Investigation of the Effect of Tubercles on Airfoil Performance

Transcription

1 Investigation of the Effect of Tubercles on Airfoil Performance ME 107: Mechanical Engineering Laboratory University of California at Berkeley Spring 2014 Group 2B Jared Carr Rafael Ferraz Songqi Gao Aaron Jameson Chang Yul Lee Daniel Lu Aaron Wienkers Cheng Hao Yuan 1

2 TABLE OF CONTENTS 1.0 ABSTRACT.. Pg INTRODUCTION. Pg EXPERIMENTAL METHODS.. Pg Apparatus. Pg Experiment Description and Data Collection.. Pg Theory.. Pg Mathematical Model Pg RESULTS & DISCUSSION Pg Performance of Standard Airfoil Pg Performance of Airfoil with Tubercles. Pg a Comparison of Lift Coefficient and Stall Behavior. Pg b Comparison of Drag Coefficient Pg c Boundary Layer Phenomenon.. Pg d Performance Based on Glide Ratio. Pg Error Analysis. Pg Limitations and Improvements. Pg CONCLUSIONS Pg REFERENCES.. Pg APPENDIX. Pg Derivation of Relation between Pressure Transducer Voltage and Pressure Differential.... Pg.19 2

3 1.0 ABSTRACT The effect of tubercles on the leading edge of a NACA 0020 airfoil section was investigated numerically and experimentally. The motivation for this experiment was to explore the ways in which airfoil performance can be improved by modifying the contour of the leading edge. Lift and drag coefficients between a standard NACA 0020 airfoil and one with a sinusoidal shaped leading edge were compared under a constant wind speed of 33.5 mph and angles of attack ranging from 0 to 20. It was found that the airfoil with leading edge tubercles stalled at a 14 angle of attack with a maximum lift coefficient of 0.48, which was earlier than the standard airfoil stall angle of 16 at a maximum lift coefficient of However, the airfoil with tubercles experienced a more gradual decline in lift coefficient after stalling compared to the standard airfoil. These effects may help aircraft attain greater maneuverability at high angles of attack and more stable post-stall behavior. 2.0 INTRODUCTION Leading edge tubercles are believed to be a solution for improving maneuverability during flight at high angles of attack. This idea was inspired by the shapes of humpback whale fins (Figure 1), which is a key attribute to the whale s agile movements in water. Motivated by the thriving UAV market, a variety of airfoil designs are being proposed, all of which are aimed to enhance controllability and agility of the aircraft. The effect of leading edge tubercles on the performance of an airfoil is thus worthy of investigation. Figure 1: Tubercles on Humpback Whale Fins [1] When analyzing the performance of an airfoil, important parameters including lift, drag, angle of attack, stall (critical) angle, and Reynolds number are considered. Lift is defined as the force acting on the airfoil perpendicular to the direction of flow, whereas drag is defined as the force parallel to the direction of flow. Generally, lift supports the airfoil in flight and is desired to be maximized whereas drag inhibits the forward motion of the airfoil and is desired to be minimized. To account for the effect of different fluid speeds on lift and drag, the said forces are often normalized by dividing by the dynamic pressure u to obtain respectively the coefficients of lift and drag. Angle of attack is the angle between the oncoming flow or relative wind and the chord line of the airfoil. Stall angle, or critical angle of attack, is the angle of 3

