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Flow over an Airfoil

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National University of Singapore
Bachelor of Technology Programme
ME2135E Fluid Mechanics II
(Lab Report)

Flow Over An Airfoil

Group: 4B
Experiment Date: 13.02.2015

1

Experiment II: Flow Over an Airfoil

1. Introduction
An airfoil is a two dimensional cross-section of an airplane wing. It may be thought of as a wing of infinite span with constant cross-sectional shape. With a forward speed, wings can generate a lift force which enables the airplane to stay airborne. Airfoil shapes are designed to provide high lift values at low drags, for given flight conditions. Airfoil studies are not only relevant for airplanes, but also applicable to wings on F1 cars and blades of a helicopter, propeller hydrofoil, and wind turbine.
A typical subsonic airfoil has a streamline profile with a fairly rounded nose (leading edge) and a sharp tail (trailing edge). A chord line is a straight line joining the leading to trailing edges, the length of which is called the chord c. the acute angle between the free stream velocity direction and the chord line is called the angle of attached a
2. Objectives and Scope
The objectives of this experiment were to investigate the pressure distribution around the airfoil and to calculate the lift and drag forces. The experiment was conducted at a specified angle of incidence relative to the wind direction and at a specified wind speed.
3. Experimental Set Up.
1) Wind Tunnel
The air flow was generated by the blower of a subsonic wind tunnel, which was of the open-circuit type. It has a working section of square cross-section, 0.3m x 0.3m.
2) Airfoil
The airfoil used in this experiment was a NACA 0015 section of chord length 106mm. it has a symmetrical profile with a maximum thickness 15% of the chord. The airfoil spanned the test section of the wind tunnel, and was supported by two end plates. One of the end plate was graduated in degree for determining the angle of attack.
3) Pressure Measurement
The airfoil has 11 static pressure taps at the mid-section (mid-span) on the upper surface.
The same tappings can be used to measure pressures on the lower surface at negative incidence, due to symmetry of the airfoil. The pressure tappings were connected to a multi-tube manometer to measure the static pressure distribution around the airfoil. The manometer was inclined at an angle θ to increase the sensitivity.
4) Velocity Measurement
2

Experiment II: Flow Over an Airfoil

The flow speed in the wind tunnel was measured by using a standard pitot-static tube and by applying Bernoulli’s Equation.
4. Procedure
a) Check that there is no air bubble in the manometer tubes. Level the manometer base, and record the inclination θ of the manometer tubes to the horizontal.
b) Start the wind tunnel motor and run it to give a specified speed in the test section, as given by the instructor. Each group will do the experiment at only one speed. For the purpose of comparing results, one group will work at the lower speed around 7.5 m/s and the other, at the higher speed around 12m/s, as assigned by the instructor. Measure the exact speed with a pitot-static tube at a location upstream of the airfoil.
c) Note the atmospheric temperature.
d) Check that the zero angle of incidence corresponds to that on the end plate, by observing the pressure reading at the leading edge. Zero incidence occurs when the leading edge pressure is a maximum (i.e. a stagnation point)
e) Take manometer readings with the airfoil at a small angle of incidence specified by the instructor. Check that the reference of the manometer readings is connected to the free-stream pressure tapping. For the purpose of comparing results at different speeds, both groups will do the experiment at the same incidence. Pressure on the other surface may be obtained from negative incidence.
f) Repeat the measurement of the wind speed in the test section.

5. Calculation of Results
Table 1. Coordinates of Pressure Tappings

Tapping No.

x mm

IyImm

x/c

1
2
3
4
5
6
7
8

0
2.5
5
10
20
30
40
50

0
3.268
4.443
5.853
7.172
7.502
7.254
6.617

0
0.025
0.049
0.098
0.197
0.295
0.394
0.492

y/c upper 0
0.032
0.044
0.058
0.071
0.074
0.071
0.065

y/c lower 0
-0.032
-0.044
-0.058
-0.071
-0.074
-0.071
-0.065
3

Experiment II: Flow Over an Airfoil

9
10
11
12
(extrapolated) c = 106mm

60
70
80

5.704
4.58
3.279

0.591
0.689
0.787

0.056
0.045
0.032

-0.056
-0.045
-0.032

106

0

1

0

0

Experiment is held under high-speed wind. Inclination angle = 30deg. Airfoil angel of incidence
3
= 8 deg = 0.14 rad/s. Static pressure = 13.8cm, pitot pressure = 11.6. ρair = 1.17kg/m , ρ
3
water = 1000kg/m .
Results obtained as the following table 2.
Table 2. Manometer Readings

Tapping No

h - h∞ upper surface (at 8o)

