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By Corte Swearingen
Reprinted from the January 2001 edition of Chemical Engineering magazine
In this article, five flow-measurement technologies are summarized: bubble, Doppler, transit-time, vortex, and magnetic.
After reviewing the basic design parameters and highlighting the pros and cons associated with each flowmeter type, process applications for each technology will be discussed. The information is then summarized at the end of this article in a table (Table 1: A Comparison of Flowmeter Parameters), which compares the various attributes of these five technologies, such as accuracy, maximum pressures and temperatures, and average costs. The intention of this article is not to recommend a flowmeter for every possible application, but rather to provide the basic knowledge needed to make an informed flowmeter selection among these types for a given application.
Anyone that has heard the pitch of a train whistle change as the train passes has experienced the Doppler effect, named after the 19th century Austrian scientist Christian Doppler. This effect can be used to measure the flow in a pipe.
Design Overview: The Doppler effect is the frequency shift that occurs when a sound source (transmitter) is in relative motion with a receiver of that sound source. In the case of a Doppler flowmeter, we have two sensors mounted or strapped on the outside of a pipe. One of the sensors is the transmitter, and transmits a high frequency (ultrasonic) signal into the pipe. This signal is reflected off particulate matter or entrained gas bubbles in the fluid. The reflected signal is then picked up by the receiving signal and the frequency difference between the transmitted and reflected signals is measured and correlated into an instantaneous flowrate or flow total (Figure 3).
The frequency is subject to two velocity changes; one upstream and the other downstream. Traveling upstream, the velocity of the wave is given as (Vs - V cosθ) where Vs equals the velocity of sound in the fluid, V equals the average fluid velocity and θ equals the angle of the ultrasonic beam to the fluid flow. Similarly, the downstream velocity is given as (Vs V cosθ). The Doppler relationship between the reflected and transmitted frequencies can now be expressed as:
fr = ft[(Vs V cosθ)/(Vs - V cosθ)]
Here, fr is the received frequency and ft is the transmitted frequency. To further simplify this equation, one can assume that the velocity of the fluid in the pipe is much lower than the velocity of sound in the pipe; that is,
V < < Vs. With this assumption, one can write:
fr = ft[(Vs V cosθ)/Vs (V cosθ)]/Vs
Which reduces further to
fr = ft[1 (2V cosθ)/Vs]
The frequency shift is given by Δf = fr-ft so that
Δf = [2(ft) cosθ/Vs]V
Because (2ft cosθ/Vs) is a constant, one can write the final equation as
Δf = kV
k = 2(ft) cosθ/Vs
This indicates that the fluid velocity in the pipe is directly proportional to the change in frequency between the transmitted and reflected ultrasonic signals. With knowledge of the pipe size, the electronics of the flowmeter will correlate the fluid velocity into a flowrate in the engineering unit of choice. Software corrections may have to be made for Vs, since the sound velocity through the medium will change with pressure and temperature fluctuations.
There are ultrasonic designs on the market that use a series of pulsed signals, as opposed to a continuous ultrasonic beam. The main advantage of the pulsed technology is that it can measure the vertical velocity profile within the pipe. Fluid flow will be faster along the middle of the pipe than along the pipe walls and the pulse-design allows one to obtain a better image the flow profile within the pipe.
Another sensor design that minimizes external noise uses dual-frequency Doppler technology to send two independent signals into the pipe at different frequencies. Since both signals are subject to the same Doppler shift, but the noise signals are random, the signals can be combined to calculate a flow velocity while subtracting out the noise.
Ultrasonic sensors can be used with a wide variety of pipe materials, but some will not allow the signal to pass through. Although pipe material recommendations will vary depending on the sensor design, you should not expect to have any problems with carbon steel, stainless steel, PVC, and copper. However, pipes made of concrete, fiberglass, iron, and plastic pipes with liners, could pose transmission problems. One should check with the particular manufacturer to ensure that the pipe material is suitable. Some Doppler designs utilize a section of pipe with built-in transducers that make direct contact with the fluid. This design, although no longer non-invasive, eliminates the problem of incompatible pipe materials.
