# Laser Doppler Velocimetry

## Objective

In this lab, you will learn the basic principles of laser Doppler velocimetry – which is a standard technique for measuring instantaneous, spatially resolved flow velocities. You will then use a laser Doppler velocimeter to explore the flowfield of a jet in a coflow. The jet is produced by the exhaust of a round pipe centered in a small, low-speed wind tunnel.

## Background

Rapid fluctuations in velocity occur in most flows of practical interest. Examples are: the boundary layer above wings and fuselage surfaces, the wakes behind obstacles in flows, jets from the nozzles of rockets and gas-turbine engines, and flows inside engine components. These fluctuations have profound effects on such things as drag, surface shear stress, boundary layer separation, mixing between fuel and air in engines, and vibrations of turbomachines and control surfaces. To understand such phenomena, we must be able to measure velocity fluctuations accurately.

There are several difficulties in making such measurements. First, we must find a method that has a measurable change in output for small changes in velocity (good signal _sensitivity_ or resolution), and which will work in the unsteady environment of a fluctuating flowfield (_robust_). Second, the device must respond faithfully, and perhaps without any time lag, to rapid fluctuations (good _temporal resolution_ or good _high frequency response_). Third, the device must respond only to the velocity in a very small, and precisely known, region (good _spatial resolution_).

While the Pitot probe used in earlier experiments can measure mean velocities, it is not suited to measuring fluctuation velocities. There is another well-known probe, the hot wire (also known as a constant temperature anemometer) that is suited to this task (under certain limitations). Its small, almost “microscopic” size gives it good spatial resolution and high frequency response. In addition, it has good signal sensitivity to velocity in constant temperature gas flows. The sensing element is a long circular cylinder, typically a tungsten or platinum wire of diameter in the range of 5 to 20 µm (2-8 ×$$10^{-4}$$inches). Slightly more rugged are hot-film sensors, which use glass rods, \~50 µm in diameter, with platinum films, typically 10 Å thick (Å = Angstrom = $$10^{-10}$$m), coated on the surface. In either case, the wire or the glass rod is fixed to two gold-plated steel needles which serve as the electric contacts to the sensor. The wire or film is kept heated by an electric current, to temperatures of 200 to 300 °C (and sometimes up to 800 °C). When air flows over the wire, energy in the form of heat is carried away by the much colder air stream (_forced convection_) because of the temperature difference between the (hot) sensor and (cold) air.

In many cases, however, probe-based approaches should be avoided so that the measurement not interfere with the flowfield (_nonintrusive_), else it change the quantity being measured. In addition to altering the flowfield, there may be several other reasons for using a nonintrusive technique. First, it may be physically difficult to design a probe that can survive in the flow to be measured. For example, consider the problem of measuring velocity inside the passages between the blades of a jet engine compressor while the engine is operating. Also it can be useful when several properties are varying simultaneously, as in a turbulent flame (e.g., inside an engine combustion chamber). For example, the velocity, pressure, and temperature may all be changing from one instant to the next. Most probes, such as Pitot tubes and hot-wires, respond to changes in several of these properties, and so it may be quite difficult to separate out the part due to velocity alone. Still another problem arises in two-phase flows (e.g., not all gas): there may be liquid droplets or solid particles that can clog or even instantly destroy sensitive probes. Examples of such applications include injection of liquid propellants or fuels sprays in rocket and aircraft propulsion systems, and water droplets and ice particles flowing around wings.

The laser Doppler velocimeter (LDV, also known as a laser Doppler anemometer - LDA) is a non-intrusive measurement device that is sensitive only to velocity. Thus, it is one of just a few techniques that can be used in complex flowfields to measure velocity. This is why, despite the greater cost and difficulty usually involved in making measurements with this technique, laser velocimeters are highly regarded instruments.

### **Principles of Operation of LDV**

When electromagnetic waves are scattered from moving objects, the scattered light has a frequency which is different from that of the incident waves. This is similar to the phenomenon that we have all observed: The horn of an oncoming car changes pitch suddenly as it passes us. The difference in frequency is known as the Doppler shift, and is proportional to the relative velocity between the moving object and the observer (or receiver). This principle is also used in radar and laser speed detection.

