This work is concerned with the multiscale prediction of the transport and sound absorption properties associated with industrial glass wool samples. In the first step, an experimental characterization is performed on various products using optical granulometry and porosity measurements. A morphological analysis, based on scanning electron imaging, is further conducted to identify the probability density functions associated with the fiber angular orientation. The key morphological characterization parameters of the microstructure, which serve as input parameters of the model, include the porosity, the weighted volume diameter accounting for both lengths and diameters of the analyzed fibers (and therefore the specific surface area of the random fibrous material), and the preferred out-of-plane fiber orientation generated by the manufacturing process. A computational framework is subsequently proposed and allows for the reconstruction of an equivalent fibrous network. A fully stochastic microstructural model, parameterized by the probability laws inferred from the database, is also proposed herein. Multiscale simulations are carried out to estimate transport properties and sound absorption. With no adjustable parameter, the results accounting for ten different samples obtained with various processing parameters are finally compared with the experimental data and used to assess the relevance of the reconstruction procedures and the multiscale computations.

1.
E. J.
Garboczi
, “
Permeability, diffusivity, and microstructural parameters: A critical review
,”
Cem. Concr. Res.
20
,
591
601
(
1990
).
2.
P. M.
Adler
and
J.-F.
Thovert
, “
Real porous media: Local geometry and macroscopic properties
,”
Appl. Mech. Rev.
51
,
537
585
(
1998
).
3.
M. E.
Delany
and
E. N.
Bazley
, “
Acoustical properties of fibrous materials
,”
Appl. Acoust.
3
,
105
116
(
1970
).
4.
D. A.
Bies
and
C. H.
Hansen
, “
Flow resistance information for acoustical design
,”
Appl. Acoust.
13
,
357
391
(
1980
).
5.
Y.
Miki
, “
Acoustical properties of porous materials—Modifications of Delany Bazley models
,”
J. Acoust. Soc. Jpn.
11
,
19
24
(
1990
).
6.
M.
Garai
and
F.
Pompoli
, “
A simple empirical model of polyester fibre materials for acoustical applications
,”
Appl. Acoust.
66
,
1383
1398
(
2005
).
7.
J.
Manning
and
R.
Panneton
, “
Acoustical model for Shoddy-based fiber sound absorbers
,”
Text. Res. J.
83
,
1356
1370
(
2013
).
8.
P.
Kerdudou
,
J.-B.
Chéné
,
G.
Jacqus
,
C.
Perrot
,
S.
Berger
, and
P.
Leroy
, “
A semi-empirical approach to link macroscopic parameters to microstructure of fibrous materials
,” in
Proceedings of the 44th InterNoise
, San Francisco, CA (August 9–12,
2015
), pp.
5468
5479
.
9.
J. L.
Auriault
,
L.
Borne
, and
R.
Chambon
, “
Dynamics of porous saturated media, checking of the generalized law of Darcy
,”
J. Acoust. Soc. Am.
77
,
1641
1650
(
1985
).
10.
D. L.
Johnson
,
J.
Koplik
, and
R.
Dashen
, “
Theory of dynamic permeability and tortuosity in fluid-saturated porous media
,”
J. Fluid Mech.
176
,
379
402
(
1987
).
11.
Y.
Champoux
and
J. F.
Allard
, “
Dynamic tortuosity and bulk modulus in air-saturated porous media
,”
J. Appl. Phys.
70
,
1975
1979
(
1991
).
12.
S. R.
Pride
,
F. D.
Morgan
, and
A. F.
Gangi
, “
Drag forces of porous media acoustics
,”
Phys. Rev. B
47
,
4964
4978
(
1993
).
13.
D.
Lafarge
,
P.
Lemarinier
,
J.-F.
Allard
, and
V.
Tarnow
, “
Dynamic compressibility of air in porous structures at audible frequencies
,”
J. Acoust. Soc. Am.
102
,
1995
2006
(
1997
).
14.
C.
Boutin
, “
Rayleigh scattering of acoustic waves in rigid porous media
,”
J. Acoust. Soc. Am.
122
,
1888
1905
(
2007
).
15.
K.
Schladitz
,
S.
Peters
,
D.
Reinel-Bitzer
,
A.
