<%BANNER%>

Effects of Isotropic Flexibility on Wings under a Plunging Motion

Permanent Link: http://ufdc.ufl.edu/UFE0044213/00001

Material Information

Title: Effects of Isotropic Flexibility on Wings under a Plunging Motion
Physical Description: 1 online resource (92 p.)
Language: english
Creator: Campos, Diego G
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2012

Subjects

Subjects / Keywords: bio-inspired -- flexibility -- fluid-structure -- interaction -- piv -- plunging
Mechanical and Aerospace Engineering -- Dissertations, Academic -- UF
Genre: Aerospace Engineering thesis, M.S.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: In recent years there has been an interest in studying and understanding natural flyers to incorporate some of their features into small engineered flying systems. Natural flyers display desirable flight characteristics, such as increased maneuverability, that could be used in the design of micro air vehicles. The present study is aimed at understanding the effect of flexibility on the aerodynamic performance and flow around plunging flexible wings. The value of wing stiffness is varied using a predetermined scaling parameter, defined as the ratio of elastic to aerodynamic forces. The first part of the study consisted of matching conditions from previous water tunnel studies to investigate the requirement of dynamic similarity using the wing stiffness parameter. This study investigates the unsteady flow phenomena generated from plunging wings with varying flexibility. The structures are then analyzed to understand the mechanisms for force production. The measurements showed that large deflections at the tip produced strong leading edge vortices. However, when the tip-root lag is greater than 70degrees, the effects are adverse resulting in no leading edge vortex development. In order to understand wing flexibility further, experiments were performed using a laser Doppler Vibrometer to understand the modal properties for each wing with varying flexibility parameter. The second set of experiments consists of studying wings that do not have twist constrained. The ratio of plunging to natural frequency is varied between the value for maximum propulsive efficiency and for maximum propulsive force. This set will allow for comparison with the previous studies, in an attempt to understand the effect of the twist on the flow, and performance. It will also serve to understand the flow phenomena for the cases of maximum efficiency and maximum force. This will provide a framework for the study of wing flexibility using force, flow and structural measurements.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Diego G Campos.
Thesis: Thesis (M.S.)--University of Florida, 2012.
Local: Adviser: Ukeiley, Lawrence S.

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2012
System ID: UFE0044213:00001

Permanent Link: http://ufdc.ufl.edu/UFE0044213/00001

Material Information

Title: Effects of Isotropic Flexibility on Wings under a Plunging Motion
Physical Description: 1 online resource (92 p.)
Language: english
Creator: Campos, Diego G
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2012

Subjects

Subjects / Keywords: bio-inspired -- flexibility -- fluid-structure -- interaction -- piv -- plunging
Mechanical and Aerospace Engineering -- Dissertations, Academic -- UF
Genre: Aerospace Engineering thesis, M.S.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: In recent years there has been an interest in studying and understanding natural flyers to incorporate some of their features into small engineered flying systems. Natural flyers display desirable flight characteristics, such as increased maneuverability, that could be used in the design of micro air vehicles. The present study is aimed at understanding the effect of flexibility on the aerodynamic performance and flow around plunging flexible wings. The value of wing stiffness is varied using a predetermined scaling parameter, defined as the ratio of elastic to aerodynamic forces. The first part of the study consisted of matching conditions from previous water tunnel studies to investigate the requirement of dynamic similarity using the wing stiffness parameter. This study investigates the unsteady flow phenomena generated from plunging wings with varying flexibility. The structures are then analyzed to understand the mechanisms for force production. The measurements showed that large deflections at the tip produced strong leading edge vortices. However, when the tip-root lag is greater than 70degrees, the effects are adverse resulting in no leading edge vortex development. In order to understand wing flexibility further, experiments were performed using a laser Doppler Vibrometer to understand the modal properties for each wing with varying flexibility parameter. The second set of experiments consists of studying wings that do not have twist constrained. The ratio of plunging to natural frequency is varied between the value for maximum propulsive efficiency and for maximum propulsive force. This set will allow for comparison with the previous studies, in an attempt to understand the effect of the twist on the flow, and performance. It will also serve to understand the flow phenomena for the cases of maximum efficiency and maximum force. This will provide a framework for the study of wing flexibility using force, flow and structural measurements.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Diego G Campos.
Thesis: Thesis (M.S.)--University of Florida, 2012.
Local: Adviser: Ukeiley, Lawrence S.

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2012
System ID: UFE0044213:00001


This item has the following downloads:


Full Text

PAGE 1

1 EFFECTS OF ISOTROPIC FLEXIBILITY ON WINGS UNDER A PLUNGING MOTION By DIEGO GUSTAVO CAMPOS A THESIS PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE UNIVERSITY OF FLORIDA 2012

PAGE 2

2 2012 Diego Gustavo Campos

PAGE 3

3 To my parents

PAGE 4

4 ACKNOWLEDGMENTS I would like to thank Dr. Lawrence Uk eiley for his guidance and support on my research. Thank you to my committee members, Dr. Peter Ifju and Dr. Rick Lind, for reviewing my work and for their valuable input. I would also like to thank Adam Hart for the time spent teaching me how to use all the equipment and for his advice, Dr. Erik S llstr m for his insight and assistance in developi ng many of the data processing routines used in this study and Amory Timpe for his help throughout this process, and for his help outside of research. Thank you to all my friends for their support I would like to acknowledge the support of AFOSR through a MURI program managed by Dr. Smith and the Florida Center for Advanced Aero Propulsion.

PAGE 5

5 TABLE OF CONTENTS page ACKNOWLEDGMENTS .................................................................................................. 4 LIST OF TABLES ............................................................................................................ 7 LIST OF FIGURES .......................................................................................................... 8 ABSTRACT ................................................................................................................... 10 CHAPTER 1 INTRODUCTION .................................................................................................... 12 Motivation ............................................................................................................... 12 Background ............................................................................................................. 14 Scaling Parameters .......................................................................................... 14 Reynolds number ....................................................................................... 15 Strouhal number ........................................................................................ 16 Reduced frequency .................................................................................... 17 Fluid St ructure Interaction Scaling Parameters ................................................ 18 Effective stiffness ....................................................................................... 19 Cauchy number .......................................................................................... 19 Elastoinertial number ................................................................................. 20 Frequency ratio .......................................................................................... 20 Aeroelastic studies (Benefits of flexibility) ......................................................... 21 Chordwise flexible studies .......................................................................... 22 Spanwise flexible studies ........................................................................... 23 Combined spanwise and chordwise flexible studi es .................................. 24 Current Study .......................................................................................................... 24 2 FACILITIES AND EXPERIMENTAL SETUP ........................................................... 26 Aerodynamic Characterization Facility .................................................................... 26 Plunging Device ...................................................................................................... 27 Motion Analysis ................................................................................................ 27 PIV Synchronization ......................................................................................... 28 Wing Models ........................................................................................................... 28 Experimental Parameters ....................................................................................... 29 Stereo Partic le Image Velocimetry .......................................................................... 30 SF PIV Measurement Setup ............................................................................. 30 SFPP PIV Measurement Setup ........................................................................ 31 Force Transducer ................................................................................................... 32 Laser Doppler Vibrometer ....................................................................................... 32

PAGE 6

6 3 DATA PROCESSING ............................................................................................. 38 Q Criterion .............................................................................................................. 38 Force Estimation ..................................................................................................... 38 Pressure Estimation ......................................................................................... 40 Momentum Balance ......................................................................................... 40 Stereo Particle Image Velocimetry .......................................................................... 42 Scheimpflug Condition ..................................................................................... 42 Calibration ........................................................................................................ 43 4 RESULTS AND DISCUSSION ............................................................................... 45 Modal Analysis ........................................................................................................ 45 Fully Suppor ted Root Studies ................................................................................. 47 Flow Field Analysis ........................................................................................... 48 SF3 model .................................................................................................. 48 SF1 model .................................................................................................. 51 Wing Deformation/Comparison Studies ........................................................... 52 Force Calculations ............................................................................................ 54 Spanwise Flexibl e Wings with Passive Pitch .......................................................... 55 Flow Field and Deformation Analysis ............................................................... 56 SFPP3 Model ................................................................................................... 57 Frequency ratio of 0.4 ................................................................................ 58 Frequency ratio of 0.9 ................................................................................ 59 SFPP2 Model ................................................................................................... 61 Frequency ratio of 0.4 ................................................................................ 61 Frequency ratio of 0.9 ................................................................................ 62 SFPP1 Model ................................................................................................... 64 F requency ratio of 0.4 ................................................................................ 64 Frequency ratio of 0.9 ................................................................................ 65 Momentum Balance ......................................................................................... 66 5 SUMMARY AND FUTURE WORK ......................................................................... 81 LIST OF REFERENCES ............................................................................................... 85 BIOGRAPHICAL SKETCH ............................................................................................ 92

PAGE 7

7 LIST OF TABLES Table page 2 1 Dimensionless kinematic scaling parameters ..................................................... 34 2 2 Kinematic and geometric properties ................................................................... 34 2 3 Material properties .............................................................................................. 34 2 4 Dimensionless fluid structure scaling parameters. ............................................. 34 2 5 ATI Nano 17 sensing range ................................................................................ 34 2 6 ATI Nano resolution for a 16bit DAQ ................................................................. 34 4 1 Modal Analysis on the wing models. ................................................................... 69 4 2 Frequency ratios for the studies in wind and water tunnel. ................................. 69

PAGE 8

8 LIST OF FIGURES Figure page 2 1 Plunging device with wing att ached. ................................................................... 35 2 2 Sinusoidal motion analysis. ................................................................................ 35 2 3 Zimmerman planform wings. .............................................................................. 35 2 4 PIV planes and coordinate system. .................................................................... 36 2 5 SF experiment setup. ......................................................................................... 36 2 6 SFPP experiment setup. ..................................................................................... 37 2 7 Shaker and wing setup. ...................................................................................... 37 3 1 Schematic of the Scheimpflug condition. ............................................................ 43 3 2 Lavision calibration t arget. .................................................................................. 44 4 1 First Mode (Bending) for wings tested in the SF experiment. ............................. 69 4 2 Second Mode (Twist Bending) for 2 wings tested in SFP P study. ...................... 69 4 3 Vorticity and Q criterion at beginning of the downstroke for the SF3 wing at the 50% location. ................................................................................................ 70 4 4 Vorticity and Q criterion at phase 75 for SF3 model at 50% spanwise location. .............................................................................................................. 70 4 5 Vorticity and Q criterion at beginning of downstroke for SF3 wing at 75% spanwise plane. .................................................................................................. 70 4 6 Vorticity and Q criterion at 75 phase for SF3 wing at 75% spanwise plane. ..... 71 4 7 Isosurfaces of Q. slices are at 50% and 75% spanwise planes. ......................... 71 4 8 Normalized velocity at phase 75 for SF3 wing at 75% spanwise plane ............. 72 4 9 Vorticity and Q criterion at beginning of the downstroke for SF1 wing ................ 72 4 10 Vorticity and Q criterion near midstroke for SF1 wing. ....................................... 73 4 11 Displacements as a funtion of phase for SF1 and SF3 wings. ........................... 73 4 12 Vorticity plots for phases where the LEV leaves TE for SF3 wing ...................... 74

