Flow and Structure Interactions of Membrane Wings at Low Reynolds Number

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Flow and Structure Interactions of Membrane Wings at Low Reynolds Number
Timpe, Amory W
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[Gainesville, Fla.]
University of Florida
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1 online resource (112 p.)

Thesis/Dissertation Information

Master's ( M.S.)
Degree Grantor:
University of Florida
Degree Disciplines:
Aerospace Engineering
Mechanical and Aerospace Engineering
Committee Chair:
Ukeiley, Lawrence S.
Committee Members:
Cattafesta Iii, Louis N
Ifju, Peter
Graduation Date:


Subjects / Keywords:
Aerodynamics ( jstor )
Aircraft wings ( jstor )
Modeling ( jstor )
Momentum ( jstor )
Near wakes ( jstor )
Pixels ( jstor )
Shear layers ( jstor )
Velocity ( jstor )
Vibration ( jstor )
Vorticity ( jstor )
Mechanical and Aerospace Engineering -- Dissertations, Academic -- UF
compliant -- dic -- flexible -- fluid-structure -- fsi -- mav -- membrane -- piv -- reynolds -- wing
bibliography ( marcgt )
theses ( marcgt )
government publication (state, provincial, terriorial, dependent) ( marcgt )
born-digital ( sobekcm )
Electronic Thesis or Dissertation
Aerospace Engineering thesis, M.S.


The inherent challenges associated with low Reynolds number flight have stemmed biologically inspired wing designs incorporating highly flexible membranes. Natural membrane wing flyers demonstrate advantages of passive flexibility, showing extremely stable and agile flight. Much of the flow and structure dynamics and how they are coupled, however, remain largely unknown. This work discusses an experimental effort to study the fluid-structure interactions of flexible membrane wings at low Reynolds number by synchronized acquisition of Particle Image Velocimetry and Digital Image Correlation. The membrane wings are batten-reinforced flat plates with multi-cell, scalloped membrane sections similar to some micro air vehicle designs. The data analyzed in this research consists of time-resolved, two-component flow measurements over the model/membrane surface as well as in the near wake, and three dimensional membrane displacement measurements. The flow over a baseline rigid flat-plate is included to compare time-averaged flow properties and investigate how the membrane wings alter the flow for possible aerodynamic advantage. A collaborative and parallel force study was performed on identical wings and some results are incorporated. Membrane wing models of varying pre-tension, created through a membrane heating process, were employed in the investigation to better understand how tension affects the flow behavior, frequency response, and flexibility of compliant wings. The time-dependent dynamics of velocity and membrane vibrations indicate that membrane fluctuations have a strong influence on the surrounding flow, affecting the shear layer emanating from the wings’ leading-edge and the development of the flow in the models’ near wake. Membrane oscillations are shown to manipulate the flow causing enhanced turbulent characteristics and favorable mean flow fields. Spectral and correlation analysis show quantitative evidence of membrane vibrations driving flow behavior both over the wing and in its wake. ( en )
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Thesis (M.S.)--University of Florida, 2012.
Adviser: Ukeiley, Lawrence S.
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by Amory W Timpe.

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2 2012 Amory W. Timpe


3 To my mother father sister and brother


4 ACKNOWLEDGMENTS Foremost, I would like to thank my advisor Dr. Larry Ukeiley for providing me with an opportunity to study and research at the University of Florida : Research and Engineering Education Facility (UF REEF); for his direction, guidance, teachings, and insight Thanks are also extended to my committee members, Dr. Lou Cattafesta and Dr. Peter Ifju for their support a nd input throughout. T o my colleagues and friends at REEF I am very appreciative; t his work would not be possible without their academic and recreational support. Particular thanks to fellow members of the REE F Unsteady Fluid Dynamics Group: Adam Hart, T aylor Lusk, Erik Sl l strm, and office mate Diego Campos for the ir camaraderie and many great discussions, both inside and outside of research Additional thanks to Zheng Zhang and Alex Arce for assistance with setup and acquisition during experiments I w ould like to acknowledge the work of Yaakov Abud a rarm a colleague and friend who also created the membrane portions of models tested and Dr. Pin Wu who assisted in developing the methods used for synchronized experiments The guidance of Dr. James P. Hub ner at the University of Alabama is also greatly appreciated. I enjoyed the collaboration of this project supported by the Air Force Office of Scientific Research (Grant FA9550 10 1 0152) under program manager Dr. Doug Smith and by the Florida Center for Advanced Aero Propulsion (FCAAP) Finally, I acknowledge the love and support of my family who have provided me with the strength and encouragement to overcome the challenges endured in research and in life.


5 TABLE OF CONTENTS page ACKNOWLEDGMENTS ................................ ................................ ................................ .. 4 LIST OF TABLES ................................ ................................ ................................ ............ 7 LIST OF FIGURES ................................ ................................ ................................ .......... 8 LI ST OF ABBREVIATIONS ................................ ................................ ........................... 11 ABSTRACT ................................ ................................ ................................ ................... 13 CHAPTER 1 INTRODUCTION ................................ ................................ ................................ .... 15 Motiva tion for Research ................................ ................................ .......................... 15 ................................ ................................ ................. 16 Research Background ................................ ................................ ............................ 17 Perimeter Reinforced Membranes ................................ ................................ ... 19 Batten Reinforced Membranes ................................ ................................ ......... 21 Free trailing edge behavior ................................ ................................ ........ 22 Precursor studies ................................ ................................ ....................... 23 The Present Research ................................ ................................ ............................ 24 2 EXPERIMENTS ................................ ................................ ................................ ...... 26 Facilities and Instrumentation ................................ ................................ ................. 26 Aerodynamic Characterization Facility ................................ ............................. 26 PIV System and Processin g Details ................................ ................................ 27 PIV processing ................................ ................................ ........................... 27 Camera arrangement ................................ ................................ ................. 28 Flow seeding ................................ ................................ .............................. 28 Stereo DIC System and Processing Details ................................ ..................... 31 Procedure and lighting ................................ ................................ ............... 31 DIC processing ................................ ................................ .......................... 32 Synchronization of PIV and DIC Systems ................................ ............................... 34 Membrane Models ................................ ................................ ................................ .. 36 Experiments Performed ................................ ................................ .......................... 39 Synchronized PIV and DIC Tests ................................ ................................ ..... 40 Independent DIC Measurements ................................ ................................ ...... 42 PIV Measurements of 80x80_2.8 Wing ................................ ........................... 43 Post Processing/Analysis ................................ ................................ ........................ 44 Dynamic Masking Algorithm ................................ ................................ ................... 44


6 3 RESULTS ................................ ................................ ................................ ............... 47 Velocity Measurements ................................ ................................ ........................... 47 Time Averaged Velocity Fields ................................ ................................ ......... 48 Streamwise velocity at low aoa ................................ ................................ .. 48 Streamwise velocity at high aoa ................................ ................................ 50 Root Mean Square Velocity Fluctuations ................................ ......................... 52 Streamwise velocity fluctuations ................................ ................................ 5 2 Vertical velocity fluctuations ................................ ................................ ....... 54 Reynolds Sh ear Stress ................................ ................................ ..................... 55 Membrane Oscillation Behavior ................................ ................................ .............. 58 Full Field Mean and RMS Properties ................................ ............................... 59 Pointwise mean and rms properties ................................ ........................... 61 Time averaged camber effect ................................ ................................ .... 62 Membrane Frequency Content ................................ ................................ ......... 62 Fluid Structure Interactions ................................ ................................ ..................... 65 Trailing Edge Vorticity Interaction ................................ ................................ ..... 65 Flow and M embrane Coupled Behaviors ................................ ......................... 69 Spectral analysis applied to flows ................................ .............................. 69 Correlation analysis ................................ ................................ ................... 70 4 CONCLUSIONS AND FUTURE WORK ................................ ................................ 98 Summary ................................ ................................ ................................ ................ 98 Future ................................ ................................ ................................ ................... 101 APPENDIX : D YNAMIC M ASKING ................................ ................................ .............. 102 LIST OF REFERENCES ................................ ................................ ............................. 106 BIOGRAPHICAL SKETCH ................................ ................................ .......................... 112


7 LIST O F TABLES Table page 2 1 Model dimension values ................................ ................................ ..................... 38 2 2 Silicone material properties ................................ ................................ ................ 38 2 3 Membrane model properties ................................ ................................ ............... 38 2 4 Dat a types acquired for each model ................................ ................................ ... 39 3 1 Estimated proportionali ty constant and natural frequency ................................ .. 72


8 LIST OF FIGURES Figure page 1 1 Low Re membrane wing flyers ................................ ................................ ........... 25 1 2 Example of lufting during LV and hotwire tests ................................ ................... 25 2 1 ACF, low speed wind tunnel ................................ ................................ ............... 27 2 2 PIV dual camera setup a nd seed disperser ................................ ........................ 30 2 3 ................................ ................................ 30 2 4 Installed DIC system and speckled model ................................ .......................... 32 2 5 Cartesian coordinate system used with both PIV and DIC data results. ............. 33 2 6 DIC images and PIV laser interference ................................ .............................. 35 2 7 TR PIV & DIC systems with model installed for synchronized data acquis i tion .. 35 2 8 BR Silicone membrane wing models with scalloped trailing edges .................... 37 2 9 Model schematic with dimensions ................................ ................................ ...... 37 2 10 Measured pre strain vs. creation temperature ................................ .................... 38 2 11 Convergence of PIV statistics vs. sample count ................................ ................. 41 2 12 Synchronous acquisition of PIV and DIC data ................................ .................... 42 2 13 Symmetric airfoil standoff mounts with 80x80_2.8 ................................ 43 2 14 Combined instantaneous PIV and DIC at center span ................................ ....... 46 3 1 contours with strea mlines for baseline rigid plate ............................. 73 3 2 ......................... 74 3 3 Umean/ ......................... 75 3 4 ................................ ............. 76 3 5 e plots at x/c = 0.3, 1.4 for high aoa ................................ ............ 77 3 6 wings at low aoa. ................................ ................ 78 3 7 s at high aoa. ................................ ............... 79


9 3 8 s at low aoa. ................................ ................ 80 3 9 s at high aoa. ................................ ............... 81 3 10 wings at low aoa. ................................ ............... 82 3 11 s at high aoa. ................................ .............. 83 3 13 ................... 84 3 14 Indication of mid point, side point, and TE point on 1.3 =8 mean plot. ........ 85 3 15 Mid Point mean and RMS deformation behavior vs. aoa ................................ .... 85 3 16 TE Point mean and RMS deformation behavior vs. aoa ................................ ..... 86 3 17 Time sweep ..... 87 3 18 PSD computed from membrane Mid, Side, and TE Points ................................ 87 3 19 Spectral content portraying unique behavior of high pre tension 4.2 wing. ....... 88 3 20 ................................ ........................... 88 3 21 .............. 89 3 22 Normalized instantaneous vorticity, *, with streamlines .................... 90 3 23 .................. 91 3 24 .................. 92 3 25 .................. 93 3 26 ................ 94 3 27 ............. 95 3 28 Correlation coefficient compute ............. 96 3 29 Cross correlation, indicating periodic nature of the correlation values ....... 97 A 1 2 nd ................................ ................... 102 A 2 Polynomial line tracking bright pixel membrane shape. ................................ .... 103 A 3 Example ma sk where membrane resides ................................ ......................... 103 A 4 2 nd ........................ 104


10 A 5 Blurred image after convolutio n with 7x7 mean filter. ................................ ....... 105 A 6 Example mask generated for dark regions. ................................ ...................... 105


11 LIST OF ABBREVIATION S ACF Aerodynamic Characterization Facility a o a Angle of A ttack APG Adverse Pressure Gradient AR Aspect Ratio BR Batten Reinforced CMOS Complementary Metal Oxide Semiconductor DFT Discret e Fourier Transform DIC Digital Image Correlation FFT Fast Fourier Transform FOV Field of View FSI Fluid Structure Interaction (s) IA Interrogation Area L/D Lift/Drag; Aerodynamic Efficiency LCO Limit Cycle Oscillation LE/TE Leading Edge/Trailing Edge MAV(s) Micro Air Vehicle(s) PIV Particle Image Velocimetry POD Proper Orthogonal Decomposition PR Perimeter Reinforced PSD Power Sp ectral Density Re Reynolds Numbe r REEF Research and Engineering Education Facility RSS Reynolds Shear Stress St Strouhal N umber


12 TKE Turbulent Kinetic Energy TR Time Resolved UA University of Alabama UF University of Florida We Weber Number 1D One Dimension al 2D Two Dimensional 3D Three Dimensional


13 Abstract of Thesis Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Master of Science FLOW AND STRUC T U RE INTERACTI ONS OF MEMBRANE WINGS AT LOW REYNOLDS NUMBER By Amory W. Timpe May 2012 Chair: Lawrence S. Ukeiley Major: Aerospace Engineering The inherent challenges associated with low Reynolds number flight have stemmed biologically inspired wing designs incorporat ing highly flexible membranes. Natural membrane wing flyers demonstrate advantages of passive flexibility, showing extremely stable and agile flight. Much of the flow and structure dynamics and how they are coupled however, remain largely unknown. This wo rk discusses an experimental effort to study the fluid structure interactions of flexible membrane wings at low Reynolds number by synchronized acquisition of Particle Image Velocimetry and Digital Image Correlation. The membrane wings are batten reinforce d flat plates with multi cell, scalloped membrane sections similar to some micro air vehicle designs. The data analyzed in this research consists of time resolved, two component flow measurements over the model/membrane surface as well as in the near wake and three dimensional membrane displacement measurements. The flow over a baseline rigid flat plate is included to compare time averaged flow properties and investigate how t he membrane wings alter the flow for possible aerodynamic advantage A collaborat ive and parallel force study was performed on identical wings and some results are incorporated.