4 attack at which the lift coefficient is maximized at a given wind speed. During flight, exceeding this critical stall angle leads to a sudden drop in the lift coefficient and a sudden increase in the drag coefficient. Finally, Reynolds number is a dimensionless parameter that represents the ratio of inertial forces to viscous forces. In airfoil analysis, this parameter gives insight into the degree of airflow turbulence. Reynolds number also acts as a similitude parameter for scaling results to different sized airfoils. Tubercles affect the behavior of an airfoil at near-critical angles of attack. The unevenness of the leading edge channels the fluid into narrower and faster moving streams. These protrusions energize the previously laminar flow and allow the boundary layer following the leading edge troughs to stay connected to the airfoil surface at higher angles of attack, much like vortex generators on an aircraft wing. Therefore, unlike the standard airfoil, detachment of the boundary layer occurs at different angles for different points along the wingspan, resulting in a more gradual overall decrease in lift coefficient at stall. With this observation come many implications. Reduction in the abruptness of the drop in lift may provide a way to reduce the dangers associated with sudden changes in the force on the airfoil. Stalling most frequently occurs during aircraft liftoff and landing during which the angles of attack are usually the greatest and closest to the critical angle. Moreover, stalling is also most dangerous during these instances because the aircraft is close to the ground and has little space to correct for the effects of stalling. Tubercles have the potential to mitigate this danger by increasing controllability of the aircraft should stalling effects take place. Another advantage of having tubercles is the increased maneuverability [2] as a result of the more gradual stall response. Observation of humpback whale fins has shown that leading edge tubercles appear to allow for greater 3-dimensional agility when the whales hunt for prey. In this light, aircrafts have the potential to be designed to move with more freedom and built with fewer structural constraints. This experiment was designed to characterize the effects of airfoil tubercles and determine the feasibility of applying this technology in aerospace engineering. The main focus is the comparison of lift coefficients at various angles of attack, location of stall angle, and the rate of change in lift coefficient for the angles of attack following the stall angle. 3.0 EXPERIMENTAL METHODS 3.1 Apparatus A subsonic wind tunnel was used to determine the lift and drag for the two airfoils at varying angles of attack. The wind tunnel consists of three sections: nozzle, test section, and exit. Air enters a 9:1 contraction cone of the nozzle, which is screened by a honeycomb filter to decrease turbulence of the air entering the test section. This contraction cone is followed by the straight test section with the dimensions of 1 x 10 x 36 (height x width x length) in which the airfoils were mounted. The exit consists of an air outflow and a motor-driven fan whose speed is controlled by a frequency drive. A Monarch optical tachometer provides real-time measurements of the fan rotor speed. The maximum wind speed inside the test chamber that the fan-motor can generate is approximately 55 mph at the peak motor RPM. The contraction cone is fitted with a Dwyer pitot-tube paired with an Omega pressure transducer to measure the pressure drop across the entry into the test section. Lift and drag forces were calculated independently throughout the course of the experiment using the voltage readings from a strain gauge tower. The strain gauge tower features an Omega strain gauge that is capable of determining strain in a single direction. Force data were collected in orthogonal directions and transformed into lift and drag in post-processing using a MATLAB script. The strain gauge schematics are illustrated in detail below in Figure 2. Additionally, a smoke wand and camera were used to visualize the airflow past the airfoil at approximately 33.5 mph wind speed. 4

5 Figure 2: Strain gauge schematics The two airfoil prototypes were 3D-printed using an SST 1200ES Fused Deposition Modelling Machine, which uses a soluble support material and ABS+ polymer for the model material. The printer has a maximum resolution of 0. 5mm (0.010 ), 0. % of the nominal chord length. Both airfoil models have a span of 7 inches and a mean chord line of 5 inches. The sinusoidal contour of the leading edge tubercles has a wavelength of 2.1 inches and amplitude of inches from peak to peak. The weight of the standard NACA 0020 airfoil and NACA 0020 airfoil featuring leading edge tubercles are grams and grams respectively. Figure 3: 3D CAD Model of standard NACA 0020 Airfoil Figure 4: 3D CAD Model of NACA 0020 Airfoil Modified with Tubercles 5