PAGE 9

9 4 13 Phase averaged force calculations using Momentum Balance approach ........... 74 4 14 Vorticity fields ( *) for SFPP3 model. ................................................................. 75 4 15 Vorticity fields ( *) for SFPP2 model. ................................................................. 7 6 4 16 Vorticity fields (w*) for SFPP1 model. ................................................................. 77 4 17 Spanwise deformation for the SFPP3 wing. ....................................................... 78 4 18 Spanwise deformation for SFPP2 wing. ............................................................. 78 4 19 Spanwise deformation for SFPP1 wing. ............................................................. 79 4 20 Force in the streamwise direction for SFPP3 wing using momentum balance method. .............................................................................................................. 79 4 21 Force in the streamwise direction for SFPP3 wing using momentum balance method. .............................................................................................................. 80 4 22 Force in the streamwise direction for SFPP1 wing using momentum balance method. .............................................................................................................. 80

PAGE 10

10 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 EFFECTS OF ISOTROPIC FLEXIBILITY ON WINGS UNDER A PLUNGING MOTION By Diego Gustavo Campos May 2012 Chair: Lawrence S. Ukeiley Major: Aerospace Engineering In recent years there has been an interest in studying and understanding natural flyers to incorporate some of their features into small engineered flying systems. Natural flyers display desirable flight characteristics, such as increased maneuverability, that could be used in t he design of micro air vehicles The present study is aimed at understanding the effect of flexibility on the aerodynamic performan ce and flow around plunging flexible wings. The value of wing stiffness is varied using a predetermined scaling parameter, defined as the ratio of elastic to aerodynamic forces. The first part of the study consisted of matching conditions from previous wat er tunnel studies to investigate the requirement of dynamic similarity using the wing stiffness parameter. This study investigates the unsteady flow phenomena generated from plunging wings with va rying flexibility. The structures are then analyzed to under stand the mechanisms for force production. The measurements showed that large deflections at the tip produced strong leading edge vortices. However, when the tiproot lag is greater than 70, the effects are adverse resulting in no leading edge vortex development. In order to understand wing flexibility further, experiments were performed using a laser Doppler

PAGE 11

11 Vibrometer to understand the modal properties for each wing with varying flexibility parameter. The second set of experiments consists of studying w ings that do not have twist constrained. The ratio of plunging to natural frequency is varied between the value for maximum propulsive efficiency and for maximum propulsive force. This set will allow for comparison with the previous studies, in an attempt to understand the effect of the twist on the flow, and performance. It will also serve to understand the flow phenomena for the cases of maximum efficiency and maximum force. This will provide a framework for the study of wing flexibility using force, flow and structural measurements.

PAGE 12

12 CHAPTER 1 INTRODUCTION Motivation Natural flyers display many desirable flight characteristics that could be used in the desig n of micro air vehicles (MAVs) [ 1 ] [ 6 ] Insects and birds are able to handle wind gusts, avoid objects with great maneuverability, as well as hover The kinematics observed in biological flyers is complex, often involving highly deformable wing shapes and coordinated wing tail movement [ 7 ] [ 11 ] The motions involve flexing, twisting, bending and rotating the wing s throughout the flapping cycle, leading to a complex fluidstructure interaction that is not fully understood[ 12 ], [13 ] This creates highly coupled nonlinearities in structural dynamics and fluid dynamics making it a rich field of study [ 14] MAVs capable of mimicking natural flyers would prove helpful in areas such as remote sensing and information gathering for both civilian and homeland security applications. Recently there have been many vehicle concepts that were developed in order to address these mission requirements. The Aerovironment Nano Hummingbird, a small hovering ornithopter with a wingspan of 16.5 cm has demonstrated its ability to achieve controlled flight (hover and forward) strictly with the use of its flapping wings, a feature only achievable by biological flyers previously [ 15] It h over s and sustains flight for several minutes, and transmit s color video to a remote station, while closely resembling a hummingbird. Other examples of successful flapping wing MAVs are the Delfly I,II and Micro [ 16] from the Delft University of Technology, the Mic rorobotic Fly from the University of Harvard[ 17] the Mentor from SRI international and UTIAS [ 18 ] and the commercially available iBird[ 19 ] Even though there are a number of working

PAGE 13

13 vehicles, the aerodynamics, structural, and control implications of the many modes seen in biological flight are not understood enough for efficient design[ 14 ] One of the main features common to many natural flyers is their deformable wing structure Wing flexibility has been recognized as an important aspect for insect and bird flight aerodynamics [ 20 ] [ 22 ] Studies conducted by Wootton [ 23 ] on butterflies concluded that flexible wing surfaces adapt their shape in response to external fluid forces, thus chang ing aerodynamic force production during flight. Combes & Daniel [ 24] [ 26 ] have performed a series of experiments to understand the variation of wing flexural stiffness across al l insects and the influence of wing venation and force contributions to deformation. They found that flexural stiffness varies significantly amongst insects, spanning about four orders of magnitude. Likewise, venation patterns across insects are diverse. I n the case of flapping insect wings they concluded that wing flexibility was governed primarily by the inertia of wing rather than the aerodynamic forces from the aeroelastic interaction, thus they believed that wings could be treated as purely inertial, f lexible structures. These studies show the intricacy in trying to model bio inspired wings, and the many characteristics of biological flight. Rather than mimicking the characteristics of a specific flyer, this study will focus on understanding certain ch aracteristics and effects of wing deformation. This study is part of a multidisciplinary effort aimed at developing a better understanding of the effects of flexibility on the flow behavior, a nd on the force production. This study concentrates on experimen tal investigations of the flow, deformation and forces produced by wings The wings have isotropic bending characteristics and are studied under forward flight conditions. A plunging motion is

PAGE 14

14 used, in order to simplify the deformation characteristics of t he wing. This will allow for a better understanding of how the spanwise and chordwise bending of the wing affects the flow and how the fluidic structures formed relate to the generation of aerodynamic forces. The following sections of C hapter 1 contain a r eview of the research related to the study of wing flexibility. It is then followed by C hapter 2 describing the experimental setup and Chapter 3 with analytical methods used to investigate the data. Chapter 4 presents the t wo sets of experiments conducted; one on spanwise flexible wings fully supported at the root, and the second on wings partially supported While C hapter 5 presents a summary of the research, the conclusions, and future work. Background As outline d in the previous section, i n recent years there has been an interest in studying and understanding natural flyers to incorporate some of their characteristics into engineered flying vehicles In order to achieve this goal, a better understanding of the unsteady fluid phenomena generated by the win g kinematics of insects and birds to achieve the aerodynamic forces necessary for flight is desired. The mechanisms that govern the generation of aerodynamic forces are associated with the formation and shedding of vortices into the flow. Therefore, an understanding of the fluidstructure interactions between the vortex dynamics and the structural properties of the wing is of great importance. Scaling Parameters Non dimensional scaling parameters that relate wing material characteristics and the kinematics to the free stream conditions allow for a better understanding of the effects of wing stiffness By using scaling the number of parameters that describe the

PAGE 15

15 system can be reduced, and an assessment of which combination of parameters are important for certain condition can be analyzed[ 13 ] There have been several studies that have performed a nondimensional analysis to identify the character istic properties of flapping systems. Depending on the models used the parameters vary. The parameters involved are divided into two types: parameters related to the fluid dynamics and the wing kinematics, and the parameters related to the fluidstructure interaction. The following sections will present a review of the relevant parameters used in the study of wing flexibility, and the findings of the parametric investigations performed with these parameters. Re ynolds number Reynolds number (Re) represents t he ratio of inertial forces to viscous forces. In forward flapping flight the Re is selected depending on the flight conditions and the wing kinematics. The reference velocity is either the mean wing tip velocity ( ) or the forward flight velocity ( ) The Re for hovering flight and forward flight based on wing tip velocity is shown in Equation 1 1 = (1 1) Where is the fluid d ensity, is the aspect ratio, is the full stroke amplitude, is the flapping frequency, c is the chord, and is the kinematic viscosity of the fluid. If the reference velocity is the forward flight velocity the Re is written as in Equation 1 2 = (1 2) In this form the Re is based only on the chord and the flight velocity and not the flapping characteristics.

PAGE 16

16 Flapping flight is characterized by low flight speeds which result in a low c hord based Reynolds number. In this regime, the aerodynamic characteristics and the dynamics of the vortex structures have been shown to be affect ed by variations in the Reynolds Number. Studies by Shyy, et al [ 13], [27 ] and Tang et al [ 28] showed that for natural flyer configurations, the Re was the dominant parameter dictating the transient development of v ortex structures. In order to study the effect of the Re on the leading edge vortex (LEV) and the spanwise flow, Shyy et al [ 13 ] performed a numerical investigation using realis tic models of a hawkmoth, honeybee, fruit fly, and thrips. It was found that that there is a dependency on Reynolds number for the LEV structures, the spanwise flow inside the LEV, and the spanwise variation on the pressure gradient. For a Re O(102) the LE V remained attached during the entire half stroke and it connected to the tip vortex Also, some spanwise flow is observed around the upper region of the trailing edge. While f o r a Reynolds number in the O(103) and O(104) the LEV had a spiral structure, an d broke down i n the middle of the downstroke. For this case a much stronger spanwise flow inside the LEV and at the trailing edge is seen. Tang et al [ 28 ] did a numerical investigation on a 2D elliptic airfoil for Re ranging from 75 to 1700. They showed the ability of the Reynolds number to alter the flow symmetry between downstroke and upstroke. For a Re O(102) the viscosity dissi pated the vortex structures and led to sy mmetric flow, while for Re O(103) the history effect is important, leading to asymmetric flow between strokes. Strouhal number The Strouhal number describes the relative influence of the free stream velocity to the flapping frequency and amplitude. The St is defined in Equation 1 3 for a plunging wing.

