Lab 1: Introduction to Wind Tunnel Measurements

AME 30333University of Notre Dame

Spring 2017

Converted to TEX and updated by Eric Matlis January 26, 2017

Abstract

The purpose of this report is (1) to calibrate a pressure transducer, (2) to measure the free-stream velocity across the wind-tunnel, and (3) to calculate the drag coefficient on a cylinder incross-flow by measuring the wake deficit.

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1 Introduction and Objectives

This laboratory assignment provides an introduction to many aspects of aerodynamic laboratorywork. These notes are to be considered as supplementary to the lecture notes provided in class.The objectives of this lab are as follows:

1. The first objective is to understand the basic principles of wind tunnel design and measure-ment. This objective will be met through a series of experiments that require use of a smallscale in- draft style tunnel in the Hessert Laboratory. The measurements will include profilesof the free stream velocity in a standard configuration, and repeated traverses of the wakeregion downstream of a cylinder.

2. The second objective is to learn how to make measurements of pressure and velocity. Theexperiments will require the calibration of a pressure transducer, and the traversing of a Pitot-static probe.

3. The third objective will be to learn standard techniques for post-processing and presentingacquired data. Basic statistics and plotting conventions will be reviewed.

These objectives will be met using a series of relatively short experiments. The first will requirethe calibration of a pressure transducer. Most pressure transducers are linear, and the calibrationsimply requires that the voltage output be recorded with a known pressure over the range of thetransducer. The slope of this curve is the calibration constant, often computed in units of inches-of-water per volt.

The second experiment will measure the free-stream velocity across the test section of thetunnel. This is a simple experiment that will introduce you to the traverse system, the use of thetunnel, and the use of a Pitot probe. The results of the data will allow you to confirm the qualityof the tunnel velocity uniformity.

The third experiment will measure the velocity downstream of a cylinder at three locations.This data will be used to calculate the coefficient of drag on the cylinder.

A brief review of the apparatus used in the experiments is described in the following section.Section 3 provides detailed instructions on how to execute the laboratory experiments. Section 4will describe the how these data should be processed, and will provide the information required forthe assignment.

2 Experimental Apparatus

2.1 Wind Tunnel

All four laboratory exercises in this course will make use of a 2x2 subsonic tunnel in the HessertLaboratory. A schematic of the tunnel is shown in Figure 1. This facility is an indraft designthat draws air from the laboratory, through a set of screens, and then through a large contraction.The test section is roughly 24 inches on each side and roughly 6 ft in length. The air from thetest section is delivered to a centrifugal type blower which discharges vertically to the laboratoryatmosphere.

2.2 Pitot-static Probe

A pitot tube is device which is frequently used to measure the time averaged velocity. A basicschematic of a pitot tube is shown in Figure 2. The black lines represent streamlines of the

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2.2 Pitot-static Probe 3

Figure 1: Schematic of the subsonic 2x2 tunnel.

incoming flow. The gray portion of the pitot tube is metal, with two holes drilled through whichact as pressure taps represented by the red and blue portions. There is no air flow through theseholes. The streamline which approaches the blue tube is slowed to a stop, creating a stagnationpoint as shown in the schematic at point B. Thus, the pressure detected by the blue hole is thestagnation pressure. The pressure detected by the red tube is the static pressure of the approachflow.

Figure 2: Basic schematic of a pitot tube.

The information from these two pressure taps can be combined with the Bernoulli equation todetermine the speed of the flow near the location of the pitot tube. The Bernoulli equation repre-sents a momentum balance between any two points along a streamline and creates a relationshipbetween the pressure, velocity, and height at these points. Between points A and B, the Bernoulliequation reduces to

v2A2

+pAρ

=V 2B

2+pBρ

(1)

where v is the velocity at the point, p is the pressure, and ρ is the density; this equation

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2.3 Manometer 4

assumes negligible height differences, which is applicable for a pitot tube. Recalling that point B isa stagnation point, vB must be zero. Thus, if one defines 4 to be the difference in pressure betweenpoints A and B, then the Bernoulli equation can readily be rearranged to yield

v =

√2(pB − pA)

ρ=

√2∆p

ρ(2)

Thus, all that is needed to measure the fluid velocity is the difference in pressure between thetwo pressure taps or the pitot tube and the density of the fluid. The pressure at point B is thestagnation pressure, which is the pressure detected by the blue tap. The pressure at point A is thestatic pressure of the flow and is equivalent to the pressure detected by the red tap. The ideal gaslaw can be used to determine the density of the air, and the difference and pressure between thetwo pressure taps can be found with a pressure transducer.