Wiegmann
, and
J.
Ohser
, “
Design of acoustic trim based on geometric modeling and flow simulation for non-woven
,”
Comput. Mater. Sci.
38
,
56
66
(
2006
).
16.
C.
Peyrega
and
D.
Jeulin
, “
Estimation of acoustic properties and of the representative volume element of random fibrous media
,”
J. Appl. Phys.
113
,
104901
(
2013
).
17.
H. T.
Luu
,
C.
Perrot
,
V.
Monchiet
, and
R.
Panneton
, “
Three-dimensional reconstruction of a random fibrous medium: Geometry, transport and sound absorbing properties
,”
J. Acoust. Soc. Am.
141
,
4768
4780
(
2017
).
18.
O.
Umnova
,
D.
Tsiklauri
, and
R.
Venegas
, “
Effect of boundary slip on the acoustical properties of microfibrous materials
,”
J. Acoust. Soc. Am.
126
,
1850
1861
(
2009
).
19.
V.
Tarnow
, “
Compressibility of air in fibrous materials
,”
J. Acoust. Soc. Am.
99
,
3010
3017
(
1996
).
20.
V.
Tarnow
, “
Airflow resistivity of models of fibrous acoustic materials
,”
J. Acoust. Soc. Am.
100
,
3706
3713
(
1996
).
21.
B. P.
Semeniuk
and
P.
Göransson
, “
Microstructure based estimation of the dynamic drag impedance of lightweight fibrous materials
,”
J. Acoust. Soc. Am.
141
,
1360
1370
(
2017
).
22.
M. M.
Tomadakis
and
T. J.
Robertson
, “
Viscous permeability of random fiber structures: Comparison of electrical and diffusional estimates with experimental and analytical results
,”
J. Compos. Mater.
39
,
163
188
(
2005
).
23.
H. T.
Luu
,
R.
Panneton
, and
C.
Perrot
, “
Effective fiber diameter for modeling the acoustic properties of polydisperse fiber networks
,”
J. Acoust. Soc. Am.
141
,
EL96
EL101
(
2017
).
24.
H. T.
Luu
,
C.
Perrot
, and
R.
Panneton
, “
Influence of porosity, fiber radius and fiber orientation on the transport and acoustic properties of random fiber structures
,”
Acta Acust. united Acust.
103
,
1050
1063
(
2017
).
25.
C.
Jensen
and
R.
Raspet
, “
Thermoacoustic properties of fibrous materials
,”
J. Acoust. Soc. Am.
127
,
3470
3484
(
2010
).
26.
P.
Lallemand
and
L. S.
Luo
, “
Theory of the lattice Boltzmann method: Acoustics and thermal properties in two and three dimensions
,”
Phys. Rev. E
68
,
036706
(
2003
).
27.
K.
Attenborough
, “
Acoustical characteristics of rigid fibrous absorbents and granular materials
,”
J. Acoust. Soc. Am.
73
,
785
799
(
1983
).
28.
C.
Zwikker
and
C. W.
Kosten
,
Sound Absorbing Materials
(
Elsevier
,
New York
,
1949
), p.
174
.
29.
D. K.
Wilson
, “
Relaxation-matched modeling of propagation through porous media, including fractal pore structure
,”
J. Acoust. Soc. Am.
94
,
1136
1145
(
1993
).
30.
C.
Peyrega
,
D.
Jeulin
,
C.
Delise
, and
J.
Malvestio
, “
3D morphological characterization of phonic insulation fibrous media
,”
Adv. Eng. Mater.
13
,
156
164
(
2010
).
31.
H.
Talbot
, “
Analyse morphologique de fibres minerals d'isolation
” (“Morphological analysis of mineral insulation fibers”), Ph.D. thesis,
Ecole Nationale Supérieure des Mines de Paris
,
1993
.
32.
S.
Bergonnier
, “
Relationship between microstructure and mechanical properties of entangled materials
,” Ph.D. thesis,
Université Pierre et Marie Curie
, Paris,
2005
.
33.
L.
Chapelle
, “
Characterization and modelling of the mechanical properties of mineral wool
,” Ph.D. thesis,
Technical University of Denmark
, Copenhagen, Denmark,
2016
.
34.
