1 Introduction
Vortex flowmeter is a vibrating flowmeter that uses the principle of fluid vibration to measure flow. It is widely used in the field of metrology and industrial process control. However, because of its short history, lack of theoretical foundation and practical experience, there are still many tasks that need to be explored and enriched [1~2].
The basic flow equation of vortex flowmeter often quotes Karman vortex street theory, and then the frequency of vortex separation of vortex street flowmeter is only proportional to the volumetric flow under the working state of the fluid, but to the temperature, pressure and density of the measured fluid. The characteristics of viscosity and composition change are insensitive [3]. In practice, it is unclear how much additional error will be brought to the vortex flowmeter measurement in the end. Sophie Goujon-Durand studied the effect of fluid viscosity on the linearity of vortex flowmeters, and plotted the calibration curves for the vortex linearity of different viscosities [4]. Reference [5] mentions that the test of the vortex flowmeter does not change with the density of the medium through tests at different working pressures of the gas, but no specific test data is given. In this paper, the flow rate characteristics of vortex flowmeters were compared under different media densities using test methods using positive pressure sonic nozzle gas flow standard devices. The curves and trends of instrument coefficients and flow rate lower limits with density were obtained, and the test results were obtained. Analyze and explain.
2 Vortex Flowmeter Working Principle
As shown in Fig. 1, a trapezoidal column-shaped vortex generator is vertically inserted into the pipe. With the fluid flow, when the Reynolds number of the pipe reaches a certain value, a regular vortex is alternately generated on both sides of the vortex generator. For Karman Vortex Street.
Let the vortex frequency be f, the width of the vortex shedding surface be d, and the body diameter be D. According to the Karman vortex theory, we can see that:
Where: U1 is the average flow velocity on both sides of the vortex generator; U is the average flow velocity of the measured medium flow; Sr is the Strouhal number, and the vortex generator of a certain shape is constant within a certain Reynolds number range; m It is the ratio of the arch area on both sides of the vortex generator to the cross-sectional area of ​​the pipe.
The fluid is also subjected to a force in the vertical direction while generating vortices. According to Thomson's law and Kuta-Jukowski's theorem of lift [5-6], the lift is applied to the per unit length of the vortex generator. For FL, there are:
Where: cL is the lift coefficient; Ï is the fluid density.
Because the frequency of the rising force acting alternately on the generating body is the frequency of the vortex shedding, the f-frequency of the FL can be detected by the piezoelectric probe, and then the volumetric flow rate qv can be obtained from equation (1):
In the formula: K is the instrument coefficient of vortex flowmeter.
From equations (3) and (4), it can be seen that for the determined D and d, the volume flow qv of the fluid is proportional to the vortex frequency f, and f is only related to the geometrical parameters of the flow velocity U and the vortex generator, and the The fluid properties and composition are irrelevant, so it can be concluded that vortex flowmeters are not affected by fluid temperature, pressure, density, viscosity, and compositional factors. This article studies the effects of increased working pressure and changes in medium density on vortex flowmeter measurements under complex field conditions.
3 test device
3.1 Sonic nozzle working principle
The Venturi nozzle is a flow path with a gradually decreasing pore size. The smallest part of the orifice is called the throat of the nozzle, and the throat is followed by a flow path with an enlarged pore diameter. As gas passes through the nozzle, the gas flow rate at the throat will increase as the throttle pressure ratio decreases. When the throttle pressure ratio is smaller than a certain value, the throat flow rate reaches the maximum flow velocity - the speed of sound. If the throttling pressure ratio is further reduced at this time, the flow rate (flow rate) will keep the sound speed unchanged and will not be affected by the downstream pressure, but only related to the stagnation pressure and temperature at the inlet of the nozzle. At this time, the nozzle is called the speed of sound. Nozzle, flow equation [5]:
Where: qm is the mass flow through the nozzle; A* is the throat area of ​​the sonic nozzle; C is the outflow coefficient; C* is the critical flow function; P0 is the stagnation absolute pressure at the inlet of the sonic nozzle; T0 is the inlet of the sonic nozzle Absolute absolute temperature; R is a general gas constant; M is a mass of gas in kilo molar.
From equation (5), it can be seen that a nozzle with a throat diameter has only a critical flow rate. When the stagnation pressure and the stagnation temperature at the nozzle inlet are constant, the flow rate through the nozzle also does not change. It is this characteristic that causes the speed of sound. The nozzle is widely used as a standard meter in standard gas flow devices.
3.2 Sonic nozzle gas flow standard device
The sonic nozzle gas flow standard device is divided into positive pressure method and negative pressure method according to different gas source pressure. The positive pressure device changes the flow of gas through the nozzle by changing the stagnation pressure at the nozzle inlet, achieving a wider flow range with fewer nozzles, and a higher and variable air supply pressure allows it to operate at positive pressure ( In the state of absolute pressure 0.2MPa or more), the gas density is higher than that of the normal pressure device, and the test capability at different density (pressure) points can be used to study the influence of gas density change on the performance of the flow meter.