Pitot tubes have several restrictions that must be observed. First, equation 2 is only validfor situations where the Bernoulli equation remains valid between points A and B. While thisis often true, this loses validity when the fluid velocity has a Mach number of approximately 0.3or higher. Second, an accurate pitot tube requires that point B is indeed the stagnation point.Even if the pitot tube is not perfectly parallel with the flow, this will still remain true, so thepitot tube is relatively insensitive to variations in angle as long as the angle relative to the flow issmall. However, if the pitot tube is extremely misaligned to the flow direction, the blue tube mayno longer be measuring the stagnation pressure and thus the result will be erroneous. Finally, asa pitot tube requires a pressure transducer, any restrictions of the pressure transducer being usedwill also be true for the pitot tube. In particular, this means that the pitot tube will usually havea response time which is too slow for the characteristics of a turbulent flow (usually on the order ofmagnitude of hundreds of Hertz at best). Thus, pitot tubes are usually only used to measure theaverage flow velocity.

2.3 Manometer

In the course of this experiment, a manometer will be used to calibrate the electronic pressuretransducer. A manometer is generally a tube filled with a liquid subjected to a different pressureon each side of the tube; the difference in pressure creates a height difference which can be used tocalculate the pressure difference. Two sample manometers are shown in figure 3.

For either of the manometers shown in Figure 3, the difference in pressure can be calculatedby

Phigh − Plow = ρgh (3)

where Phigh is the higher pressure, Plow is the lower pressure, ρ is the density of the fluid, gis the acceleration due to gravity, and h is the difference in height measured in the direction ofgravity.

Using this equation, assuming the density of the fluid to be known, if the difference in heightcan be measured then the difference in pressure can be calculated. Note that due to the mass of thefluid, the manometer will respond relatively slowly to changes in pressure, and thus manometersare not effective devices for measuring transient data. However, for static cases, the manometerprovides a way of calculating a pressure differential without any difficult calibration.

In this lab, a tilted manometer much like the one seen on the right of Figure 3 will be used inthe calibration of the pressure transducer. The tilted manometer provides the benefit of having ahigher sensitivity along the length of the tube.

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2.4 Pressure Transducer 5

Figure 3: Manometer.

2.4 Pressure Transducer

As mentioned previously, use of a pitot tube requires the difference in pressure between the twotaps of the pitot tube to be measured. To accomplish this, use will be made of the Setra SystemsIncorporated 339H Electronic Manometer. The pressure transducer operates by subjecting eachside of an internal membrane to one of the pressures. The difference in pressure causes a deflectionin the membrane which is converted to a voltage. Therefore, the pressure transducer effectivelyconverts the difference in pressure into a voltage.

2.5 Wake Profiles and Cylinder Drag

In the wake of a cylinder, the flow is often turbulent and the velocity is lower than in the freestream. Figure 4 shows the turbulent wake behind a cylinder and the profile of the velocity deficitin the wake.

This deficit can be viewed as energy lost from the free stream and integrating it across the wakecan give a measure of the total drag force acting on a body. Given the velocity profile components,the velocity deficit (u1) can be written as:

u1 = U∞ − u (4)

Moving away from the wake u converges to U∞. The total drag (D) is found by consideringthe conservation of momentum in a control volume enclosing the cylinder. This is given by:

D = dρ

∫ L

−Lu1(U∞ − u1)dy (5)

Where:

d=width of the cylinderρ=densityL=the distance from the center of the cylinder to the highest point of the measurement region (i.e.control volume) located in the free stream (see Figure 4)

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Figure 4: Turbulent wake and velocity profile behind a cylinder.

u1=velocity in cylinder wakeU∞=free stream velocity (i.e. average velocity of profile taken without a cylinder)

Another way to express the drag force (D) is in terms of the frontal area of the body (A) andthe drag coefficient (Cd).

D = 1/2ρAU2∞Cd (6)

An empirical curve fit for the Cd of a cylinder in cross-flow is:

Cd ' 1 + 10.0Re−2/3 (7)

where Re, the Reynolds number, is:

Re =ρV d

µ(8)

Where:

ρ=densityV=velocityd=cylinder diameterµ=dynamic viscosity.

3 Experimental Procedure

During the course of the lab three separate tests will be conducted. However, before any of thesetests occur some preliminary setup is required.

