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Velocity-Based Flowmeters

The Law of Continuity for fluids states that the product of mass density (ρ), cross-sectional pipe area (A) and average velocity (v) must remain constant through any continuous length of pipe:


If the density of the fluid is not subject to change as it travels through the pipe (a very good assumption for liquids), we may simplify the Law of Continuity by eliminating the density terms from the equation:


The product of cross-sectional pipe area and average fluid velocity is the volumetric flow rate of the fluid through the pipe (). This tells us that fluid velocity will be directly proportional to volumetric flow rate given a known cross-sectional area and a constant density for the fluid flowstream. Any device able to directly measure fluid velocity is therefore capable of inferring volumetric flow rate of fluid in a pipe. This is the basis for velocity-based flowmeter designs.

Turbine flowmeters

Turbine flowmeters use a free-spinning turbine wheel to measure fluid velocity, much like a miniature windmill installed in the flow stream. The fundamental design goal of a turbine flowmeter is to make the turbine element as free-spinning as possible, so no torque will be required to sustain the turbine’s rotation. If this goal is achieved, the turbine blades will achieve a rotating (tip) velocity directly proportional to the linear velocity of the fluid:

The mathematical relationship between fluid velocity and turbine tip velocity – assuming frictionless conditions – is a ratio defined by the tangent of the turbine blade angle:

For a 45o blade angle, the relationship is 1:1, with tip velocity equaling fluid velocity. Smaller blade angles (each blade closer to parallel with the fluid velocity vector) results in the tip velocity being a fractional proportion of fluid velocity.

Turbine tip velocity is quite easy to sense using a magnetic sensor, generating a voltage pulse each time one of the ferromagnetic turbine blades passes by. Traditionally, this sensor is nothing more than a coil of wire in proximity to a stationary magnet, called a pickup coil or pickoff coil because it “picks” (senses) the passing of the turbine blades. Magnetic flux through the coil’s center increases and decreases as the passing of the steel turbine blades presents a varying reluctance (“resistance” to magnetic flux), causing voltage pulses equal in frequency to the number of blades passing by each second. It is the frequency of this signal that represents fluid velocity, and therefore volumetric flow rate.

A cut-away demonstration model of a turbine flowmeter is shown in the following photograph. The blade sensor may be seen protruding from the top of the flowtube, just above the turbine wheel:


Note the sets of “flow conditioner” vanes immediately before and after the turbine wheel in the photograph. As one might expect, turbine flowmeters are very sensitive to swirl in the process fluid flowstream. In order to achieve high accuracy, the flow profile must not be swirling in the vicinity of the turbine, lest the turbine wheel spin faster or slower than it should to represent the velocity of a straight-flowing fluid.

Mechanical gears and rotating cables have also been historically used to link a turbine flowmeter’s turbine wheel to indicators. These designs suffer from greater friction than electronic (“pickup coil”) designs, potentially resulting in more measurement error (less flow indicated than there actually is, because the turbine wheel is slowed by friction). One advantage of mechanical turbine flowmeters, though, is the ability to maintain a running total of gas usage by turning a simple odometer-style totalizer. This design is often used when the purpose of the flowmeter is to track total fuel gas consumption (e.g. natural gas used by a commercial or industrial facility) for billing.

In an electronic turbine flowmeter, volumetric flow is directly proportional to pickup coil output frequency. We may express this relationship in the form of an equation:



   f = Frequency of output signal (Hz, equivalent to pulses per second)

   Q = Volumetric flow rate (e.g. gallons per second)

   k = “K” factor of the turbine element (e.g. pulses per gallon)


Dimensional analysis confirms the validity of this equation. Using units of GPS (gallons per second) and pulses per gallon, we see that the product of these two quantities is indeed pulses per second (equivalent to cycles per second, or Hz):

Using algebra to solve for flow (Q), we see that it is the quotient of frequency and k factor that yields a volumetric flow rate for a turbine flowmeter:

