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ANALYSIS OF HIGH ANGLE OF ATTACK MANEUVERS TO ENHANCE

UNDERSTANDING OF THE AERODYNAMICS OF PERCHING

Thesis

Submitted to

The School of Engineering of the

UNIVERSITY OF DAYTON

In Partial Fulfillment of the Requirements for

The Degree

Master of Science in Aerospace Engineering

Zachary Michael Lego

Dayton, Ohio

December, 2012

ANALYSIS OF HIGH ANGLE OF ATTACK MANEUVERS TO ENHANCE

UNDERSTANDING OF THE AERODYNAMICS OF PERCHING

Name: Lego, Zachary Michael

APPROVED BY:

______Aaron Altman, Ph.D. Markus Rumpfkeil, Ph.D. Advisory Committee Chairman Committee Member Associate Professor Assistant Professor Mechanical and Aerospace Engineering Mechanical and Aerospace Engineering

______Gregory Reich, Ph.D. Committee Member Adaptive Structures Team Lead Air Force Research Laboratory

______John Weber, Ph.D. Tony E. Saliba, Ph.D. Associate Dean Dean, School of Engineering School of Engineering & Wilke Distinguished Professor

Zachary Michael Lego

2012

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ABSTRACT

ANALYSIS OF HIGH ANGLE OF ATTACK MANEUVERS TO ENHANCE

UNDERSTANDING OF THE AERODYNAMICS OF PERCHING

Name: Lego, Zachary Michael University of Dayton

Advisor: Dr. Aaron Altman

Due to their vastly unsteady aerodynamics, mimicking the flight maneuvers of natural flyers requires a deep understanding of the unsteady flow physics while also demanding the ability to expand the vehicle’s flight envelope beyond normal conditions. Experimental and computational investigations are performed to study and improve the flight performance of a perching maneuver. Flowfield images and force history data are acquired to investigate the performance of highly unsteady motions experienced during a perching maneuver. The perching motions studied are divided into two first order approximations, a rapid pitching motion and an impulsively started hold in order to follow the North Atlantic Treaty Organization Research &

Technology Organization Applied Vehicle Technology 202 (NATO RTO AVT 202) guidelines.

Both types of motions are investigated through experimental testing and using a computational

2D Discrete Vortex Method (DVM). Using the 2D DVM allows the ability to determine whether a low order, two dimensional code can accurately predict an actual 3D flowfield generated by highly unsteady motions. The pitching motions are studied experimentally using 3D plates in the

University of Dayton Low Speed Wind Tunnel (UD-LSWT). Results show that despite some 3D instabilities in the experiments, which are not produced by the DVM, overall the DVM matches the experiments well. Results are completed for varying pitch rates and the DVM matches the

iv experiment more closely for the faster, more inertially dominated pitch rates. Upper surface pressure data is also recorded in both the experiment and DVM. The results suggest that differing pressure profiles could have a substantial influence on aerodynamic forces even at high angles of attack. The impulsively started hold motions completed experimentally with 3D plates in the

AFRL Horizontal Free Surface Water Tunnel (AFRL HFWT) again produce some three- dimensional instabilities not modeled in the 2D DVM. When comparing the impulsively started results, the DVM did not match the startup of the motion in the force histories due to the use of different startup transients and the constants in the smoothing function. The DVM does well when comparing the flowfield. In an attempt to expand the available performance envelope during these types of motions variable camber is studied for both types of maneuvers using the

2D DVM and in both cases the initial results show that variable camber has the potential to positively influence the boundaries of the flight envelope during a perching maneuver.

ACKNOWLEDGEMENTS

I would first like to thank my advisor, Dr. Aaron Altman for always being there for me both academically and personally during the last few years while I was at the University of

Dayton. He has been an excellent leader for me and has only deepened my passion for experimental aerodynamics teaching me things I never dreamed of knowing both from an academic and personal standpoint.

I would next like to thank my committee members, Dr. Gregory Reich and Dr. Markus

Rumpfkeil. I would also like to thank all the rest of my professors and under their guidance in the classroom and in the field I was able to take the skills I have learned and apply them to my research in perching aerodynamics.

I would also like to thank all the members of the AFRL aircraft perching team for teaching me about perching and always being there to bounce ideas off of.

I would also like to thank all my fellow graduate students at the University of Dayton, without you my time would have been much less enhancing and exciting. I would especially like to thank Sidaard Gunasekaran for all the help he has given me both in my research and in my personal life and I look forward to all our future adventures.

I would also like to thank the University of Dayton and North Carolina State University for preparing me for all my future endeavors.

Finally, I would like to thank my family for all their love and support!

TABLE OF CONTENTS

ABSTRACT…………………………………………………………………………….…………iv

ACKNOWLEDGEMENTS……………………………………………………………………….vi

LIST OF ILLUSTRATIONS…………..………………………………………………………...viii

LIST OF TABLES………………………………………………………………………………..xii

LIST OF SYMBOLS/ABBREVIATIONS………………………………………………….…..xiii

CHAPTER 1: INTRODUCTION…………………………………….……………………………1

CHAPTER 2: DECLARATION OF THE PROBLEM……………….…………………………...3

CHAPTER 3: LITERATURE REVIEW…….…………………………………………………….8

CHAPTER 4: EXPERIMENTAL SETUP…………………………………………………….....20

CHAPTER 5: COMPUTATIONAL APPROACH……………………………………………....28

CHAPTER 6: RESULTS AND DISCUSSION………………………………………………….31

6.1 LINEAR PITCH RAMP MOTION………..……………………………………….31 6.2 IMPULSIVELY STARTED HOLD MOTION……...………………………………50 6.3 VARIABLE CAMBER………………..…………………………………………….56

CHAPTER 7: CONCLUSION…………………………………………………………………...68

REFERENCES…………………………………………………………………………………...71

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LIST OF ILLUSTRATIONS

Figure 1–1 shows a common flight path of a perching maneuver used in bird landing……...... 2

Figure 1-2 shows the relative motion of each of the three pure pitching case……………………..5

Figure 1-3 represents the velocity of a 45 degree impulsively started hold reaching maximum speed in half a chords traveled…………………………………………………………………….6

Figure 2-1 shows the flowfield evolution of a pitching motion using different experimental and computational media. [5]……………………………………………………………………………9

Figure 2-2 shows the force histories for an SD7003 airfoil undergoing a 0 to 45 degree pitching motion with a k of 0.03. The peak lift corresponds to the shedding of the LEV from the plate when comparing with Figure 2-1. [5]……………………………………………………………..10

Figure 2-3 shows experimental data for 2D flat plates pitching at different reduced frequencies. As the reduced frequency is increased the maximum lift peak is increased. Experimental data was acquired by Granlund and Ol. [5]………………………………………………………………….11

Figure 2-4 illustrates that for highly unsteady flows reduced frequency plays a much greater role in the force history than Reynolds number. (Granlund et al. [6])………………………………...12

Figure 2-5 shows that for the slower pitch rates the vortical structures are more pronounced in the flowfield due to the increased time the plate takes to reach the same angle of attack. [9]………..14

Figure 2-6 shows that spanwise flow is creating instabilities in the formation of the leading edge vortex and forcing the flow to become more unsteady. [9]……………………………………….15

Figure 2-7 shows the split wing section model configuration. [11]………………………………..16

Figure 2-8 shows that overall the lift coefficient history produced by the DVM compares well with other methods, with the exception of a small phase shift in the formation and shedding of vortices. [13]………………………………………………………………………………………..17

Figure 2-9 shows that in ideal steady conditions a variable camber wing provides better performance than a mechanically operated flap does, due to the weight reduction and smoothness of the airfoil within a flap. Data acquired by Ohanian III et al. [15]……………………………….19

Figure 3-1 shows the AFRL-HWFT test section with an oscillation rig mounted above………...20

Figure 3-2 – The University of Dayton Wind Tunnel……………………………………………21

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Figure 3-3 shows one of the flat plate models in the wind tunnel to provide a physical context for the size and location of the wings during testing………………………………………………....22

Figure 3-4 shows the wing profile section of each wing used for wind tunnel…………………..22

Figure 3-5 shows an AR 4 semi-span wing with an SD7003 airfoil. Embedded in the wing are 8 Kulite pressure transducers for measuring unsteady pressures during pitching maneuvers……...23

Figure 3-6 shows (left) Galil CDS-3310 Ethernet controller; (right) Griffin Motion Rotary Stage ……………………………………………………………………………………………………24

Figure 3-7 shows an ATI Gamma force and torque sensor……………………………………....25

Figure 3-8 shows the complete test setup needed to complete a rapid pitching maneuver and measure pressure, forces and moments…………………………………………………………...26

Figure 4-1 shows flowfield comparison of the DVM to a 45 degree impulsively started water tunnel test completed by Ol. The two show excellent agreement and similar shear layer instabilities. [20]……………………………………………………………………………………30

Figure 5-1 shows that as the reduced frequency of the same maneuver is increased the same fundamental flow features occur but they will evolve differently………………………………..33

Figure 5-2 shows that the 6 chords traveled case is more inertially dominated, and the 12 and 18 chords traveled cases are more convectively dominated…………………………………………34

Figure 5-3 shows that as the reduced frequency is decreased the lift peak is obtained at a lower angle of attack…………………………………………………………………………………….35

Figure 5-4 shows that as with the DVM, as the reduced frequency is decreased the lift peak occur at a lower angle of attack, this time in the wind tunnel results. σ = 0.25…………………………36

Figure 5-5 shows as the reduced frequency is decreased the drag decreases approaching a steady drag profile………………………………………………………………………………………..37

Figure 5-6 shows that all three reduced frequency cases have a quadratic nature and as reduced frequency decreases so does the magnitude of the drag coefficient. σ =0.25……………………38

Figure 5-7 shows how the deformation of the trailing wake seen from the vorticity contours appears to correspond to maximum lift and subsequent lift loss through the progression of the flow field…………………………………………………………………………………………39

Figure 5-8 shows that a decrease in the lift due to bound vorticity does occur once the trailing edge wake is deformed for the 6 chords traveled pitching case………………………………….41

Figure 5-9 shows lift behavior for the wind tunnel data and DVM results compare well early in the maneuver as the LEV grows and also shows a difference in peak lift and post-stall performance likely due to 3D tip effects. σ = 0.25………………………………………………42

Figure 5-10 illustrates for both the DVM and wind tunnel data there is a roughly quadratic increase in drag for the pre-stall region. Once this point is reached, the two follow different trends. σ=0.25…………………………………………………………………………………….43

Figure 5-11 demonstrates that while minor differences are seen when using different wing profiles, no major differences are seen between the cases and the DVM results compare well to all three wings. σ = 0.1……………………………………………………………………………45

Figure 5-12 compares pressure profiles for the 6 chords traveled pitching motion and it is believed that 3D effects maybe affecting the pressure distribution and thus affecting the force histories at the higher angles of attack……………………………………………………………46

Figure 5-13 shows that the maximum lift occurs at the point where the trailing edge wake begins to deform and a periodic shedding cycle begins………………………………………………… 47

Figure 5-14 shows that once the first LEV vortex has begun to shed from the plate there are some discrepancies such as the second local lift peak in the wind tunnel data that could potentially be explained by 3D wing tip effects. σ = 0.25……………………………………………………….48

Figure 5-15 expresses that during the maneuver the initial maximum lift coincides with the deformation of the trailing edge wake and that a second lift peak is seen to correspond to the convection of the TEV downstream off the plate……………………………………………….. 49

Figure 5-16 shows that once separation off the leading edge occurs differences can be seen in the lift slope gradient and also in the magnitude of the oscillatory peaks which is believed to be caused by spanwise flow effects. σ = 0.25……………………………………………………….50

