LAB2.PDF

April 1-4, 2003 ES123: Laboratory #2

Flow over a circular cylinder: An experimental study using Laser Doppler

Velocimetry Introduction We have two goals for students performing this laboratory experiment.

First, you will gain a better understanding of, and some insight into, the flow of fluid past a solid object and the manner in which the flow field evolves when the Reynolds number is large. Second, the equipment will serve as an introduction to both the theory and application of Laser Doppler Velocimetry (LDV), which is a modern and nonintrusive measurement method.

Caution This warning probably will be redundant, but just in case - DO NOT

LOOK DIRECTLY INTO THE LASER; IT WILL DAMAGE YOUR EYES.

Background The lab will make more sense if you take some time to read these notes

before attempting to do the lab. James Vlahakis and Joe Ustinowich will be present with you during the lab to help with the software and answer questions. This laboratory equipment is brand new and we are just starting to become familiar with it ourselves, so your patience is appreciated.

PLEASE READ THE ATTACHED DOCUMENT ON THE

“MINIATURE LASER DOPPLER VELOCIMETER” WRITTEN BY THE MANUFACTURER (VIOSENSE) OF THE APPARATUS.

Experiment We will generate velocity profiles at different positions in the flow for

various Reynolds numbers. We will also use dye injection in order to try to visualize qualitatively some of the flow features. Data taken from different groups will be saved in a common data file so a lot of data will be available to everyone by the end of the week.

Goals: Measure velocity profiles across the channel upstream of, at, and

downstream of the circular cylinder. Use the rotameter, which reports a volumetric flow rate, to estimate the mean velocity and the Reynolds numbers for flow through the square channel and past the cylinder. Compare the average velocity determined using the rotameter with the value computed from one of the detailed velocity distributions that you measure.

After setting up the flow apparatus and electronic equipment, choose a point to take a velocity reading. Why did you select that point? Calculate the Reynolds number for the flow in the channel. Based on this calculation, what sort of flow do you expect to see? How does this Reynolds number compare with the Reynolds number characteristic of flow past the cylinder? About 1-2 cm in front of the cylinder, measure the velocity profile across the channel (in the vertical direction). It isn’t necessary (or desirable) to go from one edge of the test section to the other. Describe the features of this profile. Now generate a profile along the centerline of the cylinder. Again, describe the features of the profile. How close can you get to the cylinder itself before your data starts to “go bad?” Generate a third profile a few centimeters downstream of the cylinder. Again, describe the profile’s features. How does it compare to the upstream profile? Using a slow injection of dye for flow visualization, describe the flow you see both upstream and downstream of the cylinder. Does this help explain the data you generated? Repeat the process for two other values of the Reynolds number. Try to obtain one set of readings at the lowest speed you can attain. Lastly, industry and academia routinely use LDV to characterize flows. Now that you’ve worked with this system, describe some of its pitfalls and, if possible, things that researchers could do to avoid them.

Some Notes on Procedure

Because we would rather have you concentrate on the data you get and understanding it, rather than the mechanics of how to get the data, we will work with you to operate the flow lab, laser and associated equipment. What follows is a quick description of the procedure. If you would like more detailed information, consult the manual or feel free to take notes. First of all, turn on the pump and the electronic equipment. From the computer screen, start the Viosense software and the oscilloscope. Open the main flow valve and wait for the intake plenum to fill (it may take a few minutes).

Once the flow has settled to a steady state, use the oscilloscope tuning parameters to find the “sine-like” data bursts. Once found, switch to the Viosense software and tune the bandpass filter so that your data looks nice. Note how it is possible to get different velocities by changing the filter settings. Take data. Data is saved in an Excel accessible format or, if you prefer, it is possible to cut and paste data graphics from the screen into a word file. Save your data in the same file as the other members of the class. Then, we will have an extensive data set after everyone has done the experiment.

Some numbers: The square plexiglass channel is 2 inches on a side. The circular cylinder has a diameter of ¼”.

