Aerodynamics Lab 3 - Direct Measurements of Airfoil Lift and Drag

Aerodynamics Lab 3 Direct Measurement of Airfoil Lift and Drag

David Clark Group 1 MAE 449 – Aerospace Laboratory

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 two-component dynamometer. Normalizing the lift and drag forces against the reference area, as well as correcting for some disturbances due to the experiment setup. The lift and drag coefficient calculated using this setup is less accurate than previous methods.

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Contents Abstract .................................................................................................................................................. 2 Introduction and Background................................................................................................................. 4 Introduction........................................................................................................................................ 4 Governing Equations .......................................................................................................................... 4 Similarity ............................................................................................................................................. 5 Boundary Corrections ......................................................................................................................... 5 Equipment and Procedure ..................................................................................................................... 7 Equipment .......................................................................................................................................... 7 Experiment Setup ............................................................................................................................... 7 Basic Procedure .................................................................................................................................. 8 Data, Calculations, and Analysis ............................................................................................................. 8 Raw Data ............................................................................................................................................ 8 Preliminary Calculations ..................................................................................................................... 9 Results .................................................................................................................................................. 13 Discussion and Conclusions .................................................................................................................. 16 References ............................................................................................................................................ 17 Raw Data .............................................................................................................................................. 17

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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 ‫ܥ‬௙ =

‫ܨ‬

1 ቀ2 ߩܸ ଶ ቁ

ோாி

‫ܣ‬ோாி

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 ‫ܴܶߩ = ݌‬ 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 ߤ=

ܾܶ ଴.ହ ܵ 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 1 ‫݌‬଴ = ‫ ݌‬+ ߩܸ ଶ 2 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 ܴ݁ =

ߩܸܿ ߤ

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.

Boundary Corrections The following experiment must consider three different corrections due to the setup of the tunnel section. First, the “squeezing” of the inviscid flow causes the streamlines to flatten and push toward the center of the test section. This effect is referred to as horizontal buoyancy. To correct for this effect, the following expressions can be defined. ∆‫ܦ‬஻ = −

6ℎଶ ݀‫݌‬ Λߪ ߨ ݀‫ݔ‬

Equation 6

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ߪ=

ߨଶ ܿ ଶ ቀ ቁ 48 ℎ

Equation 7

The parameters used in these expressions include •

h, the height of the wind tunnel section

•

Λ, the body shape factor (estimated from empirical charts)

•

dp/dx, the static pressure gradient

•

c, the chord of the foil The second consideration corrects for blockage due to equipment within the wind tunnel itself.

Like the previous correction, simple expressions have been derived to adjust the parameters. ߝ௦௕௪ = Λߪ Equation 8

ߝ௦௕௦ =

0.96ሺܸ‫݈݋‬௦௧௥௨௧ ሻ ଷ

‫ܣ‬௧௨௡௡௘௟ ଶ Equation 9

ߝ௦௕ = ߝ௦௕௪ + ߝ௦௕௦ Equation 10

ߝ௪௕ =

ܿ/ℎ ‫ܥ‬ 4 ௗ௨

Equation 11

Though some parameters have already been defined, the corrections for blockage introduce the following parameters. •

Volstrut, the volume of the strut

•

Atunnel, the cross-sectional area of the tunnel

•

Cdu, the uncorrected drag coefficient

Finally, the last set of expressions corrects for the presence of the floor and ceiling within the wind tunnel. Δߙ௦௖ =

57.3ߪ ൬‫ܥ‬௟௨ + 3‫ܥ‬௠௖ ௨ ൰ 2ߨ ସ Equation 12

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Δ‫ܥ‬௟,௦௖ = −ߪ‫ܥ‬௟௨ Equation 13

1 Δ‫ܥ‬௠௖ ,௦௖ = − Δ‫ܥ‬௟,௦௖ 4 ସ Equation 14

where •

Clu, the uncorrected lift coefficient

•

Cmc/4u, the uncorrected c/4 moment coefficient The use of each correction equation is further explained in the calculation section.

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

•

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

•

Two-component dynamometer (to measure lift and drag forces)

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. The two-component dynamometer can measure the force exerted perpendicular and parallel to the airflow, which represent the lift and drag respectively.

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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 lift and drag at each angle of attack and specified dynamic pressure was recorded.