PAGE 17

17 = 2 (1 3) Where f is the flapping frequency and h is the plunge amplitude of oscillation. Studies based on the St have found that it characterizes the vortex dynamics of the wake[ 29 ] It is linked to the aerodynamic force coefficients and the propulsive efficiency as it defines the maximum aerodynamic angle of attack and the timescales as sociated with the growth and shedding of the vortices, which produce the necessary forces for flight and swimming [ 30], [ 31 ] A study by Taylor et al [ 32] showed that both fish and natural flyers have a typical St range from 0.2 to 0.4. A series of studies with isolated pitching or plunging have shown that high peak propulsive efficiencies are reached within this interval [ 33] [ 37 ] Similar results have also been obtained for studies with wing flexibility, where an increase in propulsive efficiency was found for St > 0.2 [ 38] They found that the reason for decreases in efficiency for Strouhal numbers not within this interval may be the result of increased flow separation at higher St and a transit ion to drag at lower St [ 38], [ 39 ] Reduced f requency Reduced frequency is a measure of the unsteadiness associated with a flapping wing as it compares spatial wavelength of the flow disturbance with the chord length[ 29 ] The reduced frequency based on the forward flight speed is written in Equation 1 4 = (1 4) And it can be rewritten to be a function o f the Strouhal number as in Equation 1 5 = 2 (1 5)

PAGE 18

18 When studying pitching, plunging, and flapping systems both the St and k are often needed because of the importance of the unsteadiness, and the dynamics of the wake [ 35] Studies by Ohmi et al [ 40 ], [41] on plunging and pitching ai rfoils showed that at large incidence angles patterns in the vortex wake depend on whether the translational or rotational motion dominate the flow, which was primarily determined by the reduced frequency. FluidStructure Interaction Scaling Parameters Rec ently, in the field of flexible flapping wing aerody namics there have been numerous efforts in developing scaling arguments that characterize the complex interplay between flexibility and the resulting aerodynamics [ 14 ] [ 12 ] The scaling parameters derived depend on the types of models used, and the governing equations. Relevant FSI scaling parameters for the study of flapping and plunging flexibl e wings have been provided by Shyy et al [ 12 ] and were obtained through performing a dimensional analysis using the fluid density, flow velocity and the chord as the basis variables [ 42], [43 ] These were also derived by evaluating the kinematics and governing equations for the structure and fluid[ 13 ], [ 44] Later studies fo und that the added mass force was important in the natural flight regime. Added mass force is due to the displacement of the fluid caused by the moving wing. As the wing moves down, the fluid below it has to adjust and mov e around the wing, in this sense adding mass towards the TE. A base for the study of the added mass effects were provided from scaling relationships for aerodynamic forces and wing deflection as a function of the density ratio, natural to flapping frequency ratio, reduced frequency, and flapping amplitude[ 42 ], [ 45] These studies led to the recent interest in comprehending the connect ion between excitation frequency and the structural properties (mass, density, bending and t wisting

PAGE 19

19 modes) of natural flyers. Particular interest is placed upon the ratio of flapping to natural frequency and its relationship to the maximum propulsive force and maximum efficiency. The following segments present a brief introduction of the FSI parameters derived and the results of their studies. Effective stiffness The effective stiffness ( ) describes the ratio between the elastic bending forces and aerodynamic force s. This parameter is expressed in Equation 1 6 = (1 6) W is the air density U is the free stream v elocity, and c is the root chord. The flat plate bending stiffness ( D ) is defined in Equation 1 7 = 12 ( 1 ) (1 7) Exp erimental studies by Rausch et al [ 43 ], [46 ] on rigid and flexible flat plates have characterized flexibility by varying the parameter, while maintaining all other kinematic parameters constant. They found that a wing with an effective stiffness value greater than 1000 had no flexibility, and one with a value of 30 had significant flexibility, with the tip lagging the root by as much as 70 degrees in the cycle. They also found that a wing with too much flexibility is detrimental to force production. The drawback of using this parameter was that it did not account for the effects of fluid density ratios, thus further investig ation needed to be performed. Cauchy number Ishihara et al [ 44 ], [47 ] investigated the Navier S tokes equation and the linear iso tropic elasticity equations and they introduced the Cauchy number. This number

PAGE 20

20 describes the ratio between the fluiddynamic pressure and elasti c reaction force and is expressed in Equation 1 8 = (1 8) Where is defin ed as the maximum wing speed of the flapping motion of the leading edge center, and is the torsional stiffness. Elastoinertial number Thiria et al [ 45 ] and Ramananarivo et al [ 48 ] measured the thrust and propulsive efficiency of a self propelled flapping flyer with flexible wings in air. They introduced the elastoinertial number which describes the ratio of the inertial forces and the elastic restoring forces. Their results show that since the density ratio was high the elastic deformation of the wing was mostly balanced by the inertia. The ela stoinertial number is defined in Equation 1 9 = (1 9) Where A is the amplitude of motion, L is the plate length, is the frequency and B is the bending rigidity. Frequency ratio One of the similarities in the recent scaling parameters proposed is that they are a function of the ratio of flapping frequency to natural frequency of the material. There have been several studies that have been carried out to find the optimum ratios for aerodynamic performance in natural flyers, with focus on maximum propulsive force and maximum efficiency.

PAGE 21

21 Recent investigations showed tha t maximum propulsive force was achieved when the wings were excited at a frequency slightly lower than the natural frequency of the system [ 45], [ 48 ] [ 53 ] Masoud et al [ 50 ] utilized the lattice Boltzmann method and showed that the maximum propulsive force occurred at a frequency ratio of 0.95. It was shown that the maximum force increased when inertial effects of the wing became more important than the fluid inertia. Similarly, Spagnolie et al [ 52] showed that the forward velocity peaked when the flapping frequency was near resonance for a numerical an experimental study on a passively pitching wings. The optimum ratio for the propulsi ve efficiency was found to be only a fraction [ 45 ], [ 48], [ 50 ], [ 54] im plying operating away from resonant conditions is beneficial Vanella et al [ 54 ] performed a numerical investigation on the propulsive efficiency of flapping wings in a hovering environment. It was found that the optimum ratio for efficiency was significantly lower than that for the propulsive force, only at 0.33. The f orce s were increased due to the enhancement of the wake capture mechanism Wake capture occurs when vortices of different direction align to create jet like behavior This enhancement was consequence of stronger streamwise flow during the upstroke induced from a strong vortex at the trailing edge. Aeroelastic studies (Benefits of flexibility) The last section introduced the parameters used in the study of wing flexibility and their relation to force production. Although the advances have bee n significant, these studies have not concentrate d on the flow features and how the stiffness affects the flow hence an understanding of the underlying unsteady mechanisms used to generate the forces has not been gained. This section will focus on presenting an overview of the studies done in order to understand the benefits of wing flexibility. The main purpose is

PAGE 22

22 to understand the influence of wing compliance on the flow, specifically, on the generation and evolution of organized vertical flow structures and how they relate to the generation of aerodynamic forces. Chordwise flexible studies Hea thcote et al [ 55 ] studied the effect of chordwise flexibility on performance for an airfoil in a pure plunging motion at hovering conditions. Their results showed that the strength of the vortices, their spacing, and the timeaveraged v elocity of the induced jet depend on the airfoil stiffness, plunge frequency and the amplitude. Force measurements showed that at high frequencies an airfoil with intermediate stiffness had the greatest thrust coefficient. Another benefit that was noted in that study was the increased efficiency for the flexible airfoils, compared to the rigid ones. Similar results were found in a study by Michelin and Smith [ 49 ] where the thrust increased with flexibility, but they also found that below a certain threshold the wing is too flexible and leads to a net drag, as it cannot communicate momentum to the flow. Another study by Heathc ote and Gursul [ 56 ] investigated chordwiseflexible airfoils plunging at constant amplitudes in a water channel. This study also showed a peak in thrust for intermediate stiffness. For this case the vortices were stronger, and farther apart in the cross stream direction. The timeaveraged flow also showed a stronger induced jet. This study also observed efficiency benefits, with the flexible models showing a 15% improvement over the rig id models. The flow displayed weaker LEV for these cases. Zhao et al [ 57 ] investigated the effects of chordwise flexibility using scaled models of a fruit fly. The wings were tested at 23 different angles of attack ranging from 9 to 90 degrees Results showed that the overall lift generation of flapping wings deteriorated

PAGE 23

23 as flexibility increased, however the flexible wings could generate more lift at higher angles. This was due to the bending of the wing s urface causing an improvement in the lift to drag ratios. Spanwise flexible studies Rausch et al [ 46 ] presented the effects of spanwise flexibility on the aerodynamics of plunging, isotropic wings. The study characterized flexibility by varying the effective stiffness over three orders of magnitude (101, 103 and 104). They showed that the introduction of flexibility caused greater three dimensional flow towards the tip of the wing. It was also shown that the development o f a larger leading edge vortex was the result of an increase in plunge induced angle of attack for the cases of greater flexibility A continuation of this study [ 43] investigated the forces for these wings, with the addition of a moderately flexi ble wing ( = 180 ) Results showed that the moderately flexible wing had the largest lift coefficient history, while the very flexible wing had the smallest. Thus indicating that too much spanwise flexibility is detrimental to force production. The flow for moderat ely flexible wing was dominated by the presence of a LEV on the suction and pressure side of the wing. Heathcote et al [ 39 ] performed water tunnel studies on spanwise flexible rectangular wings in forward flight. A thrust benefit of approximately 50% was observed for an intermediate flexibility wing. The flow showed a reverse von Ka rman vortex street near the wing root, and the splitting of vortices for locations closer to the tip. Similarly, the highly compliant wing performed poorly and was characterized by large tip phase lags. This led to the formation of vorticity of one sense near the root, and opposite near the tip, thus having a weak vorticity pattern.

PAGE 24

24 C ombined spanwise and chordwise flexible studies Mountcastle and Daniel [ 58] investigated the effect of wing compliance of the hawkmoth Manduca Sexta. They found that the flexible wings yield mean advective flows with greater magnitudes and orientations more beneficial to lift when compared to stiff wings Aono et al [ 59] performed an experimental and numerical study on an aluminum wing prescribed with singleDOF flapping at 10 Hz. The flow is characterized by counter rotation vortices at the LE a nd TE that interact with the tip vortex during the wing motion. The vortices generated in the previous stroke are captured by the wing and interact with the vortices being generated in the next stroke. Beneficial mean and instantaneous thrust was seen for the most flexible case, as the elastic twisting induced changes in the effect ive angle of attack. Kim et al [ 60 ] developed a biomimetric flexible flapping wing to investigate the camber, chordwise flexibility and unsteady effects. Results showed that the camber due to the flexibility could have beneficial e ffects such as stall delay, drag reduction and LEV stabilization on flapping wing aerodynamics. These and other studies show consistent findings for the effects of flexibility [ 61] [ 63] The spanwise flexibility increases aerodynamic forces by inducing higher effective angles of attack, while the chordwise flexibility redistributes lift and t hrust by changing the projection angle with respect to the free stream [ 13] Current Study The present study is aimed at understanding the effect of flexibility on the aerodynamic performance and flow around plunging flexible isotropic wings. The value of wing stiffness is varied using a predetermined scaling parameter, defined as the ratio

PAGE 25

25 of elastic to aerodynamic forces ( ). The first part of the study consists of matching conditions from previous water tunnel studies to investigate the requirement of dynamic similarity using the wing stiffness parameter. This phase investigates the unsteady flow phenomena generated from plunging wings with va rying flexibility. The structures are then analyzed to understand the mechanisms for force production. The second set of experiments consists of studying wings that are not supported along the whole root thus allowing greater twist The ratio of plu nging frequency to the wings damped natural frequency is varied between the value for maximum propulsive efficiency and for maximum propulsive force. This data set will allow for comparison with the previous studies, in an attempt to understand the effect of the twist on the flow, and performance. It will also serve to understand the flow phenomena for the cases of maximum efficiency and maximum force. This will provide a framework for the study of wing flexibility using force, flow and structural measurem ents .

