Principles of Operation:
Why Not Make a 16MHz Velocimeter?

Contents

1. Advantages of a 16 MHz velocimeter
2. Drawbacks of a 16 MHz velocimeter
3. Practical implementation
4. Recent improvements to 10 MHz velocimeters
5. Test comparisons
6. Why would anyone want a smaller sampling volume?
7. How the sample volume relates to the spectral cutoff
8. Real spectra

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.

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.

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.

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.

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.

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.

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.

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.

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. 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.