The primary objective of this experiment is to familiarize the student with the measurement of static and stagnation pressures, and (indirectly) velocity, in a subsonic wind tunnel. Static taps and stagnation (Pitot) probes will be used to measure pressures on the surface of a 2D airfoil, in the wake region behind the airfoil and in a boundary layer next to the wind tunnel wall.
When a 2D airfoil is placed in a uniform subsonic freestream, the flow velocity near the airfoil is modified and, as evidenced by the Bernoulli equation, so is the local static pressure. The resulting chordwise pressure distribution on the surface of the airfoil may be calculated by various methods using an inviscid fluid model.* At moderate angles of attack, the flow accelerates over the upper surface of the airfoil, the surface static pressure is less than freestream over most of the chord, and the pressure coefficient, which is defined as
*From AE 3030 and Chapter 4 (Fig. 4.25) in Andersen’s Fundamentals of Aerodynamics
along the airfoil upper surface has mostly negative values. Normally, there is a large suction peak (large negative value of ) very near the leading edge on the upper surface, followed by a region of increasing static pressure (adverse pressure gradient) from there to the trailing edge. On the lower surface of the airfoil, there is a stagnation point near the leading edge, where = 1.0, and the flow accelerates thereafter. When the two pressure coefficient distributions are plotted versus chordwise location, (x/c), the area between the two curves is a measure of the normal force coefficient on the airfoil and hence of the airfoil lift coefficient.
As the angle of attack is increased, the suction peak on the upper surface grows larger and the adverse pressure gradient becomes larger as well. At some value of angle of attack, the adverse pressure gradient on the airfoil upper surface becomes strong enough that the boundary layer separates from that surface. At a sufficiently high angle of attack, the oncoming freestream flow perceives a radically modified airfoil shape. The resulting effect is termed airfoil (or wing) stall, and the included area between the upper and lower pressure distribution curves collapses. The presence of stall was evident in the force measurements on the airfoil that were conducted in a previous laboratory.
The airfoil used in this experiment (see Figure 1) has an NACA 64212 section. The chord is 14 inches and it has a thickness ratio of 14%. The airfoil extends from one side wall of the wind tunnel to the other. Therefore, it should behave like a 2D airfoil.
Figure 1. Two-dimensional wing showing pressure tap locations (light colored line at centerline of airfoil), red tufts used to visualize separation and tubing used to connect pressure taps to Scanivalve.
In the flow of a viscous fluid such as air, the flow velocity right at a solid surface is zero; i.e., the fluid can be thought of as adhering to the surface (the no slip condition). Within a small interval above the surface, the flow velocity increases rapidly from zero to a value that is of the order of the freestream velocity. The result is a velocity profile which exhibits a large velocity gradient in the direction normal to the surface. This velocity gradient gives rise to significant shear stresses, and the region within which this takes place is termed a boundary layer. Using boundary layer theory** one may show that the static pressure is constant through the boundary layer in a direction normal to the surface and that the boundary layer is a region of rotational flow so that the stagnation pressure is not constant everywhere. However, the Bernoulli equation may be used locally to find the dynamic pressure distribution within the boundary layer and hence the velocity profile if the flow is incompressible.
**See your textbook from AE 2010 and 3030. It would be helpful if you review this material before coming to the lab if you do not know what the velocity profile in the boundary layer looks like.
In the case of viscous flow over an airfoil at a moderate angle of attack, the attached boundary layers on the upper and lower surfaces join at the trailing edge. The resulting viscous-dominated flow region downstream of the trailing edge is termed a wake, within which there is a velocity deficit compared to the freestream. This deficit is a result of the flow being retarded in the airfoil boundary layers.
The surface pressure distribution on an airfoil will be measured by means of 24 static pressure taps. These are small holes on the surface of the model that are connected to stainless steel tubes within the model and thence to plastic tubing, which are ultimately connected to a pressure transducer. The pressure taps on the airfoil are located on the upper and lower surfaces in the chordwise direction at mid-span, according to the following chord-normalized horizontal positions:
Table 1: "Tap map" showing the chord-normalized positions of each airfoil static tap
The local velocity in the boundary layer on the ceiling of the wind tunnel and in the wake behind the airfoil will be measured indirectly by traversing a Pitot* tube through the region so as to measure local stagnation pressure; the velocity follows directly because the flow is incompressible. Since the static pressure is constant throughout the ceiling boundary layer, a single static tap on the ceiling (ideally at the measurement station) will yield the local static pressure anywhere in the boundary layer at that station. In the wake region, the local static pressure will be approximately constant through the wake and will be equal to the freestream static pressure. This is because the wake measurement station is located sufficiently far downstream of the airfoil that the pressure disturbance due to the airfoil is negligible.
