Environmental Engineering Reference
In-Depth Information
1.0
probe
end
a
p
parent fuel
level
0.5
0.0
-0.5
air/fuel
interface
-1.0
fuel/wate
r
interface
reflection c
o
efficient
first derivat
i
ve
-1.5
5.0
5.5
6.0
6.5
7.0
7.5
8.0
apparent distance (m)
Fig. 4.8
Reflection coefficient (and corresponding first derivative) acquired with the probe
immersed in sample #1
4.3.3.2
Frequency-Domain Approach
For a preliminary validation of the minimization algorithm, the reference parameters
for the three samples of liquids were used to generate the ideal scattering parame-
ters: the modeled
S
11
(
would correspond to those that would be measured under
ideal conditions, that is without any uncertainty due to imperfect calibration, im-
perfect equipment, noise, etc.(see Table 4.4). These ideal scattering functions were
considered as the input for the subsequent optimization routine, thus obtaining the
extrapolated results reported in Table 4.4. Analysis of the data reported in Table 4.4
f
)
Ta b l e 4 . 4
Fuel level (
H
f
), water level (
H
w
), and Cole-Cole parameters extrapolated from
'simulated' frequency-domain measurements and compared to reference values
Sample #1
Sample #2
Sample #3
Ref.
Extr.
Ref.
Extr.
Ref.
Extr.
ε
s
,
f
2.35
2.35
2.35
2.35
2.35
2.35
ε
∞
,
f
2.02
2.03
2.02
2.13
2.02
1.99
f
r
,
f
(GHz)
13.0
12.1
13.0
6.6
13.0
14.9
β
f
0.25
0.25
0.25
0.20
0.25
0.25
H
f
(mm)
283.0
283.0
219.0
219.0
335.0
334.9
ε
s
,
w
79.8
79.8
79.8
79.8
79.8
79.7
ε
∞
,
w
5.2
6.1
5.2
6.1
5.2
3.9
f
r
,
w
(GHz)
17.3
17.1
17.3
17.1
17.3
18.5
β
w
0.00
0.00
0.00
0.00
0.00
0.02
σ
0
,
w
(
mS m
−
1
)
2.58
2.58
2.58
2.59
2.58
2.44
H
w
(mm)
150.0
150.0
214.0
214.0
98.0
98.1
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