PAGE 26

26 CHAPTER 2 FACILITIES AND EXPERIMENTAL SETUP Chapter 2 provides a description of the experimental parameters, the facility, the hardware and the corresponding setups for the experiments on the spanwise flexible (SF) and spanwise flexible with passive pitch wings (SFPP) The equipment includes a particle image velocimetry system, a flapping device, wings, a load cell, and a laser Doppler Vibrometer Aerodynamic Characterization Facility The experiments conducted for this thesis have been conducted in the Aerodynamic Characterization Facility (ACF) at the University of Florida Th is wind tunnel is an open jet open return facility specifically designed for low Reynolds number experiments. The tunnel entrance is comprised of a flow conditioning system along with an 8:1 area contraction ratio. The test section inlet has a 1.07 m x 1.07 m opening. T he open test section has an axial length of 3.05 meters. The wind tunnel has the capability of achieving free stream velocities between approximately 0.5 and 22 m /s. The flow has a uniform core of at least 60% of the cross sectional area at the midpoint in the test section. The vertical and horizontal centerline mean freestream velocities vary within 0.03 m/s for a mean freestream velocity of 2 m/s. Additionally, e xperiments showed that turbulence intensities were less than 0.07% for a free stream velocity around 2 m/s which is the free stream velocity being used in these experiments. Further details of the flow quality and a more extensive description of the ACF can be found in Albertani et al [ 64]

PAGE 27

27 Plunging Device A mechanism was designed and built to perform a plunging motion for the exp eriments presented in this thesis Figure 2 1 is a photograph of the plunging mechanism. The device is driven by a Maxon EC 16 15 W Brushless DC motor with hall sensors. It contains a planetary gear head with a 57/13 reducti on ratio that provides the additional torque needed to drive the wings. The maximum input speed with the addition of the gear head is 8000 rpm. The motors MR M type encoder provides a pulse signal with 4096 pulses per revolution, which allows the EPOS2 24/5 Positioning Controller to determine the position of the motor with a precision of 1/1024th revolution or 0.35. The controller obtains position and velocity feedback from the encoder and regulates the motor. The output speed range for the motor shaft is 0 30 Hz, and is controlled to within 1% of the desired speed. The plunging mechanism works by transforming the rotation output from the motor into a reciprocating motion which slides a linear bearing. The root of the wing is attached to a structure that m oves with the bearing, thus having a sinusoidal plunging motion at the desired amplitude. Motion Analysis The plunging mechanism is designed to have a repeatable sinusoidal motion, defined by Equation 2 1 ( ) = cos ( 2 ) (2 1) W here is the plunging amplitude of the motion and f is the plunging frequency. The accuracy of the motion was verified using a high speed camera to track the wings root. In these verification experiments i mages wer e acquired at a rate of 500 Hz and an in house Matlab script was written to interpret the root locations within the images.

PAGE 28

28 Figure 2 2 presents a comparison of the commanded motion (tracking sinusoid) with the measured locat ion of the wing root (bearing position).The motion devi ates slightly at the extremes where the wing root comes to a complete stop. At these positions in the kinematic motion the loads are significantly greater After performing a spectral analysis on the acquired locations, it was determined that the desired motion is achieved to within 0.1 Hz. PIV Synchronization The relative wing position for each PIV snapshot is determined by sampling the encoder position at each instant the PIV cameras are triggered. A NI DAQ 6220 DAQ card is used to sample the motor encoder signal on two channels and the PIV trigger signal on the third. A C based computer software is utilized to process the encoder output and track the motion. The program samples when it receives the fi rst PIV trigger signal, which is then used to synchronize with the motor position. Wing Models The wings used in these experiments had a Zimmerman planform which is defined as two ellipses meeting at the quarter chord point. Specific dimensions are shown in Figure 2 3 (a) resulting in an aspect ratio of 7.65, defined by Equation 2 2 = 4 (2 2) W here S is the surface area of the wing, and b is its semispan. The wings are manufactured from 2 homogeneous isotropic materials with two different thickness values. The materials chosen were low density polyethylene (LDPE) and hi gh density polyethylene (HDPE). This provides various values that span three orders of magnitude ranging from 101 to 103. This is shown on Table 2 4 in the next section. Two

PAGE 29

29 different wing configurations are used and ar e shown in Figure 2 3 For the first wing configuration presented in Figure 2 3 (a), the wing is attached to the plunging device such that it is fully supported along the entire root, thereby constraining twist. The second wing configuration is presented in Figure 2 3 (b). This configuration varies from the first by only being attached along the first third of the wing root such that twist is unconstrained. Exper imental Parameters This section presents details of the flow, wing and motions used for the studies discussed in this thesis. As alluded to above, two sets of experiments were conducted, one for spanwise flexible wings fully supported at the root, and the second one on spanwise flexible wings attach at a portion of the LE. By fixing the kinematics and the chord based Reynolds number, the effect of the flexibility on the fluid dynamics of the plunging wings can be investigated. The flexibility is varied by c hanging the effective stiffness parameter ( ) over three orders of magnitude. The conditions in the SF experiments are matched to those in previous studies in a water channel to investigate the requirement of dynamic similarity using the effective stif fness parameter [ 46 ] Comparison of these studies provides insight into the effects of density ratio between the wing and fluid surrounding it. The SFPP studies are based on the frequency ratio (f/fn). The parameters based on the plunging frequency (k and St) are not matched, but all others are kept constant for both SF and SFPP studies. The scaling parameters, material properties and flow properties are provided in a series of tables Table 2 1 summarizes the relevant scal ing parameters associated with the flow and wing motion; Table 2 2 summarizes the kinematics and geometric

PAGE 30

30 properties; Table 2 3 summarizes the material properties, and Table 2 4 shows the fluid structure scaling parameter values. Stereo Particle Image Velocimetry A LaVision Particle Image Velocimetry (PIV) system controlled by LaVisions imaging software Davis 7.2 was used to measure the flow field around the pl unging wings. Stereoscopic PIV was used to acquire three component velocity data. The system consists of a Litron Nano L 13515 laser which is used to create a pair of 532nm pulses into light sheets in th e vertical spanwise direction. Two Imager ProX 4M ca meras were used to capture the light scattered from particles at oblique viewing angles. The cameras have a 14 bit dynamic range CCD array of 2048 x 2048 pixel resolution. The flow was seeded by a LaVision DS Aerosol Generator which used olive oil as the s Two setups are used to measure the flow around flexible wings. The following sections will outline each setup. SF PIV Measurement S etup The setup for the SF wings captured the flow on both the t op and bottom of the wing, thus allowing for the assessment of symmetry between the downstroke and upstroke. A drawback was that the laser light bloom on the wing and the spanwise wing deflection limited the field of view, thus the near wall effects were not obtained. The cameras were coupled with Sigma EX 105 mm lenses with an f number of 5.6. An average resolution of 19 pixels per mm was achieved. A picture of the setup is shown in F igure 2 5 Two wings are tested in this s tudy: An LDPE and an HDPE wing with the configuration shown in Fig ure 2 3 (a). For each wing, measurements were acquired at 6 spanwise locations ranging from 60 mm to 108 mm (50% to 90% span) where 0% and

PAGE 31

31 100% are the wing r oot and tip respectively. A schematic of the spanwise locations is shown in Figure 2 4 This shows the spanwise planes in green, and the coordinate system used throughout the study. Positive x direction indicates the flow di rection At each spanwise location, 5000 velocity fields were acquired and divided into 50 phases over the full plunging cycle. This resulted in approximately 120145 velocity fields which are used to create the mean flow fields at each phase in the plungi ng motion. The raw PIV images were processed using Davis 7.2 PIV software. The software uses a multi pass, crosscorrelation algorithm [ 65] The first pass consisted of an interrogation window of 64 pixels x 64 pixels with a 50% overlap. The two subsequent passes utilized a window size of 32x32 pixels with a 50% overlap. The estimated displacement from the each previous pass was used to displac e the raw image such that the same particle group would be correlated for smaller interrogation window sizes. SFPP PIV Measurement Setup The setup for the SFPP wings was changed in order to be able to study the near wall effects. The cameras are placed on the opposite side of the plunging mechanism, thus as the wings deform the field of view is not blocked. A picture of the setup is shown in Figure 2 6 The cameras were used with Nikon 60mm lenses with an f number of 5.6. An average resolution of 18.1 pixels per mm was achieved. Three wings with passive pitch were studied. T he wing model is shown in Figure 2 3 (b). For each wing, measurements were acquired at 4 spanwise locations ranging from 6 0 mm to 108 mm (50% to 90% span) where 0% and 100% are the wing root and tip respectively. At each spanwise location, 2500 velocity fields w ere acquired and divided into 48 phases over the full plunging cycle. This resulted in approximately 6080

PAGE 32

32 velocity fields which are used to create the mean flow fields at each phase in the plunging motion. Davis 7.2 software is used for processing the raw images. The multi pass, cross correlation algorithm differed from the SF processing in that a smaller sized window is used. The first pass consisted of an interrogation window of 64 pixels x 64 pixels with a 50% overlap. The two subsequent pas ses utilized a window size of 16x16 pixels with a 50% overlap Force Transducer An ATI Nano 17 force transducer is used to measur e the forces acting on the wing It measures force and torque in three spatial dimensions. The sensing range and resolution are given in Table 2 5 and 2 6 respectively. An NI DAQ 6220 card is used to sample the force measurements. The analog signals are sampled through 6 channels of the card at a rate of 35 kHz, and a 16 bit resolution. The digital signal is then multiplied with the 6 x 6 calibration matrix to obtain the force and torque measurements in physical units. Force measurements are taken at plunging frequencies ranging from 2 Hz to 12 Hz for each of the wings selected. Data is gathered over 1000 plunging cycles, with a total of 10 sets per frequency. The sets are then averaged to obtain the time averaged force. In addition, t are measurements are taken to eliminate the added inertial forces from the plunging apparatus and wing mass Laser Doppler Vibrometer A modal analysis was performed on the wings to determine their damped natural f requency. The structural response of the wings was measured using a noninvasive Polytec PSV400 laser Doppler Vibrometry (LDV). The LDV system consists of a PSV I -

PAGE 33

33 400 laser head with a HeNe laser that emits a linearly polarized 633 nm beam, a OFV 5000 con troller, and a PSV E 401 Junction box for synchronizing all the hardware. A Ling Dynamic Systems V201/3PA electrodynamic shaker with an attached load cell was used for the excitation. Each wing was rigidly attached to the shaker, as can be seen in F igure 2 7 For all experiments, the shaker setup is placed on a vibration isolated optical table exposed to ambient air. Therefore, the results include aerodynamic damping and would differ slightly from the true natural frequenci es which would need to be determined in a vacuum. Polytec software was used to obtain the LDV output and the load cell data to calculate the frequency response structure of the wings studied. To perform these measurements, the laser is first focused and centered on the middle of the grid spacing, such that the location error is minimized at 6 points on the wing surface. Using these six points the calibration is automatically performed by the Polytec software. A grid of approximately 60 points was created for each wing. The laser was refocused at each point to obtain the best signal to noise ratio. The shaker provided a burst chirp excitation to the wing and the response of the wing was captured by the LDV laser head. The data was acquired over the course of 5 burst chirps at each point on the grid, and then averaged to obtain the frequency spectrum at each point. Another form of excitation utilized was sine sweep excitation. Excitation frequencies were varied from 01000 Hz with sweeps over 6 seconds of lengt h. Ample time between measurements was allowed such that the structure returned to steady state.

PAGE 34

3 4 Table 21. Dimensionless kinematic scaling parameters Re k St ho 5300 1.82 0.203 0.175 Table 22. Kinematic and geometric properties Root Chord Span Velocity Frequency (SF study) f/fn (SFPP study) Plunging Amplitude c (mm.) b (mm.) U (m/s) f (Hz) h (mm.) 40 120 2.1 30 0.4, 0.9 7.00 Table 23. Material properties LDPE HDPE E (GPa) Poissons Ratio E (GPa) Poissons Ratio 0.39 0.32 1.50 0.35 Table 24. Dimensionless fluid structure scaling parameters. 1,1/32 LDPE 1, 1/16 LDPE 1,1/32 HDPE 1,1/16 HDPE 55 444 213 1,702 Table 25. ATI Nano 17 sensing range Axis US (English) SI (Metric) Fx, Fy 3 lbf 13.3 N Fz 4.25 lbf 18.9 N Tx, Ty, Tz 1 lbf in 113 Nmm Table 26. ATI Nano resolution for a 16bit DAQ Axis US (English) SI (Metric) Fx, Fy Fz 1/1280 lbf 1/288 N Tx, Ty, Tz 1/8000 lbf in 1/71 N mm

PAGE 35

35 Figure 21. Plunging device with wing attached. Figure 22. Sinusoidal motion analysis. (a) (b) Figure 23. Zimmerman planform wings. (a) model used for SF study, (b) model with unconstrained twist for SFPP study.