*Named after its inventor, Henri Pitot (1695-1771), a French hydraulic engineer.
The end of the Pitot probe is made of thin stainless steel tubing with a 0.063 inch outer diameter (OD) and a small orifice, so that the Pitot pressure data is a local measurement compared to most other dimensions. Generally Pitot probes such as ours may be oriented a few degrees (say 5-10 degrees) away from the local flow direction without any appreciable change in the measured pressure, hence a precise alignment of the probe with the local flow direction is not required. A Pitot-static probe (a Pitot tube with a downstream static pressure tap oriented normal to the stagnation hole) located upstream of the airfoil will be used to measure freestream dynamic pressure.
We can categorize this type of pressure transducer by the way the deformation of the structural element is transformed into an electrical signal. The two most common approaches are strain gage and capacitance type transducers. A strain gage pressure transducer consists of a thin circular diaphragm on the bottom of which are bonded tiny strain gages wired as a Wheatstone bridge. When the diaphragm experiences a pressure on its exposed upper surface that is different from the pressure in a small cavity under the diaphragm it deflects, and the resulting bridge imbalance is a measure of the deflection. Calibration provides the constant of proportionality between bridge imbalance (interpreted as a voltage) and applied pressure. The voltage output of this type of transducer is usually in the millivolt (mV) range and requires amplification prior to measurement. Relatively inexpensive transducers can be made by using semiconductor materials. In this case, the semiconductor resistors are “written” as a bridge circuit directly onto a substrate (e.g., silicon) that acts as the diaphragm. The strain on the semiconductor results in a change in semiconductor resistance; this is known as the piezoresistive effect. The change in semiconductor resistance is analogous to the change in metal resistors, except in for metal resistors, the change in resistance is primarily due to the change in the resistor’s cross-sectional area as it is strained. For semiconductor materials, the resistance change is related to other changes in the internal structure of the semiconductor.
The capacitance-based pressure transducer has a stretched membrane clamped between two insulating discs, which also support capacitive electrodes. A difference in pressure across the diaphragm causes it to deflect, increasing one capacitor and decreasing the other. These capacitors are connected to an electrical, alternating-current (AC) bridge circuit, producing a high level of voltage output (usually 10 Volts full scale without amplification).
Strain gage transducers can be made small, hence they can be internally mounted in a wind tunnel model. Also, they have reasonably good frequency response because of the small mass of the diaphragm and the short distance between the pressure tap and the diaphragm face. Capacitance transducers usually are not well suited for internal mounting (too large) and such systems do not have a fast response. Both types of transducers can be calibrated using a primary pressure standard such as a dead-weight tester, which supplies a pressure of precisely known magnitude, or using another (already) calibrated pressure transducer. In this lab, you will use both capacitance type and semi-conductor strain gage transducers to measure pressure.
Whereas all previous measuring devices measure only wind tunnel and/or test article pressures, the FlowKinetics 3DP1A device also measures local ambient pressure and temperature, enabling air density and thus flow speed to be calculated. As shown in Figure 5, the FlowKinetics has a selector dial for choosing the display of either pressure or velocity (with multiple options for units on each). The FlowKinetics is an independent reference in that it does not output any signals that are read during the lab; we will be using it only for a sanity check on flow speed magnitude and for the ambient pressure and temperature measurements.
A wind tunnel is a duct or pipe through which air is drawn or blown.* The Wright brothers designed and built a wind tunnel in 1901. The basic principle upon which the wind tunnel is based is that the forces on an airplane moving through air at a particular speed are the same as the forces on a fixed airplane with air moving past it at the same speed. Of course, the model in the wind tunnel is usually smaller than (but geometrically similar to) the full size device, so that it is necessary to know and apply the scaling laws in order to interpret the wind tunnel data in terms of a full scale vehicle. The wind tunnel used in these experiments is of the open-return type (Figure 6). Air is drawn from the room into a large settling chamber (1) fitted with a honeycomb and several screens. The honeycomb is there to remove swirl imparted to the air by the fan. The screens break down large eddies in the flow and smooth the flow before it enters the test section. Following the settling chamber, the air accelerates through a contraction cone (2) where the area reduces (continuity requires that the velocity increase). The test (working) section (3) is of constant area (42" × 40"). The test section is fitted with one movable side wall so that small adjustments may be made to the area in order to account for boundary layer growth, thus keeping the streamwise velocity and static pressure distributions constant. The air exhausts into the room and recirculates. The maximum velocity of this wind tunnel is ~35 mph, and the turbulent fluctuations in the freestream are typically less than 0.5% of the freestream velocity. Thus, it is termed a “low turbulence wind tunnel.”
