me2135-2 lab manual (flow over an airfoil)

7/23/2019 ME2135-2 Lab Manual (Flow Over an Airfoil)

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The National University of Singapore

Department of Mechanical Engineering

ME2135 & ME2135E

Fluid Mechanics II

Semester 4Session 2014/2015

Experiment II

Flow over an Airfoil

Venue: Fluid Mechanics Lab 2

WS2-01-47 (Ground Floor, Engineering Workshop 2)

Tel: 6516-2231

2 January 2015

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Table of Contents

List of Figures 3

Nomenclature 3

1. Introduction 5

1.1 Background 5

1.2 Lift Generation 5

1.3 Objectives and Scope 5

2. Experimental Set-up 6

2.1 Wind Tunnel 6

2.2 Airfoil 6

2.3

Pressure Measurement 62.4 Velocity Measurement 6

3. Analysis 6

3.1 Free Stream Velocity 6

3.2 Pressure Coefficient 7

3.3 Force Coefficients 7

3.4 Trapezoidal Method 8

3.5 Thin Airfoil Theory 9

4. Procedure 9

4.1 Experiment 9

4.2 Tables 10

5. Results and Discussion 10

5.1 Results 10

5.2 Discussion 11

6. Conclusions and Recommendations 11

6.1 Conclusions 11

6.2 Recommendations 11

References 12

Figures 12

Tables 16

Appendix A 19

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List of Figures

Figure 1 a) Airfoil Terminology;

b) Pressure Gradient across a Curved Streamline;

c) Streamlines over an Airfoil 12Figure 2 Airfoil in the Wing Tunnel 13

Figure 3 Schematic Diagram (Side View) of Pressure Measurement 13

Figure 4 Forces and Pressure on an Airfoil 14

Figure 5 Pressure Distribution around an Airfoil;

at a=10and Re=2.33x105 15

Figure 6 Area between Two Curves using Trapezoidal Method 16

Table 1 Coordinates of Pressure Tappings 16

Table 2 Manometer Readings 17

Table 3 Pressure Coefficients 18

Appendix A Location of Engineering Workshop 2 19

Nomenclature

A axial component of force per unit span (Fig 4)

c airfoil chord (Fig 4)

CD 2D drag coefficient,21

2

D

U c

=

CL 2D lift coefficient,21

2

L

U c

=

CP pressure coefficient,21

2

P P

U

=

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D drag force per unit span

h manometer reading (see Fig 3)

L lift force per unit span

N normal component of force per unit span (Fig 4)

P pressure

Re Reynolds number,U c

=

t airfoil thickness

U free stream velocity, 1

2

TP P

=

Greek Symbols

angle of attack

dynamic viscosity of air, = 1.84 x 10-5 Ns/m2

density of air, = 1.18 kg/m3

w density of water, = 103kg/m3

inclination of manometer with horizontal

Subscripts

T stagnation value

f front surface (upstream of maximum thickness) }

lower surface (below chord line) }

r rear surface (downstream of maximum thickness) } see Fig 4

u upper surface (above chord line) }

free-stream value }

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1. Introduction

1.1 Background

An airfoil (Figure 1a) 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 stayairborne. 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 airfoilhas 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 acuteangle between the free

stream velocity direction and the chord line is called the angle of attack (Figure 1a).

1.2 Lift Generation

The pressure in a curved flow increases radially outwards (or reduces radially inwards), in

order to accelerate the flow (Figure 1b). The curved streamlines around an airfoil result in

the pressure at the upper surface being lower than P, and the pressure at the lower surfacebeing higher P, as illustrated in Figure 1c. The pressure difference between the lower and

upper surfaces of an airfoil generates a lift force, which is the component of force

perpendicular to the direction of motion. The component parallel to the direction of motion

is called drag.

1.3 Objectives and Scope

The objectives of this experiment were to investigate thepressure 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.

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2. Experimental Set up

2.1 Wind Tunnel

The air flow was generated by the blower of a subsonic wind tunnel(Figure 2), which was

of the open-circuit type. It has a working section of square cross-section, 0.30 m x 0.30 m.

.

2.2 Airfoil

The airfoil used in this experiment was a NACA 0015 section of chordlength 101.6 mm. 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 determiningthe angle of attack.

2.3 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 wereconnected to a multi-

tube manometer to measure the static pressure distribution around the airfoil (Figure 3). The

manometer was inclined at an angle to increase the sensitivity.

2.4 Velocity Measurement

The flow speed in the wind tunnel was measured by using a standard Pitot-static tube

(Figure 3) and by applying Bernoulli's Equation.