6 Connection of the airfoil to the strain gauge tower was accomplished using a cylindrical adapter with two sections. The thinner section has internal ¼-20 threads to mount onto the strain gauge tower. The thicker section has two #10-32 tapped through-holes drilled radially at right angles. The thicker section mates with the inner surface of the hole in the airfoil with countersink screws affixing it from the top and bottom. The fixture was mounted such that one tapped hole is parallel with the line of action of the strain gauge and the other perpendicular, allowing the chord line of the airfoil to be exactly parallel or perpendicular to the line of action of the strain gauge. To adjust the angle of attack, the window, strain gauge, and airfoil assembly was rotated as a whole. This leaves an angle between the line of action of the strain gauge and the flow direction which is accounted for using coordinate transforms to determine the horizontal and vertical forces. There is also an angle between the line of action of the strain gauge and the gravity vector (weight vector) of the airfoil; this was also accounted for using trigonometric coordinate transforms during data processing. 3.2 Experiment Description and Data Collection Since both measurements of lift and drag were required for analysis, each airfoil was tested twice with the strain tower: once with the line of action of the strain gauge perpendicular to the airfoil chord line, and once with it parallel. A LabVIEW Virtual Instrument (VI) was used to record and plot the voltage measurements of the Omega strain gauge against time. Lift and drag forces were calculated from the voltage readings collected by the strain gauge using the following relation provided by the lab technician: (1) where is the force in Newtons acting on the tip of the strain gauge tower, and is the strain gauge voltage in volts. The offset was calibrated in post-processing using the zero-wind horizontal force component. Both airfoils were tested at the same wind speed of approximately 33.5 mph at varying angles of attack. The angles ranged from 0 to 20 in increments of 1, with the 0 calibrated with respect to the horizontal. The angle of attack of the airfoil was changed by rotating the circular window marked with angular measurements. Because the strain tower was rotated at each angle of attack increment, a coordinate transform was used to convert the forces from the airfoil reference frame to a fixed reference frame. The LabVIEW VI also recorded voltage readings obtained by the two Dwyer pitot-tube pressure transducer pairs inside the contraction cone. To determine the wind speed using only the pressure transducers, a relationship between voltage and wind speed was required. A Kanomax hot wire anemometer was used in a previous experiment to characterize the relationship between the pressure differential measured by the transducers and the wind speed in the testing area; details can be found in the appendix. The linearized relation produced in that experiment is ( ) ( ) (2) where is the wind speed in meters/second and is the voltage in the pressure transducers in volts. 6

7 3.3 Theory This experiment aims to scale the results for application to Unmanned Aerial Vehicles which typically have very large Reynolds numbers, upwards of This implies that the effect of viscous forces are minimal compared to that of inertial forces, and thus turbulent effects become increasingly critical to the airfoil performance. At the same time, the viscous forces are the mechanism by which boundary layers form (with the no-slip condition at the surface of the airfoil). Therefore, the competing effects of viscosity maintaining the boundary layer and turbulence energizing and steepening the velocity gradients normal to the surface of the airfoil are coexistent. The separation of these boundary layers determines the behavior of the flow around the airfoil and therefore the lift and drag characteristics of the body [3]. Stalling occurs when the laminar flow in the boundary layer becomes detached from the surface of the airfoil. This abrupt increase in pressure on the top of the airfoil due to the turbulent stagnation point departing from the trailing edge (Kutta condition) results in a sudden increase in induced drag and a corresponding decrease in lift. However, by stimulating a turbulent boundary layer, Stratford shows that the increased boundary layer flow energy moves the separation point rearward [3], increasing the critical stalling angle of the airfoil. Several methods already exist to energize the boundary layer. Vortex generators tabs evenly placed laterally along the quarter-chord are able to re-energize the boundary layer and delay stall. By increasing the local vorticity, and hence the downward cascade into turbulence, vortex generators force the boundary layer into a turbulent regime. Likewise, local surface roughness can trip the boundary layer into turbulence, which is beneficial when form (pressure) drag due to the boundary layer separation is dominant over skin friction drag. This phenomenon in the particular regime of Reynolds numbers is termed the drag crisis. The final method proposed in this report is using tubercles, where the characteristic size is chosen to operate within the regime of the drag crisis. The following derived non-dimensional values will be used to characterize the airfoil performance in the analytical model and empirical results: (3) (4) (5) (6) where is the dynamic pressure, and Ais the airfoil surface area. At the limits of testing, with an angle of attack of 20, the blockage ratio is 0.099, and thus wall and blockage effects must be taken into account [4][5]. The correction to the lift coefficient accounts for the confinement of the streamlines over the airfoil. The following correction specific to the wind tunnel and airfoil dimensions is applied to, assuming two-dimensional flow over the airfoil: (7) Additionally, since the airfoil mount was offset, an additional correction to the velocity is needed to account for the yet developing Poiseuille flow in the test section. An empirical velocity cross-sectional profile was obtained from previous lab results, and used to determine the dynamical pressure scaling in Equations 3, 4, and 6 above. 7

