ME-410
MECHANICAL ENGINEERING SYSTEMS LABORATORY
EXPERIMENT-6 CHARACTERISTICS OF AN AIRFOIL
OBJECT
The aim of this experiment is to obtain the pressure distribution around an airfoil, and
to determine the lift, drag and pitching moment variations with different angles of
attack.
THEORY
The drag force, FD is the component of force on the body acting parallel to the
direction of motion. Most of the information about the drag force on the bodies is a
result of huge number of experiments in the wind tunnels, water tunnels etc. on scaled
models. These data can be interpreted in terms of the non-dimensional drag
coefficient, CD, as
CD =
D
1
ρV 2 AP
2
AP = Maximum projected wing area (for other objects frontal area is used)
½ ρ V2 = Dynamic pressure in terms of free stream velocity V.
If compressibility and free surface effects are neglected drag coefficient is a
function of Reynolds number only. For a given configuration Reynolds number is
Re
=
ρ ⋅V
μ
⋅ t
t = maximum thickness of the airfoil section
The total drag force, FD is the sum of the friction drag and pressure drag. Fig 1
illustrates the two extremes.
V
FD =
∫τ
wall
plate−surface
.dA
τ wall
Turbulent Wake Behind a Flat Plate
Normal to the flow
Wall Shear stress does not contribute to
drag force only pressure (form) drag
Flow over a flat plate parallel to the flow
pressure gradient =0
Only friction drag
Fig-1 Flow Over a Flat Plate at Different Orientations
EXPERIMENT 6 CHARACTERISTICS OF AN AIRFOIL
1
CD = Drag coefficient
In Fig. 2 Drag coefficients for a few selected objects are given. This experimental data
is for single objects immersed in an unbounded fluid stream. Wind tunnel tests require
corrections to simulate the condition of an unbounded flow.
Fig.2 Drag coeffient for selected objects
Fig.3 Drag coefficient on a streamlined strut as a
function of thickness ratio, showing contribution of
skin friction and pressure to total drag.
By streamlining, the separated flow region can be reduced thus pressure drag
decreases. However since surface area also increases so as the friction drag, in Fig. 3,
there is an optimum streamline shape which gives minimum total drag.
Lift force FL acts on an immersed body normal to the relative motion between
fluid and the body. Fig. 4 illustrates the production of dynamic lift on a cambered
airfoil at angle of attack (α=8.6o )
Chord, c
Negative pressure on
suction (upper) surface
Positive pressure on
pressure (lower) surface
Stagnation point s
Fig. 4 Streamlines and pressure distribution about a cambered airfoil,
at angle of attack α=8.6o
EXPERIMENT 6 CHARACTERISTICS OF AN AIRFOIL
2
The lift coefficient CL is defined as
C
F
=
L
L
1
ρ .V 2 . A P
2
where AP is projected wing area and it is equal to chord times span (see Fig. 8)
Lift Coefficient From Pressure Distribution:
The lift coefficient may be calculated from the pressure distribution on the
upper and lower surfaces such as shown in Fig. 4. Referring to Fig.5 and Fig.6,
pressure coefficient CP, and the components of the resultant force, CZ and CX in
respective directions are defined as follows,
CZ =
x
C
.
d
(
)
p
∫
c
SURFACE
CP =
where
p a − pi
1
ρ .V 2
2
CX =
z
C p .d ( )
c
SURFACE
∫
Pa = Pressure on airfoil surface
Pi = Inlet pressure(reference pressure)
The ordinates of the highest and lowest points on the sections are z2 and z1
respectively. From geometry of the airfoil
CL = CZ cosα – Cx sinα
CD = CZ sinα + Cx cosα
For numerical integration of CX and CZ please refer to APPENDIX
P.dx
P.ds
P.dz
ds
Z
CL
X
CZ
O
V
α
V
α
CX
CD
Fig 5&6 Normal Pressure Force on an Element of Airfoil surface and
Coefficients of Aerodynamic Forces at Different Directions
EXPERIMENT 6 CHARACTERISTICS OF AN AIRFOIL
3
Pitching moment M is the moment acting in the plane containing the lift and the drag.
