Abstract
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.
Keywords
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsAbbreviations
- ϕ :
-
Porosity
- σ:
-
Airflow resistivity
- α∞:
-
Tortuosity
- Λ:
-
Viscous characteristic length
- \( \varLambda^{\prime} \) :
-
Thermal characteristic length
- \( V_{f} \) :
-
Volume of fluid domain
- \( V \) :
-
Total volume of porous media
- \( \varvec{v} \) :
-
Velocity field
- \( p \) :
-
Pressure
- \( \varvec{E} \) :
-
Electric field
- \( \mu \) :
-
Dynamic viscosity
References
Ashby MF, Evans AG, Fleck NA, Gibson LJ, Hutchinson JW, Wadley HG (2000) Metal foams: a design guide. Butterworth-Heinemann
Delany ME, Bazley EN (1969) Acoustical properties of fibrous absorbent materials. Appl Acoust 3:105–116
Dunn IP, Davern WA (1986) Calculation of acoustic impedance of multi-layer absorbers. Appl Acoust 19(3):321–334
Johnson DL, Koplik J, Dashen R (1987) Theory of dynamic permeability and tortuosity in fluid-saturated porous media. J Fluid Mech 176:379–402
Allard JF, Atalla N (1993) Modelling sound absorbing materials: propagation of Sound in Porous Media. Elsevier Applied Science, New York
Champoux Y, Allard JF (1991) Dynamic tortuosity and bulk modulus in air-saturated porous media. J Appl Phys 70:1975–1979
Biot MA (1956) Theory of propagation of elastic waves in a fluid-saturated porous solid. J Acoust Soc Am 28:168–191
Atalla Y, Panneton R (2005) Inverse acoustical characterization of open cell porous media using impedance tube measurements. Can Acoust 33(1):3–10
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 2009–2012
Perrot C, Chevillotte F, Panneton R (2008) Bottom-up approach for microstructure optimization of sound absorbing materials. J Acoust Soc Am 124(2):940–948
Cortis A et al (2003) Influence of pore roughness on high-frequency permeability. Phys Fluids:1766–1775
Gasser S et al (2005) Absorptive properties of rigid porous media: application to face centered cubic sphere packing. J Acoust Soc Am:2090–2099
Versteeg HK, Malalasekra W (2007) An introduction to computational fluid dynamics: The finite method. Pearson Education Ltd., New York
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 1269–1275
COMSOL Multiphysics, 5.3 Documentation
MSC ACTRAN, 17.0, user guide vol. 1 and vol. 2
Acknowledgments
This work was supported by IMPRINT INDIA grant no. 6367 from MHRD and DST, India.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2021 Springer Nature Singapore Pte Ltd.
About this paper
Cite this paper
Deshmukh, S., Ramamoorthy, S. (2021). Dependence of Macro-Scale Response of Fibrous Materials on Polygonal Arrangement of Fibers. In: Singh, M., Rafat, Y. (eds) Recent Developments in Acoustics. Lecture Notes in Mechanical Engineering. Springer, Singapore. https://doi.org/10.1007/978-981-15-5776-7_15
Download citation
DOI: https://doi.org/10.1007/978-981-15-5776-7_15
Published:
Publisher Name: Springer, Singapore
Print ISBN: 978-981-15-5775-0
Online ISBN: 978-981-15-5776-7
eBook Packages: EngineeringEngineering (R0)