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1.
Functional principles of UVP
Principles of UVP
operation are described on an example of flow with free surface.
Figure 1 - Schematic picture of UVP velocity profile measurement on a flow
with free surface.
An ultrasonic transducer
transmits a short emission of ultrasound (US), which travels along the measurement
axis Lm, and then switches over to receiving ('listening').
When the US pulse hits a small particle in the liquid, part of the US energy
scatters on the particle and echoes back. The echo reaches the transducer after
a time delay
where
t time delay between transmitted and received signal [s]
x distance of scattering particle from transducer [m]
c speed of sound in the liquid [m/s]
If the scattering
particle is moving with non-zero velocity component into the acoustic axis Lm
of the transducer, Doppler shift of echoed frequency takes place, and received
signal frequency becomes 'Doppler-shifted':
where
v velocity component into transducer axis [m/s]
c speed of sound in liquid [m/s]
fd Doppler shift [Hz]
f0 transmitting frequency [Hz]
If UVP succeeds
to measure the delay t and Doppler shift fd it is then
possible to calculate both position and velocity of a particle. Since we presume
that scattering particles are small enough to follow the liquid flow, we can
also presume that UVP Monitor has established the fluid flow component in the
given space point.
The basic feature of UVP Monitor is the ability to establish the velocity in
many separate space points along measurement axis.
Figure 2 - Illustration of terms connected with 'measuring window'.
Figure 2 gives
a graphic illustration of the measurement window, channel distance, starting
depth, maximum depth, etc.
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2. Channel width
This is the width
of a measurement volume and hence determines the spatial resolution. Channel
width is given by formula
where
w
channel width [m]
c sound velocity [m/s]
n number of cycles per pulse [1]
f0 transmitting frequency [Hz]
(In the formula,
2 in denominator means that once the pulse has reached one end of the measured
cylinder it has to cover twice the distance to the other cylinder end to come
back at the same point.)
For UVP Monitor,
the most frequently suggested number of cycles per pulse to optimise echo vs.
spatial resolution is 4. With transmitting frequency 4 MHz and sound velocity
in water 1 480 m/s, the minimum theoretical measurable channel width would be
0.74 mm. But Met-Flow transducers can generate a minimum of 2 cycles per pulse.
Why is channel width only one half of the US burst length and not the total
length (see previous Equation)? Consider the following Figure 3, illustrating
a 4-wavelength burst travelling through a theoretical measurement volume of
2 wavelengths set against transducer face (no transfer time from volume to transducer
in receiving mode):
Figure 3 - Illustration to explanation of Channel width
At t = 0 ms,
burst front reaches face 1, the close particles start generating echo, the transducer
starts reception of the latter with no delay.
At t = 0.5 ms,
burst front reaches face 2, the distant particles start to generate echo that
will reach the transducer 0.5 ms later.
At t = 1 ms,
the end of burst reaches face 1 and close particles stop generating echo while
echo from face 2 just reaches the transducer. Reception mode for the considered
channel switches off before receiving echo generated from particles beyond face
2.
Thus reception
time lasted 4 periods T0 while echo from particles contained
in a 2-wavelength volume has been measured.
Switch time: For practical considerations, the transducer switch time between
transmission mode and reception mode is negligible.
Note: With increasing
number of cycles per burst, channel width increases, and two adjacent measuring
volumes might overlap - see also 'Channel distance' and 'Overlapping'.
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3.
Channel distance
This is the distance
between two measurement volumes. The channel distance remains constant throughout
the measurement window (i.e., channels 0 - 127). It can be varied in integer
multiples of the spatial resolution (i.e., channel width) selected.
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4.
Overlapping
The "overlapping"
phenomenon is literally the overlap of two consecutive measuring volumes due
to a channel distance set smaller than the channel width itself, depending on
the US burst length.
Figure 4 - Illustration to the explanation of Overlapping
To explain overlapping
in more detail we can use the previous example of a 4-cycle 4 MHz pulse (burst
length = 4 l0, channel
width = 2 l0), but
with a channel distance set at half of channel width (channel distance = l0).
Figure 5 - Illustration to detailed explanation of overlapping
As previously at
t = 0 ms echo generation of the first measurement
volume starts at the same time as transducer reception, storing the signal in
the first channel.
At t = 0.25 ms
echo generation of the second volume starts while transducer is still receiving
echo from the first volume.