14 M embrane wing models of varying pre tension created through a membrane heating process, were employed in the investigation to better understand how tension affects the flow behavior, frequency response and flexibility of compliant wings. The time dependent dynamics of velocity and membrane vibrations indicate that membrane fluctuations have a strong influence on the surrounding flow, affecting the shear laye r em edge and the development of the flow in the near wake. Membrane oscillations are shown to manipulate the flow causing enhanced turbulent characteristics and favorable mean flow fields. Spectral and correlation an alysis show quantitative evidence of membrane vibrations driving flow behavior both over the wing and in its wake


15 CHAPTER 1 I NTRODUCTION Motivation for Research Passive and flexible lifting surfaces have been u tilized in the planforms of many flight syste ms including: Micro Air Vehicles ( MAVs ) hang gliders, paragliders, microlight wings, sails and power kites where the flexibility and passive shape adaption have demonstrated significant performance advantages [ 1 ] [ 7 ] The underlying p hysics of the fluid structure interactions, the nature of the surrounding flow and of the al vibrations, their coupled aero elastic behavior and the effects of pre tension are all key aspects that are currently being studied Much of the inspira tion for implementation of these flexible membranes and materials comes from observed biological systems with adaptive wings performing extremely agile flight and maintaining stability in turbulent and gusty conditions [ 8 ] [ 12 ] The use of flexibility in natural flyers is in particular found for those flying in the low Re ynolds number (Re) regime ranging from 10 4 through 10 5 based on chord length like various species of insects, bats and small birds [ 11 ], [ 13 ] The fluid structure interactions (FSI) are significantly different and advantageous in this regime as compared with those of more understo od high Re systems often the cause of detrimental effects A better understanding of the low Re FSI is desired. There are numerous challenges to biological and manmade flight systems operating at low Re The oncoming flow encountering the wing or planform has less initial momentum and easily separates from shearing and in the presence of a typical adverse pressure gradient (APG) aft of the wing leading edge (LE) T he separating flow can rapidly transition to turbulence and sometimes reattach as a turbulen t boundary


16 layer forming a closed region of separation designated as a separation bubble [ 15 ] This LE separation is in contrast to the trailing edge (TE) separation that is seen for airf oils of high Re systems T he phenomen on is exacerbated by the typically thin wings (minimizing weight) and sharp leading edges of low Re flyers [ 14 ] The presence of a separation bubble causes reduced lift and increas ed drag by altering the pressure distribution and changing the effective thickness and shape of the airfoil [ 15 ] ; therefore it is paramount to minimiz e the size or presence of a bubble for efficient flight [ 16 ] [ 18 ] Additional challenges include the low mass and inertia of the characteristically small and slow flying (10 20 m/s) vehicle or natural flyer as well as the turbulent low altitude flight conditions and wind gusts on the order of flight speed Also, the need for sufficient lifting planform surface area while constrained to a small total wingspan leads to low aspect ratios (ARs), which are susceptible to highly three dimensional effects and roll instabilities [ 19 ] These combined challenges easily lea d to unstable flight. It is through the use of adaptable and flexible lifting surfaces that many of these obstacl es can be overcome E xamples of manmade and biological low Re flyers that benefit from compliant wings can be seen in Figure 1 1 T he major aim of this research is to increase the knowledge and understanding of low Re flo w around membrane wing s and to experimentally characterize the fluid structure interaction s by novel implementation of synchronized Particle Image Velocimetry (PIV) and Digital Image Correlation (DIC) acquisition techniques Membrane s A Circ a 1995 the Defense Advanced Research Projects Agency (DARPA) provided a definition and vision for the MAV I t would be smaller than six inches (15 cm) in total wingspan, be easily deployable, and utilize autonomous navigation [ 20 ] Primarily as a


17 reconnaissance and sensing device, the vehicle would need to be as stable and adaptable to adverse flight conditions as possible [ 21 ], [ 22 ] Thus, after one hundred years of technological development of human flight (even spaceflight), the field of aerodynamics was pursuing extensive knowledge/designs in the envelope where nature h ad pioneered flight for millennia [ 23 ] The challenge would be met by many research institutions and governments worldwide and over a period of ten or so years, through intuition and mostly ad hoc me thods, capable MAVs were created [ 24 ] [ 26 ] This excerpt from an early MAV designer describes the difficult and i terative nature of the design/test processes while creating a working vehicle: controls checked, and then the MAV would be launched into the air by hand. The pilot would then attempt to keep the MAV in the air. All present parties would keep strict attention on the plane in order to diagnose any problems. Most free flight tests only last 2 seconds. Free flights were a very iterative process [ 27 ] As MAV development evolved, bio inspired systems were created using lightweight composite materials with flexible wing frames and latex membr anes as part of the lifting surface, pioneered at the University of Florida [ 28 ], [ 29 ] In addition to being extremely light, it was discovered that the use of flexible frames and membrane wings produc ed benefits like gust alleviation, adaptive washout, adaptive camber, geometric twisting, and delayed stall [ 1 ], [ 2 ] Through detailed study of low Re aeroelastic FSI, efficient and stable vehicles or wings could be designed smarter, specifically tailored, and m ore robustly so. Research Background W ork by Smith and Shyy (1996) investigat ed flexible membrane airfoil behavior built upon the earlier works of Thwaites, Nielsen, and others [ 30 ] [ 33 ] This lead to the


18 defin ition of membrane aeroelastic stiffness 1 2 which account for Def ined in Eqs. 1 1 and 1 2 1 is used with untensioned membranes, while 2 account s for pre tension [ 34 ] In these equations, E is the elastic modulus, 0 S is the membrane pre stress nominal pre tension is: T 0 = ( 0 while is % pre strain, t is the membrane c ell span, and is the dynamic pressure based on free stream velocity. (1 1) (1 2) In 20 03 Lian, Shyy and coworkers produced a seminal pa per laying the foundation for coupled flow and structure computational solvers and utiliz ed Proper Orthogonal Decomposition (POD) techniques to identify flow structures from the numerical results They note d the self initiated vibration of membrane wings that would be a subject of much further investigation [ 1 ] A group from Brown University including Song, Tian, Swartz, Bishop and Breuer ( et al. ) focused specifical ly on biological membrane flyers /gliders such as bats, flying squirrels, and sugar gliders ; noting the extremely high angles of attack (aoa; ) often observed ( > 30) and associated delay in stall exhibited by membrane wings The i r work has also focuse d on the importance of Weber number (We), which they define as t he ratio of aerodynamic forces to membrane stiffness as in Eq. 1 3 and appears very similar in form to the inverse of Smith and Shyy 1 & 2 parameter s from E q s 1 1 & 1 2 incorporating coefficient of lift, In some of their work pre strain was shown to impro v e aerodynamic efficiency pre stall I t was theorized that the articulating joints connected to flight surfaces of flying squirrels


19 and bats which allow ed altered membrane tension or LE shape during flight, were morphological adaptations t o take full advantage of such effects. [ 9 ], [ 11 ], [ 35 ] [ 37 ] (1 3) Once fully understood, in flight (or pre flight) alterations to membrane tension or shape in addition to the passive control could optimize the performance of manmade systems. Arbos Torrent et al. showed that small changes in LE and TE shape (flat, round) or size c an significantly affect the maximum camber and wake shedding or deficit characteristics for compli ant wings Small flat geometry seemed optimal over the 22 ) [ 38 ] Much of the work on membrane wings has been divided into two groups, depending on whether the membrane is secured to framing on all edges (perimeter reinforcement, PR) or if it has batten support and a free trailin g edge (batten reinforcement, BR). While much of the FSI and physics will be similar for any vibrating membrane configuration, planform lift and drag coefficients can differ, vibration modes will differ, and the system dynamics can be affected by attachmen t type Perimeter Reinforced Membranes Rojratsirikul, Wang, and Gursul have performed a series of studies on two dimensional then low AR latex membrane airfoils ; attaching the membrane s to rigid leading and trailing edges. They used force data and high s peed PIV to try and characterize the unsteady FSI varying Re (53, 80, 106 k ) and aoa (9 30 ) also using laser reflection and independent DIC to study membrane shapes and modes. Notable conclusions included that the membrane unsteady oscillations provide d a form of passive flow control, delaying stall compared with rigid airfoils cambered to the time


20 averaged membrane shape, and that oscillations coupled with unsteady behavior in the shear layer as well as possibly with wake vortex shedding [ 5 ], [ 39 ] Another of t heir investigations include d 2D membrane s with pre strain ( = 0, 2.5, 5%) and excess length factors where excess length is the opposite of pre strain; reporting that pre strain showed behavior similar to that of a rigid model, while excess length could reduce the amount of flow separation and induce vortex roll up [ 40 ] Gordnier and Visbal used a 6 th order Implicit LES aerodynamic solver coupled to a nonlinea r finite element (membrane displacement) solver to numerically model the FSI for the same membrane as in the Gursul studies at 8 and 14 aoa. They reported reasonable qualitative correspondence with the experimental results when sufficient grid resolution was used, capturing vortex shedding from the leading edge, vortex roll up in the shear layer and coupling of shedding with the structural vibration behavior [ 41 ] Additional coupled viscous flow numerical solvers were performed by Tiomkin, Raveh, and Arieli for 2D membrane with parameters of p re tension, Re, and membrane slack. They found that pre tension, excess length ( slack ) and elasticity did not have a major effect on the Strouhal number (St) of shedding but pre tension and aoa did significantly affect the amount of camber and location of maximal camber [ 42 ] A recent work by Gordnier and Attar detailing aeroelastic simulations of an AR = 2 flexible membrane wing with 3D effects at 16 aoa, (corresponding to the low AR experiments of Gursul et al.) showed enhanced lift and reduced separation but overall the aerodynamic efficiency ( L/D ) was less for the membran e wing than for the rigid wing [ 43 ] Although there has been reasonable agreement between experimental work a nd simulations, additional experiments are necessary as parameters such as Re, sharp vs.


21 rounded LE, and AR in addition to attachment style all show significant impact on the FSI behavior. A final recent study by Tregidgo, Wang, and Gursul (2011) at Univer sity of Bath employed independent force measurements, DIC, and PIV to further study low AR membrane wings at low Re (46 k ) sweep (0 25 by 1 ) They reported s trong tip effects which perhaps caused enhanced lift coefficients F ourier analysis of the membrane oscillations revealed regimes of specific modal vibration characteristics and a low frequency spanwise beating existed at high aoa, which was speculated to possibly cause roll instability The beating may have been associated with wing tip vorticity impingement [ 44 ] A common th eme amongst PR membrane wings is modal and beating vibrati on behavior, a 1D relation might be standing waves and nodes for a string fixed at both ends ; while the effects on control and stability are topics of further research Batten Reinforced Membr anes Tamai, Murphy, and Hu of Iowa State University (2008) did a study of the FSI for BR membrane wings (free TE) in the low Re regime, utilizing PIV. The study investigated the effects of batten spacing (1, 2, 3, and 10 battens, fixed span) Like other st udies, they found that membrane models out performed the rigid model in L/D by passive shape adaption changing the effective aoa relieving the APG on the model top surface and resist ing separation while delaying stall. It was noted that membrane stiffnes s and batten spacing are significant parameter s for performance because high flexibility wa s needed for optimal benefits, but a n overly slack free trailing edge would also known as TE flip, lufting and flapping, w hen occurring would cause increased drag and redu ced lift degrading aerodynamic performance [ 45 ]


22 Free trailing edge behavior Some discus sion is needed about the vibra tion behavior of a BR membrane which has a free TE. Starting with the basic physics, the membrane will have a resting tension value (pre tensioned or not) that should be roughly symmetric in the spanwise direction while highe r near the LE attachment and lower at the free TE in the chordwise direction This creates an area of lowest tension at the TE. When in a flow the aerodynamic pressure forces will act on the membrane surfaces and if strong enough will cause distention, wh ich increases the tension and causes an elastic response. The membrane response velocity carries inertial forces which interact further with the unsteady pressure forces and tension; therefore a vibration pattern sets up. Vibrations were found to be small below an onset velocity after which a self sustained instability occurs due to underdamping in the system At this point oscillation spectral energy increases by two orders studied by Scott and Hubner et al. [ 46 ] but was not a focus of this research. T he oscillations after onset are wave like in natu re and nearly periodic. The 1D relation mig ht be close to a vibrating string with a free end, while this would fail to account for the nonlinearities in the system and dynamic ( pressure ) driving forces. These motions were described as initiated vibra Shyy (2003) and later described as Hopf Bifurcation into Limit Cycle Oscillation s (LCO s ) in the works by Johnston, Romberg, Attar, Parthasarathy, and Gordnier (2010, 2011) [ 47 ], [ 48 ] e xplicitly studying the motions for varying pre strains ( = 2, 5, 7, 10 %) and fixed geometry If the membrane trailing edge is not highly pre tensioned, it easily yields to pressure and iner tial forces and an out of phase and chaotic behavior can exist. These flapping, w hip like motions at the TE described as by Johnston et al.


