An acoustic reflectivity method is proposed for measuring the permeability or flow resistivity of air-saturated porous materials. In this method, a simplified expression of the reflection coefficient is derived in the Darcy's regime (low frequency range), which does not depend on frequency and porosity. Numerical simulations show that the reflection coefficient of a porous material can be approximated by its simplified expression obtained from its Taylor development to the first order. This approximation is good especially for resistive materials (of low permeability) and for the lower frequencies. The permeability is reconstructed by solving the inverse problem using waves reflected by plastic foam samples, at different frequency bandwidths in the Darcy regime. The proposed method has the advantage of being simple compared to the conventional methods that use experimental reflected data, and is complementary to the transmissivity method, which is more adapted to low resistive materials (high permeability).

1.
J. F.
Allard
,
Propagation of Sound in Porous Media Modelling. Sound Absorbing Materials
(
Elsevier
,
London, UK
,
1993
), pp.
1
284
.
2.
D.
Lafarge
, in
Materials and Acoustics Handbook
, edited by
M.
Bruneau
and
C.
Potel
(
ISTE-Wiley
,
London
,
2009
), pp.
149
202
.
3.
M. E.
Delany
and
E. N.
Bazley
, “
Acoustical properties of fibrous materials
,”
Appl. Acoust.
3
,
105
(
1970
).
4.
Y.
Miki
, “
Acoustical properties of porous materials Modification of Delaney Bazeley models
,”
J. Acoust. Soc. Jpn. E
11
,
19
(
1990
).
5.
D. A.
Bies
and
C. H.
Hansen
, “
Flow resistance information for acoustical design
,”
Appl. Acoust.
13
,
357
(
1980
).
6.
D. L.
Johnson
,
J.
Koplik
, and
R.
Dashen
, “
Theory of dynamic permeability and tortuosity in fluid-saturated porous media
,”
J. Fluids Mech.
176
,
379
(
1987
).
7.
M.
Sadouki
,
Z. E. A.
Fellah
,
A.
Berbiche.
,
M.
Fellah
,
F. G.
Mitri
,
E.
Ogam
, and
C.
Depollier
, “
Measuring static viscous permeability of porous absorbing materials
,”
J. Acoust. Soc. Am.
135
,
3163
(
2014
).
8.
R. L.
Brown
and
R. H.
Bolt
, “
The measurement of flow resistance of porous acoustic materials
,”
J. Acoust. Soc. Am.
13
,
337
(
1942
).
9.
R. W.
Leonard
, “
Simplified flow resistance measurements
,”
J. Acoust. Soc. Am.
17
,
240
(
1946
).
10.
M. R.
Stinson
and
G. A.
Daigle
, “
Electronic system for the measurement of flow resistance
,”
J. Acoust. Soc. Am.
83
,
2422
(
1988
).
11.
ISO 9053,
Acoustics-Materials for Acoustical Applications—Determination of Airflow Resistance
(
ISO
,
1991
).
12.
ASTM C 522,
Airflow Resistance of Acoustical Materials
(
ASTM
,
2003
).
13.
K. U.
Ingard
and
T. A.
Dear
, “
Measurement of acoustic flow resistance
,”
J. Sound Vib.
103
(
4
),
567
(
1985
).
14.
R.
Woodcock
and
M.
Hodgson
, “
Acoustic methods for determining the effective flow resistivity of fibrous materials
,”
J. Sound Vib.
153
(
1
),
186
(
1992
).
15.
M.
Ren
and
F.
Jacobsen
, “
Method of measuring the dynamic flow resistance and reactance of porous materials
,”
Appl. Acoust.
39
,
265
(
1993
).
16.
M. A.
Picard
,
P.
Solana
, and
J. F.
Urchueguia
, “
A method of measuring the dynamic flow resistance and the acoustic measurement of the effective static flow resistance in stratified rockwool samples
,”
J. Sound Vib.
216
(
3
),
495
(
1998
).
17.
R.
Panneton
and
X.
Olny
, “
Acoustical determination of the parameters governing viscous dissipation in porous media
,”
J. Acoust. Soc. Am.
119
(
4
),
2027
(
2006
).
18.
O.
Doutres
,
Y.
Salissou
,
N.
Atalla
, and
R.
Panneton
, “
Evaluation of the acoustic and non-acoustic properties of sound absorbing materials using a three-microphone impedance tube
,”
Appl. Acoust.
71
(
6
),
506
(
2010
).
19.
N.
Sebaa
,
Z. E. A.
Fellah
,
M.
Fellah
,
W.
Lauriks
, and
C.
Depollier
, “
Measuring flow resistivity of porous material via acoustic reflected waves
,”
J. Appl. Phys.
98
,
084901
(
2005
).
20.
Z. E. A.
Fellah
,
M.
Fellah
,
N.
Sebaa
,
W.
Lauriks
, and
C.
Depollier
, “
Measuring flow resistivity of porous materials at low frequencies range via acoustic transmitted waves
,”
J. Acoust. Soc. Am.
119
,
1926
(
2006
).
21.
Z. E. A.
Fellah
,
M.
Fellah
,
F. G.
Mitri
,
N.
Sebaa
,
C.
Depollier
, and
W.
Lauriks
, “
Measuring permeability of porous materials at low frequency range via acoustic transmitted waves
,”
Rev. Sci. Instrum.
78
,
114902
(
2007
).
22.
L.
Lin
,
M. L.
Peterson
,
A. R.
Greenberg
, and
B. A.
McCool
, “
In situ measurement of permeability
,”
J. Acoust. Soc. Am.
125
(
4
),
EL123
(
2009
).
23.
R.
Dragonetti
,
C.
Ianniello
, and
A. R.
Romano
, “
Measurement of the resistivity of porous materials with an alternating air-flow method
,”
J. Acoust. Soc. Am.
129
,
753
(
2011
).
24.
J. P.
Arenas
,
R. D.
Rey
,
J.
Alba
, and
J.
Ramis
, “
Evaluation of two alternative procedures for measuring airflow resistance of sound absorbing materials
,” in
Proceedings of the ICSV20, Bangkok, Thailand, 7-11 July 2013
.
25.
M. A.
Biot
, “
The theory of propagation of elastic waves in fluid-saturated porous solid. I. Low frequency range
,”
J. Acoust. Soc. Am.
28
,
168
(
1956
).
26.
Z. E. A.
Fellah
and
C.
Depollier
, “
Transient wave propagation in rigid porous media: a time domain approach
,”
J. Acoust. Soc. Am.
107
,
683
(
2000
).
27.
J. M.
Carcione
, “
Wave propagation in anisotropic, saturated porous media: Plane-wave theory and numerical simulation
,”
J. Acoust. Soc. Am.
99
,
2655
(
1996
).
28.
M. J. Y.
Ou
, “
On reconstruction of dynamic permeability and tortuosity from data at distinct frequencies
,”
Inverse Prob.
30
,
095002
(
2014
).
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