Before turning on the wind tunnel, check the test section to ensure that there are no loosepieces that could be blown away when the wind tunnel is turned on as these could damage the

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3.1 DAQ Utility 7

motor; in particular, check for tools that have been left in the test section or test pieces that havenot yet been securely fastened. Similarly, never leave tools or unfastened pieces in the test sectionif you are not present in case someone turns on the wind tunnel without properly checking.

3.1 DAQ Utility

Most of computer management of the experiments will be accomplished through a code known asthe DAQ Utility. A picture of the DAQ Utility with various sections labeled is shown in Figure 5.

Figure 5: DAQ Utility.

Each section handles a certain aspect of the interface.

1) Analog In settings

This section of the interface controls the taking of data. In order to take data, the “Enable analogin” checkbox must be checked on (unchecking this box signifies you are not taking data). Thechannels section allows you to list which channels to record data from; for example, to record datafrom channel 0, 1, and 3, you would type in the textbox “0,1,3”. The other textboxes control thesampling frequency and the number of data points taken (i.e. setting Sampling to “100” and No.Samples to “1000” would result in 10 seconds of data).

2) Digital Out settings

This section controls signals which are output from the program. In particular, this is used tocontrol movement within the experiment; for example, in Lab 1, this will be used to change the

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3.1 DAQ Utility 8

vertical location of the pitot tube. The “Enable digital out” checkbox must be checked on to outputa signal; unchecking this box indicates you do not wish any signal to be sent out of the program.This section allows you to control the number of steps done per run and the direction; note thatyou can perform multiple runs in a row with DAQ Utility, so often the number of steps can be setto some common increment for the experiment. Step position shows the current position of what-ever is being controlled relative to the reference position. Below is the ability to set the currentposition as the reference position (i.e. the “Set Zero” button) or to return to the reference posi-tion; this is useful after many runs have been done and you wish to return to your starting position.

3) Execute section

This section actually runs the code. The Repetitions textbox allows you to set how many runs youwish to do in a row. Hitting Run, of course, Runs the program. You can utilize multiple repetitionsif you wish to obtain several sets of data without having to manually run the program multipletimes. An important utility of this as well is if you wish to take data, move the experiment, takedata, move the experiment, etc. multiple times, which will be a common occurrence in the labs.By setting the correct Analog In and Digital Out settings for each step, you can then run as manyrepetitions of this as you want. Note that if You have both “Enable analog in” and “Enable digitalout” selected, the last repetition will not perform a digital out. That is, for example, in Lab 1you will be measuring at 25 different locations; by setting the number of repetitions to 25, youwill measure 25 times but only move 24 times. The Run button changes to a Stop button whilerunning, but note that the code can only stop running in between repetitions of a run.

4) Program Status

Relays information to the user as to what is occurring in the program. Most notably, this listreports to the user the average value of data taken in a run was, which can be useful if all you needis a quick measurement of the average value.

5) Plot Current Data

This section reports the time series for the last repetition of a run. The plot in this section showsa plot of the data series measured. A drop-down box allows the user to look at other parameters,such as the standard deviation of the signal. The Clear Data button simply deletes all data thatthe code has stored (note this does NOT delete data that you have saved). Clicking the “Save.MAT” button will save the last repetition and is a useful way to save data if you are only runningone repetition (you will be prompted for what the file should be named and where it should besaved). On the other hand, if you are looking to perform multiple repetitions of a run, you shouldcheck the “Auto-save time series” checkbox. Checking this will cause the user to be prompted fora location to save the data from the runs as well as the base name. When the program is run withthis checked, the program will save an individual .MAT file for the data from each repetition of theprogram to the folder selected; the files will be named as the base name plus a different number foreach repetition.

6) Plot All Data

This section plots only overall data from the previous runs. For example, if 10 repetitions wererun, this section would plot the mean value for each repetition so that you can see trends in the

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3.2 Experimental Setup 9

mean over time; other parameters than the mean can also be looked at. The “Clear Data” buttonremoves all data stored in the program (once again, saved files are not deleted by this), and the“Save .MAT” button will save all mean values to a file. This method is useful if you wish to recordthe means of the runs but don’t care about the actual time series; for example, in Lab 1, you willuse this feature when calibrating the pitot tube to save the average voltage for various pressures.