A laser is a source of radiation that _generally_ has most of the following properties; it is: 1) well-collimated, which means the beam will not diverge or change in size much; 2) highly coherent, meaning its electromagnetic wavefronts are all in phase; and 3) nearly monochromatic, which means that the radiation is composed of a very narrow range of wavelengths. Thus, it is ideal for making measurements of Doppler shift; you can precisely and easily calculate what the shift should be for a given velocity. Unfortunately, the frequency of light is very high, and the Doppler shift caused by the kinds of velocity that we encounter is extremely small by comparison. So, if one were to shine a laser beam at a moving object, measure the incident light frequency and the scattered frequency, and try to find the difference, one would probably find that one's measuring instrument cannot make out the slight difference between these frequencies. The solution to this problem is to find the difference in Doppler shift caused by two beams, hitting the same object at slightly different angles. If one tries to measure only this difference, one can get good accuracy. This is the principle of the dual-beam interferometer-type LDV that is widely used today (see Figure 1).

![](https://lh4.googleusercontent.com/y_AmrRG5GdRRrOgIpJgi2NaWQBU38uSCt08VOo0SsAa3q48BVAbwmQbX2x2UM9yW_zWq344FrHp4sqHVmKMwjf8QIOjycRaolg_x5UuecBp6TjcbCs2reEu_QomZR4oetfO-CNPt34wX29s8HA)

> **Figure 1.** Schematic of a basic 1-component LDV system in forward-scattering mode (plan view).

#### DualBeam Laser Velocimeter

When two laser beams of the same frequency cross in a small region, stationary interference fringes are formed, as shown in Figure 2. This is because light behaves as a kind of wave, with an amplitude and a phase. At some points, the two beams are in phase and the amplitudes add together; there the light’s amplitude is large. At other points, the amplitudes cancel each other out (out-of-phase), and you get nothing at all. Thus, fringes are formed, with each bright fringe being a thin disc inside which the light intensity is large. The bright fringes are separated by dark fringes, where there is hardly any light intensity at all.

![](https://368320314-files.gitbook.io/~/files/v0/b/gitbook-legacy-files/o/assets%2Fae3610%2F-MLTt5bI7Ve_1X_lvP93%2F-MLTthfwqrffCJ4CB1BZ%2F15.png?generation=1604688732712997\&alt=media)

> **Figure 2.** Plan view of fringes formed when two laser beams cross (particle motion across fringes will yield vertical velocity in plane of paper). Note that the region with fringes looks ellipsoidal in shape

As seen from Figures 2 and 3, the region where the fringes exist is an ellipsoid of revolution. Consider a small solid or liquid particle moving perpendicular to the fringes (as shown in the figure). At the same time, imagine that a highly sensitive light detector is looking straight at the light being scattered from the ellipsoid. As that particle enters the first fringe, it starts scattering more light. The detector sees the received light intensity increasing. The intensity reaches a maximum when the particle is centered on the fringe, and decreases thereafter. As the particle reaches the center of the first dark fringe, the intensity sinks to a minimum, and the slowly starts increasing again as the particle approaches the next bright fringe.

![](https://lh3.googleusercontent.com/IysLNohLmFIz-4Nfr63GcXYCK1VZUtYbNcnVuqQRlg1OZCGpzSjKxNPEdip9ruDRNE5d3fFCVJeQo6fR_b28WHi4edio9dQXqqMoVsgIrr8Uko-uT_mgRXKjx_XyiC-OXEJBWX5sZRvt7UBCZw)

> **Figure 3.** Sinusoidal variation in the intensity of scattered light, as a particle crosses the fringes (d=fringe spacing; U=velocity component perpendicular to the fringes; Δt=time between scattering peaks or 1/Δt = Doppler frequency).

As the particle crosses the ellipsoidal region (the measurement volume of the LDV), the detector sees the light intensity oscillating in a sinusoidal fashion; this is known as a **signal burst** (as seen in Figure 3). If the particle moves faster, the same number of fringes will be crossed in less time, so that the **frequency** of the sinusoidal signal will increase. Thus, the frequency of the signal received at the detector is proportional to the speed of the particle along the direction perpendicular to the fringes. Note that it does not matter, as far as the frequency is concerned, how fast the particle is moving in other directions. Only the speed at which it crosses the fringes is important. Thus, the dual beam LDV is sensitive only to the component of velocity that is perpendicular to the bisector of the two laser beams, and in the plane of the beams.

Let us try to quantify this relationship. The frequency of the detected signal (which can be rigorously shown to be exactly equal to the Doppler shift) must be directly proportional to the velocity component, and inversely proportional to the **fringe spacing** (the distance between the middles of two successive bright fringes). The fringe spacing, _d_, for two beams of wavelength _λ_, intersecting at a half-angle _θ_, is given by:

$$
\large d=\frac{\lambda}{2\sin\theta}
$$

(1)

Thus, the Doppler shift frequency $$f_D$$ is simply,

$$
\large f_D=\frac{U}{d}=\frac{2U\sin\theta}{\lambda}
$$

(2)

where _U_ is the velocity component perpendicular to the fringes.

