Aerodynamics Lab 2

Airfoil Pressure Measurements

David Clark

Group 1

MAE 449 – Aerospace Laboratory

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Abstract

The characterization of lift an airfoil can generate is an important process in the field of

aerodynamics. The following exercise studies a NACA 0012 airfoil with a chord of 4 inches. By varying

the angle of attack at a known Reynolds number, the lift coefficient, Cl, can be determined by using a

series of pressure probes along the body of the foil. The lift coefficient of such an airfoil in flow with a

Reynolds number of 250,000 is 0.939, 0.721, 0.459, and 0 for angles of attack of 10, 7, 4, and 0 degrees

respectively. At the same but negative angles of attach, the lift coefficient is equal but opposite.

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Contents

Abstract .................................................................................................................................................. 2

Introduction and Background ................................................................................................................. 4

Introduction ........................................................................................................................................ 4

Governing Equations .......................................................................................................................... 4

Similarity ............................................................................................................................................. 5

Aerodynamic Coefficients .................................................................................................................. 5

Equipment and Procedure ..................................................................................................................... 6

Equipment .......................................................................................................................................... 6

Experiment Setup ............................................................................................................................... 6

Basic Procedure .................................................................................................................................. 7

Data, Calculations, and Analysis ............................................................................................................. 7

Raw Data ............................................................................................................................................ 7

Preliminary Calculations ..................................................................................................................... 8

Results .................................................................................................................................................... 9

Conclusions ........................................................................................................................................... 13

References ............................................................................................................................................ 13

Raw Data .............................................................................................................................................. 13

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Introduction and Background

Introduction

The following laboratory procedure explores the aerodynamic lift and drag forces experienced by a

NACA 0012 cylinder placed in a uniform free-stream velocity. This will be accomplished using a wind

tunnel and various pressure probes along an airfoil as the subject of study.

When viscous shear stresses act along a body, as they would during all fluid flow, the resultant force

can be expressed as a lift and drag component. The lift component is normal to the airflow, whereas the

drag component is parallel.

To further characterize and communicate these effects, non-dimensional coefficients are utilized.

For example, a simple non-dimensional coefficient can be expressed as

�� = ��1

2 ��� � �� �

Equation 1

where F is either the lift or drag forces, AREF is a specified reference area, ρ is the density of the fluid, and

V is the net velocity experienced by the object.

Governing Equations

To assist in determining the properties of the working fluid, air, several proven governing

equations can be used, including the ideal gas law, Sutherland’s viscosity correlation, and Bernoulli’s

equation. These relationships are valid for steady, incompressible, irrotational flow at nominal

temperatures with negligible body forces.

The ideal gas law can be used to relate the following

� = ���

Equation 2

where p is the pressure of the fluid, R is the universal gas constant (287 J/(kg K)), and T is the

temperature of the gas. This expression establishes the relationship between the three properties of air

that are of interest for use in this experiment.

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Another parameter needed is the viscosity of the working fluid. Sutherland’s viscosity

correlation is readily available for the testing conditions and can be expressed as

� = ���.�

1 + ��

Equation 3

where b is equal to 1.458 x 10-6

(kg)/(m s K^(0.5)) and S is 110.4 K.

Finally, Bernoulli’s equation defines the total stagnation pressure as

�� = � + 12 �

Equation 4

Similarity

Using the previous governing equations, we can use the Reynolds number. The Reynolds

number is important because it allows the results obtained in this laboratory procedure to be scaled to

larger scenarios. The Reynolds number can be expressed as

�� = ���

Equation 5

where c is a characteristic dimension of the body. For a cylinder, this dimension will be the diameter. As

a result, the Reynolds number based on diameter is referenced as ReD.

Aerodynamic Coefficients

Three aerodynamic coefficients are used to explore the lift and drag forces on the test cylinder.

First, the pressure coefficient expresses the difference in local pressure, the pressure at one discrete

point on the cylinder, over the dynamic pressure.

�� = � − ���1

2 ���

Equation 6

The theoretical value for Cp can be calculated as

�� = 1 − 4 !"#180° − '(

Equation 7

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The pressure coefficient can be used in the determination of the 2-D lift coefficient, Cl.

�) = cos#α( . /��)0123 − ��4��2356 �7��

89:;

89:�

Equation 8

Equipment and Procedure

Equipment

The following experiment used the following equipment:

• A wind tunnel with a 1-ft x 1-ft test section

• NACA 0012 airfoil section with a 4-inch chord and an array of 9 pressure taps along its upper

surface

• A transversing mechanism to move the pitot tube to various sections of the test section

• A Pitot-static probe

• Digital pressure transducer

• Data Acquisition (DAQ) Hardware

Experiment Setup

Before beginning, the pressure and temperature of laboratory testing conditions was measured and

recorded. Using equations 2 and 3, the density and viscosity of the air was calculated.