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 -4 -2 -0.25 2 4 6 8 10 12

Dynamic Pressure 868 868 867 865 866 867 864 868 867

Angle -4 -2 0 2 4 6 8 10 12

Dynamic Pressure 869 868 868 867 868 868 869 867 868

Lift -2.50 -0.65 1.32 2.41 5.77 8.58 9.92 10.90 8.10

Drag -0.51 -0.43 -0.28 -0.35 -0.42 -0.54 -0.63 -0.75 -2.95

Lift 1.35 1.50 3.48 5.83 7.18 8.49 9.23 10.97 8.17

Drag -0.40 -0.38 -0.41 -0.44 -0.50 -0.57 -0.58 -0.77 -2.99

Lift 1.35 1.43 3.03 4.25 5.95 8.43 10.05 10.75 9.30

Drag -0.38 -0.40 -0.40 -0.42 -0.45 -0.56 -0.67 -0.75 -2.35

Data Set 2

Data Set 3 Angle -4 -2 0 2 4 6 8 10 12

Dynamic Pressure 867 868 866 867 867 868 867 867 868 Table 1

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. ߩ=

‫݌‬ 99.1݇ܲܽ ݇݃ = = 1.1660 ଷ ܴܶ 287 ‫ ܬ‬296.15‫ܭ‬ ݉ ݇݃‫ܭ‬ Equation 15

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݇݃ ି଺ ଴.ହ ݇݃ ܾܶ ଴.ହ ൬1.827 × 10 ݉ ‫ ܭ ݏ‬଴.ହ ൰ ሾሺ296.15 ‫ܭ‬ሻ ሿ = = 1.83 × 10ହ ߤ= ܵ 110.4 ‫ܭ‬ ݉‫ݏ‬ 1+ 1+ ܶ 296.15 ‫ܭ‬ Equation 16

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

ሺ250000ሻ ൬1.83 × 10ହ ൬1.1660

݇݃ ൰ ݉‫ݏ‬

݇݃ ൰ ሺ0.1016 × 10ିଶ ݉ሻ ݉ଷ

= 38.57

݉ ‫ݏ‬

Equation 17

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 1 1 ݇݃ ݉ ଶ ‫ݍ‬ஶ = ߩܸ ଶ = ൬1.1660 ଷ ൰ ቀ38.57 ቁ = 867.37 ܲܽ 2 2 ݉ ‫ݏ‬ Equation 18

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

Averaged Data Angle -4 -2 -0.25 0 2 4 6 8 10 12

Lift 0.0667 0.7600 1.3200 3.2550 4.1633 6.3000 8.5000 9.7333 10.8733 8.5233

Drag -0.4300 -0.4033 -0.2800 -0.4050 -0.4033 -0.4567 -0.5567 -0.6267 -0.7567 -2.7633

Table 2

The lift and drag can be used in equation one to determine the lift and drag coefficients. For example, for -4 degrees angle of attack ‫ܥ‬௙ =

‫ܨ‬ 0.0667ܰ = = 0.0025 1 ଶ ݇݃ 1 ݉ ଶ ቀ2 ߩܸ ቁ ‫ܣ‬ோாி ൬ ൬1.660 ଷ ൰ ቀ38.57 ቁ ൰ ሺ0.03064݉ଶ ሻ 2 ‫ݏ‬ ݉ ோாி Equation 19

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‫ܥ‬ௗ =

‫ܨ‬ 0.4300ܰ = = 0.0162 1 ଶ ݇݃ ݉ ଶ 1 ‫ܣ‬ோாி ൬ ൬1.660 ଷ ൰ ቀ38.57 ቁ ൰ ሺ0.03064݉ଶ ሻ ቀ ߩܸ ቁ 2 ‫ݏ‬ 2 ݉ ோாி Equation 20

Below is a table of the lift and drag coefficients. These lift coefficients must be corrected for the three corrections mentioned previously.

Averaged Data Angle -4 -2 -0.25 0 2 4 6 8 10 12

Lift Coefficient 0.0025 0.0286 0.0497 0.1225 0.1567 0.2371 0.3198 0.3662 0.4091 0.3207

Drag Coefficient 0.0162 0.0152 0.0105 0.0152 0.0152 0.0172 0.0209 0.0236 0.0285 0.1040

Table 3

To begin correcting for horizontal buoyancy, the following parameters need to be calculated. ߪ=

ߨ ଶ ܿ ଶ ߨ ଶ 0.1016݉ ଶ ቀ ቁ = ൬ ൰ = 0.0228 48 ℎ 48 0.3048݉ Equation 21

∆‫ܦ‬஻ = −

ܲܽ 6ℎଶ ݀‫݌‬ 6ሺ0.3048݉ሻଶ ሺ0.3ሻሺ0.0228ሻ ൬−120.3 ൰ = 0.1463ܰ Λߪ =− ߨ ߨ ݉ ݀‫ݔ‬ Equation 22

It is important to note Λ is assuming a thickness to chord ratio is 0.3. ߝ௦௕௪ = Λߪ = ሺ0.3ሻሺ0.0228ሻ = 6.853 × 10ିଷ Equation 23

