Empirical Determination of Aerodynamic Coefficients of. a Micro-robotic Dragonfly s Wings

Transcription

1 Empirical Determination of Aerodynamic Coefficients of a Micro-robotic Dragonfly s Wings Submitted to Undergraduate Awards Engineering and Mechanical Sciences Category June 2014

2 Abstract The present study aims to characterize the aerodynamic properties of the wings developed for a micro-robotic dragonfly. First, a brief overview of aerodynamics with particular focus on flapping wings is provided. Then, the design approaches for the experimental procedure and apparatus are described. The empirical study relies on measurement of the 1-D forces (both lift and drag) on the wing, when it is subjected to the wind tunnel flow. In attempt to capture a pattern for the wing s polar diagram, quasi-steady assumption is made and data are taken for several angles of attack, the accurate variation of which is performed using a Removable Measurement Mechanism that is designed and manufactured specifically for this purpose. Although the overall patterns of variation in the measured forces as a function of angle of attack are somewhat close to expectations, the results show some inconsistencies and large error bars that suggest the need for further investigation and improvements. Normal forces behave as expected, but the magnitudes of axial forces decrease by increasing the angle of attack, which is not reasonable unless the boundary layer significantly impacts the measurements. Based on the results of this experiment, potential problems associated with the current experimental procedure are identified, and recommendations such as addition of speed and temperature measurement devices and utilization of a 2-D load cell are made in order to facilitate any potential future efforts of validating and/or improving the results of this experiment. Keywords: Aerodynamics; Micro Aerial Vehicles; Robotic Dragonfly; Experimental Design; Data Acquisition and Analysis

3 Table of Contents Abbreviations... ii Symbols... iii List of Figures... iv List of Tables... v 1. Introduction Background and Requirements Fundamentals and Equations Aerodynamics of Flapping Wings and the Quasi-steady Assumption Previous Work and Similar Experiments Requirements for Designing the Removable Measurement Mechanism Design of the Experiment and the Experimental Apparatus Overview of the Experimental Set-up Reynolds Number Determination and Wind Tunnel Selection Selection of Angles of Attack Selection of Load Cell Load Cell Placement Considerations Design of the Removable Measurement Mechanism Experimental Procedure Experimental Results and Discussion Normal and Axial Forces as Functions of Angle of Attack Normal Forces vs. Axial Forces, and on Polar Diagram Effects of Reynolds Number on the Measurements Error Analysis Conclusion and Recommendations References Appendices Appendix A - Several Removable Measurement Mechanism Designs Appendix B - Technical Drawings of the Removable Measurement Mechanism Appendix C - Error Analysis Calculations i

4 Abbreviations MAV DAQ RMM AoA SSD SEM Micro Aerial Vehicle Data Acquisition System Removable Measurement Mechanism Angles of Attack Sample Standard Deviation Standard Error of the Mean ii

5 Symbols L D N A CL CD CN CA α ρ v S Re l Lift force drag force Normal force Axial force Lift coefficient Drag coefficient Normal force coefficient Axial force coefficient Angle of attack Flow density Relative flow speed Planform area Reynolds number Characteristic length µ Fluid dynamic viscosity δ d s N F V Δ Boundary layer thickness Distance from edge of semi-infinite plane Corrected sample standard deviation Number of samples Force Voltage Error or variation in a variable iii

6 List of Figures Figure 1. Wings developed for [UNIVERSITY] s dragonfly MAV... 6 Figure 2. Aerodynamic Forces on an Airfoil (Scott, 2004)... 9 Figure 3. An Illustration of Delayed Stall, Rotational Lift, and Wake Capture unsteady mechanisms (Catching the Wake, 1999) Figure 4. Overview of experimental set-up Figure 5. Cross-sectional view focusing on load cell - wing attachment Figure 6. The load cell, attached to wing from below, connected to amplifier circuit Figure 7. The wing mounted on RRM and exposed to wind tunnel flow Figure 8. Polar diagram of another dragonfly wing model (Wakeling and Ellington, 1997) Figure 9. Polar diagram for a similar, larger scale experiment (Hubel and Tropea, 2009) Figure 10. SMD Load Cell Figure 11. Final design of the Removable Measurement Mechanism Figure 12. Results based on normal force measurements Figure 13. Results based on axial force measurements Figure 14. Relationship between normal and axial components at each angle Figure 15. Results based on normal force coefficients at several Re's Figure 16. Results based on axial force coefficients at several Re's Figure 17. Design 1: Pegs and holes: (a) bottom corner (b) top corner Figure 18. Design 2: No indexing features: (a) bottom corner (b) top corner Figure 19. Design 3: Screw holes and handle: (a) bottom corner (b) top corner Figure 20. Design 4: Screw holes and dowel holes: (a) bottom corner (b) top corner iv

7 List of Tables Table 1. List of angles of attack to be used Table 2. Trade study for different load cells Table 3. Trade study for RMM designs v

8 1. Introduction Man s curiosity about the sophisticated aerodynamic behaviour of insects, and his desire to create flying robots that mimic their agility and maneuverability, together with recent advances in microtechnology, have led to design and fabrication of Micro Aerial Vehicles (MAVs) that are intended for applications such as exploration, navigation in hazardous environments, search and rescue, nuclear plant inspection, and surveillance (Deng, 1995). In order to behave like a real dragonfly, such MAVs need to sustain flight by balancing the forces, the directions and magnitudes of which rapidly change during the flapping motion of their wings. Further insight into the aerodynamics of flapping wings, and the lift and drag forces generated by them would, thus, be highly beneficial for their development. To this point, [UNIVERSITY] had relied on previously created lift-to-drag polar diagrams available in literature, namely the diagrams presented by Wakeling and Ellington (1997), in order to build aerodynamic models for its robotic dragonfly. However, any differences in terms of shape, size, and material properties between the wings used in [UNIVERSITY] s dragonfly and the ones for which these polar diagrams were generated will result in discrepancies in their aerodynamic characteristics, hence undermining the validity of the subsequent models and computations. Therefore, creation of a new polar diagram which was specific to the wings under consideration in this project would be very useful. The results of this thesis work can also be compared with previous experimental results, and used for validation purposes on theoretical models and numerical simulations. Figure 1. Wings developed for [UNIVERSITY] s dragonfly MAV The primary goal of the project was experimental determination of the lift and drag coefficients of the wings used in [UNIVERSITY] s dragonfly, shown in Figure 1, subject to low Reynolds number flow and with quasi-steady assumptions. By achieving this goal, the project would fill the gap pertaining to the aerodynamic characteristics of the wing used in 6

