Airfoil Lift Measurement by Surface Pressure Distribution Lab 2 MAE 424

Transcription

1 Airfoil Lift Measurement by Surface Pressure Distribution Lab 2 MAE 424 Evan Coleman April 29, 2013 Spring 2013 Dr. MacLean 1

2 Abstract The purpose of this experiment was to determine the lift coefficient, leading edge moment coefficient and center of pressure of a NACA 0012 airfoil. Each of these properties was found by analyzing the pressure distribution on the upper and lower surfaces of the airfoil. The pressure distribution was found by taking pressure readings from nine pressure taps placed along the surface of the airfoil. Several different trials of this experiment were conducted each at a different Reynolds number. Much of the results discussed in this report are from the Phi group which used a Reynolds number of 153,604. It was found that at low Reynolds numbers, the lift coefficient was not largely affected by a change in Reynolds number. However, the published results for a large Reynolds number did exhibit different lift coefficients. It was also found that, discounting stall, all of the calculated properties performed very closely to that of thin-airfoil theory. Stall must be discounted because thin-airfoil theory does not account for stall. Methodology The experiment was conducted using an Eifel type, low-speed aerodynamic wind tunnel that has a 12-inch square test cross-section that is 24 inches long. The airfoil that was tested was a NACA 0012 with a chord length of 4 inches. A pitot-static tube was positioned near the top of the wind tunnels testing area to measure the dynamic pressure and static pressure in the free-stream. The airfoil had nine taps along its surface each connected to a pressure transducer. The experiment began by first taking a dynamic and static pressure reading from the pitot tube. These readings were only taken once since the free-stream velocity was constant throughout the experiment. Next, the airfoil was set to an angle of attack of zero degrees. Then a pressure reading was taken from each pressure tap. This reading corresponds to the upper pressure value. This process was then repeated up until an angle of attack of 14 degrees. After each upper pressure reading was taken, then process was performed using negative angles of attack in order to get the lower pressure readings. Using negative angles of attack is analogous to flipping the airfoil upside-down. Discussion of Results The Reynolds number was first calculated by taking the value of the dynamic pressure obtained in the beginning of the experiment and solving for the free-stream velocity. This velocity was then used to calculate the Reynolds number as shown in equation 1 where ν is the kinematic viscosity of air ( ) and c is the chord length of the airfoil (10.16 cm). Re = V c ν (1) The free-stream velocity was found to be 22.8 m/s and the Reynolds number was 153,600. Next, using MATLAB (see appendix B for code), both the upper and lower pressure readings were nondimensionalized to find the upper and lower coefficients of pressure for each angle of attack. These values were then input into equations 2 and 3 and numerically integrated to find the skin-friction and leading-edge moment coefficients respectively. C F = 1 C m,le = 0 1 (C P,l C P,u )dξ (2) 0 ξ(c P,l C P,u )dξ (3) where ξ = x/c is the non-dimensional distance along the chord length. Next, the lift coefficient at each angle of attack was calculated using the skin-friction coefficient values as shown in equation 4. 2

3 C L = C F cosα (4) Finally, the non-dimensional center of pressure was calculated by dividing the negative leading-edge moment coefficient by the skin-friction coefficient as shown in equation 5. ξ CP = C m,le C F (5) Both the upper and lower pressure coefficients were plotted versus the non-dimensional distance along the chord length. Plots were made for two angles of attack, one before the stall angle and one after. 1 Pressure Coefficients vs. ξ (α = 10 ) Pressure Coefficient C P,u Figure 1: Pressure Coefficients vs. Non-dimensional Position ξ C P,l As shown in figure 1, for an angle of attack of 10 degrees both the lower and upper pressure coefficients are very different at the leading edge of the airfoil. Then the pressures slowly converge until nearing zero at the trailing edge of the airfoil. The pressure coefficients were also plotted for an angle of attack greater than the stall angle. 3

4 0.8 Pressure Coefficients vs. ξ (α = 13 ) C P,u 0.6 C P,l 0.4 Pressure Coefficient Figure 2: Pressure Coefficients vs. Non-dimensional Position ξ As shown in figure 2, the lower pressure coefficient displays similar behavior to that of the response for an angle of attack before the stall angle. However, after the stall angle the upper pressure coefficient remains relatively constant. This is an indication of flow separation which is the main cause of stalling. At a large angle of attack the air can no longer make the turn around the leading edge of the airfoil causing the flow around the airfoil to separate. This is why the pressure does not change along the top of the airfoil. As mentioned previously, the lower pressure readings were taken using the upper pressure taps since the testing apparatus did not provide lower pressure taps. This was done by using equivalent negative angles of attack. The reason that this is allowed is because the NACA 0012 airfoil that was used in this experiment is a symmetrical airfoil. Because the shape of the upper surface is the same as that of the lower surface, the upper surface can be used to simulate both surfaces. For example, to take pressure readings for an angle of attack of 2 degrees, the airfoil can be set to that angle to take the upper pressure readings and then can be set to -2 degrees to take the lower pressure readings. If a true negative angle of attack was tested (which would require pressure taps on both sides of the airfoil, or flipping the symmetrical airfoil), it would be expected that the lower and upper pressure readings would be switched. The lift coefficient versus angle of attack was plotted with published and theoretical results. 4