TUTORIAL

Doc No. Date: Page

WP V510-008 26-Dec-2002 1 of 8

File: WP.V510.008.Laser.Doppler.Velocimeter.doc/26-Dec-2002

LASER DOPPLER VELOCIMETRY1

1. Introduction 1 2. Basic principles 1

2.1 Generation of the fringes 2 2.2 Particles 3 2.3 Scattered-light detection 4 2.4 Maximizing the signal 4

2.4.1 Focussing of the laser beams. 4 2.4.2 Optimizing the seeding. 4 2.4.3 The direction in which the light is collected. 4 2.4.4 The receiving lens. 5 2.4.5 Use of a pinhole. 5

3. Signals and signal processing 6 3.1 Sources of error 6

3.1.1 Particle averaging bias 6 3.1.2 Velocity gradient broadening 7 3.1.3 Finite transit time broadening 7

4. An alternative explanation 8 5. Other LDV systems 8

1. Introduction

Laser Doppler velocimetry (LDV) is a very mature technique for measuring particle speed from scattered light, hence fluid dynamics. For more information on the subject, please consult bibliography2 on that field.

A laser Doppler velocimeter measures the velocity at a point in a flow using light beams. It senses true velocity component, and measures that component in a sequence of near instantaneous samples. These characteristics confer several advantages - an LDV does not disturb the flow being measured (like a Pitot does), it can be used in flows of unknown direction and it can give accurate measurements in unsteady and turbulent flows where the velocity is fluctuating with time.

2. Basic principles

The easiest way to understand how a laser Doppler velocimeter works is to consider a specific example. Figure 1 shows a "One-component dual-beam system". One component because it measures one specific velocity component (U in the diagram). Dual beam because it uses two laser beams of equal intensity. The beams are generated from a single laser using a half silvered mirror (the 'beam splitter'). They are then focussed using a lens (called the sending lens). The lens also changes the direction of the beams causing them to cross at the point where they are focussed. The region where the beams intersect is where the velocity measurement is made. It is called the measurement volume.

1 Inspired from W. J. Devenport, http://www.aoe.vt.edu/aoe3054/manual/expt4/index.html 2 “Principles and practice of Laser-Doppler anemometry”, F. Durst, A.Melling and J.H.Whitelaw, 1976, Academic Press, ISBN 0-12-225250-0.

TUTORIAL

Doc No. Date: Page

WP V510-008 26-Dec-2002 2 of 8


Figure 1 A single-component dual-beam LDV system in forward scatter mode

The interference of the light beams in the measurement volume creates a set of equally spaced fringes (light and dark bands) that are parallel to the bisector of the beams (Figure 2 ). A measurement is made when a tiny particle being carried by the flow passes through these fringes. As it does so the amount of light received by the particle fluctuates with the fringes. The amount of light scattered (i.e. reflected) by the particle therefore also fluctuates. The frequency of this fluctuation is proportional to the velocity of the particle normal to the fringes.

Figure 2 Detail of the measurement volume showing the formation of fringes.

Lines represent the peaks of the light

To detect this frequency, the light scattered by the particle is collected by a second lens (the receiving lens) and focussed onto a photodetector (Figure 1 ) which converts the fluctuations in light intensity into fluctuations in a voltage signal. An electronic device known as a signal processor is then used to determine the frequency of the signal and therefore the velocity of the flow.

Below we describe in more detail each of the elements of an LDV system. If, after reading this material, you wish to find out more about LDV.

2.1 Generation of the fringes

Figure 2 shows schematically the arrangement of the light waves within the two beams. The waves are represented by lines showing where the peaks are. Since laser light is monochromatic (i.e. of one frequency and wavelength) and coherent (all adjacent and successive waves are in phase) all the peaks line up. In the measurement volume the two sets of light waves cross. Where the interfering light waves are in phase (peak aligned with peak) they add up creating a bright fringe. Where the light waves are out of phase (peak aligned with trough) they cancel creating a dark fringe. As can be seen in Figure 2, the bright and dark fringes form in lines parallel to the bisector of the beams.

