Ultrasonic Doppler flowmeter measurement principle

1. Basic working principle

The measurement principle of ultrasonic Doppler flowmeter is based on the Doppler effect in physics. According to the acoustic Doppler effect, when there is relative motion between the sound source and the observer, the sound frequency felt by the observer will be different from the frequency emitted by the sound source. This frequency change caused by relative motion is proportional to the relative speed of the two objects.

In the ultrasonic Doppler flow measurement method, the ultrasonic transmitter is a fixed sound source, and the solid particles moving with the fluid play the role of "observer" with relative motion with the sound source. Of course, it only reflects the ultrasonic waves incident on the solid particles back to the receiving data. The frequency difference between the transmitted sound wave and the received sound wave is the Doppler frequency shift of the sound wave caused by the movement of the solid particles in the fluid. Since this frequency difference is proportional to the fluid flow velocity, the flow velocity can be obtained by measuring the frequency difference. Then the flow rate of the fluid can be obtained.

Therefore, a necessary condition for ultrasonic Doppler flow measurement is that the measured fluid medium should be a two-phase medium containing a certain number of solid particles or bubbles that can reflect sound waves. This working condition is actually one of its major advantages, that is, this flow measurement method is suitable for measuring two-phase flow, which is a problem that other flow meters are difficult to solve. Therefore, as a very promising two-phase flow measurement method and flow meter, the ultrasonic Doppler flow measurement method is increasingly being used.

2. The flow equation

assumes that the angle between the ultrasonic beam and the fluid velocity is, the ultrasonic propagation velocity is c, and the velocity of the suspended particles in the fluid is the same as the fluid velocity, both u. Now, taking the reflection of the ultrasonic beam on a solid particle as an example, the relationship between the acoustic Doppler frequency difference and the flow velocity is derived.

As shown in Figure 3-39, when the ultrasonic beam encounters a solid particle on the pipe axis, the particle moves along the axis at a speed of u. For the ultrasonic transmitter, the particle leaves at a speed of u cos a, so the ultrasonic frequency f2 received by the particle should be lower than the ultrasonic frequency f1 emitted, and the reduced value is

f2－f1＝－(ucosα/c)f1

That is, the frequency of the ultrasonic wave received by the particle is

f2＝f1－(ucosα/c)f1

Where f1 is the frequency of the transmitted ultrasound;
a is the angle between the ultrasound beam and the tube axis;
c is the speed of sound in the fluid.

The solid particles scatter the ultrasound beam to the receiver. Since it leaves the receiver at a speed of u cos a, the frequency f3 of the ultrasound received by the receiver is reduced again. Similar to the calculation of f2, f3 can be expressed as

f3＝f2－(ucosα/c)f2

Substituting the expression of f2 into the above formula, we can get:

f3＝f1（1-(ucosα/c))2
＝f1（1-2(ucosα/c)＋(u2cos2α/c2))

Since the speed of sound c is much greater than the fluid speed u, the square term in the above formula can be ignored, thus we can get:

f3＝f1（1－2(ucosα/c))

The difference between the ultrasonic frequency received by the receiver and the transmitted ultrasonic frequency, that is, the Doppler frequency shift Δf1, can be calculated by the following formula:

Δf＝f1－f3＝f1－f1（1－2(ucosα/c))＝f1(2ucosα/c)

From the above formula, the fluid velocity can be obtained as

u＝(c/2f1cosα)f

The volume flow rate qv can be written as:

qv＝uA＝(Ac/2f1cosα)Δf

In the formula, A is the flow cross-sectional area of ​​the measured pipeline.

From the above flow equation, it can be seen that when the flow meter, pipeline conditions and measured medium are determined, the Doppler frequency shift is proportional to the volume flow rate, and the fluid flow rate qv can be obtained by measuring the frequency shift Δff.

5. Several discussions on the flow equation

(1) The influence of fluid medium temperature on measurement

It can be seen from the flow equation that the flow measurement result is affected by the sound velocity c in the fluid. Generally speaking, the sound velocity in the fluid is related to the temperature and composition of the medium, and it is difficult to keep it as a constant. In order to avoid the measurement results being affected by changes in medium temperature and composition, ultrasonic Doppler flowmeters generally use an external sound wedge structure to allow the ultrasonic beam to pass through the sound wedge and the pipe wall before entering the fluid. Assume that the sound velocity in the sound wedge material is c1; the sound velocity in the fluid is c; the incident angle of the sound wave entering the fluid from the sound wedge is; the refraction angle in the fluid is ; the angle between the ultrasonic beam and the fluid flow velocity is a; as shown in Figure 1, according to the refraction theorem, there is:

Substituting into the flow relationship, we can get:

From this formula, it can be seen that after adopting the acoustic wedge structure, the flow rate and frequency shift relationship only contains the sound velocity c1 in the acoustic wedge material and has nothing to do with the sound velocity c in the fluid medium. The temperature change of the sound velocity c1 is a very small number compared to the temperature change of the sound velocity c in the fluid, and has nothing to do with the fluid composition. Therefore, using appropriate materials to make the acoustic wedge can greatly improve the accuracy of flow measurement. [page]

Figure 1 Acoustic wedge and refraction of sound waves

(2) Information Window and Average Doppler Frequency Shift

In order to effectively receive Doppler frequency shift signals, the transducer of the ultrasonic Doppler flowmeter usually adopts a transceiver integrated structure, as shown in Figure 3-41. As can be seen from the figure, the reflected signal received by the transducer can only be the reflected wave of the particles in the overlapping area of ​​the two directional beams of the transmitting chip and the receiving chip. This overlapping area is called the information window of the Doppler signal.

Figure 2 Doppler information window

The signal received by the flow meter receiving transducer is the superposition of the reflected waves of all the suspended particles in the information window, that is, the Doppler frequency shift in the information window is the superposition average value. The average Doppler frequency shift Δf can be expressed as:

Where Δf is the average value of the Doppler frequency shift of all reflected particles in the information window;
ΣNi is the number of particles that produce the Doppler frequency shift Δfi;
Δfi is the Doppler frequency shift produced by any suspended particle.

From the above discussion, it can be seen that the Doppler frequency shift signal measured by the flowmeter only reflects the fluid velocity in the information window area, so the information window should be located in the area close to the average flow velocity in the pipe so that its measured value can reflect

the average flow velocity of the fluid in the pipe. However, the position of the average flow velocity area in the pipe is a function related to the Reynolds number. When the Reynolds number Re of the flow in the pipe changes, the position of the average flow velocity area will also change. Once the flowmeter is installed, the position of its Doppler information window is fixed. In order to make the measured Doppler frequency shift signal Δf correctly reflect the flow value under different Reynolds numbers Re, the velocity correction coefficient K is introduced into the flow calculation formula. The velocity correction coefficient K is a function of the Reynolds number Re and the position of the information window, and it is used to correct the measurement error caused by the above reasons. Therefore, the actual flow calculation formula of the ultrasonic Doppler flowmeter can be written as:

qv＝

In the formula, the symbols have the same meaning as before