extended abstract

MEASUREMENT of PRESSURE DISTRIBUTION OVER a Clark Y-14 AIRFOIL at VARIOUS

ANGLES of ATTACK and EVALUATION of THE LIFT FORCE ACTNG on the AIRFOIL

1. Objective

The objectives of the experiment are to measure the surface pressure distribution on an airfoil set at

various angles of attack, to calculate the pressure coefficient, the lift coefficient, and the lift force acting on

the airfoil. In addition, the uncertainty of the results has to be calculated, and the results have to be compared

with benchmark data.

2. Experiment Design

Airfoils are streamlined surfaces designed in such a way that air flowing around them produces useful

motion. Airfoils set in a velocity field or moving in still fluids are subjected to pressure and viscous

forces. Typical geometric and hydrodynamic characteristics of airfoils are illustrated in Figures 1.a and

1.b. Over the top of the airfoil the velocity of the flow is greater than the free-stream velocity. Following

from Bernoulli’s equation, the pressure over the top surface is negative (see Figure 1.b). Velocity along

the underside of the airfoil is less than the free-stream velocity and the pressure is positive. The overall

effects of the flow around the airfoil are a total lift force, L, acting normal to the free-stream direction and

a drag force, D, acting parallel to the free-stream direction. In this experiment the lift force is determined

by integrating the measured pressure distribution over the airfoil surface.

Figure 1 - Airfoils characteristics: a) geometry; b) hydrodynamics.

The experiments are conducted in the

test section of an open circuit subsonic

wind tunnel (see Figure 2) where a

uniform and steady velocity field is

established. A honeycomb flow

straightener is installed in front of the test

section to reduce flow turbulence and

increase measurement accuracy. The

tunnel has a contraction section that helps

achieving flow uniformity and quiet

operation. An electric motor controlled with a variable frequency driver (VFD) allows smooth change of

the fan rotational speed. The test section is 1ft by 1ft square, 2 ft long. The facility enables measurements

for turbulent flows up to Re = 250,000 (Re = U∞ c/ν, where U∞ is the free-stream velocity in the tunnel, c

is the airfoil cord length, and ν is the kinematic viscosity of air). A Pitot-static tube can be mounted at the

front of the test section to measure the static and total pressures required to determine the flow velocity.

A Clark Y-14 airfoil, see Figures 3.a and 3.b, is used for measurements. This airfoil was selected

because it exhibits good aerodynamic performance over a wide range of Re numbers, including the low

Test section

Electric

motor

Contraction

section

Figure 2 - Layout of the open test section wind tunnel.

range number (i.e., Re down to 50,000) and due to the availability of benchmark data for comparison. Figure

A.1 in Appendix A provides the positioning of the pressure taps in airfoil-attached coordinates.

Figure 3 – a) The location of the pressure taps and b) the geometry of the Clark-Y airfoil.

The pressure distribution around the airfoil is captured by 18 pressure taps connected through tygon

tubes to the ports of the vertical manometers that simultaneously sense the pressures at predefined airfoil

locations. Positioning of the airfoil at various angles of attack is made by rotating the table on which the

airfoil is installed.

The measured variables are the test section air temperature, free stream velocity, and pressure

distribution around the airfoil.

The data reduction equation for the pressure coefficient, CP, is given by:

      

2

2 ,,



 

 

U

pp UTppC iip

  (1)

where pi is the surface pressure measured at location i on the airfoil surface, p is the pressure in the free

stream (measured on the Pitot static port),  is air density, and U is the free-stream velocity given by

 







 

pp U

stagn2 (2)

where pstagn is the stagnation pressure measured at the tip of the free Pitot tube.

The presence of the airfoil in the test section will affect the test section velocity. You do not have to

account for this difference in velocity in your analysis.

The data reduction equation for the lift coefficient, CL, is given by

  bcU

L cULCL 2

2 ,,,



  

 (3)

where L is the lift force acting on the airfoil surface, b is the airfoil span, and c is the airfoil chord (as shown

in Figure 1.a). The lift force can be obtained by integrating the measured pressure distribution over the

airfoil

   dsppL i s

i sin  (4)

a) b)

19

where θi is the angle of surface normal to free-stream flow at each of the pressure taps (see Figure 3.b).

Angle θi can be calculated using the relationship between it and the angle of attack α and angle β (given in

Appendix A) as apparent from Figure 3.b.

