Pressure Distribution Over An Airfoil Biology Essay

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The main purpose of this experiment is to use wind tunnel to carry out test on airfoil. Moreover, this report will particular seeks to address the following areas;

The theory of wind tunnel testing, this talk about the equations (formulas) which has been developed to used to calculate the forces which are acting on the airfoil during the testing. It's also explains how the theory data can be applied to solve a real life problem such as drag force and skin friction force. It is so because, by using the theory results and understanding the forces acting upon the airfoil. The designers or engineers will be able to design airfoil for aircraft wing to reduce the drag and skin friction force. However, in this work you will find how the incidence of the angle affects the lift.

The test procedure describes the steps which were used during the experiment. For example the first step was to change the angle of attack to -4 degree and by turning the wind tunnel machine on and allowing the air to flow around airfoil. The pressure which was created by the air can be then measure through the manometer. The same procedure was used for 0 degree, 4 degree, 8 degree, 12 degree and 15 degree.

The collected data as a result from the test were used to draw a number of graphs. In the graph the pressure coefficient were plotted against x/c and C is the whole length of the chord and x is the distant from the leading edge to the cross section areas of the airfoil. However this clearly shows how the drag affects the airfoil respect to lift. This also shows the maximum lift or angle of attack. To make things simpler this work went further and created a table for analysis. Through the table the data can also evaluated for better understanding about data obtained.

Theory

The selection of an airfoil for a model aircraft depends mainly on the lift and drag characteristics of the airfoil. If no experimental data are available, theoretical methods can be used to get an approximation of these data. Various theories, assumptions and calculations have been made by various academia and the professionals. Whiles other theorists and academia agree on some calculations and assumptions others have differed opinions. In some cases they used same methodology but different assumptions and some instance have entirely differed view on these matters altogether.

Wind tunnel theory of aerodynamic characteristics was first initiated by Prandtl in dealing with fundamental conception in aerodynamics. He calculated what is termed as added drag of an aerofoil situated at a central part of a wind tunnel of a circular cross-section, assuming a semi-elliptic distribution of lift (Terazawa K and Rgakuhakusi, 1928).

Glauert went further to develop the theory even though the methodology was not different from that of Prandtl. What Glauert added to the theory is that he made his calculation assuming that the wind tunnel is rectangular. Both Prandtl and Glauert used the principle that: the boundaries of the cross-section are substituted by a set of images of a free vortices accompanying the aerofoil at proper places outside the channel so as to satisfy the boundary conditions in actual cases. In the work of Glauert, he failed to recognize the distance between aerofoil and its nearest image.

Whereas the lift can be calculated reasonable well from the frictionless pressure- respectively velocity distribution on the airfoil surface, the friction drag can be determined by an analysis of the boundary layer with a lesser degree of accuracy.

There are several methods for the design and analysis of airfoils available. For instance: profil by Professor Richard Eppler, University of Stuttgart, Germany, XFOIL by Professor Mark Drela, Massachusetts Institute of Technology, USA. However, for the sake of this work or experiment, our main focus was the forces which acted around the airfoil in the wind tunnel.

Moreover, this theory allows us to identify the forces around the airfoil and by studying and understanding the forces; we could make some assumptions and work out how the wind would behave at certain point in time on the airfoil. For instant, by changing the angle of incidence (Attack) and wind speed in the tunnel or the speed of the airplane, the wind will create pressures on the airfoil at the bottom and upper surfaces at different sections. This however increases the pressure at the bottom of the airfoil (High pressure at bottom) while at the upper area, pressure decreases (Low pressure).

In reality, this will cause the airplane to lift off from the ground at desire speed. Through that, a drag would be created on the airfoil. This shows that, by changing the angle, it will allow the airfoil (aircraft) to have different altitude, pressure and drag force.

In other words, the angle of the attack can be described as an angle between the chord line and the free stream. It can be also said as an angle at which the air hits the wing to create a lift. However, this shows that the amount of the lift is related to the angle of the attack. As the lift increases so does the angle of the attack increases.

The angle of the attack can be changing or increasing from 0 degree to 15 degree but any increment above 15 degree will cause the aircraft to stalls. This angle can be around 17 degree. This angle can also be called critical angle of attack. The diagram below depicts the angle of attack (fig 1.1).

a

Fig 1.1

This symbol α used to represent the angle of attack and V¥ is free stream velocity in the wind tunnel. However, in most cases the airfoil (wings) has pressure distribution which causes the angle of attack to change from the root to tip. Therefore, the root will have a high angle of attack. The tip has a low angle of attack and sometime it can have a negative angle.

