Ultrasonic flowmeters measure fluid velocity by passing high-frequency sound waves along the fluid flow path. Fluid motion influences the propagation of these sound waves, which may then be measured to infer fluid velocity. Two major sub-types of ultrasonic flowmeters exist: Doppler and transit-time. Both types of ultrasonic flowmeter work by transmitting a high-frequency sound wave into the fluid stream (the incident pulse) and analyzing the received pulse.

Doppler flowmeters exploit the Doppler effect, which is the shifting of frequency resulting from
waves emitted by or reflected by a moving object. A common realization of the Doppler effect is the
perceived shift in frequency of a horn’s report from a moving vehicle: as the vehicle approaches the
listener, the pitch of the horn seems higher than normal; when the vehicle passes the listener and
begins to move away, the horn’s pitch appears to suddenly “shift down” to a lower frequency. In
reality, the horn’s frequency never changes, but the velocity of the approaching vehicle relative to
the stationary listener acts to “compress” the sonic vibrations in the air. When the vehicle moves
away, the sound waves are “stretched” from the perspective of the listener.

The same effect takes place if a sound wave is aimed at a moving object, and the echo’s frequency is compared to the transmitted (incident) frequency. If the reflected wave returns from a bubble advancing toward the ultrasonic transducer, the reflected frequency will be greater than the incident frequency. If the flow reverses direction and the reflected wave returns from a bubble traveling away from the transducer, the reflected frequency will be less than the incident frequency. This matches the phenomenon of a vehicle’s horn pitch seemingly increasing as the vehicle approaches a listener and seemingly decreasing as the vehicle moves away from a listener.

A Doppler flowmeter bounces sound waves off of bubbles or particulate material in the flow stream, measuring the frequency shift and inferring fluid velocity from the magnitude of that shift.


The mathematical relationship between fluid velocity (v) and the Doppler frequency shift (f) is as follows, for fluid velocities much less than the speed of sound through that fluid (v << c):


f = Doppler frequency shift
v = Velocity of fluid (actually, of the particle reflecting the sound wave)
f = Frequency of incident sound wave
θ = Angle between transducer and pipe centerlines
c = Speed of sound in the process fluid

Note how the Doppler effect yields a direct measurement of fluid velocity from each echo received by the transducer. This stands in marked contrast to measurements of distance based on time-offlight (time domain reflectometry – where the amount of time between the incident pulse and the returned echo is proportional to distance between the transducer and the reflecting surface), such as in the application of ultrasonic liquid level measurement. In a Doppler flowmeter, the time delay between the incident and reflected pulses is irrelevant. Only the frequency shift between the incident and reflected signals matters. This frequency shift is also directly proportional to the velocity of flow, making the Doppler ultrasonic flowmeter a linear measurement device. Re-arranging the Doppler frequency shift equation to solve for velocity (again, assuming v << c),


Knowing that volumetric flow rate is equal to the product of pipe area and the average velocityof the fluid (Q = Av), we may re-write the equation to directly solve for Q:


A very important consideration for Doppler ultrasonic flow measurement is that the calibration of the flowmeter varies with the speed of sound through the fluid (c). This is readily apparent by the presence of c in the above equation: as c increases, Δf must proportionately decrease for any fixed volumetric flow rate Q. Since the flowmeter is designed to directly interpret flow rate in terms of Δf, an increase in c causing a decrease in Δf will thus register as a decrease in Q. This means the speed of sound for a fluid must be precisely known in order for a Doppler ultrasonic flowmeter to accurately measure flow.

The speed of sound through any fluid is a function of that medium’s density and bulk modulus (how easily it compresses):


c = speed of sound in a material (meters per second)
B = Bulk modulus (pascals, or newtons per square meter)
ρ = Mass density of fluid (kilograms per cubic meter)

Temperature affects liquid density, and composition (the chemical constituency of the liquid) affects bulk modulus. Thus, temperature and composition both are influencing factors for Doppler ultrasonic flowmeter calibration. Since the Doppler effect applies only to flowmeter applications where bubbles or particles of sufficient size exist in the fluid to reflect sound waves, it is only the speed of sound through liquids (and not gases) that concern us here. We simply cannot measure gas flows using the Doppler technique, and so factors uniquely affecting gas density (e.g. pressure) are irrelevant to Doppler flowmeter calibration.