ߝ௦௕௦ =

0.96ሺܸ‫݈݋‬௦௧௥௨௧ ሻ 0.96ሺ5.96 × 10ିହ ݉ଷ ሻ = = 2.021 × 10ିଷ ሺ0.0929݉ଶ ሻଷ/ଶ ‫ܣ‬ଷ/ଶ Equation 24

The volume of the strut and cross-sectional area were known. ߝ௦௕ = ߝ௦௕௪ + ߝ௦௕௦ = 6.853 × 10ିଷ + 2.021 × 10ିଷ = 8.887 × 10ିଷ Equation 25

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The correction parameters εwb, Δαsc, ΔClsc, and ΔCmc/4sc are calculated on the fly for each angle since these expressions utilize the uncorrected lift and drag coefficient, which varies for each angle of attack. For example, for 0 degrees angle of attack ߝ௪௕ =

ܿ/ℎ 0.1016݉/0.3048݉ ሺ−0.0152ሻ = −0.0013 ‫ܥ‬ௗ௨ = 4 4 Equation 26

Δ‫ܥ‬௟,௦௖ = −ሺߪሻሺ‫ܥ‬௟௨ ሻ = −ሺ0.0228ሻሺ0.1225ሻ = −0.0028 Equation 27

1 1 Δ‫ܥ‬௠,௖ ,௦௖ = − Δ‫ܥ‬௟,௦௖ = − ሺ−0.0028ሻ = 0.0007 4 4 ସ Equation 28

To further demonstrate the usage of the correction factors above, the parameters for the zero angle of attack will all be calculated. ܸ = ܸ௨ ሺ1 + ߝ௦௕ + ߝ௪௕ ሻ = 38.56

݉ ݉ ൫1 + ሺ8.874 × 10ିଷ ሻ + ሺ−0.0013 × 10ିଷ ሻ൯ = 38.86 ‫ݏ‬ ‫ݏ‬ Equation 29

‫ݍ = ݍ‬௨ ሺ1 + 2ߝ௦௕ + 2ߝ௪௕ ሻ = 867.37ܲܽ൫1 + 2ሺ8.874 × 10ିଷ ሻ + 2ሺ−0.0013 × 10ିଷ ሻ൯ = 880.87ܲܽ Equation 30

ܴ݁ = ܴ݁௨ ሺ1 + ߝ௦௕ + ߝ௪௕ ሻ = 249947൫1 + ሺ8.874 × 10ିଷ ሻ + ሺ−0.0013 × 10ିଷ ሻ൯ = 251847 Equation 31

ߙ = ߙ௨ +

57.3ߪ 57.3ሺ0.0228ሻ ൬‫ܥ‬௟௨ + 4‫ܥ‬௠,௖ ,௨ ൰ = 0 + ൫0.1225 + 4ሺ0.0007ሻ൯ = 0.03 ‫݀ܽݎ‬ 2ߨ 2ߨ ସ Equation 32

‫ܥ‬ௗ௨ =

ሺ‫ܦ‬௨ − Δ‫ܦ‬஻ ሻ ൫ሺ0.4050ܰሻ − ሺ0.1463ܰሻ൯ = = 0.0208 ሺ867ܲܽሻሺ0.0306݉ଶ ሻ ‫ݍ‬௨ ܵ Equation 33

‫ܥ‬ௗ = ‫ܥ‬ௗ௨ ሺ1 − 3ߝ௦௕ − 2ߝ௪௕ ሻ = 0.0208൫1 − 3ሺ8.874 × 10ିଷ ሻ − 2ሺ−0.0013 × 10ିଷ ሻ൯ = 0.0095 Equation 34

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Results Using the same procedure outlined above, the following table catalogs all the parameters used in calculating the corrected lift and drag coefficient. Correction Calculation Summary Uncorrected Data Experimental Angle of Attack -4 -2 -0.25 0 2 4 6 8 10 12

Average Dynamic Pressure 868.0 868.0 867.0 867.0 866.3 867.0 867.7 866.7 867.3 867.7

Experimental Angle of Attack -4 -2 -0.25 0 2 4 6 8 10 12

ε,wb 0.0013 0.0013 0.0009 0.0013 0.0013 0.0014 0.0017 0.0020 0.0024 0.0087

Experimental Angle of Attack -4 -2 -0.25 0 2 4 6 8 10 12

Corrected Angle of Attack -4.00 -1.99 -0.24 0.03 2.03 4.05 6.07 8.08 10.09 12.07

Reynolds Number Velocity 250091 38.59 250091 38.59 249947 38.56 249947 38.56 249850 38.55 249947 38.56 250043 38.58 249898 38.56 249995 38.57 250043 38.58 Corrected Data / Correction Factors Corrected Dynamic Corrected Reynolds Pressure Number 885.75 252647 885.60 252626 883.91 252384 884.59 252482 883.90 252384 884.87 252523 886.10 252698 885.46 252607 886.84 252806 898.10 254428 Corrected Data / Correction Factors ΔCm,c/4,sc 0.0000 0.0002 0.0003 0.0007 0.0009 0.0014 0.0018 0.0021 0.0023 0.0018