PAGE 36

36 Figure 24. PIV planes and coordinate system. Figure 25. SF experimen t setup. (1) Plunging device, (2) Cameras, (3) Laser Plane, (4) Test Section inlet.

PAGE 37

37 Figure 26. SFPP experiment setup. (1) Plunging Mechanism, (2) Cameras, (3) Laser Plane, (4) Test section Inlet. Figure 2 7 Shaker and wing s etup.

PAGE 38

38 CHAPTER 3 D ATA PROCESSING Chapter 3 contains and explanation of the methods used for analyzing the data. This includes discussion of t he vortex identification method, a momentum balance method to estimate aerodynamic forces from PIV data, and an explanation of PIV process ing. Q Criterion The Q criterion is a Galilean invariant technique developed to identify vortical structures present in the flow [ 66] This criterion is used in this study to visualize the evolution of the vortical structures in the flow throughout the plunging cycle. Vortices are identified as regions where the value of Q is greater than zero. The areas where the value of Q is greater than zero represent areas with a larger rotation rate that strain rate. Q criterion is defined in Equation 3 1 = 1 2 (3 1) Where and are the symmetric and anti symmetric component of respectively. These are shown in Equation 3 2 and Equation 3 3 = + (3 2) = (3 3) Force Estimation The flow field data gathered in this study is used to compute phaseaveraged forces generated by the wings. The method used is a momentum balance approac h

PAGE 39

39 described by S llstr m [ 67], [ 68 ] The control volume used in this approach spans the extent of the planes where velocity data was acquired, as a consequence in betw een the spanwise PIV planes the data has to be significantly interpolated. It must also be taken into account that the velocity fields span 40% of the total wing span, thus the total force is underestimate d. By assuming constant density ( ) and dynamic vi scosity( ) the momentum equation for a Newtonian Fluid is used to derive the balance method. The equation in Einstein tensor notation is shown in Equation 3 4 + = + + (3 4) W here is the pressure, is the force per unit volume, is the velocity tensor, and is t he Cartesian coordinate tensor. The flow is assumed to be periodic, and Reynolds decom position is performed on the component s. The bar accent denotes average whereas the tilde represents instantaneous fluctuations. Equations 3 5 to 3 7 define the velocity, pressure, and forc e respectively. = + (3 5) = + (3 6) = + (3 7) Substituting the decompositions into the momentum equation yields Equation 3 8 + + + ( + ) = + + + + (3 8)

PAGE 40

40 Equation 3 8 is averaged (Equation 3 9 ) and rearranged using the continuity equation, to obtain the expression used to solve for the relative pressure and force (Equation 3 10). + + = + + (3 9) + = + + (3 10) Pressure Estimation The pressure gradient is given by rearranging E quation 3 10 and making the assumption of no net body forces on the control volume. This makes all the terms a function of the flow velocity, and thus being able to compute it from PIV data. The gradient is shown in E quation 3 11. = + + (3 11) The pressure gradient is then integrated over the x and y directions to obtain the relative pressure with respect to the atmospheric pressure across the domain for each phaseaveraged veloci ty. Momentum Balance Equation 3 9 is integrated over a control volume to yield Equation 3 12. + = + + (3 12) Equation 3 12 is rearranged, and the divergence theorem is applied to solve for the forc e. The first term of Equation 3 13 re presents forces exerted on the flow by the wing.

PAGE 41

41 = + + (3 13) The force along the y and x axis exerted on the flow is defined by integrating a rectangular volume with bounds and .For Equations 3 14 and 3 15 only the relative pressure is required as any offset to the pressu re will cancel. = + + + + (3 14) = + + + + (3 15) The first term in Equations 3 14 and 3 15 can be rewritten by using the continuity equation. This allows for the term to be evaluated using only PIV flow data on the surface of the volume, a s shown in Equation 3 16. = | ( ) [ ] + [ ] (3 16)

PAGE 42

42 Stereo Particle Image Velocimetry Particle image velocimetry (PIV) is an optical and non intrusive method used to measure velocity in a field. The velocity distribution is obtained from a twodimensional plane by seeding the fluid with small particles, and photographing an illuminated region using two laser pulses. The local velocity is computed from the displacement of the particles between the pulses and the time between the laser pulses. The images are divided into interrogation windows to be evaluated. The particle displacements between the two independently acquired images are evaluated using a cross correlation algorithm The correlation is done on each window resulting in one velocity vector per wind ow. In order to reduce the noise and enhance a spatial resolution, a multi pass algorithm with a decreasing window size is implemented. This is done by using a larger window on the first pass, and calculating a reference vector field. The next pass uses a smaller window size, and the window is shifted between the snapshots according to the reference vector field obtained in the previous iteration. In order to obtain three component velocity data, a PIV setup with cameras looking at the same plane but from different angles is used. The out of plane velocity is obtained by mapping the twocomponent displacements from each camera into threecomponent velocities in the thin volume created by laser sheet and the camera views [ 68] This technique is used as it corrects for errors caused in 2component PIV by the out of plane velocity component in highly three dimensional flows [ 69] Scheimpflug Condition Since the cameras are mounted at oblique angles, it is difficult to have the entire field of view in focus, due to a limited depth of field. Instead of increasing the f number to increase the depth of field, which would increase error in the measurements, the

PAGE 43

43 image plane can be tilted with respect to the orientation of the camera lens and the light sheet. The Scheimpflug condition states that object, lens, and image planes must intersect at a single point, as shown in the following F igure 3 1 Calibration In order to perform a stereo PIV calibration, a photograph of a tw o level calibration target and the pinhole model is used[ 68], [ 70 ] The calibration target shown in F igure 3 2 is used to reduce the error from traversing a 1D target. The pinhole model is used to transform from the world coordinate s ystem, to a physical coordinate on the cameras image plane. For a detailed explanation of the pinhole model refer to the manuscript by Opower [ 70] Figure 31. Schematic of the Scheimpflug condition.

PAGE 44

44 Figure 3 2 Lavision calibration t arget.

PAGE 45

45 CHAPTER 4 RESULTS AND DISCUSSION Chapter 4 presents the experimental results on isotropic flexible wings under a plunging motion and involved wings fully and partially supported at the root The first set of experiments was performed on wings fully supported at the root (SF) as shown in F igure 2 3 (a). The wings have varying spanwise flexibility, characterized by varying the effective stiffness parameter ( ) This initial study builds on past work performed in a water channel by using the same planform wing and matching the scaling parameters and condition[ 46] This allows for the investigation of dynamic similarity using the effective stiffness para meter. The results can be directly compared with the rigid and flexible wings studied previously by Rausch et al [ 46 ] thus providing insight into the effects of the density ratio, on the w ing and the flow surrounding it Additionally, a structural analysis was carried out to determine the wings modal properties. This modal analysis was done on both types of wings shown on F igure 2 3 in order to design experiments based on the natural fr equency of the models The final section presents the experiments carried out on wings with spanwise and chordwise flexibility (SFPP) The wings are excited at frequencies ratios for maximum thrust and maximum efficiency as reported by the literature (Refer to Chapter 1) Modal Analysis The modal characteristics of the wing models were analyzed using the LDV system described in Chapter 2. The study is intended to provide an understanding the structural characteristics of the various wings and their support ing mechanisms used throughout this study By performing this analysis one is able to determine the damped natural frequency of the wing, as well as the expected modes of deformation that could

PAGE 46

46 be encountered when exciting the wings at different plunging f requencies. This analysis is important in the study of wing flexibility as the natural frequency of the model will drive the nature of the wing deflection. This is also an important parameter to consider when designing experiments across different fluids, since the wing behavior will be different due to the wing loading and inertia of the fluid. Also, as outlined in Chapter 1, recent studies have concentrated on developing scaling parameters that take into account the resonant frequencies of the material, as birds and insects seem to favor a certain range of frequency ratios to achieve maximum efficiency. Table 4 1 presents the results of the modal analysis performed on 3 wing models. The models are tested under both con figur ations shown in Fig ure 2 3 The results for the first two modes are shown, and the last column states whether the wings second mode was characteristic of any twist deformation. The root attached wings did not show any twis t. Their first two modes were the first and second bending mode. In contrast, the LE attached wings all showed twist as th e second mode, and their damped natural frequency was reduced by approximately 30% 40%. In all cases the second mode is approximately 4.5 to 5.5 t imes higher than the first mode Since the SFPP experiment is carried out at frequency ratios less than 1 the excitation of the second mode (twist) might not be significant. Another trend that is seen for the models tested is that as the effective stiffness increases an order of magnitude, the damped natural frequency increases significantly This is seen for both types of attachments. This could be fur ther investigated in the future, and could be used to design wing models with a specific eff ective stiffness, or natural frequency using the same family of materials.

PAGE 47

47 Figures 4 1 and 4 2 show contour pl ots of modes for the two different models with both attachment configurations. Fig ure 4 1 shows the first bending mode for the wings tested in the SF experiment. Both wings show an increased displacement from the root to the tip, characteristic of a pure bending mode. The LDPE case shows greater displacem ent as the HDPE wing as expected since it is less stiff under the same excitation. The second mode for the SF wings was a second bending mode, and did not show any significant twist. Figure 4 2 shows the second mode for the same wings but attached at the LE. These contours show evidence of the twist present in the second mode. The LDPE wing also shows significantly more deformation when compared to the HDPE wing. It must also be noted that the deformation is an order of magni tude less for the twist mode when compared to the bending mode for the rigidly attached wings. The first mode of the LE attached wings was a pure bending mode, as seen for the SF wings. Fully Supported Root Studies The following sections present a study done on spanwise flexible wings that are fully supported at the root, thus constraining twist. The models studied are the HDPE model with a of 1702, and the LDPE model with a of 55. The HDPE and LDPE root attached models will be referenced as the SF3 and SF1 for the remainder of the thesis, respectively where the number represents the order of magnitude of the effective stiffness The sections will include an analysis on the flow field, followed by an analysis on the deformations and a comparison to the water tunnel studies, and concludes with the presentation of the forces calculated using the momentum balance approach described pr eviously