The accuracy of the ultrasonic Doppler meter is typically around ±2% of full scale. Minimum concentration and particulate size required is roughly 25 PPM at 30 microns. Since some meters may require slightly larger concentrations, it is a good idea to check with the manufacturer. The vast majority of Doppler meters are used for liquids (roughly 88%) while the rest are used for gas (11%) and steam (1%) applications.
Advantages: The main advantage of the Doppler ultrasonic meter is its non-intrusive design. An acoustic-coupling compound is used on the surface of the pipe and the sensors are simply held in place to take a measurement or, for a more permanent installation, they are strapped around the pipe. Some manufacturers offer a special clamp-on probe which allows connection to smaller pipe sizes (down to 1/4-in. diameter). Other advantages include:
Disadvantages: Every flowmeter has its disadvantages and the Doppler design is no exception. The main disadvantage to the technology is the fact that the liquid stream must have particulates, bubbles, or other types of solids in order to reflect the ultrasonic signal. This means that the Doppler meter is not a good choice for DI water or very clean fluids. Although strides have been made with the Doppler technology so that it can work with smaller particulate sizes and smaller concentrations, one still needs to have some particulates present (one design avoids this problem by placing a 90-deg. elbow a few pipe diameters upstream of the flow sensor, and sensing the turbulent swirls created by the elbow). A good rule of thumb is to have a bare minimum of 25 PPM at roughly 30 microns in order for the ultrasonic signal to be reflected efficiently. Some flowmeter designs may require a little more than this, so it is advisable to check the specifications of the meter one is considering.
Note that if the solids content is too high (around 50% and higher by weight), the ultrasonic signal may attenuate beyond the limits of measurability. This possibility should also be checked with the manufacturer, referring to one's specific application. Another disadvantage is that the accuracy can depend on particle-size distribution and concentration and also on any relative velocity that may exist between the particulates and the fluid. If there are not enough particulates available, the repeatability will also degrade.
Finally, the only other potential problem of this technology is that it can have trouble operating at very low flow velocities. If you suspect this may be a problem for an application, the low-end velocity that may be obtained with a particular sensor design should be checked with the manufacturer.
Applications: Doppler meters, being non-instrusive, have a wide variety of applications in the water, waste water, heating, ventilation and air conditioning (HVAC),HVAC, petroleum and general process markets. Below is a list of viable applications:
Design Overview: Like its Doppler cousin, transit-time meters utilize an ultrasonic pulse that is projected into and across the pipe. The design works on a slightly different principle, however. The basic premise of the transit-time meter is to measure the time difference (or frequency shift) between the time of flight down-stream and the time of flight up-stream. This frequency shift can then be correlated into a fluid flowrate through the pipe. To help explain one type of transit-time design, Figure 4a shows two transducers attached to a pipe.
In this figure, V is the average fluid velocity, Z is the distance from the upstream transducer to the downstream transducer, and q is the angle between the ultrasonic-beam line and the horizontal fluid flow. The time it takes for the ultrasonic signal to go from the upstream transducer to the downstream transducer can be written as
tdown = Z/(Vs V cosθ)
where Vs is the velocity of sound through the liquid. The upstream time can be written as (Figure 4b):
tup = Z/(Vs - V cosθ)
Because the upstream and downstream frequencies can be generated in proportion to their respective transit-times, we can say the following:
fdown = 1/tdown
fup = 1/tup
where fdown and fup represent the downstream and upstream frequencies respectively. The change in frequency can then be given as
Δf = fdown - fup = 1/tdown - 1/tup
By substitution, one obtains
Δf = (Vs V cosθ)/Z - (Vs - V cosθ)/Z = (2 cosθ/Z)V
Since (2 cosθ/Z) is just a constant, one can write the final equation as
Δf = kV
k = 2 cosθ/Z
This, then, is the basic relationship used to determine flow velocity from the measured frequency shift. The flow rate can then be calculated using a Reynolds-number correction for velocity profile and by programming in the internal pipe diameter. The Reynolds-number correction takes into account the behavior of the fluid as being laminar, transitional or turbulent. These calculations are made electronically and the flowrate or flow total can then be displayed in the engineering units of choice. Interestingly enough in this instrument, the frequency shift is measured independently of Vs. This is an advantage, since corrections will not have to be made for the variance of Vs because of line-pressure and temperature fluctuations. Most transit-time applications involve liquids, but designs are available to handle gases, as well.