The UAH wind tunnel contains cutouts to allow the NACA airfoil to be mounted inside the test

section. A degree wheel is rigidly attached to airfoil such that the angle at which the foil is aligned in

relation to the fluid flow can easily be adjusted and measured.

The table below lists the distance of each tap, x, from the leading edge of the airfoil.

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Pressure Tap Locations Tap x (mm)

1 4

2 10

3 20

4 30

5 40

6 50

7 60

8 70

9 80

Table 1

Basic Procedure

To ensure the working flow is relatively laminar and within a range acceptable for study, the

procedure initiated flow with a Reynolds number of 250,000. The velocity at which the laboratory air

must be accelerated was determined by solving equation 5 for velocity. First, the density and viscosity of

the air must be calculated using equations 2 and 3 respectively.

Using the DAQ hardware, the difference in pressure between each pressure port and the reference

pitot tube was recorded for -10, -7, -4, 0, 4, 7, and 10 degrees of rotation. The raw data from this step is

included in the data section.

Data, Calculations, and Analysis

Raw Data

The following table catalogs the pressure read by the DAQ hardware for the specified rotations.

Three data sets were taken to ensure integrity.

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Data Set 1 Angle of Attack Tap 1 Tap 2 Tap 3 Tap 4 Tap 5 Tap 6 Tap 7 Tap 8 Tap 9

-10 832 590 370 275 218 176 144 122 104

-7 750 462 260 185 149 124 109 105 110

-4 570 280 107 61 47 40 43 57 79

0 -51 -192 -252 -228 -19 -159 -125 -85 -49

4 -800 -664 -580 -486 -404 -343 -290 -187 -117

7 -1553 -1115 -885 -723 -538 -453 -370 -283 -190

10 -2463 -1354 -1190 -919 -720 -582 -460 -340 -226

Data Set 2 Angle of Attack Tap 1 Tap 2 Tap 3 Tap 4 Tap 5 Tap 6 Tap 7 Tap 8 Tap 9

-10 838 597 374 274 216 173 137 113 91

-7 765 477 269 193 155 128 113 107 110

-4 565 272 101 55 42 36 39 53 76

0 52 -122 -200 -189 -159 -131 -103 -65 -27

4 -850 -699 -607 -505 -422 -361 -297 -197 -128

7 -1538 -1104 -880 -728 -538 -452 -371 -285 -192

10 -2661 -1472 -1233 -953 -750 -600 -475 -350 -234

Data Set 3 Angle of Attack Tap 1 Tap 2 Tap 3 Tap 4 Tap 5 Tap 6 Tap 7 Tap 8 Tap 9

-10 835 594 372 274 216 171 138 112 91

-7 744 454 250 176 142 117 103 100 106

-4 570 277 105 58 45 39 41 54 76

0 54 -120 -200 -188 -158 -130 -102 -65 -27

4 -902 -730 -629 -525 -438 -375 -291 -205 -139

7 -1680 -1200 -944 -707 -570 -478 -389 -296 -198

10 -2525 -1388 -1205 -934 -735 -590 -465 -347 -230

Table 2

Preliminary Calculations

First, the density and viscosity of the air at laboratory conditions was calculated. This can easily be

accomplished using equation 2 and 3.

� = ��� = 98.9=>?

287 A=BC 295.15C

= 1.1675 =BFG

Equation 9

� = ���.�

1 + ��

=H1.458 × 10JK =B

F C�.�M N#295.15 C(�.�O1 + 110.4 C

295.15 C= 2 × 10� =B

F

Equation 10

For a Reynolds number of 250,000, the velocity of the airflow must therefore be

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= �� �� � =

#250000( H2 × 10� =BF M

H1.1675 =BFGM #0.1016 × 10J F(

= 38.42 F

Equation 11

This value is determined using the definition of the Reynolds number where c, the reference length, is

the known value of the chord, 0.1016 meters. For reference, the value for q can be calculated as

Q� = 12 � = 1

2 H1.1675 =BFGM �38.42 F

� = 861.68 >?

Equation 12

All three data sets can be combined by averaging the three records for each angle.