In addition, the forces which we counted at the period of the experiment are drag, dynamic viscosity, pressure and lift. In order to understand these forces properly, equations (see below) have been developed. These equations are used to determine how much force will be at each given stage(s), condition(s) or problem(s). However, by inserting numbers or the data collected into the equations, we can work out and visualize how the forces can affect the airfoil.

The pressure on the surface of the aerofoil is not uniform. Taking airfoil used in the experiment for instance, has pressure distributions on the airfoil for a given section at various angles of attack. It is most appropriate to deal with non-dimensional pressure differences with. The pressure in this case is far upstream, being used as the datum. The pressure coefficient is defined as:

From the diagrams below, it indicates that when the angle of attack is zero thus at (), it shows that the region at the nose of the airfoil is small. Whereby at incidence angle of 6 degree the tail is positive but around most of the section it becomes negative. Therefore, at the trailing edge the pressure coefficient comes close to +1 but this does not actually reach this value. Fig 1.2 shows.

Fig 1.2

This quantity ½pV^2 is called dynamic pressure, at a low speed this dynamic pressure is the same as the difference between the stagnation pressure. The free stream pressure is represented by this symbol and it is equal to the dynamic and the stagnation pressure. According above statement, the equation below can be used to work out the non-dimensional pressure coefficient (fig 1.3).

Fig 1.3

The wind tunnel which we used to carried out the experiment; it was an open return wind tunnel. The pressure which was involved during testing was stagnation pressure and it is assumed that this pressure is equivalent to room pressure. Moreover, the free stream pressure in this case was measure in sections during the test.

In order to get accuracy results from the test, multi-tube manometer was used to measure the pressure differences. During the experiment we experienced that the difference in pressure is proportional to the difference in height of the liquid levels in the manometer. Through the measurement we came to know that the pressure coefficient was the ratio of two pressure difference (below shows manometer, fig 1.4)

Fig 1.4

This shows that we can use the differences in the height of the liquid to calculate the pressure coefficient. In other words, this can be said as the pressure coefficient is the ratio of the differences in the height of the liquid levels which being measured.

Below equation (fig 1.5) satisfy above statement.

Fig 1.5

This equation can be also used to determining the pressure coefficient (fig 1.6)

Fig 1.6

Pi - pressure at tapping i

P∞ - free stream pressure

ρ - Air density

V - Free stream velocity

S - Wing area

c - Aerodynamic mean chord

r - The manometer reading

h - The height of the liquid in the manometer

- Pressure coefficient

Procedures

This section explains the procedures followed for carrying out the experiment.

The wind tunnel is connected to a multi-tube manometer for measuring the pressure distribution around the aerofoil surfaces. Firstly, the manometer is adjusted to a 40o incline which is the optimum position for taking the readings.

Secondly, all the connections between the wind tunnel and the manometer have to be checked so that it is ensured that the pressure is measured correctly. The higher the pressure on the aerofoil, the lower the rise in liquid in the manometer will be and vice versa.

Now, it is time for setting the angle of incidence of the aerofoil. This has to be done with the wind tunnel's fan switched off as when it is switched on, the pressure outside is higher than the pressure inside and the angle setting knob would be hard to rotate.

After the angle is set to -4o for the first part of the experiment, the wind tunnel fan is switched on to 75% of its maximum power. We then wait for one minute until all the liquid in all tubes is stable and then the readings are taken down, where the manometer measures the pressure in terms of height of the liquid. In addition to the tubes measuring the pressure over the aerofoil at all tappings, there are two tubes for measuring the stagnation pressure, which may be assumed in this experiment to be the room pressure as it is an open end wind tunnel, and the free stream pressure of the wind tunnel.

Finally after all the readings have been taken down, the wind tunnel fan is shut down and the above procedures are repeated again for measuring the pressure distributions on the aerofoil surface with angles of incidence 0o, 4o, 8o, 12o and 15o. The differences in heights of the liquid in the tubes are observed with respect to alternating angles and the stalling angle is worked out.

Results

After the coefficient of pressure Cp was worked out using the formula, graphs of CP versus tapping point position on the airfoil x with respect to the chord length c i.e., x/c, for every angle of incidence tested were plotted.