Figure 5-17 shows for the Impulsively Started Hold cases after 3 chords traveled major differences are seen when comparing the DVM and PIV. These differences are thought to result from spanwise flow/tip effects on the wing in the AFRL-HFWT………………………………..52

Figure 5-18 shows similar trends between DVM and water tunnel for Impulsicely started motions except in the startup where different smoothing constants were used and at the second local lift peak where spanwise flow could be affecting the formation of the TEV………………………...53

Figure 5-19 compares the two impulsive start cases using the DVM and it is observed that prior to the peak created from the formation of a TEV the lift coefficient is larger for the lower Reynolds number case. ……………………………………………………………………………………..55

Figure 5-20 compares water tunnel and DVM Impulsive Start data for Re=10,000. Good agreement is seen between the two cases except during the startup (where smoothing occurs) and in the magnitude of the second lift peak where 3D effects are believed to be inducing shear layer instabilities not seen in the DVM…………………………………………………………………56

Figure 5-21 demonstrates a pitching motion with variable camber………………………………57

Figure 5-22 is a schematic of cambered wing…………………………………………………….58

Figure 5-23 shows as camber is added the pre-stall lift curve slope becomes greater than the flat plate case and post-stall the lift decreases at a much greater rate than the non-camber case…….59

Figure 5-24 shows that a temporal shift is seen in the drag in the pre-stalled region but once stall occurs similar magnitudes are observed………………………………………………….………60

Figure 5-25 (left) shows the L/D for the entire 0 to 90 degree pitching motion. (Right) is an exploded view of the L/D to show that as camber is increased a lower L/D can be achieved…...61

Figure 5-26 shows that varying camber can affect the formation of the LEV when comparing to a flat plate. It is also seen that when camber rate is increased it has a greater effect on the formation of the LEV………………………………………………………………………………………..62

Figure 5-27 shows as camber is added the pre-stall lift curve slope becomes greater than the flat plate case and post-stall the lift is much less…………………………………………………….63

Figure 5-28 offers that as the maximum camber percentage is increased an increase in pre-stalled lift curve slope will occur………………………………………………………………………..64

Figure 5-29 shows that as the location of maximum camber is moved aft on the airfoil a higher lift curve slope is reached from the lower effective angle of attack which keeps the flow attached…………………………………………………………………………………………..65

Figure 5-30 compares the flowfield for three different variable camber rates to a flat plate. By including camber and increasing the rate at which camber occurs the formation of LEV and TEV can be altered…………………………………………………………………………………….66

Figure 5-31 shows that as the variable rate is increased a drop in the initial lift peak is seen although a higher CLmax is encountered because the camber has delayed the formation of the LEV……………………………………………………………………………………………...67

LIST OF TABLES

Table 3-1 lists the serial number of each pressure transducer used in the SD7003 wing and also the distance of each transducer as a percentage from the leading edge………………………….23

Table 3-2 lists maximum loads and accuracy of those loads for the ATI Gamma F/T Transducer………………………………………………………………………………………..25

Table 3-3 displays the uncertainties as they propagate from different measured quantities……..27

Table 5-1 shows the range of parameters used to do analysis on a 0 to 45 degree pitch ramp motion…………………………………………………………………………………………….31

Table 5-2 lists the parameters used when completing a variable camber motion………………..59

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LIST OF SYMBOLS/ABBREVIATIONS

2D = Two Dimensional

3D = Three Dimensional a = Smoothing Constant

AR = Aspect Ratio c = Chord

CD = Drag Coefficient

CL = Lift Coefficient

CLmax = Maximum Lift Coefficient cosh = Hyperbolic Cosine Function

D = Drag Force

G = Eldredge Smoothing Function k = Reduced Frequency

L = Lift Force

LE = Leading Edge

LEV = Leading Edge Vortex n = Number of a Set

R = Variable for which Uncertainty is applied

Re = Reynolds Number

SE = Standard Error

T = Time to pitch

xiii t = Time

= Time from reference 0 to start corner of unsmoothed ramp

= plus duration of pitch upstroke

= plus hold time after upstroke of motion

= plus pitch downstroke

TE = Trailing Edge

TEV = Trailing Edge Vortex th = thickness

= Freestream Velocity

̇ = Pitch Rate

δ = Standard Deviation

= Uncertainty for a given measurement

σ = Fraction of Error bars plotted CHAPTER 1

INTRODUCTION

“I realized that if I had to choose, I would rather have birds than airplanes.”

– Charles Lindbergh

Lindbergh makes the point that while mankind has achieved the ability to fly using airplanes, the capabilities of these airplanes come nowhere close to matching the ease, skill, and command a bird has while flying. The ability to fly mimicking such natural flyers has been fantasized about since ancient times and man has made it an ultimate goal to achieve.

Since the time winged flight became realistic with the invention of gliders, people have tried to design their aircraft resembling natural flyers in a hope to provide better performance. In the 9th century BCE, Abbas Ibn Firnas[1] was known to be one of the first people to fly a

“rudimentary” glider which included no vertical tail (similar to birds), although he crashed on every landing. After Firnas in the 15th century Leonardo da Vinci[1] designed a hang glider that resembles a bird’s wing because it was fixed at the center but as it went to the tips, flexible control surfaces were included. In the 19th century Jan Wnek [1] built and flew a controllable glider which he designed to be able to twist at the trailing edge as he had seen while observing birds.

With the onset of powered flight by the Wright Flyer I, the ability to make flying more natural and efficient only intensified. Now in the time of modern flight and modern warfare where unmanned aircraft are becoming more practical, the ability to hide in plain sight has pushed the desire of mimicking birds even further, and this is due to the fact that if a plane is built to look and fly like a bird one might suspect it of actually being a bird. With this idea, the study

1 of Micro Air Vehicles (MAVs), which are defined by DARPA as a small vehicle of wingspan no more than 6 inches and having similar flight capabilities of natural flyers [2], became a staple in the research community. One large effort in the study of MAVs is to try to imitate a typical landing maneuver that birds undergo.

One such landing maneuver typically utilized by birds is perching. Perching is typically seen as a sequence of severe initial motions which transition into a smooth glide to a target where the flyer lands with near zero horizontal and vertical velocity. A common perching trajectory, shown below in Figure 1-1, has the bird flying below the target with a steady angle of attack, the bird then transitions into a dive to increase velocity, followed by a pull up maneuver to a very high angle of attack as it climbs to a position above the perch, and finally holds that angle of attack and descends smoothly onto the perch.

Figure 1–1 shows a common flight path of a perching maneuver used in bird landing.

Chapter 2 details the specific problem studied and how it is going to be solved. Chapter 3 provides an extensive look at previous works completed in this field and how they helped in the development of this thesis. Chapter 4 and 5 outline the experimental and computational setups used to provide the work done in the thesis. This is followed by the results and discussion in

Chapter 6 and by the conclusion in Chapter 7.

CHAPTER 2

DECLARATION OF THE PROBLEM

The Air Force Research Laboratory (AFRL) is currently studying perching with the end goal of designing a fully controllable aircraft that has the ability to perch. The aerodynamics of the steady phases of the maneuver at the lower angles of attack are reasonably well understood, however many questions remain during the highly unsteady phases such as the pull up and subsequent hold motions. Due to the high angles of attack and high pitch rates utilized the aerodynamics of these motions are very sophisticated. Many unknowns still remain in this matter and need to be further resolved to obtain the necessary accuracy needed to design a fully autonomous perching vehicle. Aerodynamically, it is an unknown as to whether or not these complicated maneuvers can be modeled in a simpler way that would still provide the complexity and precision but would decrease the computation needed to successfully perch. It is the purpose of this research to advance and enhance the understanding of the aerodynamics of these motions.

One analysis is to determine whether a low fidelity code can accurately model an actual flowfield in order to elucidate the necessity of three-dimensionality when studying the aerodynamics of unsteady maneuvers. The other investigation is to determine whether geometry changes such as varying camber can benefit the aerodynamics of unsteady motions such as perching

To study these motions the North Atlantic Treaty Organization Research & Technology

Organization Applied Vehicle Technology 202 (NATO RTO AVT 202) test case is used as a guideline. The NATO RTO AVT 202 which was developed to study flowfield problems related to high angle of attack motions, serves as an attractive choice due to the similarity of the research and capability to collaborate with others doing similar work. This test case outlines two primary

3 investigations. The first is a simple linear pitch ramp motion and the second is an impulsively started hold maneuver. These two motions abstract very well to actual perching because both motions can be seen as first order approximations to one of the perching motions mentioned previously and while they are slightly less complicated the simplifications do not degrade the integrity of the results because the motions are comparable and still highly unsteady.

The pull up motion used during a perching maneuver is comparable to a linear pitch ramp motion because both motions incorporate a change in angle of attack by only using rotational motions. Different rotations can be compared through the rate at which the rotation occurs, and non-dimensionally this rate is the reduced frequency, k and is shown as Equation 1-1.

̇ (1-1)

With increasing k, the speed of the motion increases and the flow behavior is less pronounced than what would be seen in a convectively dominated flow of smaller k. It is important to study both convectively and slightly more inertially dominated flows because they are the upper threshold of reduced frequencies seen while perching (Robertson saw k’s = 0.02 –

0.06 when testing perching maneuver in the AFRL μAVIARI) and less is known about them than fully inertial and fully convective flows. Reduced frequencies of 0.03, 0.045, and 0.09 are examined for a pitching motion from 0 to 45 degrees since the first two are more convective and the last is slightly inertial. Figure 1-2 shows all three motions relative to one another.

Figure 1-2 shows the relative motion of each of the three pure pitching cases.

The hold motion at the end of a perching maneuver begins at the height of the pitching motion where the bird has already reached its maximum speed and high angle of attack wing position and proceeds to hold this configuration to reduce lift and fall smoothly on the perch. The

NATO RTO AVT 202 test group states that as a first order approximation this motion can be abstracted as high angle of attack impulsively started hold motion because the angle of attack is set constant and the maximum velocity is instantaneously reached either at the beginning of the motion or after some additional ramp up in velocity. The main impulsively started motions studied in this research are 45 degree holds where the velocity is ramped from zero to a maximum in half a chord traveled and then held at that velocity for the remainder of the experiment. Figure

1-3 shows a simple schematic of the velocity in the impulsively started angle of attack hold maneuver investigated in this research.

Figure 1-3 represents the velocity of a 45 degree impulsively started hold reaching maximum speed in half a chords traveled.

To analyze these motions a 2D Discrete Vortex Method (DVM) is used and compared with experiment. The reason for using this two-dimensional code is to try and understand if a simple 2D Laplace solver can accurately predict the flow physics and force histories obtained during an actual perching maneuver. Since the DVM is a low fidelity code and does not require the computational time of higher fidelity CFD code, if proven to model the flow field and force histories of these motions to a suitable level of accuracy, it can be used as a conceptual design tool for developing an aerodynamic model for maneuvers such as perching.

To evaluate the DVM’s performance, experimental testing is completed for both the pitch ramp and impulsive start motions. To analyze the pitch up maneuver an AR 4 flat plate is placed in the University of Dayton Low Speed Wind Tunnel (UD-LSWT). The impulsively started hold motions are completed experimentally with AR 4 flat plates in the AFRL Horizontal Free Surface

Water Tunnel (AFRL-HFWT) by Granlund and Altman.