3. Experiment Process

3.1. Setup

The experiment measurement system includes: the wind tunnel, the airfoil, and the multiport

manometer (see Figure 4). The manometers on the manometer panel indicate the pressures at the surface

pressure taps. The temperature in the test section is measure with a thermometer. The angle of attack is set

using a handle, located below the test section, which rotates the table the airfoil is installed on. Before

taking the measurements, setup the targeted flow conditions in the tunnel test section. A Reynolds number

of 143000 (corresponding to 7.04 m/s free stream velocity) is recommended for the experiment to match

the testing conditions for the available benchmark data.

3.2. Data Acquisition

Each student group acquires pressures measurements (see Figure 4 for a sample pressure profile) at the

surface pressure taps located on the airfoil perimeter for the airfoil set at various angles of attack as specified

by the TA. Use the spreadsheet provided in the appendix of this handout to record the data. Make sure to

measure the free-stream velocity at the desired angle of attack.

Figure 4 – The test section with the airfoil and Pitot tube installed during a test; the manometers

indicate the pressure distribution around the airfoil.

3.3 Data Reduction

Data reduction includes calculation of the following quantities:

1. free-stream velocity U (using Equation 2 and the readings on ports 23 and 24) and the corresponding

flow Reynolds number, Re = Uc/, where c is the chord length of the airfoil, and  is the kinematic

viscosity of air (use the temperature measured by the thermometer inside the test section to determine

 from fluid property tables).

Airfoil Pitot tube

Manometers

2. pressure coefficients (using Equation 1 and the readings on ports 0 to 18) on the airfoil surface. Plot

Cp versus x/c (x is the coordinate along the chord line) for all the angles of attack employed in the

experiment. Include the uncertainty estimate for the pressure coefficient. Compare your measurements

with the benchmark data.

3. lift force on the airfoil obtained by integrating the measured pressure over the airfoil surface. Use of

the trapezoidal rule, provided in Appendix A, for the numerical integration.

4. lift coefficient, CL, given by equation (3). Calculate the lift coefficient per unit span length and plot the

points obtained experimentally with the CL /unit span length versus the angle of attack, α, provided.

Include the uncertainty estimate for the lift coefficient. Compare your measurements with the

benchmark data.

3.4. Uncertainty Assessment

Uncertainties for the experimentally measured lift coefficients will be evaluated. The block diagram

for error propagations in the measurements is provided in Figure 5. Based on previous experiments, it was

found that bias and precision uncertainty for the , U , , s, and c are negligible, hence for the present

analysis only include the bias uncertainty for  ppi . To facilitate the uncertainty analysis you will have

to estimate the bias and precision uncertainties for the individual measured variables. Note that the

uncertainty assessment does not include error sources such as undetected leaks in the pressure tubing, model

orifice effects, vibration effects on the probes and unsteady flow effects.

Figure 5 - The block diagram for the measurement system and data

reduction equations for determination of the lift coefficient.

Uncertainty in the pressure coefficient

The total uncertainty for the pressure coefficient measured at each pressure tap is given by the equation

222

CpCpCp PBU  (5)

The bias uncertainty in Equation (5) is the same as that for the pressure taps. Neglecting the correlated bias

uncertainties and discarding the terms with negligible bias uncertainties

2

)(

2

)(

2

1

22





 ppippii j

i

iCp BBB  (6)

where Bi is the bias uncertainty for the individual variable and ipi XC  are sensitivity coefficients.

The sensitivity coefficient   ppi , evaluated using the average values for the individual variables, is given

by

    2_ 2



 

 

 Upp

C

i

p

ppi   .

The precision uncertainty for each pressure tap in Equation (5) is estimated as

MSP CpCp 2 (7)

where SCp is the standard deviation of the pressure coefficients at each pressure tap evaluated for M = 10

repeated tests. Precision uncertainty will have different values for each of the 18 taps. Based on previous

measurements, an average value for the precision uncertainty will be provided.

Uncertainty in coefficient of lift

The data reduction equation for the lift coefficient is Equation 3 and it is of the form

),,,,,( cUsppfC ip   . You should only consider bias uncertainty for  ppi . The total

uncertainty for the measurement of the lift coefficient is given by

222

CLCLCL PBU  (8)

The bias uncertainty in equation (8), neglecting the correlated bias uncertainty and the terms assumed

with negligible bias uncertainty, is given by

2

)(

2

)(

2

1

22





 ppippii j

i

iCL BBB  (9)

Given the above assumptions and using the lift force determined by integration (Equation 4), the

expression for the bias uncertainty of the lift coefficient is

        





 

  

  

 



  





 

k

i

ii

ppi k

i i

L ppiCL ds

cU

B

pp

C BB

1

2

2

2 1

2

22 sin 5.0

 

(10)

Notations used in Equation (10) are defined in Appendix B (k = 29).