It is positive when it tends to increase incidence. The moment coefficient CM (with
respect to 0.25c) is defined as
CM =
M
1
ρ V 2 A P .c
2
In order to complement the theory presented in this section references can be used,
following keywords may guide you:
9
9
9
9
9
9
9
9
9
9
Effect of Flaps on Aerodynamic Characteristics of Airfoil Sections
Laminar-Flow and Conventional Airfoil Sections
Effect of Compressibility, on Drag and Lift
Lift and Drag in Automotive Applications
Designation of Airfoil Section Shapes
Optimum Shapes for Low Drag
Polar Plots (plots of CLand CD)
Lift and Circulation
Induced Drag
Stall
EXPERIMENTAL SET UP
300mm × 300mm Suction Wind Tunnel:
For better understanding refer to Fig 7
Double Butterfly Valve
Guided
Vane
Assembly
Silencer
24 Tube
Manometer
Pitot Tube
Total
Tube
Head
Effuser
Diffuser
Model Holder
Protective
Screen
Starter
20 way scanning box
Fig 7 : 300mm × 300mm Suction Wind Tunnel
The tunnel, of the open circuit type, is constructed mainly in aluminium, and
supported by a tubular steel framework. The air enters the tunnel through a carefully
shaped inlet, the entrance being covered by a protective screen. The working section
is of perplex giving full visibility and the various models are supported from one of
EXPERIMENT 6 CHARACTERISTICS OF AN AIRFOIL
4
the sidewalls or by means of the three component balance. At the upstream end of the
working section there is a static tapping and a total head tube. While at the
downstream end there is pitot static tube, which may be traversed over the full height
of the working section (Fig 8).
TOTAL HEAD TUBE
PITOT STATIC TUBE
STATIC TAPPING
305 mm
FLOW DIRECTION
128 mm
283 mm
PLANE
3
PLANE 2
MOUNTING
MODEL
AXIS
PLANE
1
Fig. 8 Dimensions of the Test Section
152 mm
UPPER SURFACE
LOWER SURFACE
After the working section a diffuser leads to the axial flow fan unit and the air
velocity is controlled by means of a double butterfly valve on the fan outlet. The fan
discharges by way of a silencer. Maximum air velocity is such that pressure
differences of the order of 300mm water are developed and these may be read with
suitable accuracy by the simple manometer provided.
As an airfoil model NACA 0012 profile is used. In Fig 9 the locations of
pressure tappings and dimensions of the model are given.
z
t =9 mm
148.5 mm
NACA 0012 AIRFOIL PRESSURE TAPPINGS: ORDINATES ‘Z'
UPPER
SURFACE
LOWER
SURFACE
1.52
7.62
15.24
22.86
41.15
59.44
77.73
96.02
114.30
129.54
0.76
3.81
11.43
19.05
38.00
62.00
80.77
101.35
121.92
137.16
Fig 9 Pressure Tapping Locations of the Airfoil Model
EXPERIMENT 6 CHARACTERISTICS OF AN AIRFOIL
5
LOAD CELLS
AFT LOAD
CABLE
STRAIN GAUGE
AMPLIFIERS
TO DISPLAY
UNIT
MOUNTING PLATE
LOAD
CELLS
CLEARANCE HOLE
MODEL
INCIDENCE
CLAMP HOLDER
MODEL
MOUNTING BEAM
CENTERING
CLAMPS
DISPLAY UNIT
AIR
FLOW IN
Fig.10 Three Component Balance
Three Component Balance :
The balance is mounted on the side wall of the test section of the tunnel, and it
will be used to measure lift and drag forces acting on the model.
Referring to Fig 10 its main framework comprises a mounting plate, which is
secured to the wind tunnel working section, and carries a triangular force plate. The
force plate and mounting plate are connected by these supporting legs, disposed at the
corners of the force plate. Each leg is attached to the force plate and mounting plate
by spherical universal joints. The effect of this is to constrain the force plate to move
in a plane parallel to the mounting plate, while leaving it free to rotate about a
horizontal axis. The necessary three-degree of freedom is thus provided.
The model support is free to rotate in the force plate for adjustment of the
angle of incidence (attack) of the model while its position may be locked by means of
an incidence clamp.
The force plate may be locked in position by two centering clamps, and these
should always be tightened when the balance is not in use, or when changing models.
