Three-dimensional reconstruction of a random fibrous medium: Geometry, transport, and sound absorbing properties

Abstract

The main purpose of this article is to present, within a unified framework, a technique based on numerical homogenization, to model the acoustical properties of real fibrous media from their geometrical characteristics and to compare numerical results with experimental data. The authors introduce a reconstruction procedure for a random fibrous medium and use it as a basis for the computation of its geometrical, transport, and sound absorbing properties. The previously ad hoc “fiber anisotropies” and “volume weighted average radii,” used to describe the experimental data on microstructure, are here measured using scanning electron microscopy. The authors show that these parameters, in conjunction with the bulk porosity, contribute to a precise description of the acoustical characteristics of fibrous absorbents. They also lead to an accurate prediction of transport parameters which can be used to predict acoustical properties. The computed values of the permeability and frequency-dependent sound absorption coefficient are successfully compared with permeability and impedance-tube measurements. The authors' results indicate the important effect of fiber orientation on flow properties associated with the different physical properties of fibrous materials. A direct link is provided between three-dimensional microstructure and the sound absorbing properties of non-woven fibrous materials, without the need for any empirical formulae or fitting parameters.

A study of some airflow resistivity models for multi-component polyester fiber assembly

“…Good reviews of some of these models can be found in refs. [4][5][6]. These models can be grouped into two main categories: theoretical models and empirical models.…”

Multiscale prediction of acoustic properties for glass wools: Computational study and experimental validation

“…Alternatively, in the quest for theoretical understanding, one may seek to better understand the mathematical or physical basis of the generalized Darcy-scale equations for macroscopic transports [9][10][11][12][13][14]. Lastly, one can consider studies based on numerical simulations [15][16][17].…”

“…It is typically hampered, however, by either the need to simplify geometry [16,18] or physics [15,22]. In recent years, however, another approach to the numerical study of diffusion and fluid flow through fibrous media has gained some popularity [17,23,24]. The idea is to numerically solve the asymptotic behaviors of the linearized Navier-Stokes and heat equations in a realistic microscopically disordered geometry, and then study how volume-averaged properties of the diffusion process and the fluid flow depend on the details of the microstructures.…”

“…In practice, the selection of the aforementioned average radius yields satisfactory results whenever the wave propagates perpendicularly to the plane to which all fibers belong. This work follows a series of recent contributions by some of the authors [17,23,24], focusing on the determination of the acoustic properties of random fibrous materials from their microstructures. In these papers, numerical simulations of fluid flow through fibrous media were fed with microstructural descriptors of increased complexity, inferred from experiments.…”

“…1. In [17], a reconstruction methodology of a random fibrous medium was proposed and validated using macroscopic measurements on the permeability and sound absorption.…”