As an example, consider an Argon-ion$$(Ar^+)$$ violet laser with a wavelength of 476.5 nm (not the one in our LDV system). If particles in an air flow are moving at 10.0 m/sec and the half-angle between the laser beams is 6.0°, then the fringe spacing is 2.28 μm, and the Doppler shift is 4.39 MHz (a frequency of 1 MHz means that the time between two successive peaks of the signal is$$10^{-6}$$sec).

#### Focal Length, Beam Spacing, and Fringe Spacing

Notice that in the above calculation, the only parameter that depended on the flow was the flow velocity; the other parameters (laser wavelength and half-angle) depend on the instrument. Thus, the LDV requires no calibration, unlike many other measurement techniques. The half-angle (_θ_) between the beams is determined using simple geometry knowing the optical setup, i.e., by the spacing (_D_) between the two beams when they come out of the front focusing lens of the LDV, and the focal length (f) of the lens, which is the distance from the middle of the lens to the focal point where the beams cross (see Figure 1).

#### Bragg Cell and Moving Fringes

While the simple dual-beam LDV system (such as that shown in Figure 1) is able to isolate and measure a single component of the flow velocity, it can not differentiate between positive and negative velocities. If the flow were to change direction, e.g., from forward to backward, a particle moving through the fringes with the same velocity magnitude would produce the same Doppler shift frequency$$f_D$$for either direction of motion. To overcome this, one of the two laser beams in a dual-beam LDV system can be passed through an acousto-optical modulator\* (called a **Bragg cell**) that can shift the beam’s frequency slightly (e.g., by 10s of MHz).

{% hint style="info" %}
\*In the acousto-optic modulator, the laser beam interacts with sound waves generated (typically by piezo-electric transducers) in an optically transparent material. The laser beam is diffracted off the index-of-refraction pattern caused by the pressure waves in the material.
{% endhint %}

When the two laser beams intersect, the fringes that are created are no longer stationary in space. The fringe pattern (i.e., the locations of the peaks and valleys) moves at a rate determined by this frequency shift. Now the detector will see a signal with an amplitude that oscillates at a frequency$$(f_{signal})$$that is different than $$f_D$$. Assuming that the fringe pattern moves in the “forward” or “positive” flow direction, the signal frequency is given by

$$
\large f_{signal}=f_{bragg}+(sign(U)\times f_D)
$$

(3)

For example reconsider the particle describe above, which was moving at 10.0 m/s through a fringe pattern with a spacing of 2.28 μm ($$f_D$$= 4.39 MHz). If the second laser beam was shifted by a Bragg cell with frequency 10.0 MHz, causing the fringe pattern to move at 10 MHz in the negative direction of the flow, then the light scattered by the particle as it moved through the measurement volume would have an amplitude that oscillated at a frequency of 10+(+4.39)=14.39 MHz if the particle was moving in the forward direction, or 5.61 MHz if it was going backward.

#### DualBeam, OneComponent, Backward Scatter LDV System

The LDV system for this lab uses a 300 mW $$Ar^+$$green laser, fiber-coupled to a transceiver unit (see Figure 4). The light coming out of the laser goes to a fiber-coupler unit that first uses a beamsplitter to separate the original beam into two beams. One of these beams is then passed through a Bragg cell that shifts the frequency by 40 MHz. The two beams are then sent to the transceiver unit through fiber optic cables. The laser beams pass through a lens in the transceiver, and are focused down, so that they cross at the focus of the lens and form the measurement volume.

![](https://lh6.googleusercontent.com/lmciV2lwl2gtlQxH6NwsaU3R5TdPqnMRrlqcD-5_-R79WerSkVFPbDnDlkle9mc5cSKolsHioPQN6icT0fZInuH85heELHNSaDF_T04ADmPyJoD-n_CHqb1Alc2nV2cgOFPBOwAiCneCzUCO3w)

> **Figure 4.** Schematic of lab LDV system with combined transmitter and receiver (transceiver) used in back-scattering mode.

#### **Light Collection and Signal Processing**

The back-scattered light from the focal volume is collected by a lens located in the transceiver, and focused in front of a photomultiplier, a light sensitive detector that can detect even very low light levels. The photomultiplier, when activated by a high voltage across it, converts incident light (photons) to an electric current (electrons) with a significant gain. Typically, a single input photon striking the photomultiplier can result in a large number (e.g., $$10^4$$) output electrons. This electron current, when passed across a high resistance, produces a voltage that we measure (see Fig. 4 in the Unsteady Combustion Lab). The photomultiplier output goes to the Photodetector Module (PDM), which also controls the photomultiplier input voltage (and thus the detector’s gain).