TUTORIAL

Doc No. Date: Page

WP V510-008 26-Dec-2002 3 of 8


Figure 3 Detail showing the relationship between fringe spacing,

light wavelength and the angle between beams

To calculate the spacing between the fringes we need to know the wavelength λ of the laser light and the angle α between the beams. Consider the enlarged region shown in Figure 3 . We see that adjacent bright fringes and light waves form an isosceles triangle of angle α and base λ/cos(α/2). Using trigonometry, verify for yourself that the height of the triangle, the fringe spacing s, is λ/(2sin(α /2)).

With the fringe spacing we can now determine the relationship between the velocity of the particle and the frequency it generates. If the fringes are a distance s apart and the velocity component of the particle normal to the fringes and in the plane of the beams is U, then the particle will cross a total of U/s fringes per second. Thus the particle will generate a signal of frequency f = U/s = 2Usin(α/2)/λ. This important expression, known as the LDV equation, enables us to relate the frequency of signals from an LDV f to the velocity of the flow U.

We can use the LDV equation now to get an order of magnitude estimate of the frequency produced by a particle traversing a typical measurement volume. Our probes have fringe spacing ranging from 5 to 10 microns. At 10m/s, the Doppler frequency will be around 1 to 2 MHz.

2.2 Particles

As mentioned above tiny particles must be present in the flow for a measurement to be made. These are referred to as seed particles, or just seeding . It is important that these particles be small enough to accurately follow all the movements of the flow. That way, when we measure the velocity of the particles, we are also measuring the velocity of the flow. Except in extreme circumstances, such as flow through shock waves, 1-micron (10 -6-meter) diameter particles are usually small enough. Such particles are present naturally in tap water but must be artificially introduced into air flows. Materials used for particles include latex (as in latex paint) or oil, water or dioctal phthalate droplets.

Note that, even in well seeded flows, the particles form only a minuscule fraction of the volume of the fluid. They therefore have no significant effect upon the flow.

TUTORIAL

Doc No. Date: Page

WP V510-008 26-Dec-2002 4 of 8


2.3 Scattered-light detection

The light scattered by the particles is focussed using a lens onto a photodetector, in our case a Avalanche PhotoDiode (APD). An APD is a photodiode that is driven at high voltage (100 to 300V). This high voltage accelerate the electrons generated by the absorption of photons to the point where they have enough energy to cascade and thus amplify the light current. APD are well suited for LDV applications and their frequency response goes from DC to hundreds of megahertz, even gigahertz.

2.4 Maximizing the signal

Even with an APD, detection of the light scattered by a 1 micron diameter particle may not be an easy task. It is therefore important to have a feel for those factors that influence the magnitude of this signal.

2.4.1 Focussing of the laser beams.

Because they are coherent and monochromatic, the laser beams focus to a very small diameter. The light intensity in the measurement volume can therefore be huge. For example, if the beams have a combined power of (10 milliWatts, small by most standards) but focus to form a measurement volume 0.3mm in diameter, then the light intensity in the measurement volume is approximately 0.01/(0.0003) 2 100000W/m2. This step is done once for all with our sensors.

2.4.2 Optimizing the seeding.

To get the strongest light signal it is best to arrange the seeding (if possible) so that there is never more than one particle in the measurement volume at any given time. If multiple particles are present then the signals they produce will, most likely, cancel out. Seeding size can influence the signal dramatically: too small, they will not be detected, too big, their visibility will be bad and may even saturate the detector. Seeding size to the order of the fringe spcing are close to ideal in terms of signal, but smaller particle are often used (typically 3 microns).

