+ All Categories
Home > Documents > HES5340 Fluid Mechanics 2, Semester 2, 2012, Lab 1 - Aerofoil and Pressure Cylinder Test by Stephen,...

HES5340 Fluid Mechanics 2, Semester 2, 2012, Lab 1 - Aerofoil and Pressure Cylinder Test by Stephen,...

Date post: 04-Aug-2015
Category:
Upload: stephenpybong
View: 503 times
Download: 0 times
Share this document with a friend
Description:
HES5340 Fluid Mechanics 2, Semester 2, 2012, Lab Report 1 - Aerofoil and Pressure Cylinder Test by Stephen, P. Y. Bong, Faculty of Engineering and Industrial Science, Swinburne Sarawak
Popular Tags:
23
SWINBURNE UNIVERSITY OF TECHNOLOGY (SARAWAK CAMPUS) FACULTY OF ENGINEERING AND INDUSTRIAL SCIENCE HES5340 Fluid Mechanics 2 Semester 2, 2012 Laboratory Report 1 WIND TUNNEL EXPERIMENT AEROFOIL AND PRESSURE CYLINDER TEST By Stephen, P. Y. Bong (4209168) Lecturer: Dr. Basil, T. Wong Due Date: 9 th November 2012 (Friday), 5pm Date Performed Experiment: 9 th November 2012 (Friday), 5 pm
Transcript
Page 1: HES5340 Fluid Mechanics 2, Semester 2, 2012, Lab 1 - Aerofoil and Pressure Cylinder Test by Stephen, P. Y. Bong

SWINBURNE UNIVERSITY OF TECHNOLOGY (SARAWAK CAMPUS)

FACULTY OF ENGINEERING AND INDUSTRIAL SCIENCE

HES5340 Fluid Mechanics 2

Semester 2, 2012

Laboratory Report 1

WIND TUNNEL EXPERIMENT

AEROFOIL AND PRESSURE CYLINDER TEST

By

Stephen, P. Y. Bong (4209168)

Lecturer: Dr. Basil, T. Wong

Due Date: 9th

November 2012 (Friday), 5pm

Date Performed Experiment: 9th

November 2012 (Friday), 5 pm

Page 2: HES5340 Fluid Mechanics 2, Semester 2, 2012, Lab 1 - Aerofoil and Pressure Cylinder Test by Stephen, P. Y. Bong

Wind Tunnel Experiment – Aerofoil and Pressure Cylinder Test Stephen, P. Y. Bong (4209168)

HES5340 Fluid Mechanics 2, Semester 2, 2012 Page 2 of 23

1.0 Introduction

The aim of the wind tunnel experiment is to measure the drag and lift distributed on pressure

cylinder and NACA0012 Aerofoil with different angle of attack. Apart from that, the pressure

distribution along the pressure points on the pressure cylinder and surface of aerofoil is being

measured as well.

2.0 Objectives

1. To identify the relationship between the velocity of air flow, angle of attack, drag and lift, and

pitching moment acting on aerofoil.

2. To observe the pressure distribution on the pressure cylinder and aerofoil.

3. To comprehend the fundamental concepts and theories of aerodynamics.

3.0 Theory

The shape of an aerofoil causes the air along the top surface to speed up resulting in a negative

pressure and the air on the lower section slow down resulting in a positive pressure. The

combination of these two pressure regions leads to a lift force being generated as illustrated in

Figure 1 and 2 below.

Figure 1: Distribution of Pressure and Viscous Shear Acting on an Aerofoil

(Crowe, C. T., et. al., 2010, p. 364)

Page 3: HES5340 Fluid Mechanics 2, Semester 2, 2012, Lab 1 - Aerofoil and Pressure Cylinder Test by Stephen, P. Y. Bong

Wind Tunnel Experiment – Aerofoil and Pressure Cylinder Test Stephen, P. Y. Bong (4209168)

HES5340 Fluid Mechanics 2, Semester 2, 2012 Page 3 of 23

Figure 2: Pressure and Viscous Forces Acting on a Differential Element of Area

(Crow, C. T., et. al., 2010, p. 365)

Drag Force, ( ) 2

2

1sincos AVCdApF D

A

D ρθτθ ⋅=+−= ∫ Eq. [1]

Lift Force, ( ) 2

2

1cossin AVCdApF L

A

L ρθτθ ⋅=+−= ∫ Eq. [2]

Pressure Coefficient, θ

ρ

2

2

0 sin41

2

1−=

−=

V

ppC p Eq. [3]

Velocity of Air Flow, ρ

)(2 ppV t −

= Eq. [4]

Pitching Moment, qScCM M= Eq. [5]

Page 4: HES5340 Fluid Mechanics 2, Semester 2, 2012, Lab 1 - Aerofoil and Pressure Cylinder Test by Stephen, P. Y. Bong