PAGE 48

48 Flow Field Analysis This section presents details of the phase averaged velocity fields throughout the plunging cycle obtained from the PIV analysis. Specifically the streamwise aligned planes studied are at the 50% and 75% spanwise stations The results presented are shown as contour plots of velocity, vorticity and Q criterion with streamlines superimposed on the field. In all of the cases the phase averages are obtained from splitting the measurements up and averaging over approximately 140 sam ples at each point as discussed previously. The white regions in the contour plots represent regions of the flow that were masked out. This was due to the laser bloom and the wing deformation blocking the field of view. Therefore, the near wall effects and the early formation of the leading edge vortices cannot be studied from this data set. A black line is plotted on each figure to clarify the wing position at each phase. This represents the wings chord location in that specific plane. The wings position and deformation is obtained by tracking the laser bloom on the PIV images to within 0.250.5 mm. The flow fields are shown for a specific phase in the fluid motion, where 0 phase indicates the beginning of the downstroke, while 180 is the beginning of t he upstroke. SF 3 model Figure 4 3 presents the SF3 wing at the beginning of the downstroke. At this phase in the plunging cycle the wing displays its largest upward spanwise deflection. Here the trailing edge vorticity start s to roll up beginning the formation of a counter clockwise vortex on top of the wing The vortex development at the leading edge cannot be seen as the wings deflection blocks the field of view. However the LEV is not seen to form until before the midstrok e, as seen in Figure 4 4 This delay in the generation of a leading edge vortex on top of wing can be explained by the flow behavior in the bottom

PAGE 49

49 of the wing at the beginning of the downstroke. Referring to Figure 4 3 a counter clockwise vortex generated during the upstroke is still present. This LEV is strong and has only been advected to about the quarter chord location, thus pulling most of the streamwise momentum under the wing. This vort ex is close to the trailing edge at a phase right before the midstroke (Figure 4 4 .), thus allowing for the formation of the LEV on top of the wing. The wake at these spanwise locations is characterized by the presence of vortices shed during the previous stroke. From Figure 4 3 it can be seen that by the beginning of the downstroke, there are four vortices in the wake. Two of the vortices are generated at the trailing edge, and shed during the upstroke. These two TE vortices can be seen clearly in Figure 4 4 where second TE vortex has just been shed. The other two vortices are due to the splitting of the leading edge vortex after it leaves the TE. One of the split vortices lies above the wing plane, while the other remains parallel to it. The separation of the vortices, also called forking, has been observed in previous studies, and is reported to be due to the chain of inclined and interconnected vortex tubes over oscillating flapping wings [ 71] [ 73] T he forking of the LEV and the wake behavior seen for this wing is characteristic of the flapping wings studied in these previous experiments This shows evidence that due to the large deformation of the wing, the flow shows similar behavior to that seen for flapping motions. Thus a flexible plunging wing with large spanwise deformations where the deformation is in phase throughout the motion, c an behave like a flapping wing. Details on the deformation characteristics for the wing are further explained later in Chapter 4 (Refer to Figure 4 10).

PAGE 50

50 Figure s 4 5 and 4 6 show vorticity and Q criterion contours at the 75% span location for the SF3 wing. The beginning of the downstroke and phase 75 are shown to draw a comparison with the same phases at the midspan shown in F igures 4 3 and 4 4 The LEV o n the underside of the wing that is generated during the upstroke can be seen in Figure 4 5 This LEV is much larger in size at this spanwise location, than at the midspan. The vortex center is located approximately at of the local chord length, and it is further separated from the wing. The wake shows the TE vortices that are shed during the upstroke, as also seen in the midspan location. From this analysis, one c an infer that the LEV and TEV seen in this plane are slices of a vortex tube, where the vorticity increases for locations closer to the tip. A three dimensional rendering of the vo rtex tube is shown in Figure 4 7 This shows isosurfaces of Q, with the contour slices at the 50 and 75% spanwise locations. The black lines represent the local chord location. As shown in Figure 4 7 a coherent vortex tube is formed, and as the wing deflects upwards at the 75% span, the tube is also pulled in that direction. The spanwise deformation influences the flow by pulling the streamwise momentum in the direction of the deformation, thus pulling the fluidic structures. At t he 75% spanwise location there is no evidence of the splitting of the LEV when compared to the midspan. This could be a consequence of the wing deflecting inwards towards the root. Figure 4 6 shows the flow field at the 75 phase. The LEV on the top surface is seen to form at this location as also seen at the midspan. At the trailing edge the LEV formed at the beginning of the downstroke is seen to shed, and correspondingly pulls the flow downwards at the aft of the wing. The vortices at this

PAGE 51

51 phase seem to ali gn. As the LEV pulls the flow towards the trailing edge, the previously shed vortex, which is not on top of the wing as well, also pulls the flow downwards at the aft of the wing. Thus as the flow is pulled down, it creates a jet like behavior between the vortices. Figure 4 8 shows the normalized velocity at this phase. This shows that the flow is highly accelerated at the aft of the wing caused by the alignment of the vortices. The remainder of the w ake also shows accelerat ed flow, which means that this is a good mechanism for thrust production. SF1 model Figures 4 9 and 4 10 show the vorticity and Q criterion for the SF1 wing at the downstroke and at the 75% spanwise location. The midspan is shown on the top row and the 75% location on the bottom row so that they could be easily compared. For the SF1 wing the vortices are found to be much weaker, than the ones for the SF3 wing The flow shows multiple vortices shed throughout the plunging cycle. However, in contrast to the SF3 wing, there is no evidence of a coherent vortex structure existing throughout the strokes. This is a result of the wing displaying excessive spanwise flexibility, which lead t o significan t tip root lag. Large lags are representative of the midspan moving upward while the wing tip deflects downwards This behavior is seen throughout the motion. The v orticity fields reveal the creation of vortices of opposite signs for the spanwise locations shown. Figure 4 10 shows this behavior in the flow, where the flow at the midspan is pulled to the top of the wing, and at the 75% location the flow is pulled downwards. This creates a fragmented and weak vorticity pattern. This behavior for highly flexible wings has been observed previously [ 39] and led to lower thrust coefficients and significantly diminished efficiencies.

PAGE 52

52 Since the wing is highly compliant there is no evidence of the formation of a LEV. This happens as the large phase lags create a fragmented vorticity pattern. This also causes the wing to have a smaller tip defor mation when compared to the SF3 wing, as the root cannot drive the motion of the tip. More detailed explanation on the deformation of the wings is given in the following section. Wing Deformation/Comparison Studies The water t unnel studies of Rausch et al [ 46] showed insignificant wing deformation for wings with effective stiffness values greater than 1400. The only model they examined that displayed spanwise bending was the wi ng with the lowest stiffness value of 30. In that study the deformations are explained in terms of the pl unge amplitude of the motion (h), where a positive percentage value signifies a motion greater than the roots motion (root motion + percentage) and a negative value, a reduction in the amplitude. The deformation was found to be 40% the amplitude of motion at the 75% location. At the midspan the deformation was only 5%. At the 75% span location, the deformation lagged the root by only 70. In contrast when performed in air, both wings showed significant spanwise deformation. All the kinematic parameters shown in C hapter 2 are matched in these studies, thus a direct comparison can be made. The deformation for the SF3 wing was 200% and 400 % of the amplitude of motion at 50% and 75% spanwise locations. The results of the deformation for the SF study are presented in Figure 4 11. Due to the inertia of the wing, the deformation at the 75% location is much larger than t hat of the flexible wing in water, even though the ef fective stiffness is two orders of magnitude greater. The SF1 wing showed the most unique behavior of all the models. It showed large tip root lag, with the tip going the opposite direction of the root for the majority of

PAGE 53

53 the motion. The deformations at th e midspan were approximately 50% the amplitude of the motion. This signifies that the motion is only half the amplitude of the input motion. The 75% spanwise locations displacement was approximately 2% less than the prescribed plunging motion of the root. The frequency ratios for each experiment can give one a better understanding of the difference in the deformation for both cases Table 4 2 shows the frequency ratios of the experiments performed in water and air. The ratios show that the measurements are carried out at significantly different ratios. Even though the parameters are matched, the wing loading for each experiment is different, as the frequency ratio seems to drive the nature of the wing deflection. The ratios f or the present experiment are an order of magnitude greater than the other in water, with the SF1 wing being excited at almost three times its natural frequency. This shows that the structural properties of the wings must be carefully studied, and must be taken into account when studying flexibility and trying to derive new scaling laws. The PIV results from the water tunnel experiments show that the flow was dominated by the formation of a LEV during the downstroke for all the cases studied. Also, the LEV was shown to separate and advect toward the trailing edge for all the cases. In water, the HDPE 1=1960) showed the formation of the LEV at the beginning of the downstroke at the 50% and 75% span locations. This vortex proceeded to advect, ultimatel y shedding from the trailing edge of the wing at the beginning of the next cycle (30) at the 50% location. The LEV leaves the trailing edge at an earlier phase of 270 for the 75% span location. The LEV for the model with a low effective stiffness began t o form at a later phase than the rigid model. It was shown that the

PAGE 54

54 vortex at the 75% location is significantly larger than at the midspan. The vortex formed at phase of approximately 60 for both spanwise locations. This coincides with the location of max imum spanwise deformation. The LEV was shown to shed from the trailing edge at a phase of 30 in the next cycle of the motion for the 50% span plane. At the 75% plane, the LEV advects downstream from the TE at the beginning of the downstroke (0). In air, the bending of the SF3 wing blocked the camera during PIV, thus the formation of the LEV is not resolvable. The LEV at the 75% spanwise location is significantly larger than at the midspan, which is similar behavior to t he LDPE wing in water. Figure 4 12 shows the vorticity at the phases where the LEV is seen to leave the trailing edge of the wing for the 50% and 75% locations. The LEV passes the trailing edge at a phase of 255 at the midspan, and 45 earlier at 75%. The SF 3 and SF1 show the LEV rising away from the trailing edge at earlier phases, than the similar models in water. At the 50% location, this occurs approximately 135 earlier. At the 75% location it occurs 150 earlier than the LDPE wing and 60 earlier than t he HDPE wing (same material as SF3). The SF1 wing in air did not show an LEV being formed. Force Calculations The force calculations are performed utilizing the control volume a pproach described in Chapter 2 The control volume spans from the 50% to the 90% spanwise locations and encompasses the entire field of view presented in the previous section. Since it only represents 40% of the total wing span, the forces are underestimated, and only represent the local forces at these locations. The force results are presented in Figure 4 13 as a function of phase throughout the plunging cycle. The SF3 and SF1 wings are represented by the blue and red lines in Figure 4 13 respectively. The maximum force in the vertical direction (Fy) for the SF3

PAGE 55

55 wing is seen to occur at the end of the downstroke, with a steep decrease after this phase. At the end of the downstroke, the leading edge vortex on top of the wing is still strong and has only been advected 40% of the chord, thus there is a large region of low pressure on the top of the wing. The lowest values of Fy occur halfway through the upstroke where the leading edge vortex created during the downstroke sheds from the trailing edge while a counter clockw ise vortex is created on the underside of the wing. The vortex develops on the underside of the wing and creates a low pressure region on the bottom. Horizontal Force (Fx) in the SF3 model is characterized by the shedding of the vortices, as these align to create jet like behavior in the wake, as previously seen in Figure 4 8 The maximum Fx is achieved in the phase of the motion where the LEV is being shed. The production of this force starts when the bending is at its maxim um and higher wing velocities are present. Similar results have been shown in previous experiments for a hovering wing [ 67] ; these results presented that the maximum streamwise force occurred slightly before the maximum spanwise bending angle. Fx and Fy for the SF1 wing are shown to be s ignificantly smaller than the SF3 wing. This is a result of a significant tip root lag which has been shown t o diminish the generation and development of unsteady vortex structures. Ultimately, insignificant amounts of horizontal and vertical forces are generated on the SF1 wing. Spanwise Flexible Wings with Passive Pitch The following sections present a study performed on spanwise flexible wings that are supported only over the first quarter chord at the root. This configuration was chosen so as not to co nstrain the twist and is presented in Figure 2 3 (b). The models studied are an HDPE model with a of 1702, an LDPE model with a of 444, and an