To increase the aerodynamic flight envelope on a vehicle by increasing or decreasing the lift and/or drag is typically advantageous. The best way to do this is to change the pressure

6 distribution on the vehicle in a way that positively affects performance. Little is known about the pressure distribution on a highly unsteady wing undergoing a perching maneuver. Thus this research also investigates the pressure distribution on an SD7003 wing doing a rapid pitching motion in the UD-LSWT. This data is compared to pressure data acquired from the DVM. After studying the unsteady pressure data it is deemed of interest to try and see if varying the camber of the wing while pitching would be advantageous. It is believed that changing the shape and/or size of a vehicle will change the pressure distribution over the vehicle and if a vehicle could vary the camber of its wings in mid-flight it might help to increase aerodynamic performance while perching. In a maneuver such as perching which deals with high local altitude gradients and high angle of attack changes, it could be perceived that varying camber would be a desirable characteristic because it would allow for the ability to increase or decrease lift and drag performance during the motion. For instance at low angles of attack right before the pitch up motion it could be advantageous to add positive camber which would increase the lift of the vehicle allowing the vehicle to use less power in order to reach the high perch location. It could also be seen as advantageous to decrease the camber at very high angles of attack where in a perching maneuver the vehicle would want to begin to decrease lift and increase drag as it attempts to slow down and land on the perch. These types of changes are commonly seen in perching maneuvers performed by actual birds.

CHAPTER 3

LITERATURE REVIEW

As mentioned in the Introduction, there has been a significant amount of work completed in the study of MAVs, especially perching. One such work helped to compile the knowledge and understanding learned during the early years of MAV research. The book “Aerodynamics of Low

Reynolds Number Flyers [3],” by Shyy et al. deals mainly in outlining the kinematics and understanding the flow features of different MAV maneuvers. In comparable studies to the ones done in this research the book outlines the fundamental flow physics of both a rotational pitching motion and a set angle of attack impulsively started motion. The book discusses that for an airfoil impulsively started at a high angle of attack a large transient vortex will form at the leading edge and will increase the lift on the airfoil. Similar results were seen by Anders [4] in 2000. In reviewing the pitching motion the author states that the flow physics look drastically different during the motion if the pitch rates were more inertially dominated than convectively dominated because in the faster, more inertially dominated motion vortices had less convective time to form and shed.

Another effort which was completed by Granlund et al. [5] looks at comparing force histories and flowfield evolution using both experimental and computational studies on high angle of attack pitching maneuvers for an SD7003 airfoil. A wall-to-wall model was tested in the

AFRL-HFWT and the results were compared to CFD done at AFRL using an implicit method large-eddy simulation solver, FDL3DI. Analogous to one of the studies in this thesis an initial 0 to 45 degree pitch case using the SD7003 airfoil with a quarter chord pivot location, Reynolds number of 50,000 and a reduced frequency of 0.03 was used as a baseline case and different case

8 were run by either changing the Reynolds number, reduced frequency, pivot location, or changing from the SD7003 airfoil to a flat plate. The flowfield and force histories for the baseline case can be seen in Figure 2-1 and 2-2 respectfully. It can be observed when comparing the force histories to the flowfield that maximum lift is reached just before the leading edge vortex begins to separate from the airfoil in the 20 to 28 degree angle of attack range depending on the model.

This investigation is particularly appropriate to the results obtained and presented in this thesis.

Figure 2-1 shows the flowfield evolution of a pitching motion using different experimental and computational media.[5]

The role of pitch rate was also studied in this paper. Pitching motions are completed using a flat plate at many different reduced frequencies ranging from 0.0025 to 0.2. The lift coefficient history can be seen for each case in Figure 2-3. From the figure it can be observed that as the pitch rate increases the maximum lift also increases. It also can be seen that for the reduced frequency cases above 0.03, additional lift is created upon the steady lift curve and it can be surmised that it comes from the increased rotation rates. While a change in the lift curve is seen at the reduced frequencies of 0.03 and 0.05 it is small compared to the changes seen at the reduced frequencies above 0.075, and it can be noted that while these lower reduced frequencies of 0.03 and 0.05 have some inertial contribution they are primarily still convectively dominated.

In a second paper by Granlund et al, the authors investigated the forces and flow fields created when undergoing a rapid pitching motion [6]. Experiments were completed in the AFRL

HFWT on a 2D flat plate, AR 2 flat plate, and AR 2 Zimmerman wing. Figure 2-4 shows the lift coefficient history for different reduced frequency pitching motions for both the AR 2 flat plate and Zimmerman wing. In analyzing the figure and comparing runs of the same reduced frequency it can be seen that both planforms have a fairly comparable lift profile even though some of the tests have been completed at differing Reynolds numbers. This assertion indicates that for highly unsteady maneuvers such as these high angle of attack pitching motions, reduced frequency has a much greater effect on the forces than Reynolds number and this is important to highlight because all three pitch cases studied in this thesis have different reduced frequencies and different

Reynolds numbers.

Figure 2-4 illustrates that for highly unsteady flows reduced frequency plays a much greater role in the force history than Reynolds number. (Granlund et al. [6])

In a similar effort to the above papers the AIAA Fluid Dynamics Technical Committee’s

Low Reynolds Number Discussion Group introduced and studied “canonical” pitch motions [7].

One of the canonical cases developed in this paper was short hold, abrupt ramp 0-40 degree motions. Similarly to Granlund et. al [5] the effects of reduced frequency, pivot point, and

Reynolds number were all studied. The reduced frequencies for these tests range from 0.35 to

1.05 and similarly to [5], as the reduced frequency is increased so does the maximum lift. The difference in the results of this paper was that all of these runs are inertially dominated and when plotting the lift coefficient divided by the reduced frequency almost all cases coalesce. This shows that for these highly inertially dominated motions while no fundamental differences were seen in the force histories, the lift curves shift up as the reduced frequency increases.

Another study of rapidly pitching 2D plates was completed by Baik et al [8]. Using the

University of Michigan water channel facility, 0 to 90 degree pitching experiments were completed for reduced frequencies of 0.2 and 1.0. For the reduced frequency of 0.2 a LEV was formed during the pitch-up maneuver. At a reduced frequency of 1.0, however, the LEV was not formed until the plate had completed the maneuver. It was reported by the AIAA FDTC-LRDG

[7] that for all inertially dominated flows as the reduced frequency increases the magnitude of the force coefficient distribution resulted in an upward shift of the lift curve as a function of the reduced frequency. From these two statements it can be concluded that for high reduced frequency motions the flow characteristics only play a small part in the force histories, because it is the kinematics that dominate. While flows investigated in this thesis are not highly inertial like in [7] and [8], the highest reduced frequency case is inertially influenced and these assertions can provide a basis for differentiating the analysis of this case compared to the other two.

A comparable effort was completed by Visbal where the flow structure over a pitching wing was investigated [9]. The results in the paper were acquired by using a sixth-order implicit method, large eddy simulation solver, the FDL3DI. Comparable to this thesis, 3 different convective pitch rates (0.05, 0.1, 0.2) for 45 degree pitching motion were examined using a flat plate wing. In comparing the vortical structures produced by each of the three different pitch rates vast differences are noted between the 3 cases investigated. Snapshots of 15 and 45 degrees angle of attack for each of the three pitch rate cases can be seen Figure 2-5. The slower pitch rates show a more dominant leading edge structure produced for each angle of attack due to the longer time available to produce the vortex resulting from the slower pitch rate. The tip vortices are more pronounced in the slower cases as the flow has more time to wrap around the edges of the plate.

Due to this increase in time these vortices have a much more pronounced effect on the flowfield of the slower pitch rate cases as they are forcing the LEV vortex further down the plate for the same angle of attack.

Figure 2-5 shows that for the slower pitch rates the vortical structures are more pronounced in the flowfield due to the increased time the plate takes to reach the same angle of attack. [9]

The process of dynamic stall on a pitching wing in 2D and 3D was also investigated in the paper. In comparing the two cases in Figure 2-6 again for 15 and 45 degrees, the vortices in the 2D case form and shed in a much smoother and less chaotic way than was seen in the 3D case. The inclusion of tip vortices and spanwise flow effects create an increase in cross-stream transfer and led to instabilities in the formation of the leading edge vortex.

Figure 2-6 shows that spanwise flow is creating instabilities in the formation of the leading edge vortex and forcing the flow to become more unsteady. [9]

In research complementary to the work performed for this thesis, Hart and Ukeiley [10] studied the flowfield evolution of the leading edge vortex for AR 4 rapid pitching motions. The experiments for this research were completed at the low Reynolds number Aerodynamic

Characterization Facility at the University of Florida REEF and the flowfield was captured using

PIV. They observed that with the development of unsteady vortex structures, stall can be delayed during a rapid pitch motion when compared to a static airfoil angle of attack sweep. Using a flat plate it was observed that as the motion progresses the leading edge vortex formed and grew in strength until it began to shed at about 27 degrees, which was much delayed from the steady state flat plate that began to shed vortices between 10 and 12 degrees. It was also observed in the paper

(only minor for the cases investigated) that tip vortices have the ability to change flow behavior by inducing spanwise flow on wing. This is directly relevant to this thesis because comparisons are made between 2D and 3D flows to help validate the DVM capabilities. If 3D flows are seen to

15 have drastically different features not seen in 2D it could impact the validity of the results produced by the DVM.

In Lukens et. al [11] the authors designed, built, and tested a split wing section configuration (Figure2-7) in the UD-LSWT and compared to a vortex lattice model developed in

MSC-ADAMS and ran using a multi-body aeroelastic simulation tool (IAMMS).

Figure 2-7 shows the split wing section model configuration. [11]

Results showed that the model matched the trends of the wind tunnel data very well and that a simplified analytical model can predict the overall features of an experiment. This helps to provide insight into how an actual vehicle would perform while presenting the most important features in the flowfield and forces histories.

Reich et al. [12] expanded on the work done by Lukens by using the split section wing to model extreme MAV maneuvers such as perching. Analytical time delay models (Steady and

Quasi-Steady Airfoil and Wing) were then used to compare with wind tunnel results on the split wing. It was found that even the 2D airfoil Time Delay Model predicted the unsteady forces of the 3D split wing reasonably well resulting in greater confidence in the accuracy of 2D models such as the DVM.

Hammer et al. investigated the validity of the low order models for high angle of attack maneuvers using the DVM [13]. One maneuver studied in this paper was a 0 to 45 degree pitch and hold. The lift coefficient history from the DVM was then compared to three CFD results, 2 analytical time delay models, and experimental data completed in the AFRL HFWT and is shown in Figure 2-8. Inspecting the figure shows that the DVM compares well to the other results helping to validate the method, but it can be seen that formation and shedding of vortices occurs out of phase in the DVM as compared to the other results. This may be due to a limitation in the code (which has since been modified by Hammer) in which the angle of attack where separation occurs was arbitrarily chosen and could have influenced a shift in the shedding phase cycle. It is unknown, though, if this was the reason for the difference as it is not evident which of these methods is correct or if this difference falls within experimental and computational uncertainty.

In the study of impulsively started flat plates, one effort in particular by Beckwith and

Babinsky is of interest [14]. While the motions studied in this paper are not necessarily high angle of attack maneuvers they do provide a good basis for comparison as the kinematics of the motion and trajectory taken are similar to what is being studied in this thesis. This paper also provides a

17 good tracking and analysis of the formation of vortices during an impulsively started maneuver.

In the post stall 15 degree angle of attack case, it was seen that an initial startup peak is reached at the start of the motion but that the maximum lift is not reached until 3.5 chords had been travelled where the LEV was able to grow in strength before it sheds off the plate while a TEV forms.

Once this initial vortex sheds from the plate no follow-on vortex created as much lift as the first vortex. It was believed that this occurs because some additional lift was created at the beginning of the motion due to the kinematics of the motion but that all subsequent vortices provide an increase in lift.

A paper by Ohanian III et al. [15] outlines an initial study done to determine whether variable camber provided better performance than a mechanically actuated flap when added to a wing. The authors designed a wing using piezoelectric wafers on the skin of the wing and compared it to a wing with a mechanical flap. Plots comparing the lift coefficient history and lift to drag ratio for both wings are shown in Figure 2-9. It must be noted that these tests were not completed during an unsteady perching maneuver and unsteady experiments may yield much different results but for the steady case, the performance of the variable camber wing was better than the mechanical flap, and this provides a nice guideline by which to explore the subject area further.

