Working principle of vortex flow meter

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Vortex Street Flow Meter I. Overview Under specific flow conditions, part of the fluid’s kinetic energy is converted into fluid vibration, and the frequency of this vibration is in a definite proportional relationship with the flow velocity (flow rate). Flow meters that operate on this principle are known as fluid vibration flow meters. Currently, there are three types of fluid vibration flowmeters: vortex flowmeters, swirl flowmeters, and jet flowmeters. Fluid vibration flowmeters have the following characteristics: 1) The output is in the form of pulse frequency, and this frequency is proportional to the actual volumetric flow rate of the fluid being measured; it is not affected by the fluid’s composition, density, pressure, or temperature ； 　　2) Wide measurement range, with a typical ratio of over 10:1 ； 　　3) The accuracy is at a medium-to-high level ； 　　4) No moving parts, high reliability ； 　　5) Simple and robust structure, easy to install, with low maintenance costs ； 　　6) It has a wide range of applications and can be used with liquids, gases, and vapors. 　　This article only introduces the vortex street flow meter (hereinafter referred to as VSF or flow meter). 　　VSF involves placing one (or multiple) bluff bodies in the fluid; the fluid separates on either side of these bluff bodies, resulting in the formation of two sets of regular vortices. Within a certain range of flow rates, the frequency of vortex separation is proportional to the average flow velocity within the pipe. By using various types of sensing elements to measure the vortex frequency, it is possible to determine the flow rate of the fluid. 　　As early as 1878, Strouhal published a paper on the relationship between the vibration frequency of fluids and flow velocity. The Strouhal number is a similarity criterion that expresses the relationship between the vortex frequency and the characteristic size of the flow-blocking element, as well as the flow velocity. Early research on vortex streets was primarily aimed at disaster prevention; for example, if the natural frequency of the steel pipes in boilers and heat exchangers coincided with the frequency of fluid vortex streets, resonance could occur, leading to equipment damage. The use of vortex street fluid vibration phenomena for measurement and research began in the 1950s, such as in anemometers and ship speedometers. At the end of the 1960s, development of closed-channel flow meters—the vortex flow meter—began, giving rise to the hot wire detection method and the thermosensitive detection method VSF. In the 1970s and 1980s, vortex flowmeters developed at an extraordinary pace; numerous types of flow obstruction elements and detection methods were developed for such flowmeters, which were then mass-produced and brought to the market. It is truly unique for a flowmeter to progress from a laboratory prototype to mass production in just a few years. 　　The production of VSF in our country has also seen rapid development, with dozens of manufacturing plants across the nation; such a surge in production has not been seen anywhere else in the world. It should be noted that the VSF is still a developing type of flow meter, with both its theoretical foundations and practical experience being relatively limited. To this day, the most fundamental equations of flow often rely on the Karman vortex street theory. This theory and some of its quantitative relationships were derived by Karman through experiments in gas wind tunnels with uniform flow fields; they differ from the laws governing vortex separation in closed pipes with three-dimensional, non-uniform flow fields. As for practical experience, it can only be accumulated through long-term application. Generally, flowmeters are calibrated at the factory under laboratory reference conditions, but deviations from these conditions are inevitable in the field. To what extent deviations from working conditions cause additional errors remains unclear in standards and manufacturer documentation to date. All these indicate that, given the rapid development of flowmeters, fundamental research must keep up; otherwise, unexpected problems often arise in practical use. This is why users have certain doubts about VSF, and it is urgent to find solutions to these issues. 　　VSF has become part of the category of general-purpose flow meters, with a variety of models developed both domestically and internationally. A full range of products with complete specifications; great emphasis is also placed on standardization. Some issues with flow meters are normal phenomena in the process of development. II. Working Principle and Structure 1. Working Principle A vortex generator (flow obstructing element) is placed in the fluid, which alternately generates regular vortices on both sides of it; these vortices are known as Karman vortices, as shown in Figure 1. The vortex rows are arranged asymmetrically downstream of the vortex generator. Let the frequency of vortex generation be f, the average velocity of the flow of the medium being measured be U, the frontal width of the vortex generator be d, and the diameter of the body through which the flow passes be D. According to the Karman vortex street principle, the following relationship holds:　　　　　　　　　　　　　　f = SrU1/d = SrU/md　　　　　　　　　　　　　　　　　　　　(1) Where U1 is the average flow velocity on both sides of the vortex generator, in m/s ； 　　　　Sr--Strouhal number ； 　　　　m--the ratio of the arcuate areas on both sides of the vortex generator to the cross-sectional area of the pipe.　　　　　　　　 Figure 1: Karman vortex street. The volumetric flow rate qv within the pipe is given by　　　　　　　　　　　qv=πD2U/4=πD2mdf/4Sr　　　　　　　　　　　　　　　(2)　　　　　　　　　　　K=f/qv=-1　　　　　　　　　　　　　　　　 (3) Where K is the metering coefficient of the flowmeter, expressed in pulses per m3 (P/m3). 　　In addition to being related to the geometric dimensions of the vortex generator and the pipe, K is also related to the Strouhal number. The Strouhal number is a dimensionless parameter that is related to the shape of the vortex generator and the Reynolds number. Figure 2 shows the relationship between the Strouhal number of a cylindrical vortex generator and the pipeline Reynolds number. As can be seen from the graph, within the range of ReD=2×104 to 7×106, Sr can be considered constant, which is the normal operating range of the instrument. When measuring gas flow rate, the flow rate calculation formula for VSF is given by equation (4). Figure 2 shows the relationship curve between the Strouhal number and the Reynolds number. In this formula, qVn and qV represent the volumetric flow rates under standard conditions (0°C or 20°C, 101.325 kPa) and under the actual operating conditions, respectively, in m3/h ； 　　 Pn and P represent the absolute pressures under standard conditions and under operating conditions, respectively, in Pa ； 　　 Tn and T represent the thermodynamic temperatures under standard conditions and under operating conditions, respectively, in K ； 　　 Zn, Z represent the gas compression coefficients under standard conditions and operating conditions, respectively. 　　As can be seen from the above equation, the pulse frequency signal output by VSF is not affected by changes in the fluid properties and composition; that is, within a certain range of Reynolds numbers, the instrument coefficient depends only on factors such as the shape and dimensions of the vortex generator and the pipeline. However, as a flow meter used in material balance and energy measurement, it is necessary to measure the mass flow rate; in such cases, the output signal of the flow meter should simultaneously indicate both the volume flow rate and the fluid density. The physical properties and composition of the fluid also have a direct impact on flow measurement. 