Passively Compliant Membranes in Low Aspect Ratio Wings

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Title:
Passively Compliant Membranes in Low Aspect Ratio Wings
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1 online resource (88 p.)
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english
Creator:
Arce, Manuel A
Publisher:
University of Florida
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Gainesville, Fla.
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Thesis/Dissertation Information

Degree:
Master's ( M.S.)
Degree Grantor:
University of Florida
Degree Disciplines:
Aerospace Engineering, Mechanical and Aerospace Engineering
Committee Chair:
UKEILEY,LAWRENCE S
Committee Co-Chair:
IFJU,PETER G
Committee Members:
LIND JR,RICHARD C

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Subjects / Keywords:
batten-reinforced -- compliant -- fluid-structure -- mav -- membrane
Mechanical and Aerospace Engineering -- Dissertations, Academic -- UF
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Aerospace Engineering thesis, M.S.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

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Abstract:
The study of mammalian flight has led to the design of bio inspired micro air vehicles. These micro air vehicles utilize passively compliant membranes to help aid in their aerodynamic performance such as flight in unsteady wind conditions. While there has been previous investigations into membrane wings there is still much that is not fully understood of the coupling between the membrane and the flow. The present study examines the fluid structure interactions of an aspect ratio 2, batten reinforced, silicone rubber membrane wing. The membranes are configured to have a free trailing edge and are scalloped by approximately 25% of the chord length; membrane geometry is based off of previous research. To further understand the effects the membranes have on the surrounding flow-field, two different membrane models are tested. The two membrane models consisted of a one percent pre-tension membrane and a four percent pre-tension membrane. The fluid structure interactions are obtained through the use of synchronized time resolved particle image velocimetry and digital image correlation. These two systems measure the two dimensional flow-field and the three dimensional surface deformations respectively. When compared to a rigid flat plate the membrane wings shear layer remained closer to the membrane’s surface producing a smaller separation bubble and decrease in wake deficit. The results show the membrane’s motion ability to drive the flow to alter the wake behavior which is typically linked to higher aerodynamic efficiency. Additionally shown, the frequency of the membrane’s motion, which is a combination of a standing wave and traveling wave, is translated to the flow and can be altered by changing the pre-tension in the membrane.
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In the series University of Florida Digital Collections.
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Includes vita.
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Statement of Responsibility:
by Manuel A Arce.
Thesis:
Thesis (M.S.)--University of Florida, 2013.
Local:
Adviser: UKEILEY,LAWRENCE S.
Local:
Co-adviser: IFJU,PETER G.

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lcc - LD1780 2013
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UFE0046357:00001


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1 PASSIVELY COMPLIANT MEMBRANES IN LOW ASPECT RATIO WINGS By MANUEL ALEX ARCE A THESIS PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE UNIVERSITY OF FLORIDA 2013

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2 2013 Manuel Alex Arce

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3 To Dawn

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4 ACKNOWLEDGMENTS I would lik e to thank Dr. Lawrence Ukeiley for his support and guidance throughout my research. Many thanks t o my other c ommittee members, Dr. Peter Ifju and Dr Rick Lind, for reviewing my work and their valuable feedback. I would also like to thank all of my office mates for their respected inputs and daily discussions both in and out of the office. A s pecial t hanks goes to Amory Timpe for spending his limited time showing me the basics of his research Additional thanks to Yaakov Abudararm, for creating the membrane models used throughout this study. I would also like to thank the support provided by th e Air Force Office of Scientific Research under program manager Dr. Doug Smith, the Florida Center for Advanced Aero Propulsion and the Air Force A special thank you to my family, without their love and support I woul d not be where I am toda y, you guys are truly the best Finally I want to thank Natalie Andrietta, for her endless amount of support while putting up w ith the long nights and short weekends.

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5 TABLE OF CONTENTS page ACKNOWLEDGMENTS ................................ ................................ ................................ .. 4 LIST OF TABLES ................................ ................................ ................................ ............ 7 LIST OF FIGURES ................................ ................................ ................................ .......... 8 LIST OF ABBREVIATIONS ................................ ................................ ........................... 10 ABSTRACT ................................ ................................ ................................ ................... 11 CHAPTER 1 INTRODUCTION ................................ ................................ ................................ .... 13 Motivation ................................ ................................ ................................ ............... 13 Background ................................ ................................ ................................ ............. 14 Previous Investigations ................................ ................................ ..................... 14 Pred ecessor Investigations ................................ ................................ .............. 19 Current Investigations ................................ ................................ ............................. 21 2 FACILITIES AND EXPERIMENTAL SETUP ................................ ........................... 23 Facilities ................................ ................................ ................................ .................. 23 Aerodynamic Charac terization Facility ................................ ............................. 23 Engineering Laboratory Design Wind Tunnel ................................ ................... 24 Models ................................ ................................ ................................ .................... 24 Experimental Equipment ................................ ................................ ......................... 25 Partic le Image Velocimetry ................................ ................................ ............... 26 Digital Image Correlation ................................ ................................ .................. 27 Synchronization ................................ ................................ ................................ 28 Experimental Description ................................ ................................ ........................ 29 Sync hronized PIV and DIC ................................ ................................ ............... 29 Independent DIC ................................ ................................ .............................. 30 Post Processing ................................ ................................ ................................ ...... 31 PIV ................................ ................................ ................................ ............. 31 DIC and PIV ................................ ................................ ............................... 32 3 RESULTS AND DISCUSSION ................................ ................................ ............... 39 Flow Field Measurements ................................ ................................ ....................... 39 Membrane Surface Deflections ................................ ................................ ............... 43 Mean and Root Mean Square Deflections ................................ ........................ 44 Ef fects of Mounting Hardware ................................ ................................ .......... 45 Mean an d Root Mean Square Deflections A long the Mid Plane ....................... 46

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6 Power Spectral Density and Membrane Motion ................................ ............... 47 Wave Speed ................................ ................................ ................................ ..... 50 Fluid Structure I nteractions ................................ ................................ ..................... 52 4 SUMMARY AND FUTURE WORK ................................ ................................ ......... 75 Summary ................................ ................................ ................................ ................ 75 Future Investigation ................................ ................................ ................................ 77 APPENDIX A 2D PIV UNCERTAINTY ................................ ................................ .......................... 79 B VIBRATIONAL ANALYSIS ................................ ................................ ...................... 80 LIST O F REFERENCES ................................ ................................ ............................... 83 BIOGRAPHICAL SKETCH ................................ ................................ ............................ 88

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7 LIST OF TABLES Table page 2 1 ................................ ................................ ...................... 36 2 2 BR membrane model dimensions. ................................ ................................ ...... 36

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8 LIST OF FIGURES Figure page 1 1 Flexible membrane MAVs ................................ ................................ .................. 22 2 1 Low speed test facilities ................................ ................................ ...................... 33 2 2 Linear relation between temperature of creation and measured pre st r ain ........ 34 2 3 Measured pre strain within the membranes ................................ ....................... 34 2 4 Aspect ratio 2 membrane models and flat plate model ................................ ....... 35 2 5 Membrane wing nomenclature ................................ ................................ ........... 35 2 6 Statistical convergences for the 1 percent pre tension membrane model at 16 AoA ................................ ................................ ................................ .............. 36 2 7 Combined fields of view from PIV cameras ................................ ........................ 37 2 8 Digital inclinometer on top of model ................................ ................................ .... 37 2 9 Experimental set up. ................................ ................................ ........................... 38 2 10 Membrane model with center suppored hardware positioned within the ELD WT ................................ ................................ ................................ ...................... 38 3 1 Normalized mean U component of the flow field with streamlines for the different models ................................ ................................ ................................ 55 3 2 Normalized Urms contours for the different models ................................ ............ 56 3 3 Normalized RSS for the different model s ................................ ........................... 57 3 4 Normalized instantaneous vorticity for the 1 percent pre tension membrane at 20 AoA ................................ ................................ ................................ .......... 58 3 5 Normalized mean membrane deflections and normalized RMS deflections through a range of AoAs for the synchronized data ................................ ............ 59 3 6 Normalized mean membrane deflections and normalized RMS deflections through a range of AoAs for the Independent DIC data with outer supported models ................................ ................................ ................................ ................ 60 3 7 Normalized mean membrane deflections and normalized RMS deflections through a range of AoAs for the Independent DIC data with ce nter supported models. ................................ ................................ ................................ ............... 61

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9 3 8 an and RMS deflections vs. AoA ................. 62 3 9 Time averaged mean camber of middle membrane for the synchronized data. ................................ ................................ ................................ ................... 63 3 10 Time averaged mean camber of middle membrane for the independent DIC data ................................ ................................ ................................ .................... 63 3 11 Trailing edge PSD for each membrane ................................ .............................. 64 3 12 First dominate frequency vs. AoA for each membrane during synchronized testing. ................................ ................................ ................................ ................ 65 3 13 First dominate frequency vs. AoA for each membrane during independent DIC testing. ................................ ................................ ................................ ......... 66 3 14 Instantaneous trailing edge membrane surface def l ections for the 1 percent pre tension membrane model. ................................ ................................ ............ 67 3 15 Instantaneous center chord membrane surface deflections for the 1 percent pre tension membrane model ................................ ................................ ............. 68 3 16 PSD in the spatial domain ................................ ................................ .................. 69 3 17 Cross correlations between spatial locations for the 1 percent pre tension membrane at 8 AoA ................................ ................................ .......................... 70 3 18 Membrane oscillations for the 1 percent pre tension model at 12 AoA ............. 71 3 19 Middle cell average wave speed vs. AoA for both membrane models ................ 71 3 20 flow field for the 1 percent pre tension membrane at 8 AoA ............................. 72 3 21 PSD of both DIC and PIV for the 1 percent pre tension membrane model ......... 73 3 22 Modified Strouhal number vs. AoA ................................ ................................ ..... 74 B 1 Accelerometer attached to the back of mounting arm ................................ ........ 81 B 2 PSD of original mounting arm ................................ ................................ ............. 81 B 3 PSD of ELD WT ................................ ................................ ................................ 82 B 4 PSD of cantilever ed mounting arm ................................ ................................ ..... 82

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10 LIST OF ABBREVIATIONS ACF Aerodynamic Characterization Facility AoA(s) Angle of Attack(s) AR Aspect Ratio BR Batten Reinforced DFT Discrete Fourier Tr ansform DIC Digital Image Correlation ELD WT Engineering Laboratory Design Wind Tunnel FOV Field of View FS I Fluid Structure Interaction IA Interrogation Area LCO Limit Cycle Oscillation MAV(s) Micro Air Vehicle(s) PIV Particle Image Velocimetry PR Perimeter Reinforced PSD Power Spectral Density REEF Research and Engineering Education Facility RSS Reynolds Shear Stress RMS Root Mean Square St Strouhal N umber 1D One Dimensional 2D Two Dimensional 3D Three Dimensional