*Anderson, p. 123
This lab is broken down into 2 major parts:
Surface pressure distribution measurement
Wind tunnel boundary layer pitot traverse survey
In all experiments during this lab, the wind tunnel should be set to maximum "throttle", which should result in a wind speed of around 16 m/s (about 35.5 mph). This may vary based on the day
The TAs will first give you a brief tour of the low turbulence wind tunnel and the associated equipment, paying particular attention to that outlined in the Background section above. Once complete, you will need to perform the following items:
In this first part of the lab, the primary goals are: (1) to get an intuitive feel of what is happening with the airfoil with the wind on at a variety of angles of attack, and (2) to directly measure the pressure distribution over the airfoil.
Configure the Scanivalve software
Go to D:\AE3610\<Semester Year>\Subsonic\ScanivalveDSALink (Real Time Scanner View) and open Instance 1 of the Scanivalve executable, setting the IP address to 192.168.1.72 (the top scanner)
Go to D:\AE3610\<Semester Year>\Subsonic\ScanivalveDSALink (Real Time Scanner View) and open Instance 2 of the Scanivalve executable, setting the IP address to 192.168.1.73 (the bottom scanner).
If either scanner won't connect, make sure all cables are properly seated and the network switch connecting the scanners is turned on
For each software instance, make sure the Scan Settings are set as per the list below (for now we will have averaging of 1 to have the fastest response with no smoothing to hide anything)
Period: 1000 microseconds
Average: 1
Frames Per Scan: 1000000 (arbitrarily high to prevent scan ending too quickly)
Conversion Units: mmHg
Units: Engineering Units
Time Stamp: No Time Stamp
Zero Correct: ON
SCAN trigger: Internal
Click CALZ in each software instance to zero-calibrate each scanner
Click Scan to start the scan, ensuring the sensors do indeed look zeroed
Following the wind tunnel operating procedure and with the help of the TAs, power on the wind tunnel to full speed
Take turns varying the airfoil's angle of attack, paying particular attention to the scanner readings throughout, as well as how the airfoil feels in your grip across its range of motion. Be sure to look for, and beyond, the stall angle of attack
Once everyone has finished, have everyone return to the control room and turn off the tunnel
Now having some insight into the angles of interest, decide amongst your group a minimum of six angles of interest at which you will log data. They must include:
Negative angle of attack (AoA)
Zero degrees AoA
Low AoA below critical angle
High AoA below critical angle
Critical AoA: the angle of attack at which lift is greatest
One Angle in the Stall Region: past critical AoA
Make sure the airfoil is at zero degrees angle of attack
For each software instance:
Stop the scan
Change the Averaging level in Scan Settings to 100 (this will give some low-pass filtering and smaller log file sizes at the expense of speed of response)
Gather pressure data at your six angles of choice:
!!! Thoroughly read all the sub-steps in this step so you understand what is about to happen !!!
Select one member of your group to be the designated "Angle of Attack Adjuster" for the wing
Hit CALZ
Click Start Data File, navigate to your group's save folder, and come up with a meaningful name for each scanner so you remember for the data reduction which was which
Create your groups save folder in the following location:
D:\AE3610Data\<Semester Year>\<Section>
Once you are comfortable with the sequence, click Scan to begin recording data to the log file and wait 10 seconds to gather some data at wind-off condition
Power on the wind tunnel to maximum speed
Once the wind tunnel is up to speed, wait around 10 seconds for the zero angle of attack condition to log some data
Cycle through your target angles of attack. For each target AoA, make sure the actual angle is recorded from the markings on the Angle Finder (it may differ slightly from the planned angle you selected), and that the adjuster doesn't disturb the airfoil for around 10 seconds to ensure good data
Once all target AoAs have been visited, return the wing to 0 degrees AoA. Wait 10 seconds, and turn off the tunnel. Wait for the fan to come to a complete stop
Click Stop and Close Data File on both Scanivalve instances
Ensure the data saved correctly by opening the saved data files from both instances. Plot at least one of the valid pressure tap columns*. You should see a trajectory starting and ending in zero mmHg, with a ramp up/down as the fan accelerates/decelerates, and multiple plateaus representing the points at which you stopped to log. If the data hasn't saved correctly, or the plateaus are not pronounced enough, re-attempt this procedure from the beginning. You may have a TA help ensure your data is acceptable
Rename your data files to include the actual angles of attack at which you took data
Close both Scanivalve Instances
*Each spreadsheet output by the Scanivalve software has 33 columns:
Column 1 = Data Index
Columns 2-17 = Pressure at each of the DSA's ports (whatever unit you used during Scanivalve logging - should have been mmHg)
Columns 18-33 = Temperature at each of the DSA's ports (degC). Note that all scanner port pressures are recorded, so you should ignore any ports that are not used by this lab.