One final work that provides insight into trying to understand the flow characteristics of high angle of attack maneuvers is by Pitt Ford and Babinsky [16].The paper investigates fitting a potential flow model to data obtained from an impulsively started high angle of attack maneuver and the authors state that the model works best without the addition of bound circulation because they argue that lift is caused by non-circulatory forces and the formation of a leading edge vortex and not by bound circulation. The argument is addressed further in a future section of this thesis to incorporate pitching motions where slightly different kinematics are implemented and could affect the relative importance of bound circulation.

CHAPTER 4

EXPERIMENTAL SETUP

As mentioned in the Introduction both the UD-LSWT and the AFRL-HFWT are used to complete the experimental testing for this thesis. The impulsively started hold motion tests are completed by Granlund and Altman in the AFRL-HWFT. This water tunnel has a rectangular test section of 46 cm wide by 61 cm high and 300 cm long with a velocity range of 3-45 cm/s. The tunnel is encased on three sides but has a free, open top surface. The turbulence intensity in the test section is estimated to be about 0.4% when the freestream velocity is towards the upper limit of 30-45 cm/s. To enable the motion of an aerodynamic model in the tunnel a three degree of freedom oscillation rig is mounted above the test section. Figure 3-1 shows the AFRL-HFWT test section and the above mounted oscillation rig. More detail about this tunnel is found in papers [5] and [6] by Granlund et. al.

Figure 3-1 shows the AFRL-HWFT test section with an oscillation rig mounted above.

The UD-LSWT is made by the Dart Company and has a 16:1 contraction ratio. This

Eiffel type wind tunnel is powered by a Hartzell Fan with a 60 HP motor. The test section is 30 inches by 30 inches and has a length of 90 inches. The maximum achievable tunnel velocity is

120 ft/s. There are 6 anti-turbulence screens on the tunnel inlet yielding turbulence intensity less than 0.1% as measured by hot-wire anemometer. A photo of the wind tunnel can be seen in

Figure 3-2.

Figure 3-2 - The University of Dayton Wind Tunnel

With the need to keep unsteady wind tunnel blockage at a minimum, the ideal size for a tunnel model is no greater than 4 inches in chord and 12 inches in semi span (or approximately

5.3% area blockage ratio). Following the NATO RTO AVT 202 test case guidelines a plate with a

4 inch chord and 8 inch semi span (AR 4) is chosen because the tunnel blockage is only 4.8% when the model is at 45 degrees relative to the free stream. A quarter inch thick piece of aluminum (which yields a th/c = 0.08) is chosen for the design as it would be able to withstand the loads applied from undergoing such a violent and rapid pitching maneuver (the entire

21 maneuver takes less than 0.1 seconds in air under the conditions tested). A photograph of one of the wind tunnel models in the tunnel test section is shown in Figure 3-3.

Figure 3-3 shows one of the flat plate models in the wind tunnel to provide a physical context for the size and location of the wings during testing.

Two plates are made to the above specifications, one with round leading and trailing edges and one with square leading and trailing edges to determine sensitivity of the measured forces to edge geometry. An SD7003 airfoil is implemented with the same planform dimensions as the flat plate models. A diagram of the wing profile section of each of the wings is shown in

Figure 3-4.

Figure 3-4 shows the wing profile section of each wing used for wind tunnel.

Tests are performed on the SD7003 wing to compare the force histories with the other plates to determine the importance of profile shape, camber, etc. in rapidly pitched wings. This wing is also used to study the unsteady pressure distribution over the top surface of the wing during a pitching maneuver. To measure the pressure eight XCQ-093-5D 5 psi differential Kulite

Semiconductor Pressure Transducers with a maximum resolution of 0.005 psi are placed along the wing chord in accordance with standard practice for interference/stagger distances. These transducers can be seen embedded in the wing in Figure 3-5. The signal number of each transducer and their respective location as a function of percent chord is shown in Table 3-1. The transducers are not collinear in the streamwise direction which may introduce some uncertainty with respect to spatial considerations of three-dimensionality and spanwise effects. It was, however, thought to be more important to organize the transducers in this way to minimize mutual interference effects since that is considered a greater concern than the spanwise effects.

Figure 3-5 shows an AR 4 semi-span wing with an SD7003 airfoil. Embedded in the wing are 8 Kulite pressure transducers for measuring unsteady pressures during pitching maneuvers.

Percent from Leading Edge 0 5 10 15 20 40 60 70 Transducer Serial Number S 159 S 508 S 160 S 408 S 405 S 404 S 407 S 406

Table 3-1 lists the serial number of each pressure transducer used in the SD7003 wing and also the distance of each transducer as a percentage from the leading edge.

To control the motion of the wing, the wing is connected at the leading edge to a Griffin

Motion Rotary Stage controlled by a Galil CDS-3310 Ethernet controller. This controller provides the ability to perform complex motions and through the use of encoders allows for precise tracking of the prescribed motion. This rotary controller also has the ability to define an absolute position. Any relative location can be reached by defining a distance from the absolute position. This feature makes it straightforward to program in a simple pitch ramp motion. It should also be noted that this controller has an accuracy of 5 arc seconds. A single degree change in position is defined as 40 arc seconds thus the accuracy of the controller is an eighth of a degree. The speed of the motion can be varied up to 50000 counts per second. This accommodates the rapid motions and differing pitch rates desired in the present study as testing is completed at 47000 counts per second. A photograph of the Galil CDS-3310 Ethernet controller and Griffin Motion Rotary Stage are shown in Figure 3-6.

Figure 3-6 shows (left) Galil CDS-3310 Ethernet controller; (right) Griffin Motion Rotary Stage

To measure the forces and moments on the wing an ATI Gamma F/T sensor is installed under the rotary stage. For each run the forces are zeroed to eliminate the force applied by the rotary stage itself. A list of the maximum force and torque that can be applied to the sensor along with the maximum precision of the sensor is shown in Table 3-2, and a picture of the ATI

Gamma sensor can be seen in Figure 3-7. It should also be noted that this sensor has a frequency response of 1800 Hz which is well within the response required for the present tests. The test

24 conditions used are a direct result of the compromise between the force transducer’s sensitivity and the rotary stage’s maximum rotational rate. Initial tare tests with the wind tunnel at zero velocity are taken before and after each set of tests so the effect of inertia forces could be removed from the total measured results. The Eldredge Smoothing Function [5] is used to smooth out any of the startup transients produced by the initial accelerations of the motion and is shown in Equation 3-1. Assuming a linear variation with time, these two tests are averaged and are then subtracted from the wind on tests.

Direction Max Force Max Torque Accuracy x ± 7.5 lb ± 25 in-lb 0.0004 lb y ± 7.5 lb ± 25 in-lb 0.0004 lb z ± 25 lb ± 25 in-lb 0.0008 lb Table 3-2 lists maximum loads and accuracy of those loads for the ATI Gamma F/T Transducer

Figure 3-7 shows an ATI Gamma force and torque sensor

( ) ( ) ( ) ( )

( ) [ ( ) ( ) ] 3-1 ( ) ( )

The force transducer is then connected to a SCXI-1520 8 Channel Universal Strain

Bridge Module in the National Instruments SCXI-1001 Chassis which is driven by a National

Instruments PCI-6259 M-series DAQ card. This system is capable of 3800 Hz across 16 channels allowing for the collection of 180 data points for a rotation that takes 0.1 second. The entire system is controlled by a LabView program that is used to acquire the data. A photograph of the setup for this test and its location within the wind tunnel is shown in Figure 3-8.

Semi span Model

Test Section Floor

Griffin Motion Systems RTS-DD 100 mm Rotary Stage

ATI Gamma Sensor

Figure 3-8 shows the complete test setup needed to complete a rapid pitching maneuver and measure pressure, forces and moments.

Uncertainty Analysis:

To determine the experimental confidence zone of each test, error bars are added to each run completed in the UD-LSWT. To determine this zone the experiments are run twenty times and the average is taken. After taking the average the standard deviation from the average is acquired. The standard experimental error is then calculated using Equation 1-2 and the confidence zone is determined as the magnitude of the error above and below the averaged experimental value.

(1-2) √

Showing every error bar for all 180 data points obtained during testing makes it hard to interpret the force histories. To reduce the number of bars on each plot, different intervals of error bars are selected and the largest error is selected to represent that group, where is equal to the fraction of error bars for a given plot. From the standard error the overall uncertainty as it propagates through various measurements and data reductions can be calculated. If an equation R, is used with n known independent variables and the standard error within those variables is 26 known, then the uncertainty can be calculated using Equation 1-3. To acquire a percentage uncertainty the calculated uncertainty is divided by the measured experimental value and multiplied by 100.

[∑ ( ( )) ] (1-3)

Applying Equation 1-3 to the measurements made for, density velocity, lift and drag force, and the force coefficients the uncertainty for each measurement is shown in Table 3-3.

Measurement Uncertainty Density 0.41% Velocity 1.93% Lift Force 5.37% Drag Force 6.98% Lift Coefficient 12.71% Drag Coefficient 15.44% Table 3-3 displays the uncertainties as they propagate from different measured quantities

CHAPTER 5

COMPUTATIONAL APPROACH

To study both the pitching and impulsive start motions and to help understand the sensitivity to including three dimensional effects when modeling these types of maneuvers the

DVM is used for computational studies. The Discrete Vortex Method developed by Hammer,

Altman, and Eastep is a low order code capable of calculating aerodynamic forces in unsteady flow for 2D airfoils [17]. The code is developed to solve the Laplace equations using the assumptions of potential flow theory.

The code uses finite vortices to create the shape of an airfoil and/or flat plate and the forces are determined at each vortex and its collocation point by using a slightly modified

Uhlman Method [18]. The reasons for using the modified Uhlman Method instead of the Bernoulli

Equation, etc., are that the equations representing the system contain no spatial derivatives, factor in vorton motion, added surface effects, incorporate added mass (the modification to the Uhlman method), and are linear for each independent variable (stagnation enthalpy, velocity, and vorticity) [19]. From this linearity the vorticity can easily be solved and then forces can be obtained

(as shown in the bulleted list) at little cost in computational time by the DVM.

 Vorticity is obtained directly from the Uhlman Equations because they are linear

 The circulation is then found from the vorticity

 The pressure difference is then determined at each vortex and its collocation point.

 Forces are found by integrating the pressures along the chord of the wing

The motivation for modifying the Uhlman method to incorporate added mass is that many different fluid media are used in testing and some of these media are much denser than their

28 counterparts. This increased density increases the absolute contribution of mass that needs to be moved around to accomplish the same maneuver. Therefore, when comparing across media added mass needs to be accounted for to accurately predict the relative contribution of the various forces measured in experimental testing.

While this code is an inviscid solver it has been validated in another work by Hammer,

Altman, Eastep to accurately predict the flowfield and forces of ostensibly viscous flows such as pitch ramp and hold motions [20]. In this work the authors provide parametric studies on a single set of kinematic parameters using different vortex strengths and sizes, different number of starting vortices, multiple different desingularization methods, and different separation angles. This sensitivity study is intended to show that upon selecting or tuning these parameters the code can accurately predict the nature of highly unsteady, highly viscous flows. It is also presented in this paper that the code is able to reproduce shear layer instability-like behavior that is previously only thought to be captured in experiments or higher fidelity simulation. Since [20] by Hammer et al. was written the authors have since updated their model for determining the point at which a vortex begins to shed from the LE, and currently use a model developed by Chabalko et al. [21]. In other works by Hammer, Altman, and Eastep results from execution of the code are compared to water tunnel tests which help validate the code for high angles of attack and rapid pitch ramp maneuvers similar in nature to those modeled in this paper [17, 20]. Figure 4-1 is an image taken from [20] and shows the flowfield produced by the DVM compared to a 45 degree impulsively started water tunnel test using dye injection for flow visualization completed by Ol. When comparing the two methods the DVM shows good agreement to the experiment by accurately predicting the shedding rate and formation of the LEV and TEV. There are also two shear layer instabilities produced in the experiment and while the locations are not identical in the DVM, the

DVM successfully reproduces similar instability-like behavior.

