Frequently Asked Questions on ultrasonic Doppler velocimetry and applications on UDV, UDVF techniques

The working principle of the DOP ultrasonic velocimeter is to detect and process many ultrasonic echoes issue from pulses reflected by microparticles contained in a flowing liquid. A single transducer emits the ultrasonic pulses and receives the echoes. By sampling the incoming echoes at the same time relative to the emission of the pulses, the variation of the positions of scatters are measured and therefore their velocities. The measurement of the time lapse between the emission and the reception of the pulse gives the position of the particles.
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The measurement of the velocity is based on the estimation of the mean phase shift of successive echoes coming from a defined depth. The algorithm used is based on the random statistical nature of each echo. The algorithm assumes that the statistical properties of all collected echoes used in the computation of the mean phase shift are stationary. This allows to transform temporal average into spatial average and to consider all processes stationary. As the inverse Fourier transform of the probability density function of a stationary process is equal to the auto-correlation function, the algorithm computes the auto-correlation of the Doppler echoes. The Doppler frequency (Fd) is then computed, and finally the velocity is extracted from Doppler equation:

The Doppler equation

where (Fe) is the emitted ultrasonic frequency and (C) is the sound speed in the liquid.

Note that the above equation is valid for bi-directional flows having an identical range for the positive and negative velocities. Our velocimeter allows to select a different range for the positive and negative velocities. This allows to measure higher velocity than the above defined value, up to two times, without loss of information concerning the direction of the flow.

The velocity component measured by the velocimeter is always the component in the direction of the ultrasonic beam. When the direction of the real velocity is known, the velocimeter can automatically compute the real velocity value by using the value of the Doppler angle.

Aliasing is a phenomena that appears when an analog signal is sampled at a frequency which is lower than the half of its maximum frequency. When such a situation appears all the frequencies above the half of the sampling frequency, known as the Nyquist frequency, are back folded in the low frequency region. This phenomena is called aliasing. The figure below illustrates the relationship between the real frequency and the measured frequency.

To avoid aliasing the analog signal should be filtered before sampling in order to remove all the frequencies above the Nyquist limit.

In pulsed Doppler ultrasound velocimetry the sampling frequency is equal to the pulsed repetition frequency (PRF). The pulsed nature of the ultrasonic emission implies that only samples are available. This means that the aliasing phenomena can not be removed, or filtered and may therefore appears. An easy way to check the presence of aliasing is to examine the evolution of the measured Doppler frequency when the pulsed repetition frequency is changed.

In ultrasonic Doppler velocimetry, the shape and lateral sizes of the sampling volumes (measured perpendicularly to the ultrasonic beam axis) are defined by the geometry of the ultrasonic beam. The longitudinal size of the sampling volumes is defined by the burst length and/or the bandwidth of the electronic receiving unit. The DOP2000 model 2125 has 6 different bandwidth values. This defines a longitudinal dimension of the sampling volume from about 0.64 mm to 3.19mm in water.

The DOP2000 defines the resolution as the distance between the center of adjacent sampling volumes. Its very fast processing capabilities allow a minimum distance between adjacent gates of 0.18mm (250ns). Distance between gates can be adjusted by step of 0.18mm.

The main differences between Laser Doppler velocimetry and ultrasonic Doppler velocimetry can be summarized as followed:

Ultrasonic Doppler velocimetry is a safe technique when applied correctly. The mean ultrasonic power is low, in the order of few milliwatts. The maximum instantaneous power, which is in the order of tens of watts during the emission of the burst, is most of the time not enough to generate cavitation. The only noticed effect is a small local increase of the temperature of the medium under investigation.

Data profiles issue from up to 10 different transducers can be measured sequentially. The user can define the functioning parameters (emitting frequency, PRF, amplification, number of gates,...) for each transducer. The instrument switches automatically from one transducer to the other after the acquisition of a user's defined number of profiles.

Signal Processing's Velocimeters can measure and record not only velocity profiles but also the echoes profiles, the Doppler energy, the flow rate, the power spectrum and of course can record raw data (I and Q signals) for further analysis.

Unfortunately not. There are two main reasons for this. The attenuation of ultrasonic waves is very strong at the frequencies used and also particles of compatible dimensions that can follow the gas flow are seldom found.

Ultrasonic Doppler Velocimetry is almost the unique technique that is capable to measure in real time a velocity profile in liquids containing a great number of particles, liquid mud. For instance, successful measurements can be obtained in concentrations in the order of 30% for mud and more then 50% in blood.