9 the dragonfly s design, and would help eliminate the errors caused by assuming the values that belong to other wing models. In order to achieve this goal, the objectives were: to gain further insight, through literature survey and review of similar experiments, into potential approaches for measuring the aerodynamic forces and accurately setting the angle of attack to derive requirement for, design, and prepare the experimental apparatus to perform the actual experiment as many times as determined to be necessary, and analyze the data to find the lift and drag coefficients at each angle of attack to identify the sources of error and the potential causes for discrepancies in the results, and provide recommendation for future continuations of this effort To accomplish the aforementioned goal and objectives, the general approach involved force measurements on a high-fidelity prototype of the wings in a low-speed wind tunnel, with the wing placed at various angles of attack. The prototypes were readily available, but an appropriate wind tunnel had to be sought out. In addition, a mechanism for accurately setting the angles of attack, while accounting for the limitations imposed by the load cells on the geometry of the set-up, had to be designed and built. For instance, utilizing a onedimensional load cell previously used by the group necessitated separate lift and drag measurements, and this requirement consequently affected the mechanism and its design. Another potential method of determining the lift and drag coefficients on a typical airfoil would involve measurement of local pressure at several points on the surface and approximation of the normal and axial force coefficients (Emami, 2007). However, utilizing such a method for this project would likely require a larger scaled model to allow for implementation of a sufficient number of pressure taps, while rescaling would entail careful consideration of such properties as rigidity. Therefore, in order to avoid unnecessary complications, an alternative method of directly taking lift and drag measurements using force transducers was employed in this project. This method, utilizing a balance system capable of measuring forces as small as 10-4 N, was among the techniques 7

10 used by Okamoto et al. (1996), and a similar technique with some modifications was also employed by Wakeling and Ellington (1997). It is hoped that completion of this project, along with future improvements on the methodology and apparatus, will assist [UNIVERSITY] with performing more accurate modelling of its robotic dragonfly using aerodynamic coefficients that are empirically determined using the actual prototypes of its MAV wings. Furthermore, the methodology and instrumentation that was developed and used can benefit future investigations regarding the aerodynamic performance of similar components, and the research in the area of MAVs in general. This document will provide a brief summary of the relevant literature survey, describe the details of apparatus design and experimental procedure, and finally, present and discuss the empirical data and results. It will also provide suggestions for future follow-up efforts on this project. 8

11 2. Background and Requirements This section summarizes some of the concepts behind aerodynamics of insects and flapping wings, and relates the current project to some of the previous research efforts in this field Fundamentals and Equations Lift is the component of force on a moving solid that is perpendicular to the direction of the fluid freestream flow, whereas drag is the component parallel to it. The force components can also be resolved relative to the geometry of the solid surface, with normal and axial components. All these parameters are shown in Figure 2. Lift and Figure 2. Aerodynamic Forces on an Airfoil (Scott, 2004) drag can be calculated from normal and axial force measurements as follows: ( ) ( ) ( ) ( ) ( ) ( ) where L is lift, D is drag, N is normal force, and A is axial force on the object, and is the angle of the attack. In this experiment, normal and axial forces were measured, because that would allow for rotation of wing and force sensor together. In attempt to come up with dimensionless variables that represent aerodynamic characteristics without dependence on area or dynamic pressure, lift and drag coefficient are defined as: ( ) ( ) where CL and CD are lift and drag coefficients respectively, ρ is fluid density, v is relative speed, and S is planform area. 9

12 With these definitions, then, Equations (1) and (2) can be modified in terms of CN and CA, normal and axial force coefficients (also normalized by denominators of (3) and (4)): ( ) ( ) ( ) ( ) ( ) ( ) Another important property in aerodynamics is the Reynolds number, which is a dimensionless quantity that measures the ratio of inertial forcers over viscous forces. In low Reynolds number flow, which will be the case in this project, viscous forces are dominant and the flow is laminar. For a given fluid/solid pair: ( ) where Re is Reynolds number, ρ is fluid density, v is relative speed, l is characteristic length, and μ is fluid dynamic viscosity. Reynolds number is frequently used to categorize different flow cases. Finally, another relationship that will be considered in this document is the Blasius approximation of laminar boundary layer thickness: ( ) where δ is boundary layer thickness, d is distance from the edge of the semi-infinite plate, and Re is Reynolds number. This relationship will be used to draw conclusions regarding estimated thickness of the boundary layer in the wind tunnel used in this project Aerodynamics of Flapping Wings and the Quasi-steady Assumption Insects are well-known for their efficient flight performance. The interaction between their flapping wings and the surrounding unsteady flow results in the insects ability to perform various aerial maneuvers, such as turning and darting forward (Wang, 2005). The elevated performance of insect wings, such as those of dragonflies, has been suggested to result from the following unsteady mechanisms (Dickinson et al., 1999): 10

13 1. Delayed Stall: At high angles of attack, the flow stream separates at the leading edge, but attaches before the trailing edge. This results in a leading edge vortex due to the circular flow of air into the separation bubble. Owing to the flapping motion, this leading edge vortex is stabilized, and it is commonly identified as an important factor that results in large increases of the lift coefficient (Sane, 2003). Figure 3 provides a visual representation of this mechanism. 2. Rotational Lift: As the dragonfly rotates in wings, an effect similar to Magnus effect, which introduces a curve to a spinning ball s trajectory, is observed. As a result of circulation, there will be a difference in the flow speed on the two (top and bottom) sides of the object, hence resulting in a pressure difference that produces lift (Dickinson et al., 1999). This effect is illustrated in Figure Wake Capture: As the wing enters the fluid field induced by vortex shedding of the previous stroke, as depicted in Figure 3, there is a large increase in drag. By increasing the flow vorticity toward the wing, this phenomenon elevates the forces. This change in force becomes particularly noticeable at higher angles of attack, in which vortex shedding from the previous stroke is stronger (Dickinson et al., 1999). Figure 3. An Illustration of Delayed Stall, Rotational Lift, and Wake Capture unsteady mechanisms (Catching the Wake, 1999) Although the proposal of the existence of these unsteady mechanisms has challenged the validity of the steady-state theory for analysis of insect flight, this project adopts quasisteady analysis, which means the instantaneous forces on the wing at any point in time are 11