If pickup signal frequency directly represents volumetric flow rate, then the total number of pulses accumulated in any given time span will represent the amount of fluid volume passed through the turbine meter over that same time span. We may express this algebraically as the product of average flow rate (), average frequency (), k factor, and time:


A more sophisticated way of calculating total volume passed through a turbine meter requires calculus, representing total volume as the time-integral of instantaneous signal frequency and k factor over a period of time from t = 0 to t = T:

We may achieve approximately the same result simply by using a digital counter circuit to totalize pulses output by the pickup coil and a microprocessor to calculate volume in whatever unit of measurement we deem appropriate.

As with the orifice plate flow element, standards have been drafted for the use of turbine flowmeters as precision measuring instruments in gas flow applications, particularly the custody transfer1 of natural gas. The American Gas Association has published a standard called the Report #7 specifying the installation of turbine flowmeters for high-accuracy gas flow measurement, along with the associated mathematics for precisely calculating flow rate based on turbine speed, gas pressure, and gas temperature.

Pressure and temperature compensation is relevant to turbine flowmeters in gas flow applications because the density of the gas is a strong function of both pressure and temperature. The turbine wheel itself only senses gas velocity, and so these other factors must be taken into consideration to accurately calculate mass flow (or standard volumetric flow; e.g. SCFM).

In high-accuracy applications, it is important to individually determine the k factor for a turbine flowmeter’s calibration. Manufacturing variations from flowmeter to flowmeter make precise duplication of k factor challenging, and so a flowmeter destined for high-accuracy measurement should be tested against a “flow prover” in a calibration laboratory to empirically determine its k factor. If possible, the best way to test the flowmeter’s k factor is to connect the prover to the meter on site where it will be used. This way, the any effects due to the piping before and after the flowmeter will be incorporated in the measured k factor.

The following photograph shows three AGA7-compliant installations of turbine flowmeters for measuring the flow rate of natural gas:


Note the pressure-sensing and temperature-sensing instrumentation installed in the pipe, reporting gas pressure and gas temperature to a flow-calculating computer (along with turbine pulse frequency) for the calculation of natural gas flow rate.

Less-critical gas flow measurement applications may use a “compensated” turbine flowmeter that mechanically performs the same pressure- and temperature-compensation functions on turbine speed to achieve true gas flow measurement, as shown in the following photograph:


The particular flowmeter shown in the above photograph uses a filled-bulb temperature sensor (note the coiled, armored capillary tube connecting the flowmeter to the bulb) and shows total gas flow by a series of pointers, rather than gas flow rate.

A variation on the theme of turbine flow measurement is the paddlewheel flowmeter, a very inexpensive technology usually implemented in the form of an insertion-type sensor. In this instrument, a small wheel equipped with “paddles” parallel to the shaft is inserted in the flowstream, with half the wheel shrouded from the flow. A photograph of a plastic paddlewheel flowmeter appears here:

A surprisingly sophisticated method of “pickup” for the plastic paddlewheel shown in the photograph uses fiber-optic cables to send and receive light. One cable sends a beam of light to the edge of the paddlewheel, and the other cable receives light on the other side of the paddlewheel. As the paddlewheel turns, the paddles alternately block and pass the light beam, resulting in a pulsed light beam at the receiving cable. The frequency of this pulsing is, of course, directly proportional to volumetric flow rate.

The external ends of the two fiber optic cables appear in this next photograph, ready to connect to a light source and light pulse sensor to convert the paddlewheel’s motion into an electronic signal:


A problem common to all turbine flowmeters is that of the turbine “coasting” when the fluid flow suddenly stops. This is more often a problem in batch processes than continuous processes, where the fluid flow is regularly turned on and shut off. This problem may be minimized by configuring the measurement system to ignore turbine flowmeter signals any time the automatic shutoff valve reaches the “shut” position. This way, when the shutoff valve closes and fluid flow immediately halts, any coasting of the turbine wheel will be irrelevant. In processes where the fluid flow happens to pulse for reasons other than the control system opening and shutting automatic valves, this problem is more severe.