Since the receiving optics are located on the same side of the tunnel as the transmitting optics, our LDV uses the **backward scatter** (or **backscatter**) configuration. It turns out that when the diameter of a scattering particle is about the size of the wavelength of the light, most of the light scattered by the particle goes right past the particle, for example a typical value would be 90% of the light in this forward scattering direction. Only about 1% of the light comes straight back along the path of the incident beams, in the backscatter direction. On the other hand, our usual experience of looking in mirrors tells us that, when the size of the scattering object (say, a mirror) is much larger than the wavelength of the light, the light will not go around the object, but gets reflected right back. Thus larger particles will scatter a larger fraction of the incident light in the backward direction.

#### **The Digital Burst Correlator**

The output from the PDM goes to the **FSA** (Frequency and Size Analyzer) digital signal processor. The burst signal is first sent through an 80 MHz low pass filter, then downmixed with a _**user-chosen**_ frequency; essentially the user-chosen frequency is subtracted from the signal. You can use this to subtract part of the shift in the signal frequency that was added by the Bragg cell. For the example given above ($$f_D$$= 4.39 MHz, 10 MHz Bragg shift), a downmix frequency of 5 MHz would convert the 14.39 MHz burst frequency to 9.39 MHz.

Selecting a downmix frequency of 40 MHz will eliminate all the 40 MHz Bragg Cell Shift, so only the Doppler frequency is left, which is proportional only to the particle velocity. Selecting 39 means 39 MHz is subtracted from the 40 MHz Bragg cell shift, leaving 1 MHz still added onto the Doppler frequency. This will allow flow reversals up to 1 MHz to be measured. With a 5 µm fringe spacing, this would correspond to flow reversals up to 5 m/s. Entering 36 means 36 MHz is subtracted from the 40 MHz Bragg cell shift, leaving 4 MHz still added onto the Doppler frequency. This would correspond to 20 m/s (assuming 5 µm fringe spacing), in terms of the maximum flow reversal velocity.

After the downmix subtraction, the signal is sent through a bandpass filter to remove content at frequencies that are nowhere near the expected frequencies based on the estimated flow velocities; this is required because there are many possible sources of spurious electrical signals (“noise”). If what remains is the true (Doppler shift) signal caused by the particle crossing the fringes, the remaining signal would ideally just have one frequency. After being filtered, the digital signal processing units digitize the signal and determine the frequency embedded in the burst (similar to what could be achieved with a discrete Fourier transform). This part of the FSA electronics is called the **burst correlator**.

Normally the first parameter to select is the Band Pass Filter setting. If you know the range of frequencies that will be in the flow, you can select the setting directly. Remember that the signal frequency (without frequency shift) is equal to the particle velocity divided by the fringe spacing. To estimate the frequency of the signal input to the signal processor, add the effective frequency shift (equal to 40 MHz minus the downmix frequency).

The system also includes a **threshold** for detection. Unless the burst signal has an amplitude of at least some minimum value, say 30 mV, the electronics can reject it. For example if the signal is too weak and buried in noise, no useful velocity measurements can be made. This fact puts the burden entirely on the operator of the system to ensure that the signal _going into the correlator is of good quality_, (good **visibility**). _In other words, if you can not see a clear Doppler signal on an oscilloscope, do not expect the burst correlator to see one either_. Of course, if you amplify a noisy signal enough, the unit will faithfully find some frequencies in the noise signal, and may output useless data. The frequency counted may be that of the nearby radio station instead of the Doppler shift, and you may get supersonic flow velocities from your low-speed flow!

#### Seeding

Note that a valid signal results only when a solid or liquid particle crosses the measurement volume. _The velocity measured is actually of these particles, not of the air itself!_ Thus, care must be used in ensuring that the particles present in the flow are those that are so small that they move at essentially the same speed as the flow. In other words, they must have very small mass, and comparatively low density. If they move at speeds different from the local air flow velocity, the drag force exerted on them must be far greater than the inertia due to their mass, so that they are again very rapidly accelerated or decelerated to the local air velocity. You can easily convince yourself that as the diameter of a particle gets smaller, this becomes a better approximation, since the mass of a sphere is proportional to the cube of the diameter, while the surface area is proportional to the square of the diameter.

Usually, in a laboratory, the air is supposed to be clean and free of dust particles. Hence, the flow must be artificially seeded with particles of the right diameter range. This is done here by means of an atomizer, which works essentially like a paint spray can. A high-pressure air supply is expanded through a small orifice or nozzle to high speed. On the way out, it hits a thin stream of liquid (mineral oil) and shatters it into tiny droplets. This flow is then rapidly decelerated and turned around a sharp corner, and forced to go upwards. All the large droplets hit the walls (low drag, high inertia - they can not turn quickly enough) and drip back down into the oil reservoir. The remaining droplets, with diameters in the range 1-10 μm, go with the air stream and mix with the main flow. If done properly, a uniformly seeded flowfield can be created.

