AE 3051, Lab #2

PRESSURE MEASUREMENTS AND FLOW VISUALIZATION IN

SUBSONIC WIND TUNNELS

By: Robert Golas

Fall Semester 2012

Abstract

The validity of theoretical surface pressure distribution, wake profiles, boundary layers,

and streamline distribution were tested in this experiment. The surface pressure distribution

coincided with theory and showed that increasing angle of attack increased the coefficient of lift

on the airfoil. The wake profile distribution should show a decreased velocity behind the airfoil

due to induced drag. The experimental data confirmed these expectations. The boundary layer

profile was expected to follow a Blasius distribution showing turbulent flow at the specified

location following the theory of incompressible flow across a flat plate and the experimental data

confirmed this expectation. Streamlines are known to follow the profile of an airfoil at low

angles of attack and then break off once stall is reached and this was also demonstrated

experimentally. There was some uncertainty regarding the pressure measurements during the

experiment. The 95% confidence interval had a range of ±0.615 mph when pressure was

converted to velocity. The recorded data was within 1.8% of the expected data. The greatest

source of error came from an offset static pressure tap which can be corrected simply by

installing more taps at different locations.

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Introduction

For an airfoil immersed in a fluid medium such as air, the mechanical forces are

transmitted at every point on the surface of the body through the pressure experienced by the

airfoil. This pressure is the cause of the aerodynamic forces and is responsible for lift and drag

on the airfoil. At low velocities, Bernoulli’s equation can be used to determine the velocity

distribution, but when a boundary layer is present it becomes more difficult. This experiment was

conducted in order to become more familiar with static and stagnation pressure and therefore

velocity in a subsonic wind tunnel. Surface pressure distribution on a 2-D airfoil was determined

using static taps and Pitot probes. The wake distribution was analyzed using a series of Pitot

probe measurements aft of the airfoil. Boundary layer distribution along a wall was also tested

using a similar technique. Finally, tufts and smoke were used in order to become familiar with

flow visualization around and airfoil.

Experimental Setup

This experiment consisted of three separate individual experiments as well as observations

made using flow visualization techniques. The first experiment looked at surface pressure

distribution along a 2-D airfoil. The airfoil used in this experiment has a NACA 64-212 section.

The chord is 14 inches and it has a thickness ratio of 14%. The two ends of the airfoil are

connected to each wall of the wind tunnel and thus, it behaves like a wing of infinite span. Tufts

are attached to the surface of the airfoil in order to visualize the flow. The airfoil also has a series

of 24 static pressure taps, one at the trailing and leading edge of the airfoil with 11 both the top

and bottom surfaces. These taps are located at midspan and are distributed in the chordwise

direction. Each of these taps is connected via plastic tubing to a pressure transducer. A Pitot-

static probe located upstream of the airfoil is used to measure freestream dynamic pressure. This

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is also connected to the pressure transducer via plastic tubing. There is also a static pressure tap

mounted on the ceiling of the wind tunnel and connected in the same fashion. A Baratron

capacitance transducer is used in order to measure freestream dynamic pressure. A Barocel

capacitance transduced is used to measure the static and stagnation pressures. For the surface

pressure distribution experiment, the 24 surface taps are connected to a Scanivalve which cycles

through the different taps and takes a measurement for each. The Scanivalve and the static

ceiling tap are both connected to the Barocel for the first experiment. A diagram of this setup can

be seen in Figure 1. For the sake of simplicity, only one of the 24 output hoses from the airfoil is

shown being connected to the Scanivalve.

Figure 1: Surface Pressure Distribution Setup Tubing Schematic

Now that everything is properly connected, the wind tunnel is turned on and the computer

data acquisition software is run in order to record the data. The software takes 1000 samples at a

rate of 10,000 samples per second and it calculates the average and root-mean-square (rms) of

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the values and stores the result for a single pressure tap. It then sends a signal to the Scanivalve

telling it move on to the next pressure tap and continues doing so until each of the 24 taps are

measured. This experiment was conducted for a zero degree, nine degree, and fourteen degree

angle of attack.