14 assumed to be independent of the magnitude of such forces prior to that time. In other words, it is assumed that the aerodynamics forces are history-independent (Wang, 2005). In general, flapping motion of the insect wings along with the flexibility and instantaneous deformations result in complicated aerodynamic behaviour that are not accurately estimated by steady-state or quasi-steady approximations, partly because such analyses fail to capture the rotational kinematics (Sane and Dickinson, 2001). Quasi-steady analysis is, however, still useful for flapping wing flight and has been used frequently in the past. Such an analysis is adequate particularly in case of dragonflies for they glide frequently, and gliding mode can be safely assumed to involve steady flow (Wakeling and Ellington, 1997). As long as the rotations at the end of wing beats are neglected, this assumption is reasonable, and it yields instructive results on minimum lift coefficient compatible with flight. In other words, even if the wing beat rotations do play a role, they will result in higher values for some of the instantaneous lift coefficients (Ellington, 1984) Previous Work and Similar Experiments Interest in insect flight and aerodynamics of flapping wings gained strength around mid- 1970s, with attempts by individuals like Bennett (1977) to describe and possibly quantify the effects of unsteady mechanisms that were proposed as potential mechanisms used by the insects. The recent progress in this field was particularly accelerated by the developments in high-speed videography, which allowed the researchers to assess and improve the accuracy of their theoretical approximations (Sane, 2003). More recently, numerical and computational models have also been developed to simulate flapping wings and their kinematics. Tethered flight experiments are other approaches for characterizing the aerodynamics of insect wings. Such experiments involve live insects restrained by means of glue or flexible tethers. For instance, Grodnitsky and Morozov (1993) conducted such studies together with several visualization techniques on 6 insect species, with a focus on the vortex formation and its effect on the aerodynamic performance. However, the forces and stroke kinematics in tethered insects are not completely the same as those of actual flight conditions either, and the transducers used in such methods measure the forces of the 12

15 entire body, which are obviously different from those generated by each wing (Sane and Dickinson, 2001). More relevant to this project are attempts by Okamoto et al. (1996) who conducted similar studies to construct the drag polar for dragonfly wings. They used multiple techniques, such as measurement of force using transducers in a horizontal wind tunnel, stroboscope photography to study gliding flight, and obtaining steady auto-rotational flight data (in which a spinning wing floats in the test section) in a vertical wind tunnel (Okamoto et al., 1996). The method used in this experiment was similar to their first method, and involved a horizontal wind tunnel and use of load cells to measure the forces. Another example of a relevant attempt is that of Dickinson and Götz (1996) who utilized a two-dimensional force transducer and a computer-controlled stepper motor, along with flow visualization techniques to study the time-dependence of aerodynamic forces present during the accelerating motion of the wing in a sucrose solution. The goal of this thesis project was to build upon the previous knowledge and expertise in the field of insect aerodynamics, and attempt to produce a more accurate polar diagram for [UNIVERSITY] s dragonfly wings, and by doing so, support the parallel modelling and computation efforts that are currently based on literature data obtained for other wing models. The method of using force transducers in a wind tunnel has been employed in some of the aforementioned research attempts, and the quasi-steady analysis that was conducted has proved useful, if not completely accurate, by some of these past empirical studies Requirements for Designing the Removable Measurement Mechanism As will be described in the following sections, the experiment made use of a low-speed wind tunnel. In order to be capable of exposing the dragonfly wing to the wind tunnel flow while avoiding interference with the tunnel s operation, it was necessary to design a Removable Measurement Mechanism (RMM) that would form part of the tunnel s bottom wall during the experiment. The following requirements were derived for this apparatus: 13

16 R-1. The RMM shall hold the load cell and the wing in place during the experiment, while providing robust mechanical support for the load cell. In order for the load cell to measure the forces on the wing, the two should be attached together, and should be kept attached during the experiment. The apparatus is responsible for holding these components in place, and for doing so with a quantifiable accuracy. In addition, the load cell operates using a strain gauge and acts like a cantilever beam: the force of interest is applied at one end, and the other end should be fixed in place to allow for bending deformations that will subsequently be captured by the strain gauge. The RMM is, therefore, also responsible for providing a support that will not be affected by the applied forces. R-2. The RMM shall allow for varying the angle of attack with steps of at least 5. There is a trade-off associated with the indexing method between the cost and manufacturing efforts, and the limitations resulting from varying the angles discretely. Alternatively, if one decides to enable the user to vary the angle continuously, the trade-off will then be between the accuracy achieved, and the versatility of the system (again, the limitation on how many and how close the angles will be). Obviously, it is preferred for the user to be able to perform measurements with smallest possible variations of the angle of attack. However, there is a minimum requirement of 5 for this experiment, which comes from the set of angles that were chosen during the experimental design. These angles are listed in Table 1, Section 3.2. R-3. The RMM should allow for setting any arbitrary angle of attack. This is a preferred requirement, as indicated by the wording should. The rationale behind this optional requirement is the same as that of Requirement R-2. A continuous indexing is preferred, since it allows the user to perform the experiment using any combination of angles of attack. However, it involves inherent inaccuracies resulting from manual setting of the angle, or significantly higher manufacturing complexity and costs associated with automating the task. Although meeting this requirement is desirable, it is not mandatory considering the finite set of angles selected for this experiment. These angles are listed in Table 1, Section

