Principles of Operation:
2. Acoustic Doppler Velocimeters

Contents

1. How velocimeters work

2. Velocimeter Accuracy

3. Why Not Make a 16MHz Velocimeter? 

1. How velocimeters work

The Acoustic Doppler Velocimeter is a versatile, high-precision instrument that measures all three flow velocity components. The measurements are insensitive to water quality which allows for a wide range of applications. Velocimeters are used in laboratories, wave basins, rivers, estuaries and oceanographic research.

Velocimeters use acoustic sensing techniques (Figure 1) to measure flow in a remote sampling volume. The measured flow is practically undisturbed by the presence of the probe. Data are available at an output rate of 25 Hz. The 3-D velocity range is 2.5 m/s, and the velocity output has no zero-offset.

Figure 1. The acoustic sensor has one transmit transducer and three receive transducers. The sampling volume is located away from the sensor to provide undisturbed measurements. Doppler velocity is derived from signals scattered by small particles. In natural bodies of water (streams, lakes, rivers, oceans, etc.) the natural occurrence of particles is sufficient for proper operation. In model tanks with running water (flumes, open channels, closed pipes, etc.) microscopic bubbles in the water column tend to act as natural seeding. In clean, quiescent water (ship models, tow tanks, and some wave flumes), seeding materials must be added to concentrations of approximately f10 mg/l. Non-soluble seeding material with sensitivity close to 1 and mean diameter of 8-10 m is available from Nortek.

Velocimeter Hardware

Figure 2. Parts of a velocimeter probe.
From left to right: cable, conditioning module, measuring probe.

A Velocimeter consists of three modules: the measuring probe, the conditioning module with cable (Figure 2) and the processing module. The waterproof conditioning module, which contains low-noise electronics, is rugged and can be deployed to 30 m in the standard configuration.

The acoustic sensor consists of one transmit transducer and three receive transducers (Figure 1). The receive transducers are mounted on short arms around the transmit transducer at 120° azimuth intervals. The acoustic beams are oriented so that the receive beams intercept the transmit beam at a point located at 50 mm or 100 mm below the sensor. The interception of these four beams, together with the width of the transmit pulse, define the sampling volume. This volume is 3-9 mm long and approximately 6 mm in diameter. All three receivers must be submerged to ensure correct 3-D velocity measurements (except for the 2D/3D probe).

Velocimeter calibration factors are determined by the speed of sound and by the angles between the transmit and receive transducers. To ensure that the correct speed of sound is used, the water temperature and salinity must be entered in the data acquisition software. The calibration angles are measured at the factory and need only be changed when a new probe is installed. Maintenance calibration is not required unless the probe is physically damaged.

The processing module performs the digital signal processing required to measure Doppler shifts. In the Laboratory Velocimeter, this computationally intensive task is implemented on a PC-board that fits any IBM-compatible computer (minimum 386/387) with full-sized slots. Several Velocimeters can be controlled by one computer, but each instrument requires a separate processing module.

In the Field Velocimeter, the processing module is a low power, stand-alone unit with its own microcomputer. This module is intended for use in underwater or power-limited applications where a full-sized computer is impractical. This unit can be interfaced to a user-supplied data acquisition system via analog outputs or to a notebook computer through the RS232 port. Nortek also supplies Windows 95/98/NT data acquisition software that can collect data from many Field Velocimeters at once.

The standard data acquisition software supplied with the Velocimeter provides real-time display of data in graphical and tabular form. The data are recorded to disk in highly compressed binary files which can be easily converted to ASCII format with the data conversion programs supplied with the system.

The Velocimeter has input/output control lines that permit synchronization with other laboratory instrumentation. Analog outputs proportional to the three velocity components are also provided for easy interface to existing data acquisition systems.

For applications which require simultaneous operation of several Velocimeters from the same computer, Nortek offers a rugged data Acquisition Computer that can operate up to eight instruments. 

2. Velocimeter Accuracy

2a) Accuracy   

The word accuracy is often used loosely to cover some combinations of bias and short-term uncertainty. Bias and short-term uncertainty are different, and they have different ramifications for the results of your data collection. Here is the difference:

• Bias is error that remains after taking long-term averages.
• Short-term uncertainty is the random error of individual measurements, which can be removed by averaging.

These errors have different sources, different consequences for your results, and are specified separately. Velocity spikes are distinctive and obvious as a source of error. The following will address each of these errors separately.

2b) Bias   

Velocimeters long-term accuracy depends on the geometry of its probes and the stability of its internal oscillators. Over most of the velocity range, bias can be measured in terms of an offset and a scale-factor error. Offsets would appear as a non-zero velocity in still water. If probe geometry were entirely fixed and repeatable, then we could determine the velocity scale factor based entirely on dimensions, frequencies and our physical model. In practice, small variations in probes require that probes be individually calibrated in the factory.

