Flow Meter Tutorial - Vortex Shedding - Flow Control July 20

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Oscillatory Flow Measurement: PART II -- The Complete Guide to Understanding Vortex Shedding Flowmeters Run New Search

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by: Don Ginesi Pages: 34-43; July, 2002

It was Theodore von Karman who discovered that when a non-streamlined object (also called a bluff body) is placed in the path of a fast moving stream, the fluid is unable to remain attached to the object on its downstream sides, and will alternately separate from one side and then the other. The fluid in the boundary layer on the bluff body becomes detached and curls back on itself. The result of this separation and back flow is the formation of vortices (also called whirlpools or eddies). Vortex formation causes fluid on that side of the bluff body to move with higher velocity than the fluid on the other side. Therefore, the fluid on the side of the vortex exerts less pressure than the fluid on the other side because it has greater kinetic energy (and less potential energy). Initially, a vortex is in a fixed position relative to the bluff body. But the vortex grows in strength and size, and eventually detaches itself, and "sheds" downstream. Then, the process reverses itself, with a vortex being created on the other side of the bluff body. This process creates a vortex street that extends downstream of the bluff body, having alternating vortices spaced at equal distances. You can actually see vortex shedding occur in water flowing through clear plastic piping with the aid of a strobe light. The vortex has an appearance that can be likened to that of a miniature tornado. However, where a tornado is funnel shaped, the vortex is shaped more like a column of fluid, as wide at the base as at the top, stretching across the entire pipe diameter.

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The vortex shedding phenomenon occurs in nature. A

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classic example is a flag waving in the wind. Vortices are shed from the flagpole, acting as a bluff body, under a moderate wind. The alternating high and low pressure zones created by the vortices on each side of the flag cause it to ripple. Vortex shedding also occurs around bridge piers and pilings, around offshore drilling platform supports and around tall buildings. Engineers must take the vortex shedding phenomenon into account when designing these structures to avoid damage to objects in the path of the vortex street. In a closed piping system, the vortex effect is dissipated within a few pipe diameters downstream of the bluff body and is not likely to cause any problem to downstream equipment.

Vortex Shedding Meter Design A vortex flowmeter generally consists of the flowmeter body and an electronics housing (the electronics can be remote mounted for safety or convenience). The flowmeter body contains the bluff body and the sensor assembly. The meter is typically made from 316 stainless steel or Hastelloy. Vortex meters can theoretically be made of any material, but are only truly cost effective in these two. Vortex meters offer a low cost of ownership and are competitive with orifice meters in regards to installed cost for sizes 6” or less. Wafer body meters (flangeless), that insert between process flanges in the pipeline, are available in sizes from 1” to 8,” and are fully rated for service between ANSI 150, 300 and 600 flanges. Flanged body meters are available in sizes ½” to 12.” Wafer meters have the lowest cost. However, wafer meters require longer mounting bolts and may not be recommended for hazardous fluids or processes that can have severe temperature cycling. A satisfactory theory of vortex shedding does not exist to allow bluff bodies to be designed. Rather, bluff body shapes and dimensions have been experimentally determined to achieve the desired balance of characteristics. There are some bluff body features that are universal to all shapes. First, the bluff body must have a width, which is a large enough fraction of the pipe diameter so that the entire flow participates in the shedding. Second, the bluff body must have protruding edges on the upstream face to fix lines of flow separation, regardless of the flow rate. Third, the bluff body length in the direction of flow must be a certain multiple of the bluff body width. All different kinds of shapes for bluff bodies exist (square, rectangular, t-shaped, trapezoidal, etc.). Testing has shown that the linearity, low Reynolds number limitation and sensitivity to velocity profile distortion/swirl vary slightly with bluff body shape. However, no testing has proven any one particular design to be substantially