### The AE3610 LDV Experiment

Our LDV system uses an in-house fabricated wind tunnel, seeding system, and manual traverse, with an off-the-shelf LDV system made by TSI Inc. The three figures below show our setup, its primary constituent parts, and a view of the test section when the laser transceiver is energized.

{% file src="https://368320314-files.gitbook.io/~/files/v0/b/gitbook-x-prod.appspot.com/o/spaces%2F-MIV0GglxIUR4tETuwA2%2Fuploads%2F0GQ7xRqHKdjGKJfWy93s%2FTSI%20LDV%20Manual.pdf?alt=media&token=aed66b64-e9b6-4a4c-bc10-16e492093ede" %}
The TSI LDV Manual can be viewed here
{% endfile %}

![](https://368320314-files.gitbook.io/~/files/v0/b/gitbook-legacy-files/o/assets%2F-MIV0GglxIUR4tETuwA2%2F-MVP_dFdmQX7VZeso9V3%2F-MVPlT_31WWVnuaorGEh%2Fimage.png?alt=media\&token=7aebf71a-c23d-4a55-b859-6e7d5d115e0e)

![](https://368320314-files.gitbook.io/~/files/v0/b/gitbook-legacy-files/o/assets%2F-MIV0GglxIUR4tETuwA2%2F-MVP_dFdmQX7VZeso9V3%2F-MVPlHrgwDti_qNmoZo4%2Fimage.png?alt=media\&token=8ab8ba39-ac01-4202-bbbe-ff5d79c90f8e)

![](https://368320314-files.gitbook.io/~/files/v0/b/gitbook-legacy-files/o/assets%2F-MIV0GglxIUR4tETuwA2%2F-MVP_dFdmQX7VZeso9V3%2F-MVPm_gjLBINKwa5GZW0%2Fimage.png?alt=media\&token=201bc3a8-8fa8-4c71-bd60-e3fd1aa16c4f)

## Turbulent (and Fluctuating) Flows and Data Reduction

### Velocity Decomposition

Turbulent flows are not only unsteady, but chaotic in character.\*

{% hint style="info" %}
\*For background material on turbulent flows, you may wish to read Anderson’s Fundamentals of Aerodynamics, 1984, Chap. 16, or Kuethe and Chow, Foundations of Aerodynamics, 4th Ed., Sections 18.1 - 18.3.
{% endhint %}

In analysis of many turbulent flows where the fluctuations in velocity are small compared to the mean velocity, we decompose the instantaneous velocity u(t) as follows

$$
\large u(t)=\overline{U}+u'(t)
$$

(4)

where $$\bar{U}$$ is the mean velocity and u′ is the fluctuating component (with u′<<$$\overline{U}$$). These may be seen from Figure 5, which illustrates how the velocity at some point would change with time in a turbulent flow.

![](https://lh5.googleusercontent.com/4Q1XKpPTM7Q7BPmtizYHkqFwEWOf9S8Vc77U32Z2IJS7gUiz8S3r_HPR6WkK6ywVHcstMBasMiLvg7CpALFeY0EIOHPWhOBsy-nVFS60CBHJoQwdYMT08PSazh26kpbb_-evez4fJ2XH14PPzQ)

> **Figure 5.** Typical velocity history at a single point in a turbulent flow.

Note that the time average of the fluctuating component, $$\overline{u}'$$, should be zero since the fluctuations are random and the u′ at any instant is as likely to be positive as negative. However, the variance $$\overline{(u')^2}$$ is not zero, and gives us a measure of the intensity of the fluctuations. The positive square root of the variance is called the root-mean-square, or RMS for short. The variance of the velocity enters directly into the time-averaged Navier-Stokes equation (as described in AE 3030). This quantity will be calculated and used here.