3. Analysis

3.1

Free Stream VelocityApply Bernoulis Equation from free stream to the nose of the pitot tube (Figure 3):

2 2

0 at pitot nose

1 1 (1)

2 2T TP U P U

=

+ = +

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The free stream velocity may be expressed as

( )sin (2)

1 1

2 2

w TT g h hP P

U

= =

The Reynolds number, Re (3)U c

=

3.2 Pressure Coefficient

( )

2

w

(4)1

2

Substitute from Equation (1),

Pressure coefficient is defined as

Pressure difference is measured by the manometer: = g h-h

P

PT

P PC

U

P PC

P P

P P

=

=

w

2

sin

where is the density of water in the manometer

g is gravitational acceleration, 9.81 m/s

and h is the reading of the manometer column (Figure 3)

Thus, pressure coefficient may be expressed t

in

( )

( )

erms of the manometer readings

sin (5)

sinP

T T

g h h h hC

g h h h h

= =

3.3 Force Coefficients

The resultant aerodynamic force that acts on an airfoil can be resolved into a pair of

orthogonal forces. The two most commonly used pairs are those which are

perpendicular andparallel to the free stream direction ( i.e. lift L and drag D forces

respectively) and thosewhich are perpendicular and parallel to the chord line (i.e. normal

N and axial A forces respectively). These components of force are shown in Figure 4.

Referring to Figure 4, the normal component of force is

( ) ( )0

6

c

uN P P dx=

where c is the chord length, Pand Puare the pressures on the lower and upper surfaces.

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The axial component of force is ( ) ( )2

2

7

t

f r

t

A P P dy

=

where Pfis the pressure upstream of the maximum thickness, Pris the pressure downstream

of the maximum thickness, and t is the maximum thickness.

From the resolution of forces, the lift and drag forces are

( )

( )

cos sin 8

sin cos 8

L N A a

D N A b

a a

a a

=

= +

Substitute Equations (6) and (7) into Equation (8a) and divide throughout by 21

2U c , the lift

coefficient is given by

( ) ( )

( ) ( ) ( ) ( )

2

Pr

0

2

1 0 0.075

Pr Pr

0 0.075 0

1cos sin

cos sin 9

t

c

L P Pu Pf

t

P Pu Pf Pf u

C C C dx C C dyc

x y yC C d C C d C C d

c c c

a a

a a

+

+

=

= +

Similarly, the drag coefficient is given by

( ) ( )

( ) ( ) ( )

2

Pr

0

2

1 0 0.075

Pr Pr

0 0.075 0

1sin cos

sin cos (10)

t

c

D P Pu Pf

t

P Pu Pf Pf u

C C C dx C C dyc

x y yC C d C C d C C d

c c c

a a

a a

+

+

= +

= + +

The integrals of the above equations are areas between pressure distribution curves in

Figure 5.

3.4 Trapezoidal Method

Each area may be approximated by several trapezoids, the width of which may be non-

uniform. The trapezoidal method, as illustrated in Figure 6, is a simple geometric

approximation to a strip between the curves y=f(x) and y=g(x) by assuming the change

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between any two points x=a and x=b is linear:

[ ] ( )( ) ( ) ( ) ( )

( ) ( ) (11)2 2

b

a

f a f b g a g bf x g x dx b a

+ +

By summing up the areas of several trapezoids, the area enclosed by the pressure

curves or loops may be approximated.

3.5 Thin Airfoil Theory

The thin airfoil theory is an inviscid theory which is used to predict the lift acting on an

airfoil. It predicts that the lift coefficient is directly proportional to the angle of attack in

radian. Analytically, the above statement can be stated as

(12)2LC a=

This prediction isquite accurate when the angle of attack is smaller than the stall angle.

When the angle of attack is small, the flow over it is attached to the upper andlower

surfaces since an airfoil is a streamlined body 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 airfoil. When this happens, flow separation is said tohave

occurred and the phenomenon is known as stall. The angle of attack at which stall firstoccurs is called the stall angle.

4. Procedure

The Experiment and Tables may be done as a group effort.

4.1 Experiment

a.Check that there is no air bubble in the manometer tubes. Level the manometer base,and record the inclination 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 15 m/s, as

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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 t h a t the zero angle of incidence corresponds to that on the end plate, by

observing the pressure reading at the leading edge (tube 1). Zero incidence occurs

when the leading edge pressure is amaximum (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, as shown in Figure 3. 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.

4.2 Tables

a. Table 1 gives the non-dimensional coordinates of the pressuretappings.

b. Record the manometer readings, at the specified angle of incidence, in Table 2.

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

5. Results and Discussion

The Results (including calculations & graphs) and Discussion should be done individually.