23 hinder aerodynamic performance In this work the phenomena wi ll be called ufting and is portrayed in Figure 1 2 P recurso r studies There has been a direct line of studies leading to this work, which were performed by researchers at the University of Alabama (UA) and the U niv ersity of Florida (UF) Mastramico and Hubner used hot wire anemometry to investigate the wake characteristics (width, momentum deficit, spectral energy) of thin, flat and cambered plates with high AR and repeating membrane cells, BR and PR versions. PR mo dels often showed broadest wake s while both BR and PR models had larger drag with narrowest and least deficit velocity, as to minimize drag, were seen for those models that had batten reinforc ed and scalloped membranes (BR S) [ 49 ] Scalloping the free TE ( similar to bat wing s, Fig ure 1 1 C ) remov es the lowest tensioned portion of the membrane cells and reduces or eliminates the deleterious lufting, discussed previous ly Hubner and Hicks performed a study on s calloping depth (12.5, 25, 37.5 % of cell span) as well as membrane cell size (cell AR = 1, 0.75, 0.5 ) to find which showed the most aerodynamically efficient lif t to drag characteristics for high aspect ratio flat plate membrane wings at low Re (<61,000). Of the tested geometries, efficiency was best for membrane cells of AR = 1, with a 25% o f cell span scallop [ 50 ] While much was learned from flow visualization force measurements, and the poi ntwise techniques of hotwire and laser vibrometry (Fig ure 1 2 ) more expansive understanding required further detailed investigation.


24 The Present R esearch This e ffort will seek to gain more insight into the FSI by expan ding to full field time resolved and synchronized flow and membrane measurements The flow data will be obtained by high speed PIV and s imultaneously, the spatially and temporally resolved 3D motions of the membrane will be captured by DIC. Synchronizati on of the two systems was a major aim to directly visualize, study, and correlate membrane and flow behavior. T he steady and unsteady FSI of flow surrounding membranes; and how structural vibrations permeate to, interact with, or otherwise influence the fl ow in a time dependent nature will be discussed. Overall, a n experimental investigation to characterize the flow and structure behavior including time averaged and dynamic responses for batten reinforced scalloped membrane wings of varying pre te nsion is presented with comparisons to a baseline flat plate Wings were created with improved membrane material (silicone) and aerodynamically beneficial geometries derived from precursor studies [ 46 ], [ 49 ], [ 50 ] Reliable pre tensioning of the silicone membranes is prescribed through a heatin g technique [ 51 ] A method is developed for su ccessful a cquisition of s ynchronized high speed PIV and DIC systems. Chapter 2 will discuss the experimental facilities and equipment used; processing details, synchronization methods; a long with various aspects of th e specific experiment s performed Results of flow field measurements structural behavior and the fluid structure interactions will be discussed and presented in Chapter 3 Ultimately, Chapter 4 will draw some conclusions and include a discussion of future directions for this research


25 A B C Figure 1 1 Low Re m embrane w ing f lyers A) PR MAV B) B R MAV C) Bat (Source s : A,B: [ 2 ] C: ) Figure 1 2 Example of lufting during LV and hotwire tests performed at UF in collaboration with UA.


26 CHAPTER 2 EXPERIMENTS The following chapter provides details of the experimental facilities testing equipment models tested, experiments conducted, and processing It shall describe precisely how experiments were set up and performed. A description of the experim ental f acilities and testing e quipment utilized along with details of how data wa s processed is included There will also be a di scussion of how models used for testing were created, the ir geometric details and in which experiments each was involved. Fac ilities and Instrumentation Aerodynamic Characterization Facility (ACF) which is a wind tunnel specifically designed for the study of low Reynolds number fluid structure interacti on problems Aerodynamic Characterization Facility The ACF is a suction style wind tunnel with an open jet test section and an open return air path It is designed specifically to create a low turbulence environment with steady flow in the range of appr oximately 1 to 20 m/s, ideal for low Re research. The air is driven by a 37.3 kW, 1.52 m diameter axial blower combined with a variable frequency drive Turbulence is minimized by straightening the flow after it passes through the bell mouth entrance with a metal honeycomb and multiple settling screens After conditioning the flow there is a settling chamber an d then the flow passes through an 8:1 are a ratio contraction. Once contracted, the flow enters the open jet test section as a 1.07 m by 1.07 m squar e jet and the test sect ion itself is 3.05 m in length. The jet test section is housed in an enclosure (3. 7 m by 4.6 m by 3. 4 m, w x l x h) Photographs of the ACF are included in Figure 2 1 At the working velocity of 10 m/s and near to the


27 jet inlet, the flow has been characterized with a potential core of 9 0% of the inlet contracted exit area and with a turbulence intensity, of 0.16%. Albertani et al. provide s a more thorough analysis of the ACF [ 52 ] A B C Figure 2 1. ACF, low speed wind tunnel. A) External View. B) Jet Exhaust C) D iffuser/Blower. PIV System and Processing Details A Dantec Dynamics time resolved (TR) particle image velocimetry system was used to acquire the flow field measurements during experi ments. Images were obtained by a pair of IDT XS 5 high speed CMOS cameras (Fig ure 2 2 A ) each equipped with Sigma EX 105 mm f length macro lenses set to f/# 2.8, and 2GB of onboard memory. The PIV system also consisted of a Lee Laser Series 800 double cavity Nd:YAG laser set to a w avelength of 5 32 nm. The laser has 6kW of power, providing 1.35 mJ/pulse. In general, the PIV system could sample double frames at a rate from 500 to 1000 Hz, limited by the speed of the cameras and at what pixel resolution the images were set to Dantec Dynam ic Studio v3.10 software was used to operate and control the system as well as to process the images. PIV p rocessing Vector fields were generated through a multi step process. The raw images were first acquired ; then a noise background image wa s created by sampling 50 images with


28 the lens caps on and taking the average The background image was then subtracted from each image of the data set s. This help ed reduce the CMOS sensor noise noise b ackground images were created as needed to adjust for temperature over time. The image sets ( with noise background removed ) were then processed by a four step, adaptive windowing correlation technique ; each refinement using 2 pa sses and reducing the interrogation area (IA) size T went from 128 by 128 pixels to a final step of 16 by 16 pixels The algorithm utilized a central difference IA offset scheme and 25% region overlap C amera arrangement The cameras were set up su ch that tw o fields of view (FOV ) were u tilized in 2D PIV fashion. O ne camera using a slightly smaller FOV w as focused over the membrane /model for improved detail and accuracy near the model surface T he second camera with a slightly larger FOV, w as focu sed on the model near wake; also slightly overlap ping s provided vector spatial resolutions of: 1.24 vectors/mm for the model camera and 0.92 vectors/mm for the wake camera. Figure 2 3 portrays the camera fields of view during acquisition including two separate experiments; one performed later, in which the seeding technique was improved Flow s eeding The seed particles used to track the flow were generated by an ATI Technologies tda 4B aerosol generator. The Laskin nozzles housed within the generator atomized olive oil into particles of diameter 1 d p as quoted by ATI. assumption for very small diameter spheres where p f ( f repr esents fluid density


29 for air f 1.2 0 kg/m 3 while p is the particle density p 970 kg/m 3 ), the relaxation time of these olive oil particles can be defined as Eq. 2 1 [ 53 ] R elaxation time defines how quickly the particles can respond to changes in the flow. Using = 1. 75 E 5 kg/m s for air (70 C) r is found as 2 8 E 5 s ( order of kHz ) which agrees well with Str mungsmechanik [ 54 ] This means the se small particles respond to the flow tendencies well and satisfactory for flow scales under investigat ion ( 2 1 ) W hen using very small particles the particle diameter at the image plane (effective particle size, d e ,) is important. Diffraction will cause the reflected light to spread as an Airy disk and this diffraction limited p article size, d s is defined as in Eq. 2 2 The effective particle size d e can be found as Eq. 2 3 [ 55 ] where M was the lens magnification (0.16 on average for these experiment s) ( 2 2 ) (2 3) In these experiments the diffraction limited spot size dominated ( d e d s ) and was calculated by Eqs. 2 2 and 2 3 as 4.3 m, approximately 1/3 the size of a pixel (12 ) The low lens f/# of 2.8 could not be avoided as to allow enough light to the sensor s while actual PIV images showed particle sizes generally on the order of 1 2 pixels T he PIV acqui sition required r elatively dense seeding to obtai n effective light intensity with the time resolved system and to allow for the desired 16 by 16 pixel s In one set of experiments the seed issued from a 3 81 c m diameter tube creating the necessarily d ense seed ing although the seed volume was found that it could sway partially in the wake cameras FOV. I n a later experiment a seed disperser was created (30.5 cm by 30.5 cm) with patterned exit ports spaced throughout PVC tube framing to


30 improve the disp ersion (Fig ure 2 2 B ) The disperser create d more uniform and still dense enough seeding over a larger volume. A B Figure 2 2. PIV dual camera setup and seed disperser. A) High s peed PIV c ameras oriented in 2D fashi on, c amera 1 is focused over the membrane/ model, while c amera 2 is focused on the near wake. B) Seed disperser for larger volume of more uniform seeding. A B Figure 2 3 PIV images showing c ombined FOV s : membrane/model camera and wake camera. A) 1.3 model (inverted) at 12 aoa denser seed B) 2.8 model (inverted) at 16 aoa dispersed seed


31 Stereo DIC System and Processing Details The method of Digital Image Correlation was used to capture the 3D membrane deformation measurements The DIC system was provided by Correlated Solutions and consisted of cameras and computer software to acquire and process images Images were acquired by two VisionResearch high speed Phantom v7.1 SR CMOS cameras which were oriented in stereo fashion each focusing on the same FOV from opposing angles The Phantom cameras had a maximum frame rate of 4800 Hz at the full resolution of 800 pixels x 600 pixels and were equipped with Tamron aspherical 28 300 mm f length macro lenses set t o f/# 5.6. The Correlated Solutions 3D 2006 software, along with Vic Snap and Phantom Camera Control v675.2 were used to acquire images, calibrate, and process Procedure and lighting S tereo calibration s were performed by taking ~100 imag es of a spatial calibration target of known dimensions while it wa s rotated, translated, and maneuvered in the field of view. The calibration images we re processed with the Vic 3D software to discover the triangulation parameters needed such that three dim ensional membrane displacements c ould be resolved To perform the DIC, a small amount of paint was used to create a random speckle pat tern o n the membrane surfaces of interest (Fig ure 2 4 B ) Light reflected from the spec kled patterns is ultimately used for gray scale correlation analysis and therefore, p roper lighting wa s an important aspect of obtaining DIC data. For these experiments, a high powered (250W) halogen light wa s shown onto the membrane surface s to provide su fficient reflection back to the camera sensor s During testing the aoa of the models we re changed which would also affect how light was reflected. Therefore, the cameras


32 were refocused and recalibrated as was necessary to obtain reliable data for desired aoa sweeps. Figure 2 4 A provides a view of the system as used for indep en dent DIC tests in the ACF B A Figure 2 4 Installed DIC s ystem and s peckled m odel. A) DIC system in ACF. B) Random speckle pattern on model center cell DIC processing T he algorithm involve d grey scale cross correlation analysis between images of the deformed membrane taken at a high frame rate while it vibrated in the flow, to a reference image acquired for each test case (aoa) when the membrane was motionless S ub pixel accuracy was achieved through cubic B spline interpolation while n ormalized s um of s quared d ifferences (NSSD) correlation criterion was used for its insensitivity to scales in lighting. The membrane region was divided into subset s of 25 by 25 pixels and a 5 pixel step size was used during processing Using the full camera resolution to focus on just the membrane cell of interest (center cell) the spatial resolution in x and z (stream and sp anwise directions Fig ure 2 5 ) of the data was 0.64


33 mm between data points In the deformation direction, y membrane displacement calculations were accurate to 0.1 mm based on static displacement tests. Membrane displ acements were calculated normal to a reference plane which wa s a uto matically generated by the software passing through the g eometric center of the membrane based on the reference image I f the membrane sagged ( for the low tension model ) then this referen ce plane might have be en created at some small angle to the solid framing surface. In these cases, p ost processing techniques were implemented to set the reference plane parallel with and flush to the model surface to correc t small deviations Once the ref erence plane was set flush computed displacements were then normal to the model surface As an independent system altogether, data generated from the DIC system did not inherently fit the PIV reference frame for combined plotting. However, knowledge of wh ere the DIC membrane data began a s x location, the model angle of attack and a 2D rotation matrix were used to rotate and translate the DIC membrane data into the correct position for combined plotting in the PIV reference frame, as in Figure 2 5 Figure 2 5 Cartesian coordinate system used with both PIV and DIC data results


34 Synchronization of PIV and DIC Systems One major goal of this research project was to successfully acquire PIV and DIC data synchronously, which would allow for a better understanding of the time dependent nature of the FSI. A sophisticated timing box controlled the complex timing of the PIV system, which included all the necessary triggers to successfully charge and fire the double cavity laser i n tune with the double frame imaging. For these reasons, the pulses generated were very short and weak, while the Phantom (DIC) cameras required a 5V square pulse to trigger and ideally would only fire on the first frame of the PIV imaging. It was discover ed that the sync out of the PIV cameras triggered only on the first image frame and as a 3V short spike. To synchronize the timing, this PIV sync out signal was sent through a Tektronix type 114 pulse Generator which was set to reshape the signal into the 5V square wave that would fire the DIC cameras with negligible time delay. This method was implemented with success to obtain synchronous PIV and DIC data for an sweep with one of the membrane models and comparisons of the membrane positions from the la ser plane showed good relation between the two systems as discussed below. One obstacle to overcome with the synchronized acquisition was the interference that the light from the PIV laser caused on the DIC measurements T he reflection of intense laser li ght would be captured by the DIC images and essentially cause large gaps in the membrane DIC calculated displacements (Fig ure 2 6 C ). To eliminate this interference, HOYA multi coated (HMC) high pass optical filters (wavel ength >600 nm) were fitted on the DIC camera lenses The filters allowed 90 % or better transmittance of light greater than 640 nm in wavelength and zero transmittance of the 532 nm


35 wavelength laser light (Fig ure 2 6 A B ) The synchronized setup of both systems in the ACF is depicted in Figure 2 7 A B C Figure 2 6 DIC images and PIV laser interference. A) DIC images s ynced with PIV, no optical filters. B) DIC images s ynced with PIV, with optical filters C) Processed DIC data with laser interference. Figure 2 7 TR PIV & DIC systems with model installed for synchronized data acquis i tion in ACF test section.