At t = 0.5 ms
stops the reception of first channel and starts immediately reception of the
second channel (storing the signal in the second channel), as echo generated
by the second volume starts effectively to reach transducer face.
BUT volume 1 is
still generating echo that will be measured and also stored in channel 2 : this
phenomenon is called overlapping.
Consequently a spatial averaging is made for each velocity channel taking into
account velocities of neighbouring channels, spatial resolution being dependent
on channel width and not channel distance. The result is smoothing of velocity
profile, which can be critical for flows with strong variations of velocity
gradient.
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5.
Measurement window
The measurement
window is defined as the distance between channels 0 (starting channel) and
127 (window-end channel). This is given as
W
= Starting channel + 127 * channel distance
where
W measurement window length [m].
The window-end
position has to be smaller than the maximum depth (that is, maximum depth >=
W), so that values are limited automatically when setting the channel distance
and starting position.
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6. Maximum depth
and Maximum velocity
The maximum measurable
depth is determined by the pulse repetition frequency Fprf:
where
Pmax maximum measurable depth [m]
c sound velocity [m/s]
Fprf pulse repetition frequency [Hz]
The maximum depth
decreases with increasing Fprf. Due to the Nyquist sampling
theorem related to Fprf, the maximum detectable Doppler
shift frequency is limited. This implies that there is a limitation on the maximum
velocity that can be measured. This limit is:
where
Vmax maximum measurable velocity component [m/s]
f0 ultrasound basic frequency [Hz]
Fprf pulse repetition frequency [Hz]
c sound velocity [m/s]
From the above
two equations, the following constraint exists for this method of measurement:
Since for a given
measuring situation both c and f0 are constant, the product
Pmax
* Vmax
is also constant.
This means that, for a given transmitting frequency, we have to compromise between
maximum measurable depth, and maximum measurable velocity.
Figure 6 - Compromise between maximum measurable depth and velocity
Please note that
the product value can be changed by change of used US frequency f0.
With lower f0 higher velocities and longer 'reach' can
be achieved. (Alas, the penalty for increased velocity range is decreased spatial
resolution…)
The possibility to optimise measurement conditions is the reason for the availability
of more US working frequencies in a single UVP Monitor model.
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7. Velocity
resolution
We can now determine
the velocity resolution. From the equation above we can derive that
Number "127"
originates from 7 data bits used during data processing (plus the 8th
bit for sign). When higher resolution is required, Vmax
must be smaller. This requires that the maximum depth Pmax
be larger (i.e., Fprf be smaller). The table below summarises
the results for water:
|
f0
[MHz]
|
Pmax
[mm]
|
Vmax
[mm/s]
|
Pmax*Vmax
[mm2/s]
|
DV
[mm/s]
|
|
0.5
|
100
|
5'476
|
547'600
|
43.1
|
|
|
750
|
730.1
|
547'600
|
5.7
|
|
1
|
100
|
2'738
|
273'800
|
21.6
|
|
|
750
|
365.1
|
273'800
|
2.9
|
|
2
|
100
|
1'369
|
136'900
|
10.8
|
|
|
750
|
182.5
|
136'900
|
1.4
|
|
4
|
100
|
684.5
|
68'450
|
5.4
|
|
|
750
|
91.3
|
68'450
|
0.7
|
|
8
|
100
|
342.3
|
34'225
|
2.7
|
|
|
750
|
45.6
|
34'225
|
0.4
|
(c = 1'480 m/s)
|
Note: The table above shows theoretical values only. During practical measurement,
other limitations apply (e.g. absorption for the maximum measurable distance).
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8.
Doppler Coefficient and the Speed Coefficient
The raw data, which
is generated and recorded on the disk, is in units of frequency detected during
the measurement time. Thus the Doppler shift frequency fD
can be obtained from the raw data using the formula
and the Doppler
coefficient is given by
where
fD Doppler frequency [Hz]
raw data data measured by UVP in internal units [1]
CDoppler Doppler coefficient [Hz]
Fprf pulse repetition frequency [Hz]
Velocity along
beam axis is given by
and the speed coefficient
is given by
where
Cspeed speed coefficient [m/(s *Hz)
= m]
v velocity component into transducer axis [m/s]
V liquid velocity [m/s]
f0 US basic frequency [Hz]
The data can be
converted to a velocity using the formula
where
q US wave incidence angle
to flow normal [deg]
These coefficients
are also calculated in the UVP review software.
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9.
