Doppler Flowmeter

In this type of flowmeter an ultrasonic wave beam with a certain frequency is sent through the pipe by the first sensor, some of this ultrasonic energy returns to the sensor from the particles inside the fluid with a frequency different from the original frequency. The difference between the initial signal and the return signal is proportional to the fluid velocity.

As already said, a sensor sends ultrasonic waves with a frequency between approximately 1 to 5 MHz to the moving particles in the fluid. Ultrasonic waves hit moving particles at \(V_{p}\) speed. The wave at frequency of \(f_{1}\) will have a wavelength equal to \(\lambda _{1}\).

\(\lambda _{1}=c/f_{1}\)

Due to the moving speed \(V_{p}\), the moving particles move away with the wavelength of \(\lambda _{1}\).

\(\lambda _{1}=(c-v_{p}\times cos \alpha )/f_{1}\)

In the next step, the returning wave frequency from inside the fluid is sensed by the transmitter sensor inside the fluid, since the return particles move further away with time, the wavelength changes according to the following formula:

For \(v_{p\ll c}\) we can say:

\(f_{2}=\frac{f_{1}\times c}{c-2\times v_{p}\times cos \alpha }\)

As a result, the frequency difference between the forward and return signal can be a linear measurement of the particle movement rate, or in other words, the fluid movement speed.

\(f_{2}-f_{1}=\Delta f=\frac{2\times v_{p}\times f_{1}\times cos \alpha }{c}\)

\(f_{2}\): The frequency of the signal received by the receiver sensor (in Hz)

\(f_{1}\): Frequency of the signal sent by the transmitter sensor (in Hertz)

\(\Delta f\): The difference between the transmitted and received frequencies (in Hz)

\(v_{p}\): Fluid movement speed (in meters per second)

\(\alpha \): The angle of the forward wave (in degrees)