Average Pressure Tap Reading Angle of Attack Tap 1 Tap 2 Tap 3 Tap 4 Tap 5 Tap 6 Tap 7 Tap 8 Tap 9

-10 835 594 372 274 217 173 140 116 95

-7 753 464 260 185 149 123 108 104 109

-4 568 276 104 58 45 38 41 55 77

0 52 -145 -217 -202 -112 -140 -110 -72 -34

4 -851 -698 -605 -505 -421 -360 -293 -196 -128

7 -1590 -1140 -903 -719 -549 -461 -377 -288 -193

10 -2550 -1405 -1209 -935 -735 -591 -467 -346 -230

Table 3

The value recorded by the DAQ represents the difference in pressure from the pressure port on the

airfoil to the pitot probe in the test section away from the foil. Inserting these values into equation 6 will

yield the pressure coefficient on the surface of the cylinder at the specified angle. For example, the

pressure coefficient for tap 1 at 0 degrees angle of attack can be calculated as

��,;,�S2T = ∆�Q�

= 52>? − 861.68>?861.68 >? = −0.031

Equation 13

Results

Using equation 6, the following table catalogs the pressure coefficient for each pressure tap at each

angle of attack.

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Pressure Coefficient Angle of Attack Tap 1 Tap 2 Tap 3 Tap 4 Tap 5 Tap 6 Tap 7 Tap 8 Tap 9

-10 -0.031 -0.311 -0.568 -0.682 -0.749 -0.799 -0.838 -0.866 -0.889

-7 -0.126 -0.461 -0.699 -0.786 -0.827 -0.857 -0.874 -0.879 -0.874

-4 -0.340 -0.679 -0.879 -0.933 -0.948 -0.956 -0.952 -0.937 -0.911

0 -0.939 -1.168 -1.252 -1.234 -1.130 -1.162 -1.128 -1.083 -1.040

4 -1.987 -1.810 -1.703 -1.586 -1.489 -1.417 -1.340 -1.228 -1.149

7 -2.846 -2.323 -2.048 -1.835 -1.637 -1.535 -1.437 -1.334 -1.224

10 -3.959 -2.630 -2.403 -2.085 -1.853 -1.685 -1.542 -1.401 -1.267

Table 4

A plot of Cp and the theoretical Cp over versus angle may better visualize the behavior of the

system.

Figure 1

The negative angle of attacks represent the lower section of the airfoil. Reorganizing table 3 to

accommodate for this fact helps to better understand the results, as well as prepare for calculating Cl.

0.000

0.500

1.000

1.500

2.000

2.500

3.000

3.500

4.000

4.500

1 3 5 7 9

-Cp

Pressure Tap

-Cp Versus Pressure Tap

-10 Degrees

-7 Degrees

-4 Degrees

0 Degrees

4 Degrees

7 Degrees

10 Degrees

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Pressure Coefficient Angle of Attack Tap 1 Tap 2 Tap 3 Tap 4 Tap 5 Tap 6 Tap 7 Tap 8 Tap 9

10 Upper -3.959 -2.630 -2.403 -2.085 -1.853 -1.685 -1.542 -1.401 -1.267

Lower -0.031 -0.311 -0.568 -0.682 -0.749 -0.799 -0.838 -0.866 -0.889

Delta 3.928 2.319 1.835 1.404 1.104 0.887 0.704 0.535 0.378

7 Upper -2.846 -2.323 -2.048 -1.835 -1.637 -1.535 -1.437 -1.334 -1.224

Lower -0.126 -0.461 -0.699 -0.786 -0.827 -0.857 -0.874 -0.879 -0.874

Delta 2.719 1.861 1.349 1.049 0.809 0.678 0.563 0.455 0.350

4 Upper -1.987 -1.810 -1.703 -1.586 -1.489 -1.417 -1.340 -1.228 -1.149

Lower -0.340 -0.679 -0.879 -0.933 -0.948 -0.956 -0.952 -0.937 -0.911

Delta 1.647 1.130 0.824 0.654 0.541 0.462 0.387 0.291 0.238

0 Upper 0.939 1.168 1.252 1.234 1.130 1.162 1.128 1.083 1.040

Lower 0.939 1.168 1.252 1.234 1.130 1.162 1.128 1.083 1.040

Delta 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000

-4 Upper -0.340 -0.679 -0.879 -0.933 -0.948 -0.956 -0.952 -0.937 -0.911

Lower -1.987 -1.810 -1.703 -1.586 -1.489 -1.417 -1.340 -1.228 -1.149

Delta -1.647 -1.130 -0.824 -0.654 -0.541 -0.462 -0.387 -0.291 -0.238

-7 Upper -0.126 -0.461 -0.699 -0.786 -0.827 -0.857 -0.874 -0.879 -0.874

Lower -2.846 -2.323 -2.048 -1.835 -1.637 -1.535 -1.437 -1.334 -1.224

Delta -2.719 -1.861 -1.349 -1.049 -0.809 -0.678 -0.563 -0.455 -0.350

-10 Upper -0.031 -0.311 -0.568 -0.682 -0.749 -0.799 -0.838 -0.866 -0.889

Lower -3.959 -2.630 -2.403 -2.085 -1.853 -1.685 -1.542 -1.401 -1.267

Delta -3.928 -2.319 -1.835 -1.404 -1.104 -0.887 -0.704 -0.535 -0.378

Table 5

The “Delta” row is the difference between low and upper pressure coefficients at the respective

pressure taps, as expressed in equation 8.