Flow direction
Since flow direction
is detected at all measured positions, the measured data can have both positive
and negative values. A positive value means the flow direction is in the beam
direction (i.e., moving away from the transducer) and a negative value means
the opposite (i.e., moving toward the transducer). It is possible to ignore
this function; this being of value when the flow has only a single direction
(i.e., no recirculating eddies) and sign detection is not needed. In this case,
the 'aliasing' that arises when computing the Doppler shift frequency is corrected,
and the maximum detectable velocity is thereby doubled.
Note: 'Aliasing'
in this case means that two velocities (with the same values but different signs)
can exist for a single measured value of 'raw data'.
It should be noted
that when sign detection is ignored, the constraint condition and the velocity
resolution described earlier become:
which can sometimes
become very useful. (Again, number "255" originates from 8 data bits
used during data processing (with no bit necessary for sign).
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10.
RF Gain
Since the attenuation
of ultrasound in liquid and solid media follow an exponential law, distant particles
give weaker echo than particles closer to the transducer. The amplification
of the received echo is therefore adjusted so that this attenuation is compensated
for. The amplification is time dependent, as illustrated in Figure 7, and is
called the gain distribution. The RF gain factor modifies the slope of the gain
distribution.
Figure 7 - Amplifier gain distribution as function of measuring distance
The gain distribution
can be adjusted by setting its start and end values. Both can be set from factor
1 to factor 9. When both are set at the same value, the distribution is constant
(flat). A factor of one is equivalent to 6dB.
Note Please note that the amplifier gain distribution changes continuously (without
gain steps). This has deep positive consequences in UVP's signal processing
and it presents one of several things which make UVP a superior instrument.
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11. US Emission
Voltage
Overall amplification
gain may also be controlled by changing the strength of ultrasound emission
through the change of voltage applied to the transducer (namely US emission
voltage). Depending on the kind of liquid, maximum depth, condition of reflectors,
etc., the user will need to optimise these parameters.
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12. Time resolution
The time resolution
of the measurement of a single profile is determined by the data acquisition
time, which itself depends on the pulse repetition frequency Fprf
or the maximum depth. It is given by the number of repetitions Nrep
used in the Doppler shift calculation and:
where
DT averaged profile measuring
time [s]
Nrep number of profile measurement repetitions
(default = 32) [1]
Fprf pulse repetition frequency [kHz]
Examples are given
in the following table:
|
Pmax
[mm]
|
Fprf
[kHz]
|
DT
[ms]
|
|
100
|
7.4
|
4.3
|
|
200
|
3.7
|
8.6
|
|
750
|
0.987
|
32.4
|
The table is calculated
for c = 1'480 m/s (water) and Nrep = 32 (default).
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13.
Measuring time
In principle the
time interval between measured profiles is equal to the time resolution DT:
where
Tmeas measurement time for a single averaged
profile [ms]
DT measurement time for a single
averaged profile (time resolution) [ms]
Please note that
Tmeas is not increased by added time TDP
(digital signal processing - DSP) used for data processing and data display
of a single averaged profile (as was the case with older UVP models using DOS
operating system and DOS software), since DSP process and PC 'data treatment'
are strictly independent due to the Windows NT multitasking capability.
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14.
Sampling time
Sometimes it is
useful for the user to slow down data acquisition. This can be the case when
longer time series are measured and the user wants to limit the data file volume.
This is why it is possible to set certain additional delay between measured
profiles.
Sampling
time is then
where
Tsamp time between stored profiles [ms]
Tmeas measurement time for a single averaged
profile [ms]
Tsi delay set by user [ms]
Please note that
at every beginning of a multi-profile measurement the DSP is internally calculating
an averaged "single profile sampling time" from the first 10 profiles
(which is displayed on the status bar) in order to have digital feedback on
sampling time (accuracy ± 1 ms).
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15. Number of
repetitions and Cycles per pulse
Depending on the
condition of the working fluid - that is, the concentration of reflecting particles
in the flow - it may be useful to change Nrep (number
of repetitions) and Cycles per pulse (number of cycles in a pulse, setting the
pulse length). When the concentration is low and the echo is weak, one or both
of these parameters can be increased to improve estimates of the measured velocity.
There is, however, a penalty: time resolution and/or spatial resolution is sacrificed.
Based on our experience, we have found that the values (Nrep=32,
Cycles per pulse = 4) are optimal. Thus we have set these to be the default
values.