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better than another. Many different sensing technologies have been used over the past 25 years to detect vortex formation. The vast majority of vortex meters sold today employ piezoelectric or capacitance sensing technologies that respond to the oscillating pressures around the bluff body by producing a low voltage output having the same frequency. These detectors are modular, inexpensive, easily replaceable and operable over wide temperature ranges. This technology allows the vortex meter to measure fluids as diverse as cryogenic liquids to superheated steam. It is the location of the sensor within the meter that gives rise to any design advantages for specific applications. Sensors can be located inside the meter body and be wetted by the fluid. The vortex pressure pulses directly stress a wetted sensor. Wetted sensors need hardened cases that can withstand process conditions and fluid corrosion/erosion. Sensors can also be located outside of the meter body. The external sensor is located so as to come into contact with a part of the meter body that does make contact with the fluid. The pressure oscillations cause this part to move, twist, bend, flex, etc., which, in turn, stresses the external sensor in contact with it. Meters with external sensors may be advantageous on extremely corrosive fluids, but can be more sensitive to vibration effects, and may not have the low flow sensitivity of wetted sensor designs. The electronics housing contains an electronics module assembly, termination connections and a rate indicator/totalizer. The housing is generally rated explosion-proof and weatherproof. The meter electronics accept the raw voltage input from the sensor and produce a conditioned pulse output for driving an external totalizer, and/or an analog output signal proportional to flow rate. All manufacturers now offer intelligent electronics options as well, which produce digital output (HART, Fieldbus Foundation, Profibus) that can directly interface to a distributed control system and allow bi-directional communications between the system and transmitter. Means are normally provided to allow the user to change the transmitter configuration in the field. The user can use buttons to change the configuration in nonhazardous areas, which permits removal of the housing cover. Alternatively, the user can use a magnetic wand, if available, to change the configuration (by activating magnetic sensors in the electronics through the glass in the housing cover) in hazardous areas.

Vortex Shedding Application Information

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Vortex meters are compatible with low viscosity (< 8 cp) liquids, gases and steam. Higher viscosity liquids can be measured, but at the expense of rangeability, and vortex meters are not practical for fluids greater than 15 cp. Most vortex meters will yield 1 percent of rate accuracy or better for all Reynolds numbers from 20,000 to as high as 10,000,000. While vortex shedding can occur at Reynolds numbers greater than 3,000, experimental data has shown that the meter factor value changes for 3,000 < Re < 10,000 by as much as 10 percent. This change in the value of the K factor is non-linear and hard to predict. Therefore, measurement at reduced Reynolds numbers can only be made with reduced accuracy (but good repeatability). Vortex meter performance is not affected by as many real world parameters as orifice plates and turbine meters, and many users of these technologies have switched to vortex meters to improve measurement accuracy and reduce maintenance costs. Vortex meters measure velocity, and infer actual volumetric flow rate from the known geometry of the meter body. In many cases, especially with gases, the user wants to measure flow in standard volumetric rate, or mass rate. Vortex meters can be programmed to internally convert actual volumetric rate into standard volumetric or mass rate if the fluid density is constant (e.g., the process pressure and/or temperature are controlled). Otherwise, the vortex meter can be used to measure standard or mass rate when used with a flow computer and external pressure and temperature measurements. The vortex meter inputs a signal to the flow computer corresponding to actual volumetric rate. The fluid density is constantly computed (using programmed algorithms or tables) from the temperature and pressure measurements. Instantaneous mass or standard volumetric rate is obtained by multiplying the actual volumetric rate from the vortex meter with the computed density value. The vortex meter does not measure to true zero flow. There is a flow cut-off point below which the meter output is automatically clamped at zero (4 mA for analog output). This is the lowest possible flow the meter can measure and is calculated from the process conditions. This is not to be confused with a programmable low flow cut-off value that the user can enter into the electronics. For many applications, this flow cut-off value does not pose a problem. However, this can be a drawback for applications where flows, during start-up or shutdown operations, or other upset conditions, can be greatly different than under normal conditions. Users may want to get an indication of flow during such conditions, although they may not need to accurately measure flow, making the use of a vortex meter questionable. Vortex meters may also be questionable for some