8 3.4 Mathematical Model The following analytical model describing the effect of tubercles on a symmetric (uncambered) airfoil makes use of the following standard aerodynamics assumptions: Incompressible working fluid (air) at these low airspeeds Large Reynolds number flow Large aspect ratio wing Incompressible flow assumption is valid because the airspeed is much lower than the Mach 0.3 critical airspeed between incompressible and compressible regimes. The large Reynolds number flow assumption derives from the calculated Reynolds number of The last assumption is valid because the airfoil spans the majority of the section of the wind tunnel. With only 1.5 inches between the wing-tip and the wall of the wind tunnel on either side, wing-tip and edge effects can be assumed negligible, such that each cross-section of the airfoil is kinematically the same, and looks like an infinitely long airfoil. The spacing on either side displaces the airfoil from the wind tunnel boundary layer effects, while also using the wall to mitigate any wing-tip vortices that would be prone to form in high lifting situations. Thus, the baseline NACA 0020 airfoil can be analyzed assuming 2-dimensional flow. It is only with the addition of tubercles that 3D effects must be considered. This symmetric NACA airfoil is given by the ordinates, ( ) ( ( ) ( ) ( ) ) (8) and so the baseline model thickness is 1 inch thick. As a first approximation, we start with inviscid thin airfoil analysis for the baseline airfoil. For a thin, symmetric, planar airfoil, the coefficient of lift is given as (9) for small angles of attack (in radians). Although thin airfoil theory fails to model stalling, typical NACA airfoils are known to stall at angles of attack anywhere between 12 and 20, and will be determined numerically for this particular airfoil. Thickness considerations will also be accounted for utilizing Computational Fluid Dynamics (CFD) software. Tubercles have been suggested to aid in increasing airfoil performance, typically by energizing the boundary layers and delaying stall. One proposed mechanism by which this occurs has been proposed [2] including the generation of span-wise vortices, much as vortex generators found on commercial airfoils do. In both the proposed tubercles and vortex generators, flow is disturbed relatively early along on the body of the airfoil, returning energy into the flow (re-energizing the boundary layer). This allows the flow to remain attached at higher angles of attack, and as a result leads to higher stall angles. In addition, having flow attached to the body eliminates any trailing wake vortices that may occur in the absence of these vortex generators, which decrease the form drag on the body. However, this comes at the cost of an increased value of skin friction drag. In the case of an airfoil with tubercles, this energizing of the boundary layers occurs not at the span-wise points where the vortex generators are installed, but rather in the troughs between the tubercles. This creates very well attached flow on these parts while creating flow separation on the higher crest points, where the flow is less energized. 8

9 The thicker sections (crests) are expected to have larger maximum magnitudes of than the thinner trough sections. In typical airfoils, the coefficient of pressure increases, starting with a value of unity at the leading edge, and reaches a maximum value at approximately the quarter chord. The pressure then proceeds to sharply recover, until it reaches the same value as at the leading edge. This recovery region dictates the separation characteristics. According to Stratford s laminar separation criterion, ( ) (10) the rate at which the coefficient of pressure recovers determines whether separation occurs, with quick recovery typically leading to separation. As the magnitude of in the trough remains smaller than that on the crest, is much smaller and thus maintains a more favorable pressure distribution. This theoretically will lead to a delayed stall on the chord-wise sections behind the troughs. Not only was the flow vorticity was localized near troughs and crests, but also flow behavior patterns. This implies that it can be expected to be possible to view the differences in separated and attached flow on each crest or trough via a visualization tool, such as a smoke wand. Figure 5: CFD simulation results for NACA 0020 Airfoil with Re = 130,000 Using XFoil simulation software, it was found that for a theoretical NACA 0020 airfoil, stall occurs at 14. Thus, consistent with assumptions made earlier, the local critical angle will be slightly higher on the cross-section of the trough, and slightly lower for the crest than this theoretical value. The characteristic amplitude, A, and wavelength of sinusoidal tubercles have been shown by Hansen to have a significant effect on the lift and drag performance of a modified airfoil. Keeping the ratio equal, increasing the tubercle amplitude reduces stall angle and maximum coefficient of lift, but gives significantly improved post-stall characteristics. Small tubercle amplitudes also grant better performance in the post-stall regime without as large a sacrifice in lift. Hansen et al [2] found that optimum performance occurred with amplitude of 3% of the chord length, and a A ratio of Due to size constraints, a compromise of these parameters was selected. The modified airfoil used had tubercles with amplitude of 5.7% the chord length and a ratio of This is shown in Figure 4 in section