2. Structure 　　VSF consists of a sensor and a converter, as shown in Figure 3. Sensors include vortex generators (flow obstructing elements), sensing elements, instrument casings, etc ； The converter includes a preamplifier, filtering and shaping circuit, D/A conversion circuit, output interface circuit, terminals, bracket, and protective cover, etc. In recent years, intelligent flowmeters have also incorporated microprocessors, display and communication modules, as well as other functional components within the converter. Figure 3 Vortex flow meter (1) Vortex generator. The vortex generator is the main component of the detector; it is closely related to the flow characteristics of the instrument (such as instrument coefficient, linearity, range, etc.) as well as its pressure loss characteristics. The requirements for it are as follows. 　　1) It can control the synchronous separation of vortices along the axis of the vortex generator ； 　　2) Over a wide range of Reynolds numbers, there is a stable vortex separation point, maintaining a constant Strouhal number ； 　　3) It can generate strong vortex streets, resulting in a high signal-to-noise ratio ； 　　4) Simple shape and structure, facilitating processing and standardization of geometric parameters, as well as the installation and combination of various detection elements ； 　　5) The material should meet the requirements of fluid properties, being corrosion-resistant, wear-resistant, and resistant to temperature changes ； 　　6) The natural frequency is outside the frequency band of the vortex street signal. 　　A wide variety of vortex generators have been developed, which can be divided into two categories: single vortex generators and multi-vortex generators, as shown in Figure 4. The basic shapes of single vortex generators are cylinders, rectangular prisms, and triangular prisms; all other shapes are variations of these basic shapes. The triangular prismatic vortex generator is the most widely used type, as shown in Figure 5. In the figure, D represents the instrument diameter. To improve the strength and stability of vortex streets, multiple vortex generators can be used, although their application is not widespread. (a) Single vortex generator (b) Dual and multiple vortex generators. Figure 4: Vortex generators. Figure 5: Triangular prism vortex generators. d/D=0.2～0.3; c/D=0.1～0.2; b/d=1～1.5; θ=15°～65°. (2) Detection elements: There are 5 ways in which flow meters can detect vortex signals. 　　1) Directly measure the differential pressure on both sides of the vortex generator using the detection element installed within it ； 　　2) Pressure guide holes are provided on the vortex generator, and detection elements are installed in these holes to measure the pressure difference on both sides of the generator ； 　　3) Detect the alternating circumflow around the vortex generator ； 　　4) Detect the alternating differential pressure on the back side of the vortex generator ； 　　5) Detect vortex rows in the wake. 　　Based on these 5 detection methods, different detection techniques (thermographic, ultrasonic, stress, strain, capacitance, electromagnetic, photoelectric, fiber optic, etc.) can be used to create various types of VSF, as shown in Table 1. Table 1: List of Vortex Generators and Detection Methods
Serial Number | Cross-Sectional Shape of Vortex Generator | Sensor | Serial Number | Cross-Sectional Shape of Vortex Generator | Sensor | Detection Method | Detection Element | Detection Method | Detection Element
1 | Method 5) Ultrasonic Beam | 9 | Method 2) Mirror/Photoelectric Element | 2 | Method 2), Method 3), Method 5) | Method 1) Cantilever/Capacitor, Cantilever/Piezoelectric Element | Thermistor | Ultrasonic Beam | Strain Element | 10 | Method 5) Diaphragm/Piezoelectric Element | 11 | Method 3) Torsion Tube/Piezoelectric Element | 3 | Method 1), Method 2) | Piezoelectric Element | Piezoelectric Element | 12 | Method 4) Torsion Tube/Piezoelectric Element | 4 | Method 1), Method 2), Method 2) | Diaphragm/Capacitor | Thermistor | Vibrating Element/Electromagnetic Sensor | 13 | Method 4) Vibrating Plate/Fiber Optic Sensor | 14 | Method 5) Ultrasonic Beam | 5 | Method 1) Diaphragm/Static Capacitor | 15 | Method 2) Strain Element | 6 | Method 1) Magnetostrictive Element | 16 | Method 1) Piezoelectric Element | 7 | Method 1) Diaphragm/Piezoelectric Element | 17 | Method 4) Strain Element | 8 | Method 2) Thermistor | 18 | Method 5) Ultrasonic Beam | (3) Converter: The detection element converts the vortex signal into an electrical signal; this signal is weak and contains various types of noise. It must be amplified, filtered, and shaped in order to obtain a pulse signal that is proportional to the flow rate. 　　Different detection methods should be equipped with pre-amplifiers with different characteristics, as listed in Table 2. Table 2 Detection Methods and Pre-amplifiers. Detection methods: Thermal, Ultrasonic, Strain-based, Stress-based, Capacitive, Photoelectric, Electromagnetic. Pre-amplifiers: Constant current amplifier, Frequency-selective amplifier, Constant current amplifier, Charge amplifier, Tuned-vibration amplifier, Photoelectric amplifier, Low-frequency amplifier. The schematic diagram of the converter is shown in Figure 6. Figure 6 Principle block diagram of the converter ⑷ Instrument body The instrument body can be of the clamping type or flange type, as shown in Figure 7. Figure 7: Instrument body. III. Advantages and limitations 1. Advantages The VSF has a simple and robust structure, and is easy to install and maintain (compared to throttle-type differential pressure flow meters, it does not require pressure guiding tubes or three-valve assemblies, thereby reducing the risk of leakage, blockage, and freezing). 　　It is suitable for a wide range of fluids, such as liquids, gases, vapors, and some mixed-phase fluids. 　　It has high accuracy (compared to differential pressure and float-type flowmeters), generally ranging from (±1% to ±2%)R of the measured value. 　　The range width can reach 10:1 or 20:1. 　　Low pressure loss (about 1/4 to 1/2 of that of orifice flow meters). 　　It outputs pulse signals proportional to flow rate, suitable for total volume measurement, with no zero drift ； 　　Within a certain range of Reynolds numbers, the output frequency signal is not affected by the fluid properties (density, viscosity) or its composition; in other words, the instrument coefficient depends only on the shape and dimensions of the vortex generator and the pipe. It is sufficient to perform calibration using one typical medium, after which it can be applied to various types of media, as shown in Figure 8. Figure 8: Strouhal numbers for different measuring media. The appropriate detection method can be selected based on the object being measured, giving the instrument high adaptability. 　　VSF is a type of flow meter among various types that is likely to require only dry calibration. 2. Limitations VSF is not suitable for measurements at low Reynolds numbers (ReD≥2×104); therefore, its application is limited in situations involving high viscosity, low flow velocities, and small pipe diameters. 　　The stability of vortex separation is affected by the distortion of the flow velocity distribution and the rotating flow; therefore, a sufficiently long straight pipe section or flow regulators (stream straighteners) should be installed based on the different types of flow obstruction elements located upstream. Generally, the length requirements for the straight pipe section in throttle-type differential pressure flow meters can be used as a reference for installation. 　　