After the first experiment is finished, the setup must be changed in order to carry out the Pitot

probe experiments. The Scanivalve is disconnected from the Barocel and the Pitot probe is

connected in its place. Everything else remains the same. The tubing schematic for this setup can

be seen in Figure 2.

Figure 2: Pitot Probe Setup Tubing Schematic

Since the Pitot probe was already in the proper position, the wake was surveyed first. The

airfoil was set to an angle of attack of 8 degrees. The data acquisition program was used to

perform the wake survey. The required values of y were all pre-programmed (16 points in all),

starting at a y=0 and extending 3 inches. The program was run at the same rate of 1000 samples

at a rate of 10,000 samples per second. When the data acquisition was complete, the probe was

returned to its initial position and the experiment was conducted again.

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With the wake survey complete, the next step was to manually raise the Pitot probe until it

was as close to the ceiling as possible. This was done by climbing on top of the wind tunnel and

adjusting the location of a mechanical stop on the lead screw/Pitot probe system. This is the

location the computer denoted as “y=0”. The distance remaining distance between the Pitot

probe and the wall was measured and found to be 0.1875 inches. The data acquisition program

was then used to traverse the probe and take data. A total of 16 unique distances from the ceiling

were selected along with two repeat data points. After the probe was been moved to a new

location away from the wall, denoted y, the software allows a short time for the pressure to settle

out to evaluate the Pitot pressure. The same sample rate as the previous two experiments was

used once again. To measure the repeatability of data, 18 measurements were then taken at the

exact same y coordinate. The Pitot-static probe tubing schematic used in all of the experiments

can be seen in Figure 3.

Figure 3: Pitot-static Probe Tubing Schematic

With the pressure experiments complete, the flow visualization experiment was conducted

next. A low velocity (29 ft/s) smoke tunnel with various models was used for the experiment.

Each individual model was mounted in the smoke tunnel, the smoke and lights were turned on,

and then the flow was initiated. During each experiment, a series of observations as well as video

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and picture records were recorded. While the model was in the smoke tunnel, the angle of attack

and flap angle (when applicable) were changed and the resulting effects were noted. The models

used were a cylinder, symmetric airfoil, an airfoil with a flap, a finite 3-D wing, and a 3-D wing

tip. When the observations were complete, the equipment was returned to the off position.

Results and Discussion

Surface Pressure Distribution

In the surface pressure distribution experiment, the data acquisition software recorded the

difference between each static pressure tap (p) and the freestream static pressure (p∞), the

freestream dynamic pressure (q∞), and the coordinate of the tap normalized by the chord length

(x/c). From this data, the coefficient of pressure was found at each point using Equation (1).

C p=p−p∞

q∞ (1)

The data was consolidated and reduced in an excel file. The data acquired was converted into

a coefficient of pressure and the results for each angle of attack at each position can be seen in

Table I.

Table I: Coefficient of Pressure for Varying Angles of Attack at Each Position

Angle of Attack0º 9º 14º

Position x/c Cp Cp Cp

Leading Edge 0 0.89156858 -1.091057573 -2.894288918Upper Surface 0.025 0.255354665 -2.305275413 -2.887781152Upper Surface 0.05 -0.047890065 -1.798722421 -2.3330692Upper Surface 0.1 -0.204723425 -1.303989029 -1.582067918Upper Surface 0.15 -0.276190843 -1.10309008 -1.174306242Upper Surface 0.2 -0.331333539 -0.97356591 -1.0289124Upper Surface 0.3 -0.401964032 -0.841098127 -0.718584716Upper Surface 0.4 -0.465413574 -0.718082441 -0.472608144Upper Surface 0.5 -0.325954611 -0.336665378 -0.216757738Upper Surface 0.6 -0.343333564 -0.335154934 -0.279491582

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Upper Surface 0.7 -0.303731885 -0.150862256 -0.282005915Upper Surface 0.8 -0.030413036 -0.038162716 -0.300218798Upper Surface 0.9 0.106785046 0.126028253 -0.115740588Trailing Edge 1 0.093007838 0.028311497 -0.254812803