Wind Tunnel Experiment – Aerofoil and Pressure Cylinder Test Stephen, P. Y. Bong (4209168)

HES5340 Fluid Mechanics 2, Semester 2, 2012 Page 4 of 23

4.0 Experimental Apparatus

1. LS 18013 educational wind tunnel

2. 3 Components Balance

3. Test Model

4. Test Model holder stand

5. 3 Components Balance Display Unit

6. NACA 0012 Aerofoil with pressure tapping

7. Pressure Cylinder

8. 16 Way pressure display unit

4.1 Wind Tunnel

Figure 3: The wind tunnel employed in the experiment to produce laminar air flow and generate pressure

distributions on the pressure points on test models

Page 5: HES5340 Fluid Mechanics 2, Semester 2, 2012, Lab 1 - Aerofoil and Pressure Cylinder Test by Stephen, P. Y. Bong

Wind Tunnel Experiment – Aerofoil and Pressure Cylinder Test Stephen, P. Y. Bong (4209168)

HES5340 Fluid Mechanics 2, Semester 2, 2012 Page 5 of 23

4.2 16-Ways Display Unit

Figure 4: 16-Way Pressure Display Unit

4.3 Pressure Cylinder

Figure 5: Pressure Cylinder

Page 6: HES5340 Fluid Mechanics 2, Semester 2, 2012, Lab 1 - Aerofoil and Pressure Cylinder Test by Stephen, P. Y. Bong

Wind Tunnel Experiment – Aerofoil and Pressure Cylinder Test Stephen, P. Y. Bong (4209168)

HES5340 Fluid Mechanics 2, Semester 2, 2012 Page 6 of 23

4.4 NACA0012 Aerofoil

Figure 6: NACA0012 Aerofoil

Page 7: HES5340 Fluid Mechanics 2, Semester 2, 2012, Lab 1 - Aerofoil and Pressure Cylinder Test by Stephen, P. Y. Bong

Wind Tunnel Experiment – Aerofoil and Pressure Cylinder Test Stephen, P. Y. Bong (4209168)

HES5340 Fluid Mechanics 2, Semester 2, 2012 Page 7 of 23

5.0 Experimental Procedures

5.1 Pressure Distribution on Pressure Cylinder and NACA0012 Aerofoil

1. The 16 Ways Pressure Display Unit, test model holder stand and aerofoil as well as the

pressure cylinder with tapping are set.

2. The 16 Ways Pressure Display Unit is switched on.

3. The wind tunnel is switched on.

4. The “RUN” button on the frequency inverter is pressed. The frequency (wind speed) is

adjusted to 10 Hz.

5. The flow in tunnel is allowed to stabilize for 2 to 3 minutes.

6. 7 and 10 pressure recordings of NACA0012 Aerofoil and pressure cylinder respectively are

recorded.

7. Step 6 is repeated for 15, 20, 25, 30, 35, 40, and 45 Hz.

8. Step 1 to 8 are repeated for Pressure Cylinder.

9. The data are analysed and the graph of pressure reading against pressure point are plotted.

10. The graphs finding are discussed.

Page 8: HES5340 Fluid Mechanics 2, Semester 2, 2012, Lab 1 - Aerofoil and Pressure Cylinder Test by Stephen, P. Y. Bong

Wind Tunnel Experiment – Aerofoil and Pressure Cylinder Test Stephen, P. Y. Bong (4209168)

HES5340 Fluid Mechanics 2, Semester 2, 2012 Page 8 of 23

6.0 Results and Calculations

6.1 Part A: Pressure Distribution on Pressure Cylinder

The pressure distributions on the pressure cylinder obtained from the experiment are tabulated in

Table 1 below.

Table 1: Pressure Distributions on Pressure Cylinder Obtained from Experiment

Pressure

Point 1 2 3 4 5 6 7 8 9 10

Reference

Pressure

(Bar)

0 -0.0065 -0.0017 -0.0016 -0.0013 -0.0003 -0.0055 -0.0014 -0.002 -0.0008

Frequency

(Hz) Average Pressure (Bar)

10 -0.0002 -0.0066 -0.0020 -0.0021 -0.0020 -0.0010 -0.0061 -0.0020 -0.0025 -0.0011

15 -0.0004 -0.0068 -0.0025 -0.0028 -0.0031 -0.0022 -0.0073 -0.0029 -0.0033 -0.0016

20 -0.0008 -0.0071 -0.0031 -0.0039 -0.0046 -0.0040 -0.0090 -0.0045 -0.0044 -0.0024

25 -0.0012 -0.0075 -0.0039 -0.0052 -0.0066 -0.0063 -0.0102 -0.0069 -0.0057 -0.0034

