Civil Engineering Reference
In-Depth Information
6.0x10
−
9
5.5x10
−
9
5.0x10
−
9
4.5x10
−
9
4.0x10
−
9
3.5x10
−
9
3.0x10
−
9
2.5x10
−
9
20
40
60
80 100 120 140 160 180
Frequency(Hz)
Figure 5.2
The measured quantity
C
Im
K
which tends to the static thermal permeability
when
ω
tends to 0 (Debray
et al
. 1997).
=
12 000 N m
−
4
s). The predicted thermal
permeability calculated from Figure 4 in Straley
et al
. (1987) for a similar medium is
equal to 4
.
8
×
10
−
9
m
2
.
ability
q
0
=
1
.
510
−
9
m
2
(the flow resistivity
σ
5.3
Classical tortuosity, characteristic dimensions,
quasi-static tortuosity
5.3.1 Classical tortuosity
Tortuosity, denoted as
α
∞
, has been precisely defined by Johnson
et al
. (1987). When a
porous frame is saturated by an ideal nonviscous fluid, the effective density of the fluid
is given by
ρ
=
α
∞
ρ
0
(5.19)
The apparent increase of the density can be explained in the following way. In a flow
of nonviscous fluid, let us denote by
υ
m
(
M
)
the microscopic velocity at
M
. The macro-
scopic velocity
υ
(
M
o
)
is obtained by averaging
υ
m
(
M
)
over a representative elementary
volume
V
around
M
0
υ
(M
0
)
=
υ
m
(M)
v
(5.20)
The tortuosity is defined by the relation
α
∞
=
υ
m
(M)
v
/υ
2
(M
o
)
(5.21)
Per unit volume of saturating fluid, the kinetic energy
E
c
is given by
1
2
α
∞
ρ
0
υ
2
(M
0
)
E
c
=
(5.22)
