The first successful aerofoil theory was developed by Zhukov sky and was based on transforming a circle onto an aerofoil-shaped contour. This transformation gave a cusped trailing edge, and so the transformation was modified to obtain a slender semi-eclipse trailing edge, which gave rise to the name Ellipto Zhukovsky.
When a stream of air flows past an aerofoil, there are local changes in velocity around the aerofoil, and consequently changes in static pressure in accordance with Bernoulli’s theorem. The distribution of pressure determines the lift, pitching moment, form drag, and centre of pressure of the aerofoil. In our experiment we are concerned with the effect of pressure distribution on lift, pitching moment coefficient (Cm), and centre of pressure. The centre of pressure can be defined as the point on the aerofoil where Cm is zero, and therefore the aerodynamic effects at that point may be represented by the lift and drag alone.
A positive pressure coefficient implies a pressure greater than the free stream value, and a negative pressure coefficient implies a pressure less than the free stream value (and is often referred to as suction). Also, at the stagnation point, Cp has its maximum value of 1 (which can be observed by plotting Cp against x/c).
Zhucovsky claimed that the aerofoil generates sufficient circulation to depress the rear stagnation point from its position, in the absence of circulation, down to the (sharp) trailing edge. There is sufficient evidence of a physical nature to justify this hypothesis and the following brief description of the Experiment on an aerofoil may serve helpful.
The experiment focuses on the pressure distribution around the Zhucovsky airfoil at a low speed and the characteristics associated with an airfoil:
- coefficient of lift,
- coefficient of pitching moment
- and centre of pressure.
The airfoil is secured to both sides of the wind tunnel with pressure tappings made as small as possible not to affect the flow,(appendix- photo 1 . The pressure difference around the airfoil is measured with twenty-five manometer readings which are recorded for each angle of attack. The manometer fluid is alcohol and has a specific gravity of 0.83 and inclined at an angle of 30 degrees. Tube 1 is left open to atmospheric pressure, while tubes 2-13 are the lower surface of the airfoil and tubes 14-24 are the upper surface of the airfoil. The pressure tapings are positioned on the airfoil at a distance x/c, noted in the results table and tube 35 is the static pressure of the wind tunnel. The dynamic pressure is given by a digital manometer. The digital readout results were used for all calculations because they are more precise.
Results
Raw data and calculated values for x/c, Cp and Cp*(x/c) can be found in the appendix.
Graphs of Cp against x/c for angles of attack -4, 7, and 15 degrees can be also be found in the appendix. These graphs determine the lift coefficient. Counting the squares method was used to determine the values of Cl. Graphs of Cp*(x/c) against x/c for angles of attack -4, 7, and 15 degrees can be also be found in the appendix. These graphs determine the pitch moment coefficient. Counting the squares method was used to determine the values of Cm. Graphs of Cl against angle of attack ,Cm against angle of attack, and Cm against Cl can be found in the appendix.
Also below is a summary of the results:
Discussion
The experiment was conducted in a low speed, closed wind tunnel, operating at approximately 50% of its speed. The aerofoil was mounted in the wind tunnel and its pressure tapings connected to a manometer inclined at 30 degrees to the horizontal. The height of the liquid in each manometer tube represented the pressure acting on each of the aerofoil tapings. The pressure in the working section, and the pressure at the venturi inlet were taken into account, and a resulting wind tunnel velocity was displayed on a digital manometer. The Reynolds number was calculated (see appendix.
Values of Cl and Cm for other angles of attack were obtained from other groups conducting the experiment, and were used to obtain more accurate graphs.
It was also found that the slope of the Cl against angle of attack graph was 4.4759, which was not relatively close to the theoretical value of 7.105. The aerodynamic centre was calculated at 23.7% of the chord length (from the slope of the Cm against Cl graph).
It was found that the lift increased with angle of attack, up to a point where the aerofoil experiences stall, and a dramatic loss of lift occurs. As there was little change in the lower surface pressure distribution, the lift was mainly generated due to the upper surface suction.
As the angle of attack increases, the height of the upper surface suction peak should increase, and move forward, indicating that the centre of pressure is moving forward. However, experimentally this was not prominent, and can be attributed to a possible disturbance in the pressure distribution around the aerofoil. At zero degrees angle of attack, for a symmetrical aerofoil, lift and Cm should equal zero. The reason that they were not zero means that the aerofoil must have had a very small angle of attack.
The discrepancy between the theoretical and experimental value of lift curve slope is due to boundary layer effects, and the effect of the thickness of the aerofoil, and thus the theoretical value needs to be multiplied by the ‘k’ value (=0.917) to obtain the experimental result.
Conclusion
The aim of the experiment was achieved with a relatively good level of experimental accuracy.
The pressure distribution over an aerofoil contributes towards the lift and pitching moment coefficient, where the increase in suction on the upper surface (due to an increased angle of attack) increases the lift, and pitching moment coefficient. The variation of pressure distribution also affects the location of the centre of pressure.
The factors which affected the pressure distribution, were mainly the thickness and the Reynolds number. However, when it comes to comparing the results with their theoretical values it is clear to see that there have been significant errors have occurred in the experiment. These are listed below.
- Human errors in reading of the manometer tubes. Where several people were involved and this led to different techniques being used it would have been best for everyone to take their own set of readings and the average value calculated using all the data. The most common error without ant doubt was parallax and this could have been avoided by using digital measuring devices.
- Calculation errors i.e. rounding off, conversion error and error occurring when the area under the graphs was calculated for the coefficient of lift.
- Experimental errors some of the tapping may have been defective and not enough tapping were provided. Also to obtain a better lift curve slope there should have more angles of attack. Also any obstructions in front of the wind tunnel such as people would create unnecessary turbulence inside the wind tunnel.
Appendix
Specimen Calculations
P = 1019 mmHg = 101900 Pa
T = 23 C = 296 K
R = 287 J/kg. K
P = ρRT : ρ = P/RT = 101900 / 287 J/kg. K x 296 K = 1.1995 kg / m3
Specimen Calculations are shown for 15 degrees angle of attack at taping hole number 11:
Calculating Cp
Cp = (Pn –Ppw) x 10mm x 0.830 x sinθ / n x 1.02 = (31.1 – 30.3 ) x 10mm x 0.830 x sin30 / 32.7 x 1.02
= 0.100
Calculating Cpx(x/c)
→ 0.100 x 0.703 = 0.070
Calculating Tunnel Speed ‘V’ for 15 degrees angle of attack
V15 = √ 2 x g x h x 1.02 = √ 2x 9.81 m/s2 x 32.7 mmH20 x 1.02 = 23.36 m/s
Ρ 1.1995 kg / m3
Calculating Average Wind Tunnel Speed ‘V’
V-4 = 24.06 m/s
V7 = 23.99 m/s
Therefore Vaverage = ( 23.36 m/s + 23.99 m/s + 24.06 m/s ) = 23.80 m/s
3
Calculating Reynolds Number
Re# = ρ x Vaverage x C / μ
= 1.1995 kg / m3 x 23.80 m/s x 0.254 m / 1.836 x 10-5 kg/ ms-1 = 3.9 x 105
Calculating the position of the pressure of the aerofoil for 15 degrees angle of attack
x = (Cm / Cl) x C = -0.183 / 0.946 x 254 mm = -49.14
Figure 1:
the monometer tubes connected to the airfoil, side view of the wind tunnel
Reference:
E.L.Houghton and P.W. Carpenter: Aerodynamics for Engineering Students, 4th Edition, Arnold, 1993, page 226.