36 Membrane Models As mentioned in the introduction, the membrane models used for this study were created with many characteristics found to be aerodynamically beneficial from an evolution of earlier studies [ 46 ], [ 49 ], [ 50 ] As a baseline, a rectangular rigid flat plate of equal dimensions was also examined The investigation involved three membrane wing models each one with five scalloped silicone membrane cells Each also had a different average spanwise pre strain value (also pre tension by model creat ion denoted by (%) and pictured in Figure 2 8 One key component o f these models was the material change from latex (previous works) to matte black silicone. While both materials share similar (untensioned) 1 values (~3.3), t he matt e black color minimized laser bloom, therefore was pertin ent in obtaining PIV data near the membrane surface The models we re all of similar geometry, symmetric about center span; e ach with a 20% of chord, c, solid leading edge and with five square membra ne cell regions 80% of c on a side. The membrane cell s were scalloped to a depth s, equal to 25 % of the The geometric dimensions can be seen in Figure 2 9 while the values are listed in Table 2 1 The silicone material itself played an important role in the creation of these models. high heat resistance allowed for a unique pre tensioning method In this method the silicone wa s heated to specific temperatur es on a hot plate before the 7075 T6 aluminum frames we re isotropic and large coefficient of thermal expansion, once cool ed the membranes contain ed a measurable spanwise pre strain ( ) This repeatable method was developed and performed at the University of Florida MAV Lab and Abudaram et al.


37 provides further details [ 51 ] The material properties of the silicone are listed in Table 2 2 while the model creation temperatures, pre strain values, and aeroelastic parameters ( 2 ) are tabulated in Table 2 3 T he silicone sheets were also pre treated by heating and cooling to prevent hysteresis effects and that the average pre strain values were computed on the cen ter cell by DIC upon model creation. Finally, the linear relation between creation temperature and calculated pre strain is displayed in Figure 2 1 0 where the slope wa s found as 0.0214% strain per degree Celsius [ / C] A B C Figure 2 8 BR Silicone membrane wing model s with scalloped trailing edges. A ) 80x80_1.3 ) 80x80_2.8 ) 80x80_4.2 Figure 2 9 Model schematic with d imensions.


38 Table 2 1. Model dimension values. Chord, c [mm] Span, b [mm] Cell chord/span Aspect Ratio Scallop Depth, s [mm] Frame thickness, t, [mm] 76.8 327. 7 61.4 4. 27 15. 4 2.8 Table 2 2 Silicone material pro perties Material Thickness, t m [mm] Durometer Hardness Test Elastic Modulus, E [kPa] Temp. Range [C] Tensile Strength [MPa] Calculated m [kg/m 3 ] Silicone Rubber 0.34 0.01 20A soft 385 62 to 218 5.52 109015% Table 2 3 Membrane model properties Model Designation Temperature of Creation [C] Measured average spanwise pre strain, [%] 0.1 2 80x80_ 1.3 60 1.3 0.46 80x80_ 2.8 130 2.8 0.99 80x80_ 4.2 200 4.2 1.49 Figure 2 1 0 Measured pre strain vs. creation temperature


39 Experiments Performed Data obtained and analyzed for this study was gathered in several sets of experiments. A major contrib ution of study was the synchronous acquisition of DIC and PIV data, which was done successfully for an sweep with the 80x80_1.3 (low pre tension) model Additionally an experiment involving PIV of the rigid flat plate baseline was performed at this time Once models of higher pre tension were obtained, independent DIC measurements were performed for all three models to compare vibration and pre tension relationships. In a parallel study and with collaboration from the University of Alabama, force measure ments for the varying pre tension models were gathered analyzed and provided Finally, PIV data was taken for a range of aoa with the 80x80_2.8 mode l utilizing improved seeding. In all tests the free stream velocity, U was set at 10 0.1 m/s and angles of attack were set manually with a digital inclinometer to 0.2. The Reynolds number as defined in Eq. 2 4 based on model chord and free stream velocity was calculated as 5 2 66 0 (~50,000) and was fixed for all tests Table 2 4 outlines the types of data acquired with each model (2 4) Table 2 4. Data types acquired for each model. Model Designation PIV obtained DIC obtained Synchronized (low pre tension) x x x (medium pre tension) x x (high pre tension ) x Rigid Plate (baseline) x


40 Synchronized P IV and DIC T ests Preliminary high speed imagery showed that membrane vibrations were on the order of 50 100 Hz. It was decided to sample as fast as the PIV system allowed in order to not just minimize temporally aliasing the membrane motions, but also to p rovide identification of many membrane shapes and to try and capture cause and effect events in the FSI. Therefore t he sampling rate was set at 800 Hz by reducing the PIV 1280 by 600 pixels. In thes e tests data sweep of 0, 4, 6, 8, 12, 16, and 24 aoa. F or the largest angle of attack case of = 24 a l arger shear layer existed and required larger camera fields of view; therefore full camera resolution was used adding to the height of view without further adjusting the camera calibrations or settings. However, t his necessarily reduced the s ampling rate to 450 Hz and lowered the maximum sample count to 81 4 samples based on camera memory As such, f or < 24 1024 samples were gathered for each case The 1024 sample count was to be utilized in calculating velocity and membrane fluctuatin g signals. A lso convergence tests were performed and even t he 814 sample count proved sufficient to converge fi r st and second order velocity statistics to 2% while for the majority of 1024 samples were used A n example of convergence of U mean and Urms velocities from data of model at 12 is provided in Fig ure 2 1 1 A photograph of the wind tunnel setup for synchronized acquisition performed with is provided in Figure 2 1 2 For these tests, t he model was inverted and centered in the ACF test section with the LE set approximately 0.3 m back fr om the inlet exit. The model inversion was necessary to capture PIV data over the top


41 membrane surface due to the PIV laser probe being constrained to issue from below the test section. The stereo DIC system was therefore placed above the test A B F igure 2 1 1 Convergence of PIV statistics vs. sample count. A ) 80x aoa, u component mean flow contours, diamonds indic ate tested convergence location B ) Running U mean and Urms for recirculated and near TE flow


42 lower surface center membrane cell speckled for these tes ts. In these and other tests, DIC was obtained only for th e central membrane cell, while 2D PIV was obtained at the model center span These regions are portrayed o n the model schematic in orange and green outline, respectively (Fig ure 2 1 2 ) Figure 2 1 2 Synchronous acquisition of PIV and DIC data ; schematic highlighting where data was obtained. Independent DIC Measurements To compare frequency and vibration details between the membrane models of varying pre tension, a set of tests were conducted where only DIC measurements were acquired In these tests t he models were installed (inverted) in the ACF in similar fashion to the combined acquisition. However, the DIC cameras were set up on a tripod below the te st section for easier access (Figure 2 4 A ) Therefore in these tests, the top


43 surface was speckled for the ce ntral membrane cell (region of interest) The sweep for these tests was expanded from the synched tests to include 10 and 30 This meant the low pre tension model was tested with again to obtain these missing angles. The total sweep was therefore: = 0, 4, 6, 8 10 12, 16, 24 and 30 A t each aoa, 1600 samples were gathered at 800 Hz At this time rectangular standoff mounts were replaced with symmetric airfoil mounts to help minimize structural vibration and any aerodynamic interference, as depicted below in Figure 2 1 3 Figure 2 1 3 Symmetric airfoil standoff mounts with 80x80_2.8 PIV Measurements of 80x80_2.8 Wing A final set of PIV tests w ere performed with the medium pre tension model (80x80_2.8 ). The selection of this level of pre tension was based on f orce data that had been obtained and analyzed in collaboration wit h UA on identical membrane wings discussed in Zhang et al. [ 56 ] Among the findings, it was seen that the lowest pre tension model was most aerodynamically efficient while the medium pre tension model was found least efficient as L/D. Each produced about equal lift, more than that of the baseline plat e and particularly at higher aoa D rag was found to be larger for the


44 membrane wings but L/D was comparable (at higher lift values) than the baseline As such, PIV data was acquired for the medium pre tension model to compare with the low pre tension and b aseline wings. Similarly for these tests, 800 Hz was chosen for the sampling rate, used to gather two sets of 1024 samples at each aoa The same field of view constraint applied at high aoa, so two sets of 814 samples were obtained at 450 Hz for = 24 T 0, 4, 8 12, 16, and 24 Additionally, this set of experiments utilized the aerodynamic mounts and the revised seed disperser previously described (Fig ure s 2 1 3 2 2 B ) Post Processing/Analysis Additional methods were utilized to improve the PIV velocity fields including vector validation, dynamic image masking, and outlier rejection Vector validation was provided by the Dynamic St udio software and checked for very large or backward facing velocity gradients when comparing each vector to neighbors in a 3x3 kernel [ 57 ] If a spurious vector was detected it was replaced with a local median vector. A dynamic masking algorithm was created t o improve flow statistics and deal with complex membrane shapes s uch that instantaneous PIV snapshots could be studied. After the dy namic masks is applied, mean and fluctuating flow statistics are only presented outside of the regions where vibrations occurred to ensure conditional flow statistics are not presented. Typically 160 convections times are averaged over and approximately 70 membrane vibration cycles, depending on vibration frequency. Dynamic Masking Algorithm One challenge of performing PIV with the repeated membrane cell wings was that both the in PIV plane membrane (center cell) as well as out of plane membranes (side cel ls) could vibrate significantly in the field of view of the model camera This would


45 create a constantly changing region where PIV data was invalid. Therefore, the 2 nd frame of each sampled image was analyzed to create a dynamic mask and then applied to the instantaneous PIV vector fields The mask s were created by first using Sobel edge detection [ 58 ] to track bright pixels ( laser reflection ) indicat ing the surface of the in plane membrane. After some spatial filtering to remove bright pixels associated with see d particles, a high order polynomial was fitted t h o se remaining, which fit intricate membrane shapes From the fitted polynomial a geometric mask could be generated below the 2D projected membrane surface and the curve was stored as a 2D membrane outlin e This outline was used to check for good correspondence with DIC calculated displacements of the center s pan (PIV plane) membrane shapes, o nce the DIC data was properly placed in the PIV reference frame T he average absolute difference between DIC gener ated membrane shape s and the pixel line generated shapes was computed across all cases as 0.091 mm (0.12% c, 27% t m ) and the average root mean square difference was computed as 0.122 mm (0.16% c, 36% t m ). Figure 2 1 4 s hows examples of how instantaneous DIC calculated membrane shapes from the center span compared with the bright pixel generated line Note that there was roughly a 2 mm border around membrane edges where DIC deformation data could not be calculated due to the lack of necessary subset overlap during processing Also the bright pixel tracking method had limitations unable to accurately track the membrane when it deflected below the model surface or when there were large gaps in between bright pixels T he DIC computations were deemed much more reliable and are used for subsequent analysis


46 To mask when an out of plane membrane was deflected up causing a shadow or dark region images were convolved with a 7x7 mean filter to smooth light g radients t hen signif icantly dark regions were detected by an Ostu gray value threshold method [ 59 ] and masked This method was also used to detect dark regions in the wake when the stream tube of dense seeding swayed in the camera FOV. Masking of wake data was no t found necessary when the seed disperser was used. Some examples of the dynamic masking methods are portrayed in the APPENDIX Figure 2 1 4 Combined instantaneous PIV and DIC at center span, compare DIC calculate d (black dashed line) & bright pixel generated (solid red line) membrane shapes


47 CHAPTER 3 RESULTS In the following chapter the results supporting this investigation into the interactions between a membrane wing and the flow at moderately low Reynolds num ber will be demonstrated. Details of the flow field features, including time averaged and fluctuating quantities will be analyzed. This will be followed by presentation and analysis of membrane oscillation characteristics and behaviors. Details and interpr etation of the instantaneous FSI and how the combined flow and membrane behaviors interact, as well as correlations between the two will be presented and discussed in the final section. Velocity Measurements Plots of the flow field results are shown throug hout this thesis as normalized quantities and in the normalized spatial coordinate system: x/c, y/c, and z/c. As reference, c is the full chord length and c = 76.8 mm, while the free stream velocity, U was 10 m/s. The measurement plane was set at z/c = 0. Model region and wake velocity data are combined for analysis of the mean flow fields and fluctuating velocities to see how they develop with changing incidence, as well as comparing the rigid baseli ne with the compliant membrane wings. Key flow traits are highlighted or expanded upon and some significant structural vibration attributes will be discussed as pertaining to flow behavior. Along with the velocity contours, plots contain model geometry fro m the PIV plane, outlined in black. For membrane models, the out of plane batten portion is represented by a dashed line. Flow fields in this section are computed statistically over all membrane positions (>50 membrane cycles occurred per sampling set). To show the volume of