Another problem common to all turbine flowmeters is lubrication of the turbine bearings. Frictionless motion of the turbine wheel is essential for accurate flow measurement, which is a daunting design goal for the flowmeter manufacturing engineers. The problem is not as severe in applications where the process fluid is naturally lubricating (e.g. diesel fuel), but in applications such as natural gas flow where the fluid provides no lubrication to the turbine bearings, external lubrication must be supplied. This is often a regular maintenance task for instrument technicians: using a hand pump to inject light-weight “turbine oil” into the bearing assemblies of turbine flowmeters used in gas service.

Process fluid viscosity is another source of friction for the turbine wheel. Fluids with high viscosity (e.g. heavy oils) will tend to slow down the turbine’s rotation even if the turbine rotates on frictionless bearings. This effect is especially pronounced at low flow rates, which leads to a minimum linear flow rating for the flowmeter: a flowrate below which it refuses to register proportionately to fluid flow rate.


Vortex Flowmeters

When a fluid moves with high Reynolds number past a stationary object (a “bluff body”), there is a tendency for the fluid to form vortices on either side of the object. Each vortex will form, then detach from the object and continue to move with the flowing gas or liquid, one side at a time in alternating fashion. This phenomenon is known as vortex shedding, and the pattern of moving vortices carried downstream of the stationary object is known as a vortex street.

It is commonplace to see the effects of vortex shedding on a windy day by observing the motion of flagpoles, light poles, and tall smokestacks. Each of these objects has a tendency to oscillate perpendicular to the direction of the wind, owing to the pressure variations caused by the vortices as they alternately form and break away from the object:


This alternating series of vortices was studied by Vincenc Strouhal in the late nineteenth century and later by Theodore von K´arm´an in the early twentieth century. It was determined that the distance between successive vortices downstream of the stationary object is relatively constant, and directly proportional to the width of the object, for a wide range of Reynolds number values2. If we view these vortices as crests of a continuous wave, the distance between vortices may be represented by the symbol customarily reserved for wavelength: the Greek letter “lambda” (λ).


The proportionality between object width (d) and vortex street wavelength (λ) is called the Strouhal number (S), approximately equal to 0.17:


If a differential pressure sensor is installed immediately downstream of the stationary object in such an orientation that it detects the passing vortices as pressure variations, an alternating signal will be detected:


The frequency of this alternating pressure signal is directly proportional to fluid velocity past the object, since the wavelength is constant. This follows the classic frequency-velocity-wavelength formula common to all traveling waves (λf = v). Since we know the wavelength will be equal to the bluff body’s width divided by the Strouhal number (approximately 0.17), we may substitute this into the frequency-velocity-wavelength formula to solve for fluid velocity (v) in terms of signal frequency (f) and bluff body width (d).


Thus, a stationary object and pressure sensor installed in the middle of a pipe section constitute a form of flowmeter called a vortex flowmeter. Like a turbine flowmeter with an electronic “pickup” sensor to detect the passage of rotating turbine blades, the output frequency of a vortex flowmeter is linearly proportional to volumetric flow rate.

The pressure sensors used in vortex flowmeters are not standard differential pressure transmitters, since the vortex frequency is too high to be successfully detected by such bulky instruments. Instead, the sensors are typically piezoelectric crystals. These pressure sensors need not be calibrated, since the amplitude of the pressure waves detected is irrelevant. Only the frequency of the waves matter for measuring flow rate, and so nearly any pressure sensor with a fast enough response time will suffice.