Lower Surface 0.898 0.154333788 0.291504851 0.266989246Lower Surface 0.8 0.080322634 0.231565155 0.27140575Lower Surface 0.7 -0.229915594 0.190473956 0.233152488Lower Surface 0.6 -0.262451965 0.1272016 0.201451057Lower Surface 0.5 -0.325402565 0.126740684 0.216769178Lower Surface 0.4 -0.349536181 0.184509941 0.311836892Lower Surface 0.3 -0.398227397 0.265498299 0.477983213Lower Surface 0.2 -0.368058396 0.425897055 0.604986118Lower Surface 0.1 -0.411748988 0.659247232 0.918111403Lower Surface 0.025 -0.56659357 1.129373302 1.188647201

The flow was observed to laminar at zero and nine degrees but the tufts began to separate

from the airfoil at fourteen degrees indicating that there was some boundary layer separation. A

graph of the coefficient of pressure for the zero degree vs. nine degree angle of attack can be

seen in Figure 4. A graph of the coefficient of pressure for the zero degree vs. fourteen degree

angle of attack can be seen in Figure 5.

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

-2.5

-2

-1.5

-1

-0.5

0

0.5

1

1.5

Cp vs. x/c

0 degrees9 degrees

x/c

Cp

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Figure 4: Cp vs. x/c for Zero and Nine Degree Angles of Attack

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

-3.5

-3

-2.5

-2

-1.5

-1

-0.5

0

0.5

1

1.5

Cp vs. x/c

0 degrees14 degrees

x/c

Cp

Figure 5: Cp vs. x/c for Zero and Fourteen Degree Angles of Attack

As expected, the zero degree angle of attack has a coefficient of pressure of approximately

one at the leading edge which is a stagnation point and therefore should be the same as the

freestream dynamic pressure. As indicated by Figure 4 and Figure 5, the location of this

stagnation point should shift toward the trailing edge on the lower surface as the angle of attack

is increased. The coefficient of pressure at the stagnation point is greater than one for both the

nine and fourteen degree angles of attack which does not coincide with theory. This issue will be

addressed in the supplemental questions section. Also as expected, the suction peak increases in

amplitude as the angle of attack is increased. This coincides with a greater negative pressure

associated with the upper surface of the airfoil. The coefficient of lift for an airfoil can be

calculated by finding the area between the curves given by the upper and lower surfaces of the

aircraft which is essentially the integral of the upper surface minus the integral of the lower

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surface from leading edge to trailing edge. Lift curves indicate that the coefficient of lift

increases as angle of attack increases. As shown in Figure 4 and Figure 5, the area between the

curves increases as angle of attacking increases. This coincides with the expected increase in

coefficient of lift.

Wake Profile

When an object is placed in a flowing fluid medium, it is expected that the object will impart

some friction to the fluid as well as disturbing the flow which will cause the flow to lose velocity

directly behind that object. With an airfoil this is equivalent to the drag experienced. There are

skin friction losses and some of the energy used to impart the pressure differential that results in

lift also causes the flow to slow down in the airfoil’s wake. There is also induced drag when a

boundary layer separates from an airfoil known as pressure drag, but that is not the case in this

experiment. The theoretical wake should be similar to what is seen in Figure 6.

Figure 6: Theoretical Wake Profile

Data was obtained using the software for two separate runs. Since both runs are extremely

similar, the data and graphs shown are for the second run only. A comparison of the two runs

will be made in the error analysis section. Since all the data obtained were pressure readings,

they had to be converted to velocities using Equation (2).

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uexperimental=√ ( p−p∞ )∗(T ¿¿room+459.67)0.0159∗Proom

¿ (2)

The values for the room variables used in Equation (2) can found in Table II.