### Data Reduction

#### **The velocity histogram**

The velocity may be expected to vary from one data point (i.e., one particle) to the next. The LDV system collects, say, the first 5,000 points to be measured, converts the time values to velocity, and then sorts these values into “bins” or velocity intervals. Thus, if the highest velocity that you expect is 20 m/s, and the lowest is 10 m/s, and you divide this range into 100, then all the data points which show velocity values between 10.0 and 10.1 m/s will go into the first “bin”, all those between 19.90 and 20.0 m/s will go into bin #100, and everything else will go somewhere in between. The mean velocity can be calculated from the binned data with the formula

$$
\large U=\frac{\sum n^iU_i}{\sum n_i}
$$

(5)

where$$n^i$$is the number of samples in the i’th bin, and $$U_i$$is the center velocity of that bin. The root-mean square (or the square-root of the variance) is calculated as:

$$
\large u_{rms}=\sqrt{\frac{\sum n_i(U_i-U)^2}{(\sum n_i)-1}}
$$

(6)

These results are usually displayed on the computer, along with a graphical display of the distribution of data points over the velocity intervals. Such a graph is called a _histogram_. The number of points in each interval has been divided by the total number of points collected. If it were a continuous function, instead of being a series of discreet values for a finite number of intervals, it would be called a _probability density function (PDF)_, whose integral, over the entire range of velocities, should thus be equal to unity.

#### **Averaging**

Usually when this procedure is used, at least$$10^3$$points are needed to yield a good result for the average velocity, and at least$$10^4$$-$$10^5$$for the RMS. This is if you collect data for a sufficiently long time, so that you have seen all the likely kinds of fluctuations that occur. However, if the flowfield is fluctuating slowly, the average calculated from just one set of data as above may be insufficient. Instead, you may have to average over many data sets, each taken at a different time. For example, suppose there are 6000 data points arriving every second, and you collect the first 3,000. This should take only 0.5 seconds. Suppose now that the flow itself is fluctuating so that the magnitude of velocity goes up and down again once in 2 seconds. Your calculated mean velocity will not be the true mean of the flow. To find the true mean, you will have to average many such data sets. Note from Eq. (6) that you cannot just average the rms values to get a better estimate for the rms; this would have to be done inside the summation sign.

## The Jet Flowfield

One feature of the laser velocimeter to bear in mind is that one must have a good idea of the flowfield before attempting to make measurements using it. Very precise measurements can be made by a careful and alert experimentalist, but not without some consideration of the flowfield. Figure 6 shows a schematic of the flow setup in our laboratory. A fan downstream of the tunnel diffuser creates a pressure difference that induces the tunnel freestream, and forces it out of the laboratory. A circular pipe brings air output from a centrifugal blower to the upstream edge of the wind tunnel test section. The flow comes out of the pipe as a jet, with a velocity that can be significantly higher than that of the test section freestream. Both the test section freestream and the flow inside the pipe are seeded with atomized mineral oil.

![](https://lh5.googleusercontent.com/p2ircKsnUps-yNSgGmjb56pZ6WCergH3IZHDjEPorI9BO5oJCUubocjR9op2xn3MgCtk-v70w0Owtk45SOFCbE9VBzi4ifpSh3eimyDArX51K2gD-gOdxgVx8Xg1f8VPhyqM7llaSZJVCgBTeg)

> **Figure 6.** Schematic of jet flow in the wind tunnel

If the jet flow leaves the pipe with a high velocity, the effect of viscosity at the edges of the jet causes the surrounding test section flow to accelerate, and the jet flow to decelerate. In fact, the flow at the edges of the jet is forced outward as it is “pulled” by the slower-moving test section air. Thus, some of the jet flow “rolls up” into vortex rings around the jet, so that some air which originated in the test section flow goes into the jet, and vice versa. Thus, there is a _mass transfer_ and _momentum transfer_ across the jet boundaries. Things rapidly become confused and unsteady at the jet edges, so that the velocity fluctuates. Not too far downstream of where the jet exits the central pipe, the fluctuations are largest inside the _**shear layer**_ at the edges of the jet. Near the center of the jet, there is still a region where the fluctuations have not reached. This is called the _**potential core**_, and the fluctuation level should be quite low here. The shear layer around the jet grows quickly so that the shear layers from opposites sides merge, and the potential core rapidly disappears as the jet goes downstream. At the same time, the mass and momentum transfer force the time-averaged velocity profile across the jet to become smoother and to gradually disappear, as the jet merges with the test section flow. _You will acquire velocity data along a vertical line extending from somewhere below the top wall to a region below the centerline of the jet._ This line is nominally near the horizontal center of the jet and nearer to the end of the test section.