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11 Abstract of Thesis Presented to t he Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Master of Science PASSIVELY COMPLIANT MEM BRANES IN LOW ASPECT RATIO WING S By Manuel Alex Arce December 2013 Chair: Lawrence S. U keiley Major: Aerospace Engineering The study of m ammalian flight has led to the design of bio inspired micro air vehicles. These micro air vehicles utilize passively compliant membrane s to help aid in their aerodynamic performance such as flight in unsteady wind conditions While there ha s been previous investigation s into membrane wings there is still much that is not fully understood of the coupling between the membrane and the flow The present study examines the fluid structure interactions of an aspect ratio 2 batten reinforced silicone rubber membrane wing The membranes are configured to have a free trailing edge and are scalloped by approximately 25% of the chord length; membrane geometry is based off of previous research. To further underst and the effects the membranes have on the surrounding flow field t wo different membrane models are tested. The two membrane m odels consisted of a one percent pre tension membrane and a four percent pre tension membrane. The fluid structure interactions ar e obtain ed through the use of synchronized time resolved particle image velocimetry and digital image correlation. These two systems measure the two d imensional flow field and the three dimensional surface deformation s respectively When compare d to a rigid flat plat e the membrane wings shear layer remained closer to the membrane surface producing a smaller

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12 separation bubble and decrease in wake deficit T he re sults show the membrane s motion ability to drive the flow to alter the wake behavior which is typically linked to higher aerodynamic efficiency. A dditionally shown, the frequency of the membrane s motion, which is a combination of a standing wave and traveling wave is translated to the flow and can be altered by changing the pre t ension i n th e membrane.

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13 CHAPTER 1 INTRODUCTION Motivation The study of n atural fly er s has been conducted by numerous r esearchers to provide meaningful analysis into the unique kinematic and aerodynamic capabilities which they possess [ 1 ] [ 5 ] One key feature of several natural flyers involves the use of a flexible w ing consisting of a membrane. Mammals with membrane wings, such as bats operate in a low Reynolds Number regime ( ) based off of their wing chord length and fly at airspeed typically less than 10m/s [ 2 ] [ 3 ] [ 6 ] These compliant wing natural fly ers have a high degree of maneuverability and are able to fly in wind gust s on the order of their flight speed [ 4 ] [ 7 ] With flight conditions similar to Micro Air Vehicles (MAVs), MAV designers have look ed to mimic feature s of biological flyers in an attempt to improve their aerodynamic s [ 8 ] One objective of the study is to develop a better understand of how the membrane and flow interact. MAV s are classified as an aircraft with a wing sp an of 6 inches (15 cm) or less and tend s to op erate at airspeed s of 15 m/s or less [ 8 ] [ 9 ] With the advancement of technology MAV s are now relatively easy to deploy and can have endurance time s of 20 60 minutes depending on its application. Payload packages are small enough allowing sophisticated controls, visual imagery and/ or task specific sensor s to be mounted on them. While MAVs may seem tailored to military applications the civilian sector can also benefit from current advances such as aiding in the fol lowing: search and rescue, wild fire monitoring, and agricultural development [ 9 ] While MAVs have been in existence for the past few decades recent b io in spired MAVs started utilizing

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14 light weight flexible lifting surfaces in an effort to mimic biological flyers to help aid in their performance. One of the main challenges with MAV design is the significant drop in aerodynamic performance associated with flight in the low Reynolds number regime In low Reynolds number flight parameters such as adverse pressure gradient, surface roughness airfoil s leading edge shape and free stream turbulence intensity may cause the flow to separate at the airf oil s lea ding edge. D epending on if the flow transition s to a turbulent flow it may entrain enough high momentum fluid to reattach it self forming a separation bubble [ 10 ] typically a dding some unsteady features Unlike flight in a high Reynolds number flow f light in low Reynolds number first experiences a separation bubble at the leading edge where the bubble then grow s longer until it reaches the trailing edge [ 11 ] Ai rfoils with long separation bubbles change the pressure distribution yielding a significant drop in lift and an increase in drag [ 12 ] In the act of bubble burst ing meaning the free shear layer is no longer attached the wing may experience a undesirable change in pitching moment [ 12 ] This investigation will look at the interactions between the fluid and structure of low aspect ratio wings in a low Reynolds number flow A further under st anding of this process would benefit the MAV commu nity as well as other applications that incorporate the use of compliant membranes such as: sail boat s hang gliders and power kites [ 13 ] [ 15 ] Background Previous Investigations The University of Florida was one of the first to adopt a flexible membrane wing within their MAV design [ 16 ] Early investigation s b y Ifju et al [ 8 ] compared a MAV with a rigid wing to various MAVs with a batten reinforced membrane wing. While different

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15 batten configurations were examined results conclude d with the membrane MAV s requiring less user input to mainta in a stable flight. Wind tunnel test s also showed the membrane MAV s obtaining a higher lift coeffici ent an d a delay in stall when compared to a rigid wing MAV Later Stanford, Ifju, Albertani and Shyy [ 17 ] investigate d the effect s between a B atten Reinforced (BR) MAV, to a P e r i meter R einforced (PR) MAV A BR wing utilizes a rigid leading edge with battens (thin strips of material /ribs ) extending from it. The membrane is attached to the batten s allowing it to have a free trailing edge Figure 1 1 B A PR wing is a rigid wing with an enclose d section removed. A membrane is then used to cover over the hollow section while being secured by its perimet er Figure 1 1 A R esults le d to a few different tre nds at low AOA s the membrane on the BR MAV would oscillate thus changing it s camber resulting in lift H owever the free trailing edge would deflect upward resulting in a nose down mov e ment thus effectively cancel ling each other. T he PR MAV had a large increase in lift from the bellowing of the membrane this was accompanied by an increase in drag Since the PR MAV membranes were allowed to move in 2D, the interactions of the wing tip vortices could possibly create a rolling instability however a further investigation w as need ed to confirm Rojratsirikul et al. [ 18 ] [ 19 ] i nvestigated the Fluid Structure Inter actions (FSIs) of a 2D latex rubber membrane airfoil with a rigid leading edge and trailing edge. Early investigations utilized timed resolved PIV to capture the 2D flow field velocities while laser reflections off of the membrane surface captured the membrane s fluctuations and vibrational modes. A h ot wire was also used to examine the spectral characteristics of near wake shedding. Results le d to a strong coupling of membrane o scillations to

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16 shear layer height with an increase in vibrati onal modes with increasing freestream velocity. There also ex is ts a possible c oupling between the vortex shedding and membrane fluctuations. The FSI s were again examined for a 2D latex rubber membrane airfoil with a rigid leading edge and trailing edge how ever different models of pre ten sion and excess length were used Results concluded, pre tension ed membranes had similar traits of ri g i d airfoils whereas membrane s with excess length had a reduction of separated flow and an increase in the number of vibra tional mode s Rojratsirikul et al. [ 20 ] continued their in vestigation s this time of a finite perimeter reinforced membrane model, in which three dimensional (3D) effect s could be analyzed. Again, membrane f luctuations, membrane modes, 2D flow field velocities and near wake shedding were investigated. Their experimental set up remained relatively similar to previous investigations h owever, membrane vibrations and modes were capture d independently by DIC. They showed the trends of the finite PR wing closely resemble d that of the solid leading and trailing edge wing. The finite PR membrane wing showed a strong coupling between the vortex shedding and membrane fluctuation s in the post stall region similar to that of their larger aspect ratio cas e Visbal et al. [ 21 ] conducted an numerical simulation to capture the FSIs obtained experimentally by Rojratsirikul et al. [ 18 ] They utilized a 6 th order implicit large eddy simulation for the fluid dynamic solver coupled with an nonlinear finite element for the membrane structural solver. The AoA for the simulated data was set to 14 to match that of the experimental data. When the ap propriate grid spacing was selected the numerical results qualitatively agreed with the experimental results. Numerical simulations were able to capture a close coupling between the membrane fluctuations

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17 and unsteady flow over the membrane as well as vorte x roll up occurring at the trailing edg e A erodynamic forces and flow field fluctuations were measured on t hi n slightly cambered BR membrane win gs Hu et al [ 22 ] varied the membrane s cell as pect ratio by either increasing or decreasing the number of battens within the wing. T his change in batten spacing was done to examine the effect s of membrane flexibility They conclude d the BR membrane wing s ha d improved aerodynamic performance when compared to its flat plate counterpart. Shown f rom PIV measurements, t he membrane wings had the ability to reduce the amount of separated flow by automatically adjust ing its camber to adapt to the pressure differences When testing the di fferent BR membrane wing s it became apparent that wing flexibility (batten spacing) was important. The highly flexible membrane wing s would experience a trailing edge flutter which would result in a decrease in lift and an increase in dra g. Numerical simul ations were performed by Smith and Shyy [ 23 ] utilizing the Reynolds a veraged Navier Stokes equation as the fluid dynamic model while employing the shear stress transport model to handle the closure problem. Young Laplace equation, a 2D elastic membrane equation, was implemented to govern the structural dynamics. The model was then compared to experimental data taken by Greenhalgh et al. [ 24 ] Sugimoto et al. [ 25 ] and Newman et al. [ 26 ] Results for coefficient of lift were within 5% of agreement at low AoA and for the lower Reynolds number ( ) experimental data. However, large deviations were experienced at high AoA s and larger Reynolds numbers. Differences i n Reynolds number, membrane support, and wall

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18 effects within the experiments were some thoughts on what may have contributed to the discrepancies [ 23 ] To help compar e with other flexible membrane investigations an aeroelastic Pi parameter was created by Smith and Shyy [ 27 ] where 1 2 are defined in Equations 1 1 and 1 2 dulus of the membrane, t is the membrane s thickness, s cell span, S represents the membrane s pre stress which is related to the pre strain within the membrane by the modulus of m conditions. These two nondimensional parameters relate the membrane s stiffness (Et) to the aerodynamic 1 parameter is used for un 2 parameter is used for pre tensioned membranes [ 27 ] 1 1 1 2 A further investigatio n into the aeroelastic response of BR membrane wings was conducted by Johnston et al. [ 28 ] Wing configurations consisted of thin flat frame s with varying batten spacing and membrane pre tension Results obtained from video imagery showed after an onset velocity the membranes would flutter resulting in wh at Johnston et al describes as Li mit C ycle O scillations (LCO s ). An increase in both membrane pre tension and number of batten s would result in an increase in onset velocity. I t was also found that after certain velocities and Ao A s the magnitude of the LCOs would start to decrease [ 28 ] [ 29 ]