Table II: Ambient Room Values

Parameter Value Unit

Proom 29.26 in. Hg

Troom 72.05 ºF

A corrected value of the velocity also needed to be derived. This corrected value was found

using Equation (3)

ucorrected=uexperimental∗uexp .average

usimultaneous (3)

This value corrected for inconsistencies in the measurement process by multiplying the

experimental velocity by the average experimental velocity and then dividing by the velocity

found by applying Equation (2) to the freestream dynamic pressure that was recorded

simultaneously. The reduced data can be found in Table III. The (q-q∞) value in Equation (2) is

seen in Table III as Mean of DP and the freestream dynamic pressure is seen as Mean of qinf.

Table III: Reduced Wake Data and Corresponding Velocities for Run 2

y (in.) Mean of DPMean of

qinf uexperimental (mph) usimultaneous (mph) ucorrected (mph)0 1.2211 1.0706 37.35780842 34.97996693 38.70902652

0.2 1.2213 1.0794 37.36086765 35.12343495 38.554069430.4 1.1973 1.0686 36.99195348 34.94727842 38.365791280.6 1.1759 1.0805 36.65987419 35.14132727 37.811426570.8 1.1391 1.0581 36.08167588 34.77515963 37.606924841 1.1099 1.0591 35.61620978 34.79158858 37.10425321

1.2 1.0913 1.0654 35.31651592 34.89491311 36.68309621.4 1.0769 1.0682 35.08273665 34.94073704 36.392480261.6 1.0685 1.0743 34.94564319 35.04036028 36.147205561.8 1.0767 1.0761 35.07947875 35.06970322 36.25528256

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2 1.0944 1.0663 35.36664126 34.90964879 36.71965492.2 1.1144 1.0682 35.68833827 34.94073704 37.02069082.4 1.1587 1.0627 36.3907728 34.85066868 37.846909062.6 1.211 1.0795 37.20299009 35.1250619 38.389371472.8 1.223 1.0717 37.38686101 34.99793259 38.719243783 1.2235 1.0611 37.39450268 34.82442323 38.92011215

A graph of both the experimental and corrected velocities vs. the y coordinate can be found in

Figure 7 and Figure 8 respectively.

34.5 35 35.5 36 36.5 37 37.5 380

0.51

1.52

2.53

3.5

uexperimental vs. y

Velocity (mph)

y (in

.)

Figure 7: Experimental Velocity vs. y Coordinate for Run 2

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36 36.5 37 37.5 38 38.5 39 39.50

0.51

1.52

2.53

3.5

ucorrected vs. y

Velocity (mph)

y (in

.)

Figure 8: Experimental Velocity vs. y Coordinate for Run 2

Both Figure 7 and Figure 8 show results that are similar to what is expected in Figure 6.

Directly in the center of the airfoil is the lowest velocity which therefore is the point

experiencing the most drag. As the probe traverses the wake, it goes from the freestream velocity

and slowly decreases velocity until it reaches the point with the most drag and then slowly

increases again until it no longer feels the effect of the airfoil and returns to freestream velocity.

Boundary Layer Profile

The analysis of the boundary layer profile is very similar to the analysis of the wake

profile. Once again, Equation (2) was used in order to determine the velocity at each point,

starting at the ceiling and ending at a point three inches from the ceiling. The same recorded

values in Table II were also used in this part of the analysis. There is a slight initial offset of the

Pitot probe. This offset is due to the fact that at the highest physical point (mechanically limited

by the equipment), the probe was still 0.1875 inches (3/16 of an inch) away from the ceiling. The

rest of the lab group may use a value of 0.3125 inches, but this value was recorded incorrectly in

the lab notes. I still have the piece of paper used to measure this offset distance and upon

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measuring it again, I found the value to be 0.1875 inches. The Pitot probe itself also has an outer

diameter of 0.028 inches. Therefore, the radius to the center of the probe is 0.014 inches. This

yields a total initial offset of 0.2015 inches. The y coordinate was normalized by the y coordinate

of the edge of the boundary layer. This point was determined by finding the y coordinate where

the velocity started to remain at a relatively constant value. The velocity was then normalized by

the corresponding velocity at this selected edge of the boundary layer. The values chosen for this

point as well as the offset information can be found in Table IV.

