Application of Doppler Principle in Ultrasonic Flow Measurement

The Doppler effect is a phenomenon first discovered by Australian physicist and mathematician Doppler in 1842 from a moving sound source:

Let's first understand the Doppler effect. In daily life, we all have this experience: when a train whistles towards an observer, he will find that the tone of the train whistle changes from low to high; when the train moves away, the tone changes from high to low. Why does this happen? This is because the pitch is determined by the different frequencies of sound wave vibration. If the frequency is high, the tone sounds high; otherwise, the tone sounds low. This phenomenon is called the Doppler effect.

The Doppler effect refers to the change in the wavelength of radiation from an object due to the relative motion between the light source and the observer. In front of the moving wave source, the wave is compressed, the wavelength becomes shorter, and the frequency becomes higher. Behind the moving wave source, the opposite effect occurs, the wavelength becomes longer, and the frequency becomes lower. The higher the speed of the wave source, the greater the effect. According to the degree of red/blue shift of the light wave, the speed of the wave source moving in the direction of observation can be calculated. The displacement of the star's spectral line shows the speed of the star moving in the direction of observation. This phenomenon is called the Doppler effect. The

Doppler effect is not only applicable to sound waves, it also applies to all types of waves, including light waves and electromagnetic waves. Scientist Edwin Hubble used the Doppler effect to conclude that the universe is expanding. He found that the frequency of light from the distant Milky Way was getting higher, that is, moving toward the red end of the spectrum. This is the red Doppler shift, or redshift. If the Milky Way is moving toward him, the light becomes blueshifted.

1. Doppler effect of sound waves

In daily life, we all have this experience: when a train whistle passes by an observer, he will find that the tone of the train whistle changes from high to low. Why does this phenomenon occur? This is because the pitch of a sound is determined by the different frequencies of the sound wave vibrations. If the frequency is high, the pitch sounds high; otherwise, the pitch sounds low. This phenomenon is called the Doppler effect, named after its discoverer Christian Doppler (1803-1853), an Austrian physicist and mathematician. He first discovered this effect in 1842. In order to understand this phenomenon, it is necessary to examine the propagation law of the sound waves emitted by the whistle when the train approaches at a constant speed. The result is that the wavelength of the sound wave is shortened, as if the wave is compressed. Therefore, the number of waves propagated within a certain time interval increases, which is why the observer feels that the pitch has become higher; on the contrary, when the train is moving away, the wavelength of the sound wave becomes larger, as if the wave is stretched. Therefore, the sound sounds low. Quantitative analysis yields f1=（u+v0）/（u-vs）f , where vs is the speed of the wave source relative to the medium, v0 is the speed of the observer relative to the medium, f represents the natural frequency of the wave source, and u represents the propagation speed of the wave in the stationary medium. When the observer moves toward the wave source, v0 takes a positive sign; when the observer moves away from the wave source (i.e., along the wave source), v0 takes a negative sign. When the wave source moves toward the observer, vs takes a negative sign; when the wave source moves away from the observer, vs takes a positive sign. It is easy to see from the above formula that when the observer and the sound source are close to each other, f1＞f; when the observer and the sound source are far away from each other, f1＜f. [page]

2. Application of Doppler effect in ultrasonic flow measurement

Assume that the angle between the ultrasonic beam and the velocity of the fluid is θ, the ultrasonic propagation velocity is c, and the velocity of the suspended particles in the fluid is the same as the fluid velocity, both of which are u. Now, taking the reflection of the ultrasonic beam on a solid particle as an example, the relationship between the Doppler frequency difference of the sound wave and the velocity is derived. As shown in the figure, when the ultrasonic beam encounters a solid particle on the axis of the tube, the particle moves along the axis at a speed of u. For the ultrasonic transmitter, the particle leaves at a speed of u cosα, 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＝-u * cosα/c * f1

, that is, the ultrasonic frequency received by the particle is

f2＝f1-u * cosα/c * f1,

where f1 is the frequency of the emitted ultrasonic wave;
a is the angle between the ultrasonic beam and the axis of the tube;
c is the speed of sound in the fluid.

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

f3 = f2 - u * cosα/c * f2.

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

From the above flow equation, we can know 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 △f.

3. Doppler effect of light waves (including electromagnetic waves)

This effect will also occur in light with wave properties, and it is also called the Doppler-Fizeau effect. Because French physicist Fizeau (1819-1896) independently explained the wavelength shift from stars in 1848 and pointed out the method of using this effect to measure the relative speed of stars. The difference between light waves and sound waves is that the change in the frequency of light waves makes people feel that it is a change in color. If the star moves away from us, the spectrum of light moves toward the red light direction, which is called redshift; if the star moves toward us, the spectrum of light moves toward the purple light direction, which is called blueshift.

Wide application of Doppler effect

1. Radar speedometer

The radar speedometer that checks the speed of motor vehicles also uses this Doppler effect. Traffic police transmit electromagnetic waves of known frequency, usually infrared, to the moving vehicles, and measure the frequency of the reflected waves at the same time. The speed of the vehicle can be known according to the change of the reflected wave frequency. Police cars equipped with Doppler speedometers are sometimes parked beside the road. While measuring the speed, they take pictures of the vehicle license plate and automatically print the measured speed on the photos.

2. Application of Doppler effect in medicine

In clinical practice, the application of Doppler effect is also increasing. In recent years, ultrasonic pulse Doppler detectors have been rapidly developed. When the sound source or reflection interface moves, such as when red blood cells flow through the heart and large blood vessels, the frequency of sound scattered from its surface changes. The direction and speed of blood flow can be known from this frequency shift. For example, when the red blood cells face the probe, according to the Doppler principle, the reflected sound frequency increases. When the red blood cells leave the probe, the reflected sound frequency decreases.

3. Doppler phenomenon in cosmological research

In the 1920s, American astronomer Slifer first discovered the red shift of the spectrum when studying the spectrum emitted by the distant spiral nebula, and realized that the spiral nebula was moving away from the earth rapidly. In 1929, Hubble summarized the famous Hubble's law based on the redshift of light spectrum: the velocity v of a galaxy is proportional to its distance r from the earth, that is, v=Hr, where H is the Hubble constant. Based on Hubble's law and the subsequent determination of the redshift of more celestial bodies, people believe that the universe has been expanding for a long time and the density of matter has been decreasing. It can be inferred that the structure of the universe did not exist before a certain moment and it can only be the product of evolution. Therefore, in 1948, Gamow and his colleagues proposed the Big Bang model of the universe. Since the 1960s, the Big Bang model of the universe has gradually been widely accepted, so that it has been called the "standard model" of the universe by astronomers.

The Doppler-Fizeau effect makes it possible for people to study the motion of celestial bodies at any distance from the earth, which only requires analyzing the spectrum of the received light. In 1868, British astronomer W. Huggins used this method to measure the apparent velocity of Sirius (that is, the speed at which an object moves away from us) and obtained a velocity value of 46 km/s.

4. Doppler effect in mobile communication

In mobile communication, when the mobile station moves toward the base station, the frequency becomes higher, and when it moves away from the base station, the frequency becomes lower, so we must fully consider the "Doppler effect" in mobile communication. Of course, due to the limitation of our movement speed in daily life, it is impossible to bring about a very large frequency shift, but in satellite mobile communication, when the aircraft moves toward the satellite, the frequency becomes higher, and when it moves away from the satellite, the frequency becomes lower, and because the speed of the aircraft is very fast, so we must fully consider the "Doppler effect" in satellite mobile communication. In order to avoid this effect causing problems in our communication, we have to make various technical considerations. It also increases the complexity of mobile communication.