M. D.
Abramoff
,
P. J.
Magalhaes
, and
S. J.
Ram
, “
Image Processing with ImageJ
,”
Biophoton. Int.
11
,
36
42
(
2004
).
35.
Y.
Salissou
and
R.
Panneton
, “
Pressure/mass method to measure open porosity of porous solids
,”
J. Appl. Phys.
101
,
124913
(
2007
).
36.
M. R.
Stinson
and
G. A.
Daigle
, “
Electronic system for the measurement of flow resistance
,”
J. Acoust. Soc. Am.
83
,
2422
2428
(
1988
).
37.
ISO 9053
:
Acoustics—Materials for Acoustical Applications—Determination of Airflow Resistance
(
ISO
,
Geneva, Switzerland
,
1991
).
38.
R.
Panneton
and
X.
Olny
, “
Acoustical determination of the parameters governing viscous dissipation in porous media
,”
J. Acoust. Soc. Am.
119
,
2027
2040
(
2006
).
39.
X.
Olny
and
R.
Panneton
, “
Acoustical determination of the parameters governing thermal dissipation in porous media
,”
J. Acoust. Soc. Am.
123
,
814
824
(
2008
).
40.
Y.
Salissou
and
R.
Panneton
, “
Wideband characterization of complex wave number and characteristic impedance of sound absorbers
,”
J. Acoust. Soc. Am.
128
,
2868
2876
(
2010
).
41.
O.
Doutres
,
Y.
Salissou
,
N.
Atalla
, and
R.
Panneton
, “
Evaluation of the acoustic and nonacoustic properties of sound absorbing materials using a three-microphone impedance tube
,”
Appl. Acoust.
71
,
506
509
(
2010
).
42.
R.
Panneton
, “
Comments on the limp frame equivalent fluid model for porous media
,”
J. Acoust. Soc. Am.
122
,
EL217
EL222
(
2007
).
43.
L.
Dormieux
,
D.
Kondo
, and
F.-J.
Ulm
,
Microporomechanics
(
Wiley
,
Chichester, UK
,
2006
), p.
344
.
44.
A.
Papoulis
and
S. U.
Pillai
,
Probability, Random Variables, and Stochastic Processes
(
McGraw-Hill
,
New-York
,
2002
), p.
82
.
45.
J.-L.
Auriault
,
C.
Boutin
, and
C.
Geindreau
,
Homogenization of Coupled Phenomena in Heterogenous Media
(
Wiley-ISTE
,
London
,
2009
), p.
476
.
46.
A.
Ern
and
J.-L.
Guermond
,
Theory and Practice of Finite Elements
(
Springer
,
New-York
,
2004
), p.
505
.
47.
D. N.
Arnold
,
F.
Brezzi
, and
M.
Fortin
, “
A stable finite element for Stokes equations
,”
Calcolo
21
,
337
344
(
1984
).
48.
C.
Sandström
and
F.
Larsson
, “
On bounded approximations of periodicity for computational homogenization of Stokes flow in porous media
,”
Int. J. Numer. Methods Eng.
109
,
307
325
(
2016
).
49.
A. E.
Scheidegger
,
The Physics of Flow Through Porous Media
(
University of Toronto Press
,
Toronto, Canada
,
1957
), p.
7
.
50.
L. M.
Schwartz
,
N.
Martys
,
D. P.
Bentz
,
E. J.
Garboczi
, and
S.
Torquato
, “
Cross-property relations and permeability estimation in model porous media
,”
Phys. Rev. E
48
,
4584
4591
(
1993
).
51.
F. M.
Auzerais
,
J.
Dunsmuir
,
B. B.
Ferréol
,
N.
Martys
,
J.
Olson
,
T. S.
Ramakrishnan
,
D. H.
Rothman
, and
L. M.
Schwartz
, “
Transport in sandstone: A study based on three dimensional microtomography
,”
Geophys. Res. Lett.
23
,
705
708
, (
1996
).
52.
J.
Guilleminot
,
C.
Soize
, and
R. G.
Ghanem
, “
Stochastic representation for anisotropic permeability tensor random fields
,”
Int. J. Numer. Anal. Methods Geomech.
36
,
1592
1608
(
2012
).
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