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A displacement-pressure finite element formulation for analyzing the sound transmission in ducted shear flows with finite poroelastic lining
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10.1121/1.3598451
/content/asa/journal/jasa/130/1/10.1121/1.3598451
http://aip.metastore.ingenta.com/content/asa/journal/jasa/130/1/10.1121/1.3598451

Figures

Image of FIG. 1.
FIG. 1.

(Color online) Geometry of the silencer benchmark.

Image of FIG. 2.
FIG. 2.

(Color online) Numerical results (fe) computed with the LQ scheme and analytical solutions (ana) for the real part of the pressure, the axial, and the radial displacement (quantities are scaled for the sake of clarity). The displacement “Disp.” (resp., the pressure “Pres.”) signifies the fluid displacement perturbation in the airway w (resp., pressure p) for , and the solid phase displacement u for (resp., pore pressure pp ). Computed with , , and f = 600 Hz.

Image of FIG. 3.
FIG. 3.

Convergence curves for the pressure. The discretization scheme is given by the line style: —, LL scheme; , LQ scheme; and – –, QQ scheme. The line thickness indicates the domain under consideration: bold line for the poroelastic domain and thin line for the fluid domain. (a) No flow case with . (b) flow with .

Image of FIG. 4.
FIG. 4.

Test case mesh.

Image of FIG. 5.
FIG. 5.

Effects of the mounting conditions, —, sliding; , clamped, for two foams: (a) XFM, (b) FM4.

Image of FIG. 6.
FIG. 6.

Effects of the shear layer with a mean Mach number ; – –, no flow; —, ; , uniform, for XFM foam. (a) Downstream propagation. (b) Upstream propagation.

Image of FIG. 7.
FIG. 7.

(Color online) Acoustic intensity field at the entrance of the liner at 1 021 Hz, —, uniform flow; , shear flow. (a) Downstream case. (b) Upstream case.

Image of FIG. 8.
FIG. 8.

Effects of the perforated plate properties on the TL (sliding condition for the foam). —, plate 2; —, plate 1; – –, no plate.

Tables

Generic image for table
TABLE I.

Three discretization schemes.

Generic image for table
TABLE II.

Error for , f = 600 Hz, computed with the LQ scheme. Displacement “Disp.” (resp., “Pressure”) signifies the fluid displacement perturbation in the airway w (resp., the pressure p), and the solid phase displacement u in the poroelastic material (resp., the pore pressure pp ).

Generic image for table
TABLE III.

Materials properties used in numerical tests Refs. 16 and 33. With the flow resistivity , the tortuosity , the viscous and thermal characteristic lengths and , the Poisson coefficient and the effective skeleton density . The effective skeleton density , where is the density of the material of the frame.

Generic image for table
TABLE IV.

Perforated screen characteristics.

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/content/asa/journal/jasa/130/1/10.1121/1.3598451
2011-07-19
2014-04-21
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: A displacement-pressure finite element formulation for analyzing the sound transmission in ducted shear flows with finite poroelastic lining
http://aip.metastore.ingenta.com/content/asa/journal/jasa/130/1/10.1121/1.3598451
10.1121/1.3598451
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