The force-sensitive detection method VSF is sensitive to mechanical vibrations in pipelines and is not suitable for use in environments with strong vibrations. 　　Compared to turbine flowmeters, it has a lower coefficient of performance and lower resolution; this value decreases as the pipe diameter increases. Generally, full-bore flowmeters are used for diameters below DN300. 　　There is still a lack of theoretical research and practical experience regarding instruments in pulsating flows and multiphase flows. IV. Classification and Brief Introduction to Various Types of Products 1. Classification Vortex flowmeters can be classified according to the following principles. 　　Based on the sensor connection method, they are divided into flange type and clamping type. 　　Based on the detection method, they are classified into thermal type, stress type, capacitive type, strain type, ultrasonic type, vibrating body type, photoelectric type, and fiber optic type, etc. 　　Based on their application, they are classified into standard types, explosion-proof types, high-temperature types, corrosion-resistant types, low-temperature types, plug-in types, and types designed for use in vehicles. 　　Based on the composition of sensor and converter, they are divided into integrated type and separate type. 　　Based on the measurement principle, they are divided into volume flowmeters and mass flowmeters. 2. Brief introductions to several types of products The performance comparison of various vortex flowmeters is shown in Table 3. Table 3 Comparison of Vortex Flow Meters Using Different Detection Methods
Name, Detection Variation, Detection Technology, Diameter/mm, Medium Temperature/°C, Range, Reynolds Number Range, Simplicity, Robustness, Sensitivity, Heat Resistance, Vibration Resistance, Pollution Resistance, Application Scope, Detection Principle, Detection Element

Thermistor Vortex Flow Meter: Flow velocity variation, Heating element/cooling, Thermistor element, 25–200, -196–+205, 15–30, 104–106, △, √, √, ×, √, ×; Clean, non-corrosive liquids and gases

Ultrasonic Vortex Flow Meter: Modulated sound beam, Ultrasonic transducer, 25–150, -15–+175, 30, 3×10³–10⁶, ×, △, √, △, √, √; Small-diameter liquids and gases

Capacitive Vortex Flow Meter: Pressure variation, Differential pressure effect, Differential pressure detection, Diaphragm/capacitor, 15–300, -200–+400, 30, 104–106, ×, △, √, △, △; Liquids, gases, steam

Stress-type Vortex Flow Meter: Differential pressure detection, Diaphragm/piezoelectric element, 50–200, -18–+205, 16, 104–106, ×, △, √, √, ×, √; Liquids, gases, steam

Vibrating-element Vortex Flow Meter: Differential pressure detection, Disk/electromagnetic, 50–200, -268–-48, 10–30, 5×10³–10⁶, √, ×, △, √, ×, ×; Ultra-low-temperature liquid gases

Pyramidal-ball/electromagnetic: -40–+427; High-temperature steam

Photoelectric Vortex Flow Meter: Differential pressure detection, Mirror/photoelectric element, 40–80, -10–+50, 40, 3×10³–10⁵, √, △, √, ×, ×, ×; Low-pressure, normal-temperature gases

Strain-type Vortex Flow Meter: Lift effect, Strain detection, Strain element, 50–150, -40–120, 15, 104–3×10⁶, △, √, ×, △, △, √; Liquids

Stress-type Vortex Flow Meter: Stress detection, Piezoelectric element, 15–300, -40–+400, 10–20, 104–7×10⁶, √, √, √, √, ×, √; Liquids, gases, steam

Note: √ = good, △ = average, × = poor. 　　The following introduces several types of VSF. 　　⑴ Stress-type VSF As shown in Figure 9, the stress-type VSF uses detection methods 1) to 4) (see Section 2.2). It applies the lift force acting on the detection element as stress on the piezoelectric crystal element, converting it into an alternating charge signal; after charge amplification, filtering, and shaping, a vortex frequency signal is obtained. Piezoelectric sensors feature fast response, strong signals, good processability, low manufacturing costs, no contact with the measuring medium, and high reliability. The instrument has a wide operating temperature range, strong adaptability in field conditions, and high reliability; it is currently the main product type of VSF. Figure 9 Stress-type vortex flow meter 1 - Gauge assembly ； 2-Trigonal prism ； 3-Table Body ； 4-Coupling ； 5-Press plate ； 6-probe ； 7-Seal gasket ； 8-Joint ； 9-Sealing gasket ； 10-bolt ； 11-pin ； 12-Nameplate ； 13-Circular nut ； 14-Bracket ； 15-Bolts. However, it is sensitive to pipeline vibrations, which is its main drawback. Over the years, manufacturers have made significant efforts to address this issue by taking measures such as improving the structure of the instrument itself, adjusting the detection locations, and optimizing signal processing ； Put effort into shock absorption methods for pipeline installation ； Certain progress has been made in providing users with guidance on selecting measurement points, but of course it is better not to proceed if the object being measured experiences significant vibration. 　(2) Capacitive VSF The capacitive VSF utilizes detection methods 1) and 2); the capacitive sensing element installed in the vortex flowmeter functions as a cantilever beam (see Figure 10). When a vortex is generated, a slight pressure difference is created on both sides, causing the vibrating element to deform slightly around its pivot point. This results in one capacitor gap decreasing (the capacitance increasing) while the other capacitor gap increases (the capacitance decreasing). The difference in capacitance is detected using a differential circuit. When the pipeline vibrates, regardless of the direction of the vibration, the inertial forces generated by the vibration act on both the vibrating body and the electrode simultaneously, causing both to deform in the same direction. Since the geometric shapes and sizes of the vibrating body and the electrode are designed to match, their degrees of deformation are identical, resulting in a differential signal of zero. This is why the capacitance sensing element has good vibration resistance. Although it is impossible to completely eliminate the effects of vibration due to manufacturing process errors, **the vibration resistance has been improved. Tests have shown that its vibration resistance exceeds 1g. Another advantage of capacitive sensors is their ability to withstand high temperatures up to 400°C. Temperature has two effects on capacitive sensing elements: it causes changes in the dielectric constant of the capacitor, and it alters the geometric dimensions of the electrodes, which in turn leads to changes in the capacitance value. On the other hand, as temperature rises, the thermal electron emission from metals increases, resulting in a higher leakage current in the capacitor. Tests have shown that when the temperature rises to 400°C, neither changes in capacitance value nor an increase in leakage current affects the basic performance of the instrument. Figure 10 Capacitive detection element 　　(3) Thermosensitive VSF 　　The thermosensitive VSF uses detection methods 2) and 3), as shown in Figure 11. Vortex separation causes local changes in flow velocity, which in turn alters the resistance value of the thermistor; the constant current circuit converts these changes in bridge resistor resistance into alternating voltage signals. This type of instrument has high detection sensitivity, a low minimum flow rate, and is insensitive to vibrations; it can be used for measuring clean, non-corrosive fluids. Figure 11: Thermal vortex flow meter R11, R12 – thermistors. ⑷ Ultrasonic VSF: The ultrasonic VSF uses detection method 5), as shown in Figure 12. As can be seen from the figure, two pairs of ultrasonic probes, T1, R1, T2, R2, are installed on the pipe wall. Probes T1 and T2 emit high-frequency, continuous sound signals, and the sound waves propagate through the fluid. As the vortices pass through the sound beam, each pair of vortices with opposite rotation directions causes a periodic modulation of the sound wave. The modulated sound wave is converted into electrical signals by the receiving probes R1 and R2, and after amplification, detection, and shaping, a vortex signal is obtained. The instrument has high detection sensitivity and a low lower flow rate limit; however, temperature affects sound modulation, and changes in the flow field as well as the presence of bubbles in the liquid have a significant impact on the measurements. Therefore, it is suitable for measuring the flow rate of gases with minimal temperature variations and liquids with a low gas content. Figure 12 Ultrasonic vortex flow sensor 　　⑸ Vibrating-element VSF 　　The vibrating-element VSF uses detection method 2), as shown in Figure 13. A cylindrical deep hole is formed axially in the vortex generator; lightweight hollow balls or disks made of soft magnetic material (vibrating elements) are placed inside this hole. The pressure difference generated by vortex separation drives the vibrating elements to move up and down, and an electromagnetic sensor located above the vibrating elements detects the vortex frequency. It is only suitable for fluids with a high level of cleanliness (such as steam), and it can be used at extremely high temperatures (427°C) as well as extremely low temperatures (-268°C), which are its features. Figure 13 Vibration-type vortex flow meter 　　⑹ Lift-type vortex mass flow meter 　　As the vortices separate, the vortex generator experiences a lift force exerted by the fluid; the magnitude of this lift force F is given by 　　　　　　　　　　　　　　F=CLρU2/2 　　　　　　　　　　　　　　　　　　　　　　where 　　CL is the lift coefficient of the vortex generator. 　　By dividing equation (5) by equation (1) and simplifying, the mass flow rate qm can be obtained: qm = ρU(π/4)D2 = πD2Sr/2CLmd×F/f 　　　　　　　　　　　　(6) It can be seen from equation (6) that the mass flow rate qm is proportional to the lift force F. Figure 14 is the block diagram. The vortex signal is extracted from the piezoelectric sensing element and, after passing through a charge converter, is processed in two paths: one path goes through an active filter, a Schmitt trigger, and an f/V converter to produce a signal proportional to the flow velocity ； The other path obtains a signal whose amplitude is proportional to ρU2, via an amplifier and a filter. These two signals are processed by a divider to obtain the mass flow rate. Figure 14 Block diagram of the principle of the lift-type vortex street mass flow meter. This method has a simple structure, but the signal amplitude is influenced by various factors such as the stability of the piezoelectric elements, the stability of the amplifier, the installation conditions on-site, and the temperature of the medium being measured; as a result, it is difficult to improve the measurement accuracy. 　　⑺ Differential pressure vortex street mass flow meter: As the fluid passes through the vortex generator, vortex separation and wake oscillations occur; part of the energy is consumed and converted, resulting in a pressure loss before and after the vortex generator. △p=CDρU2/2 (7) Where CD is the resistance coefficient of the vortex street flow sensor. 　　By dividing equation (1) by equation (7) and simplifying, the mass flow rate qm is obtained:
qm = ρU(π/4)D2 = (πD2Sr/2mdCD)(△p/f) 　　　　　　　　　　　　(8)
Figure 15 shows a block diagram of the principle behind a differential pressure vortex flow meter. The sensor outputs a frequency that is proportional to the volume flow rate; the differential pressure unit measures the differential pressure △P at specific positions before and after the vortex generator. Through calculations performed by the calculation unit, the mass flow rate qm is determined. The technical key lies in selecting a vortex generator with excellent resistance and flow characteristics, determining the location of the pressure tapping holes, and establishing a mathematical model of CD. Figure 15 Differential pressure vortex street mass flow meter V. Key considerations for selection 1. Application overview Since its industrial use began in the 1970s, the VSF has gained popularity among users and seen rapid development due to its various advantageous features. It is rare among flow meters for one developed like this to have made its way into the category of general-purpose flow meters in just over 20 years. Due to the short duration of application, both theoretical research and practical experience are relatively limited, so it is only natural that some problems arise. Years of practice have shown that the selection (choice and use) of VSF is a crucial factor in making the most of flow meters; therefore, instrument manufacturers should enhance their pre-sales services, that is, assist users in making the right choice and provide guidance on installation and commissioning. As long as this aspect is addressed, this flow meter can be considered a flow meter with good performance. 　　In the mid-to-late 1990s, worldwide, VSF accounted for approximately 3% to 5% of the total number of flow meters in use, with 50,000 to 60,000 units being produced each year; their value represented 4% to 6% of the total ； In our country, the number of units sold accounts for 6% to 8% of the total volume of flow meters (excluding household gas meters, water meters, and glass tube float flow meters), with 15,000 to 20,000 units being sold each year. 2. Selection of VSF diameter 　　It is important to choose the diameter and specifications of the VSF instrument; this is similar to the design calculations for the throttling element in differential pressure flow meters, and certain principles must be followed for making such a choice. The steps for selecting the instrument diameter are as follows. 　　First, the following working parameters must be clarified. 　　1) Fluid name, components ； 　　2) Maximum, normal, and minimum flow rates in operating condition ； 　　3) Maximum, normal, and minimum operating pressure and temperature ； 　　4) Viscosity of the medium in the operating state. 　　The output signal of VSF is proportional to the volumetric flow rate under operating conditions. Therefore, when the gas flow rate is known as a volumetric flow rate or mass flow rate under standard conditions, it must be converted into the volumetric flow rate qv under operating conditions. 　　　　　　　　　　　　　　qv = qn(pnTZ/pTnZn), in units of m3/h 　　　　　　　　　　　　　　　　(Equation 9) Where qv and qn represent the volumetric flow rates under operating conditions and standard conditions, respectively, in units of m3/h ； 　　 P, Pn--are the absolute pressures under operating conditions and standard conditions, respectively, in Pa ； 　　 T, Tn--are the thermodynamic temperatures under the working condition and standard condition, respectively, in K ； 　　 Z, Zn--represent the gas compressibility coefficients under operating conditions and standard conditions, respectively. 　　Density ρ and volumetric flow rate qv of the medium under operating conditions: ρ=ρn(pTnZn/ pnTZ) (10) Where ρ and ρn represent the density of the medium under operating conditions and standard conditions, respectively, in kg/m3 ； 　　The remaining symbols are the same as above. 　　　　　　　　　　　　　　qv = qm/ρ 　　　　　　　　　　　　　　　　　　　　　　(Equation 11) Where qm is the mass flow rate, in kg/h. 　　