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batching applications, especially when the pipe does not remain full between batches. The meter will not register flow as the fluid accelerates from zero to the cut-off value, and as the fluid decelerates back to zero at the end of the batch. This lost flow may create significant measurement errors, depending on the system dynamics, and the size of the batch. Vortex meters are also unidirectional, and will not measure or subtract any backflow from the batch total. There may be a potential problem sizing vortex meters on existing processes where the flow range to be measured is completely unknown. Many times the instrument engineer makes an educated guess on flow range. A vortex meter sized for the wrong flow range, or wrong process conditions, may need to be replaced by a different size meter entirely. Other devices, like magnetic flowmeters, orifice plates and turbine meters, are more forgiving and can be easily adapted to fit the actual process conditions after installation. Measuring gas flows when the process pressure is low (low-density gases) can be another potential problem for vortex meters. A vortex produced under such conditions does not have a strong pressure pulse, especially when fluid velocities are low. Low-density gases can potentially be measured with a vortex meter, however, rangeability may be less than the 20:1 stated previously, and extreme care must be taken in selecting the correct size meter. Measurement of multi-phase flow has lower accuracy than for single-phase fluids. The meter will measure the flow of all phases present and report it as all liquid or gas (depending on how the meter is configured). The secondary phase should be removed, if feasible, before the meter for the highest accuracy. Any secondary phase should be homogeneously dispersed and should not have any potential for sticking to or coating the meter. The most common application of vortex meters on multi-phase flow is "wet" steam (low quality steam). Ideally, the liquid phase should be homogeneously dispersed within the steam. More often, plug flow or stratified flow exists with wet steam flow. In vertical piping, the trend for wet steam is towards slug flow. Stratified flow generally develops in horizontal piping, with the liquid phase flowing along the bottom of the pipe. Under such situations, flow measurement is difficult. For best results, install the vortex meter in a horizontal line, with the meter oriented so the bluff body is in the horizontal plane (i.e., so the liquid phase passes under the bluff body and does not contribute to the vortex formation process). Testing has shown that the vortex meter factor varies linearly with the moisture content of the steam. This feature can

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be used to determine steam quality from a boiler. One vortex meter measures the mass of water into the boiler (using a flow computer with temperature compensation). A second vortex meter measures the mass flow of steam out of the boiler (using a flow computer with temperature and pressure compensation). If the steam is saturated or superheated, the two measurements should match (to within the measurement accuracy of the meters). But if the steam is wet, the readings will vary by the degree of water in the steam. Pressure drop must also be considered when selecting a vortex meter. Head loss will normally be less than 6 psi for liquid (and more typically less than 2 psi) if the meter has the same nominal size as the process piping. However, downsizing the vortex meter to achieve desired rangeability (i.e., using a 1” meter in a 2” line) can increase head losses above these levels. Be certain that the unrecovered pressure loss will not cause flashing or cavitation. Flashing and cavitation have an adverse affect on meter accuracy, and can damage the meter itself. Fluids that tend to form coatings are bad applications for vortex meters. Coating build-up on the bluff body will eventually change its dimensions sufficiently to bias the value of the K factor.

About the Author Don Ginesi is a chemical engineer with B.E./M.S. degrees from the Stevens Institute of Technology. He is a senior member of the ISA, and also a member of ASME, working on several committees devoted to the development of standards for flow measurement, including the areas of mass flow and in-situ proving of flow devices. Ginesi is currently a senior application engineer for the Automated Technology Products Division of ABB (Warminster, PA). He has over 25 years of experience in the use and application of flowmetering devices, having held similar positions with Union Carbide, Bristol Babcock and Foxboro. He was a consultant specializing in flow measurement for the four years prior to his joining ABB.

------ sidebar -----Installation Recommendations The vortex meter requires a well-developed and symmetrical fluid velocity profile -- free from any distortions or swirl, to achieve stated performance. Sufficient lengths of