In light of the single path design discussed above, note that a single ultrasonic pulse will average the velocity profile across the transit path, and not across the pipe cross-section, where better accuracy would be obtained. Some flowmeters on the market send several ultrasonic pulses on separate paths in order to average this velocity profile; these meters tend to have better accuracy than their single-pulse counterparts. Transit-time flowmeters generally exhibit accuracies of around ±1% of the measured velocity. Pipe-material recommendations are the same as those given for Doppler flowmeters.
pointed out, the main advantage of the transit-time meter is that it works non-invasively with ultrapure fluids. This allows the user to maintain the integrity of the fluid while still measuring the flow. Some of the other advantages are listed below.
Disadvantages: Transit-time flowmeter performance can suffer from pipe-wall interference, and accuracy and repeatability problems can result if there are any air spaces between the fluid and the pipe wall. Concrete, fiberglass and pipes lined with plastic can attenuate the signal enough to make the flowmeter unusable. Because these factors can vary from one design to the next, it is advisable to check with the manufacturer to ensure that the pipe material is appropriate.
As mentioned before, the transit-time meters will not operate on dirty, bubbly, or particulate-laden fluids. Sometimes, the purity of a fluid may fluctuate so as to affect the accuracy of the flow measurement. For such cases, there are hybrid meters on the market that will access the fluid conditions within the pipe and automatically chose Doppler or transit-time operations where appropriate. These units are especially useful if the unit is to be used in a wide variety of different applications which may range from dirty to clean fluids.
Applications: Transit-time meters have wide applicability for flow measurement of clean or ultrapure streams. Some of these applications are listed below.
Design Overview: At 11 a.m. on November 7th, 1940 the Tacoma Narrows suspension bridge in the state of Washington collapsed from wind-induced vibrations. The torsional motion of the bridge shortly before its collapse is an indication of the power of vortex shedding. The prevailing theory on the collapse of the bridge is that the oscillations were caused by the shedding of turbulent vortices in a periodic manner. Experimental observations have in fact shown that broad flat obstacles (also referred to as bluff bodies) produce periodic swirling vortices which generate high and low pressure regions directly behind the bluff body. The rate at which these vortices shed is given by the following equation:
f = SV/L
f = the frequency of the vortices
L = the characteristic length of the bluff body
V = the velocity of the flow over the bluff body
S = Strouhal Number and is a constant for a given body shape
In the case of the Tacoma bridge, a wind speed of approximately 40 mph caused the formation of vortices around the 8-ft.-deep, steel plate girders of the bridge. This established vortices which were shed, according to the above equation, at approximately 1 Hz. As the structural oscillations constructively reinforced, the bridge began oscillating, building up amplitude, until it could no longer hold itself together.
Another less tragic example of the vortex principle can be seen in the waving motion of a flag. The flag pole, acting as a bluff body, creates swirling vortices behind it that give the flag its "flapping" quality in strong winds.
A practical application of vortex production can be found in the design of the vortex flowmeter. In this design, a bluff body or bodies is placed within the fluid stream. Just behind the bluff body, a pressure transducer, thermistor, or ultrasonic sensor picks up the high and low pressure and velocity fluctuations as the vortices move past the sensor (Figure 5). These fluctuations are linear, directly proportional to the flowrate and independent of fluid density, pressure, temperature and viscosity (within certain limits). As given explicitly in the above equation, the frequency of the vortices is directly proportional to the velocity of the fluid. Vortex meters are very flexible and the technology can be used for liquid, gas and steam measurements. This, along with the fact that they have no moving parts, makes them a very popular choice. Accuracies are typically in the ±1% range.