Next, the sensor diameter needs to be selected. The selection of the sensor diameter is primarily based on the calculation of the lower flow limit. It should meet two conditions: the minimum Reynolds number should not be lower than the critical Reynolds number (ReC=2×104), and for stress-type VSF, the vortex intensity at the lower flow rate should be greater than the allowable value for the sensor’s vortex intensity (the vortex intensity is proportional to the lift force ρU2). For liquids, it is also necessary to check whether the minimum operating pressure is higher than the saturated vapor pressure at the operating temperature, to ensure that cavitation does not occur. 　　These conditions can be expressed mathematically as follows (12-14). In these equations, qVmin and qV0min represent the minimum volumetric flow rates under operating conditions and calibration conditions, respectively, in m3/h ； 　　(qVmin)ρ--Minimum volumetric flow rate when the vortex intensity requirement is met, m3/h ； 　　(qVmin)υ--minimum volumetric flow rate required to meet the minimum Reynolds number requirement, m3/h ； 　　ρ, ρ0--are the densities of the medium under operating conditions and calibration conditions, respectively, in kg/m3 ； 　　υ, υ0--are the dynamic viscosities of the medium under operating conditions and calibration conditions, respectively, in m2/s ； 　　Pmin--minimum operating pressure, Pa ； 　　△p--Pressure loss of the sensor at maximum flow rate, Pa; △p=CD(ρU2/2), with CD≈2; U--Average flow velocity in the pipe, m/s ； 　　PV--Saturated vapor pressure of the liquid at operating temperature, Pa. 　　Compare (qVmin)ρ and (qVmin)υ: If (qVmin)υ ≥ (qVmin)ρ, the measurable flow rate range is from (qVmin)ρ to qVmax, and the linear range is from (qVmin)υ to qVmax ； 　　If (qVmin)υ < (qVmin)ρ, the measurable flow rate range and linear range are (qVmin)ρ to qVmax. 　　When determining the flow measurement range, it is also necessary to check whether it falls within the instrument’s optimal operating range (i.e., between 1/2 and 2/3 of the maximum flow rate). Table 4 shows the flow measurement range for various pipe diameters under specific calibration conditions for a certain model of vortex flow meter. Table 4 Flow measurement range of a certain model of vortex flow meter under specific calibration conditions
Diameter DN/mm Liquid/(m³/h) Gas/(m³/h) Standard measurement range Optional measurement range Standard measurement range Optional measurement range
20 1.2～12 1～15 6～50 5～77
25 1.6～16 1.6～18 8～60 8～120
40 2～30 2～48 18～180 18～310
50 3～50 3～70 30～300 30～480
80 15～150 10～170 70～700 70～1230
100 20～200 15～270 100～1000 100～1920
125 36～360 25～450 150～1500 140～3000
150 50～500 40～630 200～2000 200～4000
200 100～1000 80～1200 400～4000 320～8000
250 150～1500 120～1800 600～6000 550～11000
300 200～2000 180～2500 1000～10000 800～18000

Note: The calibration conditions are as follows:
1. Liquid: Normal temperature water, t=20°C, ρ=998.2 kg/m³, υ=1.006×10⁻⁶ m²/s. 　　2. Gas: Air at normal temperature and pressure, t=20°C, P=0.1 MPa (absolute), ρ=1.205 kg/m3, υ=15×10-6 m2/s. 　　The pipe diameter of the instrument selected according to the above principles may not necessarily match the pipe diameter; if they differ, a special-shaped pipe should be used along with a sufficient length of straight pipe section. 　　【Example 1】Air flow measurement 　　 ⑴ Given conditions 　　 Maximum flow rate: 2000 m3/h (20°C, 101.325 kPa) 　　 Minimum flow rate: 300 m3/h (20°C, 101.325 kPa) 　　 Pipe inner diameter: 80 mm 　　 Operating pressure: 0.5 MPa (absolute) 　　 Operating temperature: 60°C 　　(2) Supplementary calculations 　　　　 　　　　 　　 (3) Selection of diameter 　　　　 Compare (qV0min)ρ and (qV0min)υ; 　　　　　　　　　　　　　　　　(qV0min)ρ > (qV0min)υ 　　Therefore, the measurable flow rate range is from (qV0min)ρ to qVmax. 　　The measurable flow rate range is 143.7 to 2000 m3/h; according to Table 4, DN100 meets the requirements. Since the diameter of the VSF is different from that of the pipeline, an eccentric pipe (diffuser) should be installed along with a straight section of pipe. 　　【Example 2】Hot water flow measurement （1）Given conditions Maximum flow rate: 18 m3/h Minimum flow rate: 6 m3/h Operating pressure: 0.25 MPa Operating temperature: 90°C Density of the fluid: 965 kg/m3 Viscosity of the fluid: 3.32×10-7 m2/s （2）Selection of pipe diameter Compare (qV0min)ρ and (qV0min)υ; since (qV0min)ρ ≤ (qV0min)υ, the measurable flow rate range is from (qV0min)ρ to qVmax. It has been found that both DN40 and ND50 can meet the requirements; DN40 is a more suitable choice. 　　(3) Check of pressure loss: The average flow velocity at maximum flow rate is Umax. According to the data provided by the manufacturer, CD = 2.2. Therefore, △p = 1.1ρU2max = 1.1×965×3.982 = 0.168×105 Pa. The lowest operating pressure at which cavitation does not occur is p = 2.7△pmax + 1.3pv = 2.7×0.168×105 + 1.3×0.7149×105 = 0.138 MPa. Thus, calculations show that cavitation will not occur. 　　The flow measurement range for saturated water vapor can be determined using the formula below, based on the gas flow measurement range shown in Table 4. Equation (15): wherein qm is the mass flow rate of water vapor, in t/h ； 　　 qv empty--volumetric flow rate of air, m3/h ； 　　 ρ--density of water vapor, kg/m3 ； 　　 ρ0--the density of air, ρ0=1.205 kg/m3. 　　The flow measurement range for saturated water vapor is shown in Table 5. 　　Calculate the flow rate range for saturated water vapor at DN100 and 0.8 MPa. 　　1) According to Table 4, the flow rate range for DN100 is 100–1000 m3/h ； 　　2) Using the saturated water vapor density table, at 0.8 MPa, ρ = 4.162 kg/m3 ； 　　3) Calculate Table 5 Saturated water vapor mass flow range unit: (kg/h) Absolute pressure p/MPa Temperature T/oC Density p/(kg/m3) 0.2 120.23 1.129 0.3 133.54 1.651 0.4 143.62 2.163 0.5 151.84 2.669 0.6 158.94 3.170 0.7 164.96 3.667 0.8 170.41 4.162 DN20 Qmin Qmax Expandable maximum upper limit 11 89 89 13 130 130 15 150 171 16 160 211 18 180 250 19 190 290 20 200 329 DN25 Qmin Qmax The maximum expandable upper limit 14 140 140 17 170 204 19 190 267 22 220 330 23 230 391 25 250 453 27 270 541 DN40 Qmin Qmax The maximum expandable upper limit 31 310 357 38 380 522 44 440 684 48 480 844 53 530 1003 57 570 1160 60 600 1317 DN50 Qmin Qmax Expandable maximum upper limit 52 520 558 63 630 816 73 730 1069 81 810 1320 88 880 1568 95 950 1813 101 1010 2058 DN80 Qmin Qmax Expandable maximum upper limit 122 1220 1429 148 1480 2090 170 1700 2738 188 1880 3379 205 2050 4013 221 2210 4642 235 2350 5269 DN100 Qmin Qmax Expandable maximum upper limit 175 1750 2233 212 2120 3266 242 2420 4278 269 2690 5279 293 2930 6270 315 3150 7254 336 3360 8233 DN125 Qmin Qmax Expandable maximum upper limit 262 2620 3489 317 3170 5103 363 3630 6685 404 4040 8249 440 4400 9798 473 4730 11334 504 5040 12864 DN150 Qmin Qmax Expandable maximum upper limit 350 3500 5025 423 4230 7348 484 4840 9627 538 5380 11879 586 5860 14019 631 6310 16321 672 6720 15824 DN200 Qmin Qmax Maximum expandable upper limit 700 7000 8933 846 8460 13064 969 9690 17115 1076 10760 21119 1173 11730 25083 1261 12610 29016 1344 13440 32993 DN250 Qmin Qmax Expandable maximum upper limit 1050 10500 13958 1269 12690 20412 1453 14530 26742 1641 16410 32998 1759 17590 39193 1892 18920 45337 2016 20160 51457 DN300 Qmin Qmax Expandable maximum upper limit 1750 17500 20100 2116 21160 29394 2422 24220 38509 2690 26900 47518 2932 29320 56438 3153 31530 65286 3359 33590 74099 DN350 Qmin Qmax Expandable maximum upper limit 2624 26240 27359 3174 31740 4008 3632 36320 52415 4035 40350 64677 4397 43970 76818 4730 47300 88862 5038 50380 100857 DN400 Qmin Qmax Expandable maximum upper