30 -0.0017 -0.0079 -0.0048 -0.0068 -0.0087 -0.0090 -0.0102 -0.0093 -0.0070 -0.0047

35 -0.0021 -0.0084 -0.0059 -0.0085 -0.0101 -0.0100 -0.0102 -0.0100 -0.0088 -0.0057

40 -0.0028 -0.0091 -0.0070 -0.0101 -0.0101 -0.0100 -0.0102 -0.0101 -0.0100 -0.0071

45 -0.0035 -0.0097 -0.0082 -0.0101 -0.0101 -0.0100 -0.0102 -0.0101 -0.0101 -0.0086

The average gauge pressure can be obtained by taking the difference of absolute pressure and reference

pressures as tabulated in Table 1 above. The numerical computations are carried out by the aid of Microsoft

Excel, and the distributions of gauge pressure on the pressure cylinder (in Pa) are tabulated in Table 2 below.

Table 2: Distributions of Gauge Pressure on

Pressure Cylinder Obtained from Experiment

Pressure Point 1 2 3 4 5 6 7 8 9 10

Frequency (Hz) Average Pressure (Pa)

10 -20 -10 -30 -50 -70 -70 -60 -60 -50 -30

15 -40 -30 -80 -120 -180 -190 -180 -150 -130 -80

20 -80 -60 -140 -230 -330 -370 -350 -310 -240 -160

25 -120 -100 -220 -360 -530 -600 -470 -550 -370 -260

30 -170 -140 -310 -520 -740 -870 -470 -790 -500 -390

35 -210 -190 -420 -690 -880 -970 -470 -860 -680 -490

40 -280 -260 -530 -850 -880 -970 -470 -870 -800 -630

45 -350 -320 -650 -850 -880 -970 -470 -870 -810 -780

Page 9: HES5340 Fluid Mechanics 2, Semester 2, 2012, Lab 1 - Aerofoil and Pressure Cylinder Test by Stephen, P. Y. Bong

Wind Tunnel Experiment – Aerofoil and Pressure Cylinder Test Stephen, P. Y. Bong (4209168)

HES5340 Fluid Mechanics 2, Semester 2, 2012 Page 9 of 23

The plot of gauge pressure distribution on pressure cylinder obtained from the experiment versus

pressure point is depicted in Graph 1 below.

Graph 1: Pressure Distribution on Pressure Cylinder

-1000

-900

-800

-700

-600

-500

-400

-300

-200

-100

0

1 2 3 4 5 6 7 8 9 10

Aver

age

Pre

ssure

(P

a)

Pressure Point

Pressure Distribution on Pressure Cylinder

f = 10 Hz f = 15 Hz f = 20 Hz f = 25 Hz

f = 30 Hz f = 35 Hz f = 40 Hz f = 45 Hz

Page 10: HES5340 Fluid Mechanics 2, Semester 2, 2012, Lab 1 - Aerofoil and Pressure Cylinder Test by Stephen, P. Y. Bong

Wind Tunnel Experiment – Aerofoil and Pressure Cylinder Test Stephen, P. Y. Bong (4209168)

HES5340 Fluid Mechanics 2, Semester 2, 2012 Page 10 of 23

6.2 Part B: Pressure Distribution on NACA0012 Aerofoil

The pressure distributions on the NACA0012 Aerofoil obtained from the experiment are tabulated

in Table 3 below.

Table 3: Pressure Distributions on NACA0012 Aerofoil Obtained from Experiment

Pressure Point 1 2 3 4 5 6 7

Reference Pressure (Bar) 0 -0.0064 -0.0017 -0.0016 -0.0013 -0.0003 -0.0054

Frequency (Hz) Average Pressure (Bar)

10 -0.0001 -0.0065 -0.0018 -0.0017 -0.0015 -0.0006 -0.0055

15 -0.0003 -0.0067 -0.0019 -0.0019 -0.0016 -0.0009 -0.0057

20 -0.0005 -0.0068 -0.0021 -0.0021 -0.0018 -0.0013 -0.0059

25 -0.0008 -0.0070 -0.0023 -0.0023 -0.0020 -0.0018 -0.0061

30 -0.0011 -0.0073 -0.0026 -0.0026 -0.0023 -0.0025 -0.0064

35 -0.0015 -0.0076 -0.0029 -0.0029 -0.0026 -0.0032 -0.0067

40 -0.0018 -0.0079 -0.0032 -0.0032 -0.0030 -0.0043 -0.0071

45 -0.0023 -0.0082 -0.0036 -0.0036 -0.0034 -0.0052 -0.0075

The average gauge pressure can be obtained by taking the difference of absolute pressure and reference

pressures as tabulated in Table 3 above. The numerical computations are done by Microsoft Excel, and the

distributions of gauge pressure on NACA0012 Aerofoil (in Pa) are tabulated in Table 4 below.