48 vibration, roughly one cycle of membrane oscillations is included as thin black lines. The time averaged membrane position is indicated as a solid red line. From the chord length and free stream velocity, a typical convective time, is computed as 0.00768 s, ~130 passed. Time Averaged Velocity Fields Analysis of the mean streamwise velocity (Umean) revealed insight into how compliant membrane surfaces included in planforms can manipulate the flow at low Re to possible aerodynamic benefit. Seen in the overall flow characteristics is a shift in behavior from low ang le of attac 2 ), which occurs Figures 3 1 3 2 and 3 3 provide the mean flow fields with streamlines for RP 1.3 and 2.8 membrane wing, respectively In these plots, dark blue indicates reversed fl ow, orange represents near free stream velocity, while enhanced or accelerated flow regions are contoured in red. The discussion that follows will be split up into a section on low aoa and high aoa as they have a different behavior once the flow is massively separated Streamwise velocity at low aoa The baseline rigid plate (RP) shows the development of the leading edge separation bubble caused by th e sharp leading edge which growing to cover 85% of begins on the plate surface, however since the measurements did not go all the way to the wall this is an approximation Above the bubble is a thin shear layer and then an accelerated region, up to 1.3U as flow curves around the recirculation area. T he low


49 momentum oncoming flow cannot withstand the sharp turning and shearing at the LE. The recirculation zone existing on top of the model will adversely affect lift generation if the pressure is high interaction of the developing recirculation with the membrane motions that greatly reduces the size of the bubble o n average and contains it mostly forward of the membrane. Additionally, streamlines show a tighter curvature above the shortened bubble and contours show higher flow acceleration, up to 1.4U occurring nearer to the rly shows these effects. Another important aspect to study is how the near wake of the models compares, since drag can typically be related to steady wake momentum deficit for incompressible flows as in Panton [ 60 ] It can be seen that the membrane wings have a broader wake deficit (y/c), caused by the membrane oscillations, w hile the wake seems narrower for However, the RP seems to cause larger wake velocity deficit s. The membrane models allowed fluid to pass from under the membrane as it oscillates, adding momentum to the wake. In Figure 3 4 velocity slice s from each model at x/c and very similar velocity around the LE (x/c = 0.2), while the RP shows a stronger but narrower wake deficit. At ~1.5 mm thinning of the shear layer height by the membrane wings at x/c = 0.2 can be seen. From the near wake location (x/c = 1.4), = 8 the RP has a wake deficit of 0.5U much greater than the membrane models at


50 0.76 U at 0.81 U while the full wake s are not captured (Fig ure 3 4 B ) Force d 8) with membrane wings showing higher efficiency by as much as 26% [ 56 ] however, by flow analysis at contrast to the force data showing low tension (1.3 ) with best L/D. Instantaneous flow analysis revealed a rush of velocity from under the me mbrane wi th each cycle which acts to keep the mean wake flow higher and will be discussed in a later section. Streamwise velocity at high aoa Contours of Umean at high angle of attac k show the membrane wings resisting flow separation and recirculation. F or the baseline RP at = 12 the recirculation bubble extend s past the TE of the model and burst s into wake, which is in stark contrast to the mean flow of the membrane wings which remain attached at 12 due to the extension of the membrane This evidence of the rigid flat p late separating at the center span location between 8 and 12 coincide s well with m any load studies for flat plates at low Re, where a shift in the Cl slope to a lower value occurs near 10 ( separation bubble breaches TE) [ 18 ], [ 50 ], [ 56 ], [ 61 ] After 12 the baseline is seen with massive separation for increasing incidence with recirculated flow extending 1.5 and 2.1 cho rd lengths into the wake at 16 and 24 respectively (Figure 3 1 ) This is in contrast with the membrane wings showing much less recirculation as well as greater velocities in the accelerated flow regions There is also a greater downward bending of the wake flow at = 24 for the membrane wings (Fig ures 3 2 3 3 ) which may be linked to lift generation from a momentum balance point of view This is backed up by force data showing Cl max near =25 a nd ~22 25% improvement in C l with comparable L/D


51 between membrane wings and the baseline here Interestingly there are some similarities in the mean flow streamlines and recirculation patterns very near the TE, as well as vibration shapes comparing the l ow tension (1.3 ) at 24 to that of the medium tension (2.8 ) at 16 possibly indicating similar average tension between these cases High aoa velocity slices are provided in Figure 3 5 comparing at x/c = 0.3, 1.4 locations. The slices for x/c = 0.3 show that the membrane wings continue to develop greater accelerated velocities and less recirculation in the forward part of the model, also slightly thinning the shear layer as indicated by steeper velocity gradient More prominent are the wake differences and development of reversed flow 0.3U for the RP at x/c = 1.4 where as the wake never reverses for the membrane w ings at this location In addition to suffering a greater deficit, the RP wake is seen to become as broad or broader than the wake of the membrane wings which differs from low aoa T hese conditions would imply that the membrane wings show increasing benefit at higher aoa, which was confirmed by the force data [ 56 ] While the flows of the membrane wings are generally very comparable to each other velocity slices at high aoa also predict that the 2.8 tension model sho uld perform best aerodynamically for this Re contrasting with the force data There are steady and unsteady membrane behaviors that lead to the more favorable time averaged flows. In brief, the membranes are seen to distend into a time averaged camber s hape, allowing the flow to more easily negotiate turning over the different angles of attack. Additionally, the TE vibrations allow jets of air to pass from


52 under the membr ane and interact wi th the low momentum shear layer. This caus es enhanced turbulent mixing and momentum transfer, discussed in the next sections. Root Mean Square Velocity Fluctuations A Reynolds decomposition is applied to the flow fields: and where is the instantaneous streamwise velocity component, is the deviation, same for vertical components. Utilizing the Urms, Vrms nomenclature for the square root of the mean squared velocity fl uctuations of U and V components, i.e., and t he statistical fluctuating flow fields are discussed. Urms and Vrms are the resolvable (from this data) components of the turbulent kinetic energy (TKE) existin g in the flow fields. Insight into where the flow turbulent energy resides is important to gain a better understanding of flows over low Re wings and to investigate what influence or affect the membrane planforms create. This is particularly true since flo w over low Re wings are highly unsteady and have demonstrated rapid transition to turbulence [ 15 ] Streamwise velocity fluctuatio ns Figure 3 6 compares normalized Urms contours at low aoa, 8 f or the three tested models. At very low incidences the membrane wings are seen having an impact on the near wake causing slightly larger Urms values than the baseline and causing a letter V 8 shows growing Urms over top of the model, which is attributed to the developing and growing shear layer emanating from the LE. For the membrane wings the shear layer appears to range. It ma y be significant that force data showed the membrane wings had maximum L/D in this range.


53 The motions o f the membranes will, by no penetration condition (viscous interactions), necessarily impart v momentum to the unsteady shear layer, often reported as sh ear layer excitement in various studies [ 5 ], [ 44 ] Discussed i n the next sectio n on membrane behavior range the vibration frequency is increasing with aoa, possibly connected to appears to reduce the area of wing whil e magnitudes are similar In Figure 3 7 high angle of attack Urms contours are presented for comparison. At = 12 it can be seen that the membrane wings begin to show a strong influence on the topside shear layer, wit h it being pulled close to the TE fluctuations. The baseline RP at 12 has begun to separate and shows its shear layer lifting away from the surface and intensifying in the wake. shows a regular p attern of larger, more intense, and further away shear layer development from both the leading and trailing edges, as the flow separates over the model and transitions to turbulence in the wake. In contrast, the membranes show a change in behavior where a region of high Urms begins to build just downstream of the membrane TE. This phenomenon has some tension dependency, with h igher magnitudes generated, as large as 0.5U by the medium pre nd T he enhanced Urms near the membrane wings is representative of the flow steady kinetic energy supply (~ ) being partially converted to turbulent kine tic energy (Urms) in part through work of the membrane motions. This occur s much more


54 for the membrane wings than for the rigid baseline. T he membrane oscillations may therefore absorb turbulent energy present in gusty flight conditions dissipating it as vibrations like a damper for the dynamic system. This adds stability to the low Re flyer in a turbulent environment Vertical velocity fluctuations The vertical fluctuations Vrms are also considered. In Figure 3 8 plo ts of normalized Vrms are shown for low aoa. There is less Vrms occurring in the shear layer at low angle of attack than Urms across all models C ompare for example = 8 where Urms values of 0.27 were common among model s while Vrms peaks around 0.17 i n this case Albeit smaller in magnitude, the models all show very similar behavior for Vrms at these low alpha cases compared with Urms. T he vertical fluctuations in this range associated with the attached shear layer, growing in size for the RP with ao a and impinging on the membrane and spreading in the wake for compliant wing models. Investigating the higher aoa cases, plotted in Figure 3 9 unique Vrms behavior is seen. At = 12 the aforementioned behavior shift is realized. For the RP, the TE is seen to cause a shear layer from the flow passing under model and bending up into the wake, a stronger Vrms exists here than Urms. This may be associated with the ben t reversed mean flow caused by the separation bubble bu rsting into the wake (Fig ure 3 1 ) and affect ing flow passing from below the model in a more direct way acceleration from around the TE can be seen in the Umean contours The membrane models appear to have very similar Vr ms to each other at 12 broader for the 1.3 wing, and increased by 10% in intensity from = 8 For the RP at 16 the lower shear layer still shows the peak of vertical fluctuations, but the overall separation and shear layer created at the LE and risi ng from the model is


55 evident as from Urms. At 24 the wake of the rigid plate is near equal in turbulence intensity, U and V components (~0.3 to 0.35U ), far from the model The membrane wings show very unique behavior with high angle of attack At 16 a oa Vrms is around 0.28U and fairly evenly distributed in the bulk of the wake (more a very large spike in the Vrms, where it jumps in magnitude to 0.49U for a much larger region than the peak in Urms and also centered slightly further downstream, at x/c = 1.3, not 1.1 The oblong shape of heavy vertical influence is also seen extending farther into the wake, beyond a full chord length f rom the model TE (x/c > 2.2), while the Urms peak extended about 0.7 chord lengths from the batten TE. Since the shape and pattern is very similar between membrane wings, it is deemed a function of angle of attack over vibration frequency ( equivalent for e ach model at 16 and 24 to be discussed in following section) or amplitude, but there is some tension dependence, as the medium tension wing shows a trend of increased magnitude for Urms and Vrms. This is an indication that the membrane presence, either t hrough altering the pressure, viscous interaction, or both is causing the flow which has no original V component to deviate in y by 50% of the free stream. This is a significant transfer of unsteady momentum occurring in the near wake and is an indication of the complex influence the membrane imparts on the flow, while also being excited by it Reynolds S hear S tress D efini ng the Reynolds Averaged Navier Stokes (RANS) equation as Eq. 3 1 ( E q. 4.21 from Pope [ 62 ] ), it is seen that there is an apparent stress term on the right hand side composed of the deviati on velocity squared tensor : T his is the Reynolds


56 Shear Stress (RSS) which acts on the flow in balance with the pressure and viscous forces For highly unsteady flows such as the ones of this study, the RSS can be a significant term governing flow behavior an d is associated with turbulent momentum transfer. (3 1) From the data in this research, t he resolvable term of the RSS tensor with density dropped (incompressible) is: ) is retained in this definition. Therefore it is the defined tely on average the RSS at that point will be positive. A quick reference for the discussion of contours: Same Sign Deviation s ( ) | Opposite Sign Deviation s ( +) First focusing on the RSS development and behavior at low aoa as shown in Figure 3 10 it is evident that the RP begins to generate momentum transfer of opposite sign deviations, or positive RSS, in the shear layer sitting above the model. At the same time, the LE and TE begin to cause same sign deviati ons as negative RSS. The membrane wings show very similar behavior between them, and at 6 the wake shows somewhat symmetric (about the axis passing through the model aoa) positive depending on if the membrane is influencing flow above or below it. At = 8 there is stronger RSS developed by the RP, while the membranes influence is heavier in the wake. The wider volume of membrane oscillation for the 1.3 membrane wing causes a larger wake influence than that of the 2.8 wing.


57 Regarding the RSS deve loped at high er aoa, as seen in Figure 3 11 t he interesting case of = 12 again highlight s the impact the membrane wings have when the plate has just shifted to separated flow in this plan e. Membrane motions interacti ng with the low momentum shear layer were shown in previous sections. What the RSS shows is a largely positive region over the TE fluctuations for this case This is sign fluctuations at any given point in the flow (on average) where (+) RSS appears fluctuations should be associated with the membrane motions up and down ( y) by viscous interaction it is seen that the membrane oscillation s impart a v component to further away hi gher momentum fluid and bring it to mix with the low u momentum fluid passing near the surface. The added momentum helps resist separation in an adverse pressure gradient, if present. The RP at 12 shows the continued development of a pattern of positive RSS over the top of the model and negative RSS from around the TE. Most likely both regions are very similar in nature and associated with random deviations pertaining to shearing and the development of turbulence. This pattern remains the same at = 16 and 24 only more intensified and pushed further into the wake. the 1.3 development of positive RSS from directly behind the membrane TE, now equal in magnitude to the positive RSS above it, which is different from 12. In this case, there is an apparent dependence on vibration amplitude, as the lower tension model has larger RSS regions in the wake of similar pattern to the medium tension, both pulling the momentum flux close to mem brane TE.


