Pressure distribution on an ellipto-zhukovsky aerofoil Essay Example

Pressure distribution on an ellipto Pressure distribution on an ellipto-zhukovsky aerofoil Paper Pressure distribution on an ellipto-zhukovsky aerofoil Paper The pressure distribution around an Ellipto Zhukovsky aerofoil with a chord of 254 mm at a range of angles of attack (-4? , 7? and 15? ) was determined and pressure contributions to lift were evaluated in a T3 wind tunnel at City University. This was carried out at a chord Reynolds number of 3. 9 x 105. Graphs for lift and pitching moment coefficients were plotted against angles of attack. A graph for Cm and Cl was also plotted from which the aerodynamic centre was determined to be 23. 7%. The value of lift curve slope was determined to be 4. 4759. Hence the value of k (the ratio of the actual lift curve slope to the theoretical one) for this aerofoil was determined to be 0. 917. The value of Cmo was also found to be 0. 0172. Specimen calculations for 15 degrees angle of attack can be found in the appendix section. LIST OF SYMBOLS Cp Pressure Coefficient Cpu Pressure Coefficient of upper surface Cpl Pressure Coefficient of lower surface Cl Lift Coefficient Cm Moment Coefficient x/c Position of pressure tapping on aerofoil divided by chord length Px Pressure at tapping x (Pa) Patm Atmospheric Pressure (Pa) ? Density of air (kg/m3) i Dynamic viscosity ? Kinematics viscosity (m/s2) h Digital manometer reading ? angle of which manometer is inclined D or t Diameter of cylinder (mm) h tunnel height (mm) V Velocity of air flow (m/s) R Molar gas constant (J/kg. K) T Temperature (K) Re Reynolds Number INTRODUCTION An airfoil is any part of an airplane that is designed to produce lift. Those parts of the airplane specifically designed to produce lift include the wing and the tail surface. In modern aircraft, the designers usually provide an airfoil shape to even the fuselage. A fuselage may not produce much lift, and this lift may not be produced until the aircraft is flying relatively fast, but every bit of lift helps. 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 Bernoullis 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: Angle of Attack (degrees) Cl Cm -4 -0. 513 0. 153 7 0. 740 -0. 166 15 0. 946 -0. 183 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.