limit 3149 31490 35734 3808 38080 52256 4359 43590 68461 4842 48420 84477 5277 52770 100334 5676 56760 116064 6047 60470 131732 DN500 Qmin Qmax Expandable maximum upper limit 4374 43740 55834 5289 52890 81650 6054 60540 106971 6725 67250 131995 7329 73290 156772 7883 78830 181351 8398 83980 205831 DN600 Qmin Qmax The maximum expandable upper limit is 5599 55990 80401 6770 67700 117576 7749 77490 154038 8608 86080 190073 9381 93810 225752 10089 100890 261146 10749 107490 296397 Absolute pressure p/MPa Temperature T/oC Density p/(kg/m3) 0.9 175.36 4.655 1.0 179.88 5.147 1.2 187.96 6.127 1.4 195.04 7.106 1.6 201.37 8.085 1.8 207.11 9.065 2.0 212.37 10.05 DN20 Qmin Qmax Expandable maximum upper limit 21 210 368 22 220 407 24 240 484 26 260 562 28 280 639 30 300 717 31 310 794 DN25 Qmin Qmax Expandable maximum upper limit 28 280 575 30 300 636 33 330 757 35 350 878 37 370 999 40 400 1120 42 420 1242 DN40 Qmin Qmax The maximum expandable upper limit is 64 640 1473 67 670 1629 73 730 1939 79 790 2249 84 840 2559 89 890 2869 94 940 3180 DN50 Qmin Qmax Maximum expandable limit 107 1070 2302 112 1120 2545 122 1220 3030 132 1320 3514 140 1400 3998 149 1490 4483 157 1570 4970 DN80 Qmin Qmax Maximum expandable limit 249 2490 5893 261 2610 6515 285 2850 7757 307 3070 8996 328 3280 10235 347 3470 11476 365 3650 12723 DN100 Qmin Qmax expandable maximum upper limit 355 3550 9208 374 3740 10181 408 4080 12120 439 4390 14057 468 4680 15993 496 4960 17932 522 5220 19880 DN125 Qmin Qmax expandable maximum upper limit 553 5530 14388 560 5600 15908 611 6110 18938 658 6580 21964 702 7020 24990 743 7430 28018 783 7830 31063 DN150 Qmin Qmax expandable maximum upper limit 711 7110 20719 747 7470 22909 815 8150 27270 878 8780 31628 936 9360 35985 992 9920 40347 1044 10440 44732 DN200 Qmin Qmax expandable maximum upper limit 1421 14210 36834 1494 14940 40727 1630 16300 48481 1756 17560 56228 1873 18730 63794 1983 19830 71729 2088 20880 79523 DN250 Qmin Qmax Maximum expandable upper limit 2132 21320 57553 2241 22410 63636 2445 24450 75752 2634 26340 87856 2809 28090 99960 2974 29740 112077 3132 31320 124225 DN300 Qmin Qmax Maximum expandable upper limit 3553 35530 82876 3736 37360 91636 4076 40760 109083 4389 43890 126513 4682 46820 143943 4958 49580 1613911 5220 52200 178928 DN350 Qmin Qmax Expandable maximum upper limit 5329 53290 112804 5603 56030 124726 6114 61140 148457 6538 65380 172199 7023 70230 195923 7436 74360 219671 7830 78300 243541 DN400 Qmin Qmax Expandable maximum upper limit 6395 63950 147336 6724 67240 162908 7336 73360 193926 7901 79010 22491 8427 84270 255899 8923 89230 286918 9396 93960 318094 DN500 Qmin Qmax expandable maximum upper limit 8881 88810 230213 9339 93390 254544 10189 101890 303010 10973 109730 351472 11705 117050 399843 12394 123940 448309 13050 130500 497022 DN600 Qmin Qmax Maximum expandable upper limit 11368 113680 331506 11954 119540 366544 13042 130420 436335 14046 140460 506055 14982 149820 575774 15864 158640 645565 16704 167040 715712 3. Accuracy of VSF The accuracy of VSF is roughly ±0.5%R～±2%R for liquids, ±l%R～±2%R for gases, and the repeatability is generally 0.2%～0.5%. Due to the low metering coefficient of VSF, resulting in low frequency resolution that decreases as the diameter increases, the meter diameter should not be too large (below DN300). 　　Wide range is a characteristic of VSF, but what matters is what the lower flow limit is. The minimum average flow velocity for liquids is generally 0.5 m/s, while for gases it is 4–5 m/s. The normal flow rate of VSF should preferably be between 1/2 and 2/3 of the normal measurement range. 　　The instrument coefficient of VSF is not affected by the properties of the medium being measured, which is a great advantage; it can be calibrated using a typical medium and then applied to other mediums, facilitating the resolution of issues related to calibration equipment. However, it should be noted that due to the large difference in flow rates of liquids and gases, the frequency ranges also differ significantly. In the amplifier circuits used to process vortex street signals, the passbands of the filters vary, as do the circuit parameters; therefore, the same circuit parameters cannot be used for different measurement media. When the medium changes, the circuit parameters should also change accordingly. 　　Furthermore, the density difference between gases and liquids is significant, and the signal strength generated during vortex separation is proportional to the density. Therefore, the differences in signal strength are also significant; the gain of liquid and gas amplifier circuits, as well as their trigger sensitivity, vary. The differences in piezoelectric charge are large, and the parameters of charge amplifiers differ as well. Even though they are all gases (or liquids, vapors), their densities vary depending on the pressure and temperature of the medium; the range of flow rates that can be used differs as well, and the signal strength changes accordingly, requiring adjustments to the circuit parameters as well. Therefore, it is not feasible to use a VSF without hardware or software modifications, by changing the medium used or the diameter of the instrument. 4. Main problems 　　VSF has been in widespread use for over a decade, but its performance has not been satisfactory. The main reasons for this can be summarized as follows. 　　1) Product quality issues, serious defects in the design principles or design schemes, as well as poor quality of the product materials and manufacturing processes. Especially in recent years, some manufacturers have pursued profits unilaterally by producing shoddy products, thus damaging VSF’s reputation. 　　2) Issues related to instrument selection and use: inaccurate process parameters provided by the user lead to improper selection ； The installation location was chosen incorrectly, and the installation did not meet the specified requirements. 　　3) On-site adjustment issues: lack of adjustment or improper adjustment during commissioning on site; proper adjustment is the key to success. 5. Applicable situations VSF is not suitable for measuring fluids with low Reynolds numbers (ReD≤2×104). At low Reynolds numbers, the Strouhal number changes with Reynolds number, resulting in reduced linearity of the instrument; high fluid viscosity can significantly affect or even prevent the formation of vortices. One limitation in selection is that it cannot be used below the critical Reynolds number. 　　VSF is applicable to a wide range of fluids, but attention should be paid to the dirtiness of the fluids. The erosion of the vortex generator by a fluid containing solid particles generates noise and wears down the vortex generator. If the short fibers present become entangled around the vortex generator, it will change the meter coefficient. 　　There is still limited experience with the use of VSF in multiphase fluids; it can generally be applied to gas-liquid flows that contain dispersed, uniform tiny bubbles, with a volume gas content of less than 7%–10%. If this value exceeds 2%, the instrument coefficient must be adjusted. It can be used in gas-solid and liquid-solid two-phase flows containing dispersed and uniform solid particles in an amount not exceeding 2%. It can be used for two streams of immiscible liquids (such as oil and water), etc. 　　