Civil Engineering Reference
In-Depth Information
exactly reproducible in the production process. Very precise predictions can be impossible
and simple approximations can be a sufficient goal. The bulk modulus appears in a
square root in the characteristic impedance and the wave number, and the adiabatic and
the isothermal values differ by a factor of 1.4. The thermal dissipation has a maximum
around the transition frequency between the isothermal and the adiabatic regime, but this
thermal dissipation is generally negligible compared to the viscous dissipation. In spite
of the possible erroneous location of the transition frequency, one-parameter models such
as the Champoux - Allard model can be used with confidence for the prediction of the
surface impedance and the absorption coefficient.
5.7
Fluid layer equivalent to a porous layer
The surface impedance at normal incidence of a layer of isotropic porous medium, given
by Equation (4.137),
Z
s
jZ
c
/(φ
tan
kl)
is identical to the impedance of a layer of
isotropic fluid with the same thickness
l
given by Equation (2.17)
Z
s
=−
=−
jZ
c
cot
k
l
if
k
=
k
(5.41)
Z
c
=
Z
c
/φ
(5.42)
These conditions are satisfied if the density
ρ
and the bulk modulus
K
of the fluid
are given by
ρ
=
ρ/φ
(5.43)
K
=
K/φ
(5.44)
With these conditions
Z
s
Z
s
=
(5.45)
At oblique incidence, with an angle of incidence
θ
,
Z
s
and
Z
s
become
jZ
c
φ
cos
θ
1
−
Z
s
=
cot
kl
cos
θ
1
(5.46)
jZ
c
cos
θ
1
Z
s
=
−
cot
k
l
cos
θ
1
(5.47)
where
θ
1
and
θ
1
(with
θ
1
=
θ
1
)
are the refraction angles defined by
k
sin
θ
1
=
k
0
sin
θ
(5.48)
k
sin
θ
=
k
0
sin
θ
(5.49)
where
k
0
is the wave number in the external medium. The porous medium can be replaced
by the homogeneous fluid layer without modifying the reflected field in the external
medium.