3.2 Experimental Setup

Below are the steps which must be completed before the individual tests will be run. Some of thesesteps may have already been completed before you arrive. Ensure all steps have been completed.

• Measure the atmospheric pressure and temperature and record the results.

• Affix the mounting block to the traverse through use of the screws attached to the mountingblock. Place the pitot tube through the hole in the mounting bracket so that the pitot tubeis parallel to the flow and facing the inlet. Tighten the set screws to clamp the pitot tubeinto position.

• There should be a high pressure tube (the stagnation pressure, or total pressure) and alow pressure tube (the static pressure) connected to the pitot tube. In order to allow boththe manometer and the pressure transducer to measure the pitot tube pressure differential,perform the following connections:

1. Connect each of these tubes to a splitter so that the pressures can be sent to two differentmeasuring devices.

2. Connect one of the high pressure tubes to the high pressure end of the manometer.

3. Connect the other high pressure tube to the positive pressure end of pressure transducer(Setra Electronic Manometer).

4. Connect one of the low pressure tubes to the low pressure end of the manometer.

5. Connect the other low pressure tube to the reference pressure end of the pressure trans-ducer. A schematic of the setup is shown in Figure 6.

• Attach the output of the pressure transducer to channel Analog Input 0. Turn on the pressuretransducer.

• The manometer being used in the current experiment is unidirectional, so if the tubing isconnected to the wrong leads it will not be able to measure the pressure differential. Youwill now run a simple test to check if the leads are attached correctly. Check to ensure thatthe wind tunnel is completely sealed and that the motor speed knob is set to zero. Turnon the wind tunnel, and set the motor speed to approximately 25 Hz. If the tubing is setup correctly, the height of the manometer should noticeably change. If the height of themanometer does not change, turn off the wind tunnel, switch the tube connections to themanometer, then try again (remember to set the motor speed to zero hertz before turningoff the motor). Similarly, if the pressure transducer shows a negative voltage at 25 Hz, thenswitch the tubing connections on the pressure transducer.

• Connect the input cables of the stepper motor driver to the first digital output channel.Currently the A/D board has no interface for digital output, so this has already been wiredinto place. Connect the output cables of the stepper motor driver to the stepper motor on the

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3.3 Pressure Transducer Calibration 10

Figure 6: Tubing schematic.

top of the traverse. Figure 7 shows images of both the stepper motor driver and the steppermotor itself. The stepper motor is used to change the height of the pitot tube within thewind tunnel. The stepper motor driver is used to control the stepper motor and acts as anintermediary between the computer and the motor.

Figure 7: Stepper motor driver (left) and stepper motor (right).

This setup of tubing, wiring, and the position of the pitot tube should not be altered duringthe course of the experiment unless you are explicitly told to do so. During the course of the labyou will be saving several time series of pressure transducer data. Because multiple lab sectionswill be performing the same lab, and because each lab section will have slightly different results,you will want to create a folder unique to your lab section. While the data recorded will likely bee-mailed, you should bring some form of portable storage device for the data. File sizes will besmall, it is unlikely that the total file size will be over 10 MB.

3.3 Pressure Transducer Calibration

The goal of this portion of the lab is to calibrate pressure transducer. Perform the following steps:

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3.3 Pressure Transducer Calibration 11

1. Ensure that cylinder is removed from the tunnel.

2. Move pitot to x position = 1 5/8”.

3. Use DAQ Utility to move pitot to y position = 0.

(a) Uncheck “Enable Analog In”

(b) No. Steps = 2000 (moves 0.5”)

(c) Direction either “Pos.” or “Neg.” depending on the current position of the pitot.

(d) Enter an integer value for Repetitions, considering that 1 repetition = 1/2” of movement.

(e) Press “Run” to move the stage.

4. Make sure that inclined monometer is level.

5. Make sure that with flow off, the monometer reads zero.

6. Set up the DAQ Utility to acquire the calibration data:

(a) Check “Enable Analog In”

(b) Channels = 0, Sampling = 1000 Hz, No. Samples = 10000

(c) Uncheck “Enable digital out”

(d) Set Repetitions = 1.

(e) Press “Clear All Data” in Plot 2 if there is any data.

7. Press “Run” to acquire data with flow off.

8. Remove the wooden gate from the test section.

9. Make sure that there are no free objects/unsecured items (screws, etc) left inside the tunnel.

10. Set the tunnel speed and then acquire data:

(a) Press “ENTER”

(b) Press “SHIFT” to move the placeholder to the 1’s or 10’s decimal place.