Like turbine meters, the relationship between sensor frequency (f) and volumetric flow rate (Q) may be expressed as a proportionality, with the letter k used to represent the constant of proportionality for any particular flowmeter:



   f = Frequency of output signal (Hz)

   Q = Volumetric flow rate (e.g. gallons per second)3

   k = “K” factor of the vortex shedding flowtube (e.g. pulses per gallon)


This means vortex flowmeters, like electronic turbine meters, each have a particular “k factor” relating the number of pulses generated per unit volume passed through the meter4. Counting the total number of pulses over a certain time span yields total fluid volume passed through the meter over that same time span, making the vortex flowmeter readily adaptable for “totalizing” fluid volume just like turbine meters.

Since vortex flowmeters have no moving parts, they do not suffer the problems of wear and lubrication facing turbine meters. There is no moving element to “coast” as in a turbine flowmeter if fluid flow suddenly stops, which means vortex flowmeters are better suited to measuring erratic flows.

A significant disadvantage of vortex meters is a behavior known as low flow cutoff, where the flowmeter simply stops working below a certain flow rate. The reason for this is the cessation of vortices when the fluid’s Reynolds number drops below a critical value and the flow regime passes from turbulent to laminar. When the flow is laminar, fluid viscosity is sufficient to prevent vortices from forming, causing the vortex flowmeter to register zero flow even when there may be some (laminar) flow through the pipe.

The phenomenon of low-flow cutoff for a vortex flowmeter at first seems analogous to the minimum linear flow limitation of a turbine flowmeter. However, vortex flowmeter low-flow cutoff is actually a far more severe problem. If the volumetric flow rate through a turbine flowmeter falls below the minimum linear value, the turbine continues to spin, albeit slower than it should. If the volumetric flow rate through a vortex flowmeter falls below the low-flow cutoff value, the flowmeter’s signal goes completely to zero, indicating no flow at all.

The following photograph shows a Rosemount model 8800C vortex flow transmitter:

The next two photographs show close-up views of the flowtube assembly, front (left) and rear (right):



Magnetic Flowmeters

When an electrical conductor moves perpendicular to a magnetic field, a voltage is induced in that conductor perpendicular to both the magnetic flux lines and the direction of motion. This phenomenon is known as electromagnetic induction, and it is the basic principle upon which all electro-mechanical generators operate.

In a generator mechanism, the conductor in question is typically a coil (or set of coils) made of copper wire. However, there is no reason the conductor must be made of copper wire. Any electrically conductive substance in motion is sufficient to electromagnetically induce a voltage, even if that substance is a liquid (or a gas5).

Consider water flowing through a pipe, with a magnetic field passing perpendicularly through the pipe:

The direction of liquid flow cuts perpendicularly through the lines of magnetic flux, generating a voltage along an axis perpendicular to both. Metal electrodes opposite each other in the pipe wall intercept this voltage, making it readable to an electronic circuit.

A voltage induced by the linear motion of a conductor through a magnetic field is called motional EMF, the magnitude of which is predicted by the following formula (assuming perfect perpendicularity between the direction of velocity, the orientation of the magnetic flux lines, and the axis of voltage measurement):



  ε= Motional EMF (volts)

   B = Magnetic flux density (Tesla)

   l = Length of conductor passing through the magnetic field (meters)

   v = Velocity of conductor (meters per second)


Assuming a fixed magnetic field strength (constant B) and an electrode spacing equal to the fixed diameter of the pipe (constant l = d), the only variable capable of influencing the magnitude of induced voltage is velocity (v). In our example, v is not the velocity of a wire segment, but rather the average velocity of the liquid flowstream (). Since we see that this voltage will be proportional to average fluid velocity, it must also be proportional to volumetric flow rate, since volumetric flow rate is also proportional to average fluid velocity6. Thus, what we have here is a type of flowmeter based on electromagnetic induction. These flowmeters are commonly known as magnetic flowmeters or simply magflow meters.