5 1.6 Lift Coefficient vs. Angle of Attack Lift Coefficient Re = (Phi) 0.2 Re = 160,000 (Sandia) Re = 3,230,000 (NACA) Theoretical Angle of Attack (degrees) Figure 3: Lift Coefficient vs. Angle of Attack As shown in figure 3, Reynolds number does seem to impact the lift coefficients. The lower Reynolds number clearly had a lower maximum lift coefficient that occurred at a lower angle of attack while the higher Reynolds number had a greater maximum lift coefficient at a higher angle of attack. Each experimentally determined response demonstrates the same general shape in that the lift coefficient increases linearly with angle of attack until it approaches the stall angle where it levels off and then begins to decrease. The theoretical lift coefficient was determined using thin-airfoil theory. Thin-airfoil theory states that the lift coefficient increases by 2π units per radian as demonstrated by equation 6. C l = 2πα (6) Thin-airfoil theory, however, does not account for stall. This is illustrated in figure 3 by the fact that the theoretical lift coefficient increases linearly and never levels off. The theoretical lift coefficient does match the experimentally determined data very closely for the linear part of the response. This means that, disregarding stall, the NACA 0012 airfoil performed as thin-airfoil theory predicted. Figure 4 shows the lift coefficient versus angle of attack results from several different trials of this experiment each at a different Reynolds number. 5

6 0.8 Lift Coefficient vs. Angle of Attack Lift Coefficient Re = (Phi) Re = (Tau) Re = (Omega) Re =84489 (Zeta) Angle of Attack (degrees) Figure 4: Lift Coefficient vs. Angle of Attack Figure 4 shows that the lift coefficient response does not change much at relatively low angles of attack. However, there are some small differences. For examples, it seems that somewhere between a Reynolds number of about 102,200 and 136,000 the maximum lift coefficient and thus stall angle does change. But within these two subsets of data, the stall angle remained the same. As stated previously and reinforced by this figure, no matter what the Reynolds number is the lift coefficient will always be the same for the linear portion of the response. In figure 4, even after stall when the lift coefficients began to level all, they all re-converged at a lift coefficient of about 0.5. The moment coefficient of the leading edge was plotted versus angle of attack for several trials of the experiment using a range of Reynolds numbers. 6

7 Moment Coefficient (Leading Edge) vs. Angle of Attack Re = (Phi) Re = (Tau) Re = (Omega) Re =84489 (Zeta) Moment Coefficient (Leading Edge) Angle of Attack (degrees) Figure 5: Leading Edge Moment Coefficient vs. Angle of Attack As shown in figure 5, the response exhibits an almost logarithmic shape. The moment coefficient begins at a low value, which is expected because the resultant force vector on the airfoil is relatively small during level flight. Then, as the angle of attack increase, the leading edge moment coefficient becomes more and more negative until eventually leveling off at the stall angle. The negative slope of the response is expected because the moment should decrease until the stall angle and then stop changing because lift is no longer increasing. There is a small dip in moment coefficient in the Omega groups trial. This is not expected and is likely due to some experimental anomaly or error. The non-dimensional position of the center of pressure was plotted versus angle of attack for several Reynolds numbers. 7