/

1

2

3

4

5

6

7

8

9

10

11

12

13

14

-4

21

28.6

33

38.2

49.4

53

49.6

42.8

33

44

47.4

49.4

51.6

52

0

14

45.8

48.4

52

58.4

59.8

53.8

43.8

29.6

38

39

37.8

35

33

4

38

64

63

64

65

63

52.4

43.2

27

33

32.8

29.2

24.2

21.4

8

63

71.5

70

69

65

58.8

46

42.2

27.8

31.6

30.2

25.6

20.2

17.6

12

87

80.4

76

72

62

49.5

43

43.2

28

30.2

27.8

22.4

17

14.8

15

93

88

76.5

70

57

46

43

43.4

26.6

28.4

25.4

20.4

15.4

13.8

The table above shows the pressure recorded at 14 different points on the airfoil that was obtained in the lab.

c

x

x/c

1

140

0

0

2

140

6

0.042857

3

140

9.5

0.067857

4

140

15

0.107143

5

140

38.5

0.275

6

140

63.5

0.453571

7

140

90

0.642857

8

140

116.5

0.832143

9

140

8

0.057143

10

140

12.5

0.089286

11

140

26.5

0.189286

12

140

52

0.371429

13

140

78

0.557143

14

140

103.5

0.739286

Table showing positions of tappings on the airfoil

hi-h∞

1

2

3

4

5

6

7

8

9

10

11

12

13

14

-4

-13.8

-6.2

-1.8

3.4

14.6

18.2

14.8

8

-1.8

9.2

12.6

14.6

16.8

17.2

0

-19.6

12.2

14.8

18.4

24.8

26.2

20.2

10.2

-4

4.4

5.4

4.2

1.4

-0.6

4

5.8

31.8

30.8

31.8

32.8

30.8

20.2

11

-5.2

0.8

0.6

-3

-8

-10.8

8

32

40.5

39

38

34

27.8

15

11.2

-3.2

0.6

-0.8

-5.4

-10.8

-13.4

12

57

50.4

46

42

32

19.5

13

13.2

-2

0.2

-2.2

-7.6

-13

-15.2

15

65

60

48.5

42

29

18

15

15.4

-1.4

0.4

-2.6

-7.6

-12.6

-14.2

Table showing difference between gauge pressure and stagnation pressure

Cp

1

2

3

4

5

6

7

8

9

10

11

12

13

14

-4

0.6330

0.2844

0.0826

-0.1560

-0.6697

-0.8349

-0.6789

-0.3670

0.0826

-0.4220

-0.5780

-0.6697

-0.7706

-0.7890

0

0.9515

-0.5922

-0.7184

-0.8932

-1.2039

-1.2718

-0.9806

-0.4951

0.1942

-0.2136

-0.2621

-0.2039

-0.0680

0.0291

4

-0.3021

-1.6563

-1.6042

-1.6563

-1.7083

-1.6042

-1.0521

-0.5729

0.2708

-0.0417

-0.0312

0.1563

0.4167

0.5625

8

-1.7778

-2.2500

-2.1667

-2.1111

-1.8889

-1.5444

-0.8333

-0.6222

0.1778

-0.0333

0.0444

0.3000

0.6000

0.7444

12

-3.3529

-2.9647

-2.7059

-2.4706

-1.8824

-1.1471

-0.7647

-0.7765

0.1176

-0.0118

0.1294

0.4471

0.7647

0.8941

15

-4.3333

-4.0000

-3.2333

-2.8000

-1.9333

-1.2000

-1.0000

-1.0267

0.0933

-0.0267

0.1733

0.5067

0.8400

0.9467

Table showing different values of coefficient of pressure Cp calculated using formula

After all values were recorded and calculations have been made, the graphs were ready to be plotted and they were as follows:

The 6 graphs above show the pressure distribution over the airfoil at different angles of incidence. On each graph the pressure on the upper surface is marked in squares and on the lower surface is marked in diamonds.

After theses graphs have been plotted, it was time for the area under the curve for every graph to be calculated thus working out the coefficient of lift CL. The calculation of the coefficient of lift can show us easily where the airfoil stalling angle is; which is the angle at which the coefficient of lift is the maximum.

Calculating area under the graph

To calculate the area of the graph, several triangles were used. To find an area of a triangle this formula was used

For example for triangle A:

A= ½ x Base x Height

A=1/2 x 0.04 x 0.24

A=0.0048

Rest of the calculations for this graph was done in similar way.