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19 Predecessor Investigations The c ollaboration s between the University of Florida and the University of Alabama built the foundation which this study is based off of In 2008 Mastramico and Hubner [ 30 ] started investigating the wake characteristic of a solid plate compared to that of different membrane model s, PR, BR and BR scalloped, by means of hot wire anemometr y. Results conclude d with the BR scallope d membrane producing a consistent reduction in the local profile drag coefficient when compared to the solid plate, PR and BR models. The BR scalloped membrane also produced a smaller but wider wake deficit when com pared to the other models. To further understand the effect s of membrane geometry Hicks and Hubner [ 31 ] conducted a parametric study. L oad data and hot wire anemometry was taken on BR membranes with varying cell depth, batten spacing and trailing edge scalloped depth. Their findings le d to trends such as scalloping the trailing edge of membrane s decreased both the lift and the drag. H owever scalloping had a greater effect on the drag thus improving the overall aerodynamic efficiency. Another trend was while scalloping had a slight decrease in lift an increase in the cell geometry, the me mbrane s chord and span size, le d to a large increase i n li ft. A BR membrane wing with a cell aspect rati o of 1 and a 25 percent scalloped (with respect to the chord) trailing edge resulted in being the most aerodynamically efficient To that point, all investigation consisted of a membrane model composed out of latex rubber with zero pre tensioning. Working with the latex rubber material provided a few challenges, models degraded within a week s time A lso applying a consistent and repeatable pre tension in the membrane was nearly impossible. These challenges le d into an investigation comparing the flow response and membrane vibrations to changes

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20 in membrane material properties. Scott et al [ 32 ] examined the membrane osc illations and flow field fluctuations of both a latex rubber membrane and a silicone rubber membrane. Synchronized hot wire anemometry and laser vibrometry allowed correlations to be obtained between the membrane s oscillations and the flow field fluctuations. At velocities below the membrane s onset velocity membrane s flutter was not visually present which resulted in a low coherence between the FSIs At these pre onset velocities, t he membrane s would vibrate at their respective natural freque ncies However after the membrane would start its LCOs a large coherence (>0.5) was present. While the latex and silicone rubbers had slightly different frequencies at both pre onset velocity and during it s LCOs both material s exhibited the same trends. A budaram et al [ 33 ] investigated in a method to accurately obtain a desired pre tension within a membrane. Their investigation used a silicone rubber material where t he silicone rubber was heated and attached to a frame, the strain was then measured by DIC. The results conclude d with the silicone rubber obtaining a linear strain vs. temperature curve. With this relationship for the silicone rubber new flexible membrane wing models with specific pre tension were created and later investigated by Timpe et al [ 34 ] [ 35 ] Their models had a high aspect ratio (4.3) multi cell ed silicone rubber membrane in a BR wing with a scalloped trailing edge Timpe et a l. investigated the FSIs by s ynchronized time resolved PIV and DIC Results showed the membrane wings had a reduction in both the shear layer height and wa ke deficit compared to its flat plate counterpart. Furthermore, a strong coupling existed between the membrane s frequency and the dominate flow field frequency. When the memb rane s characteristics were changed by AoA and/ or tension, so did its corresponding flow field At a parallel time

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21 Zha ng et al. [ 36 ] studied the lift characteristics of the s ame membrane models as Timpe et al. Results showed the high aspect ratio, scalloped trailing edge membranes when co mpared to it s flat plate counterpart had an improved aerodynamic efficiency Current Investigations The present study is aimed a t gaining further knowledge in to the fluid and structure interactions of low aspect ratio compliant membrane wings in a low Reynolds number flow Characteristic s of the streamwise flow field and 3D membrane surface deformations are acquired by synchronizing a time resolved PIV system and DIC system. The analysis will include the structural dynamics of both the membran e oscillations and the unsteady flow field measurements A flat plate model will be used as a baseline case in which the membrane models flow field can be compare with. Additionally, t he motion in which the membrane travels in will be analyzed and an attem pt will be made to describe the standing wave and traveling wave coupling. Finally, correlations between the membrane s oscillations and flow field will be examined The remainder of this thesis will be structured as follows. Chapter 2 will describe the e xperimental set up in cluding the facili ties equipment, models and processing techniques This will be followed by the results and discussion of the flow field and membrane surface deformations in C hapter 3 Finally, Chapter 4 will bring some conclusions about the fluid and structure interactions followed by a brief discussion on further investigations

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22 A B Figure 1 1 Flexible membrane MAVs. A) PR MAVs B) BR MAVs (source [ 17 ] )

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23 CHAPTER 2 FACILITIES AND EXPERIMENTAL SETUP This chapter is laid out as follows, an overview of the two different testing facilities will be provided Next, the wing geometry and the steps involved in creating the membrane wings will be discussed Then a detail ed description of the equipment used to acquire data will be given. This will be follow by a description of the experiments conducted along with the e xperimental setup Finally the pre and post processing techniques used will be discussed Facilities The experiments preformed within this investigation were conducted in two different faci l i ties. The first experiments were conducted at the University of Research and Engineering Education Facility (REEF) using the Aerodynamic Characterization Facility (ACF). The second set of experiments were performed at the Wind T unnel (ELD WT) Aerodynamic Characterization Facility The ACF is an open jet open return wind tunnel specifically designed for experiments in the low Reynolds number regime A photograph of the facility is included in Figure 2 1 A Flow enters the facility where it passes through a 3.05 m square bell mouth entrance before it goes through a conditioning region. The conditioning re gion consists of a metal honeycomb and several screen s followed by a constant area settling region. After the 1.4 meter long settling region the flow under goes an 8 to 1 area ratio contraction Finally, after the contraction, the flow exits the inlet of the o pen jet test section with dimensions of 1.07 m by 1.07 m D ownstream of the inlet (3.05 m) lies the

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24 diffuser which houses an inline 50 Hp axial blower with a variable frequency drive Experiments conducted u sing hot wire anemometer in the ACF yielded a t ur bulence intensity of 0.16% at a freestream velocity o f 10 m/s which is the velocity utilized for all experiments conducted in this study More details describing the ACF and flow qualit y can be found in Albertani et al [ 37 ] Engineering Laboratory Design Wind Tunnel The ELD WT is a low turbulence close d loop, recirculating facility and is displayed in Figure 2 1 B The a ir is moved through the tunnel by an inline 200 Hp axial blower with variable frequency drive Tu r ning v ein s are used at each intersection to help direc t the flow around the bend s Air enters the conditioning region where it passes through an aluminum honeycomb and several anti turbulence screens. Next, the air then goes through a 25 to 4 area ratio contraction where it finally enters the test section at a cross sectional area of 0 .61 m by 0.61 m ( 24 in by 24 in ) Using hot wire anemometer the E LD WT of 0.1% at a freestream velocity of 10 m/s. M ore details describing the ELD WT and flow quality can be found in Sytsma [ 38 ] Models Throughout all experiments three m odels were investigated two different membrane wing models and a rigid flat plat e where the rigid plate model was only used during PIV experiments All of the models had an aspect ratio (span/chord length) equal to 2 with a rectangular outer dimension of 152.4 mm by 76.2 mm (6 in by 3 in) Each model was constructed out of 7075 T6 aluminum and had a thickness of 0.8 mm. The membrane wings had cut outs in the aluminum where flexible material was utilized to fill in the structure creating the batten reinforced wing geometry. Two different

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25 membrane wings were tested, the first membrane wing had a 1 percent pre tensioned memb rane while the second membrane wing had a 4 percent pre tensioned membrane As mentioned in the introduction, the membrane wings utilized in this study were constructed out of silicone rubber due to advantages over latex rubber in terms of the life spa n The process that Abudaram et al. [ 33 ] developed was used t o obtain a desired pre tension within the membrane The silicone rubber is first heat ed and cooled down s everal times via a hot plate to prevent hysteresis effect s When heated the silicone rubber under goes an isotropic expansion. Thus, when adhered to the metal frame and allowed time for cooling a measurable strain is present within the membrane. Figure 2 2 show s the linear relationship between the temperat ure of creation and measured pre strain within the silicone Figure 2 3 shows the p re strain within the mem brane at creation while Table 2 1 provides the membrane model s properties The B R frames consisted of three symmetric membrane cells, each membrane s trailing edge was scalloped 25 percent (with respect to the chord ) as Hubner et al [ 31 ] found this to be the most aerodynamically efficient configuration Models used during testing can be seen in Figure 2 4 while nomenclature and geometric representation of the membrane model is provide d in Figure 2 5 Table 2 2 list the geometric dimensions of the membrane models Experimental Equipment Two different non intrusive measurement techniques were implemented within this investigation to measure both the velocity field and the membrane motions The flow field was measured by PIV and the membrane surface deformations were measured by DIC. Both systems were synchronized together where each PIV snap shot would trigger the DIC system.

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26 Particle Image Velocimetry Two components of velocity ( U and V ) were acquired using a ime R esolved PIV system from Dantec Dynamics This system consisted of a series 800 do uble cavity ND:YAG (Lee Laser) and t wo Integrated D esign Tools XS 5 hi gh speed CMOS cameras equipped with Nikon 105 mm lens set to an f number equal to 2.8. Timing and acquisition [ 39 ] During synchronized testing, the sampling rate was set to 800 Hz, this was the max sampling rate based on the PIV cameras at selected resolution It was previously found that the membranes tend to oscillate between 50 90 Hz, meaning a sampling rate of 800 Hz would provide adequate time resolved data [ 34 ] Since images are stored on board the cameras limited memory, the cameras original resolution of 1280 pixels by 1040 pixels was decrease to 1280 pixels by 600 pixels. This reduction in pixels was done to obtain more images at the desired sampling rate. Assuming a normal distribution, the PIV data was within the 95 percent confidence interval by the 300 th sample. Figure 2 6 shows the statistical convergences fo r the PIV data with the 1 percent pre tension membrane model at 16 AoA. U ncertainty with in the PIV data was found to be 5 .6 percent of the freestream condition, further information on PIV uncertainty can be found in APPENDIX A Two high speed PIV cameras were used to capture the flow above the models and within the near wake region The first camera, t he model camera had a field of view of 85.35 mm by 4 0.01 mm which resulted in a 15 pixels/mm calibration. The second camera, the wake camera had a field of view of 116.3 mm by 54.53 mm, which resulted in an 11 pixel/mm calibration. The cameras were arranged so there was an overlapping section between each camera, this region had a size of 6.35 mm. Figure 2

