Lift and Drag Forces on an Aerofoil Outline An aerofoil placed in a wind tunnel is subject to a motion of air of constant velocity. The purpose of the experiment is to examine the lift produced by the aerofoil at negative and positive angles of attack from 0 to 30 degrees in increments of 3 degrees. Additionally, the drag force in terms of the drag coefficient is determined for two angles of attack through the von Karman integral method. Theory The aerofoil pictured below has six pitot tubes attached at regular intervals measuring the pressure on the foil. They are attached to a manometer. There are also two pitot tubes measuring total and static pressure located upstream in the wind tunnel. The dynamic head measured by the manometer is converted into pressure values of Pascal’s and expressed as the dimensionless coefficient Cp. The values are then plotted for each set of degrees of attack as a function of the position ratio x/c.
Transcript
Lift and Drag Forces on an Aerofoil
Outline
An aerofoil placed in a wind tunnel is subject to a motion of air of constant velocity. The purpose of the experiment is to examine the lift produced by the aerofoil at negative and positive angles of attack from 0 to 30 degrees in increments of 3 degrees. Additionally, the drag force in terms of the drag coefficient is determined for two angles of attack through the von Karman integral method.
Theory
The aerofoil pictured below has six pitot tubes attached at regular intervals measuring the pressure on the foil. They are attached to a manometer. There are also two pitot tubes measuring total and static pressure located upstream in the wind tunnel. The dynamic head measured by the manometer is converted into pressure values of Pascal’s and expressed as the dimensionless coefficient Cp. The values are then plotted for each set of degrees of attack as a function of the position ratio x/c.
The area between the two curves for each angle of attack is equivalent to the net lift force on the aerofoil. In order for the lift force to actually be produced the aerofoil needs to be sufficiently thin. This is because its dimensions and geometry need to have an inclination to flow in a fluid space as governed by the Euler equations. The lift on the aerofoil is expressed as lift coefficient Cl and is evaluated numerically using Simpsons rule for each angle set.
Finally, velocity data for a second pitot tube mounted downstream in the wake for 15 and 30 degrees of attack is utilized in calculation of the drag force expressed as the drag coefficient Cd. This is done through the von Karman Integral method numerically using the trapezium rule. The results are then plotted against angle of attack.
Method
A barometer was read to obtain a value for atmospheric pressure and room temperature. The wind tunnel was then turned on and values for total and static head were obtained with the help of an AF10A manometer pictured below. Values of head at six locations on the aerofoil were measured for -30 to +30 degrees using a protractor to adjust the aerofoil.
Results
The raw data is presented in the following table:
Analysis
Calculation of an accurate value for the density of air using room temperature and atmospheric pressure:
Patm=750mmHg×101.325 kPa760mmHg
=99.99×103Pa
T=19.0+273.15=292.15K
R=287.05 J kg−1K−1
ρair=PatmRT
= 99.99×103
287.05×292.15=1.19kg m−3
ρair=1.19kg m−3
Calculation of the free stream air velocity using the forward pitot static tube:
Pdynamic=12ρairU
2
Pdynamic=ρH 2O×g×∆h
∆ h=Ptotal−P∞
P∞=Pstatic
∆ h=Ptotal−P static
Average∆h=0.026261905m
Pdynamic=998 kgm−3×9.81ms−2×0.026261905m
Pdynamic=257 Pa
U=√ 2×Pdynamicρair
U=√ 2×2571.19
U=20.78ms−1
Calculation of the aerofoil Reynolds number (based on the chord length).
ℜ=Ulv
Kinematic viscosity of air at 20oCv=1.51×10−5m2 s−1
chord lengthl=0.0749m
ℜ=20.78×0.07491.51×10−5
ℜ=103070
Calculation of C p for top and bottom surfaces, for each angle alpha:
Position ratio where c is the chord length 0.0749m.
Graph of pressure distribution at +15 and -15 degrees plotted as graph of pressure ratio Cp as function of position ratio. See Appendix A for plots of all other angles of attack.
The lift coefficient Cl expressed by the following two formulas is derived by finding the area between the two curves of upper and lower surface. This is done by using Simpsons rule in Excel.
C l=F L
12ρairU
2 A
The lift coefficient values are plotted against angle of attack.
0 5 10 15 20 25 30 350.00
0.10
0.20
0.30
0.40
0.50
0.60
0.70
0.80
0.90
1.00
Lift Coefficient Cl vs Angle of Attack
Angle of Attack Alpha
Cl
Having now obtained the lift coefficient of the aerofoil it is now necessary to derive the drag coefficient to complete a basic efficiency analysis of the foil. Mathematically Cd can be evaluated using the von Karman integral method shown below:
The calculations are performed using data available on the Exeter Learning Environment available only for 15 and 30 degrees angle of attack. The area under the y – fy curve is obtained using the trapezium rule shown below. Where fy is equivalent to
the function: U x
U¿). Cd is obtained by multiplying the area by 2/c c being the chord length.
Finally a graph of drag coefficient Cd vs angle of attack is plotted:
There are several sources of uncertainty that provide a degree of error in the results obtained. First of all random error in taking manometer and angle readings significantly affects the precision of results and further manipulation must account for this error.
Additionally, upon reaching a certain angle of attack the effect of stall is present where the foil no longer produces sufficient lift and manometer readings fluctuate. This is due to a boundary layer of extreme turbulence especially on the lower side of the foil leading to fluctuations in pressure at the pitot tubes.
Conclusion
Based on experimental data and calculations conducted it is evident that the aerofoil produces lift efficiently from 3 to 15 degrees of attack showing a decline in efficiency rate from 15 to 30 degrees.
The drag coefficient increases with increased angle of attack which is reasonable with reference to flow theory.
To obtain further information about the aerofoil a polar graph of Cd vs Cl can be plotted to analyze the relationship between the drag force on the aerofoil and the lift produced which can be utilized in wing design and exploitation. For example control systems on an aircraft can use the data in feedback and account for disturbance.
Grc.nasa.gov, (2015). Inclination Effects on Lift. [online] Available at: https://www.grc.nasa.gov/www/k-12/airplane/incline.html [Accessed 15 Oct. 2015].
Wahiduddin.net, (2015). Equations - Air Density and Density Altitude. [online] Available at: https://wahiduddin.net/calc/density_altitude.htm [Accessed 14 Oct. 2015].