Generally speaking, in-line vortex meters are available in line sizes ranging from 1/2 to 16". Insertion vortex meters that are installed in the top or sides of a pipe can be used for even larger pipe sizes. This makes them versatile in a wide variety of applications (Figure 6).
One final remark concerns the Reynolds number limitations for these flowmeters. For vortex meters, vortices will not be shed under a Reynolds number of approximately 2000. From roughly 2000 to 10,000, vortices will be shed but the resulting fluctuations are non-linear in this range. Typically, a minimum Reynolds number of 10,000 is required in order get optimum performance from the vortex flowmeter. This number can vary from one design to another, so it is advisable to check with the manufacturer.
Advantages: The advantages of a vortex meter are many. They are summarized below:
Disadvantages: There are only a couple of things to watch out for when considering a vortex meter. First, they are not a good choice for very low fluid velocities, and therefore cannot be recommended below about 0.3 ft/sec. At this low flowrate, the vortices are not strong enough to be picked up accurately.
In addition to the above, be aware that a minimum length of straight-run pipe is required upstream and downstream of the meter for the accurate creation of vortices within the flowmeter. Ten pipe diameters before and after the point of installation are typically recommended, but the minimum length could be greater if there are elbows or valves nearby. This is only a disadvantage if the installation area does not allow for this straight run of pipe.
Applications: Vortex meters have become extremely popular in recent years and are used in a variety of applications and industries. Below is a summary of some of the main uses of a vortex meter.
Vortex meters are also used widely in the oil, gas, petrochemical, and pulp & paper industries.
Design Overview: The basic design principle of the magnetic flowmeter (Figure 7) is derived from Faraday's law of induction, which states that the voltage generated in a closed circuit is directly proportional to the amount of magnetic flux that intersects the circuit at right angles.
In this design, magnets are positioned above and below the pipe to produce a magnetic flux (B) along the Y-axis. Because of the movement of conductive fluid, at right angles to this magnetic field and at a velocity V along the Z-axis, a potential is induced into the flow stream. The instantaneous voltage produced between the electrodes is proportional to the fluid flow through the pipe. For this design, one can rewrite Faraday's Law as follows:
E = kBdV
E = the induced voltage between the sensing electrodes
k = a constant
B = the magnetic flux density
d = the distance between electrodes (equivalent to the pipe diameter)
V = the velocity of the fluid
Linear flow through a pipe can be expressed as the volumetric flowrate Q, divided by the cross-sectional area of the pipe A; therefore one can write
V = Q/A = 4Q/πd2
Substituting this into the Faraday equation gives
E = (4k/πd)BQ
This can be solved for the volumetric flow rate Q, and leads to
Q = (πd/4k)E/B
This final equation shows that the volumetric flowrate Q is directly proportional to the induced voltage, E, between the electrodes.
There are two main methods of producing the magnetic flux density, B, across the pipe; alternating-current (a.c.) excitation, or pulsed, direct-current (d.c.) excitation.
In order to avoid past polarization problems encountered in a d.c.-excitation design, some magmeters use an a.c. excitation voltage. In this design, an a.c. voltage is used to create the magnetic field which, in turn, produces a varying-voltage signal across the electrodes. This is not a problem since the amplitude of the voltage, E, will still be proportional to the fluid velocity.
However, the development of some induction voltages across both the transformer coils and the electrodes is undesirable. For induction voltages that are 90 degrees out of phase with the signal voltage (called quadrature voltages), a phase-sensitive filtering circuit eliminates the unwanted voltage. Induction voltages that are in phase with the signal voltage can be eliminated with special zeroing procedures but this usually requires the fluid flow in the pipe to be fully stopped before zeroing; this may not be feasible in some applications.