To control the traverse and acquire data, we use a LabView VI, shown below in Figure 7. The main display on the VI is the large graph in the center, which shows airspeed derived from the Baratron.
Open the SubsonicWindTunnel Application VI found in D:\AE3610\<Semester Year>\SubsonicWindTunnel
Choose the correct file location D:\AE3610Data\<Semester Year>\<Section> and give it an arbitrary filename (this file will not be saved).
Click "END TEST"
Under Traverse Position in the VI, select the VISA Resource Name dropdown and Select COM4. If COM4 is not available, ensure the peripherals are plugged in. Select the Visa Resource Name dropdown and click Refresh. Then select the dropdown again and select COM4.
Start the VI again by pressing the Run button (white arrow on the top left of the window) and choose the correct file location D:\AE3610Data\<Semester Year>\<Section> and give it a sensible filename (this file will be saved).
Input ambient pressure and temperature from FlowKinetics into the Air Density Calculation part of the VI, which should yield a realistic air density (note that the graph will not input until this is done, otherwise it will be trying (unsuccessfully) to plot NaNs)
Zero the Baratron voltage by clicking Tare on the VI. Make sure you do this with the wind tunnel off, and check that the airspeed reading is centered around 0 m/s. If not, hit Tare again.
Take a screenshot of the VI (like below, but with values populated) to remember your settings and have the image as a reference for future use.
If the traverse ever hits a physical limit, always immediately hit the E-Stop paddle to prevent damage and/or injury. The stepper cannot move without power, even if the Arduino continues to send pulses to it.
If the traverse hits a limit it will typically make a grinding noise so keep an ear out for that happening. You will also possibly see the Arduino Motion Status reporting something different from what you see. In either case, initiate the E-Stop procedure and re-initialize.
Since the Arduino and stepper motor are not synchronized (that is to say there is no feedback of the actual stepper position, only a running tally of the number of pulses sent to it which translates to linear position), it is crucial to initially synchronize the two. To do this, the Arduino commands the stepper downwards until it hits the bottom limit switch, at which point it moves slightly up to de-activate the switch and sets its current position to home.
Initial power on and zero:
Check the position of the traverse carriage. If it is clear of the bottom limit switch, no action is necessary.
If it is touching the limit switch, have a TA turn off power to the stepper motor using the E-STOP and manually twist the aluminum shaft coupler until the carriage is clear of the bottom limit switch. Turn the power back on once the carriage is clear by pressing the GREEN E-STOP button.
Have a TA power cycle the Arduino by pressing its reset button (top-most of the two small black buttons on the circuit board). Alternatively, you can unplug it from the USB hub under the wind tunnel and plug it back in.
Press the GREEN E-STOP button if you have not already done so.
Prep the LabView VI for serial communications with the Arduino:
Stop the VI running if it isn't already stopped by clicking "END TEST"
Under Traverse Position in the VI, select the VISA Resource Name dropdown and click Refresh. Select the correct device in the list (COM4) and run the VI. Ensure you are in your group save folder and select an arbitrary file name. Successful communication is known to have occurred if the Arduino Motion Status and Arduino Time start outputting legible values.
As of 8/24/2023 the correct device is COM4.
Note that the VI only polls the VISA Resource Name once on initialization... changing the dropdown mid-experiment will not change anything. To make changes, you must stop the VI, change the dropdown, and then re-initialize the VI.
Occasionally, nothing can be done within the VI to get the serial communication going. In this event, fully shut down LabView (including the shortcut window that comes up when you close the VI) and open up the VI again, whilst simultaneously having a TA power cycle the Arduino.