17 R-4. The RMM shall be able to cover the dedicated gap in the wind tunnel bottom wall with a part that fits within a in x envelope. This is a constraint on the dimensions of at least part of the apparatus. The selected wind tunnel has a gap in the bottom surface that is dedicated to placing a customized removable plate, hence allowing for customization of the model s placement inside the tunnel and the associated measurements. This gap is where the RMM will also attach to, and by doing so, it will expose the wing to the flow while covering the gap and allowing the tunnel to operate as an enclose system. The dimensions are those of the gap; therefore, the RMM should have a part with these dimensions to cover this gap. R-5. The RMM shall allow for measurement of both lift and drag forces, or axial and normal forces at a given angle of attack. The goal of this project is to construct the drag polar of the wings, for which both lift and drag values at each angle of attack are required. As described in Section 2.1, these forces can also be calculated using axial and normal forces. Depending on the design and whether it would be convenient to measure the forces parallel and perpendicular to the flow, or parallel and perpendicular to the wing surface, the apparatus should enable the user to measure a pair of orthogonal forces. R-6. The RMM shall be electrically insulated from the load cell. The body of the load cell (SMD , described in more detail later) is made of steel, and when it comes into contact with another electrically conductive material, it fails to operate and measure the voltage variations due to consequences of grounding. The apparatus shall, therefore, ensure isolate the load cell from other conductive components electrically. R-7. The RMM shall avoid interfering with the normal operation of the wind tunnel and disrupting the flow. The wind tunnel operates by suction: it sucks the air. If the apparatus is not secured properly, or if part of it comes off due to the suction, the wind tunnel will no longer operate as it is supposed to because the gap in the bottom wall will no longer be 15

18 covered. As another example, if there are large protrusions or holes on the surface that will be facing the inside of the tunnel, the flow will be disrupted, hence resulting in erroneous measurements. To avoid these problems, the inward-facing surface of the apparatus should be free of such features and/or defects, and should blend smoothly with the remaining portions of the bottom wall. 16

19 3. Design of the Experiment and the Experimental Apparatus This chapter describes some of the considerations regarding the experimental set-up: 3.1. Overview of the Experimental Set-up The overall experimental set-up consisted of the following parts, laid out as shown in Figure 4. Figure 5 shows a cross-sectional view focusing mounting the wing on the load cell. A low-speed wind tunnel, running at 2 m/s - 3 m/s for a Reynolds number of A load cell for measuring the force A DAQ or a multimeter for measuring the output voltage An amplifier secret to enable reading the low voltage changes resulting from small forces encountered in this experiment A 30 V power supply to power the circuit Figure 4. Overview of experimental set-up A Removable Measurement Mechanism (RMM) that forms part of the wind tunnel s bottom wall, and has been designed to address the needs of this particular project. This mechanism, the design of which is further described in detail in Section 3.6, will be used to hold the load cell and the wing in place, and set the angle of attack as required. It should be noted that, typically, for airfoils used in such configurations an upper surface is added to enclose the airfoil and eliminate the finite wing effects. For this experiment, however, addition of this surface was deemed unnecessary, because such effects will make the results even closer to what should be expected when the dragonfly actually attempts Figure 5. Cross-sectional view focusing on load cell - wing attachment to take flight in an open environment. As a result of this decision, there will be finite wing 17

20 effects on the forces as well. Figure 6 and Figure 7 are pictures of the real set-up, and they show the wing inside the wind tunnel, as well as the load cell and its circuitry. Figure 7. The wing mounted on RRM and exposed to wind tunnel flow Figure 6. The load cell, attached to wing from below, connected to amplifier circuit 3.2. Reynolds Number Determination and Wind Tunnel Selection The Reynolds number associated with insect wings can be as low as 10, or as high as 10,000, and is highly dependent upon the insect size and flow speed (Sane, 2003). Regions with such Reynolds number are classified as intermediate regions. For Sympetrum sanguineum, which is the dragonfly species based on which [UNIVERSITY] has modelled its robotic MAV, a value of around 1000 seems reasonable. Using Equation (7) in Section 2.1 for Reynolds number, along with ρ = ρ air 1.23 kg/m3, l m (based on the datasheet of the wings), and μ 18.3 x 10-6 Pa.s, one can conclude that at given a flow of approximately v 3 m/s, the Reynolds number will be about Re Flow speeds of around 2 3 m/s, thus, were deemed appropriate for this project. Two options were considered for a low-speed wind tunnel, and eventually one with a lower speed was selected, was more closely examined, and was eventually used for this experiment because in addition to its easier access, it is capable of creating a stable flow at as slow as 3 m/s, whereas the other option operates reliably with only as low as 11 m/s and reducing the speed beyond this threshold will induce oscillations and instabilities in 18

21 the flow. Upon further investigation of the selected wind tunnel, it was determined to meet the needs of this project with its low flow speed that can enable an experiment that closely resembles the conditions in which the [UNIVERSITY] robotic dragonfly is expected to operate. However, as will be suggested at the end of this document, re-examining the stability and reliability of the flow using a flow speed measurement device (such as a Pitot tube) prior to potential future experiments is recommended Selection of Angles of Attack Figure 8. Polar diagram of another dragonfly wing model (Wakeling and Ellington, 1997) Figure 9. Polar diagram for a similar, larger scale experiment (Hubel and Tropea, 2009) Based on the previous similar experiments, such as the one corresponding to the polar diagram presented by Wakeling and Ellington (1997) for their Sympetrum sanguineum model wings, shown in Figure 8, and a larger scale flapping wing experiment involving determination of drag polar by Hubel and Tropea (2009), shown in Figure 9, a number of different angles of attack covering a wide range was determined to be sufficient for an informative polar diagram. In order to capture the flow separation, angles as large as were also deemed appropriate to include. Table 1 provides the list of angles used in this experiment. Small variations of 5 were used for the region close to 0 (as the boundary between positive and negative angles of attack), followed by larger steps of 10. Again, selection of these particular angles was partly inspired by the aforementioned past experimental efforts. When designing the apparatus to enable setting the angle of attack, several indexing methods were considered, and the current design provides high-precision 19