58 for the membrane wings there is significantly different behavior and complex RSS patterns generated by t hem, similar between the two. A relatively large region of approximately double the magnitude from all previous cases, neg ative RSS (~ 0.12) develops downstream of the tightly vibrating TE. Above that, a strong positive RSS is seen. The interactions near to the TE are also stronger than for other cases and a tightly packed pattern of positive, negative, positive alternating R SS near the TE indicates flow structures being developed there, to be shown in the section on FSI Instantaneous analysis of the deviation velocities showed the same sign fluctuations producing the strong ( ) RSS as jets of air passing over and under the membrane cause d deviations of up and forward ) or down and reversed ( and ) in tune with vibrations. T con vecting straight back in the stream direction and ing to conv ect back along the axis through the model angle of attack. Fourier analysis showed the deviations occurring at the membrane oscillation frequency and will be discussed further in the following section Overall, the enhanced momentum transport generated by the membrane wings and pulled in to the TE is a sign of increased work and energy transference between the flow and model through membrane interactions. While similar patterns were found amongst the membrane wings, th e re wa s stronger RSS generated by the m edium tension wing as with the Urms and Vrms turbulence components Membrane Oscillation Behavior Time resolved DIC measurements allowed for in depth analysis of the membrane dynami cs across all three pre tensions, bringing the 4.2 high tension wing into the discussion. As discussed in the introduction, the membrane motions are a combined


59 effect of dynamic pressure forces, tensions restoring forces, and inertial forces associated with the mass which may include gravitational effect s. The stiffness of the thickness, t m giving units of N/m, to compare with bending stiffness E I for 3D structures ( units of N m 2 ). For the silicone material used, E was calcula ted from DIC of load tests as 385 kPa [ 51 ] and t m was measure d as 0.34 0.01 mm. Therefore, E t m is found as 130.9 N/m. Modeling the membrane behavior as a simple dynamic system, the natural frequency (Hz) should be estimated as in Eq. 3 2 a property of the proportio nality constant, K, and the mass. K has the units of N/m and will be considered as the K = Et m K = 130.9 N/m. Introducing the scalloped chord length, c s c s = 0.6c = 46.1 mm. Mass can be estimated as c s m m (3 2) Finally, computing the natural frequency from Eq. 3 2 it is found as ~ 57.6 Hz. Using ncluding pre tension in the K term gives K = 132.6, 134.6, and 136.4 respect 2.8 and 4.2 The natural frequency estimations are then 58.0 58.4 and 58.8 Hz (Table 3 1 ) T hese estimations do not account for nonlinearites, system complexity, or damping and will be compared with actual vibration frequencies obtained during experiments. Full Field Mean and RMS Properties The full field membrane displacement s are time averaged to find the mean shapes and fluctuations are quantified by the root mean square technique. These values are normalized by the chord, c. In Figure 3 12 contours of mean membrane displacements for each membrane wing are shown for


60 synchronized PIV DIC tests was obtained from lower membrane surface so a 2mm border of membrane edges is missing whereas portions of the solid frame were included during independent DIC tests to capture the entir e cell and more easily orient the data. Both acquisition methods showed very agreeable data with no noticeable differences. Some of the common membrane trends are noticeable, such as that there is a clear reliance on pre tension for maximum mean distention with lower tension allowing larger distention Also, each membrane shows that the time average d position is maximal near the membrane geometric centers. Finally, it can be seen that high angle of attack will increase the mean displacement. These trends w ere found to hold across all angles of attack. In Figure 3 1 3 (8, 12 ) contours of the normalized RMS displacements are shown as y/c, are shown From these plots it is shown that the TE has the larg est fluctuation behavior, and that there is typically nodal behavior between the geometric center (midpoint) and the TE. The shape of the RMS comes from the primary vibration behavior as a wave of distention that emanates from near the membrane LE and trav els to the free TE growing in amplitude wh ich repeats nearly periodically with unsteady driving (pressure) forces, and therefore possibly a limit cycle oscillation as discussed by Johnston et. al [ 47 ], [ 48 ] However, the behavior becomes less periodic under higher tensions and for high aoa. There are less clear overall trends for RMS, with each pre of attack of maximum TE vibration. Spanwise waves were not apparent i n the RMS behavior. Figure 3 1 4 provides an indication of where much of the following analysis occurs with each pre tension, i.e., the Mid Point at th e geometric center (z/c =0, x/c = 0), the Side


61 Point near one side and at x/c = 0, and the TE Point at z/c = 0 and near the membrane TE. Note that the Mid Point and TE Point lie in the PIV laser plane. Pointwise m ean and rms p roperties To better under stand the mean and RMS properties of the membranes across all (symmetric spanwise) deformation characteristics, much information can be learned from t he Mid Point and the TE Point. Figure 3 15 gives the mean deformation s with RMS plotted as bars of the Mid Point s for the full sweep. In this manner it can be seen that the lower tension will always distend further on average and shows larger RMS at low angle of attac k. The average distention increases vs. aoa with larger gradient from = 0 to 1 2 than after that point even though average dynamic pressure force is linear with angle of attack by frontal area This implies that the average membrane position is a fu nction of the flow state (separation) and average pressure felt A similar plot is shown for the TE points vs. aoa, each pre tension in Figure 3 1 6 Although each pre tensions shows unique behavior, from the RMS f luctuations, it is clear that at lower aoa the fluctuations are much higher before a behavior shift when the fluctuations steady out around = 16 This coincides well with when the flow was found to impinge with the membrane more directly through attached shear layer discussed in the previous section At 24 aoa, the low and medium pre tension (1.3 2.8 ) wings show some excitement (RMS) b ut the highest tension does not, possibly already having reached a material limit being under high average force (pressure + tension). By = 30 all the models show very little RMS behavior and the same trend of larger average displacement for lower tens ion There is the apparent shift in RMS after separation conditions at 12 where the membrane becomes much steadier.


62 Each wing shows a different angle where TE fluctuations are greatest, with the trend of higher aoa for higher tension. That is the 1.3 wi ng RMS peaked at 4 while a link of this showing possible aerodynamic benefit could not be created from the force data. T he max imum statistical displacement achieved through mean or fluctuation was for the 1.3 wing, a t 0.068 y/c or ~5.2mm, while up to 10 mm was seen in instantaneous positions Time average d camber effect As noticed in the previous flow section, the membranes exhibit a steady effect of a time averaged cambered shape. Since a true camber is fixed by the relation of the rigid airfoil shape it cannot adapt for changing flow conditions or aoa. The membrane mean shape, however, adapts to changing pressure condition. Figure 3 1 7 shows how the membrane produces a camber as t he difference in mean displacements at the Mid and TE points, for the low and high pre tension cases. In the plot, dashed lines represent the mean TE Point positions at each aoa, while the mean Mid Point positions are in solid lines. The difference between the Mid and TE points estimates the time averaged camber and it can be seen that it exits for both the high and low pre tension models across the full range. The phenomena is particularly shown for low pre tension at < 16 ~2.4 times that of the high pre tension model in this range. The low tension model also showed max L/D (among all models) here the effect is most p rominent This implies a possible connection between this steady effect and average aerodynamic loads. Membrane Frequency Content decomposition from the previous section, are used to compute spectra by


63 FFT or discrete Fourier transforms (DFT). The finite range Fourier transform defined as Eq. 3 3 (Bendat and Piersol [ 63 ] ) is used on signals of length N, where N=1024 sync h ed ), or N = 800, using two ensembles from 1600 sample sized independent DIC tests, incorporating DFTs. The bin width, is determined as 24, This provid ed sufficient frequency resolution to identify peak frequencies in the membrane vibrations. Ultimately, the Welch method was utilized to compute one sided Power Spectral Densities (PSD) as in Eq. 3 4 [ 63 ] using a rectangular wind ow with 50% overlapping due to the nearly periodic behavior of t he membrane cycle oscillations. ( 3 3 ) (3 4) Computing the PSD at the Mid, Side, and TE Points indicated in Fig ur e 3 1 4 revealed that the membranes showed a peak fr equency at each angle of attack. Often, many harmonics were present as in the examples for 1.3 at = 8 and 2 8 at = 24 shown in Figure 3 1 8 These spectra curves are representative of other aoa cases for the low and medium pre tension wings. The harmonics are due to the nearly period ic wave behavior and nonlinearities in the system, with the silicone material as a possible cause. It should also be noted that the Side Point showed the same frequency content as the Mid and TE Points, indication of minimal spanwise oscillation behavior, which was also not detected visually. The power of the spectra revealed that the TE > Mid >


64 Side, which wa s expected based on the RMS behavior and was found to be consistent across models and angle of attacks The high tension (4.2 wing) showed a unique behavior at 16 aoa A ssumingly under higher average combined pressure and tension forces than othe r membranes here, the membrane hit an apparent resonance, where two modes were seen in the RMS plot and spectra show ed a 90 Hz peak, much higher frequency than for all other cases (Fig ure 3 19 A ). Additionally, the spectr a captured a change in oscillation behavior > 16 post resonance For these cases, spectra show ed broad lower frequency peaks as dominant, with the wave frequency emerging as 2 nd or 3 rd peaks (Figure 3 19 B C ) this more complex post resonance behavior was not seen for the lower tension models. The RMS plots for this wing at high aoa are shown in Figure 3 20 vibration frequencies are plotted vs. aoa in Figure 3 21 From the plot it is clear that higher pre tension leads to higher vibration frequencies and that there is a dependence on angle of attack. The behavior is very similar up to = 12 with frequency increasing slowly at lowest then quickly over 6 12 After 12 the low and medium tension models taper toward a limit of approximately 60 Hz, while the high tension model hit the resonance discussed previously at 16 Then the d ominant peaks were much lower (perhaps beating behavior) while the wave nature was still noticed visibly, and showed similar planning out as lower tension models, stabling at ~89 Hz for high aoa. These frequency trends are very similar to those found by T regidgo for perimeter reinforced membranes [ 44 ]


65 As for comparing the estimated resonant frequencies to actual frequencies obtained, there is very reasonable agreement. Before the divergent behavior at higher aoa, the average vibration frequencies by model ( = 0 to 12 ) are 51, 56, and 66 Hz, low, medium, high pre tension, respectively, the overall a verage being 57.7 Hz. The estimated natural frequency for an un t en s ioned baseline from Eq. 3 2 was found as 57.6 Hz, but this d oes not explain the differences for varying pre tension and may be coincidence; however the correct approximate frequency range was predicted without accounting for nonlinear or resonant effects From averages over aoa, it can be stated that increasing th e pre strain will increase the vibration frequency by approximately 5.5 or 6.9 Hz per % strain [Hz/ ], the difference being accounting for the apparent resonance or not Fluid Structure Interactions Utilizing the synchronized membrane and flow information for the 1.3 membrane wing further insight into the time dependent fluid structure interactions c an be gained. From the time averaged and statistical flow properties, there was particular evidence of interactions at the membrane TE for high angles of attack ( 12 ). This will be investigated by analyzing time dependent streamlines and vorticity. FFT performed on the time resolved deviation velocity signals to show relevant flow frequencies and how they correspond with membrane oscillation frequencies. Finally, correlations between membrane and flow unsteady signals will be shown and di scussed. Trailing Edge Vorticity Interaction Vorticity is formed by flow interacting with physical boundaries; therefore a significant interaction between the membrane and the flow will typically involve generation of


66 vorticity, a measure of rotation in the flow field. If vortices are created, they can ad vect in and affect surrounding flow transferring momentum and energy For this study, vorticity is calculated as defined in Eq. 3 5 [ 64 ] which is the component resolvable from the acquired 2D PIV data and shows twice the solid body rotation about the z axis. As defined, negative vorticity spins clockwise ( ) and positive vorticity spins counter clockwise (+) Vorticity values are further normalized by c and U as defined in Eq. 3 6 (3 5 ) (3 6) The normalized instantaneous vorticity *, is combined with instantaneous membrane positions and model geometry (of just the cent er cell) to analyze TE phenomena in Figures 3 2 2 to 3 2 5 Since membrane cycles were seen as not truly periodic the convective time, defined previously as the transit time fo r a particle moving at the free stream velocity to travel the chord length ( = 0.00768 s), is used to introduce a normalize d time for use with the time resolved data as The real time passed in the sequence is t Information plotte d is only a small sample in time but will represent what is seen to repeat often within the vibration cycles at each aoa. In Figure 3 2 2 is plotted for a short time series for the model at = 8 in which the membra ne begins maximally distended up and heads downward during its cycle. At this angle of attack, it is seen that there is no significant vorticity generated at the membrane TE as the flow protrudes up from under the membrane smoothly and joins the flow from over the top surface. However, there is strong vorticity generated by shearing at the LE (shear layer) present and it is seen impinging on the membrane in and then allowed to advect over the surface somewhat as the membrane


