Civil Engineering Reference
In-Depth Information
L
c
R
L
c
Figure 5.13
Cell geometry for a circular cross - section.
in the microporous part varies on the mesoscale. Combining these two conditions Sgard
et al
. (2005) propose the following design criterion for perforated materials:
α
∞
m
q
0
m
φ
m
η
2
P
0
ρ
0
(
1
φ
p
)
D(
0
)
−
1
(5.124)
This
criterion
shows
that
the
design
parameters
consist
of
the
resistivity
η
q
0
m
)
, porosity and tortuosity of the microporous medium, and a geometrical
parameter,
(
1
−
(σ
m
=
φ
p
)
D(
0
)
, defined from the mesoscopic structure. Both porosity and
resistivity of the substrate should be as large as possible while tortuosity as low as
possible. The mesostructure parameter,
(
1
φ
p
)
D(
0
)
, has to be evaluated for the
specific geometry and should also be as small as possible. For example, in the case of
circular perforations D(0) is given by (Tarnow 1996)
−
ln
1
φ
p
φ
p
2
L
c
4
π
3
2
+
D(
0
)
=
−
2
φ
p
−
(5.125)
πR
2
L
c
and
L
c
is the size of the cell (see Figure 5.13). In consequence, a low
φ
p
with a large hole diameter must be chosen. Moreover, since the increase of absorption
occurs around
ω
d
with a bandwidth depending on the design parameters, a small value of
ω
d
is needed to increase absorption at low frequencies, meaning again that a very porous,
highly resistive, weakly tortuous substrate material should be selected. These conclusions
are confirmed by a numerical parameter study in the case of straight holes with constant
cross-section along the thickness and experimental work (Atalla
et al
. 2001, Sgard
et al
.
2005). Results show that significant enhancements of the absorption properties can be
obtained over a selected frequency band by adjusting the mesopore profile. Moreover,
interesting absorbing properties can be obtained when coating a double porosity medium
with an impervious screen.
with
φ
p
=
Appendix 5.A: Simplified calculation of the tortuosity for a
porous material having pores made up of an alternating
sequence of cylinders
The cylinders are represented in Figure 5.A.1. Let
υ
1
be the velocity in the cylinders of
section
S
1
and length
l
1
,and
υ
2
the velocity in the cylinders of section
S
2
and length
l
2
.