PAGE 56

56 LDPE model with a of 55 so as to examine stiffness parameters varying several orders of magnitude. These will be referred as the SFPP3, SFPP2 and SFPP1 models for the remainder of the thesis. The numbers represent the order of magnitude of the effective stiffness parameter. For an explanation on the setup and processing used on this set refer to Chapter 2 section on SFPP setup. As previously mentioned, the study is carried ou t to understand the effect of the flexibility on the unsteady fluid phenomena generated over the strokes, and how these could be related to the production of aerodynamic forces. The studies are done on two different frequency ratios 0.4 and 0.9.The low er ratio wa s reported as the ratio of maximum efficiency [ 44], [48 ], [ 50], [ 54 ] and the one close to unity (almost excited at the natural frequency) is for the maximum thrust [ 44 ], [ 48 ] [ 54] The sections will include an analysis on the flow field and the deformations of the wing, followed by an analysis on the local forces generated using the momentum balance approach. Flow Field and Deformation Analysis This section presents details of the phase averaged velocity fields characteristics obtained from the PIV analysis and the deformation characteristics of the wings The flow fields studied are at the 50% 60%, 75% and 90% spanwise planes. The results are shown as contour plots of vorticity with streamlines superimposed on the field. The field of view was changed from the one used in the SF study so that the early formation of the LEV and the near wall effects could be studied. The drawback is that only one side of the wing is visible; however since the motion is symmetric the upstroke motion would represent what is expected to be seen on the opposite side of the wing. The entire flow field results pres ent phase averaged information.

PAGE 57

57 The contour plots are presented for the entire downstroke, and the beginning of the upstroke. The last row of the figures presents phase 225. The white regions in the contour plots represent regions of the flow that were masked out. These regions are due to the flapping mechanism being in the lower part of the field of view (FOV), and the laser bloom for regions close to the wing A black line is plotted on each figure to clarify the wing position at each phase. This represe nts the wings chord location in that specific plane. The wings position and deformation is obtained by tracking the laser bloom o n the PIV images to within 0.5 mm. The flow fields are shown for a specific phase in the fluid motion, where 0 phase indicat es the beginning of the downstroke, while 180 is the beginning of the upstroke. The first two columns show the wing excited at a frequency ratio of 0.4, and the last two at a frequency ratio of 0.9. Columns A and C show the 50% spanwise plane, and columns B and D show the 75% location. It must be noted that part of the design of the wing was to allow for a geometric twist to be passively induced. After examining all wings, it was found that this w as not accomplished as desired. The wings showed a geometric twist that was lower than 1.5 at all phases, thus not being significant in this study as the spanwise deformation drives the flow for all cases This was also in the range of the deviation found by using the PIV laser bloom tracking algorithm. Thus it c ould not be resolved. For future experiments a more reliable method should be used to determine the twist. SFPP3 M odel The flow and spanwise deformation result for the SFPP3 wing are shown on Figures 4 14 and 4 17 respectively. For clarity purposes, blue in the vorticity fields represents clockwise rotation, and red (yellow) show counter clockwise rotation.

PAGE 58

58 Frequency ratio of 0.4 The flow for this ratio is mostly characterized by the formati on and shedding of a LEV, and a TEV. The LEV is seen to start to form at 45, and it continues to grow as it advects towards the TE. At the end of the downstroke, it is present at around the mid chord, and it pulls the streamwise momentum to the top of the wing. This might impede the formation of the LEV, as the following stroke starts. As the upstroke starts, the LEV from the previous stroke still advects toward the TE, but it is weakened as the wing moves in its path. The shed LEV can be seen in phase 45, located around half a chord away from the TE. Column B shows the flow at the 75% location. The LEV is stronger for this location. Right after the midstroke it is seen that the vortex is large, and it is almost the length of the lo cal chord. The shed vort ices at this location appear weaker than at the midspan. This could be due to the large deformations seen for this frequency ratio. The vortices appear at similar locations for both spanwise locations, thus it could be inferred that these are slices of a v ortex tube. The formation and growth of a leading edge vortex tube is important in these flows as it creates large regions of low pressure on top of the wing. This in turn allows the wing to have an improved lift performance for phases where the LEV is present. In addition, as also shown for the SF3 wing, as the LEV is advected towards the TE, it is able to align with the TEV s that are shed, and create jet like behavior in the wake, which could also improve thrust generation. In the case of this wing, the s hed vortices are not as strong, and they are weaker for locations close to the tip. Even though they are still vortex tubes, they are not able to pull as much momentum, making the wake capture mechanism much weaker. During the motion only one TEV is formed and shed. The TEV is seen to form at 45, and it is shed immediately after, as seen in the midstroke.

PAGE 59

59 The formation of the fluidic structures is explained by the flexibility characteristics of the wing. The results of the deformation (Figure 4 17) show that at this frequency ratio the deformation can be as large as 3.5 times the amplitude of the motion for the planes studied, which leads to significantly higher wing accelerations as we approach the tip The largest spanwis e bending is seen at the beginning and end of the downstroke. One important feature that allows structures to be formed is that the wing deformation is in phase with the root throughout the cycle. And this coupled with the larger wing velocities, allow for the generation of higher vorticity. The fact that they are in phase means that for a complete downstroke the whole wing is moving downwards, thus only clockwise vorticity is generated at the LE on top of the wing. This behavior allows the wing to have a v orticity field that is not fragmented in the spanwise direction, thus being beneficial for force generation. A drawback of this wing is that the large spanwise deformation of about 3.5 times the amplitude means the wing moves into the root, thus weakening the vortex tubes present. This could help explain the weaker LEV and TEV vortex seen for the 75% location. The LEV is further weakened by the change of direction that happens at the end of the downstroke. Frequency ratio of 0.9 The flow field for this freq uency ratio is significantly different than at the lower frequency ratio. The reason for this difference comes from the deformation of the wing. At this ratio the wing is out of phase with the root. For a larger portion of the motion the root and the 50% and 75% locations go in opposite directions. This phase lag could create a weak vorticity field throughout the span of the wing as it is fragmented. This means that vorticity of opposite signs are created at the locations studied. As the root plunges down, CW vorticity is present at locations close to the root, but at the midspan

PAGE 60

60 and closer to the tip, CCW would be generated, t hus being detrimental to aerodynamic force production, as seen previously. The deformation is also not as large as at the lower ratio. For this case the largest deformation is about 35% at the 75% spanwise location, and only about 10% at the midspan, thus a large increase in wing acceleration might not be achieved. The 50% and 75% locations deflect in the same direction. Since at these planes the wing behaves similarly, coherent vortex structures can be formed, but only locally The flow field at the 50% location can be seen in Figure 4 14 column C. 75% spanwise plane is shown in column D. A LEV is formed around the midstroke for both locations. The formation is blocked in the figure views due to the placement of the flapping mechanism, but by studying the upstroke, and the streamlines it can be seen. The LEV sheds at the end of the downstroke. Immediately after the motion c hanges from down to upstroke a counter c lockwise TEV is formed and shed. This immediate shedding of the vortices allows the vortices to align, but not in a favorable direction. As seen the wake is characterized by the presence of at least 5 vortices at the midspan, 2 counter clockwise vortices one TEV and from the LEV shedding and 3 clockwise TEV shed during the downstroke. At the 75% location, only a clockwise TEV shed and the shed LEV are present The additional TEV from the transition between strokes is not present. This is evidence that the spanwise deformation moving into the root, coupled with the lag does not allow for coherent vortex tubes to be formed. T his also causes the shed vortices to be weaker at this location. The behavior of a fragmented vorticity field can be explained more clearly by looking at the results from the lower frequency ratio. The behavior of locations closer to the root would be simil ar to

PAGE 61

61 that seen in column A of F igure 4 14 where the shed vortices are seen to angle in the upward direction, and a LEV is formed. Whereas in this case the vortices are angled down during the downstroke and there is no LEV formed on top of the wing. When compar ed to the lower frequency ratio, it can be seen that this type of deformation is unfavorable for the formation of strong fluidic structures. Even though more vortices are formed, the deformation does not allow a strong LEV to be formed, thus larger regions of low pressure on top of the wing might not be encountered. SFPP2 Model The vorticity fields and the deformation for the model with intermediate flexibility can be seen in Figure 4 15 and 4 18. Similar trends as the ones see n for the SFPP3 wing are present for this wing. Frequency ratio of 0.4 The SFPP model flow at this ratio is dominated by the formation of an LEV that is destroyed as the wing moves into its path. At the beginning of the downstroke, the flow shows that ther e is only a wake with a velocity gradient in the plane of the wing, thus behaving like a flat plate. As it plunges down, the LEV starts to form, and pulls the flow towards the wing. By phase 45, the flow has already been redirected downwards. The LEV keeps growing, spanning the majority of the chord by phase 135 As the wing comes to a stop, the vortex reaches the TE, but as soon as the motion continues the wing moves into its path and the vortex is destroyed. The behavior of the LEV at the 75% location i s very similar. At this location two TEV, shed during the downstroke, can be seen. These vortices are present at the midspan but are very weak, having little to no effect on the direction of the flow. As explained previously, the generation of a strong LEV is favorable for force generation. For this wing, from the midstroke to the end of the

PAGE 62

62 downstroke the LEV creates a region of low pressure on top of the wing. The vortex is large as it encompasses almost the length of the local chord. A drawback is that no strong structures are being shed, so there is no interaction between the LEV and a shed vortex, thus significant thrust may not be generated. At the 75% spanwise location, there is small vortex interaction at the midstroke and later phases but its effect is almost negligible, as will be explained in the momentum balance section. Similar to the deformation of the SFPP3 wing the SFPP2 wing shows the wings almost completely in phase with the root. The deformation is not as large, being around 2 2.5 times the amplitude of the motion Since the wing is almost in phase throughout the locations studied, the LEV is able to be formed, but this minor phase lag causes the wing to impede its growth, and it is not shed as its full strength. This provides further evidence that a favorable wing design would need to have spanwise deformation that is in phase with the root thus providing larger wing accelerations and an environment where the LEVs can be generated. Frequency ratio of 0.9 At this ratio a small LEV vortex is seen to form near the end of the strokes, as well as several TE vortices formed during the wings transition to downward motion. As seen in the beginning of the downstroke, there are 3 TEV that have been shed, and a fourth vortex that is the shed LEV. The f low behavior is similar to that of the SFPP3 wing. This is mostly due to the spanwise deformations also having a large phase lag with the root. The major difference is that this wing experiences higher deformation thus the vortices that are created are st ronger. As the wing plunges down, the flow is pulled to the top of the wing as seen by phase 45 Also the vorticity present in the TE angles upwards. By the midstroke, a

