ME2135E Fluid Mechanics B

Experiment :

Flow Past an Aerofoil

Venue : EW2 -01-47

The National University of Singapore

Bachelor of Technology Programme Mechanical Engineering

CONTENTS

Table of Contents 2 List of Illustration 2 List of Definition and Symbols 3 Introduction 4 Description of Equipments 4 Theory of Operation 4 Procedure 6 Results 7 References 7 List of Illustrations

Figure 1 Forces and Pressure on the Aerofoil 8 Table 1 Coordinates of Pressure Tappings 9 Table 2 Pressure Readings 10 Table 3 Pressure Coefficients 11 2

List of Definition and Symbols A axial force per unit span c aerofoil chord

cd 2-D drag coefficient, = cU

D2

21

'

cl 2-D lift coefficient, = cU

L2

21

'

cp pressure coefficient, = 2

21

U

pp

D drag force per unit span L lift force per unit span N normal force per unit span P pressure

Re Reynolds number, = cU

T aerofoil thickness

U free stream velocity Greek Symbols angle of attack dynamic viscosity, (air) = 1.84 x 10 -5 Ns/m2 air density (see equation (6) in page 6 ) Subscripts f front surface (upstream of maximum thickness) } l lower surface (below chord line) } r rear surface (downstream of maximum thickness) } see Fig. 1 u upper surface (above chord line) } free stream value }

3

INTRODUCTION This manual provides guidance on the conduct of the experiment on Flow Past An Aerofoil. The objective is to investigate the pressure distribution at different angle of attack and to calculate the lift and drag forces. A description of the apparatus is given below, followed by the theory of operation and procedure. You should read and thoroughly understand them before commencing the experiment.

DESCRIPTION OF EQUIPMENTS

The aerofoil used in this study is a NACA 0015 section. It has a symmetrical profile with a maximum thickness of 15% of the chord of 10.16 cm. The aerofoil spans the working section of the Armsfield Low Speed Wind Tunnel and is supported by two end plates; one of which is graduated in degree for determining the angle of attack. The mid-section of the aerofoil has pressure tappings which are connected to a multi-tube manometer.

THEORY OF OPERATION Fundamental Aerodynamics Wings are slender devices which are attached to the fuselage (body) of an aeroplane. With a forward speed, wings can generate lift force which enables the aeroplane to stay airborne. An aerofoil is the cross-sectional shape of a wing. A typical subsonic aerofoil has a streamline profile with a fairly rounded nose (commonly known as a leading edge or LE) and a sharp tail (commonly known as a trailing edge or TE). A chord line is a straight line joining the LE to the TE; the length of which is called the chord c. The acute angle between the free stream and the chord line is called the angle of attack (). Any resultant force that acts on an aerofoil can be resolved into a pair of orthogonal forces. The two most commonly used pairs are those which are perpendicular and parallel to the free stream direction ( i.e. lift (L) and drag (D) forces respectively) and those which are perpendicular and parallel to the chord line (i.e. normal (N) and axial (A) forces respectively). These forces are schematically shown in Figure 1. Since an aerofoil is a stream line body, the flow over it is attached to the upper and lower surfaces when the angle of attack is small. However, as the angle of attack increases, a certain critical angle will be reached at which the flow can no longer stay attached to the upper side of the aerofoil. When this happens, flow separation is said to have occurred and the phenomenon is known as stall. The angle of attack at which stall first occurs is called the stall angle of attack. The thin aerofoil theory is an inviscid theory which is used to predict the lift acting on an aerofoil. It predicts that the lift coefficient is directly proportional to the angle of attack in radian. Analytically, the above statement can be stated as cl = 2. The prediction of the above theory is quite accurate when the angle of attack is smaller than the stall angle.

4

Force Coefficients Referring to Figure 1, the normal force is

N = (1) c

ul dxpp0

,)(

where c is the chord length;

pl is the pressure on the lower surface, and

pu is the pressure on the upper surface. The axial force is

A = (2)

2/

2/

,)(t

trf dypp

where,

pf is the surface pressure upstream of the maximum thickness,

pr is the surface pressure downstream of the maximum thickness, and

t is the maximum thickness. From the resolution of forces, the lift and drag forces are L = Ncos Asin (3) D = Nsin + Acos (3a) In non-dimensional form, the lift coefficient is given by

( ) ( ) = c t t prpfpupl dyccdxcccc 0 2/ 2/1 sincos1

( ) ( ) ( )[ ] += cydcccccxdcc uprpflprpfpupl 075.0 075.010 sincos (4) Similarly, the drag coefficient is given by

( ) ( ) ( )[ ] ++= cydcccccxdccc uprpflprpfpupld 075.0 075.010 cossin (5)

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PROCEDURE Experiment 1. Level the manometer base, and record the inclination of the tubes.