## Procedure and Data to be Taken

### Preliminary calculations

The specifications for our LDV system and software configuration are as follows:

* Laser wavelength, $$\lambda$$ : 514.5 nm (Argon-Ion green)
* Beam separation, $$D$$: 50 mm
* Focal length, $$f$$: 362.6 mm
* Approximate range of measured velocities, $$U$$: -2 to 15 m/s
* Bragg cell frequency: 40 MHz
* Burst threshold: 30 mV

Calculate the following parameters:

1. Beam intersection half-angle, $$\theta$$&#x20;
2. Fringe spacing, $$d$$&#x20;
3. Doppler frequency, $$f_d$$, at each end of the velocity range (assuming no Bragg)
4. Assuming no bandpass filter is implemented, what is the absolute minimum downmix frequency needed to enable the required negative velocities to be measured?
5. Given a downmix frequency $$f_{dm}$$ and an ideal bandpass filter that operates between $$f_1$$ and $$f_2$$Hz, write a closed-form expression for the minimum and maximum observable velocities of the final system
6. Using your answer from Q5, select an integer-number downmix frequency to input into FlowSizer, and select a band pass filter from the available options in "LDV Controls" (see pic below for precise options). Provide the minimum and maximum observable velocities using these settings.&#x20;

![FlowSizer band pass filter options](https://368320314-files.gitbook.io/~/files/v0/b/gitbook-legacy-files/o/assets%2F-MIV0GglxIUR4tETuwA2%2F-MVTZt2tpfkbEA3MMLW6%2F-MVT_9I7E3glLMF55szv%2Fimage.png?alt=media\&token=a47fae15-6ca8-479f-a23c-becd53b3406d)

{% hint style="info" %}
Hint: everything you need to answer these questions is in this manual, but you may also get some better insight from the LDV manual (linked below), and the FlowSizer auto min and max velocity calculation
{% endhint %}

{% file src="https://368320314-files.gitbook.io/~/files/v0/b/gitbook-x-prod.appspot.com/o/spaces%2F-MIV0GglxIUR4tETuwA2%2Fuploads%2F0GQ7xRqHKdjGKJfWy93s%2FTSI%20LDV%20Manual.pdf?alt=media&token=aed66b64-e9b6-4a4c-bc10-16e492093ede" %}
The TSI LDV Manual can be viewed here
{% endfile %}

### Preparing the experiment

{% hint style="danger" %}
_**Please note the following safety precautions very carefully:**_

1. Your eyes, and your friends' and instructors' eyes, can get hurt by lasers. Take no chances or shortcuts: laser beams travel a lot faster than you can react! To ensure safety, no one who has not read the instructions thoroughly can be allowed near the experiment. Anyone disobeying safety rules will be ordered out of the lab immediately.​
2. **Wear laser eye protection at all times once the laser has been powered on!**
3. Remove all rings and watches when working in the vicinity of lasers.
4. Do not go to the back side of the test section unless directly supervised by a TA.
5. Do not lean over the laser beam, or stick your head between the laser transceiver and the test section when the laser is on.
6. Do not touch the laser or fiber optic coupler, whether the laser is on or off. If they go out of alignment, the TA will realign the system. Also, do not touch the transceiver unless instructed to.
7. Be very careful where you move the traverse: you must know clearly where all the reflections are (if any)!
{% endhint %}

The TAs will now give you an overview of the equipment and lead you through configuration of the experimental hardware and software.

### Testing the equipment and learning the data acquisition workflow

We will now go through a sample experiment to demonstrate operation of the system and how to acquire data:

1. Verify the traverse is set such that the transceiver probe is aligned in the center of the jet and the direction of the probe is in the direction of flow (the yellow warning label is on the left when viewing the probe from behind, and angle dial is on 90)
2. Open both seeding valves and verify successful seeding. Have a TA help you troubleshoot lack of successful seeding.
3. In FlowSizer, click on _**Setup**_ under the _**Home**_ tab and set _**Maximum Particle Measurement Attempts**_ to 100,000 - this is a temporary change that will buy more time for this demonstration (capture time = MPMA / data rate). Also ensure _**Screen Update Interval**_ is set to 0 and _**Time Out**_ is set to 0.  ​
4. Have one TA stand at the seeder blower control (currently at around 1900rpm), then immediately after hitting _**Begin Capture**_ have him/her smoothly but quickly ramp the speed down and up a couple of times, before returning to 1900rpm. The Velocity 1 Realtime graph should show this change in speed with a slight delay, until you hit _**Stop Capture**_ or the 100,000 points have been observed (which they shouldn't have been in this time frame).
5. Close the seeding valves and set the laser to **STANDBY,** but otherwise leave everything where it is
6. Click _**Save**_ and call the file something meaningful like DemoRun
7. Click on _**Data Sets To CSV File**_ and select the relevant metrics, shown in the figure below, before clicking _**Export**_
8. Verify the data exported correctly by navigating in Windows Explorer to the run folder and opening the CSV file. Select the first three columns and click Insert > Scatter to generate a quick preview plot to verify the data makes sense and matches, as shown in the figure below
9. Return the _**MPMA**_ setting to 10,000 in FlowSizer _**Setup**_

