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

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

Keywords

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

Nomenclature

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

Notes

Acknowledgments

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

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Copyright information

© Springer Nature Singapore Pte Ltd. 2021

Authors and Affiliations

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

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