This test device uses a positive pressure method, the working flow range is 2.5 ~ 666m3/h working conditions, the working pressure range is 0.1 ~ 0.5MPa gauge pressure, the device structure shown in Figure 2. The working principle is: First, the air in the atmosphere is sent to the pipeline by the air compressor, and the water vapor is removed by the cold dryer to enter the high-pressure gas storage tank. After the pressure of the storage tank rises to a certain value, the regulator valve is adjusted. The downstream pipeline pressure is stabilized at a suitable value. After the regulator valve is adjusted, the high-pressure gas entering the test pipeline flows through the vortex flowmeter, the stagnant container, the sonic nozzle group, the air exchange pipe, and the silencer, and finally reaches the atmosphere. Among them, the sonic nozzle group is composed of 11 different sonic velocity nozzles connected in parallel downstream of the stagnation vessel. By controlling the switching valve at the downstream of the sonic nozzle, the sonic nozzle combination can be arbitrarily selected so as to change the flow of the measured instrument. purpose. By collecting the temperature transmitter T1 and the pressure transmitter P1 signal on the stagnation vessel, the mass flow through the sonic nozzle can be obtained by substituting the formula (5), that is, the mass flow through the vortex flowmeter. The temperature T and pressure P at the vortex flowmeter can calculate the air density under the working state, and then get the actual volume flow rate. Then according to the detection of the output pulse of the vortex flowmeter in the same time interval, the vortex flowmeter can be finally realized. Research on flow coefficient characteristics such as meter coefficient.
All of the above work processes are controlled and processed in real time by the computer system. After analysis and testing, the test device accuracy is 0.5.
4 Flow Characteristics Test Study
4.1 Test plan
In the positive pressure sonic nozzle gas flow standard device, by adjusting the stagnation pressure to change the density of the medium, a large number of tests were performed on the 50mm vortex flowmeter in four different media densities. Through data analysis, the impact of medium density changes on the flow characteristics of vortex flowmeters is examined in two ways: 1) Investigation of vortex flowmeter meter coefficients affected by density changes, verification of Karman vortex street theory, and 2) Investigation of vortex flowmeter measurements The change trend of the lower limit with density changes is explained from a theoretical perspective.
4.2 Test data and analysis
In order to ensure that the sonic nozzle achieves the speed of sound in the throat, combined with the regulating range of the regulating valve, the test is performed at a gauge pressure of 0.13 MPa, 0.2 MPa, 0.3 MPa, and 0.4 MPa, and the corresponding air medium density is 2.774 kg/m3, respectively. 3.619 kg/m3, 4.78 kg/m3, 5.987 kg/m3. Due to the limited capacity of the high-pressure gas storage tank (12m3), in order to avoid rapid pressure drop in the pipeline when the flow is large, the maximum flow point for the test is selected at 176m3/h (corresponding flow rate is 25m/s); the minimum flow point is the lower limit of flow. One of the flow characteristics to be studied in this paper is determined by the test results. The test shall be conducted in strict accordance with the national metrological verification procedures [7]. The pressure variation shall not exceed 1 KPa in the entire flow range at each medium density. During each verification of each flow point, the compressed air temperature shall not exceed 0.5°C.
According to the data obtained from the experiment, the curve of the vortex meter coefficient with the flow rate at different air densities as shown in Fig. 3 can be plotted, and the flow characteristics of the vortex flowmeter can be found in Table 1.
Among them, vortex flowmeter meter coefficient 
, linearity EL, uncertainty σr formula [7]:
Where: (Ki) max, (Ki) min is the maximum and minimum value of each flow point coefficient Ki; Kij is the jth meter coefficient value of the i th flow point; Ki is the average meter factor of the i th flow point .
From Figure 3 and Table 1, the following conclusions can be summarized:
(1) The quotient coefficient of the vortex at various points has a good similarity with the flow rate curve K-qv. The K value fluctuates greatly at small flow rates and reaches a peak at the flow point of 22m3/h, after which the K value tends to be constant and the stability is better with the increase of the density, because of the Straw that affects the vortex meter factor. The Hal number Sr is a function of the Reynolds number Re, and Re is defined as:
Where μ is the dynamic viscosity. When the flow velocity U is the same, Re increases correspondingly when Ï increases. According to the Sr-Re curve [5], Sr will tend to be flatter, so the stability of the K value increases with increasing the density of the medium.
(2) With the increase of the density of the medium, the vortex flowmeter meter coefficient changes very little, and the maximum relative error is:
It is verified that the vortex flowmeter obtained by Karman vortex street theory is not affected by the change of fluid density and is very suitable for gas flow measurement.
(3) As the density of the medium increases, the uncertainty and linearity of the vortex flowmeter do not change. The accuracy of the vortex flowmeter is 1.5, and it is not affected by changes in fluid density.
(4) As the density of the medium increases, the lower limit of the flow of the vortex flowmeter decreases and the range increases. This is because, according to Formula (2), the lift FL acting on the vortex generator is proportional to the density Ï of the fluid to be measured and the square of the flow velocity U. When the compressed air density Ï rises, under the condition that the detection sensitivity of the vortex flowmeter (ie lift FL) is not changed, the measurement flow rate U will be reduced correspondingly, and the lower limit qvmin of the vortex flowmeter will be reduced accordingly. The above process can be expressed as the following:
Where α is a constant, the visible flow lower limit qvmin is proportional to the reciprocal of the square root of the air density in the corresponding state. This is the theoretical analysis of the lower flow limit of the vortex flowmeter decreasing with increasing medium density. Combine the actual data in Table 1 and plot the plot 4q2/1min−Ïvmin-curve:
As can be seen from Figure 4, the experimental results 
The curve basically conforms to the linear relationship described in equation (10), except that the error at the point where the air density is 4.682 kg/m3 is greater, due to the discontinuity in the regulation of the flow point by the sonic nozzle standard device (at the flow point 14.8 There is no intermediate flow point between m3/h and 9.9m3/h).
5 Conclusion
(1) With the increase of the density of the medium, the vortex flowmeter has a very small coefficient of variation, and the maximum relative error is only 0.405%. It is verified that the vortex flowmeter is hardly affected by the variation of fluid density.
(2) With the increase of the density of the medium, the lower limit of the flow of the vortex flowmeter is reduced and the range is extended. This phenomenon is theoretically analyzed based on the lift equation acting on the vortex generating body.
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