22 indexing with steps of 5 due to Requirement R-2, which was in turn derived based on the angles listed in Table 1. List of angles of attack to be used Step Angle of Attack Selection of Load Cell As mentioned previously, the selected method for determining the aerodynamic coefficients relies on force measurements. This will be performed using a so-called load cell, which operates based on electrical signal variations resulting from strain gauge measurements, and using a data acquisition system (DAQ) or multimeter, these voltage variations can be converted and stored as computer data. Finally, using a mapping of voltage to force, the obtained electrical signals can be converted to their corresponding force magnitudes. Three types of load cell which had been previously used by [UNIVERITY] were considered for this purpose. Listed in Table 2 are the advantages and disadvantages of each. Finally, the change in voltage was converted to corresponding force using previously constructed calibration tables. Initially, the decision was to use SMD , which is manufactured by Strain Measurement Devices Inc., and can handle loads of up to 9.9 kg. Its high stiffness relative to SMD prevents damages resulting from excessive oscillations that were suspected to result from the wind tunnel flow. Based on previous tests, this sensor shows a variation of N/V, where positive direction of the force is defined as upward from the load cell s top surface. However, during the experiment some problems were experienced that were associated with either the amplifier circuit or a damaged load cell. As a result, the experiments were conducted again using SMD , which is much more flexible and more sensitive. The original concern regarding resonance resulting from flow-induced oscillation was found to be unnecessary, and not resonance effects were observed. This 20

23 load cell has a transformation factor of ( ± ) N/V, where positive direction of the force is defined as upward from the load cell s top surface. Table 2. Trade study for different load cells Load Cell Advantages Disadvantages SMD SMD Very sensitive to force variations (good for small forces) Compact and small (easier to secure on apparatus) High maximum load capacity Compact and small (easier to secure on apparatus) 1D only (requires separate lift and drag runs) Vulnerable to vibrations (can be permanently damaged due to oscillations resulting from flow) 1D only (requires separate lift and drag runs Relatively stiff (less sensitive to the very small forces encountered in this project) L-shaped 2-D Load Cell 2D nature allows for simultaneous lift and drag measurements Still under development Involves coupling between the data obtained from the two dimensions Relatively large Using a 2-D cell to conduct simultaneous measurements of both lift and drag would, of course, be advantageous, but [UNIVERSITY] s current 2-D load cell is not completely ready for use yet. Some coupling has been observed between lift and drag measurements, which does not make sense. Using SMD and SMD required separate normal and axial force measurements at different angles of attack, which was considered as one of the potential causes of inconsistency in the obtained data. For illustration purposes and to show what a load cell typically looks like, a model of SMD used when designing the Removable Measurement Mechanism is shown in Figure Load Cell Placement Considerations Another concern was how to avoid the load cell influences on the flow and vice versa; that is, how to prevent disruption of flow due to the presence of the load and avoid incorrect sensor measurements caused by the direct flow impact. The load cell could be placed together with the wings inside the wind tunnel, or it could be external to the tunnel and be 21

24 supported by other fixtures. The latter approach obviously would not suffer from this problem, but the downside would be potential influences caused by wind tunnel s bottom wall on the forces on the wing prototype because of its close proximity to the wall. This is particularly important considering the expected boundary layer thickness as a result of a low Reynolds number. In order to avoid the complications Figure 10. SMD Load Cell associated with having the load cell inside, however, the option of an external load cell was chosen. In addition, as part of the experimental set-up, it was decided to place the wing vertically inside the tunnel, as shown in Figure 4, which would reduce the boundary layer effects and further justify the decision of having the load cell isolated from the flow Design of the Removable Measurement Mechanism Extensive effort was put in designing and iterating over the design of the main part of experimental set-up, namely the Removable Measurement Mechanism RMM) used to conduct the measurements and vary the angle of attack. Several designs were considered and compared against each other. Table 3 briefly summarizes this trade study, and shows a comparison between several competing designs. A visual overview of each design has been provided in Appendix A. For ease of access, the design requirements that were previously derived in Section 2.4 have been listed below. For a detailed description on the rationale behind each item, please refer to Section 2.4: R-1. The RMM shall hold the load cell and the wing in place during the experiment, while providing robust mechanical support for the load cell. R-2. The RMM shall allow for varying the angle of attack with steps of at least 5. R-3. The RMM should allow for setting any arbitrary angle of attack. R-4. The RMM shall be able to cover the dedicated gap in the wind tunnel bottom wall with a part that fits within a in x in envelope. 22

25 R-5. The RMM shall allow for measurement of both lift and drag forces, or axial and normal forces at a given angle of attack. R-6. The RMM shall be electrically insulated from the load cell. R-7. The RMM shall avoid interfering with the normal operation of the wind tunnel and disrupting the flow. As the final decision, Design 4 was selected and manufactured for this experiment. Appendix B provides its technical drawings. This design, a model of which is shown in Figure 11, consists of a Rectangular Supporting Frame that is latched to the wind tunnel using 4 latching pieces at the corners of its 2 sides, and a Circular Rotating Plate that can be attached to or removed from the frame using ¼-20 screws. Some features include: There are 72 Screw Holes on the Rectangular Supporting Frame, which are intended to allow for discrete variations of angle of attack with multiples of 5, from 0 to 360. These holes are threaded and allow for attaching the Circular Rotating Plate (which also has 4 of the matching holes), once the desired angle is set by aligning the lower and upper holes. Although 4 holes have been provided on the Circular rotating Plate for this purpose, using only 2 will suffice in creating a secure attachment. This design was deemed to have the highest robustness and stability among all solutions considered, as shown in Table 3. Both vertical and horizontal forces are expected to be exerted by the wind tunnel s flow on the Circular Rotating Plate. For the final design (Design 4), resistance against these forces is provided not only via the screws, but also by the flanges that will be pushed against those of the Rectangular Support Frame. All other designs that were considered had the rotating plate sit on the frame from the top, as a result of which they would lack the stability effects resulting from the flanges of the plates countering the vertical forces. There is 1 rectangular cubic Load Cell Support Bracket on the Circular Rotating Plate. The purpose of this is to provide both mechanical and electrical ground for the load cell, and it had been originally dimensioned specifically for SMD When the need for using SMD arose, a similar bracket had to be fabricated to accommodate the new dimensional requirements. Since two separate measurements of normal and axial forces are required, the wing should be placed with its surface along or normal to 23