10 4.0 RESULTS & DISCUSSION Throughout this experiment, one significant parameter used for judging airfoil performance is the stall angle, with a larger stall angle signifying better performance. In addition, the pre-stall behaviors, post-stall behaviors, and glide ratios of each airfoil are examined to compare performance of the standard and modified airfoils. 4.1 Performance of Standard Airfoil Before the airfoil with tubercles could be tested and analyzed, a baseline must be established for comparison. To do so, a standard NACA 0020 airfoil was tested in the wind tunnel with wind speed of 33.5 MPH and angles of attack ranging from 0 to 20. By using the lift and drag force data acquired from converting the strain gauge voltage reading into the necessary force readings via Equation 1, the lift and drag coefficients were calculated using Equations 3 and 4. Further corrections to the lift coefficient were accounted for using Equation 7. Figure 6: Lift coefficient vs angle of attack, standard NACA 0020 airfoil Figure 6 above indicates that the standard airfoil experienced stall at an angle of approximately 16, with a maximum coefficient of lift of To visualize the separation, the smoke wand was used to generate a visible stream over the airfoil. When the airfoil was rotated to angles of attack greater than 16, greater degrees of boundary layer detachment were observed, such as in Figure 7 below. Note that in order to mitigate wall effects, a negative angle of attack was used, giving more room to deflected streamlines above the model. Pre-stall and post-stall behavior can also be examined in Figure 6. In the pre-stall regime, the lift coefficient increases almost linearly, with the exception of a jump between 4 and 5. Theoretically and intuitively, this jump should not exist and is likely due to experimental error. This discontinuity can be 10

11 attributed to combining data from separate test sessions where configuration and calibration may have differed. The post-stall behavior for this airfoil is characterized by the sharp drop in coefficient of lift immediately after the stall angle, dropping from 0.65 to Figure 7: Boundary layer separation at 16 angle of attack. To judge whether or not the data obtained from testing the standard airfoil was valid, a comparison was made with theoretical results of a NACA 0020 airfoil obtained with simulation software, Xfoil. This simulation was run with conditions similar to those found in the experiment, notably a Reynolds number of 130,000, and the coefficient of lift results are shown below in Figure 8. Figure 8: Theoretical lift coefficient vs angle of attack simulated in Xfoil, standard NACA 0020 airfoil. Re=130,000 Comparing this plot to the experimental results shown in Figure 6, there are several important 11

12 things to note. The first is that the linearly increasing pre-stall behavior and the sudden drop in lift coefficient shown in the post-stall behavior are also consistent between the experimental results and the theoretical results. Secondly, the theoretical simulation predicts a stall angle of 14, a value smaller than the experimentally discovered stall angle of 16. This difference can be explained by the surface roughness of the test airfoil creating turbulence beneficial to boundary layer attachment, resulting in a larger stall angle. It is also important to notice that the magnitude of the two graphs is inconsistent, such that the theoretical maximum coefficient of lift is significantly higher than the experimental maximum, 1.2 vs However, this discrepancy is also likely due to imperfections of the airfoil, such as 3D printing resolution, and the inability of the simulation software to account for conditions present within the wind tunnel, such as wall effects. Therefore it can be concluded that the experimental results for the standard airfoil are valid and can be used as a baseline comparison for the performance of the airfoil with tubercles. 4.2 Performance of Airfoil with Tubercles Following the establishment of a baseline with which to compare airfoil performance, the NACA 0020 airfoil with added tubercles was tested in the wind tunnel under similar test conditions as the standard airfoil. Below is a comparison of the data collected to that of the standard airfoil test, along with a discussion of the observed benefits and disadvantages of the addition of tubercles over the standard airfoil. 4.2a Comparison of Lift Coefficient and Stall Behavior Figure 9: Lift coefficient vs angle of attack, NACA 0020 airfoil with tubercles vs. unmodified airfoil 12