A factory-calibrated velocimeter should have a scale-factor bias that is less than 1% of the measured velocity. A velocimeter will retain this accuracy as long as its probe remains unbent. Thus far we have found the offset to be too small to measure (which is what we expect based on theory).

Bias increases near the extremes of a velocimeter's velocity range because velocities that would be measured beyond the extremes wrap around to the opposite end of the range. You can avoid this bias by keeping the maximum observed speed toward the middle of the velocimeter's maximum range.

2c) Short-term uncertainty   

Most of the rest of this page is devoted to short-term uncertainty, expressed in terms of noise level. Velocimeter's short-term uncertainty is small compared with most other acoustic sensors, largely as a result of the algorithm they use. Small short-term uncertainty comes from collecting acoustic echoes with exceedingly high correlation. However, because sources of decorrelation can be both internal and external, a probes noise level is not entirely intrinsic to the probe itself, but it depends also on the environment in which it is measuring. Primary exrternal sources of decorrelation include mean speed, turbulence and nonuniformity in the scatterers.

2d) Spikes   

In many velocimeter measurements, velocity spikes are the dominant source of error. Spikes can be disproportionate sources of error because they can have such large values compared with the mean velocity. Large spikes are easy to see, so they can be removed from the data, but it appears that even despiked data have higher noise levels than comparable data without spikes (see Laboratory Velocimeter Tests in a Flume).

The source for spikes is not well understood. Spikes may occur as a result of the environment itself, but it is clear that the velocimeter hardware and algorithms are a primary source of spikes. This conclusion is based on our experiences with the Vector Velocimeter. The Vector incorporates substantial improvements, both in its hardware and its algorithm, and as a consequence, it sees far fewer spikes in its data relative to our older velocimeters. The new algorithm, retrofitted into our olde velocimeters reduces spikes in them as well.

2e) How individual measurements are collected   

A velocimeter transmits acoustic pings into the water at a high rate, typically many hundreds per second. The ping rate is fixed within each velocimeter according to its acoustic frequency and velocity range. The sample rate, or the rate at which the velocimeter reports data, is much smaller than the ping rate to allow each measurement to average multiple pings. Every time a velocimeter reports a result, it computes the result using all the available pings, then clears its buffers and starts a new average. If it sends data out at, say, 25 Hz, each output value will include twice as many pings as it would it it were sending data out at 50 Hz.

2f) Uncertainty, variance and standard deviation

Uncertainty is often measured in terms of measurement variance or standard deviation. These two are related:

variance = (standard deviation)²        (1)

The standard deviation is the size of the typical variation you would expect in a measurement, around the true value you are trying to measure. For example, imagine you were to make many measurements of an unvarying velocity. The best estimate of the true velocity is the mean of your measurements, and the uncertainty of each of your measurements is the standard deviation of the collection of measurements.

2g) Averaging

When you average a collection of velocity measurements, your average is a better estimate of the true velocity than each individual estimate. The uncertainty of the average is reduced according to:

variance(mean) = variance(individual measurements)/N            

std dev(mean) = std dev(individual measurements)/N^1/2        (2)

In other words, if you reduce the variance of individual measurements by a factor of 2, you can collect data twice as fast.

2h) Variance and Noise Level   

The velocimeter's noise level, also called the noise floor, is its most fundamental measure of measurement uncertainty. If you know the noise level, you can easily compute the expected variance or standard deviation of your measurements for any sample rate. Velocimeter uncertainty is a random white noise. This means that each velocity estimate is independent of the next, and it means that the noise has no preferred frequency.

The noise level varies widely according to the characteristics of the velocimeter, how it is set up, the characteristics of the flow, and the acoustic scattering environment. Here is how the noise level and measurement variance are related:

variance = (noise level) * (sample rate) /2        (3)

You can use (2) to turn (3) into an equation for standard deviation. Table 1, below, shows how the variance and standard deviation depend on the sample rate. Note that Table 1 is mathematically identical to (2). For example, remember that each 1 Hz measurement has roughly 100 times as many individual measurements in its average as a single 100 Hz measurement. Then (2) tells us that the 100 Hz measurement should have 100 times the variance of the 1 Hz measurement, which is what you see in Table 1:

Table 1. Measurement variance and standard deviation for different sample rates. This table assumes a noise level of 10^-4 m²s^-2Hz^-1. Remember that noise levels vary widely in practice.

2i) Noise level and real data   

The velocity noise level limits the frequency range over which you can obtain useful data. Figure 1 sketches the spectrum of turbulence observations made by a typical velocimeter. The shape of the turbulent spectrum shown is characteristic of the "inertial subrange", the frequency range in which large eddies break into smaller eddies, which break into even smaller eddies, and so on. In the case shown in Figure 1, the noise level limits the maximum useful frequency to around 2 Hz..