The forces acting on the force plate are transmitted by flexible cables to strain
gauge load cells, which measure respectively the aft, and fore lift forces and the drag
force. The drag cable which lines horizontally, acts on a line through the center of the
model support, while the two lift cables act vertically through points disposed
equidistant from the center of the model support and in the same horizontal plane with
the support.
The sum of the forces on the fore and aft lift tapes thus gives the lift on the
model, while the difference when multiplied by 0.127 gives the pitching moment in
Newton-meters.
A drag balance spring acts on the force plate to apply preload to the drag load
cell.
The output from each load cell is taken to a strain gauge amplifier carried on
the mounting plate and hence via a flexible cable to a display unit comprising a set of
EXPERIMENT 6 CHARACTERISTICS OF AN AIRFOIL
6
three electronic voltmeters, showing the output from the respective load cell circuits
(Fig 10 Lower right)
Computer Control With the Wind Tunnel:
The software COMPEND W which runs on a PC is interfaced with threecomponent balance, the 20 way scanning valve which constraints also the pressure
transducers and single axis traverse mechanism.
When the equipment interface for computer control and data acquisition,
COMPEND W is used with the wind tunnel, it is possible to present experimental
results rapidly and clearly on the video display unit, with copies available for analysis
from the printer.
Each data point recorded by COMPEND W is the mean of several separate
readings taken over a specified time period. Hence high frequency fluctuations can be
averaged.
Setting up the system and running COMPEND will be demonstrated by your
lab assistant during experiment.
20 Way Scanning Valve:
The 20 way scanning valve provides a method of performing 20 pressure
measurements in sequence automatically. Tubes are connected to 20 solenoid valves
on a common manifold. These valves are appeared in turn to allow the pressure to act
on a sensitive differential pressure transducer with a full scale range of 500mm H2O.
The opening of the valves can be manually stepped using the up and down buttons,
automatically stepped at a present time interval or controlled by COMPEND W when
scanning valve is set to PULSE mode. Thus data from any pressure port on the airfoil
model can be obtained by selecting the pressure port number.
The two additional pressure transducers (PRESSURE 2 [P2] and PRESSURE
3 [P3]), have a full scale range of 700mm H2O. These transducers are used too
measure dynamic pressure at the inlet and exit of the test section. Thus connected to
total and static tubes differentially at these locations (see Fig 8).
TEST PROCEDURE
1. Read Fluid Mechanics Laboratory Rules and Regulations before starting
which is posted in technicians’ room.
2. Check whether the centering clamps are tight, set the airfoil support at zero
incidence and tighten the incidence clamp.
3. Switch on the mains supply in the force display unit. It is desirable to allow a
warm up time of fifteen minutes for the load cells before taking any readings.
During this time record atmospheric pressure and temperature.
4. Release the centering clamps. Record zero readings of aft lift, fore lift and
drag.
5. Start the electric motor, which drives the wind tunnel. Set the tunnel speed
using the butterfly valve. Record inlet dynamic pressure as a difference of inlet
static and total pressure manometer readings. Use this value to calculate wind
velocity.
6. Press ‘Hold Display’ button on the display unit. Record the readings of the
digital voltmeter.
EXPERIMENT 6 CHARACTERISTICS OF AN AIRFOIL
7
7. By 4° increments, increase the angle of attack and make a series of
measurements of lift and drag up to 20° of attack. The angles may be set by
releasing the incidence clamp, rotating the model support to the desired angle
and retightening the clamp.
THE CENTERING CLAMP MUST BE LOCKED BEFORE RELEASING THE
INCIDENCE CLAMP OR HANDLING THE FORCE PLATE IN ANY WAY
OTHERWISE THERE IS A RISK OF DAMAGING THE LOAD CELLS.
Due to blockage of the airfoil at high angles of attack, tunnel velocity may
change, make the experiment at fixed tunnel speed by regulating with the butterfly
valve.
Pressure distribution on the airfoil
8. Set the airfoil to an angle of attack selected by your lab assistant
9. Record pressure from [P1] cell on the COMPEND main screen at the
displayed scanning positions. The scanning will continue manually until the
pressure at all twenty points on the airfoil have been measured and recorded.
10. Record the dynamic pressure for the calculation of free stream velocity from
PRESSURE 3 cell on the COMPEND main screen.