Figure 4-1 shows flowfield comparison of the DVM to a 45 degree impulsively started water tunnel test completed by Ol. The two show excellent agreement and similar shear layer instabilities. [20]

CHAPTER 6

RESULTS AND DISCUSSION

6.1 LINEAR PITCH RAMP MOTION

As mentioned earlier three main cases with reduced frequencies of 0.03, 0.045, 0.09 are studied to investigate the linear pitch ramp motion as outlined by the NATO RTO AVT 202 guidelines. The test case suggests if air is the media of choice, achieving a 0 to 45 degree rotation in 6 chords traveled should be pursued because it is still a relatively quick enough motion to ensure unsteady flow. Since the chord of the wing is limited to 4 inches only two parameters, velocity and pitch rate, are left to work with to achieve the reduced frequency range. A velocity of 21 feet per second and pitch rate of 650 degrees per second are chosen to acquire a k = 0.09 as they are within the capabilities of the instrumentation used. To achieve the slower reduced frequencies the velocity of the tests are simply doubled and then tripled, producing motions of 12 and 18 chords of convective travel. Changing the reduced frequency by increasing the velocity would clearly also change the Reynolds number for each case but as seen by Granlund et. al. in

[6] for these highly unsteady maneuvers reduced frequency plays a much more dominant role than Reynolds number. Table 5-1 shows the parameters used for testing a linear pitch ramp motion.

Chords Traveled Tunnel Velocity (ft/s) Pitch Rate (deg/s)Reduced FrequencyReynolds Number 6 21 650 0.09 45,000 12 42 650 0.045 90,000 18 64 650 0.03 135,000 Table 5-1 shows the range of parameters used to do analysis on a 0 to 45 degree pitch ramp motion.

As flow visualization is not acquired in the wind tunnel, the only visualization available came from the DVM. To understand the nature of each of these three cases, the runs are first completed by the DVM and compared amongst each other. Figure 5-1 shows the flowfield comparison for each of the three cases. Evaluating the three cases against one another it can be discerned that while each of the cases performs the same type of motion and fundamental flow features are seen in all three, the flowfield evolution is quite different for each of the three cases.

The highest reduced frequency case of 0.09 shows the least temporally evolved flowfield. A full

LEV is formed and is beginning to shed while the TEV is beginning to form as the motion is completed. In the 12 chords traveled case where the motion is half as rapid, a full LEV is formed, and then a full TEV is formed. The upstream propagation of this TEV forces the initial LEV vortex off the plate and the LEV is eventually convected downstream. Once this convection occurs another LEV begins to form as the motion is completed. The 18 chords traveled case is proportionally slower than the 12 chords traveled case (approaching a more quasi-steady state).

Unlike in the 6 chords traveled case (but similar to the 12 chords traveled case), the motion is long enough to allow for both formation and shedding of both LEVs and TEVs. 2 LEVs and 2

TEVs form and shed and another LEV is forming before the 18 chords traveled motion is completed. It is also apparent from the figure that as the reduced frequency is increased the LEV and TEV have increased strength as evidenced by the darkening of the blue and red in the vorticity contours, when going from 18 chords traveled to 6 chords traveled.

Figure 5-1 shows that as the reduced frequency of the same maneuver is increased the same fundamental flow features occur but they will evolve differently.

In an attempt to compare the flow topology resulting from these three motions more closely, Figure 5-2 is created so the flowfields can be compared at similar angles of attack. As can be observed in the figure, separation does not occur until at least the 25 degree location when the trailing edge wake deforms (well past the angle of attack this would occur in steady testing, similar to [10] by Hart). The 6 chords traveled case is a more inertially dominated test condition than the other two cases. On the other hand, the 18 chords traveled is more convectively dominated shedding multiple vortices and inducing separated flow closer to the steady range.

Unlike in the 6 chords traveled case (but similar to the 18 chords traveled case), the motion of the

12 chords traveled run is long enough to allow for both formation and shedding of both LEVs and

TEVs. Unlike in the 18 chords traveled case (but similar to the 6 chords traveled case), the trailing edge wake deforms well past the typical separation point in a steady flow for the 12 chords traveled case. From these two observations it can be deduced that the 12 chords traveled case with a reduced frequency of 0.045 is more convectively dominated but begins to show hints of inertial effects. There seems to be a phase shift between the flowfield developments of the

33 three cases in Figure 23. The 40 degree image for the 6 chords traveled case is most comparable to the 25 degree image in the 12 chords traveled run and 20 degree image in the 18 chords traveled case. This demonstrates that the flowfield changes with changing reduced frequency as shown in [5] by Granlund.

Figure 5-2 shows that the 6 chords traveled case is more inertially dominated, and the 12 and 18 chords traveled cases are more convectively dominated.

Wind tunnel tests using the same parameters are completed to compare with the DVM.

To complete the tests the wind tunnel velocity is set, and then a single test is repeated 20 times and averaged. To better control the initial transients from the startup of the motion, Eldredge smoothing was applied up to the 7.5 degree mark in the wind tunnel data. All three initial cases are completed in the wind tunnel using the flat plate with rounded edges and compared with the

DVM. To determine functional dependence upon wing profile cross-sectional shape, the fastest case of reduced frequency 0.09 was also run using the flat plate with square edges and the wing with an SD7003 airfoil.

Investigation of all cases compared against one another:

After studying the flow field properties from the DVM, the force histories are acquired and compared between the three cases. Lift and Drag coefficient histories with each of the three

34 reduced frequency cases can be seen below for both the DVM and rounded edge flat plate wind tunnel tests. Figure 5-3 compares the lift coefficient history produced by the DVM for each of three reduced frequency cases. The highest lift peak is seen at the highest reduced frequency. It is also noted that as the reduced frequency is decreased the lift peak shifts left approaching a more quasi-steady lift value although the Reynolds number is increasing as the curves shift left. This phenomenon which is also seen in Granlund et. al. [6] is believed to occur because reduced frequency is believed to play a more dominant role in the evolution of the flow during unsteady motions than Reynolds number.

Figure 5-3 shows that as the reduced frequency is decreased the lift peak is obtained at a lower angle of attack.

In a similar respect Figure 5-4 compares the lift coefficient history recorded in the wind tunnel for each reduced frequency studied. Comparable to Figure 5-3, it can be seen in the plot that again the largest initial lift peak is seen in the highest reduced frequency case. It is also observed that CLmax moves left as the reduced frequency decreases, as also seen in Figure 5-3.

Figure 5-4 shows that as with the DVM, as the reduced frequency is decreased the lift peak occur at a lower angle of attack, this time in the wind tunnel results. σ = 0.25

When comparing the physical evolution of the two lift coefficient plots the trends seem to match more closely for the higher more inertially dominated reduced frequency than in the two slower runs. A similar feature is seen in Visbal [9] where for a faster pitch rate case the tip vortices have less time to build up strength and subsequently affect the flowfield similarly to slower pitch rates. Hence the reason the DVM matches the wind tunnel better at the higher reduced frequency is because 3D effects are less prominent in this case since the motion is more rapid and the tip vortices have less time to disturb the flowfield.

In reviewing the drag coefficient data from the DVM in Figure 5-5, before about 20 degrees angle of attack each of the three cases have a quadratic nature. Upon reaching about 20 degrees the two lower reduced frequency cases remain roughly quadratic as would be expected in a steady flow with the additional feature of small peaks caused by the creation of vortices.

Although the faster reduced frequency case has a rapid increase in drag thought to be caused by inertial influence. For this case once the LEV begins to shed off the plate a small drop in the drag coefficient is seen but then it begins to rise again before the motion is completed as the TEV

36 begins to form. It should also be noted that as the reduced frequency is decreased the drag coefficient approaches a more steady drag profile as expected because by decreasing the reduced frequency the flow approaches a more quasi-steady state.

Figure 5-5 shows as the reduced frequency is decreased the drag decreases approaching a steady drag profile.

In a similar fashion to Figure 5-5, the drag coefficient history is plotted for the three pitch cases completed in the wind tunnel and is shown in Figure 5-6. With a similar result to what is produced by the DVM, it is seen that each of the cases have a quadratic nature. What is distinctly different between the two figures is that the effect of the primary vortices is less pronounced in the wind tunnel data. It is again believed that the introduction of the spanwise flow in the wind tunnel is affecting the development of the LEV and TEV causing them to be less distinguishable than in 2D.

Figure 5-6 shows that all three reduced frequency cases have a quadratic nature and as reduced frequency decreases so does the magnitude of the drag coefficient. σ =0.25

Investigation of the more inertially dominated 6 chords traveled case:

As the 6 chords traveled case was initially run in the DVM before wind tunnel testing had occurred it was of interest to compare both the force history and flow visualization produced in the DVM before comparing with the wind tunnel testing. Figure 5-7 shows this comparison with some very revealing results. During the beginning of the motion before separation has occurred, the lift curve slope is linear and the drag profile is quadratic. This type of behavior resembles that of an airfoil under steady conditions. Thus, while the motion is perceived as more inertially dominated at this reduced frequency, there are still traces of a convective quasi-steady motion.

After leading edge separation has occurred, where there is a discontinuity in the force history, the lift curve remains relatively linear as the LEV builds up strength (as seen by the vorticity contour snapshots for the DVM flow visualization) and size until about 3 chords traveled where the lift coefficient reaches its peak. The LEV does not stop growing at 3 chords traveled so there is likely another reason for the reduction in lift coefficient.

Figure 5-7 shows how the deformation of the trailing wake seen from the vorticity contours appears to correspond to maximum lift and subsequent lift loss through the progression of the flow field.

It is also observed in Figure 5-7 that at around the 3 chords traveled point the trailing edge wake starts to deform forced by the large LEV which is causing flow separation. At this point the lift peaks and indeed begins to decline at a very swift rate. This can be interpreted as a violation of the analytical Kutta condition which would result in a release of bound circulation, and provide an expected reduction of lift. This begs the question of how much lift is actually contained in the LEV, how much lift from the super circulatory effects of the motion itself (which were previously thought to be the dominant factors) and how much is due to bound circulation.