13 As shown in Figure 9 above, the modified airfoil differed from the standard airfoil in several key aspects. First, the lift coefficient for the NACA 0020 airfoil with tubercles peaks at a stall angle of 14, earlier than the previously determined stall angle of 16 for the standard NACA 0020 airfoil. This suggests the tubercles are ineffective in delaying stall, as there is a marked decrease in performance compared to the standard airfoil. Pre-stall behavior is almost identical between the two airfoils, featuring a similar rate of gain in lift as the angle of attack increased. Despite this, the maximum lift coefficient achieved by the modified airfoil is only 0.48, lower than the 0.65 of the standard airfoil. However, because there was a sudden jump in the lift data of the standard airfoil, conclusions concerning the true maximum lift coefficient cannot be confidently made. As a tradeoff for this loss of performance in the pre-stall and stall regimes, the post-stall behavior of the modified airfoil benefited from a more gradual decrease in lift coefficient. Instead of a sudden drop in lift coefficient once the stall angle is exceeded, seen by the drop from a lift coefficient of 0.65 at an angle of attack of 16 to a lift coefficient of 0.47 at an angle of attack of 18 for the standard airfoil, the lift coefficient for the modified airfoil only drops from 0.48 to 0.40 from an angle of attack of 14 to 18. This demonstrates that in the post-stall regime airfoil performance is greatly stabilized with the addition of tubercles. Hansen et al. [2] noted the same behavior for a NACA 0021 airfoil modified with tubercles, confirming that tubercles aid the post-stall behavior of an airfoil at the cost of decreased pre-stall and stall performance, at least for symmetric airfoils of a similar shape. 4.2b Comparison of Drag Coefficient Figure 10: Drag coefficient vs angle of attack, NACA 0020 airfoil with tubercles vs unmodified airfoil Comparison of the drag characteristics of the modified and standard airfoils, as illustrated in Figure 10, yielded little of note. Both airfoils experienced drag of similar magnitude across the majority of 13

14 angles of attack, as well as displayed similar trends in drag growth. Since higher drag results in higher energy loss, this indicates that the modified airfoil will not require more power output to maintain a given speed. 4.2c Boundary Layer Phenomenon As discussed in Section 3.4, tubercles are postulated to modify the boundary layer behavior such that the boundary layer remains attached at specific cross sections of the airfoil at angles of attack greater than the stall angle. To investigate this effect, flow visualization was carried during testing out by adding smoke, generated by a smoke wand, to the airflow generated by the wind tunnel. Figure 11 below shows that the boundary layer remained attached at an angle of attack of 20, an angle greater than the measured stall angle for either the standard or modified airfoil. However, this phenomenon only occurred when the smoke trail ran through the troughs formed between the tubercle crests. When the smoke trail ran on top of the tubercle crests, the boundary layer detached from the airfoil surface, as shown in Figure 12. From these observations, it is reasonable to infer that the overall boundary layer across the span of the airfoil is an amalgamation of attached and detached sections on the crests and troughs of the tubercles respectively, confirming the postulation outlined in section 3.4. This could explain why the addition of tubercles causes a more gradual decrease in lift after exceeding the stall angle of the airfoil, as the drop in lift occurs due to sudden boundary layer separation. If the addition of tubercles delays specific sections of the airfoil from experiencing severe boundary layer separation at angles of attack greater than the stall angle, then the modified airfoil would lose a smaller portion of its lift to boundary layer separation compared to a standard airfoil which experiences boundary layer separation uniformly across its entire length upon exceeding the stall angle. Further investigation of varied tubercle wavelengths and amplitudes with flow visualization could help to further confirm or deny the veracity of this phenomenon. Figure 11: Boundary layer attachment over tubercle trough, 20 angle of attack 14

