct that are plotted for a wide range of the parameters (i-iv) of the problem.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Sound propagation in a lined nozzle with shear and bias flows

Campos

Legendre²

2018

International Journal of Aeroacoustics

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“…6 " 9 A good synthesis of the results obtained in these studies is presented by Goldstein. 10 Further investigations have been carried out by Scott 11 and Koutsoyanis et al 12 Other studies pertinent to this problem are those of Refs. 13-17. In distinction with these previous studies our treatment is essentially numerical and does not rely on approximation techniques such as the method of steepest descent or the method of stationary phase.…”

Section: Introductionmentioning

confidence: 98%

“…A proof of this point may be based on a discussion presented by Goldstein 10 (pp. [10][11][12][13][14][15][16][17][18][19][20][21][22] in an analysis of wavemotion in a region of mean flow velocity adjustment. According to Goldstein, when the thickness 6 of the adjustment region is much smaller than the wavelength X it is possible to replace the velocity profile by a fictitious velocity discontinuity which a) sustains no force in the transverse direction and b) follows the local fluid motion.…”

Section: Introductionmentioning

confidence: 99%

Sound source radiation in two-dimensional shear flow

Candel

1983

AIAA Journal

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A fundamental problem encountered in the analysis of aerodynamic noise is that of acoustic source radiation in nonhomogeneous flow. Exact numerical solutions have been obtained recently for source radiation near a plane interface and a shear discontinuity by directly synthesizing the wavefield from its spatial Fourier transform. This method is applied here to stratified flow configurations and the structure of the radiated field is obtained for several shear layer velocity profiles of practical interest. NomenclatureAj (a),Bj(ot) = amplitudes of outgoing and incoming waves in layerj c = sound speed d = layer thickness / = complex number, V -1 k = wavenumber f = spatial extension of the calculation domain L = layer index corresponding to a selected value of attenuation M = Mach number N = number of points in the discrete Fourier transform = pressure = Fourier transform of pressure = total number of shear discontinuities used to represent the flow = cumulated transfer matrix = layer transfer matrix = mean flow velocity = Cartesian coordinates '= spatial wavenumber, argument of Fourier transform = branch points of jj = phase or damping factor for waves in layer j = delta function = spatial sampling period = spatial wavenumber sampling period = interfacial displacement = polar angle measured with respect to the x axis = wavelength = angular frequency P P Q s T U x,z a. Ax 0 A CO Subscripts * j = reduced (dimensionless) quantity = layer index

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“…For instance, in the Theory of Sound, Rayleigh 45 uses geometric acoustics to show in which direction the sound is deflected according to the direction of the wind. Subsequently, varieties of studies were then led on the effect of shear flows on acoustic propagation, from a simple flow velocity discontinuity 33,34,47 , to piece-wise constant profiles 1,52 or continuous parallel shear flows 23,26,28 . Many other papers deal with the propagation of sound in parallel shear flow in the presence of walls, either for ducts 44 or for reflection problems 5,8,21,25,31,36,40,41 .…”

Section: Introductionmentioning

confidence: 99%

Non-reciprocal scattering in shear flow

Saverna

Aurégan

Pagneux

2019

The Journal of the Acoustical Society of America

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This work presents a study of scattering phenomena in shear flows and its application to impedance walls. These flows are described by a dimensionless shear layer thickness and a mean Mach number. Both transmission through a given shear layer and reflection on an acoustic treatment are studied. We show that the dimensionless thickness of the shear layer may be an interesting tool to reach perfect absorption or large lateral displacement of a Gaussian beam.

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Acoustic resonances and sound scattering by a shear layer

Cited by 9 publications

References 1 publication

Sound propagation in a lined nozzle with shear and bias flows

Sound propagation in a lined nozzle with shear and bias flows

Sound source radiation in two-dimensional shear flow

Non-reciprocal scattering in shear flow

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