Aerodynamics Lab 2 Airfoil Pressure Measurements
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 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 1 = +
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 =
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. 8 :; 9
) = cos#α( .
8 : 9
7 /)0123 − 4 23 56 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 1 2 3 4 5 6 7 8 9
x (mm) 4 10 20 30 40 50 60 70 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
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
Data Set 2 Angle of Attack
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
Tap 9
Data Set 3 Angle of Attack
Tap 1
Tap 2
Tap 3
Tap 4
Tap 5
Tap 6
Tap 7
Tap 8
-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=>? =B = = 1.1675 G 287 A 295.15C F =BC Equation 9
=B JK . . H1.458 × 10 F C . M N#295.15 C( O =B = = = 2 × 10 110.4 C F 1+ 1+ 295.15 C Equation 10
For a Reynolds number of 250,000, the velocity of the airflow must therefore be 8|Page
=B #250000( H2 × 10 M F F = = = 38.42 =B H1.1675 G M #0.1016 × 10J F( 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 1 1 =B F Q = = H1.1675 G M 38.42 = 861.68 >? 2 2 F 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
-10
835
594
372
274
217
173
140
116
Tap 9 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 =
∆ 52>? − 861.68>? = = −0.031 Q 861.68 >? 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.
-Cp Versus Pressure Tap 4.500 4.000
-Cp
3.500 3.000
-10 Degrees
2.500
-7 Degrees -4 Degrees
2.000
0 Degrees 1.500
4 Degrees
1.000
7 Degrees
0.500
10 Degrees
0.000 1
3
5
7
9
Pressure Tap
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.
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Pressure Coefficient Angle of Attack 10
7
4
0
-4
-7
-10
Tap 1
Tap 2
Tap 3
Tap 4
Tap 5
Tap 6
Tap 7
Tap 8
Tap 9
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
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
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
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
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
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
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; 7 7 ×Z + Z 2 X XY; Equation 14
VW?;,;S2T =
3.928 + 2.319 × |0.0393 − 0.0984| = 0.18 2 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#106B(#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) 0.985 0.993 0.998 1.000 0.998 0.993 0.985
trap 1 0.184 0.135 0.082 0.000 -0.082 -0.135 -0.184
trap 2 0.204 0.158 0.096 0.000 -0.096 -0.158 -0.204
trap 3 0.159 0.118 0.073 0.000 -0.073 -0.118 -0.159
trap 4 0.123 0.091 0.059 0.000 -0.059 -0.091 -0.123
trap 5 0.098 0.073 0.049 0.000 -0.049 -0.073 -0.098
trap 6 0.078 0.061 0.042 0.000 -0.042 -0.061 -0.078
trap 7 0.061 0.050 0.033 0.000 -0.033 -0.050 -0.061
trap 8 0.045 0.040 0.026 0.000 -0.026 -0.040 -0.045
Cl 0.939 0.721 0.459 0.000 -0.459 -0.721 -0.939
Table 6
Cl vs Angle of Attack 1.500
1.000
0.500
Cl
0.000
-15
-10
-5
0
5
10
15
-0.500
-1.000
-1.500 Angle of Attack (Degrees)
Figure 2
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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 p t row u q V
98900 22 1.1675 2E-05 861.68 38.42
R= b= S=
287 1E-06 110.4
T= c= Re=
295.15 0.1016 250000
Data Set 1 Angle of Attack
Tap 1
Tap 2
Tap 3
Tap 4
Tap 5
Tap 6
Tap 7
Tap 8
-10
832
590
370
275
218
176
144
122
Tap 9 104
-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
Tap 9
Data Set 2 Angle of Attack
Tap 1
Tap 2
Tap 3
Tap 4
Tap 5
Tap 6
Tap 7
Tap 8
-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
Tap 9
Data Set 3 Angle of Attack
Tap 1
Tap 2
Tap 3
Tap 4
Tap 5
Tap 6
Tap 7
Tap 8
-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
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