Table 4: Distribution of Gauge Pressure on NACA0012 Aerofoil Obtained from Experiment

Pressure Point 1 2 3 4 5 6 7

Frequency (Hz) Average Pressure (Pa)

10 -10 -10 -10 -10 -20 -30 -10

15 -30 -30 -20 -30 -30 -60 -30

20 -50 -40 -40 -50 -50 -100 -50

25 -80 -60 -60 -70 -70 -150 -70

30 -110 -90 -90 -100 -100 -220 -100

35 -150 -120 -120 -130 -130 -290 -130

40 -180 -150 -150 -160 -170 -400 -170

45 -230 -180 -190 -200 -210 -490 -210

Page 11: HES5340 Fluid Mechanics 2, Semester 2, 2012, Lab 1 - Aerofoil and Pressure Cylinder Test by Stephen, P. Y. Bong

Wind Tunnel Experiment – Aerofoil and Pressure Cylinder Test Stephen, P. Y. Bong (4209168)

HES5340 Fluid Mechanics 2, Semester 2, 2012 Page 11 of 23

The plot of gauge pressure distribution on NACA0012 Aerofoil obtained from the experiment

versus pressure point is shown in Graph 2 below.

Graph 2: Pressure Distributions on NACA0012 Aerofoil

-500

-450

-400

-350

-300

-250

-200

-150

-100

-50

0

1 2 3 4 5 6 7

Aver

age

Pre

ssure

(P

a)

Pressure Point

Pressure Distribution of NACA0012 Aerofoil

f = 10 Hz f = 15 Hz f = 20 Hz f = 25 Hz

f = 30 Hz f = 35 Hz f = 40 Hz f = 45 Hz

Page 12: HES5340 Fluid Mechanics 2, Semester 2, 2012, Lab 1 - Aerofoil and Pressure Cylinder Test by Stephen, P. Y. Bong

Wind Tunnel Experiment – Aerofoil and Pressure Cylinder Test Stephen, P. Y. Bong (4209168)

HES5340 Fluid Mechanics 2, Semester 2, 2012 Page 12 of 23

6.3 Part C: Measurements of Drag, Lift and Pitching Moment

The drag and lift forces acting on NACA0012 Aerofoil as well as the pitching moment collected from the

experiment are tabulated in Table 5 below.

Table 5: Drag; Lift and Pitching Moment on NACA0012 Aerofoil

Pump (Hz) Pitch, M (N-m) Drag, FD (N) Lift, FL (N) Alpha, α Beta, β

15 -0.383 -0.02383 -0.3745 0 11

20 -0.746 -0.0396 -0.7536 0 11

25 -1.205 -0.0366 -1.1914 0 11

30 -1.7766 -0.0852 -1.7678 0 11

35 -2.465 -0.0914 -2.4594 0 11

15 -0.04775 0.01225 -0.05425 5 0

20 -0.1006 0.032 -0.1104 5 0

25 -0.16275 0.05875 -0.1715 5 0

30 -0.2562 0.0684 -0.2574 5 0

35 -0.371 0.107 -0.389 5 0

15 -0.059 0.003 -0.08 15 0

20 -0.123 0.0202 -0.1366 15 0

25 -0.2126 0.0344 -0.2196 15 0

30 -0.326 0.0584 -0.319 15 0

35 -0.46075 0.0795 -0.45625 15 0

Based on the results tabulated in Table 5 above, the distributions of pitching moment, drag force

and lift force acting on NACA0012 Aerofoil are plotted against the wind speed as illustrated in

Graph 3, 4 and 5 respectively.

Graph 3: Pitching Moment of NACA0012 Aerofoil

-2.5

-2

-1.5

-1

-0.5

0

15 17 19 21 23 25 27 29 31 33 35

Pit

chin

g M

om

ent

(N·m

)

Wind Speed (Hz)

Pitching Moment of NACA0012 Aerofoil

Alpha = 0, Beta = 1 Alpha = 5, Beta = 0 Alpha = 15, Beta = 0

Page 13: HES5340 Fluid Mechanics 2, Semester 2, 2012, Lab 1 - Aerofoil and Pressure Cylinder Test by Stephen, P. Y. Bong

Wind Tunnel Experiment – Aerofoil and Pressure Cylinder Test Stephen, P. Y. Bong (4209168)

HES5340 Fluid Mechanics 2, Semester 2, 2012 Page 13 of 23

Graph 4: Distribution of Drag Force Acting on NACA0012 Aerofoil

-0.1

-0.08

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

0.08

0.1

0.12

15 17 19 21 23 25 27 29 31 33 35

Dra

g (

N)

Wind Speed (Hz)