Following on the theme of requiring bubbles or particles of sufficient size, another limitation of Doppler ultrasonic flowmeters is their inability to measure flow rates of liquids that are too clean and too homogeneous. In such applications, the sound-wave reflections will be too weak to reliably measure. Such is also the case when the solid particles have a speed of sound too close to the
that of the liquid, since reflection happens only when a sound wave encounters a material with a markedly different speed of sound. In flow measurement applications where we cannot obtain strong sound-wave reflections, Doppler-type ultrasonic flowmeters are useless.

Transit-time flowmeters, sometimes called counterpropagation flowmeters, use a pair of opposed sensors to measure the time difference between a sound pulse traveling with the fluid flow versus a sound pulse traveling against the fluid flow. Since the motion of fluid tends to carry a sound wave along, the sound pulse transmitted downstream will make the journey faster than a sound pulse transmitted upstream:


The rate of volumetric flow through a transit-time flowmeter is a simple function of the upstream and downstream propagation times:


Q = Volumetric flow rate
k = Constant of proportionality
t up = Time for sound pulse to travel from downstream location to upstream location (upstream, against the flow)
t down = Time for sound pulse to travel from upstream location to downstream location
(downstream, with the flow)

An interesting characteristic of transit-time velocity measurement is that the ratio of transit time difference over transit time product remains constant with changes in the speed of sound through the fluid. This means transit-time ultrasonic flowmeters are immune to changes in the fluid’s speed of sound. Changes in bulk modulus resulting from changes in fluid composition, or changes in density resulting from compositional, temperature, or pressure changes are irrelevant to this type of flowmeter’s measurement accuracy. This is a tremendous advantage for transit-time ultrasonic flowmeters, particularly when contrasted against Doppler-effect ultrasonic flowmeters.

A requirement for reliable operation of a transit-time ultrasonic flowmeter is that the process fluid be free from gas bubbles or solid particles which might scatter or obstruct the sound waves. Note that this is precisely the opposite requirement of Doppler ultrasonic flowmeters, which require bubbles or particles to reflect sound waves. These opposing requirements neatly distinguish applications suitable for transit-time flowmeters from applications suitable for Doppler flowmeters, and also raise the possibility of using transit-time ultrasonic flowmeters on gas flowstreams as well as on liquid flowstreams.

One potential problem with the transit-time flowmeter is being able to measure the true average fluid velocity when the flow profile changes with Reynolds number. If just one ultrasonic “beam” is used to probe the fluid velocity, the path this beam takes will likely see a different velocity profile as the flow rate changes (and the Reynolds number changes along with it). Recall the difference in fluid velocity profiles between low Reynolds number flows (left) and high Reynolds number flows (right):


A popular way to mitigate this problem is to use multiple sensor pairs, sending acoustic signals along multiple paths through the fluid (i.e. a multipath ultrasonic flowmeter), and to average the resulting velocity measurements. Dual-beam flowmeters have been in use for well over a decade at the time of this writing (2009), and one manufacturer even has a five beam ultrasonic flowmeter
model which they claim maintains an accuracy of +/- 0.15% through the laminar-to-turbulent flow regime transition.

Some modern ultrasonic flowmeters have the ability to switch back and forth between Doppler and transit-time (counterpropagation) modes, automatically adapting to the fluid being sensed. This capability enhances the suitability of ultrasonic flowmeters to a wider range of process applications. Ultrasonic flowmeters are adversely affected by swirl and other large-scale fluid disturbances, and as such may require substantial lengths of straight pipe upstream and downstream of the measurement flowtube to stabilize the flow profile.

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