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27 7 shows the model camera and wake camera field s of view along with the overlapping region. Vector f ields were computed using an adaptive correlation method. Before this process was done, a mean background was subtracted from each image set. The background subtraction helped reduce the noise the cameras sensor experienced. A four step iterative process w ith an adaptive window cross correlation algorithm was applied to each data set [39] An initial interrogation area (IA) of 128 pixels by 128 pixels with a 25 percent overlap was applied. Each pass reduced the IA size until the final 16 pixel by 16 pixel IA size was achieved. The vector fields were then imported into MATLAB for further processing. Digital Image Correlation The 3D membrane surface deformations were me asured using a high speed Correlated Solutions DIC system This system utilizes two Vision Research high speed Phantom V7.1 SR CMOS cameras equipped with Tamron AF 28 300 mm aspherical lens set to an f number equal to 7.8. The cameras were controlled using Phantom cameras 675.2 control software and the d eformation s were obtained using Correlated Solutions VIC 3D 2 010 software [ 40 ] To help provide uniform lighting a 250 watt halogen lamp was shined on the membranes speckle d pattern During synchronized tests the sampling rate of the DIC system was matched to that of the PIV system, 800 Hz. Later independent DIC tests also sampled data at 800 Hz in order to keep consistent wi thin the different experiments. DIC works by comparing the random speckle d pattern on an area of investigation when no loads are applied to that of the same area as it travels through its motions. VIC 3D applies a gra y scale cross correlation method to eac h subset to obtain the deformations. To obtain a random speckle d pattern on the membranes, a light mist of paint from an aerosol can that had a

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28 modified tip was applied. This was found to create speckles of paint random enough to be processed, speckles can be seen in Figure 2 4 The subset siz e was selected to be 19 pixels by 19 pixels with a step size of 3. This resulted in a grid spacing of 0.57 mm in both the x and z directions (streamwise and spanwise directions ). A Gaussian weight was applied to the subset such that the center was weighted. To better achieve sub pixel accuracy an optimized eight coefficient interpolation filter was applied. A normalized squared difference correlation criterion was selected speci fically for its ability to be unaffected by scale in lighting [ 40 ] The coordinate system which displacement values originate from is based off the reference image. The orig in is located at the mass centroid of all measured points within the reference image. The Y axis (vertical axis, axis where displacement values are located) is normal to the best fit plane within the reference image. After displacement values were obtained they were imported into MATLAB for additional post processing Synchronization To synchronize the PIV system with the DIC system posed a unique challenge. The DIC cameras needed a 5 volt signal for an external trigger and the PIV cameras produced a 3 vo lt pulse on its sync out port. This 3 volt pulse conveniently was only produced on the first frame of each image pair The pulse was sent to a Tek tronix type 114 Pulse Generator where it reshaped the signal to a 5 volt square wave with negligible time dela y. Due to the set up, with the PIV laser firing in the direction of the DIC cameras, HOYAs multi coated high pass optical filters were place over the lens. These filters are designed to block light with a wavelength < 600 nm thus not allowing any of the la sers 532 nm light to shine through.

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29 Experimental Description The data presented within the study was collected in two different data sets. The first data set consisted of synchronized PIV and DIC in order to understand the interactions between the flow and the membrane. W hile the second data set consisted of independent DIC measurements to get a more detailed understanding of the membrane s motions Synchronized PIV and DIC S ynchronized PIV and DIC experiments were conducted in the ACF at 10 m/s The Reynolds number, Equation 2 1 based on freestream velocity and chord length was calc this value was kept fixed throughout all tests. Figure 2 9 A shows the experime ntal set up where the PIV and DIC measurements were synchronized. This s et up was such that the PIV laser probe was positioned beneath the model D ue to the limit ed length of the laser probe the model s need ed to be inverted. Since the model s were inverted and positioned in the center of th e ACF s inlet the DIC cameras were place d above the inlet and out of the flow. The DIC cameras were adjust ed so the field of view obtained was the speckle d pattern of all three membrane cells ( the speckle d pattern was applied to the underside of the membr ane model s ). The PIV cameras were positioned on the side of the inlet normal to the model s span. The first camera (model camera) focused on the leeside flow of the models while the second camera (wake camera) focused on the are a directly downstream of the model s Synchronized d ata was take n on two models, the 1 percent pre tension membrane wing, and 4 percent pre ten sion membrane wing. Independent PIV data was taken on the flat plate wing so there would be a baseline case for comparison of the membrane wings A collection of 1044 synchronized images of PIV

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30 and DIC data were acquired for all models at a range of AoA s (4, 8, 12, 16, and 20). Again only PIV data was taken on the flat plate case A digital inclinometer was used to manually set the model s AoA to 0.2, Figure 2 8 2 1 Independent DIC F urther motion w a s c onducted in the ELD WT These experiment s were to supplement the synchronized data previously taken. M odel s and air speed during these experiments remained the same as previous, a 1 percent pre tension membrane model and a 4 percent pre tensio n membrane model were tested at 10 m/s Test s consisted of in dependent DIC experiments at a range of AoAs of 4, 8, 12, 16, 20, 24, 28, and 32. Since this was the first time these experiments were conducted in the ELD WT a new mount ing arm needed t o be created. To insure the mount ing arm and wind tunnel did not influence the membrane s motions, vibration tests were taken on both the mounting arm and the wind tunnel, for further information see APPENDIX B Even though PIV data was not taken the models were still inverted to match previous experiment s The DIC cameras and lamp were position ed above the test secti on such that all three membrane cell s fit into the cameras field of view. Again the membrane wings were support ed as they were in the previous experiment, two thin symmetric airfoil hangers attached to the outer portion of the wing s. The hangers were the n attached to a circular rod, experime ntal set up can be seen in Figure 2 9 B To further analyze the influence of the wing tip vortices the model s mounting hardware was changed to a singl e airfoil hanger supporting the center of the membrane s frame.

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31 E xperiment s were repeated at AoA s of 8, 16 and 24 while being supported only by the center mount. Figure 2 10 s how s the membrane wing being support ed by the single airfoil hanger. Post Processing The flow field fluctuations and membrane oscillations were further analyzed by calculating the statistic al mean and Root Mean Square ( RMS ) values. Additional calculation consisted of obta ining Power Spectral Densit ies (PSD) and cross correlations of the time dependent data Extra operations involved applying a dynamic m ask to the PIV vector s as well as an ou tlier detection. All post processing operations were done in MATLAB R2010b. PIV The PIV vector s (both U and V components) were imported into MATLAB where a dynamic mask was applied to each time frame The dynamic masks were used to remove data where the outer membrane would cast a shadow covering the center membrane (where PIV data was taken at). Additionally, a mask was applied to each time frame when the center membrane extended past the chord line into the flow field After the masks were applied, a Multivariate Outlier Detection (MVOD) was implemented to eliminate any spurious vectors. MVOD is a non spatial dependent operation that looks at the vector field s as a whole A multivariate projection is calculated for each data poin t where all projection s are compare d to a scalar threshold, f urther information can be found in Griffin et al [ 41 ] The MVOD would typically eliminate 5 percent or less s purious vectors, however since overs 1000 vectors were acquired the statistics of mean flow properties were determined to still converge.

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32 DIC and PIV Ensemble averages of the velocity field and membrane displacements were used due to the fact they were fou nd to be stationary in time at a given spatial location. Each ensemble was separated by it s mean and fluctuating component based on classical Reynolds decomposition, Equation 2 2 T he mean and RMS flu ctuation s were calculated by Equations 2 3 and 2 4 provide by Bendat and Pierso l [ 42 ] 2 2 2 3 2 4 The dominant frequency of both the membrane s oscillations and velocity field s fluctuations were obtained by a Discrete Fourier Transform (DFT) to compute spectra. Equation 2 5 shows the Fourier transform at discrete frequencies. Equation 2 6 is used to calculate the frequency resolution within the data where N is the record length and F s is the sampling frequency. Only one record of length 1 044 was used in the s ynchronized data resulting in a frequency resolution of 0.77 Hz. The independent DIC data was broken into a record length of 586 and averaged over 5 blocks which resulted in a bin width of 1.37 Hz In the end, Equation 2 7 was used to compute the one sided Power Spectra Density (PSD) This equation used Welch method while implementing a rectangular window with 50 pe rcent overlap. Additionally, a correlation analysis was also computed on the independent DIC data. Equation 2 8 was used to compute the correlation bet ween the membrane fluctuat ion s at one specific location X, with the

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33 membrane fluctuations at a different spatial location Y T he cross correlation is normalized so the value of the autocorrelation computed at t=0 is equal to one. 2 5 2 6 2 7 2 8 A B Figure 2 1 Low speed test fac ilities. A) ACF located at REEF ( source [ 37 ] ) B) ELD WT Photo courtesy of author.

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34 Figure 2 2 Linear relation between tem perature of creation and measured pre st r ain. Figure 2 3 Measured pre strain within the membranes.

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35 Figure 2 4 Aspect ratio 2 membrane models and flat plate model Photo courtesy of author. Figure 2 5 Membrane wing nomenclature. Green line represents plane where PIV data was taken at b c s

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36 Table 2 1 Membrane s properties. Models Average Spanwise Pre Strain [%] 0.1 Temperature of Creation [C] 2 Membrane T hickness [mm] Silicone Rubber Elastic Modulus [Kpa] 1.0 45 0.36 0.34 385 4.0 190 1.43 Table 2 2 BR membrane model dimensions. All values are in units of mm. Span, b Cell S pan, Chord, c Cell C hord Aspect Ratio Scallop Depth, s Batten W idth Frame T hickness 152.4 45.7 76.2 6 1 2 15.2 3.82 2.8 Figure 2 6 Statistical convergences for the 1 percent pre tension membrane model at 16 AoA.

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37 Figure 2 7 Combined fields of view from PIV cameras. Figure 2 8 Digital inclinometer on top of model. Photo courtesy of author.

