Relationship between length and accuracy of straight pipe section of turbine flowmeter

Turbine flowmeter is the main type of velocity flowmeter. When the fluid to be measured flows through the turbine flowmeter sensor, under the action of the fluid, the impeller is forced to rotate, and its rotational speed is proportional to the average flow velocity of the pipeline. At the same time, the blade periodicity The magnetic flux generated by the electromagnet is cut and the magnetic flux of the coil is changed. According to the principle of electromagnetic induction, a pulsating potential signal, that is, an electric pulse signal, is generated in the coil, and the frequency of the electric pulsation signal is proportional to the flow rate of the fluid to be measured. The main external factor affecting the accuracy of the turbine flowmeter is the flow state of the fluid. The turbine flowmeter characteristic curve should maintain a good linear relationship, and the fluid flowing through the flowmeter should be a fully developed flow pattern.
1. The relationship between the rotation coefficient and the length of the downstream straight pipe segment The rotational strength of the swirling flow is expressed by the rotation coefficient, which is defined as the ratio of the angular momentum flux to the axial momentum flux:

Where: ω -- circumferential speed;
u -- axial velocity;
R -- the radius of the pipe;
A -- the cross-sectional area through which the fluid flows;
ρ -- density.
For the swirling flow in a circular tube, the angle of rotation at r = 0.95R is the largest, ie:

Using a number of iterative methods, it is programmable to calculate the Sw value that satisfies a certain precision at a certain value (X is a multiple of the diameter D of the tube):

The constants b and c are related to fluid properties, Reynolds number and flow rate and need to be determined experimentally. For incompressible fluids, b=0.030~0.085, c=0.10~0.50. In general, the larger the flow rate, the greater the attenuation of the swirling flow. It can be seen from equation (3) that the longer the straight pipe segment after the swirling flow occurs, the weaker the strength of the swirling flow, and the smaller the influence on the accuracy of the turbine flowmeter. .
2. Experimental design and results analysis In order to obtain the ideal rotating fluid during the experiment, a generator simulating a plurality of intensity rotating streams was used in the experiment, and the rotating flow generator was installed at the starting point of the upstream flow of the flow meter.
The experiment uses the weighing method to record the mass pulse number N, N multiplied by the mass pulse constant (0.08333), which is the mass value (kg), while recording the time and the number of pulses of the turbine transmitter, at each flow rate. The point is repeated three times, three sets of data are recorded, and a total of five flow points are selected to cover the measurement range of the turbine flow meter. The flow rate Q=0.08333N/t, the meter factor is:

The meter coefficient K is linear with the number of revolutions Sw. The accuracy of the meter is:

Where α and d are both undetermined coefficients.
According to the experimental results of multiple sets of pulse numbers and flow data, the instrument accuracy δ value can be calculated. The values ​​of α and d can be determined by performing a least squares regression on the δ-X equation and the δ and X data. Generally, for incompressible fluids, α=1.15~2.20, d=0.016~0.11.
3. Preliminary prediction of straight pipe length and flowmeter accuracy In engineering design, α and d values ​​are determined based on fluid properties, flow rate and Reynolds number. In this way, according to the formula (5), the length of the straight pipe section can be predicted initially according to different flowmeter accuracy requirements, or the length of the straight pipe section can be determined, and the accuracy of the flowmeter is predicted.
When δ = 0.2%, the length of the straight pipe required at different flow rates is shown in Table 1.
Table 1 Required length of straight pipe at different flow rates

When X=30, the accuracy of the meter under different flow rates is shown in Table 2.
Table 2 Predicted instrument accuracy under different flow rates

The accuracy of the flowmeter and the prediction of the straight pipe section provide a theoretical reference for selecting the straight pipe section of the appropriate length for the turbine flowmeter with different accuracy requirements.
4. Conclusion (1) The number of rotations Sw is exponential with X, that is, as the downstream distance X increases, the intensity of the swirling flow decays exponentially. The index coefficients c and α are related to the properties of the medium, the Reynolds number and other parameters.
(2) For any rotating flow source, as the downstream distance increases, the rotational flow intensity decays faster in the large flow region, while in the small flow region, the rotational flow intensity decays more slowly, so the flow to the small flow In the design of the pipeline, it is necessary to lengthen the straight pipe section to reduce the influence of the swirling flow on the accuracy of the flowmeter.
(3) Regardless of the direction of the rotating flow, the closer the flow meter is to the rotating flow source, the worse the accuracy δ of the flow meter, and the accuracy of the flow meter can be predicted initially according to equation (5).