Table IV: Boundary Layer Edge and Offset Information

δedge 2.8015

uedge 35.50532818initial offset 0.1875

pitot tube radius 0.014

total offset 0.2015

All of the data was compiled into a table. The compiled data for the boundary layer can be

found in Table V. The selected y coordinates can also be seen in Table V. The points selected

represent the inner edge of the boundary layer closest to the ceiling, a few points in the middle to

verify that the shape is correct, and then a cluster of points near the suspected edge of the

boundary layer.

Table V: Boundary Layer Profile Data

y (in.) yactual (in.) yactual/δedge u (mph) u/uedge

0 0.20150.07192575

4 24.49078401 0.687723222

0.1 0.30150.10762091

7 26.08397145 0.732461357

0.2 0.40150.14331608

1 26.76305104 0.7515305220.3 0.5015 0.17901124 27.61221494 0.775375807

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4

0.4 0.60150.21470640

7 28.03326671 0.787199319

1 1.20150.42887738

7 31.32755538 0.879705906

1.2 1.40150.50026771

4 32.24798681 0.9055524471.4 1.6015 0.57165804 33.25990619 0.933968052

1.6 1.80150.64304836

7 33.78495151 0.948711797

1.8 2.00150.71443869

4 34.28196387 0.9626683512 2.2015 0.78582902 34.95872287 0.981672351

2.6 2.8015 1 35.61139602 1

2.7 2.90151.03569516

3 35.59534545 0.999549286

2.8 3.00151.07139032

7 35.73474393 1.003463722.9 3.1015 1.10708549 35.68833827 1.002160607

3 3.20151.14278065

3 35.76032128 1.004181955

0.1 0.30150.10762091

7 26.52713526 0.744905795

3 3.20151.14278065

3 35.90067095 1.0081231

The normalized values from Table V are plotted in Figure 9 with yactual/δedge as the ordinate

and u/uedge as the abscissa. For comparison, a theoretical boundary layer profile is shown in

Figure 10.

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0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 1.050

0.20.40.60.8

11.2

Normalized y Coordinate vs Normalized Velocity

u/uedge

yact

ual/

δedg

e

Figure 9: Experimental Boundary Layer Profile

Figure 10: Theoretical Boundary Layer Profile

As shown Figure 9 and Figure 10, the experimental boundary layer profile closely

coincides with the theoretical boundary layer profile. Figure 9 also shows that the velocities

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above the point chosen at the edge of the boundary layer stay relatively constant as expected. For

the sake of accuracy, the group decided to repeat the boundary layer experiment to verify that the

edge of the boundary layer was at the point selected and the repeated data verified that.

Smoke Tunnel Visualizations

The smoke visualization gave a much better understanding of how a flow reacts to a

model placed in a fluid flow field. Each of the images shown are pictures taken during the

experiment with extra flow lines drawn to better represent what was seen in the lab.

CylinderThe cylinder was the first model analyzed. The flow observed looked like two alternating

sine waves behind the cylinder. A sine wave was produced from the top surface of the cylinder

and then a sine wave was produced from the bottom surface of the cylinder. These two would

continuously oscillate and appeared to have a phase margin of approximately 180 degrees.

Figure 11 shows the two alternating sine waves superimposed on top of each other

Figure 11: Appearance of the Two Superimposed Sine Waves

As shown in Figure 11, there appears to be a sink directly behind the cylinder where there

is boundary layer separation. Figure 12 shows the wake of the cylinder with only one of the sine-

like waves behind the cylinder.16

Figure 12: Downstream Flow around a Cylinder

The group attempted to create an induced lift on the cylinder by rotating the cylinder while in

the flow but physical limitations of the equipment would not allow the cylinder to be rotated fast

enough to generate lift. Theoretically the flow around the cylinder should be completely uniform.

