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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

P

D

AV

DC2

21 ρ

=

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

μρ tV ⋅⋅

=Re

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

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

∫−

=surfaceplate

wallD dAF .τ

Fig-1 Flow Over a Flat Plate at Different Orientations

EXPERIMENT 6 CHARACTERISTICS OF AN AIRFOIL 1

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.3 Drag coefficient on a streamlined strut as a function of thickness ratio, showing contribution of skin friction and pressure to total drag.

Fig.2 Drag coeffient for selected objects

CD

= D

rag

coef

ficie

nt

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


The lift coefficient CL is defined as


where A is projected wing area and it is equal to chord times span (see Fig. 8)

P

LL

AV

FC

..21 2ρ

=

P

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 C , and the components of the resultant force, CP Z and CX in respective directions are defined as follows,

∫=SURFACE

pZ cxdCC )(. ∫=

SURFACEpX c

zdCC )(.

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

2.21 V

ppC iaP

ρ

−= Pa = Pressure on airfoil surface

Pi = Inlet pressure(reference pressure)

where

Fig 5&6 Normal Pressure Force on an Element of Airfoil surface and Coefficients of Aerodynamic Forces at Different Directions

V

O

Z

X CL

α

P.ds

P.dx

P.dz

ds

V α CDCX

CZ

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

cAV

MCP

M

.21 2ρ

= In order to complement the theory presented in this section references can be used, following keywords may guide you:

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 C


Land CD) Lift and Circulation Induced Drag Stall

EXPERIMENTAL SET UP

mmmm 300300 × Suction Wind Tunnel:

For better understanding refer to Fig 7

Double Butterfly Valve

Starter

Silencer Diffuser Effuser

20 way scanning box

24 Tube Manometer

Model Holder

Pitot Tube Total Head Tube

Protective Screen

Guided Vane Assembly

mmmm 300300 ×Fig 7 : 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

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).

PLANE 3

PLANE 2 MOUNTING

MODEL AXIS

PLANE 1

FLOW DIRECTION 305 mm

283 mm128 mm

STATIC TAPPING PITOT STATIC TUBE

TOTAL HEAD TUBE

Fig. 8 Dimensions of the Test Section

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.

148.5 mm

z

UPP

ER

SU

RFA

CE

LO

WE

R S

UR

FAC

E

152

mm

NACA 0012 AIRFOIL PRESSURE TAPPINGS: ORDINATES ‘Z'

t =9 mm

UPPER SURFACE

1.52

7.62

15.24

22.86

41.15

59.44

77.73

96.02

114.30

129.54

LOWER SURFACE

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



LOAD CELLS

AFT LOAD CABLE

CENTERING CLAMPS

TO DISPLAY UNIT

LOAD CELLS

INCIDENCE CLAMP

STRAIN GAUGE AMPLIFIERS

MOUNTING PLATE

CLEARANCE HOLE

MODEL MODEL

HOLDER MOUNTING BEAM

AIR FLOW IN

DISPLAY UNIT

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


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 three-component 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.

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

wateriair

gPV ρρ

...2Δ=

is the upstream dynamic pressure in mH O. where ΔPi 2

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 = A – A (Lift force from aft load cell in Newtons) OFF ON F = F - F (Lift force from fore load cell in Newtons)OFF ON D = D - D (Drag force from drag load cell in Newtons) ON OFF

3. Calculate C


L, CD and CM using force balance readings directly. 4. Tabulate FD, FL, M, CL, CD and CM with respect to angle of attack.

5. Calculate pressure coefficients; where


Pa : Static pressure on the surface of the airfoil in Pa.

2..21 V

PPC

air

iaP

ρ

−=

P : Inlet static pressure iV : 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.

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 X which has a known uncertainty δXi i. The form of representation of this variable and its uncertainty is

imeani xmeasuredxx δ±= )(

Which should be interpreted as

∑=

=n

iimean x

nx

1.1

• The best estimate of is , where ix meanx • There is an uncertainty in X that may be as large as δX . The value of δXi i i 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

fnn σσ .)