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relaxation piping are required upstream/downstream of the meter to condition the flow. Each manufacturer supplies guidelines for piping requirements. Generally, these recommendations are the same as given in ASME Fluid Meters for a 0.7 β orifice plate. Do not trust general recommendations for vortex installations. Many manufacturers will state piping requirements of 15D upstream and 5D downstream. This is usually the recommendation for a single elbow upstream of the meter, and not for any combination of fittings preceding the elbow. Improper installation (misalignment of the meter and/or gaskets or improper relaxation piping) will affect accuracy, but not repeatability. Flow straighteners can be installed upstream of the meter to reduce the amount of relaxation piping required. Remember that some relaxation piping is always required, even when a flow straightener has been installed. For example, 9 diameters of straight pipe are generally recommended between the discharge of many flow straighteners and the inlet of the meter. On approximately 40 percent to 50 percent of all applications, you will need to install a vortex meter using concentric reducers/expanders to neck down process piping. Install the required amount of relaxation piping recommended for the installation conditions. This relaxation piping must have the same bore as the meter. Vortex meters can be installed vertically, horizontally or at any angle. Allow liquids to flow against gravity to keep the pipe full. When the liquid is moving with gravity, elevate the downstream piping above the meter installation level to maintain a full pipe. Install the meter to avoid standing liquid when the pipe is empty. Also plan for the installation, so as to avoid formation of gas bubbles in liquid flow. Check valves may be used when installing a vortex meter to keep it full of liquid when there is no active flow in the process. Mating flanges on the process piping must be of the same nominal size as on the flowmeter. Flanges with a smooth bore, similar to weld neck flanges, are preferred. Do not use reducing flanges. Most performance specifications are based upon using Schedule 40 or Schedule 80 mating pipe. The mating pipe should be of good quality, and have an internal surface free from mill scale, pits, holes, reaming scores, bumps, etc. for a distance of 4 diameters upstream and 2 diameters downstream of the meter. The bores of the adjacent piping, meter and gaskets must be carefully aligned to prevent steps. Control valves should always be installed at least 5D downstream of the vortex meter. When the control valve must be located upstream, most manufacturers recommend a minimum of

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30 pipe diameters between the valve and the meter. Pressure and/or temperature measurements are required when users want to measure flow in mass units. Pressure taps can be located upstream or downstream of the meter (within 3 to 4 pipe diameters), and follow the same guidelines as taps for orifice plates. Temperature elements should be located 5 to 6 diameters downstream and should be as small as possible. Some vortex meter designs allow sensor replacement without process shutdown. Vortex meters that require the process shutdown for sensor replacement will need to be installed using block valves, or in bypass piping, if unscheduled process shutdown poses a problem. Excessive pipe vibration or process noise can affect vortex measurement accuracy. Mechanical pipe vibration can be eliminated by placing proper piping supports on either side of the meter, or by rotating the meter in the process piping so that the sensor is located in a plane different than the vibration. Process noise (from chattering valves, steam traps, pumps, etc.) is hydraulically connected to the meter by the fluid. Process noise can cause the meter to read higher than expected, or create a flow signal when there is no flow in the pipe. Vortex electronics include some kind of noise filtering circuitry. Increasing the noise reduction in the electronics will generally remedy process noise effects. However, increasing noise reduction may adversely affect the low flow sensitivity of the meter. The ability to filter out the effects of hydraulic noise varies from design to design and may be an important issue to consider in selecting a vortex vendor. The vortex meter electronics should be able to effectively eliminate any adverse effects of hydraulic noise on the measurement accuracy without reducing the measurable flow range. Use the following guidelines when sizing a vortex meter if you feel process noise can be a problem. First, make sure the maximum flow rate you need to measure is at least 33 percent of the maximum capacity of the meter. Second, the lowest flow you need to measure should be at least twice the value of the meter's cut-off flow rate. Inspect the flowmeter prior to installation and measure the dimensions of the bluff body width and the inside flow tube diameter. The ratio of these dimensions can be used to determine if the flow tube ever requires recalibration for ISO 9000 verification. You can remove the meter after a period of time in service, and remeasure these dimensions. Manufacturers can often give you guidelines as to how variations in this ratio will affect long-term meter accuracy. Of course, the meter must be flow calibrated to determine the new K factor value if significant

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dimensional variations do occur. -D.G.