Click "Go Home" - the traverse will move down slowly until it hits the bottom limit switch, then goes up a couple of millimeters before setting this position as Home.
Re-synchronization procedure - If at any point the Arduino and stepper motor become unsynchronized, repeat the procedure outlined in Step 1 above.
Traverse reset procedure - Since there is no software stop command in the LabView VI, and the traverse sequence takes a good period of time, you can reset the traverse by pressing the Arduino's hardware reset button (top-most button of the two small black buttons on the circuit board) or power cycling it by unplugging and re-plugging the USB. You may also want to restart the VI to get a new, clean, log file.
For the following three tests, if the Labview VI Application starts lagging suddenly and/or if the plotting becomes discontinuous, restart the VI. Do this by ending the test, closing the entire application, and restarting the program. Do this ONLY IF TIME PENDING!!
Prep the probe for the boundary layer survey:
Run the VI and select an arbitrary file name in your group's data save folder
Click on "Go Home"
Have a TA install a plug over the wake stagnation hole if it is not already there
Re-zero the Baratron in the VI
Following the wind tunnel operating procedure, turn on the wind tunnel and set it to maximum speed
Once the wind tunnel is at maximum speed, click Initiate Boundary Layer Traverse at which point the hard-coded survey sequence will commence as follows:
Return home
Set Motion Status to LOGGING for "X" seconds
Note: The LabView VI will automatically log when it sees the Motion Status LOGGING flag
Traverse "Y" inches to the next logging position, during which time the Motion Status will read RUNNING
Repeat until the final position is logged
Return home
After the probe returns Home, stop the VI and power down the wind tunnel
Open the log file in Notepad, copy and paste its contents into a new MS Excel spreadsheet, and save the file with a meaningful file name into your groups data folder
Make a quick plot to sanity check the data is all there, if not you will need to re-run the experiment. The file format is as follows: Column 1 = Time (s), Column 2 = Traverse Position (inches), Column 3 = Baratron Output (Volts).
Note (As of 1/16/2024): --The boundary layer stagnation probe is positioned just outside the sidewall of the tunnel at the start of the boundary layer survey. It traverses sideways 4 inches during the test.
Once you have verified all data has been successfully acquired:
Follow the wind tunnel operating procedure to power down the tunnel
Unplug both power cables in the control room; peripherals and e-stop
Close the VI without saving
Have your TA upload your data files from the Wind Tunnel PC to Canvas
Make a tubing schematic of all the probes/taps/instruments in the experiment. Peruse the "Results Needed for Report" section below to see what exact information is expected for your schematics. You may run your schematic by the TAs to ensure it is correct.
Be VERY CAREFUL not to pull the tubes out of the ports!!
A tubing schematic showing how the pitot-static probe, the ceiling static tap, and the traverse probe are connected to the Baratron, FlowKinetics, and the Scanivalves
A diagram or table documenting the Scanivalve port numbers and pressure tap labels
Two CSV files, one per Scanivalve instance, containing the surface pressure of the wing at a minimum of 6 different angle of attacks
A screenshot of the LabView VI containing the ambient temperature and pressure conditions you obtained from FlowKinetics
A LabView log file and corresponding excel spreadsheet containing the boundary layer traverse data
Boundary Layer Survey
Convert the recorded Baratron voltage into wind speed (u) using the Baratron pressure scaling factor, the Bernoulli Equation, and the ambient atmospheric conditions recorded in the LabView VI
δ is defined as the height above the wind tunnel floor where the velocity becomes essentially the same as freestream velocity (>99%)
Make a tubing schematic figure showing all connections necessary for the measurement of (a) the airfoil static pressures and (b) the boundary layer velocity profile. Indicate what each tube is connected to at both of its ends and label each tube as to what pressure it contains. Note: you only need one figure since the tubing setup does not change during this experiment.
A screenshot of the LabView VI containing information about the ambient temperature, pressure, and calculated density.
On one figure, plot the pressure distribution at zero angle of attack as a standard and also plot the pressure distribution at the negative AoA, low AoA, and high (before critical angle) AoA for which you recorded data.
On a second figure, plot the pressure distribution at zero angle of attack as a standard and also plot the pressure distribution at the high (before critical angle) AoA, critical AoA, and stall AoA
Plot data points only; do NOT draw lines or smooth curves between them. Furthermore, average the multiple data points recorded for each static port so you are plotting one point for each static port at a given angle of attack.
On all plots, make sure to plot the lower and upper surface data on the same figure! You should have a total of 2 figures.