26 Table 3. Trade study for RMM designs (Refer to Appendix A for Design Descriptions) Criteria Design 1 Design 2 Design 3 Design 4 Accuracy of Angles Very High Pegs can be manufactured for nearly perfect fit Low Requires manual adjustments Error different every time owing to human involvement Low/High Depends on which mode is used: continuous mode will be low like Design 2, but discrete mode can be same as Design 4 Very High Dowel holes can provide up-to in positional accuracy Robustness and Stability Low Horizontal stability against wind provided by pegs No vertical stability against suction Very Low No vertical and/or horizontal resistance against suction and/or wind motion High Both horizontal and vertical stabilities by screw May require sealing to prevent air leak Very High Screw helps with both horizontal and vertical stabilities, and upper flanges counter vertical forces as well Versatility Very Low High Very High Low Only limited to discrete angles (multiples of 10 ) Smaller angles would requires more and smaller pegs Has no limits on the angles achieved, and covers the continuous range of 0 to 360. Provides both discrete and continuous angle operations Only limited to discrete angles, but holes of smaller diameters are more feasible than such pegs required to improve Design 1 Ease of Fabrication and Cost High Large waste caused by melting off the material around pegs Low Simple design, with no holes or protrusions Very High Inclusion of handle will require an additional CNC setup, resulting in higher cost than Design 4 High Least number of CNC set-ups needed, but adding and smoothening dowel holes increase complexity Ease of use Low High Low/High Low Requires lifting the circular plate and placing it back in rotated position for every angle Involves no lifting or screwing, but requires measurements for setting the angle Depends on which mode is being used: continuous mode will be easy, but discrete mode will need screwing Requires screwing in order to prevent the circular plate from falling 24

27 Figure 11. Final design of the Removable Measurement Mechanism the bracket s side surface. Located between the center of the Circular Rotating Plate and tangent to the Load Cell Support Bracket s side surface is as Hole for Wing Spar. This one is to allow of the MAV wing s spar to pass through, hence enabling the wing to remain inside the tunnel, while all the other features and the load cell are on the other side and external to the flow. Due to manufacturing limitations, this hole could be smaller than 0.75 mm diameter, which was determined to be still small enough to not introduce considerable jets into the flow resulting from suction. In addition to a circular pattern of ¼-20 screw holes used for fixing the plates to each other, there is a matching pattern of dowel holes (not threaded) that will increase the angle s accuracy. With the addition of this feature, the positional error for the centreline of the holes was reduced to in, which considering the radial distance of ±5.00 in from the centre for the dowel holes, this translates into around ±0.01 angular error. 25

28 3.7. Experimental Procedure Finally, before proceeding to the results of the experiment, it is worthwhile to briefly mention the experimental procedure followed to obtain the result presented in Chapter 4, in case further measurements are desired in the future, or should there be a follow-up project attempting to address some of the issues in the apparatus or in the procedure: 1. The load cell was attached to its support on the RMM using 4-40 screws. To avoid electrical shorting, the load cell s steel body was isolated from the surrounding metals using electrical tape and nylon screws. 2. The wing was mounted on the RMM by attaching the wing spar to the load cell using nuts on a screw that goes through the load cell s hole. The orientation depends on whether normal or axial component of the force is being measured. 3. The RMM was latched to the wind tunnel. 4. The SMD load cell was connected to the amplifier circuit, which was then powered with a 30 V power supply. 5. After about 10 min (to allow the sensor and the circuitry to warm up), the initial voltage was measured before starting the wind tunnel. 6. The wind tunnel was turned on using different valve settings for each speed. Based on previous measurements done by FCET, frequencies of 5.75 Hz, 6.87 Hz, and 8.00 Hz were used for approximate flow speeds of 2 m/s, 2.5 m/s, and 3 m/s. 7. Measurements of the amplifier circuit s output voltage were taken. For the sake of consistency, measurements were taken after 30 s of changing the angle of attack. As mentioned previously, SMD has transformation factor of ( ± ) N/V, which was multiplied by the change in voltage (with respect to the initial voltage obtained in Step 5). 8. The angle of attack was varied by removing the ¼-20 screws, rotating the circular plate to the desired angle, and screwing it back in place. A dowel was placed in its hole to provide higher angular accuracy (positional accuracy of in). 9. Steps 7 and 8 were repeated for all angles listed in Table 1 (in a randomized order). 10. Once all the measurements for one component of force (normal or axial) were taken, Steps 2 through 9 were repeated for the other component. 26

29 4. Experimental Results and Discussion This chapter provides a summary of the data and results obtained from the experiment, and attempts to discuss the results and how they can be improved Normal and Axial Forces as Functions of Angle of Attack Figure 12 and Figure 13 show the results based on 3 trials (for each force component) with a flow of approximately 3 m/s. It should be noted that the measurements for each of the trials involved turning the wind tunnel off and on again, as a result of which there might have been significant changes in flow properties and speed. Figure 12. Results based on normal force measurements Figure 13. Results based on axial force measurements 27

30 The overall trend of the normal force as a function of angle of attack is reasonable and expected, but that of the axial force is not. As the angle of attack increases, the difference in the pressure above and below the wing increases, resulting in a higher normal force, unless separation occurs (at very high angles of attack). This is captured by Figure 9, although as evident by the large error bars, the results of various trials were not very consistent. The axial force, however, is somewhat unexpected, as it decreases as the angle of attack increases. Similar to drag (which becomes more and more influenced by the axial component at higher angles), increasing the angle of attack would typically entail an increase in axial force as well. This is not the case in Figure 10. In addition, in some trials, negative axial forces were also experience, which does not make much sense either. A potential explanation of these unexpected occurrences is the boundary layer of the wind tunnel. The wind is very small, and with its relatively short spar, at least part of it would fall into the boundary layer region, in which the viscous effects dominate. Referring back to Equation (8) in Section 2.1, we have: Clearly, for a given point inside the wind tunnel, this relationship predicts larger boundary layer thickness for lower Reynolds number flows. This is logical, since the definition of Reynolds number itself is related to the ratio of inertial forces over viscous forces, and for the cases of low Reynolds number encountered in this research, one would expect the viscous forces to have more significant effects on the entire follow, particularly near the boundary layer. For a Reynolds number of 1600 (for which these results were obtained), assuming the wing is around 0.5 m away from the point at which boundary layer starts (which is still a relatively low estimate), the boundary layer can be approximate to be ~ 6 cm thick, which is quite significant considering the very small size of the MAV wing Normal Forces vs. Axial Forces, and on Polar Diagram Shown in Figure 14 is the normal vs. axial components of the force, where each data-point corresponds to one of the angles of attack at which both components were measured. It should be noted that this is not what is typically defined as a polar diagram, since that will 28

