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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
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)
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]
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
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
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
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.
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
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
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
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
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
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
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
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
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
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)
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)
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.
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).
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.
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.
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.