6 7 moves down. It is not known whether vorticity interacting with the membrane at low aoa is associated with the increase in vibration frequency with aoa, found during this range. Similar plots of for = 12 can be seen for consecutive samples of a time sequence in Figu re 3 2 3 At this angle of attack the membrane is vibrating at its highest overall frequency for the 1.3 wing (62 Hz) and (+) opposite deviation RSS being generated near the membrane TE (Fig ure 3 11 ). In the current vorticity plots, at = 0.0 0 0 the membrane is passing down and the highly unsteady shear layer shows some larger vortex rollup over the membrane surface similar to those discussed by Rojratsirikul et al. at similar Re with PR models [ 5 ], [ 40 ] As the membrane decelerates at the bottom of its cycle, stops and just begins to mo ve up ( = 0.651, 0.814) a rush o f fluid from under the membrane shoots up and creates a counter clockwise spinni ng vorticity ( + ) as it mixes with the unsteady fluid pulled down by the membrane as well as the free stream fluid This swirling structure pulls streamlines from higher momentum fluid father above the membrane as it advects downstream, which helps keep the low momentum fluid from separating as easily. Even as the vortical structure has passed out of the frame ( = 1.302), the influence of its presence is still seen in t he bent streamlines around the trailing edge For the next case of = 16 is plotted in Figure 3 2 4 In this series, at = 0.00 0, the membrane is just about the reach the top of its cycle and briefly stop before accelerating back in the other direction. As soon as it begins its descending motion, the air rushing from under it ( = 0.163) immediately interacts with the fluid pulled down by the TE and again a counter clockwise vort icity structure forms ( = 0.326). Possibly due to stronger pressure forces, the structure appears larger than for similar ones at 12 and


68 is seen interacting with the shear layer ( negative vorticity ) reaching back from the LE, protruding higher over the model surface than at lower aoa ( = 0. 488) A complex behavior that sends streamlines toward the descending membrane is seen ( = 0. 651 to 0.977). The membrane reaches the bottom of its cycle at = 1.139 and stream lines continue to pa ss down under the membrane influenced by its passage and the receding vort icity structure. Addressing plots of for = 24 plotted in Figure 3 2 5 at = 0. 000, the membrane has just reached the bottom of its cyc le and is about to pass upward. Recall that the sampling frequency for this case was 450 Hz so approximately 44% more time passes between frames. The flow is seen as very unsteady with a large shear layer and some reversed flow at = 0.00 0. As the me mbrane TE begins to deflect up ( = 0.579) a rush of fluid passes from under the membrane and initially into the recirculated flow as well as up into the shear layer. As soon as the membrane hits the top of its cycle and snaps back down again, the flo w immediately rolls up as a counter clockwise vortical structure ( = 0.868). At = 1.157, the structure has dispersed but persists and interacts with separated flow still influencing high momentum fluid to pull down into the unsteady region ( = 1.447). It can be implied from the RSS plots of Figure 3 11 that the counter clockwise vortical structures here are shed into the wake and intensify causing increased turbulent transport and hence the large negative RSS, as right location.


69 Flow and Membrane Coupled Behavior s Through much of the investigation, there is obvious evidence of the interactions and inter dependence between the membrane and flow behaviors. Spectral analysis and correlations are employed to try and quantify how and where the flow and membrane interactions are most coupled. Spectral a nalysis applied to flows In the same manner as described in the previous section with fluctuating membrane signals, velocity power spectra are used to find the dominant frequencies in the fluctuating flow. By investigating many locations throughout the flow fields, it is found that the membrane peak vibration f requency also emanates to the flow, giving it the same spectral peaks. In other words, the membrane oscillations are felt throughout the flow field as the dominant resolvable frequency content, even upstream of the membrane There is a dependence of proxim ity, particularly to where the membrane fluctuations are high like at the TE, causing a more power in the PSD peak. Only within the recirculated region or near the LE in the shear layer were membrane frequencies sometimes not found, while in these cases, b roadband spectra was seen, without peaks. In Figure 3 2 6 location from the 1.3 wing at = 8 overlaid by the PSD of the membrane TE location at that angle of attack. The infor deviation signals share the same peak frequency of 52 Hz and even some of the harmonics associated with the membrane oscillations. Note also that the wake locations show larger power, this is because the magnitudes of the fluctuating velocity are greater in the wake. The overall trend seen for this model and aoa as well as others, is that the


70 TE frequency will b e seen in the flow and that the power will generally be associated with proximity moving forward from the membrane TE or downstream from it; with wake locations showing stronger peaks dependent up on velocity deviations. With the power associated with the m embrane frequency dominating by many orders other resolvable flow frequency content, it is interpreted that the membrane driving the flow around it and in the wake, though also initially excited by it. Correlation analysis C orrelations between the membrane and the flow ar e computed for specific locations on the membrane (center span PIV plane ) with the entire fluctuating flow component variables for further insight The c orrelations are calculated as linear correlation coefficient with zero time lag, define d by Eq. 3 7 In this equation represents the fluctuating membrane displacements while velocity component These correlations were computed with data from the 1.3 wing synch ronized acquisition sets. (3 7 ) To check for the significance of the correlation values the criterion is used. A t 100 degrees of freedom (sample count) an r of 0.254 where r is defined the same as Eq. 3 7 above, can be considere d significant at a level of 0.01. Considering that 1024 samples were used for these cases (1024 degrees of freedom ) values were seen ofte n reach ing 0.8 to 0.9, the correlations are considered very high and statistically significant with 99% confidence The positive and negative correlation values were seen to oscillate at the peak membrane frequency of whichever case was investigated. Fig ure 3 2 7 contains


71 contours of the correlation coefficient between TE point of the membrane indicated with a green diamond in the plots, with fluctuating velocity components for = 8, 12, 16 Figure 3 28 for The TE location is chosen because of the power in the signal at this location proximity power trend. s, there is a clear dependence on aoa for strength of correlation, which is most likely a function of the power ( variance ) or amplitude of the TE vibrations, which is seen diminish ing with increasing However, unique patterns are seen and notably strong negative correlations dominate near the TE Point, while the wake shows region s of positive and negative correlation. When the correlations are interpreted physically, it seems logical that the flow wo uld decelerate locally, i.e., deviate below its mean value ( distended above its mean The positive region downstream could be flow that accelerated from a cambered shape (TE down) that has advected there from an earlier time making it difficult to interpret To this point, the full cross correlation function is plotted from one location (x/c = 0.8, y/c = 0.1 = 8 ) to show how oscillating (+) and ( ) in time at the peak membrane frequency ( while also advecting in space) and that the zero time lag val ue may not be near the maximum (Fig ure 3 2 9 ) correlation contours show the oppo site trend near the membrane TE. A large positive correlation region near and above the TE exists. S imilar of correlation diminish es overall for higher aoa. The wake is characterized with a more


72 uniform region of correlation as the flow shifts in y The large region of strong positive correlation at 8 is a sign of the flow locally accelerating f U where correlation was negative The oscillatory nature of the correlations from Fig ure 3 2 9 imply that the fluid in this region is pull ed down ( at a later time when the membrane passes down. These correlations suggest that the membrane fluctuations are most significant at l ow aoa, that there is a limit to the extent of influence upstream of the membrane, and that the whole flow fields (and wakes), U and V components are oscillating with the membrane peak freque ncy, a significant presence. Table 3 1. Estimated proportionality constant and natural frequency. Model pre Estimated K [N/m] Estimated [Hz] 1.3 (%) 132.6 58.0 2.8 (%) 134.6 58.4 4.2 (%) 136.4 58.8


73 = 0 = 12 = 4 6 6 4 8 Figure 3 1. Umean/U contours with streamlines for baseline rigid plate.


74 Figure 3 2. Umean/U


75 8 Figure 3 3. Umean/U embrane wing.


76 A B Figure 3 4. Umean/U


77 A B C Figure 3 5. Umean/U slice plots


78 Figure 3 6. Urms/U contours Baseline Rigid Plate M embrane W ing M embrane W ing 0 0 4 4 6 6 -8 8


79 Figure 3 7. Urms/U aoa. Baseline Rigid Plate embrane W ing M embrane W ing 12 16 24


80 Figure 3 8. Vrms/U Baseline Rigid Plate 0 4 6 -8


81 Figure 3 9. Vrms/U Baseline Rigid Plate embrane Wing 12 16 24


82 Figure 3 10. RSS/U 2 Baseline Rigid Plate 0 4 6 -8


83 Figure 3 11. RSS/U 2 contour Baseline Rigid Plate 1 1 2 1 1 6 2 4


84 1.3 wing 8 12 Figure 3 12. Mean membrane displacements y/c, for 1.3 8 and 4 2 wings. 8 12 Figure 3 1 3 RMS


85 Figure 3 1 4. Indication of mid point, side point, and TE point on 1.3 =8 mean plot. Figure 3 15. Mid Point mean and RMS deformation behavior vs. aoa, 1.3 red, 2.8 black, and 4.2


86 Figure 3 1 6 TE Point m in blue.


87 Figure 3 1 7 Time averaged displacements (camber) of mid and TE points, full sweep, comparing low and high pre tensi on, 1.3 and 4.2 A B Figure 3 1 8 PSD computed from membrane Mid, Side, and TE Points showing peak vibration and harmonics. A) 1.3 wing at 8 B) 4 2 16


88 A B C Figure 3 19. Spectral content portraying unique behavior of high pre tension 4.2 wing. A) = 16 high frequency (resonant) peak and harmonic. B) 24 low freq uency peak dominant. C) = 30 three peaks present, low is dominant. Figure 3 A B C


89 Figure 3 membrane wings.


90 n = 0 .000 n = 0.163 n = 0. 326 n = 0 .488 n = 0 .651 n = 0 814 n = 0 .977 n = 1.139 n = 1.302 Figure 3 2 2 Normalized instantaneous vorticity, *, with streamlines for 1.3


91 n = 0.000 n = 0.163 n = 0.326 n = 0.488 n = 0.651 n = 0.814 n = 0.977 n = 1.139 n = 1.302 Figure 3 2 3 12


92 n = 0.000 n = 0.163 n = 0.326 n = 0.488 n = 0.651 n = 0.814 n = 0.977 n = 1.139 n = 1.302 Figure 3 2 4 1 6


93 n = 0. 000 n = 0. 289 n = 0. 579 n = 0. 868 n = 1.157 n = 1.447 Figure 3 2 5 24


94 A B Figure 3 2 6 A) Locations of PSD indicated by diamonds over Umean plot. B) PSD of


95 Figure 3 2 7 8 6


96 Figure 3 28. 12 16


97 Figure 3 2 9 Cross correlation, indicating periodic nature of the correlation values and that ) is not always near to maximum correlation.


98 CHAPTER 4 CONCLUS IONS AND FUTURE WORK S ynchronous acqui sition of time resolved PIV and DIC data sets, as well acquisitions made independent from each other have been performed to study, in detail, the fluid structure interactions of low Re membrane wings. Mean, fluctuatin g, and instantaneous flow and membrane properties have been explored and discussed The m ulti cell, batten reinforced and scalloped membrane wings were created under heating to create varying pre = 4.2%) In a collaborative and parallel effort force data was obtained for the same wings. A rigid flat plate of identical aspect ratio was incorporated as a baseline wing. Summary Mean streamwise flow analysis showed the baseline plate having a growing separation bubble (originating from the leading edge) at low aoa before completely separating near 12 aoa T he membrane win gs demonstrated a reduc tion of the size of the separation bubble, keep ing the flow attached to higher angles of attack, and showed higher wake velocities. At higher angles of attack, the baseline case showed r ecirculated flow extending far into the wake w hile membrane wings showed much less recirculation in all cases. A t high aoa, and a favorable downwashed wake was seen for membrane wings Force data confirmed better aerodynamic ef ficiency for membrane wings and continued lift generation at high aoa coinc id ing with mean flow interpretation. The medium pre favorable wake velocities through flow analysis but could not be validated with force data.


99 Root mean square flow fluctuations and Reynolds shear stress values portrayed growing shear layers from the leading and trailing edges for the rigid plate. For the membrane wings, shear layers were seen being pulled t ighter to the surface and also impinging and interacting with membrane oscillations, up to 12 aoa. At high aoa, enhanced turbulent mixing and momentum transport was seen for the membrane wings At 24 aoa particularly large stream and vertical flow fluctuation s were seen in the near wake, driven by the membrane motions. Analysis of the membrane vibrations, incorporating the high pre wing as well, showed trends of dependence on angle of attack (average pressure), pre tension (average tension), and flow behavior. When the shear layer wa s interacting with membrane, there wa s an increase in the RMS fluctuations. At these lower angles of attack, the membrane motions appear driven by the capture of dynamic pressu re around the quarter chord location, which travels the length and gets released at the trailing edge P eak frequencies on average were found in the range of the estimated natural frequency ~58 Hz The vibration frequencies a re much faster than typical dep loyable control surfaces (while the membrane itself is very lightweight and actuates freely ) which can assist as passive control during gusty flight condition s The high pre tension case showed that under high tension, unique vibration behaviors can arise, but fluctuations and mean distention are greatly reduced. Time averaged membrane sh apes showed adaptive cambering with the extent largely dependent upon pre tension. There was an association of largest passive cambering and most efficient aerodynamic perf ormance from force data by the low pre tension model

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100 Plots of the i nstantaneous vorticity field revealed much about the time dependent nature of the FSI. At low angle of attack, shearing from the LE was seen to interact with the membrane distended up and then pass closely to the surface when it was down. As aoa is increased, the membrane trailing edge genera te d vortical structures by allowing a rush of fluid to pass under it, which quickly interacts with fluid being pulled down by the returning membrane mo tion. This typically creates a count er clockwise vorticity structure that was found to affect streamlines of high and low momentum flow, enhancing the momentum transport. Vortex roll up and shear layer excitement, as reported in other studies, were also se en in flow o particularly as the flow tended toward separation at 12 The coupled flow and membrane behavior, as well as insight into where the membrane oscillations were most influential were investigated through spectral and correlation analyses. Membrane frequency content was seen throughout the flow field, as the flow was forced to oscillate at the membrane s dominant frequency T he power of the spectra depended on deviation magnitudes and was greater in the wake and near the membrane TE. Contours of the correlation coefficient showed that the membrane and flow fields were highly correlated and that local flow acceleration s and decelerations were caused by the membrane motions Correlations were shown to oscillate at the me mbrane frequency and have spatial and temporal dependence. The membrane influence was considerably weak er upstream of it, while still statistically significantly correlated. There was also a dependence of correlation strength on angle of attack with gene rally lower values found at higher angles, likely dependent on the reduction of membrane vibration amplitude.