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38 A B Figure 2 9 Experimental set up. A) Synchronized experimental set up within the ACF. B) Independent DIC set up within the ELD WT. Photos courtesy of author. Figure 2 10 Membrane model with center suppored hardware positioned within the ELD WT Photo courtesy of author. PIV Cameras PIV laser DIC light DIC Cameras Inverted model in seeded air DIC Cameras DIC light Inverted model with center supported hardware

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39 CHAPTER 3 RESULTS AND DISCUSSION This chapter will present and discuss the results obtained for the fluid structure interactions of a low aspect ratio, passively compliant BR membrane win g in a low Reynolds number flow. The results will be discussed in the fo llowing manner; first, the flow field measurements obtained from 2 component PIV will be examined. This will be followed by the membrane s surface deflections measured by DIC. Finally, correlations between the flow field and membrane oscillations will be provided. Flow F ield Measurements The 2 component ( U component and V component) flow f ield measurements were acquired us ing the time resolved PIV system discussed in the previous chapter The flow above a flat plate model a nd in its near wake region, provide d a baseline case to compare the effects of the membranes This baseline case was u sed to compare both the 1 percent pre tension and 4 percent pre tension membrane models In all the plots presented here all length scales and velocity scales have been normalized by the full chord length (76.2 mm) and freestrea m velocity (10 m/s) PIV dat a was obtained in the streamwise direction along the center of the middle cell for the membrane models and also in the center of the flat plate model Data was recorded on each model at five different Ao As, 4, 8, 12, 16, and 20. The analysis include s both mean and turbulent time averaged velocity fields to highlight different aspects within the flow field First, the time averaged U component (, U mean) can be see n in Figure 3 1 The color scale for these plots has been chosen such that regions of dark blue represents reverse flow (U<0). This is followed by in Figure 3 2 The third time averaged quantity evaluates the Reynolds Shear Stress (RSS) term Equation 3 1 shows the Reynolds

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40 Averaged Navier Stokes equation obtained from Pope [43] where t he last term is the RSS term. Keeping note of the negative sign in front of the RSS term, when both and are of the same sign on average, the RSS will be a negative value. However, when both and are of the opposite signs on avera ge the RSS will be a positive value, Figure 3 3 For all of these figures the flat plate cases (column A) have a solid wing geometry frame superimposed on the PIV plots to help visualize the flow. The membrane models (columns B and C) have a 20 percent solid leading edge frame geometry while the remaining 80 percent of the frame is represented by dashed li nes to de note the battens. Also within the figure s one cycle of membrane oscillations obtained from DIC have been superimposed to further help visualize the flow dynamics. 3 1 Examining the flat plate model the evolution of the streamwise velocity component for the flow field is shown in Figure 3 1 At 4 AoA the flow slightly increases in amplitude over the leading edge and appears to remain attached as it traverses down the wing. As the AoA is increased the flow still remains attached however there is a noticeable decrease in ve locity nea r the surface. Comparing the flat plate model to its larger aspect ratio counterpart investigated by Timpe et al [34] the lower aspect ratio wing experiences a delay in A o A before the flow becomes stalled For thi s wing stall sets between 8 and 12 degrees while for the larger aspect ratio wing this happens at angles of slightly less than 8 The same delay in stall was also seen in Zhang et al. [ 36 ] were they measured force data on both low and high aspect ratio flat plate model s This delay is consider to be the effects attributed to the stronger influence the wing tip vortices have on the flow surrounding the model Torres a nd Mueller [ 44 ] proposed as

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41 the aspect ratio decrease s the effects of wing tip vortices become stronger. The separated flow [ 44 ] [ 45 ] It is not un til 12 AoA does the flow above the flat plate model experience reverse flow. The flow at 12 no longer has enough momentum to remain attached thus separating and creating a separation bubble. Due to the size of the separation bubble, reverse flow is now present within the near wake of the model resulting in a significant increase in wake deficit. Using a steady control volume approach the near wake momentum deficit can be proportionally related to drag hence a n increase in wake deficit is an indication of an increase in drag [ 46 ] As the flat plate is increased to a higher AoA s an increase in the shear layer height, amount of reverse flow and wake deficit were all observed Finally at the last an gle reco r ded, 20 AoA, the flat plate experienced a massive separated region above the surface as well as a large amou nt of reverse flow in the near w ake creating a massive wake deficit. The flow field for the 4 p ercent pre tension membrane model and 1 percent pre tension membrane model Figure 3 1 Figure 3 3 columns B and C respectively, will be compared to the baseline flat plate case. When examining the plots there are a few trends that initially stand out. One of the first trends to note is the r ed uction in shear layer height Examining the U RMS fluctuations in Figure 3 2 this reduction can be seen throughout all AoAs tested. The membrane s compliant feature is seen to he lp pull the shear layer closer to the membrane surface. As the shear layer remains closer to the membrane s surface an increase in the amplitude of the streamwise fl ow at the leading edge is noted. The m embrane models demonstrated accelerated flow at the l eading edge of approximately 15 percent greater than the flat plate case. Another trend to note

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42 is the significant decrease in reverse flow above the model s surface and in the near wake Comparing with the flat plate model at 1 2 AoA where a large separat ion bubble was present the flow over the membrane model s have a relatively small separation bubble closer to the leading edge Increasing the AoA further highlights the reduction in both the amount of reverse flow as well as the amount of turbulent flow in the near wake the membrane models produce compare d to the flat plate model Part of the reduction in reverse flow can be attributed to the membrane models being able to change their camber in the presence of a pre ss ure difference The increase in camber effectively allows the flow to reattach whereas in the flat pl ate case the flow remains separated Examining the near wake leads to another trend, the membrane models have a m ajor decrease in peak wake deficit veloc ities. At lower AoAs the membrane models have a smaller but wider wake deficit H owever at higher AoA s, a narrowing of the wake and a substantial decrease in deficit is experienced. Looking at both the RSS and instantaneous vorticity generated by the mem brane model s lead s to some insight on how the membrane motions hel p aid in the reduction of reverse flow present in the near wake Figure 3 3 and Figure 3 4 respectively. Examining the RSS obtained for the flat plate cases mome ntum transfer of positive sign (opposite sign deviations) is seen within the shear layer. While momentum transfer of negative sign (same sign deviations) is seen beginning at the lead ing edge and trailing edge. As AoA is increased RSS continues to grow. Me mbrane models share similar features at low AoA with positive RSS seen in the shear layer as well as negative RSS seen at the leading edge and trailing edge At highe r AoA influences become s apparent. The membrane models have a slight reduction in positive

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43 RSS (lower momentum fluid) within the shear layer while the negative RSS produced at the rear of the model is seen to mo ve closer to the trailing edge helping to introduce high momentum fluid in to the near wake. Observing the instantaneous v orticity generate d by the 1 percent pre tension membrane at 20 AoA plot A of Figure 3 4 shows high momentum fluid build ing up on the lower surface of the membrane T his build up creates a pressure bubble that traverse s down the membrane then at the trailing edge the high pressure is released p lot s B and C. T he release of high pressure into the lower pressure region at the trailing edg e cause s a vo rtex structure of opposite sense (compared to the leading edge) to form plot D T he vortex structure introduced at the trailing edge interacts with the shear layer reducing its overall size These structures also introduce mixing into the nea r wake allow ing higher momentum fluid to mix with lower mo mentum While both membrane models had similar features the 1 percent p r e tension membrane seemed to slightly out preform the 4 percent pre tension membrane based on the size of the separation bubble, shear layer height and wake deficit. This is further supported by the results obtain by Zhang et al. [ 47 ] where force mea surements were taken on identical membrane models. The 1 percent pre tension membrane had a slight improvement in aerodynamic efficiency compared to the 4 percent pre tension membrane model Membrane Surface Deflections The 3D surface membrane deflections were captured using the high speed DIC system discussed in the previous chapter The intent of inv estigating the membrane surface deflections is to provide a better understanding of th e membrane s motions and how it is affected by the fluid flow. All lengt h scales wit h this section have been normalized by the full chord length. The membrane models will first be analyzed

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44 qualitatively by looking at their mean deformations and RMS fluctuations. Further analy sis will include trends on mean shape variations. Ne xt, the PSD of the membrane s fluctuations in both the temporal and spatial directions will be investigated to further analyze the membrane s motions Finally correlations between spatial location s will be compared in an attempt to describe the wave like nature which the membrane moves in Within each section, the synchr onized DIC results will first be introduced followed by the later independent DIC results. Mean and Root Mean Square Deflections The time averaged mean deflections of the membrane models were calculated via Equation 2 3 Figure 3 5 plots the mean deflections of both the 1 percent pre tension model and the 4 percent pre tension model through a range of AoA s: 4, 8, 12, 16, and 20 The outer frame and battens for the membra ne models have been superimposed in the contour plots to better help establish the orientation in which the membranes lie. M embrane models shared similar trends, both model s experienced an increase in deflections as AoA is increased ( increase in aerodynamic loading) One feature to note about the deflections is the asymmetric shape that the outer m embranes ex hibit (discussed later ) whereas the middle membrane exhibits a symmetric distribution. The symmetric displacements at the middle membrane are similar to the results of the higher aspect ratio membrane models obtained by Timpe et al. [ 35 ] whose data was taken at the center membrane where 3D tip effects were thought to be of minimal influence. These similar traits can also be found in the independent DIC case s later investigated Figure 3 6 One discrepancy to note is the deflection s at the leading edge of the left membrane. After construction the left membrane had a slight sag at static conditions. The sag at the leading edge allowed th e membrane to have an

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45 increase i n deflection at that specific location Normally, the area experiencing the sag should show minimal deflections, as in the synchronized case. As previously stated, the bulk deflections rem ained similar The me mbrane s fluc tuations are shown in the RMS plots Figure 3 5 Since the membrane models are BR and have s calloped trailing edges, b oth models experienced max fluctuations at the center trailing edge for all tested cases. While looking at the contour plots no clear trend stands out however one item is noted, membrane fluctuations dramatically decrease after a certain AoA s This decrea se was also experienced in the independent DIC case s shown in Figure 3 6 Another similar feature was the greater fluctuation s experienced at the oute r edges of the left and right membranes. The wing tip vortices were thought to be the cause of these asymmetric fluctuations how ever the mounting hardware was also believed to be a contributing factor since the models were supported by the outer edges Eff ects of Mounting Hardware During both the synchronized and indepen dent experiments the membrane models were support ed by two airfoil shaped hanger s, one at either side of the mod el, hangers can be seen in Figure 2 8 The mounting hardware was convert ed such that the models would now be supported at the center of the model by a s ingle airfoil shaped hanger Figure 2 10 This change was done to rule out any suspicions whether the outer supports were contributing to the asymmetric deformations. N ormalized mean deflections and RMS plots of the center s upported models are shown in Figure 3 7 Qualitatively looking at the plots, the presence of the asymmetry experienced at the outer membranes is just a s defined as in the cases with the outer supported hardware. Mean deflection plots remain comparable however the RMS plots had a slight