15 Figure 12: Boundary layer detachment over tubercle crest, 20 angle of attack 4.2d Performance Based on Glide Ratio Figure 13: Glide Ratio vs angle of attack, NACA 0020 airfoil with tubercles vs standard airfoil 15

16 The final parameter with which the performance of the two test airfoils was compared was glide ratio. In aerodynamics, the glide ratio of an airfoil refers to the ratio of the produced lift and drag of an airfoil or aircraft, previously shown in Equation 5. A high glide ratio is indicative of better climb performance for an aircraft due to the implication of the craft s ability to produce a significantly larger amount of lift than drag. As can be seen in Figure 13 above, the glide ratio for the standard airfoil was larger than that of the modified airfoil at angles of attack of 4 to 6. Nonetheless, because the data from these angles likely resulted from error, a confident conclusion about the glide angle at this regime cannot be made. At higher angles of attack, however, the glide ratio for the modified airfoil showed improvement over the glide ratio of the standard airfoil, specifically in the range of 6 to 14. Since this range of higher performance for the modified airfoil is greater than that of the standard airfoil, it is suggested that the addition of tubercles is beneficial to improving airfoil performance with respect to glide angle. In the application to UAVs, tubercles are now shown to allow slower flight at higher angles of attack without the detrimental efficiency drop when operating on the back of the power-curve. This is very desirable for UAVs because this allows shorter takeoff and landing rollouts in areas otherwise unaccommodating to UAV operation. These results are easily scaled to prototype size given similar values for e A and e, the Reynolds numbers referencing a characteristic length of the tubercle amplitude, and wavelength, respectively. 4.3 Error Analysis These wind tunnel experiments, like all laboratory tests, were subject to error from multiple sources. Sources common to all tests are instrumentation and experimentation, which lead to precision errors. Unique to these wind tunnel tests are model imperfections and enclosed wind tunnel considerations which lead to bias errors. In these experiments all dependent variables were measured using sensors with a finite precision, in most cases with an error of 1%. However, the LabVIEW VI used for data collection averaged multiple samples for each data point, effectively eliminating the sensors precision error. Angle of attack was read from an angular scale with tick marks every 1, so an error of up to half a degree is expected. As mentioned, both airfoils were 3D printed with a finite resolution of 0.25mm layer thickness, meaning the models have significant surface roughness. This surface roughness energizes the flow boundary layer, delaying stall, and making it harder to distinguish the boundary layer effects due to the tubercles. Additionally, the model was affixed with screws that protruded from the airfoil surface. These screws affect airflow over the body, likely producing similar boundary layer effects. However, because these bias errors were present for both the standard and modified airfoils, their effect can be neglected when comparing the two models. These tests were performed in an enclosed wind tunnel, which imposes flow boundary conditions at the wind tunnel walls, affecting experimental results. The degree to which these boundaries affect tests depends on the model shape and cross sectional blockage of the tunnel. This error can be accounted for using a correction for quasi-streamlined flow, given by Equation 7 [4]. 4.4 Limitations and Improvements Before reaching any broad conclusions from the results of this experiment, it is important to note that the validity of the results obtained is limited by the scope of the experiment. This experiment was limited by time and resource constraints and as a result only a narrow band of independent variables could be tested. The following recommendations serve to expand the scope and efficiency of future iterations of this experiment. First of all, the wind tunnel was limited by a maximum wind speed of 65 miles per hour. Due to 16