Drag of NACA0012 Aerofoil

Alpha = 0, Beta = 11 Alpha = 5, Beta = 0 Alpha = 15, Beta = 0

Page 14: HES5340 Fluid Mechanics 2, Semester 2, 2012, Lab 1 - Aerofoil and Pressure Cylinder Test by Stephen, P. Y. Bong

Wind Tunnel Experiment – Aerofoil and Pressure Cylinder Test Stephen, P. Y. Bong (4209168)

HES5340 Fluid Mechanics 2, Semester 2, 2012 Page 14 of 23

Graph 5: Distribution of Lift Force Acting on NACA0012 Aerofoil

-2.5

-2

-1.5

-1

-0.5

0

15 17 19 21 23 25 27 29 31 33 35

Lif

t (N

)

Wind Speed (Hz)

Lift of NACA0012 Aerofoil

Alpha = 0, Beta = 11 Alpha = 5, Beta = 0 Alpha = 15, Beta = 0

Page 15: HES5340 Fluid Mechanics 2, Semester 2, 2012, Lab 1 - Aerofoil and Pressure Cylinder Test by Stephen, P. Y. Bong

Wind Tunnel Experiment – Aerofoil and Pressure Cylinder Test Stephen, P. Y. Bong (4209168)

HES5340 Fluid Mechanics 2, Semester 2, 2012 Page 15 of 23

6.4 Part D: Wind Velocity

The stagnation pressures and static pressures in the pitot tube obtained from the experiment are

tabulated in Table 6 below.

Table 6: Stagnation and Static Pressures

in the Pitot Tube Obtained from the Experiment

Pressure Point 11 12

Reference Pressure

(Bar) 0 0.0002

Frequency (Hz) Average Pressure (Bar)

10 -0.0001 -0.0002

15 -0.0004 -0.0008

20 -0.0008 -0.0015

25 -0.0012 -0.0025

30 -0.0017 -0.0037

35 -0.0022 -0.0050

40 -0.0028 -0.0065

45 -0.0034 -0.0081

The velocity can be computed by Bernoulli’s equation, in which it states that the stagnation pressure

is the summation of static and dynamic pressures. The pressure points “11” and “12” as indicated in

Table 6 above are the points at which the stagnation and static pressure acting on respectively. The

dynamic pressure and the wind velocity are computed by Microsoft Excel and tabulated in Table 7

below.

Table 7: Dynamic Pressure and Wind Velocity Computed from Bernoulli's Equation

Pressure Point 11 12

Dynamic

Pressure (Pa)

Wind

Velocity

(m/s) Frequency

Average Pressure (Pa)

Stagnation

Pressure

Static

Pressure

10 -10 -40 30 7.059312

15 -40 -100 60 9.983375

20 -80 -170 90 12.22709

25 -120 -270 150 15.7851

30 -170 -390 220 19.11671

35 -220 -520 300 22.3235

40 -280 -670 390 25.45271

45 -340 -830 490 28.52987

Page 16: HES5340 Fluid Mechanics 2, Semester 2, 2012, Lab 1 - Aerofoil and Pressure Cylinder Test by Stephen, P. Y. Bong

Wind Tunnel Experiment – Aerofoil and Pressure Cylinder Test Stephen, P. Y. Bong (4209168)

HES5340 Fluid Mechanics 2, Semester 2, 2012 Page 16 of 23

6.5 Sample Calculations

The average pressure at pressure point “3” with frequency of 25 Hz has been selected for the

sample calculations for Part A (Pressure Cylinder) and Part B (NACA0012 Aerofoil).

6.5.1 Sample Calculations for Part A (Pressure Cylinder)

Based on the experimental pressure distribution on pressure cylinder tabulated in Table 1 above, the

reference pressure and average pressure (f = 25 Hz) at pressure point “3” are preference = -0.0017 Bar

and pavg = -0.0039 Bar. Therefore, the average gauge pressure as listed in Table 2 (Row 6; Column

4) can be calculated as follows:

( )

( )[ ]

Pa 220−=

×−−−=

×−=

Bar 1

Pa 10Bar 0017.00039.0

Bar 1

Pa 10Bar

5

5

referenceavg pppg

6.5.2 Sample Calculations for Part B (NACA0012 Aerofoil)

As listed in Table 3, the reference pressure and average pressure (f = 25 Hz) at point “3” are preference

= -0.0017 Bar and pavg = -0.0023 Bar respectively. Thus, the average gauge pressure as listed in

Table 4 (Row 6; Column 4) can be obtained from following computation:

( )

( )[ ]

Pa 60−=

×−−−=

×−=

Bar 1

Pa 10Bar 0017.00023.0

Bar 1

Pa 10Bar

5

5

referenceavg pppg

6.5.3 Sample Calculations for Part D (Wind Velocity)

The average pressure at a frequency of 25 Hz has been selected for the determination of dynamic

pressure and wind velocity. As listed in Table 6, the stagnation and static pressures (f = 25 Hz) are

pstagnation = -0.0012 Bar and pstatic = -0.0025 Bar respectively with a reference pressure of 0 and 0.002

Bar at pressure points “11” and “12”.