31 be based on lift force vs. drag force, as opposed to normal and axial forces. However, although the results shown in Figure 14 were not perfectly repeatable, there is a slight, yet interesting resemblance between this figure and the polar diagram generated by Wakeling and Ellington (1997) for another dragonfly wing model, shown in Figure 9. Looking at this figure, one begins to wonder: are the forces measured in this experiment actually the normal and axial forces, or are they 2-D forces at an angle with respect to body-fixed frame s axes? That is, is the load cell capable of measuring the force only in the direction perpendicular to itself, or will its measurements be affected by the component of force in the other direction as well? These are questions that should be considered in the future, and they lead to some of the suggestions made in Section 5. On the other hand, when one uses Equations (1) and (2) to determine the lift and drag forces based on normal and axial measurements, followed by Equations (3) and (4) for non-dimensionalizing the forces into coefficients and plotting a polar diagram for [UNIVERSITY] dragonfly wing, the results are not even remotely similar to Figure 14, nor are they similar to any other polar diagram. The reliability of the data and experimental apparatus was, therefore, undermined because of the inconsistent and strange shapes of the polar diagrams (which were deemed to be too erroneous to include in this report) Effects of Reynolds Number on the Measurements Figure 15 and Figure 16 show the results obtained for 3 different Reynolds numbers, all of which still fall under the intermediate Reynolds number category. The value of Re was estimated based on the speeds of 2.0 m/s, 2.5 m/s, and 3.0 m/s, and the corresponding valve frequencies (based on previously calibrated tables) were set. Figure 14. Relationship between normal and axial components at each angle The pattern observed in Figure 15 is difficult to explain, since there does not seem to be a good reason for having Re = 1600 data points between the other two, while they have the 29

32 Figure 15. Results based on normal force coefficients at several Re's Figure 16. Results based on axial force coefficients at several Re's largest Reynolds number. These Reynolds numbers are fairly close, and one would not expect the forces to go back up again after Re = 1300, but it is the case in Figure 15. Figure 16, on the other hand, is reasonable with its pattern of reduction in the axial force as a result of an increase in Reynolds number. This figure is particularly insightful because it provides further evidences for the aforementioned point that some of the inconsistencies discussed in Section 4.1 have to do with boundary layer thickness: At Re = 1100, the nonuniformity of the changes in the results as function of angle of attack is significantly more pronounces than the non-uniformity at the other two Reynolds numbers. This may be in part because of the boundary layer thickness (which increases significantly with reduction of flow speed), which might be larger and more troublesome in the case of Re =

33 4.4. Error Analysis Several sources of error were identified for this experiment, some of which may have had significant impacts on the results and the meaningfulness of the plots shown in Sections 4.1 and 4.2. These sources, from most influential to least (in this writer s opinion) include: Errors in conversion of wind tunnel valve frequency to speed, and deviations in flow speed resulting from turning the tunnel on and off which were unaccounted for Impact of axial forces on normal force measurements and vice versa Sensor drift and variations of the load cell s output voltage over time as a result of temperature variations, successive loading, or other unidentified causes Variations in flow density over time, as a result of changes in ambient temperature Angular inaccuracy in wing placement owing to manual mounting, resulting in a constant off-set from all desired angles of attack Instrumental measurement errors associate with the multimeter Angular inaccuracy in angles of attack resulting from rotating the plate in place and positional inaccuracy of the dowel Some errors bounds can be quantified based on the results from multiple trials and/or instrumental errors. For the case of Re = 1600, 3 trials were performed, as a result of which an average with its associated errors bars was obtainable, as shown in Figure 12 and Figure 13. For relevant calculations, the reader is referred to Appendix C. The largest standard errors of the mean (SEM) of the normal forces were found to occur at the smallest and largest angels testes, namely -30 and 60, with values of ~ ±0.3 mn, which is significant compared to the measured voltages themselves. At -30 and 60, the SEMs of the axial component were found to be ~ ±0.04 mn and ~ ±0.1 mn, respectively. Additionally, some attempts can be made to take the known instrumental errors into account as well. In order to compare these influences with the SEM, error propagation relationships were used, which are summarized in Appendix C. As an example of the results of this analysis, the propagated uncertainties on the calculated forces with the angles of attack of -30 and 60 (for which SEMs were highest) were calculated to be 0.05 mn for 31

34 normal forces. As for axial forces, they were found to 0.06 mn and 0.04 mn at -30 and 60, respectively. As can be seen from these values, the propagated effect of independent variables on the resultant forces is typically less than SEM at each angle of attack, which suggests that improving the consistency of the results will be much more beneficial than improving the accuracy of the load cell and the multimeter; however, one should also consider the fact that part of the inconsistencies in the results may, in fact, be because of flaws or inadequacies in the measurement devices, such as potentially low sensitivity of the load cell that results in difficulties in capturing the changes in the force (particularly for the case of axial force component). 32

35 5. Conclusion and Recommendations As presented in this report, an experimental procedure and apparatus has been developed and utilized for obtaining force measurements on the [UNIVERSITY] dragonfly s wing, all in attempt to gain insight into the aerodynamic performance of the wing and quantify some its force coefficient by making quasi-steady assumptions. The experiment was able to capture the large effect of angle of attack on magnitude of the forces experienced by the wing. Although some meaningful patterns for normal and axial forces were generated, the associated errors resulting from inconsistent measurement data deemed too high, as a consequence of which the reliability of the results were questioned. Unfortunately, the polar diagrams that were generated based on these data had no consistency or reasonable pattern, hence further strengthening the suspicion about the adequacy of the experimental apparatus. Even though acceptable polar diagrams were not generated because of lack of time, many sources of error and potentials for improvement have been identified, addressing which as part of the future efforts is highly likely to solve the current problem. It is recommended by this writer that any future attempts should first strongly consider replacing the 1-D load cell with a reliable 2-D load cell. This not only will highly simplify the procedure and reduce measurement errors by eliminating the need for separate normal and axial measurements, but also will ensure correct interpretation of the data by preserving the 2-D nature of the force. In any case, regardless of what type of load cell will be used, it is crucial to eliminate or sufficiently reduce the undesirable output voltage variations that may result from changes in ambient temperature, temporary elastic deformation of the load cell s beam due to successive loading, or simply signal problems associated with the amplifier circuit or the load cell itself. As further improvements that should also be simple to implement, one might want to consider adding two other measurement devices to the apparatus: a Pitot tube for accurately measuring the flow speed; and a thermometer for accurately measuring the flow temperature, hence allowing for a good estimation of the flow density and its change over time. 33

