Page 448 - The Mechatronics Handbook

0066_Frame_C19 Page 70 Wednesday, January 9, 2002 5:27 PM

ultrasonic
transducer 1

l

flow velocity v
θ

ultrasonic
transducer 2

FIGURE 19.57 Principle of the transit-time ultrasonic flowmeter.

The reflected ultrasound does not consist of a single frequency, but a spread of frequencies resulting
from reflections from a range of different sized discontinuities, which may also be travelling at different
velocities travelling through the detection area. For liquids the frequency of the transmitted ultrasound
may lie in the range from 500 kHz up to a few megahertz. At 500 kHz discontinuities must have a diameter
of approximately 50 µm in order to reflect ultrasound back to the receiver. Increase in the operating
frequency will allow the detection of smaller particles, but at the cost of reducing the penetration of the
transmitted signal into the fluid. The flowmeter is also sensitive to changes in flow velocity profile and
the spatial distribution of discontinuities in the flow. As a result the accuracy of Doppler flowmeters is
poor, typically ±5% of full scale. However, this can be improved by calibrating the flowmeter on-line.
Since there is a large acoustic mismatch between steel and air, clamp-on Doppler flowmeters cannot be
used for metering gas flows or, of course, totally clean liquids where there are insufficient reflecting particles
or bubbles to produce a reliable Doppler signal.
Figure 19.57 illustrates the basic principle of the ultrasonic transit-time flowmeter. Two ultrasonic
transducers are mounted on either side of the pipe, so that ultrasound can be transmitted across the
fluid flowing in the pipe. The difference in the time it takes for a pulse of ultrasound to travel between
transducer 1 and 2 (with the flow) and transducer 2 and 1 (against the flow) is given by

q
2lv cos
∆T = ---------------------------- (19.68)
2
2
2
c – v cos q
Since the velocity of sound in the fluid c is much greater than the velocity of the fluid v, then

∆T ≈ 2lv cos q (19.69)
---------------------
c 2

Therefore, if the velocity of sound in the fluid is constant, then there is a linear relationship between ∆T
and v.
Although this method is elegant and straightforward in principle, in practice there are difficulties since
∆T can be small, and the change in ∆T that occurs with changing fluid velocity is even smaller (typically
fractions of microsecond per meter). In addition, as Eq. (19.68) shows, if the temperature of the fluid
changes then c will change. Measurement of, and correction for, changes in the fluid temperature are
usually needed. Transit-time flowmeters, therefore, require the measurement complex signal conditioning
and processing.

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