Pulsating flow and rotating flow can have a severe impact on VSF. If the pulsation frequency coincides with the frequency band of the vortex street, it can cause resonance that disrupts normal operation of the equipment, leading to a \"lock-in\" phenomenon in the vortex street signal, at which point the signal remains fixed at a certain frequency. "Locking is related to factors such as pulsation amplitude, vortex generator shape, and blockage ratio. The pulsation threshold for the normal operation of VSF remains to be determined through testing. Since the 1980s, flow measurement experts at home and abroad have conducted numerous experimental studies on the application of VSF in multiphase flows and pulsating flows, and technical reports issued by the International Organization for Standardization (ISO) also address this topic. 6. Cost-effectiveness Among various flowmeters, the VSF offers good cost-effectiveness, making it an economical choice for flow measurement. The basic performance of VSF is above average; its purchase cost is lower than that of quality-type, electromagnetic, and positive-displacement types, while its installation, operation, and maintenance costs are lower than those of throttle-type, positive-displacement, and turbine types. If it is used merely as a monitoring instrument in control systems, dry calibration can be employed to save on the costs associated with periodic calibration. VI. Precautions for Installation and Use 1. Precautions for Installation VSF is a flow meter that is sensitive to distortions in the pipe flow velocity distribution, rotational flows, and flow fluctuations; therefore, due attention must be paid to the installation conditions of the pipes on-site, and the requirements specified in the manufacturer’s instructions must be followed. 　　VSF can be installed indoors or outdoors. If it is installed in a well where flooding is possible, a saliva-type sensor should be used. Sensors can be installed on pipes horizontally, vertically, or at an angle. However, when measuring liquids and gases, care must be taken as to the installation position in order to avoid interference from bubbles and droplets, as shown in Figure 16. Figure 16 Installation of multiphase fluids (a) Installation of instruments for measuring gas flow with liquid content ； (b) Installation of flow meters for gaseous liquids VSF must ensure that there is a sufficient length of straight pipe sections upstream and downstream, as shown in Figure 17. The variations in data across different sources may be due to the fact that vortex generators have not yet been standardized, and it remains to be determined how much the differences in their shape and size affect the results ； Experimental research on the required straight pipe length for various flow restrictors is still insufficient; in other words, it is not yet mature. Compared to throttle-type differential pressure flowmeters, work in this area is still in its initial stages. Figure 17 Requirements for the length of straight sections upstream and downstream of a vortex street flowmeter (a) A 90° elbow ； (b) Concentric expansion ； (c) Concentric contraction fully open valve ； (d) Two 90o elbows on different planes ； (e) Control valve partially open ； (f) Two 90o elbows in the same plane. The connection between the sensor and the pipeline is shown in Figure 18. When connecting to pipes, pay attention to the following issues. Figure 18 Connection of sensor to pipeline 　　1) The inner diameters D of the upstream and downstream pipes are equal to the inner diameter D` of the sensor, with the difference satisfying the following condition: 0.95D ≤ D` ≤ 1.1D. 　　2) The piping should be concentric with the sensor, and the coaxiality should be less than 0.05D`. 　　3) The gasket must not protrude into the pipeline, and its inner diameter may be 1–2 mm larger than the inner diameter of the sensor. 　　4) To perform flow interruption checks and clean the sensor, a bypass pipe should be installed as shown in Figure 19. Figure 19 Schematic diagram of the bypass pipe. 5) Reducing the impact of vibrations on VSF should be regarded as a key issue in the on-site installation of VSF. First, when choosing the location for installing the sensor, try to avoid areas with vibration sources. Secondly, the use of elastic hoses for connection in small-diameter pipes can be considered. Thirdly, installing pipe supports is an effective vibration reduction method; one such pipe support method is shown in Figure 20. Figure 20 shows an example of pipeline support installation. A complete set of components, including straight sections at the front and back as well as flow regulators, is a measure to ensure high-precision measurements; particularly, installing these components in the manufacturing plant helps guarantee the quality of the installation. Figure 21 illustrates an example of such installation. Figure 21: Pipeline installation for high-precision measurements. For electrical installations, it is important to use shielded or low-noise cables to connect the sensors and converters, with the distance between them not exceeding the values specified in the user manual. During wiring, it should be kept away from high-power power cables, and preferably protected by a separate metal sleeve. The \"one-point grounding\" principle should be followed, with the grounding resistance to be less than 10Ω. Both the integral and separate types should be grounded on the sensor side, and the grounding point of the converter housing should be at the same potential as that of the sensor. 2. Precautions for Use 　　(1) Inspections before powering on and allowing flow after on-site installation 　　1) There should be no leaks at any flanges, valves, pressure measurement ports, temperature measurement ports, or connections on the main pipes and bypass pipes ； 　　2) Does the pipeline vibration meet the specifications outlined in the manual? ； 　　3) Is the sensor installed correctly? Are the electrical connections in all parts in good condition? 　　(2) Static debugging with power connected: When power is supplied but no flow is present, the converter should have no output; the instantaneous flow reading should be zero, and there should be no change in the cumulative flow. If this is not the case, first check whether interference signals are being introduced due to poor shielding or grounding of the signal lines, or severe vibrations in the pipes. If it is confirmed that the above reasons are not the cause, the potentiometer inside the converter can be adjusted to reduce the amplifier gain or increase the trigger level of the shaping circuit until the output becomes zero. 　　(3) Flow dynamic tuning: Close the bypass valve and open the upstream and downstream valves. Once the flow becomes stable, the converter outputs continuous pulses with uniform pulse widths; the flow rate indication remains stable without any fluctuations. By adjusting the valve opening, the output changes accordingly. Otherwise, the potentiometer should be carefully checked and adjusted until the instrument output triggers correctly without any missed pulses. If the instrument malfunctions, refer to Table 7 for solutions. 　　(4) Instrument coefficient correction The instrument coefficient of VSF is calibrated under laboratory conditions; when it is used in the field, the working conditions differ from those in the laboratory, so the instrument coefficient needs to be corrected. KVO = f/qv, where the value represents pulses per m3 (16). KV = EtEREDKVO (17). Here, KVO and KV represent the instrument coefficients under laboratory conditions and field operating conditions, respectively ； 　　 Et--temperature correction coefficient ； 　　 ER--Reynolds number correction factor ； 　　 ED--Diameter correction factor. 　　The remaining symbols are the same as before. 　　