A pressure transducer is a device that converts a pressure to a quantity that may be readily measured. For example, a traditional U-tube manometer is a pressure transducer, where pressure difference is interpreted as the height of a column of liquid. This is an example of devices known as gravitational transducers. Modern electronic transducers, which convert pressure into a voltage that may be easily measured by means of a digital voltmeter or an analog-to-digital converter (ADC), are typically elastic transducers. The most common types of electronic pressure transducers use the deformation of a diaphragm or similar structural element to sense pressure.
A common pressure transducer for rapidly changing conditions, based on the piezoelectric effect, will be introduced in later labs.
The Baratron, shown in Figure 2, is a capacitance-based transducer (of a specific brand name) to measure freestream dynamic pressure. For this device, the differential pressure ΔP is related to the transducer voltage V by the relation , where R is the responsivity of the transducer, which for our Baratron is 1.016 mmHg/Volt (1 mmHg is essentially equivalent to 1 Torr). Thus, in order to measure ΔP, we need only measure a simple analog voltage which can be done via a multimeter, DAQ device, or similar. At its maximum sensing range of 10 Torr, our Baratron will output roughly 10V, but other sensing ranges are available for purchase.
The Scanivalve Digital Sensor Array is a bank of piezoresistive pressure transducers you will use to simultaneously measure the 24 pressures on the airfoil surface. The Scanivalve system (Model DSA 3217/16PX) is composed of two units (see Figure 4), each having 16 differential pressure transducers with a maximum pressure range of 0.18 psi (or 5” ). The reference pressure for the Scanivalve array comes from a static pressure tap in the wind tunnel ceiling. The average linearity error for the pressure transducers, as determined by the manufacturer, is ±0.03% of full-scale. Each unit has its own analog-to-digital converter and controller that converts the measured voltages into pressures based on a stored set of calibrations. The units are connected to our data acquisition computer via ethernet.
The Pitot probe is clamped onto a traveling nut that moves along a lead screw mounted vertically underneath the wind tunnel test section (see Figure 5). The lead screw is driven by a stepper motor, which is a pulsed direct current (DC) motor capable of shaft rotation in either direction, with a known holding torque and number of steps per revolution. Every time a 5V pulse is received by the stepper motor driver, it commands the stepper to move one step, thus a sequence of pulses can be sent to achieve different types of motion. In our case, an Arduino is used to generate this pulse sequence and is hard-coded to repetitively extend the traverse a set distance before waiting for a period of time to allow data gathering. Since we are commanding rotary motion to achieve linear motion, we need to know the mapping. This is a property of the lead screw called "pitch", expressed in threads (or revolutions) per unit length, and is known from the manufacturer or by directly measuring the threads. Between the number of steps per revolution of the stepper, SPR (steps per revolution), and the pitch of the lead screw, TPD (threads per unit distance), the number of steps, S, required to traverse a desired distance, D, is thus given by . The AE3610 traverse (as of Fall 2021) has a SPR of 400 and a TPD of 5 threads per inch. Thus, to travel a quarter of an inch, we would require the transmission of 500 steps/pulses by the Arduino.
Surface Pressure Distribution - Convert the measured pressure differences and free stream dynamic pressures to local (pressure coefficients). The log file format is defined in the procedure above.
From the result, select a value of δ and
is defined as the flow velocity at δ
Calculate the non-dimensional quantities and , where y is the vertical distance from the floor of the wind tunnel, and u is the flow velocity at y
Plot figures showing the chord-wise pressure coefficient distribution () on the airfoil vs. non-dimensional chordwise position, x/c, where c is the airfoil chord length. The standard in aerodynamics format is to plot as the ordinate with negative upward, and x/c as the abscissa.
Plot a figure showing the shape of the non-dimensional boundary layer profile. Plot as the ordinate vs. as the abscissa. Again, plot data points only (not connected with curves) and make sure you plot only one averaged point per traverse position.
Upper Tap Label
x/c
Lower Tap Label
x/c
LE
0
L1
0.025
U1
0.025
L2
0.1
U2
0.05
L3
0.2
U3
0.1
L4
0.3
U4
0.15
L5
0.4
U5
0.2
L6
0.5
U6
0.3
L7
0.6
U7
0.4
L8
0.7
U8
0.5 (DEAD)
L9
0.8
U9
0.6
L10
0.898
U10
0.7
TE
1
U11
0.8
U12
0.9