------sidebar 2 -----Vortex Shedding Flow Equations and Sizing Vortex shedding frequency is directly proportional to the velocity of the fluid in the pipe, and therefore the volumetric flow rate. Frequency of shedding is independent of fluid properties, such as density, viscosity, conductivity, etc. The only limitation is that turbulent flow must exist for vortex shedding to occur. The relationship between vortex frequency and fluid velocity is expressed as: (1) St = f * d/v Where St is the Strouhal number, f is the vortex shedding frequency, d is the width of the bluff body and v is the average fluid velocity. The value for the Strouhal number is determined experimentally, and is generally found to be constant over a very wide range in Reynolds numbers. The Strouhal number represents the ratio of the interval between vortex shedding and bluff body width. Normally, a vortex interval is about six times the shedder width. The Strouhal number is considered to be a dimensionless calibration factor and can be a basis by which to characterize differently shaped bluff bodies. Two different bluff bodies would act identically as vortex shedders if they had identical Strouhal numbers. Equation (1) can be rearranged as: (2) v = (f * d)/St Since volumetric flow rate Q is defined as the product of the average fluid velocity and the cross sectional area available for flow (A): (3) Q = A * v = (A * f * d * B)/St Where B is the blockage factor and is defined as the full bore area of the pipe less the blockage area of the bluff body, divided by the full bore area of the pipe. Equation (3) can be rewritten as: (4) Q = f * K Where K is defined as the meter coefficient. As with other frequency producing flowmeters, such as turbine meters, the K factor can be defined as pulses per unit volume (pulses per gallon, pulses per cubic foot, etc.). All that is needed is to

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determine how many pulses are being generated per unit time to determine flow rate, or count pulses to totalize flow. Typical vortex frequencies range from as low as one or two pulses per second, to thousands of pulses per second, depending upon the flowing velocity, flowing medium and meter size. Meters measuring gas normally have frequencies about 10 times the frequencies encountered on liquid applications. The K factor is normally determined by calibration in a flow lab, using a convenient fluid, typically water. Water calibrations typically cover Reynolds number ranges from 20,000 to the high hundreds of thousands. Gas and steam applications however, often correspond to Reynolds numbers in the hundreds of thousands up to 10,000,000. Testing at various laboratories has proven the value of the vortex meter factor does vary between liquid and gas/steam Reynolds number ranges. For this reason, accuracy of the meter is decreased when used on gas and steam, based on a water calibration. In addition, experimental information indicates that the calibration factor at moderate Reynolds numbers is not sensitive to edge sharpness or dimensional changes, as those of square edged orifice meters. Normal erosion of the bluff body due to the presence of a secondary phase has a minimal affect on the flowmeter accuracy. This was demonstrated by a two-year test of a vortex meter on limestone slurry. The K factor of the meter was found to have changed by approximately 0.3 percent from the original factory calibration, even though the bluff body and flow tube were badly scarred and pitted by the slurry. This was a highly controlled test to determine the effects of erosion on accuracy, and vortex meters are not recommended for slurry measurement. Inherent rangeability is fixed by the size of the meter and the fluid it will be used on. The sensor generally requires a minimum strength pressure pulse to be able to distinguish vortex formation from flow noise (pressure pulse strength is a function of the product of fluid density times the square of velocity), and highly turbulent flow must be maintained at all times. For example, a typical two-inch vortex meter has a flow range of 13 to 290 GPM for water at 60ºF. This range takes into account the need to maintain turbulent flow under all conditions, and the minimum pressure pulse requirements of the sensor. The flow range would be different for other liquids that have a density and viscosity that differ from water. If the user wants to measure a specific flow range in a two-inch pipe that does not fall within the range of the two-inch meter, say 5 to 50 GPM, they would need to install a meter that could handle that range, in this case a oneinch vortex meter, into the process piping. You select the vortex meter size to achieve a desired flow range and never to match the

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process piping. Selecting a vortex meter to match existing piping, and not to measure the desired flow range, has been the greatest single reason for misapplication and dissatisfaction. You can typically expect equal to or greater than 20:1 rangeability on gas and steam, and equal to or greater than10:1 on liquids, if the vortex meter has been sized properly for the application. While vortex meter equations are relatively simple compared to orifice plates, there are many rules and guidelines that must be made and which can become quite hard to remember. Most manufacturers offer free computer software to allow quick sizing of vortex meters for any application. This software can be downloaded over the Internet from the manufacturers Web site. The user just has to enter the fluid properties (density and viscosity) and desired flow range, and the program automatically and painlessly does the rest. -D.G. Subscribe | Email | Site Map | Search | FAQ | Advertise

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