According to Munson & Okiishi (2009), the density of air at standard atmospheric pressure at a

temperature of 20 ºC is ρ = 1.204 kg/m3. The Bernoulli’s equation is given by

2

2

staticstagnation

Vpp

ρ+= where

2

2Vρ

is the dynamic pressure

Page 17: HES5340 Fluid Mechanics 2, Semester 2, 2012, Lab 1 - Aerofoil and Pressure Cylinder Test by Stephen, P. Y. Bong

Wind Tunnel Experiment – Aerofoil and Pressure Cylinder Test Stephen, P. Y. Bong (4209168)

HES5340 Fluid Mechanics 2, Semester 2, 2012 Page 17 of 23

Making the velocity V the subject of the equation gives:

m/s 15.79=

×−−−

=−

=3

5

staticstagnation

kg/m .2041

Bar 1

Pa 10Bar)] 0025.0(Bar 0012.0[2)(2

ρ

ppV

7.0 Discussions

7.1 Comparison of Experimental and Theoretical Results

7.1.1 Part A: Pressure Distributions on Pressure Cylinder

Based on the plot of pressure distribution on pressure cylinder as depicted in Graph 1 in the

preceding section, it was found that the pressure readings of gauge pressure obtained from the

numerical computations are negative. This is due to the pressure at each pressure point are

measured relative to the reference pressure (atmospheric pressure).

Apart from that, at any frequency, it had been observed that the greatest pressure distribution on the

pressure cylinder occurred at pressure point “2”. The occurrence of this phenomenon is due to the

fact that the pressure point “2” is the stagnation point where the local velocity of the air flow is zero

in ideal condition. In contrary, the velocity of the air flow at the stagnation point is the smallest (not

equal to zero) in real-life application. The deceleration of air particles in the boundary layer is

resulted by the divergence of air flow.

Another two significant observations in the pressure cylinder test is the pressure drop as the air flow

through the pressure point “2” to pressure point “6”, and the sudden increase in pressure at pressure

point “7” to pressure point “10”. As the flow of air passed through the stagnation point, the upsurge

in velocity and decrease in pressure of air flow occurred. This can be expounded by introducing the

Bernoulli’s equation. Based on Munson & Okiishi (2009, p. 102), Bernoulli states that the

stagnation pressure (or total pressure) is constant along the streamline in which the velocity of the

air flow is inversely proportional to the static pressure. The sudden increase in pressure at point “7”

is due to the formation of vortices as a result of the occurrence of flow separation as illustrated in

Figure 7 below:

Figure 7: Flow Pattern around a Cylinder (Crow, C. T., et. al., 2010, p. 169)

Page 18: HES5340 Fluid Mechanics 2, Semester 2, 2012, Lab 1 - Aerofoil and Pressure Cylinder Test by Stephen, P. Y. Bong

Wind Tunnel Experiment – Aerofoil and Pressure Cylinder Test Stephen, P. Y. Bong (4209168)

HES5340 Fluid Mechanics 2, Semester 2, 2012 Page 18 of 23

In order to compare the experimental pressure distributions on the pressure cylinder obtained from

the pressure cylinder test and the theoretical results which had been studied by Bertin & Cummings

(2009, p. 123), a plot of pressure coefficient with respect to the variation of angle associated with

each pressure point is required. The pressure coefficient of the experimental pressure distribution

with the corresponding angle of each pressure point can be determined by Eq. [3]. The

computations are carried out by using Microsoft Excel, and the pressure coefficients are tabulated in

Table 8 below.

Table 8: Pressure Coefficients (Cp) of Experimental Pressure Distribution on Pressure Cylinder

Pressure

Point

Angle Theta, θ Pressure Coefficient,

θ2sin41−=pC Degree Radians

0 0 0 1

1 13.5 0.235619 0.782013048

2 27 0.471239 0.175570505

3 40.5 0.706858 -0.68713107

4 54 0.942478 -1.618033989

5 67.5 1.178097 -2.414213562

6 81 1.413717 -2.902113033

7 94.5 1.649336 -2.975376681

8 108 1.884956 -2.618033989

9 121.5 2.120575 -1.907980999

10 135 2.356194 -1

The plot of experimental pressure coefficients versus angle of each pressure point are shown in

Graph 6 below.