5.1 Results

a. Calculate the free-stream velocity and the Reynolds number.

b. Plot CPand CPuagainst x/c as illustrated in Figure 5. Extrapolate your curves to the

trailing edge x/c = 1.

c. Plot CPf and CPr against y/c as illustrated in Figure 5. Clearly indicate whether it

corresponds to the lower or upper surfaces. Make sure that the pressure distributions

are continuous at the leading and trailing edges, y/c=0; that is, (CPf)u can only be

joined to (CPf); and (CPr)ucan only be joined to (CPr). In this plot, two pressure loops

should be obtained. Check carefully to ascertain whether each loop is contributing to

a positive or negative axial force

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d. The lift and drag coefficients, CLand CD, may be obtained from the integration of the

pressure coefficient curves as indicated by Equations (9) and (10). The definite

integral is the area between the pressure curves or net area enclosed by the pressure

loops, as shown in Fig 5. Be careful with the signs of the areas!

e. Calculate the lift-drag ratio CL/CD.

5.2 Discussion

a. State the value of the maximum CPand its location (x/c, y/c). Do you expect the value

of maximum CPto be higher, if you increased the angle of incidence?

b. Was the shear stress along the airfoil included in the pressure measurement by the

manometer? Hence, statewhether your experimental CLand CDcorresponded to the

total lift and drag on the airfoil. Suggest another method to measure lift and drag otherthan pressure distribution.

c. Compare your experimentally measured CLwith the Thin Airfoil Theory predictionof

CL= 2.

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?

6. Conclusions and Recommendations

6.1 Conclusions

This experiment investigated the pressure distribution over an airfoil at a small angle of

attack with the flow. The pressure distribution curves were integrated to obtain the lift and

drag forces on the airfoil. The experiment illustrated the concept of lift and drag forces

generated by a streamlined body moving through air. It demonstrated the significance of the

non-dimensional lift and drag coefficients.

6.2

Recommendations

Further studies include experiments at other angles of attack to investigate the variation of

lift with incidence and determine the stall angle. Studies at higher Reynolds number will be

interesting to show the effect of boundary layer transition on the surface from laminar to

turbulent flow.

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References

1. Anderson J.D. Fundamentals of Aerodynamics, McGraw Hill.

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

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

a)

b)

c)

Figure 1. a) Airfoil Terminology; b) Pressure Gradient across a Curved Streamline;

c) Streamlines over an Airfoil

P

P

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Figure 2. Airfoil in the Wind Tunnel

Figure 3. Schematic Diagram (Side View) of Pressure Measurement

airfoil

end late

multimanometer

flow flow

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Figure 4. Forces and Pressure on an Airfoil

P

(Pf)u

(Pr)u

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Figure 5. Pressure Distribution around an Airfoil; at a=10and Re=2.33x105

-3

-2.5

-2

-1.5

-1

-0.5

0

0.5

1

1.5

0.000 0.200 0.400 0.600 0.800 1.000 1.200

-3

-2.5

-2

-1.5

-1

-0.5

0

0.5

1

1.5

-0.100 -0.050 0.000 0.050 0.100

Cp

x/c

CPu

CP

cP

y/c-y/c

lower surface upper surface

(cPf)u

(cPr)u

(Cpf)

(cPr)

( )1

0

area between curvesP Pu

xC C d

c

=

( ) ( )0 0.075

Pr Pr

0.075 0

horizontal shading vertical shading

net area within loops Pf Pf uy y

C C d C C d c c

+

= +

+ve

-ve -ve

trailing edge

leading edge

leading edge

trailing edge

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Figure 6. Area between Two Curves using Trapezoidal Method

Table 1. Coordinates of Pressure Tappings

Tapping No. x mm |y| mm x/cy/c y/c

upper lower

1 0 0 0 0 0

2 2.5 3.268 0.025 0.032 -0.032

3 5 4.443 0.049 0.044 -0.044

4 10 5.853 0.098 0.058 -0.058

5 20 7.172 0.197 0.071 -0.071

6 30 7.502 0.295 0.074 -0.074

7 40 7.254 0.394 0.071 -0.071

8 50 6.617 0.492 0.065 -0.065

9 60 5.704 0.591 0.056 -0.056

10 70 4.58 0.689 0.045 -0.045

11 80 3.279 0.787 0.032 -0.032

12 (extrapolated) 101.6 0 1 0 0

Note: c = 101.6 mm

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Table 2. Manometer Readings

Atmospheric temperature (at beginning of experiment):(at end of experiment) :

Airfoil angle of incidence, a:

Manometer inclination to horizontal, :

Manometer reading of dynamic pressure, hT-h, (at beginning of experiment):(at end of experiment) :

Manometer readings of pressure distribution, h- h (see Fig 3)

Tapping No.h-h h- h

upper surface (at a) lower surface (at -a)

1

2

3

4

5

6

7

8

9

10

11

12(extrapolated)

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Table 3. Pressure Coefficients (from Equation 5)

Tapping No.cPu cP

upper surface (at a) lower surface (at -a)

1

2

3

4

5

6

7

8

9

10

11

12(extrapolated)

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Appendix A. Location of Engineering Workshop 2

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me2135-2 lab manual (flow over an airfoil)

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