The flow would divert as it reaches the cylinder and then reconvene in parallel streamlines after

it passes the cylinder. This is due to the fact that mathematically there should be a net zero drag

around the cylinder in an ideal inviscid flow. Realistically, the flow is viscous and regardless of

how small the viscosity, the flow will acquire a small vorticity resulting in small boundary layer

as it passes the cylinder. This results in boundary layer separation behind the cylinder due to

induced pressure drag. The lower pressure on the trailing side of the cylinder results in drag

downstream which therefore results in a wake behind the cylinder.

Symmetric Airfoil without FlapThe symmetric airfoil without a flap was the next model analyzed. At approximately zero

angle of attack, the airfoil performed as expected. The flow was laminar and followed the shape

of the airfoil. The shape of the airfoil can be seen in each of the streamlines as the distance from

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the airfoil increases since the flow can essentially “feel” the airfoil. This can be seen in Figure

13.

Figure 13: Laminar Flow around a Symmetric Airfoil

At a small angle of attack, the streamlines can be seen following the profile of the airfoil

creating lift and turning the flow. The initial effects of stall can also be seen at this angle of

attack. This can be seen in Figure 14.

Figure 14: Flow around a Symmetric Airfoil at Small Angle of Attack

Finally, at high angles of attack, full stall can be observed. This is characterized by full

flow separation from the airfoil. A visual representation can be seen in Figure 15.

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Figure 15: Flow Separation and Stall of a Symmetric Airfoil at High Angle of Attack

Airfoil with FlapThe airfoil with a flap model was placed in the smoke tunnel and set at a moderate angle

of attack. In this configuration, the airfoil performed similar to the symmetric airfoil at a small

angle of attack. The flow was relatively laminar and followed the profile of the airfoil which can

be seen in Figure 16.

Figure 16: Airfoil with a Zero Flap Angle at Moderate Angle of Attack

As the flap angle is increased, the flow follows the flap and is turned. Changing the flap

angle essentially increased the camber of the airfoil causing an increase in lift. This also shifts

the lift curve left which therefore decreases the stall angle. At a moderate flap angle as shown in

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Figure 17, the flow begins to turn but it also begins separating more from the airfoil which will

eventually lead to stall.

Figure 17: Airfoil with a Moderate Flap Angle at Moderate Angle of Attack

At a high flap angle of approximately 45 degrees, the airfoil mimics a highly cambered airfoil

which greatly shifts the lift curve left. This shift causes boundary layer separation and therefore

leads to stall. The flow separation can be seen in Figure 18.

Figure 18: Airfoil with a Large Flap Angle at Moderate Angle of Attack

3-D Wing Tip and Finite WingThe 3-D wing tip and finite wing models both displayed tip vortices. When the wing

generates lift, the upper surface has a lower pressure than the lower surface. As the air flows

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from below the wing out and around the tip to the top of the wing in a circular fashion, vortices

are formed which feature a low pressure core. An example of the tip vortex is shown in Figure

19.

Figure 19: Wing Tip Vortex Formation

This vortex formation is exacerbated by higher angles of attack as shown if Figure 20.

Figure 20: Wing Tip Vortex Formation at a High Angle of Attack

The finite wing shows the formation of vortices on each wing tip as well as the

downwash wake caused by the wing. This wake remains for quite a long time and is the source

of wake turbulence. The two vortices will never meet and combine since they are rotating in

opposite directions. The model of the finite wing vortex is referred to as a horseshoe vortex due

to its similar shape. A representation of the horseshoe vortex behind a finite wing can be seen in

Figure 21.

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Figure 21: Horseshoe Vortex behind a Finite Wing at Moderate Angle of Attack

Supplemental Questions

Based on the Blasius Solution for incompressible flow over a flat plate found in

Fundamentals of Aerodynamics, Fourth Edition by John D. Anderson Jr., Equation (4) is the

equation used to find the local Reynolds number.

ℜx=(5.0∗xδ )

2

(4)

In this equation represents the distance from the beginning of the flat plate and δ is the

thickness of the boundary layer. Using δedge from Table IV as the thickness of the boundary layer,

the Reynolds number was calculated over a range of x values as shown in Table VI.

