Civil Engineering Reference
In-Depth Information
It has also be shown by Lafarge (1993) that a physical intrinsic parameter, the trapping
constant
of the porous structure which only depends on the geometry of the frame, is
related to
q
0
by
=
1
/q
0
(5.10)
The evaluation of the dynamic thermal permeability of a porous frame can be per-
formed by solving the diffusion-controlled trapping problem (Lafarge 2002, Perrot
et al
.,
2007). This is beyond the scope of this topic.
A justification of the existence of the dynamic thermal and viscous permeability under
the long-wavelength condition, and therefore of the use of an equivalent fluid, can be
obtained by the homogenization method.
5.2.2 Direct measurement of the static permeabilities
The viscous static permeability can be evaluated from the flow resistivity measured
with the techniques previously described. The thermal static permeability can be eval-
uated from measurements of the bulk modulus
K
at sufficiently low frequencies. At
these frequencies the use of a Kundt tube generally does not provide precise results. A
method developed by Tarnow to measure the compressibility of air in glass wools at low
frequencies is described in Lafarge
et al
. (1997).
A short description of the method with simplified calculations is given in what follows.
As shown in Figure 5.1, the sample is set in a long tube where a loudspeaker creates
a plane field. A microphone measures the pressure around the
λ
/4 resonance, where the
pressure is close to zero. Frequencies as low as 25 Hz can be reached with a tube longer
than 3.5 m. The surface impedance
Z
s
is given by Equation (4.137),
jZ
c
φ
cot
(k
1
l).
Z
s
=−
Loudspeaker
Microphone
M
1
d
Porous layer
M
2
l
Figure 5.1
The experimental setup. The distance from the porous layer to the micro-
phone is
d
and the thickness of the layer is
l
.