We may state the relationship between volumetric flow rate (Q) and motional EMF (E) more precisely by algebraic substitution. First, we will write the formula relating volumetric flow to average velocity, and then manipulate it to solve for average velocity:

Next, we re-state the motional EMF equation, and then substitute for  to arrive at an equation relating motional EMF to volumetric flow rate (Q), magnetic flux density (B), pipe diameter (d), and pipe area (A):

Since we know this is a circular pipe, we know that area and diameter are directly related to each other by the formula . Thus, we may substitute this definition for area into the last equation, to arrive at a formula with one less variable (only d, instead of both d and A):


If we wish to have a formula defining flow rate Q in terms of motional EMF (E), we may simply manipulate the last equation to solve for Q:


This formula will successfully predict flow rate only for absolutely perfect circumstances. In order to compensate for inevitable imperfections, a “proportionality constant” (k) is usually included in the formula7:



   Q = Volumetric flow rate (cubic meters per second)

   E = Motional EMF (volts)

   B = Magnetic flux density (Tesla)

   d = Diameter of flowtube (meters)


Note the linearity of this equation. Nowhere do we encounter a power, root, or other nonlinear mathematical function in the equation for a magnetic flowmeter. This means no special characterization is required to calculate volumetric flow rate.

A few conditions must be met for this formula to successfully infer volumetric flow rate from induced voltage:

   • The liquid must be a reasonably good conductor of electricity

   • Both electrodes must contact the liquid

   • The pipe must be completely filled with liquid

   • The flowtube must be properly grounded to avoid errors caused by stray electric currents in the liquid

The first condition is met by careful consideration of the process liquid prior to installation. Magnetic flowmeter manufacturers will specify the minimum conductivity value of the liquid to be measured. The second and third conditions are met by correct installation of the magnetic flowtube in the pipe. The installation must be done in such a way as to guarantee full flooding of the flowtube (no gas pockets). The flowtube is usually installed with electrodes across from each other horizontally (never vertically!) so even a momentary gas bubble will not break electrical contact between an electrode tip and the liquid flowstream.

Electrical conductivity of the process liquid must meet a certain minimum value, but that is all. It is surprising to some technicians that changes in liquid conductivity have little to no effect on flow measurement accuracy. It is not as though a doubling of liquid conductivity will result in a doubling of induced voltage! Motional EMF is strictly a function of physical dimensions, magnetic field strength, and fluid velocity. Liquids with poor conductivity simply present a greater electrical resistance in the voltage-measuring circuit, but this is of little consequence because the input impedance of the detection circuitry is phenomenally high. Common fluid types that will not work with magnetic flowmeters include deionized water (e.g. steam boiler feedwater, ultrapure water for pharmaceutical and semiconductor manufacturing) and oils.

Proper grounding of the flowtube is very important for magnetic flowmeters. The motional EMF generated by most liquid flowstreams is very weak (1 millivolt or less!), and therefore may be easily overshadowed by noise voltage present as a result of stray electric currents in the piping and/or liquid. To combat this problem, magnetic flowmeters are usually equipped to shunt stray electric currents around the flowtube so the only voltage intercepted by the electrodes will be the motional EMF produced by liquid flow. The following photograph shows a Rosemount model 8700 magnetic flowtube, with braided-wire grounding straps clearly visible:


Note how both grounding straps attach to a common junction point on the flowtube housing. This common junction point should also be bonded to a functional earth ground when the flowtube is installed in the process line. On this particular flowtube you can see a stainless steel grounding ring on the face of the near flange, connected to one of the braided grounding straps. An identical grounding ring lays on the other flange, but it is not clearly visible in this photograph. These rings provide points of electrical contact with the liquid in installations where the pipe is made of plastic, or where the pipe is metal but lined with a plastic material for corrosion resistance.

Magnetic flowmeters are fairly tolerant of swirl and other large-scale turbulent fluid behavior.

They do not require the long straight-runs of pipe upstream and downstream that orifice plates do, which is a great advantage in many piping systems.