1( 5,0

−=

where σ is the deviation for a finite number of measurements, given as f

2

1

1 . ( )n

f i mi

x xn

σ=

= −∑ ean

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,


5.022

2

21

1

......]).().[( ++= xdxdqx

dxdqq δδδ


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)


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

Do you think they are reasonable? Why or why not? 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

APPENDIX NUMERICAL INTEGRATION OF C AND CX Z

X

Cp3 5

Cp19 17

Cp 3 1

Cp 0 2

Cp18 20

17

1820

5

19

421 2

3

0

1

Cz

C =152 mm

FLOW

Direction

Z

CCW

21920

21

PPP

CCC

+=

221

0

PPP

CCC

+=Assume

2Ji PP

ij

CCC

+=

Cp ij= Pressure coefficients acting on the airfoil panel between pressure tapping positions i and j

Define

ij xxx −=Δ

ij zzz −=Δ

∑ Δ−=

)_(

_

.1

CCWgoingpanels

allforPZ xC

cC

ij

For all panels (going CCW)

∑ Δ=

)_(

_.1

CCWgoingpanels

allforPX zC

cC

ij

For all panels (going CCW)



FORMAT OF THE LAB. REPORT SHORT EXPERIMENT

OBJECTIVE 5 ( 1 page long at most )

SAMPLE CALCULATIONS 30 GRAPHS 15

(On graph paper with acceptable format) CONCLUSION 20 INDIVIDUAL PERFORMANCE 10

QUIZ 20

TOTAL 100

LONG EXPERIMENT

ABSTRACT & OBJECTIVE 5 NOMENCLATURE & REFERENCES 5 INTRODUCTION 5 THEORY 5 EXPERIMENTAL PROCEDURE 5 SAMPLE CALCULATIONS 50 GRAPHS 20 DISCUSSION & CONCLUSION 25 INDIVIDUAL PERFORMANCE 10

QUIZ 20

TOTAL 150 You are expected to bring the following materials.

CALCULATOR FLUID MECHANICS TEXT BOOKS ME-410 LECTURE NOTES

NO OTHER MATERIAL WILL BE ALLOWED FOR USE IN SHORT

EXPERIMENTS.


ME - 410 CHARACTERISTICS OF AN AIRFOIL

DATA SHEET

NAME: AMBIENT CONDITIONS STUDENT NO:

Temperature ( Co ) LAB DATE: Pressure ( mmHg ) LAB GROUP: SUPERVISOR SIGN: ΔPi, Inlet Dynamic Pressure (mm H2O) [P3] =

Alpha (α) A, Aft Load Cell [N] F, Fore Load Cell [N] D, Drag load Cell

[N] Data # Degree AOFF AON FOFF FON DOFF DON

1 2 3 4 5 6 7 8 9 10

UNCERTAINITY ANALYSIS ( AUXILARY TEST DATA SHEET ) Δpi [ P3] Aft (A) Fore (F) Drag (D) Δpi [ manometer]

Sample # mm H2O [ N ] [ N ] [ N ] mm H2O 1 2 3 4 5 6 7 8 9 10


PRESSURE DISTRIBUTION OVER THE AIRFOIL

LOWER SURFACE UPPER SURFACE ANGLE OF ATTACK Pa Pa-Pi Pa Pa-Pi ( o )

No (mm H2O)

(mm H2O) No

(mm H2O)

(mm H2O)

1 2 3 4 (mm H2O) 5 6 7 8 9 10

11 12

INLET STATIC

PRESSURE (Pi)

13 14 15 16 17 18 19 20

INLET DYNAMIC

PRESSURE (ΔPi)

TABLE-1

No CP x(mm) z(mm) Cpij dxij dzij Cpij*dxij Cpij*dzij 21 152.00 0.00 -22.46 3.08 19 129.54 3.08 -15.24 1.69 17 114.30 4.77 -18.28 1.76 15 96.02 6.53 -18.29 1.41 13 77.73 7.94 -18.29 0.93 11 59.44 8.87 -18.29 0.22 9 41.15 9.09 -18.29 -0.96 7 22.86 8.13 -7.62 -1.01 5 15.24 7.12 -7.62 -1.71 3 7.62 5.41 -6.10 -2.82 1 1.52 2.59 -1.52 -2.59 0 0.00 0.00 0.76 1.86 2 0.76 1.86 3.05 2.12 4 3.81 3.98 7.62 2.41 6 11.43 6.39 7.62 1.30 8 19.05 7.69 18.95 1.34

10 38.00 9.03 24.00 -0.26 12 62.00 8.77 18.77 -1.04 14 80.77 7.73 20.58 -1.68 16 101.35 6.05 20.57 -2.10 18 121.92 3.95 15.24 -1.79 20 137.16 2.16 14.84 -2.16 SUM=

me-410 - metu mechanical ... direction of motion. most of the information about the drag force on...

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