Dependence of Macro-Scale Response of Fibrous Materials on Polygonal Arrangement of Fibers

Conference paper
Part of the Lecture Notes in Mechanical Engineering book series (LNME)


Absorption characteristics of fibrous material inherently depend on the microscopic shapes and the dimensions of the fibers. Periodic Unit Cell (PUC) modeling approach is used for the optimization of arrangements of fibers. Periodic hexagonal and square arrangement of fibers are considered here for study. Five Johnson and Champoux-Allard (JCA) parameters and the transmission loss are computed to evaluate the effect of these two structure configurations. Steady Stokes and electric boundary value problem has been solved for estimation of the airflow resistivity, tortuosity and viscous characteristic length, while porosity and thermal characteristic length are estimated directly from mesh geometry. This study underlines the effects due to the change in fiber arrangements on to absorption characteristics of 50 mm thick sample size of the rigid porous medium. It is observed that for equal centric diameter of fibers hexagonal configuration yields better transmission loss compared to square configuration of fibers over frequency range of 0–8 kHz.


PUC Transmission loss Porosity Airflow resistivity Tortuosity Thermal characteristic length Viscous characteristic length 





Airflow resistivity




Viscous characteristic length

\( \varLambda^{\prime} \)

Thermal characteristic length

\( V_{f} \)

Volume of fluid domain

\( V \)

Total volume of porous media

\( \varvec{v} \)

Velocity field

\( p \)


\( \varvec{E} \)

Electric field

\( \mu \)

Dynamic viscosity



This work was supported by IMPRINT INDIA grant no. 6367 from MHRD and DST, India.


  1. 1.
    Ashby MF, Evans AG, Fleck NA, Gibson LJ, Hutchinson JW, Wadley HG (2000) Metal foams: a design guide. Butterworth-HeinemannGoogle Scholar
  2. 2.
    Delany ME, Bazley EN (1969) Acoustical properties of fibrous absorbent materials. Appl Acoust 3:105–116CrossRefGoogle Scholar
  3. 3.
    Dunn IP, Davern WA (1986) Calculation of acoustic impedance of multi-layer absorbers. Appl Acoust 19(3):321–334CrossRefGoogle Scholar
  4. 4.
    Johnson DL, Koplik J, Dashen R (1987) Theory of dynamic permeability and tortuosity in fluid-saturated porous media. J Fluid Mech 176:379–402CrossRefGoogle Scholar
  5. 5.
    Allard JF, Atalla N (1993) Modelling sound absorbing materials: propagation of Sound in Porous Media. Elsevier Applied Science, New YorkCrossRefGoogle Scholar
  6. 6.
    Champoux Y, Allard JF (1991) Dynamic tortuosity and bulk modulus in air-saturated porous media. J Appl Phys 70:1975–1979CrossRefGoogle Scholar
  7. 7.
    Biot MA (1956) Theory of propagation of elastic waves in a fluid-saturated porous solid. J Acoust Soc Am 28:168–191CrossRefGoogle Scholar
  8. 8.
    Atalla Y, Panneton R (2005) Inverse acoustical characterization of open cell porous media using impedance tube measurements. Can Acoust 33(1):3–10Google Scholar
  9. 9.
    Leclaire P et al (1996) Determination of the viscous and thermal characteristic lengths of plastic foams by ultrasonic measurements in helium and air. J Appl Phys 2009–2012Google Scholar
  10. 10.
    Perrot C, Chevillotte F, Panneton R (2008) Bottom-up approach for microstructure optimization of sound absorbing materials. J Acoust Soc Am 124(2):940–948CrossRefGoogle Scholar
  11. 11.
    Cortis A et al (2003) Influence of pore roughness on high-frequency permeability. Phys Fluids:1766–1775Google Scholar
  12. 12.
    Gasser S et al (2005) Absorptive properties of rigid porous media: application to face centered cubic sphere packing. J Acoust Soc Am:2090–2099Google Scholar
  13. 13.
    Versteeg HK, Malalasekra W (2007) An introduction to computational fluid dynamics: The finite method. Pearson Education Ltd., New YorkGoogle Scholar
  14. 14.
    Brown RJ (1980) Connection between formation factor for electrical resistivity and fluid-solid coupling factor in Biot’s equation for acoustic waves in fluid-filled porous media. Geophysics 1269–1275Google Scholar
  15. 15.
    COMSOL Multiphysics, 5.3 DocumentationGoogle Scholar
  16. 16.
    MSC ACTRAN, 17.0, user guide vol. 1 and vol. 2Google Scholar

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© Springer Nature Singapore Pte Ltd. 2021

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringIndian Institute of Technology BombayMumbaiIndia

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