Measurement of Pressure Distribution, Drag, Lift , and Velocity for an Airfoil
Aerodynamics Lab 3 - Direct Measurements of Airfoil Lift and Drag
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Transcript of 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
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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
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
�� = ��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.
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.
∆�� = − 6ℎ
" Λ$ %�%&
Equation 6
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$ = "
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.
)*+, = Λ$
Equation 8
)*+* = 0.96/01*23425�246678
9
Equation 9
)*+ = )*+, + )*+*
Equation 10
),+ = �/ℎ4 �;4
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.
Δ=*> = 57.3$2" B�84 + 3�C>
D4E
Equation 12
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Δ�8,*> = −$�84
Equation 13
Δ�C>D,*> = − 1
4 Δ�8,*>
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 Dynamic Pressure Lift Drag
-4 868 -2.50 -0.51
-2 868 -0.65 -0.43
-0.25 867 1.32 -0.28
2 865 2.41 -0.35
4 866 5.77 -0.42
6 867 8.58 -0.54
8 864 9.92 -0.63
10 868 10.90 -0.75
12 867 8.10 -2.95
Data Set 2 Angle Dynamic Pressure Lift Drag
-4 869 1.35 -0.40
-2 868 1.50 -0.38
0 868 3.48 -0.41
2 867 5.83 -0.44
4 868 7.18 -0.50
6 868 8.49 -0.57
8 869 9.23 -0.58
10 867 10.97 -0.77
12 868 8.17 -2.99
Data Set 3 Angle Dynamic Pressure Lift Drag
-4 867 1.35 -0.38
-2 868 1.43 -0.40
0 866 3.03 -0.40
2 867 4.25 -0.42
4 867 5.95 -0.45
6 868 8.43 -0.56
8 867 10.05 -0.67
10 867 10.75 -0.75
12 868 9.30 -2.35
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.
� = ��� = 99.1GHI
287 JGKL 296.15L
= 1.1660 GKM9
Equation 15
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� = ���.�
1 + ��
=B1.827 × 10OP GK
M R L�.�E S/296.15 L5�.�T1 + 110.4 L
296.15 L= 1.83 × 10� GK
M R
Equation 16
For a Reynolds number of 250,000, the velocity of the airflow must therefore be
= �� �� � =
/2500005 B1.83 × 10� GKM RE
B1.1660 GKM9E /0.1016 × 10O M5
= 38.57 MR
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
UV = 12 � = 1
2 B1.1660 GKM9E �38.57 M
R �
= 867.37 HI
Equation 18
All three data sets can be combined by averaging the three records for each angle.
Averaged Data Angle Lift Drag
-4 0.0667 -0.4300
-2 0.7600 -0.4033
-0.25 1.3200 -0.2800
0 3.2550 -0.4050
2 4.1633 -0.4033
4 6.3000 -0.4567
6 8.5000 -0.5567
8 9.7333 -0.6267
10 10.8733 -0.7567
12 8.5233 -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
�� = ��1
2 ��� � �� �= 0.0667W
B12 B1.660 GK
M9E �38.57 MR �E /0.03064M5
= 0.0025
Equation 19
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�; = ��1
2 ��� � �� �= 0.4300W
B12 B1.660 GK
M9E �38.57 MR �E /0.03064M5
= 0.0162
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 Lift Coefficient Drag Coefficient
-4 0.0025 0.0162
-2 0.0286 0.0152
-0.25 0.0497 0.0105
0 0.1225 0.0152
2 0.1567 0.0152
4 0.2371 0.0172
6 0.3198 0.0209
8 0.3662 0.0236
10 0.4091 0.0285
12 0.3207 0.1040
Table 3
To begin correcting for horizontal buoyancy, the following parameters need to be calculated.
$ = "
48 ��ℎ�
= "
48 B0.1016M0.3048ME
= 0.0228
Equation 21
∆�� = − 6ℎ
" Λ$ %�%& = − 6/0.3048M5
" /0.35/0.02285 B−120.3 HIM E = 0.1463W
Equation 22
It is important to note Λ is assuming a thickness to chord ratio is 0.3.
)*+, = Λ$ = /0.35/0.02285 = 6.853 × 10O9
Equation 23
)*+* = 0.96/01*23425�9/ = 0.96/5.96 × 10O�M95
/0.0929M59/ = 2.021 × 10O9
Equation 24
The volume of the strut and cross-sectional area were known.
)*+ = )*+, + )*+* = 6.853 × 10O9 + 2.021 × 10O9 = 8.887 × 10O9
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
),+ = �/ℎ4 �;4 = 0.1016M/0.3048M
4 /−0.01525 = −0.0013
Equation 26
Δ�8,*> = −/$5/�845 = −/0.02285/0.12255 = −0.0028
Equation 27
Δ�C,>D,*> = − 14 Δ�8,*> = − 1
4 /−0.00285 = 0.0007
Equation 28
To further demonstrate the usage of the correction factors above, the parameters for the zero
angle of attack will all be calculated.