Graph 6: Plot of Pressure Coefficient (Cp) vs. Angle (θ)

-3.5

-3

-2.5

-2

-1.5

-1

-0.5

0

0.5

1

0 45 90 135

Pre

ssure

Coef

fici

ent

(Cp)

Angle (θ)

Pressure Coefficient (Cp) vs. Angle (θ)

Page 19: HES5340 Fluid Mechanics 2, Semester 2, 2012, Lab 1 - Aerofoil and Pressure Cylinder Test by Stephen, P. Y. Bong

Wind Tunnel Experiment – Aerofoil and Pressure Cylinder Test Stephen, P. Y. Bong (4209168)

HES5340 Fluid Mechanics 2, Semester 2, 2012 Page 19 of 23

Figure 8: Theoretical pressure distribution around a circular cylinder, compared with data for a subcritical

Reynolds number and that for a supercritical Reynolds number. [From Boundary Layer Theory by H.

Schlichting (1968)]

(Bertin, J. J. & Cummings, R. M., 2009, p. 123)

By comparing the experimental pressure distribution obtained from the pressure cylinder test and

the theoretical results studied by Bertin & Cummings (2009, p. 123) as illustrated in Figure 8 above,

the plot of experimental pressure distribution follows the same trend and acts consistently to the

series of theoretical pressure distribution. But, if comparisons are made based on the plot of

experimental pressure distribution as shown in Graph 1, there has large deviations in pressure

distributions with respect to theoretical results at the frequencies or wind velocities which range

from 30 Hz to 45 Hz due to the occurrence of experimental errors which will be discussed in

subsequent section.

7.1.2 Part B: Pressure Distribution on NACA0012 Aerofoil

Based on the plot of experimental pressure distribution on NACA0012 Aerofoil in Graph 2, it had

been observed that the pressure distributions at each of the pressure point are approximately similar

to each other except the pressure readings at pressure point “5”, “6” and “7”. As illustrated in Graph

2 above, the pressure distributions at pressure point “5”, “6” and “7” have large deviations from the

pressure distributions at other pressure points. As a verdict, the experimental pressure distributions

are relatively close to the theoretical results in which the pressure distributions at each of the

pressure point must be equal.

Page 20: HES5340 Fluid Mechanics 2, Semester 2, 2012, Lab 1 - Aerofoil and Pressure Cylinder Test by Stephen, P. Y. Bong

Wind Tunnel Experiment – Aerofoil and Pressure Cylinder Test Stephen, P. Y. Bong (4209168)

HES5340 Fluid Mechanics 2, Semester 2, 2012 Page 20 of 23

7.1.3 Lift Distribution on NACA0012 Aerofoil

According to the distribution of lift force on NACA0012 Aerofoil as tabulated in Table 5 above, the

readings of the lift force are negative. This is due to the fact that the lift force is acting in the

vertical direction in which the direction of gravitational acceleration is assumed to be positive.

Based on the plot of distribution of lift force on NACA0012 against the wind velocity as depicted in

Graph 5, the lift force acting on the NACA0012 Aerofoil is proportional to the velocity of the air

flow. The general definition of lift 2

21 SVCF LL ρ⋅= can be employed in the interpretation of this

phenomenon. Based on the definition of lift, the velocity of the air flow is crucial parameters which

affect the magnitude of lift. In addition, the increase in angle of attack (α) will also result in upsurge

of the lift force since the lift force can be expressed in terms of angle of attack as the Kutta

condition proposes, Γ= 0VlFL ρ or .2

0 απρ SVFL =

7.1.4 Distribution of Drag on NACA0012 Aerofoil

Based on the distribution of drag force on NACA0012 Aerofoil as shown in Graph 4, it had been

observed that the drag is proportional to the velocity of the air flow for angle of attack of 5 and 15

degrees. On the other hand, for an angle of attack of 0 degree, the increase in velocity of air flow

results in the reduction of drag force.

For angle of attack of 5 and 15 degrees, the phenomenon of increase in drag force as the velocity of

air flow increases can be expounded by the general definition of drag .2

21 SVCF DD ρ⋅= The inter-

relationship between drag force and wind velocity are clearly interpreted. According to the general

definition of drag, the velocity of the air flow is a significant parameter in which the drag forces are

greatly influenced. Apart from that, the variation in the angle of attack (5 to 15 degrees in this case)

does not leads to large increment in drag force as for an aerofoil with low angle of attack, the drag

force acting on it are primarily skin friction drag which induced by viscous shear as mentioned by

Crowe (2010, p. 385).

Page 21: HES5340 Fluid Mechanics 2, Semester 2, 2012, Lab 1 - Aerofoil and Pressure Cylinder Test by Stephen, P. Y. Bong

Wind Tunnel Experiment – Aerofoil and Pressure Cylinder Test Stephen, P. Y. Bong (4209168)

HES5340 Fluid Mechanics 2, Semester 2, 2012 Page 21 of 23

7.1.5 Pitching Moment

According to Bertin & Cummings (2009, p. 217-218), pitching moment is one of the component of

total moment generated from the resultant force acting at a distance from the center of gravity of

the airplane as manifested in Figure 9 below.