Finally, to calculate the pressure coefficient, a final table will be constructed to numerically integrate

each angle of attack’s pressure tap readings. For example, the first trap and lift coefficient for 10

degrees is exemplified below.

VW?�X = #∆��(X + #∆��(XY;2 × Z7�X

+ 7�XY;

Z

Equation 14

VW?�;,;�S2T = 3.928 + 2.3192 × |0.0393 − 0.0984| = 0.18

Equation 15

To numerically integrates the integral of equation 8, Cl can be calculated as.

�) = cos #\( ] VW?�X^

X

Equation 16

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�) = cos#106�B(#0.184 + 0.204 + 0.159 + 0.123 + 0.098 + 0.078 + 0.061 + 0.045( = 0.939

Equation 17

The table below outlines the numerical integration for each angle of attack.

Numerical Integration Table x/c 0.0393 0.0984 0.196 0.295 0.393 0.492 0.590 0.688 0.787

cos(α) trap 1 trap 2 trap 3 trap 4 trap 5 trap 6 trap 7 trap 8 Cl

0.985 0.184 0.204 0.159 0.123 0.098 0.078 0.061 0.045 0.939

0.993 0.135 0.158 0.118 0.091 0.073 0.061 0.050 0.040 0.721

0.998 0.082 0.096 0.073 0.059 0.049 0.042 0.033 0.026 0.459

1.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000

0.998 -0.082 -0.096 -0.073 -0.059 -0.049 -0.042 -0.033 -0.026 -0.459

0.993 -0.135 -0.158 -0.118 -0.091 -0.073 -0.061 -0.050 -0.040 -0.721

0.985 -0.184 -0.204 -0.159 -0.123 -0.098 -0.078 -0.061 -0.045 -0.939

Table 6

Figure 2

-1.500

-1.000

-0.500

0.000

0.500

1.000

1.500

-15 -10 -5 0 5 10 15

Cl

Angle of Attack (Degrees)

Cl vs Angle of Attack

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Conclusions

The lift coefficient of a NACA 0012 airfoil with a chord of 4 inches in flow with a Reynolds number of

250,000 is 0.939, 0.721, 0.459, and 0 for angles of attack of 10, 7, 4, and 0 degrees respectively. At the

same but negative angles of attach, the lift coefficient is equal but opposite.

References

“Aerodynamics Lab 2 – Airfoil Pressure Measurements”. Handout

Raw Data

Aero Lab 1

Fall 07

R= 287

p 98900 b= 1E-06

t 22 S= 110.4 T= 295.15

row 1.1675 c= 0.1016

u 2E-05 Re= 250000

q 861.68

V 38.42

Data Set 1 Angle of Attack Tap 1 Tap 2 Tap 3 Tap 4 Tap 5 Tap 6 Tap 7 Tap 8 Tap 9

-10 832 590 370 275 218 176 144 122 104

-7 750 462 260 185 149 124 109 105 110

-4 570 280 107 61 47 40 43 57 79

0 51 -192 -252 -228 -19 -159 -125 -85 -49

4 -800 -664 -580 -486 -404 -343 -290 -187 -117

7 -1553 -1115 -885 -723 -538 -453 -370 -283 -190

10 -2463 -1354 -1190 -919 -720 -582 -460 -340 -226

Data Set 2 Angle of Attack Tap 1 Tap 2 Tap 3 Tap 4 Tap 5 Tap 6 Tap 7 Tap 8 Tap 9

-10 838 597 374 274 216 173 137 113 91

-7 765 477 269 193 155 128 113 107 110

-4 565 272 101 55 42 36 39 53 76

0 52 -122 -200 -189 -159 -131 -103 -65 -27

4 -850 -699 -607 -505 -422 -361 -297 -197 -128

7 -1538 -1104 -880 -728 -538 -452 -371 -285 -192

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10 -2661 -1472 -1233 -953 -750 -600 -475 -350 -234

Data Set 3 Angle of Attack Tap 1 Tap 2 Tap 3 Tap 4 Tap 5 Tap 6 Tap 7 Tap 8 Tap 9

-10 835 594 372 274 216 171 138 112 91

-7 744 454 250 176 142 117 103 100 106

-4 570 277 105 58 45 39 41 54 76

0 54 -120 -200 -188 -158 -130 -102 -65 -27

4 -902 -730 -629 -525 -438 -375 -291 -205 -139

7 -1680 -1200 -944 -707 -570 -478 -389 -296 -198

10 -2525 -1388 -1205 -934 -735 -590 -465 -347 -230