1
2
3
4
5
6
7
8
9
10
11
12 (extrapolated)
Formula used for calculation:

Free stream velocity U∞ =

Reynolds number Re =

13.8
19.3
18.1
17.5
16.8
15.8
15.3
15.0
14.8
14.6
14.3

PT  PS
1 / 2 a ir

14.2
11.7
12.4
12.8
13.6
13.7
13.8
13.9
13.0
14.0
13.8

2 wgh sin 30

air

=

airU∞c air ,

Pressure coefficients Cpu/l =

h - h∞ upper surface (at -8o)

PA  PS
1 / 2 airU∞2

-2

,

Δh = (hs - ht)x 10

μ= 1.84 x 10-5 kg/ms

=

2 wg (hs  hp) sin 30
airU∞2
4

Experiment II: Flow Over an Airfoil

Sample calculations:
PT  PS
2 wgh sin 30
U∞ =
1 / 2 a ir =
air
2 1000  9.81 ( 13.8-11.6 )  0.01 sin 30
=
= 13.582
1.17

airU∞c air =

Re =

1.17 13.582 0.106 1.84 10 - 5) = 91,545,63


At tapping number 2
Pressure coefficients at upper surface
Cpu =

2 wg (hs  hp) sin 30
airU∞2

2  1000 9.81 (13.8  19.3)  102 sin30
=

1.17  13.5822

= 2.50

Pressure coefficients at lower surface

2 wg (hs  hp) sin 30
airU∞2

Cpl =

2  1000 9.81 (13.8  11.7)  102 sin30
=

1.17  13.5822

= 0.954

Follow the sample calculations, we can get the table 3 as shown below.
Table 3. Pressure Coefficients.

5

Experiment II: Flow Over an Airfoil

Tapping No
1
2
3
4
5
6
7
8
9
10
11
12 (extrapolated)

Cpu upper surface (at 8o)

Cpl upper surface (at -8o)

0.00
-2.500
-1.954
-1.682
-1.364
-0.909
-0.682
-0.545
-0.455
-0.364
-0.227

-0.182
0.954
0.636
0.455
0.091
0.045
0.000
-0.045
0.364
-0.091
0.000

6. Graph
1) Plot Cpl and Cpu against x/c. Extrapolate curves to the trailing edge x/c=1.

Area A = 0.774
2) Plot Cpf and Cpr against y/c. Clearly indicate whether it corresponds to the lower or upper surfaces. Make sure that the pressure distributions are continuous at the leading and

6

Experiment II: Flow Over an Airfoil

trailing edges, y/c=0; that is, (Cpf)u can only be jointed to (Cpf)l; and (Cpr)u can only be jointed to (Cpr)l.

Area B = 0.041, Area C = -0.1215
3) The lift coefficient CL and the drag coefficient CD
CL = cosα(Area A) - sinα(Area B - Area C)
=cos0.14 x 0.774 - sin0.14(0.041+0.1215)
= 0.749
CD = sinα(Area A) + cosα(Area B - Area C)
=sin0.14 x 0.774 + cos0.14(0.041+0.1215)
= 0.1275
4) The lift-drag ratio CL/CD
CL/CD = 0.749/0.1275 = 5.875

7. Discussion
a. State the value of the maximum Cp and its location (x/c, y/c). Do you expect the value of maximum Cp to be higher, if you increase the angle of incidence.
7

Experiment II: Flow Over an Airfoil

Max Cp = 0.954 @ x/c = 0.032, y/c = -0.032。
The Cp is depending on the static pressure which will not change in this experiment. Thus, even increase the angle of incidence, we will not get higher value of the Cp.
b. Was the shear stress along the airfoil included in the pressure measurement by the manometer? Hence, state whether your experimental CL and CD corresponded to the total lift and drag on the airfoil. Suggest another method to measure lift and drag other than pressure distribution.
No, the shear stress along the airfoil is not included in the pressure measurement.
The experimental CL and CD are partial value only, which are not corresponded to the total lift and drag on the airfoil.
We can use the load sensors to measure the force.
c. Compare your experimentally measured CL with the Thin Airfoil Theory Prediction of CL =
2πα.
Experimental result: CL= 0.749
Theoretical result: CL= 2πα = 2xπx0.14 = 0.879
d. Compare your experimental lift coefficient with the other group, which was obtained at a different speed. Do you expect the CL to be higher if the speed was higher? The lift coefficient is almost the same.
As we can see from the formula, the coefficient does not vary with the speed but only the airfoil angle of incidence, α.
8. Conclusion
From this experiment, we can understand the pressure distribution around the airfoil and also the lift and drag forces which keep the airfoil flying. It clearly demonstrated the non-dimensional lift and drag coefficients as well.

8

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