Pitt-Ford et. al. [16] argues that in an impulsively started motion using his potential flow model, the dominant production of lift comes from the LEV and bound circulation can be ignored. Within the model investigated in [16] the authors imposed a Kutta condition at the trailing edge, which by Kelvin’s Theorem results in a total net change in circulation of zero meaning that the force must be coming from the presence of a leading edge vortex. In the present

39 research an analytical Kutta condition is adhered to as long as the flow has not separated where the trailing edge wake is still attached, but once the flow becomes separated Kelvin’s condition no longer applies exclusively to the bound circulation on the plate. Here, it is understood that once flow separation occurs the analytical Kutta condition is broken. During this time in the flow a rather large reduction in lift (two-fifths of the entire lift) is seen, and some of this loss could potentially be caused by a loss of bound circulation over the wing once the Kutta condition is broken. While these two arguments are in opposition neither is incorrect based on the analyses performed. Figure 5-8 shows a breakdown of the lift coefficient for the 6 chords traveled case run in the DVM (which has not been smoothed or corrected for aspect ratio). When separating out the different contributions to the lift coefficient the lift due to shed vorticity constantly rises until the

LEV is shed from the plate. Although, the total lift starts to decline before this occurs. This must be due to the bound vorticity contribution. The bound vorticity contribution of the lift coefficient has a linear increase until the first vortices are shed from the leading edge, after this a linear decrease in the lift coefficient is observed until it abruptly drops off and goes to zero. One possible explanation for the first initial linear decrease is that these initial shed vortices are creating a change in the pressure profile on the wing thus changing the bound vorticity and its contribution to lift. One possible explanation for the large drop in the bound vorticity lift could be the result of breaking an analytical Kutta Condition in the DVM when the deformation of the trailing edge wake occurs. This deformation causes the formation of the TEV vortex and it can be seen from the flowfield images that as the TEV rolls up on the plate a larger magnitude of opposite sign vorticity appears on the plate causing the reduction. During this drop in lift there is a plateau in the force until it finally drops to zero, this plateau is believed to be from the TEV rolling up onto the plate causing a small instability in the code. Thus, the method would suggest that without modeling bound circulation in a pitching case, where the plate starts at a pre- separation angle of attack, less total lift would be seen during the motion until the TEV is formed where the bound vorticity begins to lose its effect on the plate. Being that these results are

40 produced by the DVM and have not been validated by experiment or higher order CFD, it is unclear of their accuracy, but they present an interesting opportunity for further investigation of the unsteady flow physics in these types of motions.

Figure 5-8 shows that a decrease in the lift due to bound vorticity does occur once the trailing edge wake is deformed for the 6 chords traveled pitching case.

Figure 5-9 compares the DVM results to the lift coefficient data acquired in the wind tunnel using the rounded edge flat plate. For this run of the DVM and subsequent runs when compared with 3D experimental data, the force data produced by the DVM will be corrected for aspect ratio by using Prandtl’s steady lifting line theory. As these maneuvers are not steady, it is understood that this approximation is not absolutely correct. It is, however, deemed reasonable since two of the motions are essentially quasi-steady and the other motion is on the low end of being inertially dominated. The two lift coefficient force histories agree well during the initial motion where they are both quasi-linear until CLmax is reached. For both cases once this maximum point is reached both histories agree well in general form albeit with a magnitude shift between the two curves. Where the curves differ is the location and magnitude of the CLmax. Back in Figure

2- 6 it was noted that fundamental flow differences are observed when comparing a 2D versus 3D

41 simulation due to the addition of tip vortices and spanwise flow created in the 3D simulation.

Since the flow was not affected by tip vortices and spanwise flow in the 2D simulation it was determined that the LEV is more stable as it grows in the 2D case of Figure 2-6. The difference in magnitude seen in Figure 5-8 could then be attributed to spanwise flow created by the wing tip vortices rolling up on the plate interfering with the stability of the LEV, and inducing flow separation earlier than in the 2D scenario.

Figure 5-10 which shows the drag coefficient history for both cases also notes similar trends. While the magnitudes are slightly different during the pre-stalled region of the flow both the wind tunnel data and DVM have a roughly quadratic nature although they begin to deviate in the post-stall region. By the end of the motion both obtain similar magnitudes. Without flowfield data to support the assertion it is believed that these differences may again be attributed to spanwise flow effects which could be affecting the formation and shedding of the LEV. Another difference which cannot be easily extracted from the plot (due to scaling) is the magnitude of the

42 initial drag coefficient. The DVM which is modeled as an infinitely thin plate has almost no initial drag. The drag coefficient seen in the wind tunnel though, which has a thick rounded leading edge is an order of magnitude higher.

A Blasius laminar skin friction coefficient estimate yields an initial drag coefficient on the order of 10-3 which is on the same order of magnitude as the DVM. The larger drag coefficient magnitude obtained from the wind tunnel which is of the order 10-2. This could be associated with the larger thickness to chord ratio of 8% and the blunt leading edge. Another possibility could be that a magnitude of 10-2 is minimum precision of a force measurement when using the ATI Gamma sensor.

Finally in comparing the lift force histories from all three different plate shapes (flat edges, rounded edges, and SD7003 airfoil) to the DVM (infinitely thin flat plate) in Figure 5-11, it is noticed that little difference is seen between the two flat plates themselves as both seem to

43 follow a similar pattern. As no significant difference is noted between the two plates it is believed that either no difference occurs in the force or the differences are within the measurement uncertainty. The square edge plate just like the rounded edge plate closely follows the DVM until

CLmax is reached where the rounded edge plate and the square edge plate under predict the magnitude of the force obtained from the 2D DVM. This phenomenon can again be attributed to spanwise flow interfering with the forming and shedding of the LEV on the 3D wing. A larger variation is seen between the SD7003 wing and the other two 3D flat plates. A greater zero lift value is obtained by SD7003 presumably from the camber of the airfoil and a larger CLmax is also achieved. The pre-stall lift curve slope is very similar to the other two plates it is just shifted to the left by the camber. When comparing the SD7003 wing to the DVM pre-stall agreement is seen to be reasonable. Although it is believed that 3D effects are influencing the flow after stall has begun the rate at which the slope of the lift curve decreases is more rapid than the other three cases. With no flow visualization it is difficult to speculate whether the flowfield is being profoundly influenced by wing profile section but it is inferred nonetheless that no relevant influence occurs because no associated changes in the force histories are observed.

Using the SD7003 wing which includes the Kulite pressure transducers along the chord, upper surface pressure data is recorded for the six chords traveled case and compared with the

DVM. Figure 5-12 shows this comparison at 0, 10, 15, and 45 degrees angle of attack, up to 70% chord where the last transducer is located. When comparing the two at the low un-stalled angles of attack it can be noted that they both follow a very similar trend which supports the results in

Figure 5-10, demonstrating good force agreement pre-stall. The 45 degree case does not agree as well. When comparing the pressure profiles it can be seen that higher pressures are seen towards the extremities of the chord of the plate. Lower pressures are seen in the middle of the plate for the wind tunnel data where the DVM shows high pressure coefficients at the front of the plate.

Then a slow decrease in pressure occurs along the remainder of the chord. It is possible that spanwise flow is affecting the flow topology in the experiment causing it to have a different pressure profile (subsequently affecting forces) by influencing the LEV characteristics. This

45 could explain the substantial drop in pressure seen at the 40% chord location in the wind tunnel data and not in the DVM. When studying the flow topology produced by the DVM at 45 degrees angle of attack, also shown in Figure 5-11, it can be seen that the large suction peak corresponds to the same location on the plate as the LEV. In the wind tunnel tip effects and spanwise flow could be affecting the formation of the LEV and TEV to the point of forcing them to propagate downstream. This could be creating the large rise in the pressure seen at the 70% chord in the wind tunnel and not in DVM although it is ambiguous in the absence of experimental flow visualization.

Investigation of the more convectively dominated chords traveled cases:

As with the 6 chords traveled case, both flow visualization and force histories are obtained by the DVM for the 12 chords traveled case. They are plotted in Figure 5-13 as a means to study how the forces are affected by the evolution of the flowfield. It can be extracted from the plot that a linear pre-stall lift curve slope is produced similar to the 6 chords traveled case. Then in the post-stall region once the trailing edge wake begins to deform a large loss in lift is seen. In

46 contrast to the 6 chords traveled case the force histories and flowfield evolution are more convectively dominated processes. Peaks and valleys are created in the force histories that correspond to the establishment of a Von Karman shedding cycle.

Figure 5-13 shows that the maximum lift occurs at the point where the trailing edge wake begins to deform and a periodic shedding cycle begins.

A comparison of the lift coefficient history from the DVM and wind tunnel for the 12 chords traveled case can be seen in Figure 5-14. At first observation it seems that both follow the same evolution with only minor differences. Upon a more detailed analysis this is true in the pre- stalled region where both tests have a quasi-linear lift curve of similar slope, but a major difference is seen in the post-stall region. At approximately the 8 chords traveled location the

DVM produces a local lift peak that is not seen in the 3D wind tunnel force history. When examining the flowfield produced by the DVM at this temporal location the peak corresponds to the formation and shedding of the first TEV. This difference could be due to tip effects forcing the TEV to convect off the plate at earlier time/lower strength than in the 2D DVM in the absence of three dimensional effects.

Force histories and flow visualization are obtained by the DVM and can be seen in Figure

5-15 for the 18 chords traveled case in a similar fashion to the previous two cases. Much like the

12 chords traveled case a shedding cycle occurs during the motion and the first lift peak is reached just before the trailing edge wake begins to deform. Also similar to the 12 chords traveled case the drag coefficient behavior is relatively quadratic with minor fluctuations that correspond to the formation and shedding of vortices.

The lift coefficient history results of the DVM and wind tunnel can be seen in Figure 5-

16. The initial lift curve slopes match reasonably well until leading edge separation is observed in the DVM. At this point the DVM shows an increase with a shallower gradient than the wind tunnel data. These gradients occur until a CLmax is reached and a TEV begins to form. At this point the DVM forms a periodic shedding cycle for the remainder of the maneuver. The wind tunnel data, however, shows that once the maximum peak lift is reached the force drops

(comparable to the DVM) but then levels out and experiences smaller magnitude oscillations. The oscillations occur at the same temporal phase locations as the DVM and have a comparable

Strouhal number of 0.212 and 0.209. Of the three test cases the 18 chords traveled has the slowest relative rotation and again when comparing with Visbal [9] the presence of the tip vortices (and any associated spanwise flow induced instabilities) are most prevalent at the slower rotations because of the larger time the tip vortices have to strengthen and affect the flowfield by causing the primary vortices to become unstable. These 3D features are thought to be damping the relative

49 force magnitudes because less prominent vortices are being created when compared to the 2D

DVM. Similar results were also observed in Granlund et al [5] on low Reynolds number, low AR flat plates at high angle of attack experiments completed in the AFRL-HFWT. It also must be noted here that the validation of results for the 12 and 18 chords traveled cases which are more convectively dominated is a more complicated process because any perturbation of the flowfield has enough residence time to affect the total evolution of the flow.

6.2 IMPULSIVELY STARTED HOLD MOTION

Two main Impulsive Start motions were investigated. In both cases a flat plate is placed at 45 degrees and the velocity is ramped from zero to the maximum velocity in half a chord traveled. The difference between the two cases analyzed is a change in Reynolds number. The first case studied has a Reynolds number of 10,000 and is increased to 20,000 for the second case.

As mentioned in the Introduction these motions were completed experimentally in the AFRL-

HFWT and compared with the DVM. PIV images are provided by Granlund/Altman for the

Reynolds number of 10,000, and Figure 5-17 shows Granlund’s/Altman’s PIV along with vorticity data acquired in the DVM for both cases. No PIV was obtained for the Re=20,000 case.

The three cases have reasonably good flowfield agreement until the 3.5 chords traveled mark where the PIV starts to deviate from the two DVM runs. Although difficult to discern from the figure due to size, when comparing the three plots at 3 chords traveled, shear layer instabilities are beginning to occur in the PIV resolved flowfield causing the shear layer to change shape and most likely influencing the flowfield.

This is not seen in the 2D DVM plots so it is believed that these instabilities are being induced from 3D spanwise flow effects in the water tunnel. When comparing the two DVM cases to one another very similar agreement occurs at similar chords traveled distances/times. The major difference that is seen between the two DVM runs is the strength of the shed vortices in the flowfield. Although difficult to discern in the figure (due to scale) the vortex strength is larger for the Re=10,000 case as denoted by the darker shades in some of the individual vortices. This is also seen quantitatively when comparing the maximum circulation at each chords traveled location. For instance at the 2 chords traveled location the maximum circulation magnitude seen

in the LEV at Re=10,000 is -0.00131 where it is only -0.000873 in the Re=20,000 case.