CALCULATIONS
1. Free stream velocity
V=
2
ρ air
.ΔPi .g .ρ water
where ΔPi is the upstream dynamic pressure in mH2O.
2. Drag, lift forces and pitching moment at each angle of attack
FD = D
FL = (A+F)
M = 0.127 (F-A)
where A, F and D are obtained after correcting the readings by zero readings
as follows
A = AOFF – AON
F = FOFF - FON
D = DON - DOFF
(Lift force from aft load cell in Newtons)
(Lift force from fore load cell in Newtons)
(Drag force from drag load cell in Newtons)
3. Calculate CL, CD and CM using force balance readings directly.
4. Tabulate FD, FL, M, CL, CD and CM with respect to angle of attack.
EXPERIMENT 6 CHARACTERISTICS OF AN AIRFOIL
8
5. Calculate pressure coefficients;
where
P − Pi
CP = a
1
.ρ air .V 2
2
Pa : Static pressure on the surface of the airfoil in Pa.
Pi : Inlet static pressure
V : free stream velocity
and complete Table 1 in Appendix.
6. After obtaining the pressure distribution around the airfoil, using Table 1 and
the expressions given in Theory and Appendix, calculate lift and drag
coefficients.
COMPARE them with the ones you measured directly from the balance.
GRAPHS
Draw the following curves on graph paper
a) On the same graph plot CL, CD and CM vs. the angle of incidence. Label the curve
with the Reynolds number of the flow.
b) Plot CP vs. x/c along the chord direction at the selected angle of attack.
EXPERIMENT 6 CHARACTERISTICS OF AN AIRFOIL
9
UNCERTAINTY ANALYSIS
1.INTRODUCTION
As the second part of the experiment, you will perform an uncertainty analysis
for the wind tunnel experiment.
The term uncertainty is used for refer to a ‘ possible value that an error may
have ‘. It is necessary to make distinction between single sample and multiple sample
uncertainty analysis. The distinction hinges on whether or not a ‘ large’ or ‘small’
number of independent data points are taken at each test point and on how the data are
handled.
2. THEORY
2.1. Describing a variable
Consider a variable Xi which has a known uncertainty δXi. The form of
representation of this variable and its uncertainty is
xi = x mean (measured ) ± δxi
Which should be interpreted as
x mean
1 n
= .∑ xi
n i =1
•
The best estimate of xi is x mean , where
•
There is an uncertainty in Xi that may be as large as δXi . The value of δXi can be
taken as 2σ for a single sample analysis or as nσ where n is the coefficient that
can be taken from Z-distribution table for a desired confidence level.
σ is the standard deviation of the data set, given as
σ =(
n 0 ,5
) .σ f
n −1
where σf is the deviation for a finite number of measurements, given as
σf =
1 n
.∑ ( xi − xmean ) 2
n i =1
2.2 The Root Sum Square (RSS)
The uncertainty of a result may depend on the uncertainties of the individual
measured quantities and on how these quantities are combined. In general if a result Q
is a function of more than one variable Xi, then the expected value Qmean will be
calculated through the expected values of the affecting, Ximean, and will have an
overall uncertainty,
δq = [(
dq
dq
.δ x1 ) 2 + (
.δ x 2 ) 2 + ......] 0.5
dx1
dx 2
EXPERIMENT 6 CHARACTERISTICS OF AN AIRFOIL
10
The partial derivatives of q with respect to Xi ‘s are the sensitivity coefficients for the
result q with respect to measurement Xi. When several independent variables are used
in the function of q, the individual terms are combined by RSS method. Then,
Q = Qmean ± δq
2.3. Single Sample Analysis
Unlike a multiple sample experiment, in which the variable error in a set of
measurements can be determined from variance of the set itself, simple sample
experiments require an auxiliary experiment in order to estimate the variable
component of the uncertainty. This usually takes the form of a set of independent
observations of the process at a representative test condition over a representative
interval of time. The principal difficulty here is finding σ, the standard deviation of
the population from a smaller than infinite set of observations. σ is different from the
standard deviation of the set of observations made in the auxiliary experiments, but
can be estimated from it, as given above.
In single sample uncertainty analysis, each measurement is assigned three
uncertainty value, its zeroth, first, and Nth order uncertainties.