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46 increasing in fluct uations at the outer membranes. Even though the outer supports may have cause a slight decrease in fl uctuations at the outer cells, bulk deflections as well as the asymmetric deformations still exist ed T hese plots help support the hypothesis mad e earlier, stating the asymmetric deformation s were caused by th e wing tip vortices and not hardware induced Mean and Root Mean Square Deflections A long the Mid P lane To obtain a better understand ing of the membrane surface changes with AoA deformations along the midpoint of each membrane are investigated Figure 3 8 plot s the normalized mean deflections of the left middle, and right membranes at their respective geometric centers as a function of AoA. Additionally within the plots are error bars which represent the normalized RMS fluctuations at the same midpoint location. Furthermore, both sets of synchronize DIC data and independent DIC data have been included, column s A and B respectively. When comparing the membrane models it becomes evident that pr e tension has a significant effect on the me mbrane s deflections. The 1 percent pre tension membrane allows for greater flexibility throughout all AoAs compared to the 4 percent pre tension model. Looking at the RMS fluctuations at 8 AoA for all plots th ere exists an induced excitation that leads to an increase in fluctuation s At higher AoAs ( >20 ) the membrane s fluctuations significantly decrease. The decrease in fluctuations is a byproduct of the increased aerodynamic loading causing the membrane to stretch, thus not allowing the membrane to oscill ate as freely. When comparing the synchronized data to the independent DIC data a slight discrepancy in RMS fluctuation s is noted While the trend of RMS fluctuations generally remain ed the same the fluctua tions in the independent case experienced a noticeable decrease in magnitude Even though the RMS fluctuations did not agree between data

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47 sets the magnitude of the mean deflections reasonably agree. The discrepancy in the RMS fluctuations is thought to be a byproduct of the new stiffer mounting arm. The stiffer mounting arm was thought to decrease the amplitude of the membrane oscillations while still allowing a mean defection due to the aerodynamic load ing however a further investigation wil l need to be c onducted. One of the aerodynamic benefits from the use of a passively compliant membrane is the camber associated with its flexibility. Figure 3 9 and Figure 3 10 plots the time averaged mean camber for both membrane models (synchro nized DIC data is shown in Figure 3 9 and independent DIC data is shown in Figure 3 10 ). Averaged mean camber is plotted at the center chord for the middle membrane. As shown in the normalized mean deflection plots, camber increases with AoA. Both data sets and pre tensions have similar features in the presence of a pressure difference. T he 1 percent pre tension membrane is abl e to increase its camber on average 2.3 times greater than the 4 percent pre tension membrane. Max deflection tends to be closer at the leading edge of the models at lower AoAs. When AoA is increased a transition of max deflection occurs, shifting the max closer to the trail ing edge. At the higher AoA s ( >20 ) the average mean camber for each model tend s to level off reach ing a constant camber. The c onstant camber suggests the models have reached their respective material limits. Power Spectral D ensity and Membrane Motion The membrane motions have further been examined by looking at the trailing edge fluctuations The frequency power spectrum was calculated using Equation 2 7 Figure 3 11 shows the P S D obtained at the center of the trailing edge of each membrane cell (left, middle and right) for the 1 percent pr e tension membrane column A

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48 and the 4 percent pre tension membrane column B. While only AoAs of 8 12 and 16 are shown angle s of 4 20 24 28 and 32 exhibits simila r feature and their graphs have been omitted. A discussion of the full range of AoAs is soon to follow. The different cells within the 1 percent p re tension model all tend to experience the same dominate frequency disregarding the 8 AoA. At the 8 AoA the middle membrane seems to experience a peak shifting phenomena shifting dominate frequency slightly higher. Each cell within the 4 percent p re tension model also experience s the same domin ate frequency as each other Furthermore an additional peak at a higher frequency is also present throughout all AoAs. The additional peak experienced within the PSD is thought to be contributed to the RMS fluctuations, where the membranes are seen to have two distinct peaks in the RMS plots Again at 8 AoA the high er frequency experiences a slight peak shifting phenomena. Using the PSD for each model Figure 3 12 and Figure 3 13 plot the membrane s first dominate frequency as a funct ion of AoA S ynchronized DIC data is shown in Figure 3 12 and independent DIC data is shown in Figure 3 13 From these plots one can observe the effects of both the pre tension and the added aerodynamic tensioning as the wing is brought to higher A o A s. The 1 percent pre tension membrane tends to h ave a lower frequency compared to the 4 percent pre tension membrane as one would expect based on a h igher tension in the membrane. Furthermore there is a general trend in the frequency of the membranes, where frequency increases with increasing AoA This is expected as the aerodynamic load increases the membrane with increasing AoA While the flow provides the excitation for the membranes, the not shedding from the wing, which has been

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49 reported for some ca ses of fully supported membrane wings [ 19 ] [ 48 ] As the models AoA is further increased the membrane s oscillations level s off where again the membranes seem s to have reached their material limits. T he membrane s motions were again examined by looking at the trailing edge fluctuations how ever, this time they were observed qualitative ly. Figure 3 14 plots the center trailing edge fluctuat ions for the 1 percent pre tension model at AoAs of 4, 12, and 20. Comparing the different cells within the model (left, middle, and right) at low AoAs the membranes appear to be random ly phase d The y are thought to have started their cycles of oscillations and randomly come in and out of phase with each other. However, at higher AoAs, where there is a stronger aerodynamic loading present the membranes are seen beating with each other and appear to be in phase. Continuing examining the membrane models qualitative ly, Figure 3 15 plots a segment of instantaneous membrane surface fluctuations at the cen ter chord of the middle cell These instantaneous snapshot s are used in calculat ion of the time averaged mean camber shown in Figure 3 10 The vertical axis within Figure 3 15 represents the chordwise direction of the model while the horizontal axis represents time in milliseconds. The plots are for the 1 percent pre tension membrane model at AoAs of 4, 12, and 20. S imilar behavior can be seen at other AoA s as well as in the 4 percent pre t ension membrane model The norma lized deflections visually show the wave type behavior of the membrane s motion The motions display features of both a standing wave and traveling wave. A pure standing wave would plot straight vertical lines of alternating colors, portions of a standing wave can be seen in the upper region s of the plots (near the trailing edge of the model). A pure tra veling wave would plot diagonal

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50 line s of alternating colors, this can be seen in the middle portion of the plots (mid chord of the model). While these p lots visua is a combination of a stand ing wave and a traveling wave a more detail description was desired. A Fourier transform into wave number space was compute d to obtain the wavelength of the traveling wave. The PSD was agai n calculated using Equation 2 7 this time in the spatial direction. Figure 3 16 plots the PSD for the 1 perc ent pre tension membrane at AoA s of 8 and 16. Examination of the plots conclude the PSD could not resolve a dominate spatial frequency for the membrane. The signal is thought to be likely aliased due to the poor spatial resolu tion. The bin size for the PSD calculated by Equation 2 6 equaled 0.022 With a spatial frequency of 0.022 the largest wavelength that can be resolved is a 45.5 mm wave. What can be taken from these plots is the membrane s ) spatial frequency which tra nslates to the membrane h aving a wavelength larger than (> 45.5 mm). Using Equation 3 2 where F is t he dominate temporal frequency wavelength, the membrane model s have a w ave speed of at least 2.61 m/s. Again, a more detailed description of the membrane was sought after. 3 2 Wave Speed One of the goals within this investigation was to ex plain the wave like nature of the membranes. A correlation between the spatial locations was calculated by Equation 2 8 Each spatial location along th e center chord was compared to the first spatial location. Figure 3 17 plot s the results of the correlations for the 1 percent pre tension model at 8 AoA. Plot A shows the autocorrelation of the first spatial location at

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51 x/c=0.22 As the correlation plots continue, the spatial distance is incremented by 20 spatial locations (equivalent to 0.14 in the nondimensional length scale). Plots B and C both show a shift in peak correlation stating the membrane is behaving like a traveling wave. The additional peaks at both are due to the periodic characteristics of the signal. One i nteresting feature that all membrane model s exhibit is a temporary transition to a standing wave. Examining plots C and D, where the correlation compares the x/c=0.5 location and x/c=0. 6 4 location, the correlation remain s relatively stationary. This stationary portion of the correlation resembles that of a standing wave. Th is notion of a standing wave can be further supported by Figure 3 18 This figure shows the membrane s motion through one cycle of o scillations for the 1 percent pre tension model at 12 AoA. Within the oscillations there exists one position where the membrane typically passes through This point can be thought of as a type of node where two traveling waves intersect and cancel each o ther. At this intersection the sum of the waves is approximately zero Reverting back to Figure 3 17 plot E shows the correlation at the x/c=0.78 location. The correlation slightly changes however the membrane returns to the trend of a standing wave. Using the data from the correlations analysis and knowing the distance between each spatial location along with the time between each signal, a wave speed for each membrane can be calculated. To help resolve some of the ambiguity in picking a tau a least squares method was applied to the correlations previously obtain ed T he result s of this method can be seen in Figure 3 17 where the red line represents the new approximate d correlation. Wave speeds were obtained at 15 different spatial locations and averaged. Figure 3 19 plots the average wave speed as a function of AoA for both

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52 membrane models T he 4 percent pre tension membrane produced higher wave speeds throughout all AoAs as one would expec t based on the h igher tension in the membrane A t the lower AoAs, the higher wave propa gation is thought to be due to the location of the shear l ay er. Since the shear layer is relatively close to the membrane s surface, some of the higher free stream velocity is entrained and transitioned into the membrane aiding in the wave speed As the AoA is increased t he shear layer gr o w s in both size and height thus not allowing the higher momentum fluid to reach the membrane s surface The wave propagation rel ies on the tensioning within the membrane as well as the tensioning associated with the increase in aerodynamic loading. As AoA is increased the membrane s frontal projection area is also increas ed this allows a larger portion of the membrane to experienc e an increase in loading This increase in loading is proportional to the tension ing within the membrane where an increase in tension leads to an increase in wave speed. Fluid S tructure Interactions The synchronization of the flow field fluctuations and membrane oscillations highlighted some of the coupl ings associated with the membrane and flow Since PIV and DIC were acquired simultaneously, both of their respective PSD are compared. The PSD of the flow field was obtained in the same fashion as in the membrane s PSD. Figure 3 20 A shows the normalized U component of the velocity field for the 1 percent pre t ension membrane model at 8 AoA T he diamond shapes signify the locations where PSD was calculated. Figure 3 20 B plots the PSD at each of the diamond l ocations along with the previously found PSD of the middle membrane s trailing edge. One of the main features in Figure 3 20 B is the presence of t he membrane s dominate frequency appearing through out the flow field This suggests the membrane motions