Figure 9: Reference axes of the airplane and the corresponding aerodynamics moments

(Bertin, J. J. & Cummings, R. M., 2009, p. 217)

Based on Figure 9 above, it can be clearly seen that the pitching moment is the moment about the

lateral axis (y-axis of the coordinate system) due to the distribution of drag and lift forces acting on

the aerofoil that must be counter-balanced. The pitching moment generated as a result of

distribution of drag (form drag and skin drag), and lift can be calculated by introducing the moment

coefficient which can be mathematically expressed as CM = M/qSc, where M, q, S, and c are the

pitching moment, dynamic pressure, planform area, and chord length respectively.

According to the plot of pitching moment versus the velocity of air flow as illustrated in Graph 3

from Section 6.3, as the velocity of the air flow increase, the pitching moment increases. The

occurrence of this phenomenon can be explained based on the dimensionless relationship between

moment coefficient and dynamic pressure as discussed above. The increase in the velocity of air

flow will result in the upsurge of pitching moment due to the increment of dynamic pressure. Apart

from that, based on the plot of pitching moment against the velocity of air flow, there is only a

slight variation in pitching moment with small increment of angle of attack.

Page 22: HES5340 Fluid Mechanics 2, Semester 2, 2012, Lab 1 - Aerofoil and Pressure Cylinder Test by Stephen, P. Y. Bong

Wind Tunnel Experiment – Aerofoil and Pressure Cylinder Test Stephen, P. Y. Bong (4209168)

HES5340 Fluid Mechanics 2, Semester 2, 2012 Page 22 of 23

7.2 Experimental Errors and Suggestions

1. Cause of Experimental Errors: The vibration of air pump is induced with the increase in

velocity of air flow. This is due to the fact that both the air pump and wind tunnel are placed on

a same table. Therefore, as the pumping of air is initiated, and vibration is induced, the entire

wind tunnel as well as the test models (Pressure Cylinder and NACA0012 Aerofoil) inside will

vibrate as well. Thus, this will leads to the occurrence of experimental errors in the reading of

pressure distributions.

Suggestion: The air pump should be placed on a different table so that the vibrations induced

during the suction process can be greatly reduced. Apart from that, a small gap or vacant spaces

should be provided so that the readings of pressure distribution on the test models will not be

affected by the vibrations induced by the air pump.

2. Cause of Experimental Errors: Human errors will occurred in the measurement of angle

associated with each of the pressure point on the pressure cylinder. This will results in small

percentage of errors in pressure coefficients computed from the experimental pressure

distributions.

Suggestion: A manufacturer’s catalogue should be provided, so that all the dimensions of the

test models are clearly stated, and the measurements of the angle associated with each of the

pressure point can be neglected. As a result, the probabilities of the occurrence of human errors

during collection of data can be diminished.

3. Cause of Experimental Errors: The flow of air through the air pump was not steady in the

beginning of experiment, in which consequences the occurrence of fluctuations of pressure

readings shown in the display unit.

Suggestion: In order to minimize the possibilities of the existence of this experimental error, it

is strongly recommended that the pressure readings can be taken after a period of 10 to 15

minutes for steady flow after the velocity of air flow has been adjusted, since a certain period of

time is required for the air pump to operate to its optimum conditions.

8.0 Conclusions

Based on the experimental results obtained from the aerofoil and pressure cylinder tests, it can be

concluded that this experiment possesses the ability to bear out the fundamental theories of aerofoil

and fluid flows across cylinder such as drag and lift, and pitching moment are valid. As a verdict,

the objectives of this experiment were accomplished.

Page 23: HES5340 Fluid Mechanics 2, Semester 2, 2012, Lab 1 - Aerofoil and Pressure Cylinder Test by Stephen, P. Y. Bong

Wind Tunnel Experiment – Aerofoil and Pressure Cylinder Test Stephen, P. Y. Bong (4209168)

HES5340 Fluid Mechanics 2, Semester 2, 2012 Page 23 of 23

9.0 References

Bertin, J. J. & Cummings, R. M., 2009, Aerodynamics for Engineers, 5th

Edn., Pearson Education,

Inc., United States of America.

Crowe, C. T.; Elger, D. F.; Williams, B. C. & Roberson, J. A., 2010, Engineering Fluid Mechanics,

9th

Edn., John Wiley & Sons (Asia) Pte Ltd, Asia.

Lab Sheet: Wind Tunnel Experiment (Aerofoil and Pressure Cylinder Test)

Munson, B. R.; Young, D. F.; Okiishi, T. H.; Huebsch, W. W., 2009, Fundamentals of Fluid

Mechanics, 6th

Edn., John Wiley & Sons, Inc., United States of America.


Recommended