Figure 1. Spectra of velocity noise level, turbulence and the resulting measurement. The noise level plotted is typical for velocimeters (actual noise levels can vary several orders of magnitude from this value). The turbulent spectrum shown falls as f^-5/3, where f is frequency. The spectrum of the resulting measurement is the sum of the turbulent spectrum plus the noise level.

2j) How do we specify the noise level?   

It turns out that noise levels are difficult to specify because they depend on many factors, including factors that are outside the instrument (i.e. flow velocity and turbulence). This dependence is apparent, for example, in Laboratory Velocimeter Tests in a Flume. We specify velocimeter noise level in terms of single-measurement, single-component random noise (i.e. short-term uncertainty) that is equal to 1% of the velocity range at 25 Hz. Results in New Velocimeter Processing Algorithms Reduce Variance  are consistent with this specification. For example, for 1 m/s velocity range, this specification gives a 2-component noise level of 1.6 x 10^-5 m²s^-2Hz^-1 (the noise level of a two-component velocity is double double thie level for a single component). The observed 2-component noise level for 1 m/s velocity range in New Velocimeter Processing Algorithms Reduce Variance  was 1.8 x 10^-5 m²s^-2Hz^-1 when using our old algorithm, and 7 x 10^-6 m²s^-2Hz^-1 when we used our new algorithm. In Laboratory Velocimeter Tests in a Flume,  variance in smooth flow was around 1 x 10^-5 m²s^-2Hz^-1, and about a factor of 10 higher in turbulent flow. This order-of-magnitude difference between smooth and turbulent flow illustrates the general difficulty in specifying the noise level.

This means that the best way to determine a velocimeter's noise level in your application is to collect data in the same conditions. You can also estimate noise level with existing data collected in similar conditions. When you consider existing data, look carefully at how the data was collected and the nature of the flow, keeping in mind that noise level for a velocimeter can vary by orders of magnitudes as these factors change.

3. Why Not Make a 16MHz Velocimeter?

Nortek has considered producing a higher frequency velocimeter, but we have chosen not to do so. As with everything acoustic, changing frequencies has advantages and drawbacks; We find the drawbacks of a 16 MHz velocimeter to outweigh the advantages.

3a) Advantages of a 16 MHz velocimeter  

Advantages are measured in terms of variance or noise level. Changing from 10 to 16 MHz should lead to the following differences:

• Frequency difference. If everything else stays the same, changing from 10 to 16 MHz reduces variance by a factor of about 2.5 (=1.6²).
• Faster ping rate. Higher frequency allows faster ping rates, reducing variance another factor of about 1.6.
• Smaller sample volume. Reducing the length of a sample volume by a factor of 1.6 increases the variance by 1.6.
• The net result of all of the above should be a drop in variance of a factor of about 2.5. 

3b) Drawbacks of a 16 MHz velocimeter

The primary drawback of a 16 MHz velocimeter is that it needs roughly 10 times as much scattering material in the water to operate correctly. This difference is the result of three factors:

• A 16 MHz velocimeter has a transmitting transducer that is about half the size of a 10 MHz transducer.
• Shock formation reduces the maximum possible acoustic intensity.
• Attenuation at 16 MHz is higher than at 10 MHz.
• These three differences add up to a reduction in signal strength of a factor of about 10. To make up for this difference, a 16 MHz velocimeter requires about ten times as much scattering material in the water, all else being the same. If you have inadequate scattering material in the water, the velocimeter's performance can be seriously degraded. While many tanks and natural environments have adequate scattering material, sites with inadequate backscatter are also common.

Most laboratory tanks must be seeded to enable proper operation of a velocimeter--operation of a 16 MHz velocimeter requires 10 times the seeding of a 10 MHz velocimeter. In some cases, the additional seeding can impair visibility. In many cases, it is not practical to seed the tank.

Operation in natural environments can be even more difficult. Many natural environments have relatively low backscatter, and a 10x reduction in backscatter renders data unusable. It is rarely practical to seed a natural environment, and the act of seeding the environment changes the flow.

3c) Practical implementation  

Switching from 10 to 16 MHz adds problems in implementation which may reduce its benefits. Velocimeters are highly sensitive to signal correlation, and small reductions in correlation lead to large reductions in data quality. There are a number of sources for decorrelation, both internal and external to the instrument, and some of these grow with frequency. This means that you cannot take for granted that a 16 MHz velocimeter will achieve its theoretical improvement.