8 Non Dimensional Center of Pressure vs. Angle of Attack Re = (Phi) Re = (Tau) Re = (Omega) Re =84489 (Zeta) Non Dimensional Center of Pressure Angle of Attack (degrees) Figure 6: Non-dimensional Center of Pressure Position vs. Angle of Attack The center of pressure for a thin airfoil is defined as the position along an airfoil where the moment is equal to zero. Similar to figure 4, figure 6 once again shows the same grouping of responses whereas the two lower Reynolds numbers share similar responses and the two higher Reynolds numbers share their own similar responses. All four responses, however, still exhibit similar shapes. Each center of pressure begins at around a value of 0.3 and slowly descends until about Then the center of pressures for each trial shoot up and all converge at about Overall, there is a very small change in the center of pressure throughout the experiment. Out of all four trials the position only ranged from about 0.23 to This is compared to the theoretical center of pressure for thin-airfoil theory which is one-fourth of the chord length, or 0.25 in non-dimensional terms. In general, the experimentally determined center of pressure is relatively close to the theoretical value if stall is discounted, which is acceptable since thin-airfoil theory does not account for stall. Also, from thin-airfoil theory it is stated that the aerodynamic center and the center of pressure are located at the same point. There are some discrepancies between the results found through this experiment and the results that would be expected from an actual flying aircraft. For example, in this experiment the free-stream velocity remained constant for all angles of attack. This is obviously not what occurs in the real world. If an aircraft were to maintain its velocity during a climb (positive angle of attack), it would have to increase its engines. It is also nearly impossible to maintain an exact constant velocity during a climb even with the use of the engines. This would be extremely difficult to simulate in a wind tunnel with a fixed airfoil. Conclusions In conclusion, this experiment performed as expected. Discounting stall, the experimental results proved to be nearly identical to those of thin-airfoil theory. It was also found that at low Reynolds numbers, the lift coefficient was not drastically affected by a change in Reynolds number. The leading edge moment coefficient 8

9 was also found to be similar for different Reynolds numbers. The moment coefficient was found to decrease nearly logarithmically until leveling off at the stall angle. The center of pressure was also found to behave similarly to that of thin-airfoil theory, but again discounting stall. Even though the results of this experiment lined up closely with theory, there are still some unexplained anomalies that may be due to experimental error. Most importantly, the calculation of the free-stream velocity, and consequently Reynold number, may not have been accurate. The free-stream velocity was determined using the dynamic pressure reading that was assumed to be in the free-stream. It is possible that there was some kind of turbulence that effected this reading because of the nature of man-made wind. Another source of error was the angle of attack setting. The divisions on the dial were very small and difficult to see. Also, there was a 0.5 degree error on the dial itself, and since the dial does not have divisions for a half of a degree, this further adds to a potential error. Another source of error could be in the readings themselves. The pressure readings were read off of a pressure transducer and input by hand into Excel. It is entirely possible that once of these readings could have been entered incorrectly. However, any major errors would have been apparent in the resulting plots. A final source of error could be in the pressure transducer. The transducer was not calibrated prior to beginning the experiment. Also, it was fed pressure by small tubes connected to each tap on the airfoil; it is possible that there were leaks in these tubes which could have affected the pressure readings. References [1] Anderson, John. Fundamentals of Aerodynamics. 5th ed. New York: McGraw-Hill, Print. [2] Jacobs EN, Ward KE, Pinkerton RM Characteristics of 78 related airfoil sections from tests in the variable-density wind tunnel. T.R. No. 460, NACA 1932 [3] Sheldahl RE, Klimas PC Aerodynamic characteristics of seven airfoil sections through 180 degrees angle of attack for use in aerodynamic analysis of vertical axis wind turbines. SAND , 1981, Sandia National Laboratories, Albuquerque, New Mexico Appendix A Data Samples Table 1: Lift Coefficient vs. Angle of Attack Angle of Attack (degrees) Lift Coefficient

10 Table 2: Leading Edge Moment Coefficient vs. Angle of Attack Angle of Attack (degrees) Moment Coefficient Table 3: Non-dimensional Center of Pressure vs. Angle of Attack Angle of Attack (degrees) Center of Pressure Appendix B MATLAB Code %MAE 424: Lab 2 %Data Processor function data = ProcessData(group) data = ParseData(group); rho = 1.205; %density of air at STP nu = 1.51*10^-5; %kinematic viscosity of air at STP c = 10.16; %chord length in centimeters data.u = sqrt((2 * data.qinf) / rho); data.re = (data.u * (c/100)) / nu; fields = fieldnames(data.pressure); for i=1:numel(fields) this = data.pressure.(fields{i}); data.cpu(:,i) = this(:,1)./ data.qinf; data.cpl(:,i) = this(:,2)./ data.qinf; end cpdiff = data.cpl - data.cpu; data.cf = trapz(data.xi, cpdiff); 10

11 %data.cmle = sum(-data.xi*trapz(data.xi, cpdiff)); for j=1:numel(fields) for i=1:(numel(data.xi)-1) cmle(i,j) = (data.xi(i+1) - data.xi(i)) * ((data.xi(i)*cpdiff(i,j) + data.xi(i+1)*cpdiff(i+1,j)) end end data.cmle = -sum(cmle); data.cl = data.cf.*cosd(1:1:14); data.xicp = -data.cmle./ data.cf; end 11