Some magnetic flowmeters have their signal conditioning electronics located integral to the flowtube assembly. A couple of examples are shown here (a pair of small Endress+Hauser flowmeters on the left and a large Toshiba flowmeter on the right):

Other magnetic flowmeters have separate electronics and flowtube assemblies, connected together by shielded cable. In these installations, the electronics assembly is referred to as the flow transmitter (FT) and the flowtube as the flow element (FE):


This next photograph shows an enormous (36 inch diameter!) magnetic flow element (black) and flow transmitter (blue, behind the person’s hand shown for scale) used to measure wastewater flow at a municipal sewage treatment plant:


Note the vertical pipe orientation, ensuring constant contact between the electrodes and the water during flowing conditions.

While in theory a permanent magnet should be able to provide the necessary magnetic flux for a magnetic flowmeter to function, this is never done in industrial practice. The reason for this has to do with a phenomenon called polarization which occurs when a DC voltage is impressed across a liquid containing ions (electrically charged molecules). Electrically-charged molecules (ions) tend to collect near poles of opposite charge, which in this case would be the flowmeter electrodes. This “polarization” would soon interfere with detection of the motional EMF if a magnetic flowmeter were to use a constant magnetic flux such as that produced by a permanent magnet. A simple solution to this problem is to alternate the polarity of the magnetic field, so the motional EMF polarity also alternates and never gives the fluid ions enough time to polarize.

This is why magnetic flowmeter tubes always employ electromagnet coils to generate the magnetic flux instead of permanent magnets. The electronics package of the flowmeter energizes these coils with currents of alternating polarity, so as to alternate the polarity of the induced voltage across the moving fluid. Permanent magnets, with their unchanging magnetic polarities, would only be able to create an induced voltage with constant polarity, leading to ionic polarization and subsequent flow measurement errors.

A photograph of a Foxboro magnetic flowtube with one of the protective covers removed shows these wire coils clearly (in blue):


Perhaps the simplest form of coil excitation is when the coil is energized by 60 Hz AC power taken from the line power source, such as the case with this Foxboro flowtube. Since motional EMF is proportional to fluid velocity and to the flux density of the magnetic field, the induced voltage for such a coil will be a sine wave whose amplitude varies with volumetric flow rate.

Unfortunately, if there is any stray electric current traveling through the liquid to produce erroneous voltage drops between the electrodes, chances are it will be 60 Hz AC as well8. With the coil energized by 60 Hz AC, any such noise voltage may be falsely interpreted as fluid flow because the sensor electronics has no way to distinguish between 60 Hz noise in the fluid and a 60 Hz motional EMF caused by fluid flow.

A more sophisticated solution to this problem uses a pulsed excitation power source for the flowtube coils. This is called DC excitation by magnetic flowmeter manufacturers, which is a bit misleading because these “DC” excitation signals often reverse polarity, appearing more like an AC square wave on an oscilloscope display. The motional EMF for one of these flowmeters will exhibit the same waveshape, with amplitude once again being the indicator of volumetric flow rate. The sensor electronics can more easily reject any AC noise voltage because the frequency and waveshape of the noise (60 Hz, sinusoidal) will not match that of the flow-induced motional EMF signal.

The most significant disadvantage of pulsed-DC magnetic flowmeters is slower response time to changing flow rates. In an effort to achieve a “best-of-both-worlds” result, some magnetic flowmeter manufacturers produce dual-frequency flowmeters which energize their flowtube coils with two mixed frequencies: one below 60 Hz and one above 60 Hz. The resulting voltage signal intercepted by the electrodes is demodulated and interpreted as a flow rate.

Ultrasonic Flowmeters

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. Doppler flowmeters bounce sound waves off of bubbles or particulate material in the flow stream, measure the frequency shift, and infer fluid velocity from the magnitude of that shift.


If the reflected wave returns from a bubble advancing toward the ultrasonic transducer9, 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.