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101 Future While some details of low Reynolds flow and membrane wing interactions were discovered in this study, there is much more to understand. The unsteady vorticity interactions, high turbulence intensities and RSS behavior all indicate the complexity and three dimensionality of the flow. In future study, spanwise and 3 component streamwise PIV could be incorporated to investigate flow in betw een membrane cells (batten plane) and in the n earest wake of trailing edge interactions. The wing aspect ratio is also important, the effects at the wingtips, and how they interact with or alter membrane vibrations should be s tudied. A study dedicated to t ension effects could be carried out with the improved mounting and seeding developed in the progression of this work. This coupled with another th o rough and precise loads study may enlighten answers to the sometimes contrasting results from the present res earch T he medium pre tension model (2.8 ) showed most favorable flows throughout while the low pre tension (1.3 ) wing showed the most efficient aerodynamic forces. The high correlation values found lend themselves as a basis of mathematical decompositio n such as POD or stochastic estimati on techniques. F rom these or future synchronized data sets, low order predictive models could be generated which govern the highly unsteady and coupled fluid structure problems Mutual flow and structure solvers will be more easily validated and honed by experiments such as these. The results of this work have shown a dependence of the flow behavior on membrane oscillation frequency and amplitude While characterized, the details and intricacies of mechanisms driving the membrane oscillations, and how those vibrations may be modeled as a predictable dynamic system, remain to be discovered.

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102 APPENDIX DYNAMIC MASKING This appendix will demonstrate a n example of the dynamic mask ing techniques as el at 12 aoa. Figure A 1 shows the raw image, 2 nd PIV frame where the in PIV model surface. The 1 st step is to track the bright pixels by Sobel edge detec tion and to remove bright seed pixels by looping spatial filtering until only pixels involved with the laser reflection of the model and membrane surface remain. The 2 nd step is to apply a high order polynomial fit curve to the bright pixels which gives a line that outlines the me mbrane shape, to be stored (Figure A 2 ). The 3 rd step is to use the tracked shape to close a geometry that outlines membrane regions and define the shape of the masks (Fig ure A 3 ). Finally, the mask black white image would be reshaped into a grid size that could be fitted with the PIV vector matric es and the process was repeated for all images. Figure A 1. 2 nd

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103 Figure A 2 Polynomial line tracking bright pixel membrane shape Figure A 3 Example mask where membrane resides created using bright pixel line and known model batten TE point. The following method was used to track dark regions created by the out of plane (side cell) membranes or if seeding swayed in the wake frame. Figure A 4 provides an example of an image where an out of plane membrane created a shadow that hid the in plane membrane and would cause invalid PIV data.

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104 Si nce the seed could cause very pixilated regions of lighter and darker light intensities, the image is blurred by a 7x7 mean filter convoluted with the original image (Fig ure A 5 ). The blurred image was then turned directl y into a mask by black white conversion, using an Ostu developed gray scale detection function to dictate wh ich regions were dark or light. The mask is shown in Figure A 6 Finally, it should be noted that these dynamic masks were combined with a static surface to create the final mask used with velocity data. Figure A 4. 2 nd frame PI aoa showing shadow from out of plane membrane.

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105 Figure A 5 Blurred image after convolution with 7x7 mean filter. Figure A 6 Example mask generated for dark regions.

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106 LIST OF REFERENCES [1] Progress in Aerospace Sciences vol. 39, no. 6 7, pp. 425 465, Oct. 2003. [2] xed membrane wings for micro Progress in Aerospace Sciences vol. 44, no. 4, pp. 258 294, May 2008. [3] Based Micro Air Vehicle Applied Mechanics Reviews vol. 58, no. 4, p. 283, 2005. [4] Alleviating 47th AIAA Aerospace Sciences Meeting pp. 1 16 Jan 2009 [5] P. Rojr structure interactions of Experiments in Fluids vol. 46, no. 5, pp. 859 872, Feb. 2009. [6] AIAA Aviation Technol ogy, Integration, and Operations Conference pp. 1 13 Sep 2010 [7] Disciplinary Design of High Aspect Ratio, Gravity Control ICAS 2000. [8] A. Hedenstrm, L. C. Johansso n, M. Wolf, R. von Busse, Y. Winter, and G. R. Science (New York, N.Y.) vol. 316, no. 5826, pp. 894 7, May 2007. [9] Bioinspiration & biomimetics vol. 1, no. 4, pp. S10 8, Dec. 2006. [10] model and span efficiency of flapping flight in bats based on time resolved PIV Experi ments in Fluids Mar. 2011. [11] AIAA Journal vol. 46, no. 8, pp. 2096 2106, Aug. 2008. [12] ane AIAA 46 th Aerospace Sciences Meeting pp. 1 12 Jan. 2008

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107 [13] of Flexible Wings: an Experimental Investigation Applied to Biologically Inspired European Micro Air Vehicle Conference and Flight Competition pp. 17 21 Sep 2007 [14] Characteristics of a Three AIAA Fluid Dy namics Conference pp. 1 16 Jun 2008 [15] Turbulent Transition of a Low Reynolds Number AIAA Journal vol. 45, no. 7, pp. 1501 1513, Jul. 2007. [16] C. P. Haggmark, A. A. Bakchinov, and P. H. Alf Philosophical Transactions: Mathematical, Physical and Engineering Sciences vol. 358, no. 1777, pp. 3193 3205, 2000. [17] Aeronautical Research Council Reports and Memoranda Stationary Office, London, 1969. [18] Aspect Ratio, Thin/Flat/Cambered Journal of Aircraft vol. 37, no. 5, pp. 825 832, Sep. 2000. [19] Annual Review of Fluid Mechanics vol. 35, no. 1, pp. 89 111, Jan. 2003. [20] Design and Integration Encyclopedia of Aerospace Engineering pp. 1 12, 2004. [21] Components, Fabrication, and Flight [22] ements at Low Reynolds Numbers for Fixed Wing Micro RTO AVT / VKI Special Course on Development and Operation of UAVs for Military and Civil Applications 1999. [23] T rends in Ecology & Evolution vol. 17, no. 9, pp. 415 422, 2002. [24] T. J. Mueller, Fixed and Flapping Wing Aerodynamics for Micro Air Vehicle Applications (Progress in Astronautics and Aeronatics Series, Vol.195) AIAA, 2001.

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108 [25] J. M. Grasmeyer and M. AIAA Aerospace Sciences Meeting pp. 1 9 Jan. 2001 [26] Air Vehicle Journal of Aircraft vol. 43, no. 2, pp. 290 3 05, 2006. [27] Aerial Vehicle Design design report, Mar. 2004. [28] Air Vehicl SAMPE conference pp. 1 12, May. 2001. [29] 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 [30] Theory of Sails. I. Two Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences vol. 261, no. 1306, pp. 402 422, May 1961. [31] Journal of Applied Me chanics vol. 30, no. 3, p. 435, 1963. [32] dimensional Journal of Fluid Mechanics vol. 206, pp. 463 475, 1989. [33] Aerodynamic Applied Mechanics and Engineering vol. 44, pp. 1 16, 1984. [34] membrane airfoil in turbule Physics of Fluids vol. 8, no. 12, p. 3346, 1996. [35] Fluid Dynamics vol. 2866, June, pp. 1 12, 2006. [3 6] R. M. Waldman, A. J. Song, D. K. Riskin, S. M. Swartz, and K. S. Breuer, 38th AIAA Fluid Dynamics Conference pp. 1 13 2008 [37] D kinema tics and gliding performance The Journal of experimental biology vol. 209, no. 4, pp. 689 701, Feb. 2006.

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109 [38] S. Arbos and trailing 49th AIAA Aerospace Sciences Meeting pp. 1 16 Jan. 2011 [39] induced vibrations of low aspect ratio rectangular membrane wi Journal of Fluids and Structures pp. 1 14, Jul. 2011. [40] strain and excess length on unsteady fluid Journal of Fluids and Structures vol. 26, n o. 3, pp. 359 376, Apr. 2010. [41] 2009 DoD High Performance Computing Modernization Program pp. 73 80 2009 [42] S. Tiomkin, D. E. Raveh, and R. Ari dimensional 29th AIAA Applied Aerodynamics Conference pp. 1 23 Jun 2011 [43] Flexible Membrane Wing, 50th AIAA Aerospace Sciences Meeting pp. 1 17 Jan 2012. [44] 41 st AIAA Fluid Dynamics Conference pp. 1 20 Jun 2011 [45] H. Hu, M. Membrane Airfoils at Low Reynolds Journal of Aircraft vol. 45, no. 5, pp. 1767 1778, Sep. 2008. [46] Vibration on the Flow Field Surro unding Flat 49th AIAA Aerospace Sciences Meeting pp. 1 17 Jan 2011. [47] Characterization of Limit Cycle Oscillations in Membrane Wing Micro Air Vehic Journal of Aircraft vol. 47, no. 4, pp. 1300 1308, Jul. 2010. [48] P. J. Attar, R. E. Gordnier, J. W. Johnston, W. a. Romberg, and R. N. Part I: Flutter and Limit Cycle Analysis for Fixed Journal of Vibration and Acoustics vol. 133, no. 2, p. 021008, 2011.

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110 [49] 26th AIAA Aerodynamic Measurement Technol ogy and Ground Testing Conference pp. 1 13 2008 [50] edge scalloping effect on flat plate membrane Aerospace Science and Technology vol. 1, pp. 1 11, Jan. 2011. [51] Y. J. Abudaram, P. G. Ifju, J. tension 50th AIAA Aerospace Sciences Meeting pp. 1 11 Jan 2012. [52] ic Characteri 47th AIAA Aerospace Sciences Meeting pp. 1 10 Jan. 2009 [53] 2nd ed. Springer, 2007. [54] L. Str particle image Measurement Science and Technology vol. 8, pp. 1406 1416, 1997. [55] Current Science vol. 79, no. 1, pp. 51 60, Jul. 2000. [56] Z. Zhang, J. P. Hubner, A. Timpe, L. Ukeiley, Y. Abudar Aspect Ratio on Flat 50th AIAA Aerospace Sciences Meeting pp. 1 15 2012 [57] DynamicStudio Product Manual v3.10 2010. [58] Image Processing vol. 147002, no. 3, pp. 1 12. [59] IEEE Systems, man and Cybernetics vol. 9, no. 1, pp. 62 66, 1979. [60] R. L. Panton, Incompressible Flow 3rd ed. J. Wiley, pp. 71 144 2005. [61] AIAA Journal vol. 49, no. 6, pp. 1135 1150, Jun. 2011. [62] S. B. Pope, Turbulent Flows Cambridge University Pr ess, pp. 85 87 2000

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111 [63] J. S. Bendat and A. G. Piersol, Random Data: Analysis and Measurement Procedures 4th ed. Wiley, pp. 368, 545 2010 [64] Y. A. Cengel and J. M. Cimbala, Fluid Mechanics: Fundamentals and Applications McGraw Hill Higher Educatio n, pp. 144 145 2006

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112 BIOGRAPHICAL SKETCH Amory Timpe was born in the year of 1986 in the city of Athens, Georgia. He survived as the middle child with an older brother and younger sister, whom he dearly loves. P rior to previous recollection, h is family moved to Winter Haven, Florida, where feats of a erospace e ngineering and human flight. His other passion from a young age is one f or the sport of hockey, even living in sunny Florida He decided to pursue high school education at the International Baccalaureate (IB) world school housed at Bartow Senior High to ensure the best chance of becoming an a erospace e ngineer graduating in 2005. Accepted to the University of Flori da, the next years were spent living and learning in Gainesville, Florida. In Gainesville he enjoyed participating Hockey Club, holding office and traveling to play tournaments against rival s chools. An avid sports and Gators fan, he w as fortunate to participate in intramural sports and to witness multiple NCAA national titles during his undergraduate studies. He began undergraduate research in his junior year where he was able to assist with wind tunnel testing and airfoil designs, un der guidance of Dr. Lou is Cattafesta. In the fall of 2009 he graduated with a B.S. in m echanical e ngineering. Continuing research he began a m a s project in the fall of 2010 to study low Re membrane wing and flow interaction s with advisor Dr. La wren ce Ukeiley. With the completion of his m a erospace e ngineering, Amory hopes to find work in the a erospace technology industr y after graduating in May of 2012.