3d) Recent improvements to 10 MHz velocimeters  

We have implemented an improved algorithm in our 10 MHz velocimeters, which reduces velocity variance by a factor of 1.5-3, relative to older velocimeters. This improvement provides much of the benefit that would accrue from switching to 16 MHz, but without the drawbacks. For example, you can now sample at 50 Hz with the same data quality you would have gotton before at 25 Hz. The differences resulting from the improved algorithm have been proven with real data.

3e) Test comparisons  

The only way to be sure about the relative merits of 10 and 16 MHz velocimeters is to compare them. And indeed, recent test results from the University of Delaware's Ocean Engineering Laboratory  show that current-generation NDVs produce lower measurement noise levels than 16 MHz velocimeters. The test found an NDV's noise level to be about a factor of two lower than the noise level of an older 10 MHz velocimeter, while in an equivalent test, a 16 MHz velocimeter's noise level was marginally higher than the noise level of the same comparison instrument.

3f) Why would anyone want a smaller sampling volume?  

The sampling volume limits the size of turbulent eddies that a velocimeter can resolve. It effectively smoothes out eddies, for example, that are the same size as the volume. A smaller volume is attractive because it allows you to resolve finer eddies. Figure 1, below, puts this smoothing into perspective.

Figure 1. Effects of smoothing associated with the size of the sampling volume. The actual spectrum of the velocity is shown with the green line. The blue lines show two examples of how sample volumes smooth the spectrum. The letters A, B and C mark places on the spectrum (see text).

The green line in Figure 1 represents a typical turbulent spectrum that might be observed by a velocimeter. The low-frequency end of the spectrum is called the inertial subrange, where eddies break into smaller eddies. The viscous subrange starts at the high end of the spectrum (A) where the spectrum bends downward. This bend is the result of viscosity, which dissipates the smallest eddies. Today's acoustic sensors are unable to resolve the viscous subrange--to do this you will need a laser Doppler velocimeter.

A velocimeter is unable to resolve the viscous subrange because its sampling volume is too large, The letters (B) and (C) mark spectral cutoffs associated with smoothing by a velocimeter's sampling volume. The cutoff (B) and (C) differ by the sampling volumes. Cutoff (C) is at a lower frequency because the diameter of its sampling volume is 1.5 times as large as the diameter of the sampling volume that produces cutoff (B). This factor of 1.5 difference is about equal to the difference in diameters between 10 and 16 MHz velocimeters. The factor of 1.5 in diameter turns into a difference of about 4 in the sampling volume.

The difference in sampling volume is a moot point if the spectrum is limited by the velocity noise level. If the measurement noise is above the part of the spectrum where the sample volume cutoff occurs, then the sample volume is unimportant.

3g) How the sample volume relates to the spectral cutoff   

A velocimeter observing turbulent fluctuations because velocities fluctuate both in time and in space. It turns out that spatial fluctuations are the most important--we see these as turbulent eddies advect past the probe, moving with the mean water speed. To interpret these spatial fluctuations, researchers invoke Taylor's frozen turbulence hypothesis, which mostly says that advected spatial fluctuations are larger than the temporal fluctuations by themselves.

Because a velocimeter cannot resolve turbulent eddies that are smaller than the sampling volume, the observed spectrum cuts off instead of following the real spectrum down to viscous scales. The frequency cutoff will occur at a frequency that can be approximated as:

f_cutoff = U/d

where f_cutoff is the bend in the spectrum, U is the mean velocity and d is the characteristic length scale of the measurement volume, typically the diameter. With a mean velocity of 0.5 m/s and a cell diameter of 6 mm, this cutoff occurs at around 80 Hz. However, even though velocimeters can sample faster than 80 Hz, their noise levels are sufficiently high that this part of the spectrum will be buried in the noise.

In most circumstances, the diameter of the measurement volume controls the frequency of the cutoff. This is because velocimeter probes are normally oriented at right angles to the flow. In Figure 1 above, cutoffs B and C are based on a difference of 1.6 in characteristic length scale. However the difference in diameter between 6 mm and 4.5 mm is only 1.3, which means that the cutoffs B and C would be separated by only half the separation shown in Figure 1.

3h) Real spectra   

Figure 1 is a schematic that illustrates the characteristics of real spectra. There are many factors that can move the instrument's noise level, the actual turbulent spectrum and the sampling volume cutoffs back and forth, or up and down relative to one another. You can read about factors that play a role in a velocimeter's noise level in Velocimeter Accuracy Velocimeter Accuracy. The sampling volume cutoff will change depending both on the size of the sampling volume and the mean velocity--the velocimeter responds to eddies that advect by the probe (Taylor's frozen turbulence hypothesis plays a role here), so the frequency cutoff is a function of the size of the eddies and the speed at which they advect.

If you believe that the sampling volume is important in your application, it may be worth investigating to ensure that its noise level is sufficiently low to enable you to take advantage of a smaller volume.