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53 are driving the surrounding flow field The powers associated with the flow field s dominate frequency are dependent upon location relative to the membran e Powers at the leading e dge are significantly less than the power s associated with the flow around the trailing edge and n ear wake. The near wake provides the highest power s due to the large fluctu ations experienced within the U component of velocity. Figure 3 21 plots the PSD of the velocity field s fluctuating U component at the x/c= 1.0 and x/c= 2.0 location s for AoA s of 12 and 16 (plots A and B respectively). Although the higher frequencies of the velocity spectra are likely aliased due to the spatial resolution of the PIV, one can still clearly resolve a peak in the spectra. While the results for the 4 and 20 AoA s along with 4 percent pre ten sio n are not shown, these cases also exhibit similar behaviors. The me mbrane s dominate frequency appear s throughout the flow field while higher powers are seen in the trailing edge and the near wake of the models The S trouhal number for the membrane mod els was then investigated. This nondimensional number is used for describing oscillations with in fluid flow Equation 3 3 shows a modified Strouhal number where F is the wake frequency, L is the projection length of the model, and V is the freestream velocity. Using the membrane s dominate frequency previous ly f ound as the flow field s dominate frequency the modified Strouhal number i s evaluated. Figure 3 22 plots the modified Strouhal number vs AoA for both membrane models Additionally within the plot is an approximate Strouhal number ( ) where Fage and Johansen [ 49 ] showed for a rectang ular flat plate at lower A oAs ( < 30 ) the modified Strouhal number varied between 0.15 0.22 E xamining Figure 3 22 the Strouhal number incre ases with increases AoA until 28 w here it then starts to decrease This decrease is thought to be a byproduct of the model s reaching

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54 their material limits. Comparing the membrane models trend to the trend obtain ed by Fage and Johansen the membrane models appear to driving the surrounding flow significantly altering it from a traditional rectangular flat plate model 3 3

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55 AoA Flat Plate Model 4% Membrane Model 1% Membrane model 4 8 12 16 20 A B C Figure 3 1 Normalized mean U component of the flow field with streamlines for the different models. Column A) flat plate model. Column B) 4 percent pre tension model. Column C) 1 percent pre tension model

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56 AoA Flat Plate Model 4% Membrane Model 1% Membrane model 4 8 12 16 20 A B C Figure 3 2 Normalized Urms contours for the different models. Column A) flat plate model. Column B) 4 percent pre tension model. Column C) 1 percent pre tension model

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57 AoA Flat Plate Model 4% Membrane Model 1% Membrane model 4 8 12 16 20 A B C Figure 3 3 Normalized RSS for the different models. Column A) flat plate model. Column B) 4 percent pre tension model. Column C) 1 percent pre tension model

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58 Time(ms) t=0 A t=2.5 B B t=3.75 C C t=5.0 D D Figure 3 4 Normalized i nstantaneous vorticity for the 1 percent pre tension membrane at 20 AoA.

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59 1% Membrane Model 4% Membrane Model AoA Mean RMS Mean RMS 4 8 12 16 20 Figure 3 5 Normalized mean membrane deflections and normalized RMS deflections through a range of AoA s for the synchronized data.

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60 1% Membrane Model 4% Membrane Model AoA Mean RMS Mean RMS 4 8 12 16 20 Figure 3 6 Normalized mean membrane deflections and normalized RMS deflections through a range of AoA s for the Independent DIC data with outer support ed models

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61 1% Membrane Model 4% Membrane Model AoA Mean RMS Mean RMS 8 16 Figure 3 7 Normalized mean membrane deflections and normalized RMS deflections through a range of AoA s for the Independent DIC data with center supported models.

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62 A B Figure 3 8 Membrane s center n ormalized mean and RMS deflections vs. AoA Column A) S ynchronized data. Column B) Independent DIC data

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63 Figure 3 9 Time averaged mean camber of middle membrane for the synchronized data. Figure 3 10 Time averaged mean camber of middle membrane for the independent DIC data.

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64 8 12 16 A B Figure 3 11 Trailing edge PSD for each membrane. Column A) 1 percent pre tension membrane model. Column B) 4 percent pre tension membrane model.

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65 Figure 3 12 First dominate frequency vs. AoA for each membrane during synchronized testing.

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66 Figure 3 13 First dominate frequency vs. AoA for each membrane during independent DIC testing.

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67 4 12 20 Figure 3 14 Instantaneous trailing edge membrane surface def l ections for the 1 percent pre tension membrane model.

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68 4 8 12 Figure 3 15 Instantaneous center chord membrane surface deflections for the 1 percent pre tension membrane model.

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69 8 16 Figure 3 16 PSD in the spatial domain.

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70 Figure 3 17 Cross correlations between spatial locations for the 1 percent pre tension membrane at 8 AoA. Plot A) Autocorrelation at x/c= 0.22 location P lot B) Cross correlation at x/c= 0.36 location Plot C) Cross correlation at x/c=0.5 location Plot D) Cross at x/c=0.64 location Plot E) Cross correlation a t the x/c=0.78 location. A B C D E

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71 Figure 3 18 Membrane oscillations for the 1 percent pre tension model at 12 AoA. approximates the location where two traveling wave s intersect and cancel each other Figure 3 19 Middle cell average w ave speed vs. AoA for both membrane models.

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72 A B Figure 3 20 PSD of both the middle membrane s trailing edge and select locations of the flow field for the 1 percent pre tension membrane at 8 AoA. Plot A) U mean plot specifying the exact locations where PSD was obtained at. Plot B) Plot s the PSD of the specified location s in plot A along with the PSD of the middle membrane s trailing edge.

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73 12 A 16 B Figure 3 21 PSD of both DIC and PIV for the 1 percent pre tension membrane model. Plot A) 12 AoA. Plot B) 16 AoA.

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74 Figure 3 22 Modified S trouhal number vs. AoA

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75 CHAPTER 4 SUMMARY AND FUTURE WORK This study investigated both the fluid and structure characteristic of a low aspect ratio, batten reinforced, multi cell, scalloped membrane wing in a low Reynolds number flow. Two different membrane models were investiga ted, the first model had a 1 percent pre tension membrane while the second model had a 4 percent pre tension membrane. A time resolved PI V system was synchronized with a high speed DIC system allowing the streamwise flow field and 3D membrane surface defor mations to be captured simultaneously. Analysis of the data resulted in structural dynamics of both the membrane osc illations and the unsteady flow field measurements. This was follow ed by another investigation consisting only of independent DIC data. Whil e the independent DIC data was conducted in a different facility, the experimental set up remained relatively similar to the synchronized set up. Analysis of this data set resulted in similar structural dynamics of membrane oscillations as in the synchronized data. Furthermore, the wave like motion of the membrane s move ments was explored Summary Time averaged flow field s of both membrane models and a flat plate model were obtained by PIV. Examining the normalized U component of the flow field e ven at low AoA ( ) it was apparent the membrane models have more desirable flow features than that of a flat plate. The membrane models had a noticeable increase in flow velocity at the leading edge as well a s in the near wake At higher AoA s ) the separated flow above the flat plate model grew becoming large enough to create a massive wake deficit. T he membrane models had a significantly less amount of reverse flow present resulting in a considerabl y less wake deficit. Comparing both membrane

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76 model s the 1 percent pre tension membrane showed a slight improvement in both a smaller separation bubble and wake deficit compared to the 4 percent pre tension model This slight improvement was also seen in th e force data obtained by Zhang et al. [ 36 ] The Reynolds shear stress term and U RMS fluctuations provided insight on both momentum transport and shear layer growth. At low AoAs ( ) the membrane model s had a slight decrease in shear laye r size c ompared to the flat plate case. At larger AoA s membrane model s continued to have a smaller shear layer size as well as in increase momentum transport and turbulent mixing. Analysis of the m embrane deflection s le d to the following trends, a s AoA was increased the mean deflection (averaged camber) also increased. While the 1 percent pre tension membrane had greater deflections throughout all AoA a t higher AoA both membrane model deflections level ed off where the models seem to have reach ed their material limits. A s imil ar trend was also found in the frequency which the membranes oscillate at Frequencies increased with AoA w h ere the 4 percent pre tension membrane generally vibrated at a high er frequency throughout the AoA s E ventually the frequencies level ed off and started to decrease at the higher AoA. RMS fluctuations shared similar experiences, as AoA was increase d the fluctuations also increased. However the fluctuation s quickly subsided as the AoA was increased to higher angles. I n preliminary results the outer asymmetric deflection s were thought to be a byproduct of both wing tip vortices and mounting hardware effect s F inal results show mounting hardware had no major effect on the asymmetric deflections however fluctuations did increase at the outer membrane s when the center mount ing hardware was used.

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77 The synchronized experiments were able to provide hig hlights in the coupled membrane and flow interactions. Comparison s of the membrane s dominate frequency to the flow field s d ominate frequency showed the membrane s ability to influence the surrounding flow. There is a dependency on location within the flow field however flows approximately close to the trailing edge and near wake had apparent membrane fluctuation s present Examination of the instantaneous vortices shows the membrane s ability to produce a positive vortex structure at the trailing edge. These structures introduce d higher momentum fluid in the near wake aiding in a more favorable wake. While FSIs were present at all AoA s angles at which the membrane fluctuations were substantial produced superior interactions. ed and found to be a combination of a traveling wave and standing wave. A high pressure bulge would develop at the leading edge of the membrane This bulge would then traverse down the membrane where at an approximate location of x/c = 0.65 the membrane would transition to a standing wave and release the higher momentum fluid into the trailing edge. Wave speed was shown to be a function of pre tension and AoA. The h igher pre tension membrane allowed a faster wave prorogation compared to the lower pre tension model. T he aerodynamic loading associated with increasing AoA was also thought to increase the wave speed Future Investigation This study was a continuation of previous research to further understand the fluid structure interactions, particular ly within this investigation of a low aspect ratio flexible membrane wing. Membrane models showed signs of highly 3D deflections as well as asymmetric deflections, w hile the flow results showed a strong dependence on

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78 membrane oscillations. B oth of these features enlighten some aspect of the FSIs however there is much that is lef t unanswered Future studies can incorporate streamwise stereo PIV as well as spanwise 3 component PIV measurements These measurements can examine the presence of spanwise flow as well as the interactions between membrane cells and battens Furthermore a n investigation on how the outer membranes i nteract with the wing tips vortices can be studied. Different plan e s of spanwise stereo PIV can be conducted to see the evolution of the membrane s interactions. To better link experimental results with numerical studies a Dynamic Mode Decomposition (DMD) can be conducted on past and/or current data to generate a low order predictive model where there model s could be used to help v alidate current fluid structure solvers. While this study as well as others have provided more knowledge of low Reynolds number flight of passively compliant wings there is still much that is not well understood about the fluid structure interactions

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79 APPENDIX A 2D PIV UNCERTAINTY Bias uncertainty in the PIV veloc ity measurement is obtained by computing the root sum square of the individual uncertainties used to determine velocity as explained by Coleman and Steele [ 50 ] The velocity obtained by each interrogation area is measured via Equation A 1 where t is the ti me interval between laser pulses is the pixel width of the calibration target, D is the particle displacement, and is the measured width of the calibration target. A 1 The bias uncertainty is shown in equation A 2 where the terms represent the partial derivative s of Equation A 1 (the magnitude of velocity) taken with respect to the denoted subscripted variables. These terms are better known as the absolute sensitivity coefficients. The terms represent the un certainty in each measurement denoted by the subscripted variable is the bias uncertainty of the particle displacement is the bias uncertainty in the physical width (resolution of the device used to measure the distance). is the bias uncertainty in pixel width of the calibration image. Lastly, is the bias uncertainty in the time between laser pulses It should be noted that this method does not account for incorrect PIV vectors that were not removed by outlier rejection. The random uncertainty, Equation A 3 follows that provided by Coleman and Steele [ 50 ] Where the total uncertainty is obtain by computing the root sum square of both the bias uncertainty and random uncertainty A 2 A 3

