2-White Paper – Transite Time, Small Bore Ultrasonic Flow Meters

Atrato White Paper.
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Transit Time Small Bore Ultrasonic Flow Meters

The measurement of the low flowrates of liquids in small tubes is difficult using conventional transit time ultrasonic techniques for two reasons. Firstly, if a diametrical beam is employed then the defining equation for the transit time difference between the upstream and downstream directions has a constant of proportionality which includes the diameter of the tube. Thus as the tube diameter becomes smaller the transit time difference for a given velocity becomes proportionally smaller. This is usually overcome by employing multiple reflections or more commonly an axial flowmeter in which the length over which the transit time difference is measured is an axial length which is de-coupled from the dimension of the diameter.

Small Bore Ultrasonic Flow Meters – Transit Time

Figure 1 shows the operation of a diametrical flow meter in which the cross section of the channel is circular. An ultrasonic wave is transmitted from transducer 1 and received by transducer 2 to measure the transit time upstream. A second ultrasonic wave is transmitted from transducer 2 and received by transducer 1 to measure the transit time downstream.

transit time small bore ultrasonic flowmeters
Atrato transit time small bore ultrasonic flowmeters – diametrical transit time
transit time small bore ultrasonic flowmeters
The transit time difference between the downstream and upstream waves is given by (see above)

where ΔT is the difference in the transit times; T12 is the propagation from transducer 1 to transducer 2; T21 is the propagation from transducer 2 to transducer 1; v is the average axial velocity measured along the beam; θ is the angle between the direction of propagation and the pipe axis; l is the length of the path over which the integration is made and c is the speed of sound in the fluid. Thus:

transit time small bore ultrasonic flowmeters

Small Bore Ultrasonic Flow Meters – Flow Rate

The average velocity measured along the beam is then used to compute the average velocity across the cross section of the channel and hence the flowrate of the fluid through the channel.

Diametrical ultrasonic flowmeters employing a single beam are known to be sensitive to velocity profile changes which occur as a consequence of the change in Reynolds Number in fully developed flow or by upstream flow disturbances caused by pipe work such as bends or reducers and valves. Multi-chordal or multi-path flowmeters use the transit time measurements over one or more paths in the cross section of the flowmeter to improve the velocity profile averaging across the whole of the of the cross section of the flow and thus reduce the effects of varying velocity profiles. These are however not appropriate for small metering techniques.

transit time small bore ultrasonic flowmeters

At low flowrates, particularly in small diameter tubes, the transit time differences become difficult to measure. For such applications multiple reflections or axial designs are commonly used. In the reflecting methods as shown in figure 2 the ultrasonic beam transits the flowtube several times (typically 2 or 4 times) by reflecting the the walls of the flowtube and thus increasing the transit times and the transit time differences. The number of reflections is usually limited to either 1 or 3 since the width of the beam may lead to interference between reflections. Axial designs as shown in figure 3 are used to decouple the length over which the transit time difference is measured from the diameter of the pipe. The effective length of the flowmeter changes from being the geometric distance between the transducers at high flows to be somewhat shorter at low flow because of flow creeping round the bend at the exit of the flowmeter. Such a flowmeter cannot be cleaned using a ball shaped pig. See Image above.

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