Cl 0.0024 0.0274 0.0476 0.1172 0.1499 0.2268 0.3057 0.3499 0.3906 0.3021

Lift Coefficient 0.0025 0.0286 0.0497 0.1225 0.1567 0.2371 0.3198 0.3662 0.4091 0.3207

Drag Coefficient 0.0162 0.0152 0.0105 0.0152 0.0152 0.0172 0.0209 0.0236 0.0285 0.1040

Corrected Velocity 38.98 38.98 38.94 38.96 38.94 38.96 38.99 38.97 39.01 39.26

ΔCl,sc -0.0001 -0.0007 -0.0011 -0.0028 -0.0036 -0.0054 -0.0073 -0.0084 -0.0093 -0.0073

Cdu 0.0107 0.0097 0.0050 0.0097 0.0097 0.0117 0.0154 0.0181 0.0230 0.0984

Cd 0.0104 0.0094 0.0049 0.0095 0.0094 0.0113 0.0150 0.0175 0.0222 0.0941

Table 4

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Cl versus Angle of Attack

2.5000

Force Measurement Method (Lab 3) Pressure Method (Lab 2)

2.0000

Xfoil Results NACA Data (Re=130000) 1.5000

Naca Data (Re=330000)

Cl

1.0000

0.5000

0.0000 -4.00

-2.00

0.00

2.00

4.00

6.00

8.00

10.00

12.00

-0.5000 Angle of Attack (Degrees) Figure 1

Figure 1 contains the various lift coefficients versus angle of attack for all the methods described previously, as well as the previous lab session.

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0.0400

Cd versus Angle of Attack Force Measurement Method (Lab 3)

0.0350

Xcode Results NACA 0012 (Re=170000)

0.0300

NACA 0012 (Re=330000)

Cd

0.0250

0.0200

0.0150

0.0100

0.0050

0.0000 -4.00

-2.00

0.00

2.00 4.00 Angle of Attack

6.00

8.00

10.00

Figure 2

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L/D versus Angle of Attack 100 Force Measurement Method (Lab 3) Xfoil Results 80

NACA 0012 (Re=170000) NACA 0012 (Re=330000)

60

L/D

40

20

0 -4

-2

0

2

4

6

8

10

-20

-40 Angle of Attack Figure 3

Discussion and Conclusions Comparing the lift coefficient curves plotted in figure 1, the pressure measurement method most closely matches the NACA data. The worst method was the force measurement technique, which was the only method that did not recognize zero lift at a zero angle of attack. The Reynolds number had very little effect on the lift coefficient. The best method for determining the drag coefficient is the force measurement method. As Reynolds number increases, the amount of drag decreases. The accuracy of the computer simulation is dubious. The software would not solve reliably, and several data points were off the charts. The force measurement method should not be the recommended procedure for determining the lift and drag coefficients due to the poor control and lack of repeatability.

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12

References

“Aerodynamics Lab 3 – Direct Measurement of Airfoil Lift and Drag.” Handout

Raw Data Aero Lab 1 Fall 07 p t row u q V

99100 23 1.165950252 1.82773E-05 867.3710308 38.57246947

R= b= S=

287 0.000001458 110.4

T= c= Re= span= Aref

296.15 0.1016 250000 0.3016 0.030643

Data Set 1 Angle -4 -2 0 2 4 6 8 10 12

experimental angle -4 -2 -0.25 2 4 6 8 10 12

experimental q 868 868 867 865 866 867 864 868 867

Lift -0.25 -0.065 0.132 0.241 0.577 0.858 0.992 1.09 0.81

Drag -0.051 -0.043 -0.028 -0.035 -0.042 -0.054 -0.063 -0.075 -0.295

experimental angle -4 -2 0 2 4 6 8 10 12

experimental q 869 868 868 867 868 868 869 867 868

Lift 0.135 0.15 0.348 0.583 0.718 0.849 0.923 1.097 0.817

Drag -0.04 -0.038 -0.041 -0.044 -0.05 -0.057 -0.058 -0.077 -0.299

Data Set 2 Angle -4 -2 0 2 4 6 8 10 12 Data Set 3

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Angle -4 -2 0 2 4 6 8 10 12

experimental angle -4 -2 0 2 4 6 8 10 12

experimental q 867 868 866 867 867 868 867 867 868

Lift 0.135 0.143 0.303 0.425 0.595 0.843 1.005 1.075 0.93

Drag -0.038 -0.04 -0.04 -0.042 -0.045 -0.056 -0.067 -0.075 -0.235

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