= 4/1 + )*+ + ),+5 = 38.56 MR X1 + /8.874 × 10O95 + /−0.0013 × 10O95Y = 38.86 M
R
Equation 29
U = U4/1 + 2)*+ + 2),+5 = 867.37HIX1 + 2/8.874 × 10O95 + 2/−0.0013 × 10O95Y = 880.87HI
Equation 30
�� = ��4/1 + )*+ + ),+5 = 249947X1 + /8.874 × 10O95 + /−0.0013 × 10O95Y = 251847
Equation 31
= = =4 + 57.3$2" B�84 + 4�C,>D,4E = 0 + 57.3/0.02285
2" X0.1225 + 4/0.00075Y = 0.03 ZI%
Equation 32
�;4 = /�4 − Δ��5U4� = X/0.4050W5 − /0.1463W5Y
/867HI5/0.0306M5 = 0.0208
Equation 33
�; = �;4/1 − 3)*+ − 2),+5 = 0.0208X1 − 3/8.874 × 10O95 − 2/−0.0013 × 10O95Y = 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
Average Dynamic Pressure Reynolds Number Velocity
Lift Coefficient
Drag Coefficient
-4 868.0 250091 38.59 0.0025 0.0162
-2 868.0 250091 38.59 0.0286 0.0152
-0.25 867.0 249947 38.56 0.0497 0.0105
0 867.0 249947 38.56 0.1225 0.0152
2 866.3 249850 38.55 0.1567 0.0152
4 867.0 249947 38.56 0.2371 0.0172
6 867.7 250043 38.58 0.3198 0.0209
8 866.7 249898 38.56 0.3662 0.0236
10 867.3 249995 38.57 0.4091 0.0285
12 867.7 250043 38.58 0.3207 0.1040
Corrected Data / Correction Factors
Experimental Angle of Attack ε,wb
Corrected Dynamic Pressure
Corrected Reynolds Number
Corrected Velocity ΔCl,sc
-4 0.0013 885.75 252647 38.98 -0.0001
-2 0.0013 885.60 252626 38.98 -0.0007
-0.25 0.0009 883.91 252384 38.94 -0.0011
0 0.0013 884.59 252482 38.96 -0.0028
2 0.0013 883.90 252384 38.94 -0.0036
4 0.0014 884.87 252523 38.96 -0.0054
6 0.0017 886.10 252698 38.99 -0.0073
8 0.0020 885.46 252607 38.97 -0.0084
10 0.0024 886.84 252806 39.01 -0.0093
12 0.0087 898.10 254428 39.26 -0.0073
Corrected Data / Correction Factors
Experimental Angle of Attack
Corrected Angle of Attack ΔCm,c/4,sc Cl Cdu Cd
-4 -4.00 0.0000 0.0024 0.0107 0.0104
-2 -1.99 0.0002 0.0274 0.0097 0.0094
-0.25 -0.24 0.0003 0.0476 0.0050 0.0049
0 0.03 0.0007 0.1172 0.0097 0.0095
2 2.03 0.0009 0.1499 0.0097 0.0094
4 4.05 0.0014 0.2268 0.0117 0.0113
6 6.07 0.0018 0.3057 0.0154 0.0150
8 8.08 0.0021 0.3499 0.0181 0.0175
10 10.09 0.0023 0.3906 0.0230 0.0222
12 12.07 0.0018 0.3021 0.0984 0.0941
Table 4
Figure 1 contains the various lift coefficients versus angle of attack for all the methods described
previously, as well as the previous lab session.
-0.5000
0.0000
0.5000
1.0000
1.5000
2.0000
2.5000
-4.00 -2.00 0.00
Cl
Figure 1
contains the various lift coefficients versus angle of attack for all the methods described
previously, as well as the previous lab session.
2.00 4.00 6.00 8.00
Angle of Attack (Degrees)
Cl versus Angle of Attack
Force Measurement Method (Lab 3)
Pressure Method (Lab 2)
Xfoil Results
NACA Data (Re=130000)
Naca Data (Re=330000)
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contains the various lift coefficients versus angle of attack for all the methods described
10.00 12.00
0.0000
0.0050
0.0100
0.0150
0.0200
0.0250
0.0300
0.0350
0.0400
-4.00 -2.00 0.00
Cd
Figure 2
0.00 2.00 4.00 6.00
Angle of Attack
Cd versus Angle of Attack
Force Measurement Method (Lab 3)
Xcode Results
NACA 0012 (Re=170000)
NACA 0012 (Re=330000)
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8.00 10.00
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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.
-40
-20
0
20
40
60
80
100
-4 -2 0 2 4 6 8 10 12
L/D
Angle of Attack
L/D versus Angle of Attack
Force Measurement Method (Lab 3)
Xfoil Results
NACA 0012 (Re=170000)
NACA 0012 (Re=330000)
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References
“Aerodynamics Lab 3 – Direct Measurement of Airfoil Lift and Drag.” Handout
Raw Data
Aero Lab 1
Fall 07
R= 287
p 99100 b= 0.000001458
t 23 S= 110.4 T= 296.15
row 1.165950252 c= 0.1016
u 1.82773E-05 Re= 250000
q 867.3710308 span= 0.3016
V 38.57246947 Aref 0.030643
Data Set 1
Angle experimental
angle experimental
q Lift Drag
-4 -4 868 -0.25 -0.051
-2 -2 868 -0.065 -0.043
0 -0.25 867 0.132 -0.028
2 2 865 0.241 -0.035
4 4 866 0.577 -0.042
6 6 867 0.858 -0.054
8 8 864 0.992 -0.063
10 10 868 1.09 -0.075
12 12 867 0.81 -0.295
Data Set 2
Angle experimental
angle experimental
q Lift Drag
-4 -4 869 0.135 -0.04
-2 -2 868 0.15 -0.038
0 0 868 0.348 -0.041
2 2 867 0.583 -0.044
4 4 868 0.718 -0.05
6 6 868 0.849 -0.057
8 8 869 0.923 -0.058
10 10 867 1.097 -0.077
12 12 868 0.817 -0.299
Data Set 3
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Angle experimental
angle experimental
q Lift Drag
-4 -4 867 0.135 -0.038
-2 -2 868 0.143 -0.04
0 0 866 0.303 -0.04
2 2 867 0.425 -0.042
4 4 867 0.595 -0.045
6 6 868 0.843 -0.056
8 8 867 1.005 -0.067
10 10 867 1.075 -0.075
12 12 868 0.93 -0.235