• The zeroth order uncertainty of a measurement is the RSS combination of all
the fixed and random uncertainty components introduced by the measuring
system.
• The first order uncertainty of a measurement describes the scatter that would
be expected in a set of observation using the given apparatus and
instrumentation system, while the observed process is running. The first order
uncertainty includes all effects of process unsteadiness as well as the variable
error effects from the measuring system. The first order uncertainty interval
must be measured in an auxiliary experiment.
• The Nth order uncertainty of a result is a measure of its overall uncertainty,
accounting for all sources of fixed and variable errors. This is the value that
should be reported as the overall uncertainty. The Nth order uncertainty is
calculated as the RSS combination of the first order uncertainty δXi,1, and the
fixed errors from every source.
3. PROCEDURE
Make a simple sample analysis by performing an auxiliary experiment at a
certain airfoil position (with fixed incidence and fixed tunnel speed).
a) Take the necessary data after disturbing the system and returning back to
the fixed operating point. You can disturb the system in various ways like
playing with the butterfly valve, angle of attack or their combination, but
make sure that you take the disturbance back so that you are at fixed
operating point again, just then you can take your readings.
b) Referring to the above terminology and to the lecture notes, make an
uncertainty analysis for the following terms and report their Nth order
uncertainty;
• Inlet Dynamic Pressure Readings both for manometer and transducer(ΔPi )
• Display unit readings (A,F,D)
EXPERIMENT 6 CHARACTERISTICS OF AN AIRFOIL
11
Assume that all the fixed error on the display unit readings are corrected by
subtracting zero values at the specific angle of attack. Also assume that there is no
fixed error on Δh (inlet dynamic pressure manometer).
c) Find out the uncertainty for Re, CL , CD by performing RSS method.
d) Use inlet dynamic pressure manometer to find the fixed error of the inlet
pressure transducer.
DISCUSSION & CONCLUSION
Discuss what have you observed during the experiment, NOT WHAT YOU DONE.
Also discuss the results
9 Do you think they are reasonable? Why or why not?
9 Compare the behaviour of curves and relate them to each other etc….
Write about the shortcomings of the experiment and your recommendations.
Note that the originality of the discussions is for your benefit. Remember what is
graded is the degree to which you can correctly comment on the experiment and the
results.
REFERENCES
1. Moffat, R. J. ; “Describing the Uncertainties in Experimental Results”;
Experimental Thermal and Fluid Science no:1 pp.3-17 ;1988.
2. Moffat, R. J. ; “Using Uncertainty Analysis in the Planning of the Experiments”;
Journal of Fluid Engineering Vol. 107 pp. 173-182 ; 1985
3. Moffat, R. J. ; “Contributions to the Theory of Single Sample Uncertainty
Analysis”; Journal of Fluid Engineering Vol. 104 pp. 250-260 ; 1982
4. Abernety, R. B. ; Benedict, R. P. ; Dowdell, R.B. ; “ASME Measurement
Uncertainty”; Journal of Fluid Engineering Vol. 107 pp. 161-164 ; 1985
5. Dauherty, Robert L. ; “ Fluid Mechanics with Engineering Applications”;1985
6. Fox, Robert W. ; “ Introduction to Fluid Mechanics ”;1985
7. ME-483 Experimental Techniques in Fluid Mechanics Lecture Notes by O. Cahit
Eralp, 2002
8. Lecture notes by Orhan Kural
EXPERIMENT 6 CHARACTERISTICS OF AN AIRFOIL
12
APPENDIX
NUMERICAL INTEGRATION OF CX AND CZ
C =152 mm
Cz
Cp18 20
X
20
FLOW
4
21
2
19
Direction
17
0
5
CCW
Cp19 17
Cp3 5
C P21 =
Assume
C ij =
Define
CZ = −
C
X
=
1
c
1
c
C P20 + C P19
C Pi + C PJ
Cp 3 1
C P1 + C P2
2
Cp ij= Pressure coefficients acting
on the airfoil panel between
pressure tapping positions i and j
2
C Pij . Δ x
for For
_ all
all panels
panels
(going
( going
_ CCW)
CCW )
∑
1
3
C P0 =
2
∑
Cp 0 2
Z
18
C
P ij
for _ all
For all panels
panels
(going_CCW)
( going
CCW
)
.Δ z
EXPERIMENT 6 CHARACTERISTICS OF AN AIRFOIL
Δ x = x j − xi
Δ z = z j − zi
13
FORMAT OF THE LAB. REPORT
SHORT EXPERIMENT
Â
Â
Â
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OBJECTIVE
( 1 page long at most )
SAMPLE CALCULATIONS
GRAPHS
(On graph paper with acceptable format)
CONCLUSION
INDIVIDUAL PERFORMANCE
5
30
15
20
10
QUIZ
20
TOTAL
100
LONG EXPERIMENT
Â
Â
Â
Â
Â
Â
Â
Â
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ABSTRACT & OBJECTIVE
NOMENCLATURE & REFERENCES
INTRODUCTION
THEORY
EXPERIMENTAL PROCEDURE
SAMPLE CALCULATIONS
GRAPHS
DISCUSSION & CONCLUSION
INDIVIDUAL PERFORMANCE
5
5
5
5
5
50
20
25
10
QUIZ
20
TOTAL
150
You are expected to bring the following materials.
