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Journal of the Acoustical Society of America / Volume 124 / Issue 4 / JASA EXPRESS LETTERS

On the dynamic viscous permeability tensor symmetry

J. Acoust. Soc. Am. Volume 124, Issue 4, pp. EL210-EL217 (2008); (8 pages)

Camille Perrot1, Fabien Chevillotte1, Raymond Panneton1, Jean-François Allard2, and Denis Lafarge2

1Groupe d’Acoustique de l’Universite de Sherbrooke (GAUS), Department of Mechanical Engineering, Universite de Sherbrooke, Quebec J1K 2R1, Canada camille.perrot@usherbrooke.ca, fabien.chevillotte@usherbrooke.ca, raymond.panneton@usherbrooke.ca
2Laboratoire d’Acoustique de l’Université du Maine (LAUM), UMR CNRS 6613, Avenue Olivier Messiaen, 72085 Le Mans Cedex 9, France jean-francois.allard@univ-lemans.fr, denis.lafarge@univ-lemans.fr

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Based on a direct generalization of a proof given by Torquato for symmetry property in static regime, this express letter clarifies the reasons why the dynamic permeability tensor is symmetric for spatially periodic structures having symmetrical axes which do not coincide with orthogonal pairs being perpendicular to the axis of three-, four-, and sixfold symmetry. This somewhat nonintuitive property is illustrated by providing detailed numerical examples for a hexagonal lattice of solid cylinders in the asymptotic and frequency dependent regimes. It may be practically useful for numerical implementation validation and∕or convergence assessment.

© 2008 Acoustical Society of America

Article Outline

  1. Introduction
  2. Symmetry of the dynamic viscous permeability tensor
  3. Flow simulation in a hexagonal porous structure
  4. Conclusion

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KEYWORDS and PACS

Keywords

acoustic wave propagation, aeroacoustics, flow through porous media, periodic structures, permeability, tensors

PACS

  • 43.50.Gf

    Noise control at source: redesign, application of absorptive materials and reactive elements, mufflers, noise silencers, noise barriers, and attenuators, etc.

  • 43.55.Ev

    Sound absorption properties of materials: theory and measurement of sound absorption coefficients; acoustic impedance and admittance

  • 43.20.Wd

    Analogies

  • 43.58.Ta

    Computers and computer programs in acoustics

ARTICLE DATA

History
Received 18 Mar 2008
Accepted 08 Jul 2008
Revised 26 Jun 2008
Published online 22 Sep 2008
Digital Object Identifier
http://dx.doi.org/10.1121/1.2968300

PUBLICATION DATA

ISSN

0001-4966 (print)  

Publisher

$abstract.society.value is a Member of CrossRef Acoustical Society of America

  1. P. M. Adler, “Flow in spatially periodic structures,” in Porous Media: Geometry and Transports, edited by H. Brenner et al. (Butterworths, London, 1992), pp. 144–185.
  2. C. Y. Wang, “Stokes slip flow through square and triangular arrays of circular cylinders,” Fluid Dyn. Res. 32, 233–246 (2003). [Inspec]
  3. M. Born and E. Wolf, “Optics of crystals,” in Principles of Optics (Cambridge University Press, Cambridge, 2002), pp. 790–849.
  4. S. Torquato, “Relationship between permeability and diffusion-controlled trapping constant of porous media,” Phys. Rev. Lett. 64, 2644–2646 (1990). [ISI] [MEDLINE]
  5. D. Lafarge, “Modèles linéaires de propagation,” in Milieux poreux et poreux stratifiés (Linear Models of Propagation in Porous Media and Stratified Porous), Matériaux et Acoustique (Materials and Acoustics), edited by M. Bruneau and C. Potel (Lavoisier, Paris, 2006), pp. 143–187.
  6. D. L. Johnson, J. Koplik, and R. Dashen, “Theory of dynamic permeability and tortuosity in fluid-saturated porous media,” J. Fluid Mech. 176, 379–402 (1987).
  7. H. Darcy, Les Fontaines Publiques de la Ville de Dijon (Victor Dalmont, Paris, 1856).
  8. H. I. Ene and E. Sanchez-Palencia, “Équations et phénomènes de surface pour l'écoulement dans un modéle de milieu poreux (Equations and surface phenomena for flow through a porous media model),” J. Mec. 14, 73–108 (1975). [Inspec]
  9. E. Sanchez-Alencia, “Fluid flow in porous media,” in Non-Homogeneous Media and Vibration Theory (Springer, Berlin, 1980), pp. 149–154.
  10. J.-L. Auriault, “Dynamic behaviour of a porous medium saturated by a Newtonian fluid,” Int. J. Eng. Sci. 18, 775–785 (1980). [Inspec] [ISI]
  11. J.-L. Auriault, L. Borne, and R. Chambon, “Dynamics of porous saturated media, checking of the generalized law of Darcy,” J. Acoust. Soc. Am. 77, 1641–1650 (1985)JASMAN000077000005001641000001. [ISI]
  12. C. Perrot, F. Chevillotte, and R. Panneton, “Dynamic viscous permeability of an open-cell aluminium foam: Computations vs experiments,” J. Appl. Phys. 103, 024909–8 (2008)JAPIAU000103000002024909000001.
  13. R. J. S. Brown, “Connection between formation factor for electrical-resistivity and fluid-solid coupling factor in Biot equations for acoustic waves in fluid-filled porous media,” Geophysics 45, 1269–1275 (1980)GPYSA7000045000008001269000001.
  14. Comsol 3.4, WTC-5 pl. Robert Schuman, 38000 Grenoble, France.
  15. N. Martys and E. J. Garboczi, “Length scales relating the fluid permeability and electrical conductivity in random two-dimensional model porous media,” Phys. Rev. B 46, 6080–6090 (1992). [ISI] [MEDLINE]


Figures (click on thumbnails to view enlargements)

FIG.1
Identification of two-dimensional rectangular periodic unit cells for vertical (RV) and horizontal (RH) wave propagations through a hexagonal lattice of solid cylinders.

FIG.1 Download High Resolution Image (.zip file) | Export Figure to PowerPoint

FIG.2
Dynamic viscous permeability of a hexagonal lattice of solid cylinders: There is an almost perfect superposition of the permeability values computed from any orthogonal line pairs perpendicular to the sixfold axis of symmetry, suggesting that this property might be used for a convergence check.

FIG.2 Download High Resolution Image (.zip file) | Export Figure to PowerPoint

FIG.3
Vertical (top) and horizontal (bottom) static scaled velocity fields obtained by solving the steady Stokes problem in principal directions of the periodic porous structure.

FIG.3 Download High Resolution Image (.zip file) | Export Figure to PowerPoint

FIG.4
Vertical (top) and horizontal (bottom) scaled electric fields obtained by solving the electric problem in principal directions of the periodic porous structure.

FIG.4 Download High Resolution Image (.zip file) | Export Figure to PowerPoint



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