![Step 4 - Observing jet velocity change ](https://368320314-files.gitbook.io/~/files/v0/b/gitbook-legacy-files/o/assets%2F-MIV0GglxIUR4tETuwA2%2F-MVP_dFdmQX7VZeso9V3%2F-MVPrf77EVUPtFJsHO4S%2Fimage.png?alt=media\&token=288abcd5-81d5-470d-8426-1bd7fe968779)

![Step 6: Selecting data sets to export](https://368320314-files.gitbook.io/~/files/v0/b/gitbook-legacy-files/o/assets%2F-MIV0GglxIUR4tETuwA2%2F-MVP_dFdmQX7VZeso9V3%2F-MVPseDrQBQv0Y5YK8Bl%2Fimage.png?alt=media\&token=59769238-1559-404b-9b5d-01e0d024641b)

![Step 7: Verifying the data saved correctly in Excel](https://368320314-files.gitbook.io/~/files/v0/b/gitbook-legacy-files/o/assets%2F-MIV0GglxIUR4tETuwA2%2F-MVP_dFdmQX7VZeso9V3%2F-MVPsz5uOMgJG0-lW_eH%2Fimage.png?alt=media\&token=0fe00430-ecd4-45cf-ac34-18362d003abc)

### Taking Data

Now you are comfortable with the workflow, it's time to capture real data:

1. Move the traverse to the zero position (top of the test section)
2. Open both seeder valves and verify successful seeding. Have a TA help you troubleshoot lack of successful seeding.
3. Set laser to **RUN**
4. Obtain the jet profile data by performing a short capture at each traverse position:
   1. Follow the steps in the previous section to obtain a measurement at the zero position
   2. Having decided on a traverse distance (it doesn't have to be constant throughout the test section... bear in mind the expected profile of the flow in the freestream and the jet), move the traverse to your next position and obtain another measurement.&#x20;
   3. Repeat Step 2 until you have traversed 155mm downwards (just off the bottom of the test section). **You will need to keep a manual list of all traverse positions since this is not logged (or perhaps save your run with a meaningful name).**
5. Go back and repeat the measurements for at least TWO locations (the first point being in the free stream and second in the shear layer), but with different **Bandpass Filter/Downmix Frequency** settings
6. Return the filter settings to their proper values, and change the **Burst Threshold** value to 150 mV and repeat the measurements in the shear layer (to see if the original threshold value was a reasonable choice)
7. Return the **Burst Threshold** to its original value, and repeat the shear layer measurement two more times. The first time, turn off (or nearly off) the free stream seeder. The second time turn the free stream seeder back on and turn off (or nearly off) the jet seeder.
8. _Rotate the transceiver_ by 90 degrees counter-clockwise and acquire vertical velocity component data at the same location used above in the jet shear layer (and additional locations if you wish). Note, you will need to adjust the **Bandpass Filter** and **Downmix** **Frequency** settings to account for the fact that: 1) the vertical velocities are less than the axial velocities and 2) the vertical velocity can be both upward and downward. When you are done taking data, rotate the transceiver back to its original orientation.
9. Set the laser to **STANDBY,** close the laser aperture, and close the seed valves, but keep everything else running while you check your data (in case you need to go back and get anything else)
10. If you didn't do it as you went along, export all your runs to CSV and verify the data looks reasonable. If it doesn't go back and collect any data points.
11. Sanitize your safety glasses and then assist the TAs in their shutdown procedure if required

## Data to be Taken

1. LDV system settings (burst threshold, band pass filter, downmix frequency, and transceiver orientation), and vertical measurement position for each run.
2. Velocity measurements for each run.

## Data Reduction

1. Show your calculations for fringe spacing in the laboratory report.
2. Show your calculations for the filter settings, i.e., what velocities correspond to your chosen filter settings

## Results Needed For Report

1. Table containing the LDV settings and vertical positions for each run.
2. A plot of the normalized mean axial velocity profile in the jet, $$\overline{U}/U_\infty$$versus location, where $$U_\infty$$is the value of $$\overline{U}$$ in the free stream of the wind tunnel.
3. A plot of the normalized turbulence intensity profiles in the jet, _normalized two ways_: first, $$u_{rms}/U_\infty$$ and second, $$u_{rms}/\overline{U}$$ .
4. A plot of the instantaneous axial velocities at two locations: in the wind tunnel free stream and in the jet shear layer.
5. Histograms of the velocity values recorded at interesting points in the flow (note, the histograms produced by the TSI software may not be helpful – you will probably have to make your own histograms).
6. A comparison between the points taken with different filter, burst threshold and seeder settings.
7. A comparison of the axial and vertical velocities (mean and rms) acquired at the same jet locations.