2.4.3 The direction in which the light is collected.

The amount of light scattered by the particles is a strong function of direction relative to the incident beams. (Physically this is because the size of the particles is comparable to the wavelength of the light.) Figure 4 shows the relative intensity of light scattered in different directions relative to the incident beams for a typical beam wavelength and particle size. Most of the light is scattered in the direction of the beams (to the right in the figure). Thus many LDV systems are arranged with the receiving lens and photodetector on the opposite side of the flow to the laser - these are called forward scatter systems. Figure 1 is a forward scatter system. Unfortunately it is often necessary to have all the equipment on the same side of the flow, or there is simply no clear optical path through the far side of the flow. In this case it is the light that scatters back towards the laser is collected- as you can see this is much weaker. We call such LDVs (e.g. Figure 5 ) back scatter systems. This is the architecture retained for our probes.

TUTORIAL

Doc No. Date: Page

WP V510-008 26-Dec-2002 5 of 8


Figure 4 Variation of light intensity scattered from a micron-sized particle as a function of angle relative to

incident beam. Radius indicates intensity plotted on a logarithmic scale, each circular grid line being a factor of 10. (from Durst et al. (1976))

Figure 5 A single-component dual-beam LDV system in back scatter mode

2.4.4 The receiving lens.

The proportion of the scattered light that is focussed on to the photodetector increases with the area of the lens and decreases as the inverse square of the distance from the measurement volume to the lens. Using a larger lens, and putting it closer to the measurement point can therefore greatly increase the magnitude of the detected signal.

2.4.5 Use of a pinhole.

A pinhole is a mask placed over the front of the photodetector that admits light only through a small hole located at the point where scattered light from the measurement volume is focussed. The pinhole prevents light scattered from other parts of the beams or apparatus from entering the detector and producing noise. Such noise can easily drown the signal. The pinhole can also be used

TUTORIAL

Doc No. Date: Page

WP V510-008 26-Dec-2002 6 of 8


to restrict the measurement volume size by making it small enough to admit light only from a portion of the measurement volume.

3. Signals and signal processing

The electronic signal given out by the photodetector contains periods of silence (while there are no particles in the measurement volume) randomly interspersed with bursts of signal (when a particle passes through the measurement volume). Figure 6 shows a idealized signal burst. The overall shape of the burst is a consequence of the fact that the laser beams producing the measurement volume will inevitably be stronger at their center than at their edges. As the particle passes through the edge of the measurement volume where the fringes are weakly illuminated the signal fluctuations are also weak. As the particle passes through the measurement volume center the signal fluctuations become larger and then decay again. Note that the fluctuations are not centered about zero because you cannot have a negative light intensity. As a consequence the signal can be split into two parts - a low frequency part called the 'pedestal' and a high frequency part that actually contains the Doppler signal.

Raw signal and pedestal

Filtered signal FFT from signal Speed distribution

Udf fringeDoppler =×

Figure 6 Anatomy of a typical LDV signal burst generated when a particle passes through the measurement

volume

Modern signal processors use digital technology to analyze each burst and extract the frequency and thus velocity at that instant. The hardware has to be quite sophisticated because the frequencies are so high. Typically such processors have 'burst-detection' circuits to tell them when there is a signal. They then digitize that signal and determine its frequency. To determine the frequency processors either autocorrelate the signal or take its Fourier spectrum . Thus we talk about 'autocorrelation processors' or 'burst spectrum analyzers'.

3.1 Sources of error

Laser Doppler anemometers are among the most accurate flow measurement devices. However, they are not immune to errors and, as with any other measurement technique, it is important to know the sources of error when making an LDV measurement.

3.1.1 Particle averaging bias

One problem with laser Doppler velocimeter is that they only sense the velocity when there is a particle in the measurement volume. Thus when using an LDV one collects a sequence of velocity samples each generated when a particle passed. Unfortunately such a set of samples is biased - when

TUTORIAL

Doc No. Date: Page

WP V510-008 26-Dec-2002 7 of 8


the flow velocity is high, more particles will pass through the volume in a given time than when it is low. Thus if we simply average the velocity samples we will get an estimate of the mean flow velocity that is too large. The estimated velocity variance will also be in error. This is called particle averaging bias . It is largest when measuring air flows (where there isn't usually much seeding) and/or reversing flows in which the velocity can instantaneously be very small. There are several fixes to this problem that are currently a topic of debate in the research community. One solution is to weight each velocity sample by the amount of time it takes until the next particle arrives (transit time weighting). We will meet particle average bias again when we make measurements.

