Environmental Engineering Reference
In-Depth Information
perspectives in the field of industrial monitoring, which not only does require accu-
racy and reliability, but also low cost and portability of the involved devices.
4.2
Estimation of Levels and Permittivities of Industrial
Liquids Directly from TDR
In this section, a TDR-based method for simultaneous quantitative and qualitative
monitoring of liquids is described. As outlined in the previous chapters, the level of
liquids in tanks can be inferred from the travel time of the electromagnetic signal
along the probe. The basic idea concerns the use of a perfectly-matched coaxial
probe immersed in a lossless non-dispersive liquid. Under these circumstances, the
unknown dielectric characteristics can be evaluated from (3.14), as
1
2
−
ρ
r
=
ε
app
=
ε
(4.1)
1
+
ρ
where
is the reflection coefficient in time domain.
The quantitative measurement of liquid level is based on the spatial localization
of different interfaces. This task can be performed simply by considering the reflec-
tion coefficient (or, even better, its derivative) versus the apparent distance. In fact,
the clear peaks occurring at significant discontinuities are associated with a local
maximum (or minimum) of the reflection coefficient derivative curve; hence, they
spatially localize the points associated with different interfaces. For example, in the
TDR waveform of the system schematized in Fig. 4.1, a strong drop of the reflection
coefficient would be clearly detectable at the air-liquid interface (due to the different
dielectric constant of air and of the liquid).
Once the dielectric characteristics of the liquid are known, the level of the liq-
uid (or height,
H
) can be evaluated directly from (3.5), which is rewritten here for
convenience:
ρ
H
app
√
ε
H
=
(4.2)
app
where
H
is the physical length of the probe portion immersed in the liquid under
test (LUT), and
H
app
is the corresponding apparent distance.
To summarize, the adopted measurement method comprises the following steps:
1. first, the apparent liquid level (
H
app
) is evaluated from the derivative of the mea-
sured TDR waveform;
2. secondly, using (4.1), the measured reflection coefficient value is used to calcu-
late the apparent dielectric constant value of the considered medium; finally,
3. equation (4.2) allows retrieving the liquid level,
H
.
In spite of the simplicity of the listed steps, there are some important aspects that
must be considered to obtain accurate results: these aspects are thoroughly discussed
in subsection 4.2.2.
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