Temperature correction coefficient Et: Et=1/ (18). In this formula, αb and αx represent the linear expansion coefficients of the material constituting the sensor body and the vortex generator, respectively, in units of (°C•mm)-1 ； 　　 t, to--represent the operating temperature and calibration temperature, respectively, in °C. 　　Reynolds number correction factor ER: When using the expanded measurement range, and when the measured value exceeds the specified lower limit for Reynolds number, a Reynolds number correction must be applied to the instrument coefficients. Table 6 shows the data provided by a certain manufacturer (due to the lack of standardization in the vortex generators, there may be variations in the data across different switches). Table 6 Reynolds number correction factor ER Reynolds number range ER Reynolds number range ER 5×103＜Re＜6×103 6×103＜Re＜7×103 7×103＜Re＜8×103 8×103＜Re＜9×103 1.12 1.08 1.065 1.065 9×103＜Re＜104 104＜Re＜1.2×104 1.2×104＜Re＜1.5×104 1.5×104＜Re＜4×104 1.047 1.036 1.023 1.011 Pipe diameter correction factor ED The pipe diameter must fall within the specified range; in such cases, the actual deviation between the pipe diameter and the inner diameter of the sensor housing can be corrected using the pipe diameter correction factor ED. 　　　　　　　　　　　　　　ED=（DN/D）2 　　　　　　　　　　　　　　　　　　　　(Equation 19) Where DN is the actual inner diameter of the sensor body, in mm ； 　　D--Piping inner diameter, mm. ⑸ Fault symptoms, causes, and troubleshooting methods VSF has various detection methods, and there are significant differences among sensors and measurement circuits. However, common faults in these instruments share certain characteristics. Several instrument faults along with corresponding solutions are listed in Table 7. Table 7 Fault Handling
Fault Phenomenon | Possible Causes | Treatment Methods
------------------|------------------|--------------------
Output signal present when no flow occurs after power is applied | 1) Poor input shielding or grounding, leading to electromagnetic interference. 2) The instrument is located near high-voltage equipment or high-frequency pulse interference sources. 3) Severe vibrations in the pipeline. 4) Excessively high sensitivity of the converter. | 1) Improve shielding and grounding to eliminate electromagnetic interference. 2) Install the instrument away from interference sources; use isolation measures and improve power filtering. 3) Implement vibration damping measures, enhance signal filtering, and reduce the amplifier’s sensitivity. 4) Lower the sensitivity and increase the trigger level.
No output signal after power and flow are applied | 1) Power supply failure. 2) Broken input signal lines. 3) Fault in a stage of the amplifier. 4) Damaged detection elements. 5) No flow or extremely low flow rate. 6) Blocked pipeline or stuck sensor. | 1) Check the power supply and grounding. 2) Inspect the signal lines and terminals. 3) Check the operating point and examine the components. 4) Inspect the sensing elements and wires, as well as the valves; increase the flow rate or reduce the pipe diameter. 5) Clean the pipeline and the sensor.
Irregular and unstable output signal | 1) Strong electrical interference signals. 2) The sensor is dirty or damp, resulting in reduced sensitivity. 3) Excessively high sensor sensitivity. 4) Damaged sensor or poor wire connections. 5) Presence of two-phase flow or pulsating flow. 6) Effects of pipeline vibrations. 7) Unstable process flow. 8) The sensor is not installed concentrically or the gasket protrudes into the pipe. 9) Disturbances from upstream and downstream valves. 10) The pipeline is not fully filled with fluid. 11) Wrappings inside the pipe. 12) Cavitation phenomenon. | 1) Strengthen shielding and grounding. 2) Clean or replace the sensor; increase the amplifier gain. 3) Reduce the gain and increase the trigger level. 4) Inspect the sensor and wires. 5) Improve process flow management to eliminate two-phase flow or pulsating flow. 6) Implement vibration damping measures. 7) Adjust the installation position. 8) Check the installation condition and correct the inner diameter of the gasket. 9) Extend the straight pipe section or install a flow regulator. 10) Change the location and method of installing the flow sensor. 11) Remove any wrappings. 12) Reduce the flow velocity and increase the pressure inside the pipe.
Large measurement errors | 1) Insufficient length of the straight pipe section. 2) Zero drift in the analog conversion circuit or incorrect full-scale adjustment. 3) Excessive fluctuations in supply voltage. 4) The instrument has exceeded its calibration period. 5) Large difference between the sensor and the pipe inner diameter. 6) The sensor is not installed concentrically or the gasket protrudes into the pipe. 7) The sensor is dirty or damaged. 8) Presence of two-phase flow or pulsating flow. 9) Pipeline leakage. | 1) Extend the straight pipe section or install a flow regulator. 2) Calibrate the zero point and scale markings. 3) Check the power supply. 4) Have it calibrated promptly. 5) Check the pipe inner diameter and adjust the instrument coefficients. 6) Adjust the installation and repair the gasket. 7) Clean and replace the sensor. 8) Eliminate two-phase flow or pulsating flow. 9) Fix the leakage.
Leakage in the measurement tube | 1) Excessively high pressure inside the pipe. 2) Incorrect selection of nominal pressure. 3) Damaged seals. 4) Corroded sensor. | 1) Adjust the pipe pressure and change the installation position. 2) Use a sensor with a higher nominal pressure rating. 3) Replace the seals. 4) Implement anti-corrosion and protective measures.
Abnormal whistling sound from the sensor | 1) Excessively high flow velocity, causing intense vibrations. 2) Cavitation phenomenon. 3) Loose components inside the sensor. | 1) Adjust the flow rate or replace the instrument with one having a larger diameter. 2) Adjust the flow rate and increase the liquid flow pressure. 3) Tighten the loose components.

VII. Standards and Calibration Procedures
Although VSF is a relatively new type of flow meter among general-purpose flow meters, China formulated specialized standards for VSF back in the 1980s (ZBN 12008-89) as well as calibration procedures (JJG 620-89), indicating that it receives significant attention within the industry. The professional standards were revised in 1998 and changed to JB/T 9249-1999. The calibration regulations were merged with those for other velocity-type flowmeters to form a new set of regulations, JJG 198-94. However, since the new regulations cover a large variety of velocity-type flowmeters (as many as 8 types!) ), it becomes difficult to take into account some of the characteristics of VSF in the regulations; as a result, some of these regulations seem vague or entirely absent, making implementation somewhat challenging. JJG 620-89 still has some reference value. 　　Foreign countries also attach great importance to the development of VSF standards. In the early 1990s, the International Organization for Standardization (ISO) established a drafting working group to prepare an international standard for VSF. A committee draft was submitted in 1993 (ISO/CD 12764), and by 1997 it was published as a technical report (ISO/TR 12764:1997). For various reasons, ISO classifies certain documents that are not suitable to be adopted as international standards as technical reports – for example, those that do not have sufficient support, those for which the technology is still in an immature stage, or those intended solely as reference materials. It seems that VSF documents are not yet mature enough to be issued as international standards. Industrially advanced countries **such as the US and Japan have established VSF** standards (ASME/ANSI MFC-6M-1987 and JIS Z8766-1989).