3.1.2 Velocity gradient broadening

Velocity gradient broadening tends to increase the measured variance of the velocity signal by an amount given by

2

∂∂∆ yU

Here ∂U/∂y is the mean velocity gradient at the point where the measurement is being made and ∆ is the standard deviation of the distribution with Y of particles passing through the measurement volume (typically ∆ is about 1/4 of the measurement volume diameter). The source of this error is illustrated in Figure 7 which shows a cross section through the measurement volume. If the measurement is being made in a flow with a velocity gradient (such as a boundary layer) then successive particles passing through the measurement volume may have different velocities by virtue of their different positions in the gradient. So, even if the flow is completely steady, the LDV will measure a velocity fluctuation. This error may be corrected simply by subtracting the extra variance from the measured value.

Figure 7 The origins of velocity-gradient broadening

3.1.3 Finite transit time broadening

Finite transit time broadening tends to increases the measured variance of the velocity signal by an amount

( )222 NU ,

TUTORIAL

Doc No. Date: Page

WP V510-008 26-Dec-2002 8 of 8


where U is the mean velocity of the flow and N the number of fringes in the measurement volume (measurement volume diameter / fringe spacing s). This error comes from the fact that, when processing a signal burst, we are trying to deduce a frequency from a limited number of cycles. The fewer the number of fringes, the less cycles and thus the larger the potential error. Differing errors on successive bursts from particles traveling at the same speed give the impression of a velocity fluctuation when there is none. This error may be corrected simply by subtracting the extra variance from the measured value.

4. An alternative explanation

The explanation we have given of how a laser Doppler velocimeter works, in terms of particles passing through equally spaced fringes, is known as the fringe model. As is often the case with optics there is an alternative explanation. This is referred to has the heterodyne model. In this view we begin by considering a particle passing through just one of the laser beams in the measurement volume and scattering some of that light. Because the particle is moving, the frequency of the scattered light is slightly different from that in the beam, i.e. it has a Doppler shift. (The same Doppler shift is heard as the drop in pitch of a police-car siren as it races past.) If we could measure the frequency of this scattered light directly then an LDV would only need one beam. However, it is far too high (near 1015Hz) so instead we make use a second laser beam. Since the second beam is at a different angle, the light scattered from it has a different Doppler shift. When the light scattered from the two beams is collected at the front of the photodetector, interference (called heterodyning) occurs. Because of the difference in frequency, this interference produces 'beats' - fluctuations in the light intensity at a fixed point. The beat frequency, which is equal to the frequency difference between the two sets of scattered light, is low enough to be measured. It is related to the velocity of the particle via the same LDV equation derived above. That is because the fringe and heterodyne models are exactly equivalent explanations of the same physical phenomenon.

5. Other LDV systems

The one-component dual-beam system we have described above is probably the most common LDV system. It is also easily extended. Using two or three one-component systems, aligned so that their measurement volumes overlap, two or three velocity components can be measured simultaneously. Single systems using three or more beams intersecting at a point can also be used to measure multiple components.

Other types of LDV system also exist. Reference beam systems use only a single laser beam to illuminate particles in the flow. Light scattered by the particles is combined at the photodetector with a second, very faint, beam that comes directly from the laser. The resulting heterodyning makes the Doppler frequency measurable. Reference beam systems are less common than dual beam systems since they are more difficult to set up, usually produce noisier signals, and suffer from greater errors. The Phase Doppler anemometer (PDAs) is an extension of the laser Doppler velocimeter that usually uses two receiving lenses and photodetectors. PDAs not only measure the particle velocity but, by comparing the phase of the signals seen by the two detectors, the particle size. Particle sizing - as this is called - is necessary in the analysis and monitoring of many industrial processes, products and of pollution. The inkjet printer (which squirts tiny ink droplets at the paper) is an example of one such product.

Documents

LAB2.PDF