Triangle A

 

Base

 

0.04

Area

0.0048

Triangle B

 

Base

 

0.04

Area

0.0052

Triangle C

 

Base

 

0.11

Area

0.0143

Triangle D

 

Base

 

0.11

Area

0.0088

Triangle E

 

Base

 

0.05

Area

0.004

Triangle F

 

Base

 

0.26

Area

0.0078

Triangle G

 

Base

 

0.24

Area

0.01356

Triangle H

Base

 

0.1

Area

0.005

Triangle I

 

Base

Height

 

0.1

0.1

Area

0.005

Triangle J

 

Height

Base

 

0.3774

0.224

Area

0.042269

Total Area = 0.0048+0.0052+0.0143+0.0088+0.004+0.0078+0.01356+0.005+0.005+0.042269

Total Area= 0.1107288

To find the area between the graphs for this particular graph, several triangle, trapezium and rectangle were used.

A (Triangle)

x

Y

0.1

0.51

Area

0.0255

F (Triangle)

x

y

0.04

0.8

Area

0.016

To find the area of a rectangle:

Area = a x b

Area=0.06x0.3

Area=0.018

C (Rectangle)

x

y

0.06

0.3

Area

0.018

Following calculation were made to find the area of a trapezium:

Therefore for D (Trapezium):

h=0.2

Similarly in the same way E (Trapezium) was calculated.

D (Trapezium)

h=0.2

a

b

0.05

0.04

Area

0.009

E (Trapezium)

h=0.2

a

b

0.04

0.03

Area

0.007

Trapezium Rule:

To calculate B (Trapezium):

h = 0.04

Area = 0.04/2 ((0.51+0.26) + 2(0.5+0.49+0.47+0.45+0.41+0.39+0.36+0.32+0.3+0.29+0.26+0.25+0.24+0.24+0.23)

Area= 0.2234

To calculate G (Trapezium):

h= 0.04

Area = 0.04/2 ((0 + 0) + 2(0.1+0.12+0.22+0.33+0.42+0.52+0.6+0.66+0.72+0.78+0.79+0.78+0.76+0.72+0.69+0.61+0.55+0.46+0.39+0.2)

Area =0.4168

Total Area = 0.0255+0.016+0.018+0.009+0.007+0.2234+0.4168

Total Area = 0.7157

To find the area between the graphs, several triangles and trapeziums were used.

B (Triangle)

x

y

0.09

1.37

Area

0.06165

D (Triangle)

x

y

0.09

0.2

Area

0.009

E (Triangle)

x

y

0.06

1.35

Area

0.0405

F (Triangle)

x

y

0.06

0.58

Area

0.0174

G (Triangle)

x

y

0.02

0.28

Area

0.0028

To calculate A (Trapezium):

h= 0.04

Area = 0.04/2 ((0 + 0.56) + 2(0.54+0.5+0.48+0.42+0.39+0.33+0.29+0.22+0.18+0.12+0.09+0.05)

Area = 0.1556

To calculate C (Trapezium):

h= 0.04

Area = 0.04/2 ((0.81 + 1.62) + 2(0.9+1+1.11+1.23+1.35+1.48+1.6+1.62+1.64+1.66+1.7+1.7+1.69+1.68 1.67+1.65)

Area = 0.9958

Total Area=0.06165+0.009+0.0405+0.0174+0.0028

Total Area=1.27375

B (Triangle)

 

 

X

 

 

0.05

Area =

0.018

 

To find the area between the graphs, following calculations were done:

A (Triangle)

 

 

X

0.58

Area=

0.2088

C (Triangle)

 

 

X

 

 

0.06

Area =

0.0204

 

E (Triangle)

X

0.06

Area

0.054

F (Triangle)

X

Y

0.06

0.45

Area

0.0135

To calculate the D (Trapezium)

h= 0.04

Area = 0.04/2 ((0.68 + 2.1) + 2(0.7+0.72+0.8+0.9+1.01+1.2+1.3+1.4+1.52+1.6+1.69+1.75+1.8+1.85 1.91+1.96+2)

Area = 0.9958

Total Area= 0.2088+0.018+0.0204+0.054+0.0135+0.9958

Total Area= 1.3347

To find the area between the graphs, following calculations were done:

A (Triangle)

 

x

y

 

0.74

0.89

Area

0.3293

 

B (Triangle)

 

x

y

 

0.04

0.89

Area

0.0178

 

D (Triangle)