Â
Â
Â
CALCULATOR
FLUID MECHANICS TEXT BOOKS
ME-410 LECTURE NOTES
NO OTHER MATERIAL WILL BE ALLOWED FOR USE IN SHORT
EXPERIMENTS.
EXPERIMENT 6 CHARACTERISTICS OF AN AIRFOIL
14
ME - 410
CHARACTERISTICS OF AN AIRFOIL
DATA SHEET
NAME:
STUDENT NO:
AMBIENT CONDITIONS
Temperature ( Co )
Pressure ( mmHg )
LAB DATE:
LAB GROUP:
SUPERVISOR SIGN:
ΔPi, Inlet Dynamic Pressure (mm H2O) [P3] =
Alpha (α)
Data #
1
2
3
4
5
6
7
8
9
10
A, Aft Load Cell [N]
Degree
AOFF
AON
D, Drag load Cell
[N]
F, Fore Load Cell [N]
FOFF
FON
DOFF
DON
UNCERTAINITY ANALYSIS ( AUXILARY TEST DATA SHEET )
Sample #
1
2
3
4
5
6
7
8
9
10
Δpi [ P3]
mm H2O
Aft (A)
[N]
Fore (F)
[N]
EXPERIMENT 6 CHARACTERISTICS OF AN AIRFOIL
Drag (D)
[N]
Δpi [ manometer]
mm H2O
15
PRESSURE DISTRIBUTION OVER THE AIRFOIL
LOWER SURFACE
No
Pa
(mm
H2O)
Pa-Pi
(mm
H2O)
UPPER SURFACE
No
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
Pa
(mm
H2O)
ANGLE OF ATTACK
( o)
Pa-Pi
(mm
H2O)
(mm H2O)
INLET
STATIC
PRESSURE
(Pi)
INLET
DYNAMIC
PRESSURE
(ΔPi)
TABLE-1
No
21
19
17
15
13
11
9
7
5
3
1
0
2
4
6
8
10
12
14
16
18
20
CP
x(mm)
152.00
129.54
114.30
96.02
77.73
59.44
41.15
22.86
15.24
7.62
1.52
0.00
0.76
3.81
11.43
19.05
38.00
62.00
80.77
101.35
121.92
137.16
z(mm)
0.00
3.08
4.77
6.53
7.94
8.87
9.09
8.13
7.12
5.41
2.59
0.00
1.86
3.98
6.39
7.69
9.03
8.77
7.73
6.05
3.95
2.16
Cpij
EXPERIMENT 6 CHARACTERISTICS OF AN AIRFOIL
dxij
dzij
-22.46
3.08
-15.24
1.69
-18.28
1.76
-18.29
1.41
-18.29
0.93
-18.29
0.22
-18.29
-0.96
-7.62
-1.01
-7.62
-1.71
-6.10
-2.82
-1.52
-2.59
0.76
1.86
3.05
2.12
7.62
2.41
7.62
1.30
18.95
1.34
24.00
-0.26
18.77
-1.04
20.58
-1.68
20.57
-2.10
15.24
-1.79
14.84
-2.16
SUM=
Cpij*dxij
Cpij*dzij
16