A displacement-pressure finite element formulation for analyzing the sound transmission in ducted shear flows with finite poroelastic lining.

In the present work, the propagation of sound in a lined duct containing sheared mean flow is studied. Walls of the duct are acoustically treated with absorbent poroelastic foams. The propagation of elasto-acoustic waves in the liner is described by Biot's model. In the fluid domain, the propagation of sound in a sheared mean flow is governed by the Galbrun's equation. The problem is solved using a mixed displacement-pressure finite element formulation in both domains. A 3D implementation of the model has been performed and is illustrated on axisymmetric examples. Convergence and accuracy of the numerical model are shown for the particular case of the modal propagation in a infinite duct containing a uniform flow. Practical examples concerning the sound attenuation through dissipative silencers are discussed. In particular, effects of the refraction effects in the shear layer as well as the mounting conditions of the foam on the transmission loss are shown. The presence of a perforate screen at the air-porous interface is also considered and included in the model.

[1]  J. Remacle,et al.  Gmsh: A 3‐D finite element mesh generator with built‐in pre‐ and post‐processing facilities , 2009 .

[2]  Franck Sgard,et al.  Behavioral criterion quantifying the edge-constrained effects on foams in the standing wave tube. , 2003, The Journal of the Acoustical Society of America.

[3]  K. Bathe.  Finite Element Procedures , 1995 .

[4]  E. N. Bazley,et al.  Acoustical properties of fibrous absorbent materials , 1970 .

[5]  D. Pridmore‐Brown,et al.  Sound Propagation in a Fluid Flowing through an Attenuating Duct , 1958 .

[6]  Oleg A. Godin,et al.  Reciprocity and energy theorems for waves in a compressible inhomogeneous moving fluid , 1997 .

[7]  Christophe Geuzaine,et al.  Gmsh: A 3‐D finite element mesh generator with built‐in pre‐ and post‐processing facilities , 2009 .

[8]  G. Elias,et al.  Finite-element method to study harmonic aeroacoustics problems , 2001 .

[9]  R. J. Astley,et al.  A finite element scheme for attenuation in ducts lined with porous material: Comparison with experiment , 1987 .

[10]  R. J. Astley,et al.  Stability and accuracy of finite element methods for flow acoustics. II: Two‐dimensional effects , 2005 .

[11]  Walter Eversman,et al.  Effect of Boundary Layer on the Transmission and Attenuation of Sound in an Acoustically Treated Circular Duct , 1971 .

[12]  A. W. Guess.  Calculation of perforated plate liner parameters from specified acoustic resistance and reactance , 1975 .

[13]  J. Mercier,et al.  Time-harmonic acoustic propagation in the presence of a shear flow , 2007 .

[14]  K. S. Peat,et al.  A finite element analysis of the convected acoustic wave motion in dissipative silencers , 1995 .

[15]  Ray Kirby,et al.  The impedance of perforated plates subjected to grazing gas flow and backed by porous media , 1998 .

[16]  H. Galbrun.  Propagation d'une onde sonore dans l'atmosphère et théorie des zones de silence , 1931 .

[17]  R. Kirby.  Simplified Techniques for Predicting the Transmission Loss of a Circular Dissipative Silencer , 2001 .

[18]  Raymond Panneton,et al.  BOUNDARY CONDITIONS FOR THE WEAK FORMULATION OF THE MIXED (U, P) POROELASTICITY PROBLEM , 1999 .

[19]  Leo L. Beranek,et al.  Acoustical Properties of Homogeneous, Isotropic Rigid Tiles and Flexible Blankets , 1947 .

[20]  A. Craggs,et al.  A finite element model for rigid porous absorbing materials , 1978 .

[21]  R. Jeremy Astley,et al.  Numerical methods for noise propagation in moving flows, with application to turbofan engines , 2009 .

[22]  Walter Eversman,et al.  Aft Fan Duct Acoustic Radiation , 1998 .

[23]  Nils-Erik Hörlin,et al.  A 3-D HIERARCHICAL FE FORMULATION OF BIOT'S EQUATIONS FOR ELASTO-ACOUSTIC MODELLING OF POROUS MEDIA , 2001 .

[24]  M. K. Myers,et al.  On the acoustic boundary condition in the presence of flow , 1980 .

[25]  J. Allard.  Propagation of Sound in Porous Media: Modelling Sound Absorbing Materials , 1994 .

[26]  Fabien Treyssede,et al.  A numerical method for vibro-acoustic problems with sheared mean flows , 2004 .

[27]  P. Mungur,et al.  Acoustic wave propagation in a sheared fluid contained in a duct , 1969 .

[28]  Yeon June Kang,et al.  SOUND PROPAGATION IN CIRCULAR DUCTS LINED WITH NOISE CONTROL FOAMS , 2001 .

[29]  M. A. B•oT,et al.  Theory of Propagation of Elastic Waves in a Fluid-Saturated Porous Solid . I . Low-Frequency Range , 2011 .

[30]  N Atalla,et al.  Investigation of the convergence of the mixed displacement-pressure formulation for three-dimensional poroelastic materials using hierarchical elements. , 2003, The Journal of the Acoustical Society of America.

[31]  C. Zwikker,et al.  Sound Absorbing Materials , 1949 .

[32]  Yeon June Kang,et al.  Finite element modeling of isotropic elastic porous materials coupled with acoustical finite elements , 1995 .

[33]  Raymond Panneton,et al.  Enhanced weak integral formulation for the mixed (u_,p_) poroelastic equations , 2001 .

[34]  Ml Munjal,et al.  Sound propagation in ducts with bulk reacting lining in the presence of laminar mean flow , 1996 .

[35]  Benoit Nennig,et al.  A mode matching method for modeling dissipative silencers lined with poroelastic materials and containing mean flow. , 2010, The Journal of the Acoustical Society of America.

[36]  A. Cummings,et al.  Sound attenuation of a finite length dissipative flow duct silencer with internal mean flow in the absorbent , 1988 .

[37]  Olivier Doutres,et al.  Validity of the limp model for porous materials: a criterion based on the Biot theory. , 2007, The Journal of the Acoustical Society of America.

[38]  Comparison of a finite element model with a multiple-scales solution for sound propagation in varying ducts with swirling flows , 2004 .

[39]  Raymond Panneton,et al.  A mixed displacement-pressure formulation for poroelastic materials , 1998 .

[40]  Sw Sjoerd Rienstra.  Contributions to the theory of sound propagation in ducts with bulk-reacting lining , 1983 .

[41]  Fabien Treyssède,et al.  A mixed finite element method for acoustic wave propagation in moving fluids based on an Eulerian-Lagrangian description. , 2003, The Journal of the Acoustical Society of America.

[42]  Patrick R. Amestoy,et al.  Multifrontal parallel distributed symmetric and unsymmetric solvers , 2000 .