2. Start the wind tunnel motor and run it to give a speed of about 15 m/s in the test

section. Note the atmospheric pressure and temperature.

Calculate the density of air (in kg/m3) from

( )773.0057.1100

773.0

1

+=

Tair (6)

where T is the atmospheric temperature in C. Measure the exact speed with a pitot tube at a location upstream of the aerofoil.

3. Set the aerofoil at zero angle of incidence by observing the pressure readings at

the leading edge (tube 1) at a few angles. Zero incidence occurs when the

leading edge pressure is a maximum (i.e. a stagnation point)

4. Take pressure readings at the incidence of 4, 8, 12 and 16. Pressure on the other surfaces may be obtained from negative incidences.

5. Slowly increase the angle of attack until stall occurs. Note the stall angle. (Stall

occurs when the flow separates from the leading edge pf the aerofoil. When stall

is developing, the pressure distribution on the upper side of the aerofoil is

unstable. However, when stall is fully developed, the pressure distribution

becomes stable and uniform).

6. Repeat the measurement of the wind speed in the test section, as well as the

atmospheric temperature and pressure.

Tabulation 1. Complete Table 1 to obtain the non-dimensional coordinates of the pressure

tappings.

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2. Record the manometer readings at various angles of incidence in Table 2.

3. Compute and tabulate the pressure coefficients in Table 3.

Graphs 1. Plot cpl and cpu against x/c at each incidence. Extrapolate your curves to x/c = 1.

2. Plot cpf and cpr against y/c at each incidence. Clearly indicate whether it

corresponds to the lower or upper surfaces, and note that (cpf)u can only be

joined to (cpf)l. In this plot, two pressure loops should be obtained. Check

carefully to ensure that each loop is contributing to a positive or negative axial

force.

3. cl and cd may be obtained from the integration of the pressure distribution as

indicated by Equations (4) and (5). A planimeter may be employed to

mechanically compute the area bounded by the curves.

RESULTS 1. Plot cl and cd against on the same graph.

2. Compare the experimentally measured cl with the Thin Aerofoil Theory prediction

of cl = 2. Discuss the similarity and discrepancy observed. 3. What would you expect the lift and drag forces to be when = 0?

4. Does the cd which you have obtained give the total drag on the aerofoil?

Explain why.

5. Explain from the pressure distribution why there is a lift force.

6. Comment on the pressure distribution on the aerofoil when stall is reached.

REFERENCES

1. Anderson, J.D. Jr. Fundamental Aerodynamics, McGraw Hill.

2. Bertin, J.J. and Smith, M.L., Aerodynamics for Engineers, Prentice Hall.

3. Kermode, A.C., Mechanics of Flight, Pittman.

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Figure 1. Forces and Pressure on the Aerofoil

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Table 1

Coordinates of Pressure Tappings

Tapping No. x (mm)

y (mm)

x/c y/c

1 0.0 0.000

2 2.5 3.268

3 5.0 4.443

4 10.0 5.853

5 20.0 7.172

6 30.0 7.502

7 40.0 7.254

8 50.0 6.617

9 60.0 5.704

10 70.0 4.580

11 80.0 3.279

Note : c = 10.16 cm

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Table 2

Pressure readings Manometer inclination : Pitot pressure (at the beginning of the experiment) : (at the end of the experiment) : Static pressure (at the beginning of the experiment) : (at the end of the experiment) : Atmospheric pressure (at the beginning of the experiment) : (at the end of the experiment) : Atmospheric temperature (at the beginning of the experiment) : (at the end of the experiment) : Stall angle : Manometer readings at various

tapping

+ 4 + 8 + 12 + 16 - 4 - 8 - 12 - 16

1

2

3

4

5

6

7

8

9

10

11

10

Table 3

Pressure Coefficients

Free Stream Velocity, = U

Reynolds Number, Re =

Coefficients at various Cpl Cpu

Tapping 4 8 12 16 4 8 12 16

1

2

3

4

5

6

7

8

9

10

11

11

12