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Recent Developments in Acoustics pp 161–171Cite as

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

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

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.

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Abbreviations

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

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Acknowledgments

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

Author information

Authors and Affiliations

  1. Department of Mechanical Engineering, Indian Institute of Technology Bombay, Mumbai, 400076, India

    Sagar Deshmukh & Sripriya Ramamoorthy

Authors
  1. Sagar Deshmukh
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  2. Sripriya Ramamoorthy
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Corresponding author

Correspondence to Sripriya Ramamoorthy .

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Editors and Affiliations

  1. Department of Physico-Mechanical Metrology, CSIR-National Physical Laboratory, New Delhi, Delhi, India

    Mahavir Singh

  2. Mechanical Engineering Department, Aligarh Muslim University, Aligarh, Uttar Pradesh, India

    Yasser Rafat

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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

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  • DOI: https://doi.org/10.1007/978-981-15-5776-7_15

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  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-15-5775-0

  • Online ISBN: 978-981-15-5776-7

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