Note that 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). 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.

Doppler-effect ultrasonic flowmeters obviously require flowstream containing bubbles or particulate matter. In many applications this is a normal state of affairs (municipal wastewater, for example). However, some process fluids are simply too clean and too homogeneous to reflect sound waves. In such applications, a different sort of ultrasonic velocity detection technique must be applied.

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

   tup = Time for sound pulse to travel from downstream location to upstream location (upstream, against the flow)

   tdown = Time for sound pulse to travel from upstream location to downstream location (downstream, with the flow)

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.

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, 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 transition10.

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.

Advances in ultrasonic flow measurement technology have reached a point where it is now feasible to consider ultrasonic flowmeters for custody transfer measurement of natural gas. The American Gas Association has released a report specifying the use of multipath ultrasonic flowmeters in this capacity (Report #9). Just like the AGA’s #3 (orifice plate) and #7 (turbine) high-accuracy gas flow measurement standards, the AGA9 standard requires the addition of pressure and temperature instruments on the gas line to compensate for changes in gas pressure and temperature, so that a flow computer may calculate either true mass flow or volumetric flow in standardized units (e.g. SCFM).

A unique advantage of ultrasonic flow measurement is the ability to measure flow through the use of temporary clamp-on sensors rather than a specialized flowtube with built-in ultrasonic transducers. While clamp-on sensors are not without their share of problems11, they constitute an excellent solution for certain flow measurement applications.


1“Custody transfer” refers to measurement applications where a product is exchanging ownership. In other words, someone is selling, and someone else is buying, quantities of fluid as part of a business transaction. It is not difficult to understand why accuracy is important in such applications, as both parties have a vested interest in a fair exchange. Government institutions also have a stake in accurate metering, as taxes are typically levied on the sale of commodity fluids such as natural gas.

2It is important to note that the vortex-shedding phenomenon ceases altogether if the Reynolds number is too low. Laminar flow produces no vortices, but rather stream-line flow around any object placed in its way.

3Note that if flow rate is to be expressed in units of gallons per minute as is customary, the equation must contain a factor for minutes-to-seconds conversion: f =kQ/60

4This k factor is empirically determined for each flowmeter by the manufacturer using water as the test fluid (a factory “wet-calibration”), to ensure optimum accuracy.

5Technically, a gas must be super-heated into a plasma state before it is able to conduct electricity.

6This is an application of the transitive property in mathematics: if two quantities are both equal to a common third quantity, they must also be equal to each other. This property applies to proportionalities as well as equalities: if two quantities are proportional to a common third quantity, they must also be proportional to each other.

7The colloquial term in the United States for this sort of thing is fudge factor.

8We know this because the largest electrical noise sources in industry are electric motors, transformers, and other power devices operating on the exact same frequency (60 Hz in the United States, 50 Hz in Europe) as the flowtube coils.

9In the industrial instrumentation world, the word “transducer” usually has a very specific meaning: a device used to process or convert standardized instrumentation signals, such as 4-20 mA converted into 3-15 PSI, etc. In the general scientific world, however, the word “transducer” describes any device converting one form of energy into another. It is this latter definition of the word that I am using when I describe an ultrasonic “transducer” – a device used to convert electrical energy into ultrasonic sound waves, and visa-versa.

10See page 10 of Friedrich Hofmann’s Fundamentals of Ultrasonic Flow Measurement for industrial applications paper.

11Most notably, the problem of achieving good acoustic coupling with the pipe wall so signal transmission to the fluid and signal reception back to the sensor may be optimized. Also, there is the potential for sound waves to “ring around the pipe” instead of travel through the fluid with clamp-on ultrasonic flowmeters because the sound waves must travel through the full thickness of the pipe walls in order to enter and exit the fluid stream.

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Comments (1)Add Comment
Great Job
written by Bryan, November 07, 2012
This was a fantastic article and very helpful.
Thank you

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