 

x

y

 

0.04

2.8

Area

0.056

 

E (Triangle)

 

x

y

 

0.04

0.65

Area

0.013

 

F (Trapezium)

 

a

b

 

0.09

0.04

Area

0.04875

 

To calculate the C (Trapezium)

h= 0.04

Area = 0.04/2 ((0.75 + 2.8) + 2(0.73+0.75+0.8+0.85+0.91+1.01+1.11+1.25+1.4+1.6+1.8+1.9+2.1+2.2 2.35+2.5)

Area = 1.0014

Total Area= 0.3293+0.0178+0.056+0.013+0.04875+1.0014

Total Area=1.46625

To find the area between the graph following calculations were done:

A (Triangle)

 

x

y

 

0.64

0.96

Area

0.3072

 

B (Triangle)

 

x

y

 

0.04

0.96

Area

0.0192

 

C (Triangle)

x

y

0.04

1

Area

0.02

E (Triangle)

 

x

y

 

0.04

3.4

Area

0.068

 

F (Triangle)

 

x

y

 

0.04

0.9

Area

0.018

 

To calculate D (Trapezium):

h= 0.04

Area = 0.04/2 ((1 + 3.4) + 2(1+1+1+1+1.02+1.04+1.1+1.18+1.3+1.42+1.6+1.8+2+2.2+2.4+2.6+2.8)

Area = 1.1464

Total Area= 0.3072+0.0192+0.02+0.068+0.018+1.1464

Total Area=1.5788

After the coefficient of lift CL was calculated for the different angles of incidence, a graph of CL versus angle of incidence was plotted and was as follows:

Angle of Incidence

Lift

-4

0.110729

0

0.7157

4

1.27375

8

1.3347

12

1.46625

15

1.5788

Discussion

For the first set of graphs of Cp versus x/c obtained, the shapes are correct. If an airfoil has a positive angle of attack it means it is climbing thus the pressure distribution on the top surface of the airfoil must be less than the pressure distribution on the lower surface. When the angle of incidence had a positive value, the pressure distribution on the lower surface was always higher than the upper surface. Visually this can be seen clearly on the graphs as the squared curve was always above the diamond curve meaning pressure was higher on the lower surface.

However, when the angle of incidence had a negative value the scenario was completely reversed meaning the pressure distribution on the upper surface became higher than the pressure distribution on the lower surface thus the airfoil is in a state of descending. This can also be seen visually from the graph with an angle of incidence of -4o as the squared line this time was below the diamond line meaning a higher pressure on the upper surface than on the lower surface.

After that, the coefficient of lift on the airfoil for the different angles of incidence was calculated via the area under the curve of the first set of graphs. A graph of the coefficient of lift versus angle of incidence was then plotted and it only complemented the preceding results. At -4o, the lowest coefficient of lift was attained. As the angle was increased gradually the coefficient of lift kept rising until it reached a maximum value at 15o which is the stalling angle. In the end, the values complement the results as they have proven that the maximum coefficient of lift was achieved at 15o which is the stalling angle.

Conclusion

From the experiment, it can be concluded that in an aircraft, lift is caused by an upward force that is resulted from the difference in pressure between the top and the bottom surface of the wings. This difference in pressure is due to the design of the airfoil, and the amount of the lift is dependent on the angle at which the wing is inclined.

In addition, the pressure distribution over an airfoil changes with varying angles of incidence and the coefficient of lift can be calculated from a Cp versus angle of incidence graph. However, the coefficient of lift can be also changes with varying angles of incidence. This shows, the maximum coefficient of lift is achieved at the stalling angle.

However, in spite that the theory and the calculations followed were correct, two errors have been made. Firstly, in many cases the pressure height was unstable, meaning it was playing between many values so an average value was taken which may have caused in turn some errors in calculations. Another error was that an angle higher than 15o should have been tested so that it can be seen that the coefficient of lift would drop at any angle above 15o thus confirming that 15o is the stalling angle.

In the nutshell, by understanding the whole concept that has been explained above, we will be able to use it to deal with real life situations. That is, if we are able to know the forces that are exerted on an airfoil, we will be able to design airfoil to reduce the forces such as drag force. By doing so, the plane will be able to lift off (take-off) smoothly at short distance. That however improves the fuel efficiency because if the drag force reduces it for example from 100 per cent to 45 per cent, it will allow the aircraft to use less fuel when compared with the one which has no drag reduction.

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