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A mode matching method for modeling dissipative silencers lined with poroelastic materials and containing mean flow
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10.1121/1.3506346
/content/asa/journal/jasa/128/6/10.1121/1.3506346
http://aip.metastore.ingenta.com/content/asa/journal/jasa/128/6/10.1121/1.3506346

Figures

Image of FIG. 1.
FIG. 1.

(Color online) Geometry of the silencer.

Image of FIG. 2.
FIG. 2.

Roots in the complex β-plane at 400 Hz for XFM foam with silencer A.

Image of FIG. 3.
FIG. 3.

Modulus of modal pressure profile related to markers shown in Fig. 2 at 400 Hz for silencer A filled with XFM foam: , , . For r < r 1, acoustic pressure p and for r 1 < r < r 2 pore pressure pp . The amplitude max is scaled to 1.

Image of FIG. 4.
FIG. 4.

Modulus of modal displacement profile related to markers shown in Fig. 2 at 400 Hz for silencer A filled with XFM foam: , , . For r < r 1, acoustic axial displacement wz and for r 1 < r < r 2 solid phase axial displacement uz . The amplitude max. is scaled to one.

Image of FIG. 5.
FIG. 5.

Trajectory of the roots in the complex β-plane with respect to the frequency ranging from 100 () to 2500 Hz (*) for XFM foam without flow.

Image of FIG. 6.
FIG. 6.

Trajectory of the roots in the complex β-plane at 400 Hz with respect to the Mach number ranging from 0 () to 0.8 (*) for XFM foam with silencer A.

Image of FIG. 7.
FIG. 7.

TL for silencer A without flow and XFM foam, 78000 degrees of freedom (DOFs) 3D FE calculation (Ref. 10), MMM with 5, 7, and 13 modes, ⋯ MMM with 15 modes.

Image of FIG. 8.
FIG. 8.

TL for silencer B without flow and XFM foam, 100000 DOFs 3D FE calculation (Ref. 10), ⋯ MMM with 16 modes.

Image of FIG. 9.
FIG. 9.

TL for silencer A with an M = 0.2 flow and RGW2 wool, 78000 DOFs 3D FE calculation (Ref. 10), ⋯ MMM with 16 modes, 14000 DOFs Limp model FE calculation (Refs. 2, 23).

Image of FIG. 10.
FIG. 10.

TL for silencer A with a filled with the XFM foam, no-flow case, upstream propagation, downstream propagation with |M| = 0.1 and |M| = 0.3.

Image of FIG. 11.
FIG. 11.

TL for silencer A with an M = 0.2 flow and XFM foam, 78000 DOFs 3D FE calculation (Ref. 10), ⋯ MMM with 15 modes.

Image of FIG. 12.
FIG. 12.

TL for silencer A with an M = 0 flow and RGW2 wool, 78000 DOFs 3D FE calculation (Ref. 10), ⋯ MMM with 16 modes, 14000 DOFs limp model FE calculation (Refs. 2, 23).

Tables

Generic image for table
TABLE I.

Finite difference scheme coefficients.

Generic image for table
TABLE II.

Numerical computation of a specific root at 1730 Hz with one circular ring (center) and two circular rings (right). Bold character indicates the correct digits.

Generic image for table
TABLE III.

Silencer dimensions (Ref. 37) in meters.

Generic image for table
TABLE IV.

Materials properties used in numerical tests (Refs. 20, 43). With the resistivity σ, the tortuosity αinf, the viscous and thermal characteristic lengths Λ and Λ′, the Poisson coefficient v, and the effective skeleton density ρ 1 . The effective skeleton density ρ 1 = (1 − ϕ)ρ s , where ρ s is the density of the material of the frame.

Generic image for table
TABLE V.

Convergence of TL predictions (in decibels) with respect to the number of modes K.

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/content/asa/journal/jasa/128/6/10.1121/1.3506346
2010-12-01
2014-04-21
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: A mode matching method for modeling dissipative silencers lined with poroelastic materials and containing mean flow
http://aip.metastore.ingenta.com/content/asa/journal/jasa/128/6/10.1121/1.3506346
10.1121/1.3506346
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