Table VI: Reynolds Numbers for a Range of Flat Plate Lengths

x (in.) x (ft.) Rex

240 20 183477300 25 286683360 30 412823420 35 561898480 40 733907540 45 928851

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Though the length of the flat plate from the start of the wind tunnel to the location of the

Pitot probe was not measured, I estimated the length to be approximately 35 feet if not greater.

From theory, turbulent flow begins to occur with a Reynolds number around 5x105. The length

corresponding to this Reynolds number is 33 feet. Therefore a length greater than this value

indicates turbulent flow and a length less than this value indicates laminar flow. For the

approximated length of the flat plate from the start of the wind tunnel to the Pitot probe, this

equation shows that turbulent flow is occurring at this location. Figure 22 shows a comparison of

turbulent and laminar boundary layers.

Figure 22: Turbulent vs. Laminar Boundary Layers

Accordingly, the experimental data shown in Figure 9 matches that of a turbulent

boundary layer. When performing a curve fit using the data acquisition software, the data points

matched a Blausis boundary layer fit much better than a laminar boundary layer fit as well.

As Equation (4) shows, the Reynolds number with the length of the flat plate. Due to this,

the boundary layer effects increase the further down the wind tunnel the flow gets. This

difference in the boundary layer can cause small changes in the static pressure tap readings

depending on where it is located. If the static pressure tap is not exactly where the experiment is

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taking place, there may be a small difference between the static pressure at the actual location of

the tap and the static pressure at the location of the experiment. The data gathered does indicate

that there is error introduced due to this difference in location. By looking at Figure 4 and Figure

5, it is obvious that the coefficient of pressure for the higher angles of attack reaches a value

greater than one. For incompressible flow, this should be impossible since the maximum static

pressure experienced by the airfoil should be the static pressure of the freestream. Since the static

pressure of the freestream is being recorded at a location other than exactly where the airfoil is

located, there is a discrepancy between the two values which yields a pressure coefficient greater

than one.

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Conclusions

This purpose of this experiment was to become more familiar with static and stagnation

pressure and therefore velocity in a subsonic wind tunnel and to confirm that theoretical flow

matches actual fluid flow. Surface pressure distribution on a 2-D airfoil was measured using

static taps and Pitot probes. The data showed that increasing angle of attack caused an increased

in the pressure differential across the airfoil therefore increasing the lift coefficient. Theory states

that increasing angle of attack will increase lift which was confirmed experimentally. Since the

static freestream pressure tap is not located at the exact same location where the surface pressure

experiment was conducted, some of the pressure coefficients reached values greater than one.

Relocating this pressure tap would more than likely remedy this error. Theory also indicates that

drag in the wake of an airfoil slows the flow of the fluid around it. The wake distribution was

analyzed using a series of Pitot probe measurements aft of the airfoil. The results showed that the

flow velocity indeed slows behind an airfoil due to pressure drag and surface friction drag.

Incompressible flow flat plate theory shows that after a certain distance, the boundary layer

begins to separate from the plate which causes turbulent flow. By traversing the boundary layer

with a Pitot probe, a boundary layer profile was developed which matched a typical Blausis

boundary layer curve. Repeated measurements at a point beyond the boundary layer indicated

that the Pitot probe is both accurate and precise. Aerodynamic theory has also described how a

fluid should flow around a different assortment of models. By using a smoke tunnel and making

careful observations, these theoretical streamlines were also confirmed. By comparing these

different theoretical models with experimental data in this experiment, the theories have been

reinforced and confirmed to be accurate.

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Appendix: Error Analysis

Pressure Error

During any experiment there is bound to be issues with repeatability, accuracy and

precision of the equipment being used. The largest source of error in this series of experiments

was consistency in measuring the pressure in the wind tunnel. These pressure measurements

were also used to calculate the velocities which were therefore also not extremely reliable.

During the boundary layer profile analysis, a data run was completed in which the y coordinate

was held constant at 3.0015 inches and a series of 18 separate measurements were recorded. The

recorded data can be found in Table VII

.