The precision uncertainty in Equation (10) was estimated as

MSP CLCL 2 (11)

where SCL is the standard deviation of the lift coefficients evaluated for M = 10 repeated tests. Based on

previous measurements, an average value for the precision uncertainty will be provided to facilitate the

uncertainty analysis.

4. Data Analysis

Measurements obtained in the experiments will be compared with benchmark data. Benchmark data

for pressure distribution coefficients and lift coefficients on a Clark-Y airfoil set at various angles of attack

and Re are those of Marchman and Werme (1984). The benchmark data is plotted in Figure 6.

b)

Figure 6 - Reference data (Marchman and Werme, 1984); a) Distribution of the pressure coefficients for

 = 0, 4, 6, 8, 12, 14 and Re = 143,000; b) Variation of the lift coefficient with the angle of attack.

-1.5

-1

-0.5

0

0.5

1

1.5

0 20 40 60 80 100

C p

X/C

AOA = 0, Re = 143000

-1.5

-1

-0.5

0

0.5

1

0 20 40 60 80 100

C p

X/C

AOA = 6, Re = 143000

-2.5

-2

-1.5

-1

-0.5

0

0.5

1

1.5

0 20 40 60 80 100

C p

X/C

AOA = 13, Re = 143000

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

0 20 40 60 80 100

C p

X/C

AOA = 16, Re = 143000

a)

Discussion

Answer the following questions: 1. If the lift L is a function of the free-stream velocity U∞, density ρ, chord c, angle of attack α, and

viscosity ν, what are the dimensionless groups (π parameters) that characterize this problem? 2. How do the experimental measurements of the pressure distribution apply to a full-scale aircraft having

a similar airfoil section?

5. References

AIAA (1995). AIAA- 071 Standard, American Institute of Aeronautics and Astronautics, Washington,

DC.

Granger, R.A. (1988). Experiments in Fluid Mechanics, Holt, Rinehart and Winston, Inc. New York, N.Y.

Marchman III, J.F. and Werme, T.D. (1984). “Clark-Y Performance at Low Reynolds Numbers,”

Proceedings AIAA 22nd Aerospace Science Meeting, Reno, NE.

Robertson, J.A. and Crowe, C.T. (1993). Engineering Fluid Mechanics, 5th edition, Houghton Mifflin,

Boston, MA.

Stern, F., Muste, M., Beninati, L-M., Eichinger, B. (1999). “Summary of Experimental Uncertainty

Assessment Methodology with Example,” IIHR Report, Iowa Institute of Hydraulic

Research, The University of Iowa, Iowa City, IA.

White, F.M. (1994). Fluid Mechanics, 3rd edition, McGraw-Hill, Inc., New York, N.Y.

APPENDIX A

SPECIFICATIONS FOR THE EXPERIMENTAL FACILITY COMPONENTS

Station number

% of chord

PRESSURE DATA

α1= α2= α3= α4=

1 0

2 5

3 10

4 20

5 30

6 40

7 50

8 60

9 70

10 80

11 5

12 10

13 20

14 30

15 40

16 50

17 60

18 70

19 80

COORDINATES OF AIRFOILS – please note that the stations listed below do not

coincide with the station number listed in the table above. Please sync the data in these

two tables based on the “% of chord” instead.

Note: The units for the y-coordinate values of the airfoil listed in this table are in millimeters.

APPENDIX B

SPECIFICATIONS FOR THE EXPERIMENTAL FACILITY COMPONENTS

The relevant geometrical notations are

provided in Figure 3.b. The positioning of the

pressure taps on the airfoil surface is specified

in Figure 3.a.

Airfoil Geometry:

- maximum thickness, t = 0.014 m; - airfoil wing span, b = 0.289 m; - chord length, c = 0.089 m

Angle notations:

- surface to chord line angle, ; - angle of surface normal to free-stream

flow, ;

- angle of attack, .

The numerical values for the airfoil

relevant geometrical characteristics are

provided in the table to the right.

Lift force can be computed using the

trapezoidal scheme for the numerical

integration

       dsppL is i sin

       iiiiii i

spppp ,1,11 sin 2

1   

Station Beta (º) Theta (º)

1 0 0

2 115.8 125.8

3 102.6 112.6

4 97.1 107.1

5 93.2 103.2

6 89.8 99.8

7 86.7 96.7

8 83.9 93.9

9 81.9 91.9

10 81.1 91.1

11 265.5 275.5

12 272.4 282.4

13 272.4 282.4

14 272.4 282.4

15 272.4 282.4

16 272.4 282.4

17 272.4 282.4

18 272.4 282.4

19 272.4 282.4

Name: ME 495 Lab

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