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80 APPENDIX B VIBRATIONAL ANALYSIS In the set up for the independent DIC experiments a new mounting arm need ed to be constructed. During construction of the mount, the question of whether the frequency at which the mounting arm v fluctuations was proposed This led into a vibrational analysis to obtain the mounting frequency A PCB Piezotronis triaxial accelerometer was adhered to the back of one support hanger shown in Figure B 1 where the membrane was removed prior to testing. The accelerometer was positioned such that the x axis pointed in the spanwise direction, the y axis pointed in the streamwise direction. Initial testing showed the mounting arm having spike s in frequency at 6 4 85 and 128 Hz, Figure B 2 plots the PSD for all three axes of the frequency 90 Hz Afte r further investigations where the accelerometer was adhered to the sidewall of the tunnel, it was found that the 64 Hz obtained in the mounting arm was actually being transfer red from the tunnel. The 85 Hz was found to be the natural frequency of the moun ting arm itself. Figure B 3 plot s the PSD for the accelerometer attached to the sidewall. After n umerous different configurations, the design of the mo unting arm was changed T his time the mount would be supported by an 80/20 stand positioned next to the side wall. This would allow the mount ing arm to be cantilever ed into the ELD WT while not actually making contact with the sidewall Figure B 4 plot s the PSD of the cantilever ed mounting arm. The new design not only shifted the frequency experienced

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81 within the mount it also stiffen ed the mount produc ing a lower overall power for the accelerations experienced in each direction Figure B 1 Accelerometer attached to the back of mounting arm. Photo courtesy of author. Figure B 2 PSD of original mounting arm.

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82 Figure B 3 PSD of ELD WT. Figure B 4 PSD of cantilever ed mounting arm.

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83 LIST OF REFERENCES [1] D kinematics and gliding performance J ournal of Experimental Biology vol. 209, no. Pt 4, pp. 689 701, Feb. 2006. [2] S. Swartz, J. Iriarte American Institute of Aeronautics and Astronautics Aerospace Sciences pp. 1 10, 2007. [3] D. K. Riskin, D. J. Willis, J. Iriarte Daz, T L. Hedrick, M. Kostandov, J. Chen, D. mplexity of bat wing kinematics Journal of Theoretical Biology vo l. 254, no. 3, pp. 604 15, Oct. 2008. [4] W. Shyy, M. Berg, an d D. Ljungqvist, Flapping and flexible wings for biological and micro air vehicles Progress in Aerospace Sciences vol. 35. 1 999. [5] feeding bat, Glossophaga soricina, flying at different flight speeds and Stro Journal of Experimental Biology, vol. 209, no. 19, pp. 3887 3897, Oct. 2006. [6] X. Tian, J. Iriarte Diaz, K. Middleton, R. Galvao, E. Israeli, A. Roemer, A. Sullivan, A. Song, S. and Dynamics of Bat F Bioinspiration & Biomimetics vol. 1, no. 4, pp. S10 8, Dec. 2006. [7] A Song, X. Tian, E. Israeli, R. Galvao, K. Bishop, S. Swartz, and K. Breuer, AIAA J. vol. 46, no. 8, pp. 2096 2106, Aug. 2008. [8] P. G. Ifju, D. A. Jenkins, S. Ettinger, Y. Lian, W. Shyy, and M. R. Waszak, Wing 40 th AIAA Aerospace Sciences Meeting pp. 1 13 2002 [9] J ournal of Aircraft vol. 36, no. 3, pp. 523 529, May 1999. [10] Turbulent Transition of a Low Reynolds Number AIAA J ournal vol. 45, no. 7, pp. 1501 1513, Jul. 2007. [11] Reynolds Annual Review of Fluid Mechanics vol. 1 5, no. 1, pp. 223 239, Jan. 1983.

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84 [12] M. Gaster, The S tructure and B ehaviour of Laminar Separation B ubbles Aeronautical Research Council Reports and Memoranda no. 3595. 196 7 [13] The Aerodynamic Theory of Sai ls Proceedings of the Royal Society of London. Series A, Mathematical, Physical and Engineering Sciences vol. 261 no. 1306, pp. 402 422, 1961. [14] I. M. Kroo, Aerodynamics, Aeroelasticity, and Stability of Hang Gliders National Aeronautic and Space Administration Technical Memorandum no. 81269 Ap ril, 1981. [15] G. M. October 2007. [16] P. G. If materials for Micro Air V SAMPE conference pp. 1 12, May. 2001 [17] Progress in Aer ospace Sciences vol. 44, no. 4, pp. 258 294, May 2008. [18] P. Rojratsirikul, Z. S tructure Interactions of Membrane Airfoils at Low Reynolds N Experiments in Fluids vol. 46, no. 5, pp. 859 872, Feb. 2009. [19] strain and excess length on unsteady fluid Journal of Fluids and Structures vol. 26, no. 3, pp. 359 376, Apr. 2010. [20] P. Rojratsirikul, M. S. Genc, induced vibrations of Journal of Fluids and Structures vol. 27, no. 8, pp. 1296 1309, Nov. 2011. [21] to Micro Air Vehicles DoD High Performance Computing Modernization Program Users Group Conference pp. 73 80, J un. 2009. [22] Membrane Airfoils at Low Reynolds Journal of Aircraft vol. 45, no. 5, p p. 1767 1778, Sep. 2008. [23] Physics of Fluids vol. 8, no. 12, p. 3346, Aug 1996. [24] dimensional inextensible flexible AIAA J ournal vol. 22, no. 7, pp. 865 870, Jul. 1984.

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85 [25] T. SUGIMOTO a dimensional Journal of t he Japan Society for Aeronautical and Space Sciences vol. 36; no.409; pp .86 93 1988 [26] dimensional impervious sails: experimental Journal of Fluid Mechanics vol. 144, pp. 445 462, Jul. 1984. [27] Physics of Fluids vol. 7, no. 9, p. 2175, May 1995. [28] Ch aracterization of Limit Cycle Oscillations in Membrane Wing Micro Air Journal of Aircraft vol. 47, no. 4, pp. 1300 1308, Jul. 2010. [29] P. J. Attar, B. J. Morris, W. a. Romberg, J. W. Johnston, and R. N. Parthasarathy, zation of Aerodynamic Behavior of Membrane Wings in Low Reynolds AIAA J ournal vol. 50, no. 7, pp. 1525 1537, Jul. 2012. [30] Membran 26th AIAA Aerodynamic Measurement Technology and Ground Testing Conference pp. 1 13 2008 [31] edge scalloping effect on flat plate membrane Aerospace Science and Technology vol. 15, no. 8, pp. 670 680, Dec 2011. [32] AIAA Journal vol. 50, no. 3, pp. 755 761, Mar. 2012. [33] Y. J. Abudaram, P. G. Ifju, J. P. Hubner lling Pre Tension of Silicone Membranes on Micro Air V ehicle Flexible W AIAA 50th Aerospace Sciences Meeting pp. 1 11, Jan 2012. [34] a AIAA 50th Aero space Sciences Meeting pp. 1 22 Jan 2012 [35] A. Timpe, Z. Zhang, J. P. Experiments in Fluids, vol. 54, no. 3, p. 1471, Feb. 2013.

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86 [36] Z. Zhang, J. P. Hubner, A. Timpe L. Ukeiley, Y. Abudaram, and P. Ifju, Aspect Ratio on Flat AIAA 50th Aerospace Sciences Meeting pp. 1 15, Jan 2012. [37] R. Albertani, P. Khambatta, A. Hart, L. Ukeiley M. Oyarzun and L. Cattafesta, 47th AIAA Aerospace Sciences Meeting pp. 1 10 Jan. 2009 [38] [39] [40] [41] of multivariate outlier detection to fluid velocity m Exp eriments in Fluids vol. 49, no. 1, pp. 305 317, Apr. 2010. [42] J. S. Bendat and A. G. Piersol, Random Da ta : Analysis and Measurement Procedures 4 th Edition Hoboken, NJ, USA: John Wiley & Sons Inc., 2010. [43] S. Pope, Turbulent flows Cambridge, United Kingdom: Cambridge University Press 2000. [44] G. E. Torres and T. J. AIAA Journal vol. 42, no. 5, May 2004. [45] Y. C. Liu and F. Aspect Ratio Thin Journal of Mechanics vol. 28, no. 01, pp. 77 89, Mar. 2012. [46] R. L. Panton, Incompressible flow 3 rd Edition Hoboken, NJ, USA: John Wiley & Sons Inc., 200 5 [47] AIAA 51th Aerospace Sciences Meeting pp. 1 17, Jan. 2013. [48] and simulations of the vortex structures generated by low aspect ratio plunging Phys ics of Fluids vol. 25, no. 6, June 2013. [49] ow of Air behind an Inclined Flat Plate of Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences v ol. 116, no. 773, pp. 170 197, Sep. 1927.

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87 [50 ] H. W. Coleman and W. G. Steele, Experimenta tion, Validation, and Uncertainty A nalysis for E ngineers 3 rd Edition Hoboken, NJ, USA: John Wiley & Sons Inc., 2009.

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88 BIOGRAPHICAL SKETCH As a child Alex Arce was always interested in the way thing s operated This resulted in discussion s a part you r toys ? want to know how it work s interest continued to follow Alex all the way through high school. After graduating Alex enroll ed in an auto mechanic tr ade school At the end of the 14 months of training he graduated and obtained a job at an auto collision repair shop. During this time Alex enjoyed working on automobiles however he completely convinced this was the lifestyle he wanted. Alex contin ued working while he enrolled at a local community college where he earned his Associate of Arts degree. Upon completion in 2008, Alex was accepted to the University of Florida as a transfer student within the mechanical and a erospace department During hi novice rowing team, where later he th e n joined the varsity team. In the beginning of his senior year Alex decided to volunteer his free time in a fluids lab. After a few months he was offered an undergraduate research position, this is where he started to find a n appreciation for research In fall 2011, Alex graduated with a dual Bachelor of Science in both m echanical and aerospace e ngineering In spring 2012 he started his graduate degree u nder the guidance of Dr. Lawrence Ukeiley Alex continues to conduct research and expects to graduate with a M aster of Science in a erospace e ngineering in December 2013.