17 this limitation, scaling the experiment to the cruising speed of a commercial aircraft was impossible. Increasing the wind speed limit would allow for exploration of a wider range of applications. Data collection was also hindered by apparatus setup. For example, in order to measure the angles of attack, visual measurement via a protractor printed on the wind tunnel wall was necessary, introducing an element of human error. Replacing this system with a calibrated electronic sensor would largely reduce this error. In addition, the strain gauge mount was only able to measure force in one direction, giving neither lift nor drag but components of both. Having a strain gauge tower where the strain gauge can be fixed in parallel or perpendicular with the airflow direction while adjusting the angle of attack on the airfoil would yield more direct and convenient measurements of lift and drag. Aside from apparatus limitations, there are many areas in which the airfoils could be improved or explored. For instance, the surface roughness of the FDM airfoil does not properly reflect the roughness of commercial aircraft and would be more properly reproduced using a CNC-machined aluminum test airfoil. Additionally, only a NACA 0020 airfoil was used in this experiment. This limits applicability to symmetric airfoils of a chord to thickness ratio equal to 5, and fails to account for other potential wing types and shapes. Testing a larger variety of symmetric and cambered airfoil profiles would broaden the scope of this experiment, allowing for more specific results and comprehensive conclusions. The flow was also rather well controlled in terms of speed and direction using the wind tunnel. However, real world conditions are anything but controlled. Therefore, from this experiment, it is still unclear as to how well an airfoil with leading edge tubercles will fare in more sporadic conditions. In response to all these limitations, more trials with different configurations and testing conditions must be carried out to create a more comprehensive, convincing, and applicable model. A final recommendation would be to carry out further testing of these specific airfoils at various wind speeds. During the experiment, only a single wind speed, 33.5 mph, was used during testing which limits the obtained results to applications with Reynolds numbers in the range of 130,000. Testing a wider range of wind speeds would expand the applicability of the results. 5.0 CONCLUSIONS Addition of leading edge tubercles onto a NACA 0020 airfoil decreased the critical angle, but also reduced the abruptness of loss in lift after stalling. In compromise, pre-stall lift coefficients and maximum lift coefficient (at stall) were decreased. Leading edge tubercles caused the flow at different points along the wingspan to experience local flow detachment at different angles of attack: later at troughs and earlier at crests. The resultant effect is a more gradual flow detachment in overall and a less sudden drop in lift following stall, which can increase the predictability and controllability of aircraft motions at near-critical angles of attack. With these findings, there are significant implications to future advancements in aerodynamics engineering of small aircraft. In particular, the possibility of unprecedented movement and agility emerges and can lead to revolutionized designs. However, this experiment also manifested potential problems in attempting to model a real UAV with the two airfoils. Limitations of flow speed, flow direction, and edge effects were present in the analysis of the results. These problems limit the extent to which the results obtained could be used. These limitations also suggest that there may be potentially important yet overlooked aspects of the two different airfoils and opens the possibility and need for future investigations on these uncovered attributes. 17

18 6.0 REFERENCES [1] Watts, P The Influence of Passive, Leading Edge Tubercles on Wing Performance [2] Hansen, K.L Performance Variations of Leading Edge Tubercles for Distinct Airfoil Profiles, AIAA Journal. [3] Stratford, B. S The Prediction of Separation of the Turbulent Boundary Layer J. Fluid Mech [4] ESDU 80024, Blockage corrections for bluff bodies in confined flows, [5] Rasuo, Bosko. "On status of wind tunnel wall correction." 25th ICAS CONGRESS

19 7.0 APPENDIX 7.1 Derivation of Relation between Pressure Transducer Voltage and Pressure Differential Assuming the pressure of any particular cross section of the test section is constant, and the air behaves as an incompressible, irrotational fluid, a modified form of the Bernoulli's Equation can be used to obtain the velocity of the free stream. (A1) Furthermore, because mass is conserved across the contraction cone: (A2) Combining these equations and setting h 1 h because height changes are negligible, the free stream airspeed after the contraction cone is given by ( ) ( ( ) ) (A3) where 1 and are the pressure before and after the contraction cone respectively and is the frictional loss. A 1 and A are the cross sectional areas before and after the contraction cone, known for this wind tunnel to have a 9 to 1 ratio. However, because the pressure transducer measures voltage rather than pressure, a conversion between voltage readings and pressure differential is needed. This conversion factor from voltage to pressure differential is given as: ( ) (A4) where is the density of pure water and gis the height of the water column of a gauge located inside the wind tunnel that reads pressure from different heights of water. 19