Figure 5-18 compares the lift coefficient histories of the two impulsive start cases run using both the DVM and water tunnel data. Throughout the motion all cases exhibit similar trends. An initial ramp in lift coefficient is seen for all cases while the velocity is increasing to its maximum. When comparing between the two methods a phase shift and magnitude difference is seen in the initial ramp up due to different Eldredge smoothing function constants. Once the run reaches its velocity plateau the lift coefficient begins to decrease until an increase occurs. When comparing back to the flow visualization this seems to correspond to the formation and shedding of a TEV. Similar results were seen by Beckwith [14]. The TEV appears to influence the water

52 tunnel data much more than in the DVM. When comparing the flow topology in these two cases at roughly the same convective time (in Figure 5-17) shear layer instabilities are present in the water tunnel images that are not seen in the DVM. These instabilities seem to be attracting the

LEV towards the plate creating more influence on surface pressure (and thus more force). The origins of these instabilities are unclear however they could be due to an increase in cross-stream momentum transfer from spanwise flow across the wing.

Decomposing Figure 5-18 into a comparison of the two DVM runs helps to emphasize the fundamental differences between the two cases. Figure 5-19 shows this comparison.

Examining the figure shows a very good agreement until CLmax is reached. Once reached the only real difference between these two cases is that the lower Reynolds number case has a larger lift coefficient until the second local peak is reached, and then similar values are reached. When comparing the flowfield vorticity plots above it is not fully understood why this difference in lift

53 is seen as both cases experience similar evolutions. Nevertheless it is believed to be due to the lower Reynolds number case operating nearer to an optimal Reynolds number where maximum lift is generated by the LEV. In Zhang and Schluter[22] for unsteady maneuvers there is a critical

Reynolds number that provides the best lift and drag performance. For tests below this critical

Reynolds number (Re=6,000), as the Reynolds number was increased an increase in lift was shown. Once this critical Reynolds number is reached all subsequent cases tested above this value showed a decrease in the overall lift. The authors state that they believe this optimal Reynolds number occurs in a region where the viscosity is sufficiently low enough not disturb the overall generation of the LEV but still sufficiently large enough to inhibit the generation of small-scale turbulence that would still disturb the coherence of the LEV as would be seen in an actual maneuver. The critical Reynolds number of these impulsive start cases cannot be fully determined without testing a larger range of Reynolds numbers but the critical Reynolds number is considered one possible explanation for the results seen here.

Figure 5-20 investigates the variations between the experimental and computational results for the Reynolds number 10,000 case. While both have a quasi-linear increase as the velocity is ramped up the results from the water tunnel show a steeper gradient and more linear trend than the DVM which has some buildup before going completely linear. Again, this difference is accounted for from the use of different Eldredge smoothing equation constants between the water tunnel and DVM. Once the maximum lift is reached in both cases the two seem to follow very similar trends and match well in magnitude. In both cases there is a decrease after CLmax until another local lift peak is seen. The main difference is in the second lift peak magnitudes. When comparing the vorticity plots for these two cases at the 3 chords traveled location in Figure 5-17 it is noted that a slightly different TEV evolution is observed and that shear layer instabilities are present in the experiment and not in the DVM. Again, these differences may be due to spanwise flow induced by tip effects that are not modeled in the DVM.

6.3 VARIABLE CAMBER

In order to provide the maximum degree of control and the greatest number of options in approaching a perch, variable wing geometry becomes an appealing option. One way to affect the lift and drag performance of an airfoil is to either increase or decrease the camber. In a steady attached flow greater lift will be achieved by increasing camber. Little is known, however, as to what would happen in an unsteady flow where camber is varied, something birds do effortlessly when perching. The typical way birds vary their camber is by starting with little to no camber and increasing the camber while in a maneuver to help increase the extents of the flight envelope and allow them better control when landing. Figure 5-21 shows an example of a wing starting as a flat plate (zero camber) and linearly increasing camber through an angle of attack change.

Figure 5-21 demonstrates a pitching motion with variable camber.

One goal of this thesis is to investigate variable camber using the DVM. The capability to address variable camber problems on a stationary wing was programmed by Hammer previously.

Slight alterations are made to allow variable camber while completing an unsteady motion. As shown in previous sections of this thesis the DVM compares reasonably well to experiments on highly unsteady, high angle of attack motions. There is little experimental research available (to validate the DVM) for variable camber performed during an unsteady motion. The results in the following section are therefore provided with the caveat that the forces and flowfield produced by the DVM may not be an exact representation of an actual wing in a real maneuver but the results can begin to identify trends to help analyze whether variable camber could be beneficial during perching. Analogous to the two motions previously investigated in this thesis variable camber studies were performed on pitching and hold motions.

The first variable camber motion studied is a 0 to 45 degree linearly pitching motion. A baseline case of a flat plate at Reynolds number 30,000 and reduced frequency of 0.1 is used to complete the maneuver. Seven additional cases are completed where variable camber is included and the parameters used to study them are shown in Table 5-2. The parameters varied for these studies are:

 maximum camber location,

 maximum camber, and

 rate of camber

The maximum camber location is defined as the location along the chord where the camber is the greatest and was chosen at 35% and 50% chord because the maximum camber of an

SD7003 airfoil is at 35% chord and 50% allows for the study of circular arcs. The maximum camber is defined as the highest camber percentage achieved at the maximum camber location.

20% and 50% camber were chosen because these large changes in camber would provide distinct differences in the flowfield and force history data. Figure 5-22 shows a diagram of both the maximum camber location and maximum camber.

Figure 5-22 is a schematic of cambered wing

The rate of camber is defined as a constant linear increase in camber variation where the camber goes from the initial state to the maximum camber in a fraction of the time to pitch

(denoted as capital T). For instance a camber motion that is completed in half the time of the pitching motion would be defined as 0.5T. It should also be noted that the first 3 test runs shown in Table 5-2 are also completed for a 0 to 90 motion to compare how or if the change in camber affects the flow in the very low lift region above 45 degrees.

Maximum Maximum Camber Location Case Number Camber Rate Camber % (% Chord) 1 20 35 1T 2 20 35 0.5T 3 20 35 0.2T 4 20 50 1T 5 20 50 0.2T 6 50 35 1T 7 50 35 0.2T Table 5-2 lists the parameters used when completing a variable camber motion

Investigating the 0 to 90 degree motion which is most comparable to an actual perching maneuver yields insight into what dominant features are seen throughout a full motion. Figure 5-

23 shows the force histories for the 0 to 90 degree variable camber cases. An increase in lift curve slope is seen as camber is added pre-stall and a decrease in lift is noted post-stall. Of particular note, all three variable camber cases reach their maximum lift much earlier than the flat plate data. This could be seen as beneficial in perching because not only can a lower minimum lift be achieved but it can be achieved much earlier than a non-cambered case.

Figure 5-23 shows as camber is added the pre-stall lift curve slope becomes greater than the flat plate case and post-stall the lift decreases at a much greater rate than the non-camber case.

In comparing the drag coefficients for the same case in Figure 5-24 very similar phenomena occur. In the beginnings of the motion similar drag coefficients are acquired but as vortices begin to shed from the plates a temporal shift in the drag coefficient history is seen between 20 and 50 degrees. Higher drag is seen for the flat plate at each angle of attack when compared to the three camber cases. Even with this difference in the pre-stalled region, in the post-stall region all four histories reach similar magnitudes.

Figure 5-24 shows that a temporal shift is seen in the drag in the pre-stalled region but once stall occurs similar magnitudes are observed.

The previous plot shows promise for increasing the viable aerodynamic flight envelope while perching but the lift over drag was calculated to determine if this was true in a quantitative sense. The lift over drag ratio can be seen for the 0 to 90 degree case in Figure 5-25. Comparing the different runs in the first 15 degrees of motion it is seen that there is a range in L/D from about 5 to 20. This large range in L/D gives the flyer the ability to re-correct or alter its trajectory if the current path is not desirable and needs to be changed to successfully perch. Consequently, the more rapidly the camber is increased, the lower the L/D produced throughout the motion. This agrees well with previous assertions. This would reduce the amount of energy needed for the motion and allow for more a greater range of controllability of the system.

Figure 5-25 (left) shows the L/D for the entire 0 to 90 degree pitching motion. (Right) is an exploded view of the L/D to show that as camber is increased a lower L/D can be achieved.

A comparison of the flowfield for the 0 to 45 degree case for the different rates is seen in

Figure 5-26. The figure shows the flowfield of the first three variable camber cases compared with the baseline flat plate. When comparing across a single angle of attack it can be noticed that varying the camber effects the formation of the LEV by temporally delaying its growth. For instance when investigating the 35 degree image for the flat plate and trying to identify the best match cambered cases. For the first camber case the 40 degree image matches the most closely and for the second camber case the 45 degree image matches the most closely. Thus when comparing to the results from the flat plate a 5 and 10 degree temporal phase shift can be seen in the evolution of the flowfield for the first two camber cases. This delay in the flowfield should subsequently affect the force histories. When studying the last camber case due to the speed and violence of the camber change the evolution of the LEV actually seems similar to the flat plate except the that the LEV is pushed further down the plate causing the flow to separate at an earlier angle of attack and thus causing the formation of the TEV to occur earlier than is seen in either of the other three cases. Also there is a difference in the onset of boundary layer instabilities in the shear layers of both the LEV and TEV in this case when compared to the flat plate, 1T, and 0.5T cases.

A comparison of the force histories for these variable camber cases is seen in Figure 5-

27. As the camber is increased the pre-stall lift slope curve is also increased to values even higher than 2π. Lift curve slopes larger than 2π are regularly seen for inertially dominated pitching motions (Granlund in [5]). Post-stall each of the variable camber cases generates much less lift than the flat plate. From the temporal phase shift in the flowfield evolution of the LEV seen above in Figure 5-26 and the differences in force in Figure 5-27, it can be inferred that the camber is affecting flow separation and the formation of the LEV and thus affecting the lift.

Similarly it can be noted that as the rate of camber change is increased the overall lift coefficient at that temporal location is decreased most likely due to an effective decrease in angle of attack at the leading edge as a function of increase in camber. From these assertions it is easy to understand that this phenomenon would be good in a perching application. Increased lift is

62 achieved early in the motion where high lift is needed to reach the perch but once there, a reduction of lift would be beneficial as the vehicle attempts to slow down and land.

Figure 5-27 shows as camber is added the pre-stall lift curve slope becomes greater than the flat plate case and post-stall the lift is much less.

Figure 5-28 compares how differences in the maximum camber percentage affect the force histories. All variable camber cases have a greater pre-stall lift curve slope when compared to the flat plate in the region before vortex shedding occurs. In addition, as the percentage of maximum camber is increased (along with increasing camber rate) an increase in pre-stall lift slope is also seen. If a vehicle is at a much lower height than the perch and needs to correct its trajectory to a steeper one, the best way to achieve that trajectory would be to increase lift. This figure suggests that a good way to achieve an increase in lift would be to increase the maximum camber during the motion.

Figure 5-28 offers that as the maximum camber percentage is increased an increase in pre-stalled lift curve slope will occur.

The last comparison processed from the test cases seen in Figure 5-29 was to determine the effect of location of maximum camber along the chord. As the location of camber is shifted aft a larger pre-stall lift curve slope is seen. It can be inferred that this increase in lift is due to that fact that as the pitching motion is underway more of the wing is at a lower effective angle of attack than the flat plate. This keeps the flow attached longer. Thus, similar to increasing the camber rate and the percent camber, shifting the location of maximum camber further downstream along the chord allows for better pre-stall performance during a perching maneuver.

With a decrease in lift post-stall when compared with the flat the flight envelope for lift coefficient has been expanded. By adding this lower available lift to the flight envelope the ability for a softer landing on the perch is also achieved.