(c) Press “UP” and “DOWN” until the desired Hz value is reached.

(d) Press “ENTER” to store the tunnel speed.

(e) Press “FWD” to start the tunnel.

(f) Wait a few seconds for the tunnel to steady.

(g) Record the water height on the inclined manometer in your notes.

(h) On the DAQ Utility, press “Run” to acquire the pressure transducer voltage.

(i) After the acquisition has finished, press “STOP” to turn off the tunnel.

11. Repeat step 10 until all tunnel speeds have been acquired (5, 10, 15, 20, 25, 30 Hz).

12. Press “Save .MAT” in Plot 2 in the DAQ Utility. Name the file “pressure cal.mat”.

13. Turn off tunnel by pressing “STOP”.

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3.4 Traverse of Tunnel Freestream 12

3.4 Traverse of Tunnel Freestream

This portion of the experiment will attempt to measure the general velocity profile of the tunnelflow.

1. Move the pitot to x location = 1 5/8”

2. Move the pitot to y location = -6 inches.

(a) Uncheck “Enable Analog In”

(b) No. Steps = 2000 (moves 0.5”)

(c) Direction = “Neg.”

(d) Repetitions = 12

(e) Press “Run” to move the stage.

3. Turn tunnel on to 25 Hz.

4. Acquire a pressure profile

(a) Check “Enable Analog In”

(b) Direction = “Pos.” or “Neg.” depending on current pitot probe location.

(c) Repetitions = 25

(d) Clear existing mean data by clicking ”Clear All Data” in plot 2.

(e) Click “Run” to start the acquisition

(f) When acquisition finishes, click “Save .MAT” in Plot 2. Name the file“tunnel profile pos1.mat”.

5. Turn off tunnel by pressing “STOP”

• NOTE: It is very important that you be careful when selecting up or down. Going the wrongdirection could break the motor if it tries to move outside its operational position or couldbreak the pitot tube if pressured too hard to go through the floor.

3.5 Cylinder Wake Profiles

1. Mount the 2” diameter cylinder in the wind tunnel.

2. Make sure all windows are closed and locked.

3. Make sure there are no free objects/unsecured items left inside the tunnel.

4. Turn on the tunnel to 25 Hz.

5. Repeat steps (4) of the previous section to acquire the cylinder wake profiles at 15 5/8”, 195/8”, 23 5/8”. Name the files “cylinder profile pos1.mat”, “cylinder profile pos2.mat”, and“cylinder profile pos3.mat” respectively.

This is the end of the experiment. Return all materials to the state they were in when youbegan the experiment before leaving the lab.

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4 Data Processing

This section will describe how your data should be processed and plotted. The results should bestapled together with a coversheet. The coversheet should have your name, date, and a list offigures with captions. All commands entered for data processing should be written as a matlabscript file. Include this code at the end of your report.

All figures should be numbered and include a caption. Make sure all axes are labeled properly andreadable.

4.1 Pressure Transducer Calibration

The output from this portion of the experiment should be a time series of voltages from the pressuretransducer with corresponding pressure values in units of inches of water. Average each of thesevoltages to obtain an average voltage for each wind tunnel speed. Plot the results as voltage vs.pressure in units of Pa. The data should be represented by individual points on the graph. Includea linear fit. Include the equation of the line on the plot as well as the standard deviation of the fit(in Pa).

4.2 Traverse of Tunnel Free Stream

You should have a file containing the average voltage value from the Pitot tube as a function oftraverse position for one location for an empty tunnel. Convert these average values into velocityin m/s, and plot the velocity as a function of position in units of mm. The data points should berepresented as points on the graph that are of appropriate size. The dots should be connected byline segments in order to make the figure more readable.

Below the figure provide brief comments on the uniformity of the tunnel and the variability of thedata in the center of the test section.

4.3 Traverse of Cylinder Wake

You should have a file containing the average voltage value from the Pitot tube as a function ofthe traverse position for the three different locations downstream of the cylinder. Convert thesevalues to velocity. Plot the velocity values as a function of position for these three cases plus theundistorted inlet condition.

Below the figure, provide some comments on the data. Be quantitative when possible.

Calculate the drag on the cylinder at each of the three streamwise locations using the two methodsdescribed in Section 2.5 (equations 5 and 6). Discuss and compare the results of each streamwiselocation to the theoretical value obtained from equation 6. Discuss reasons for any difference.

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