Table VII: Repeated Pressure Measurements at 3.0015 inches

Mean of DP Mean of qinf Velocity (mph)1.1368 1.0837 36.045230531.1137 1.0601 35.677127861.0983 1.0477 35.429601441.1169 1.0603 35.728346731.1127 1.0597 35.661106881.0994 1.0529 35.447339221.1203 1.0631 35.782686461.1218 1.0705 35.806633651.1195 1.0692 35.769908071.1233 1.0723 35.830564831.1071 1.0552 35.571256021.1063 1.062 35.558401651.1068 1.0552 35.566436171.112 1.0591 35.6498879

1.1061 1.0535 35.555187331.1016 1.0538 35.482788181.1109 1.0586 35.632250951.1097 1.0576 35.61300068

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Using this data, a graph of the normal/Gaussian probability distribution was created. That

graph can be seen in Figure 23.

35 35.2 35.4 35.6 35.8 36 36.2 36.40

0.5

1

1.5

2

2.5

3Normal/Gaussian Probability Distribution of Freestream Velocities

Figure 23: Probability Distribution of the Repeated Pressure Measurements

The precise values determined from the distribution are shown in Table VIII

Table VIII: Probability Distribution Values

Mean 35.65598636Sigma 0.153687027

One Sigma Range ±0.30737

Two Sigma Range ±0.61475

When the pressure measurements were originally taken while traversing the boundary

layer, the final two measurements were repeat measurements of points that were already

measured; one was beyond the boundary layer edge and one was at the wall. The measurement at

the wall had a variation of 0.44 while the measurement in the freestream had a variation of 0.14.

These are both well within the 96% confidence range that was expected. As mentioned earlier,

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two runs were completed while surveying the wake profile. The corrected velocity for each run

can be seen on the same graph in Figure 24.

36 36.5 37 37.5 38 38.5 39 39.50

0.5

1

1.5

2

2.5

3

3.5

ucorrected vs. y

run 2run 1

Velocity (mph)

y (in

.)

Figure 24: Wake Profile Comparison of Two Separate Runs

As Figure 24 indicates, both runs were extremely close and never varied outside of the

two sigma range in comparison to each other. Figure 24 also shows, however, that the freestream

velocity is at approximately 39 mph which is 3.5 mph faster than the mean found in the boundary

layer test. While the instruments are definitely precise, there may be accuracy issues associated

with the Pitot probe. The boundary layer data may have some residual turbulent effects that are

still slowing down the flow. This could explain the higher velocity toward the center of the wind

tunnel. There may also be an unaccounted variable affecting the wake data. Since the wind

tunnel velocity is set to 35 mph and the Pitot probe at the boundary layer edge consistently

measured a value around 35.5 mph, something may be increasing the flow velocity in the center

of the tunnel.

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In the supplemental questions section, the problem with the placement of the static

freestream pressure tap was discussed. This is the largest source of error found in the experiment.

The pressure coefficient reached a maximum value of 1.18 which is very far past the theoretical

maximum pressure coefficient of one. These are all measuring errors that can be corrected. The

pressure readings at 0.3 and 0.3 as the x/c coordinate on the airfoil also ran consistently high in

each data run. This may be caused the pressure taps not being completely perpendicular to the

surface of the airfoil or it may just be the effect of an unaccounted for variable in the experiment.

In order to correct these pressure reading errors, there are a few changes that could remedy the

situation. A series of freestream static pressure taps can be installed in the ceiling of the wind

tunnel at various distances from the beginning of the wind tunnel. With this setup, the pressure

tap that corresponds with the location of the experiment can be selected, therefore giving more

accurate data. An experiment similar to the boundary layer test that traverses the entire tunnel

may also provide a more accurate representation the actual flow in the wind tunnel. The fan itself

may also provide some error if the fan blades are not all identical and there is an uneven flow

imparted to the wind tunnel. The voltage controller for the fan also fluctuates throughout the

experiment. Since the wind tunnel was set to 35 mph and the mean velocity was 35.656 mph

there is an uncertainty of 1.87%

29