Figure 5-29 shows that as the location of maximum camber is moved aft on the airfoil a higher lift curve slope is reached from the lower effective angle of attack which keeps the flow attached.

In a manner similar to the pitch cases, variable camber was also included in 45 degree impulsively started hold motions. The case of Reynolds number 10,000 used in the previous impulsive start study was used as the baseline case in this study. Three variable camber cases were performed. The three cases chosen all have the same parameters except that the camber is changed for 1, 2, and 4 chords traveled. Figure 5-30 shows the vorticity contours produced by the

DVM for each of the 4 impulsive start maneuvers. When comparing at a single angle of attack and moving from left to right the change in camber seems to affect the formation of both the LEV and TEV by changing their shape and pushing them closer to the plate. For instance at 4 chords traveled in the flat plate the LEV has already begun to shed from the plate and a well formed

TEV is already present where in each of the camber cases the LEV is sitting close to the plate building strength while the trailing edge wake flow just begins to wrap up on the plate to form a

TEV. This effect is more pronounced as the camber rate is increased as it can be seen that at a temporal location of 4 chords traveled the .25T case has the least developed LEV and TEV.

Figure 5-31 shows the force history for these same cases compared in Figure 5-30. As previously noticed from Figure 5-30 the lift would be decreased in the variable camber cases early in the motion because the vortex formation process is being delayed by the variable camber.

What is not expected is that while the lift is decreased early in the motion, a greater CLmax is seen as the camber rate is increased. This is most likely due to the closer proximity to the plate and the slower temporal formation of the LEV providing greater time to grow the LEV circulation.

Therefore a very short hold maneuver would likely be beneficial to the end of the perching maneuver where a decrease in lift is desired. For a typical perching maneuver where the hold requires more time this motion is likely less advantageous because lift is increasingly added. One

66 place this type of technique might still be useful is immediately before perching where the increase in lift would allow for more flexibility during the motion. This could potentially allow for more controllability during landing.

Figure 5-31 shows that as the variable rate is increased a drop in the initial lift peak is seen although a higher CLmax is encountered because the camber has delayed the formation of the LEV.

CHAPTER 7

CONCLUSION

The linear pitch motion which is abstracted from a high angle of attack pull up motion seen during a perching maneuver is found to be a good first order approximation when studying perching. Investigations are completed to study this maneuver further to enhance the knowledge of the evolution of these motions. Pitching studies are completed at reduced frequencies of 0.03,

0.045 and 0.09 which range from convectively dominated to slightly inertially dominated flows.

For a more inertially dominated flow a larger initial lift peak is reached due to additional force created during the motion. As reduced frequency is decreased the lift peak occurs earlier in the force history evolution and the magnitude of the drag coefficient is shifted down. This shift occurs even though the Reynolds number is increased as the reduced frequency decreased. From steady assumptions it has been shown that as Reynolds number is increased the lift peak would shift to a later temporal location and the magnitude of the drag coefficient would increase. As this is not the case in the present results reduced frequency influences the force history more than

Reynolds number.

It was another goal of the pitching studies to determine if a 2D DVM code could accurately model the flowfield and force histories of an actual 3D wing undergoing a rapid pitching motion so the computationally less expensive DVM could be used in conceptual modeling and design. When comparing data acquired by a 2D DVM with 3D wind tunnel data the

DVM had the ability to accurately predict all the flow features seen in an actual test except 3D instabilities. These instabilities are most likely caused by spanwise flow over the wing. While the

DVM could not accurately model this phenomenon because it is a 2D code it still recreated

68 comparable force histories. At the higher, slightly more inertially dominated reduced frequency of

0.09, the DVM matches the experiment much better than in the other two cases. It is believed a better match occurs because tip vortices and the inherent spanwise flow they create have less time to develop and strengthen during the higher reduced frequency runs. The DVM is less accurate compared with the experimental data in the slower reduced frequency cases. In the cases which are convectively dominated 3D effects become more prevalent because the relative rotation is slower allowing the tip vortices to become more developed and prominent in the flowfield. It is also noted that a more convectively dominated flow would be inherently more difficult to match results between any two experiments. This might be the case because the flowfield and force histories are heavily dependent on the formation and shedding of vortices that if only slightly perturbed alters the entire flow topology. In noting the above discrepancies when comparing the

DVM with experimental results it is still believed that the DVM is a powerful tool. While it cannot perfectly model the flow it provides practicable accuracy and could definitely be used as a first line model for pitching cases to determine whether a supposed scenario would achieve the desired performance needed for perching.

High angle of attack impulsively started hold motions are also investigated in this thesis and are abstracted from high angle of attack hold motions seen in perching maneuvers. Two tests at 45 degrees angle of attack are completed with Reynolds number of 10,000 and 20,000 in both the AFRL-HFWT and the DVM. When comparing vorticity contours for the three cases (no flow diagnostics are completed for the Re=20,000 water tunnel case) it is observed that both DVM cases follow nearly identical behavior except that the vortex strength is greater for the lower

Reynolds number case. When comparing the flowfield from DVM to the water tunnel very good agreement is seen until about 3 chords traveled where a TEV begins to form and shear layer instabilities begin to appear in the water tunnel images. It is believed that these instabilities are due to 3D tip effects inducing spanwise flow over the wing because these features are not seen in the DVM which has been previously seen to produce such features. Comparing only the two

DVM cases the lower Reynolds number case has a greater lift coefficient throughout the motion matching with the increased vortex strength well shown in the associated vorticity plots. When comparing the same case across the two cases it can be seen that there is a peak in the lift curve for both cases in the region where the shear layer instabilities occur and that this peak is larger in the 3D water tunnel data presumably due to the vortex being pushed closer to the plate by the instabilities. While the DVM was not able to model the flowfield or force histories perfectly it is again believed that the DVM does do a reasonable job on the impulsive start holds and could again be used a first order approximation.

Varying camber is an additional degree of freedom that could be used to affect the flowfield for a given set of kinematics. Previous to these studies, variable camber was thought to be beneficial while perching because birds have been observed to employ similar techniques but those assertions had yet to be studied. While not yet validated for this implementation, the DVM is used to try and understand the trends that would occur during variable camber motion. There are no known experimental results available so that provides additional incentive to try.

Additional pre-stall lift is created during the pitching motion by adding variable camber to the previously studied pitching motions. Post-stall the lift is decreased when compared to a flat plate.

During the high angle of attack hold motion it can be seen that the initial lift curve slope is decreased as the variable camber rate is increased. This continues until the LEV has completely formed where an increase in the overall lift is observed. This increase in lift at the end of the hold is not advantageous because a very low lift is desired although it does allow for an increase in the flight envelope which could provide better controllability post-stall. All other trends observed from the camber study seem to be positive for perching because camber seems to expand the available flight envelope of aerodynamic coefficients when compared to a fixed camber plate.

This allows the vehicle to reach needed lift and drag magnitudes it was previously unable to reach with just a flat plate wing. Thus, variable camber can be advantageous to perching and should be investigated further too fully determine its potential impact on an actual flight.

REFERENCES

[1] Couch, T., “Wings: A History of Aviation from Kites to the Space Age,” W.W Norton & Co., New York, New York, 2004.

[2] Whelan, D. A., “TTO Overview” DARPATech’99, 1999.

[3] Shyy, W. Lian, Y., Tang, J., Vieru, D., and Liu, H., Aerodynamics of Low Reynolds Number Flyers, Cambridge Aerospace Series, Cambridge University Press, 2008.

[4] Anders, J. B., “Biomimetic flow control, AIAA 2000-2543, Archive Set 752.

[5] Granlund, K., Ol, M., Garmann, D., Visbal, M., and Bernal, L., “Experiments and Computations on Abstractions of Perching,” AIAA 2010-4943, Applied Aerodynamics Conference, Chicago, 2010.

[6] Granlund, K., Ol, M., Bernal, L., “Flowfield Evolution vs. Lift Coefficient History for Rapidly-Pitching Low Aspect Ratio Plates.” AIAA 2011-3118, Theoretical Fluid Mechanics Conference, Honolulu, 2011.

[7] Ol, M., Altman, A., Eldredge, J., Garmann, D., and Lian, Y., “Résumé of the AIAA FDTC Low Reynolds Number Discussion Group’s Canonical Cases,” AIAA 2010-1085, Aerospace Sciences Meeting, Orlando, 2010.

[8] Baik, Y.S., Aono, H., Rausch, J., Bernal, L., Shyy, W., and Ol, M., “Experimental Study of a Rapidly Pitched Flat Plate at Low Reynolds Number,” AIAA 2010-4462, Fluid Dynamics Conference, Chicago, 2010.

[9] Visbal, M., “Flow Structure and Unsteady Loading Over a Pitching and Perching Low- Aspect-Ratio Wing,” AIAA 2012-3279, Fluid Dynamics Conference, New Orleans, 2012

[10] Hart, A., Ukeiley, L., “Leading Edge Vortex Development on a Pitching Flat Plate at Low Reynolds number,” AIAA 2012-3154, Fluid Dynamics Conference, New Orleans, 2012

[11] Lukens, J. M., Reich, G. W., Sanders, B., “Wing Mechanization Design and Analysis for a Perching Micro Air Vehicle,” AIAA 2008-1794, Structures, Structural Dynamics, and Materials Conference, Schaumburg, 2008.

[12] Reich, G., Eastep, F., Altman, A., and Albertani, R., “Transient Poststall Aerodynamic Modeling for Extreme Maneuvers in Micro Air Vehicles,” Journal of Aircraft, Vol. 48, No. 2, 2011.

[13] Hammer, P., Altman, A., and Eastep, F., “A Discrete Vortex Method Application to High Angle of Attack Maneuvers,” AIAA 2011-3007, Applied Aerodynamics Conference, Honolulu, 2011.

[14] Beckwith, R. M. H., Babinsky, H., “Impulsively Started Flat Plate Wing,” AIAA 2009-789, Aerospace Sciences Meeting, Orlando, 2009.

[15] Ohanian III, J. O., Karni, E. D., Olien, C. C., Gustafon, E. A., Kocherberger, K. B., Gelhausen, P. A., Brown, B. L., “Piezoelectric Composite Morphing Control Surfaces for Unmanned Aerial Vehicles,” SPIE Vol. 7981 79815K-12, 2011.

[16] Pitt Ford, C. W., Babinsky, H., “Lift and the Leading Edge Vortex,” AIAA 2012-0911, Aerospace Sciences Meeting, Nashville, 2012.

[17] Hammer, P., Altman, A., and Eastep, F., “A Discrete Vortex Method for Application to Low Reynolds Number Unsteady Aerodynamics,” AIAA 2010-4391, Applied Aerodynamics Conference, Chicago, 2010.

[18] Robertson, D., Joo, J., and Reich, G., “Vortex Particle Aerodynamic Modeling of Perching Maneuvers with Micro Air Vehicles,” AIAA 2010-2825, Structures, Structural Dynamics, and Materials Conference, Orlando, 2010.

[19] Uhlman, J., “An Integral Equation Formulation of the Equations of Motion of an Incompressible Fluid,” Naval Undersea Warfare Center Technical Report, 1992.

[20] Hammer, P., Altman, A., and Eastep, F., “Discrete Vortex Method Investigation of Canonical Pitch Ramp-Hold Case,” AIAA 2011-667, Aerospace Sciences Meeting, Orlando, 2011.

[21] Chabalko, C. C., Snyder, R. D., Beran, P. S., Parker, G. H., “The Physics of an Optimized Flapping Micro Air Vehicle,” AIAA 2009-801, Aerospace Sciences Meeting, Orlando, 2011.

[22] Zhang, X., Schluter, J. U., “Numerical study of the influence of the Reynolds-number on the lift created by a leading edge vortex,” Physics of Fluids 24, 065102, 2012.