36 Finally, in addition to improving the measurement capability of the apparatus, another modification to consider would be using a longer spar or a higher speed flow in order to avoid the tunnel s boundary layer as much as possible. Both of these suggestions will require the user to ensure that the aerodynamic problem of interest is unchanged by accounting for additional parameters. More specifically, if one decides to use a longer spar, he/she shall be aware that this will increase the effect of the spar s flexibility on the measurements, and he/she should take appropriate measures to either eliminate or account for this effect. Similarly, if one chooses to operate the wind tunnel at a higher speed in attempt to reduce the boundary layer thickness and flow instabilities, he/she should rescale the model in order to maintain the desired Reynolds number, while this action will require careful consideration of such properties as rigidity. Although this project is complete and an experiment for empirically determining the force coefficient of the [UNIVERSITY] dragonfly MAV was designed and performed during this research project, and the results show some high-level patterns, further related work is certainly needed in order to improve the obtained results and construct a meaningful polar diagram. It is hoped that, by building upon the groundwork set by this thesis project and by addressing some of the identified issues, future efforts will be able to obtain a more accurate quantitative aerodynamic characterization of the [UNIVERSITY] micro-robotic dragonfly s wings. 34

37 6. References Bennett L Clap and Fling Aerodynamics An Experimental Evaluation. The Journal of Experimental Biology [Internet]. [cited 2014 Feb 14] 69: Available: Catching the Wake Scientific American [Internet]. [cited 2014 Apr 5]. Available from: Deng X Flapping Flight for Biomimetic Robotic Insects: System Modeling and Flight Control in Hover [dissertation]. [Internet]. [Berkeley (CA)]: University of California at Berkeley; [cited 2013 Oct 13]. Available from: by subscription. Dickinson M. H., Fritz-Olaf L., Sanjay P. S Wing Rotation and the Aerodynamic Basis of Insect Flight [Internet]. [cited 2014 Feb 14] 284: Available: by subscription. Dickinson M. H., Götz K. G Unsteady Aerodynamic Performance of Model Wings at Low Reynolds Numbers. The Journal of Experimental Biology [Internet]. [cited 2014 Feb 14] 174: Available: Ellington C. P The Aerodynamics of Hovering Insect Flight. VI. Lift and Power Requirements. Philosophical Transactions of the Royal Society of London, Series B, Biological Sciences [Internet]. [cited 2014 Apr 5] 35(1122): Available: by subscription. Emami M. R. [Internet] Aerodynamic Forces on an Airfoil. Toronto (ON): University of Toronto Undergraduate Aerospace Laboratories [cited 2013 Oct 13]. Available from: Grodnitsky D. L., Morozov P. P Vortex Formation during Tethered Flight of Functionally and morphologically Two-Winged Insects, Including Evolutionary Considerations on Insect Flight. The Journal of Experimental Biology [Internet]. [cited 2014 Feb 14] 182: Available: Hubel T. Y., Tropea C Experimental Investigation of a Flapping Wing Model. Experiments in Fluids [Internet]. [cited 2013 Nov 24] 46(5): Available from: by subscription. 35

38 Okamoto M., Yasuda K., Azuma A Aerodynamic Characteristics of the Wings and Body of a Dragonfly. The Journal of Experimental Biology [Internet]. [cited 2013 Oct 13] 199: Available from: Sane S. P Aerodynamics of Insect Flight. The Journal of Experimental Biology [Internet]. [cited 2014 Feb 12] 206: Available from: Sane S. P., Dickinson M. H The Control of Flight Force by a Flapping Wing: Lift and Drag Production. The Journal of Experimental Biology [Internet]. [cited 2014 Feb 14] 204: Scott J. [Internet] Lift & Drag vs. Normal & Axial Force. AeroSpace Web. [cited: 2014 Feb 14]. Available: Wakeling J. M., Ellington C.P Dragonfly Flight: I. Gliding Flight and Steady-state Aerodynamic Forces. The Journal of Experimental Biology [Internet]. [cited 2013 Oct 13] 200: Available from: Wang Z. J Dissecting Insect Flight. Annual Review of Fluid Mechanics [Internet]. [cited 2014 Feb 14] 37: Available from: 36

39 7. Appendices 7.1. Appendix A - Several Removable Measurement Mechanism Designs (a) (b) Figure 17. Design 1: Pegs and holes: (a) bottom corner (b) top corner Circular pegs at 10 that lock into a pattern of holes on the supporting frame Requires lifting up the plate, rotating, and putting it back in place 37

40 (a) (b) Figure 18. Design 2: No indexing features: (a) bottom corner (b) top corner No features to fix the circular plate in place, hence allowing for continuous rotation with no restriction on the angles of attack achieved May not be secure enough against wind tunnel suction and tendency to rotate in place Required manual rotation using the handle 38

41 (a) (b) Figure 19. Design 3: Screw holes and handle: (a) bottom corner (b) top corner Screw holes can be smaller than circular pegs of Design 1, allowing for smaller intervals Addition of handle enables both continuous and discrete operations Highly complicated and large manufacturing costs (several CNC set-ups) Holes only on one half to save cost and time of manufacturing 39

42 (a) (b) Figure 20. Design 4: Screw holes and dowel holes: (a) bottom corner (b) top corner Includes 2 rows of holes: one for fixing the plates together, one for angular accuracy Circular plate attaches the support from below, hence increasing stability No more handle, and only 1 bracket for load cell (will require rotating the wing in place, but simplifies the manufacturing) 40