PAGE 63

63 small TEV is shed, and a second one begins to form. By phase 135 the 50% location has reached it maximum deflection and transitions to its downward motion, creating a vortex of the opposite sign that gets shed immediately as well as the LEV that was formed under the wing The LEV is seen to form around phase 180 ( end of downstroke). The flow at the 75% location is slightly different, in that the vortices seem to have more of an effect on the flow, which is due to higher wing acceleration as it bends more than at the midspan. The TEV and the LEV vortices that get shed together during the transition (around 135) can be seen clearly at the end of the downstroke. These vortices also align, but do not form a jet that is favorable for thrust production. The deformation (Figure 4 18) shows that the phase lag for this wing is also significant. The phase lag is of about 130. This means that for the majority of the motion the root goes the opposite way. Deformation is also smaller for this frequency ratio. The midspan is seen to move about the amplitude of motion, whereas the 75% location is deformed about 2.5 times the amplitude. As seen for this wing also, the deformation drives the behavior of the flow, and determines whether strong fluidic structures favorable for force generation can be created throughout the cycles. The different deformations at each location create a complex vorticity pattern, similar to that of the SF1 wing and the SFPP3 at a high ratio. The only phases at which the LEV is allowed to for m, is when the root reaches the end of the downstroke, and the midspan and 75% locations are halfway through the downward motion, thus deformation is not as high. When these locations reach their highest deformation the LEV reaches the TE and is affected by the wing moving in its way as soon as the wing transi tions. The LEV

PAGE 64

64 gets shed but it has been weakened, and as the wing transitions an additional TEV vortex is shed. In essence, the phase lag causes the shedding of coupled vortices. SFPP1 M odel The flow and spanwise deformation result for the SFPP1 wing are shown on Figures 4 15 and 4 18 respectively. This wing was the most flexible, and had a low natural frequency, thus the frequencies of excitation tested are low. At the ratio of 0.4 the plunging frequency is 2.7 Hz, and at a ratio of 0.9 it is 6.1 Hz. In consequence, the low frequency motion has little energy, and does not affect the flow or the wing significantly. Frequency ratio of 0.4 As stated previously the inertia of the wing at this ratio is small. This causes the motion to not have a significant effect on the flow. As seen in Figure 4 15, there are no clear vortex structures created during the motion. The 50 and 75% locations show a wake with a veloci ty gradient at the back of the TE, but that is the only discernible feature in the flow The deformation results on Figure 4 19 show that at this ratio the wing was in phase with the root. The spanwise bending is small, only about 18% at the extremes, and both 50 and 75% locations behave the same. This shows that the wing mostly behaves like a rigid plate plunging at a slow rate. This deformation bends the flow slightly upwards throughout the downstroke, but does not have any other effect on the flow. Results for this wing show that a wing that is too flexible is not able to drive the flow, as the energy of the motion is small for low frequency ratios.

PAGE 65

65 Frequency ratio of 0.9 At this ratio the flow is mostly dominated by the formation of a LEV right before the end of the downstroke. The deformation shows that there is a significant lag between the root and the spanwise locati ons studied. At the midspan the lag is of 100 and at 75% span it is 120. Thus an adverse or fragment ed vorticity field is also expected of this wing. The amplitudes are also larger when compared to the ratio of 0.4. The midspan deforms about 120%, whereas the 75% location deflects as much as 240%. This deformation influences the strength and form ation of the fluidic structures, being able to form an LEV that is stronger than the one seen for theSFPP2 wing at the same ratio. This shows that the wing deformation or the induced amplitude of the motion is an important parameter, as the higher the deformation, the higher the wing velocities experienced for that wing. This allowing for the generation of LEVs of greater strength. As seen in the vor ticity fields, at the midspan the LEV is seen to form at the end of the downstroke. At this phase the midspan and the 75% are at the middle of their motion, so the deformation is small, and the LEV is able to form. As the motion continues the location of all three planes are similar so the LEV continues to grow, but as soon as they start deviating significantly the vortex weakens and gets shed. This is very similar to the SFPP2 wing, where the vortex forms and sheds at the same phase. The LEV at 75% is spans almost the length of the local chord, whereas at the midspan it is only about 20% the local chord. The size of the vortex means there is a large region of low pressure on top of the wing, which could lead to higher lift at this phase. This vortex is also seen to interact with the CCW shed during the motion, thus pulling the flow further down, and to the right, as it i s a favorable jet like behavior. The vortex is seen to shed right before the midstroke for the 75% location, which coincides

PAGE 66

66 with the location of maximum spanwise location. At the midspan there is no evidence of the vortex being shed. This is likely due to the vortex being weak and once the wing moves in its path as it transitions to move downwards the vort ex is destroyed in the process. As seen for both the SFPP3 and SFPP2, the deformation for this wing is similar as a function of phase. For this wing, at the low ratio the motion of all planes are mostly in phase, but at the higher ratio the w ing experiences significant lags of about 120. The only difference is that for this wing, the lower ratio did not produce higher spanwise bending, as in the case o f the SFPP3 and SFPP2 models. The higher deformation allowed for higher wing acceleration, and thus a strong vortex could be generated. The problem is that the phase lags do not allow it to grow for the entirety of the motion and it gets weakened as soon as the wing changes direction. Momentum Balance The momentum balance method was used to calculate the local Fy (Thrust direction) forces for the SFPP wings. It must be noted that the control volume encompasses the spanwise planes studied for this wing, thus the results are only for 40% of the wing. This should result in underestimated calculations. There are also 4 planes for this portion of the wing, thus the flow is interpolated in between the planes to use this method. Even though the forces might not apply to the whole wing, by examining the fluidic structures generated, the deformation of the wing, and the forces generated locally at these locations, an understanding of how flexibility affects the performance can be gained. This allows for the study of w hat unsteady fluid mechanisms have an effect on the thrust production for the wings studied. The results for the SFPP3, SFPP2 an d SFPP1 wings are presented in F igures 4 20, 4 21 and 4 22

PAGE 67

67 respectively. Results are shown as a function of phase, where the blue lines represent the frequency ratio of 0.4 and red the frequency ratio of 0.9. The SFPP3 model shows the most significant force generation. The maximum Fy force is seen near the start of the upstroke. Around these phases, the LEV formed during the downstroke is being shed, and it interacts with the TEV vortices, creating beneficial vortex alignment for the generation of thrust. Once the LEV leaves the TE, and its strength is diminished, the thrust also drops significantly. As seen at the end and beginning of the cycle, only drag is present. From Figure 4 14 at the beginning downstroke all that is present is a shear off the TE which only contributes to drag. At the higher ratio due to the significant phase lag experienced, no coherent vortex tubes are expected to form throughout the wing, thus there are no mechanisms to produce thrust. For this case all that is seen is signifi cant drag. This is mostly due to the vortex street that is formed through the cycle. As explained previously, the vortices are not aligned favorably. In addition the spanwise deformation is small at this rat io, thus there is no benefit from higher wing vel ocities. The SFPP2 wing did not show significant thrust generation. At the ratio of 0.4, the wing shows thrust from midstroke to the end of the downstroke. From Figure 4 15, it can be seen that at these phases the LEV is located around the middle of the chord, and it pulls the streamwise momentum towards the TE of the wing. This flow then interacts with the TEV shed, which pulls the flow further down and to the right Once the LEV is destroyed by the motion of the wing, ther e is decay in the Fy force. The thrust produced is significantly lower than for the SFPP3 wing, due to the vortices only having a significant interaction at the 75% location, as the midspan did not show large TEV being

PAGE 68

68 shed. For the higher ratio, the thrus t is produced at the end of the cycle. At the beginning of the downstroke (Figure 4 15) only an unfavorable vortex street is present thus only drag is seen. As the wing plunges down, the LEV forms and aligns with the TEVs to create a jet like behavior. As in the 0.4 ratio case, the amount of thrust is not significant because this interaction is only strong at the 75% location. The SFPP1 wing showed the most unique behavior. At the low frequency ratio, the low inertia of th e wing did not create any significant vortical structures. All that is observed is a shear off the TE. As seen in Figure 4 22 this leads to a constant drag of 0.25 mN At the higher frequency ratio, higher spanwise deformation is observed thus stronger vortical structures are formed. This wing shows larger thrust than the SFPP2 m odel, and could be linked to this significantly greater deformation which leads to higher wing velocities. At the beginning of the cycle, the wake shows only a velocity gradient thus only drag with values similar to those seen for the 0.4 ratio case are observed. Significant thrust generation occurs at the beginning of the upstroke, where the LEV is large at the 75% location, and aligns with the TEV vortices. This behavior can be seen in column D, last row of Figure 4 16.

PAGE 69

69 Table 41. Modal Analysis on the wing models. Material Thickness (in.) 1 Attachment Mode 1 (Hz.) Mode 2 (Hz.) Twist Mode (2nd mode) HDPE 1/16 1702 Root 45 228 No 1/16 1702 LE 30 145 Yes LDPE 1/16 444 Root 24 130 No 1/32 55 Root 10.5 60 No 1/16 444 LE 15 82 Yes 1/32 55 LE 6.8 34 Yes Table 42. Frequency ratios for the studies in wind and water tunnel. Water Tunnel Wind Tunnel 1 f /f n f/f n O(10 1 ) 0.17 2.83 O(10 3 ) 0.03 0.67 Figure 41. First Mode (Bending) for wings tested in the SF experiment. Figure 42. Second Mode (Twist Bending) for 2 wings tested in SFPP study. Left shows the HDPE wing, and right shows the m ost flexible LDPE wing. These are the same models as the SF experiment models, but attached at the LE.

PAGE 70

70 Figure 43. Vorticity and Q criterion at beginning of the downstroke for the SF3 wing at the 50% location. Figure 44. Vorticity and Q crite rion at phase 75 for SF3 model at 50% spanwise location. Figure 45. Vorticity and Q criterion at beginning of downstroke for SF3 wing at 75% spanwise plane.

PAGE 71

71 Figure 46. Vorticity and Q criterion at 75 phase for SF3 wing at 75% spanwi se plane. Figure 47. Isosurfaces of Q. slices are at 50% and 75% spanwise planes.

PAGE 72

72 Figure 48. Normalized velocity at phase 75 for SF3 wing at 75% spanwise plane. Jet like behavior (higher accelerated flow) in the region where the vortices align. Figure 49. Vorticity and Q criterion at beginning of the downstroke for SF1 wing. Top: Midspan. Bottom: 75% span.

PAGE 73

73 Figure 410. Vorticity and Q criterion near midstroke for SF1 wing. Top: Midspan. Bottom: 75% Span Plane Figure 4 11. Displacements as a funtion of phase for SF1 and SF3 wings. Phase [deg]y/h 0 30 60 90 120 150 180 210 240 270 300 330 360 -5 -4 -3 -2 -1 0 1 2 3 4 5

PAGE 74

74 (a) (b) Figure 412. Vorticity plots for phases where the LEV leaves TE for SF3 wing. (a) 50% span. (b) 75% span. Figure 413. Phase averaged force calculations using Momentum Balance approach. SF3 wing in blue, and SF1 in red.

PAGE 75

75 A 50% f/fn= 0.4 B 75% f/fn= 0.4 C 50% f/fn= 0.9 D 75% f/fn= 0.9 Figure 4 14. Vorticity fields ( *) for SFPP3 model.

PAGE 76

76 A 50% f/fn= 0.4 B 75% f/fn= 0.4 C 50% f/fn= 0.9 D 75% f/fn= 0.9 Figure 415. Vorticity fields ( *) for SFPP2 model.

PAGE 77

77 A 50% f/fn= 0.4 B 75% f/fn= 0.4 C 50% f/fn= 0.9 D 75% f/fn= 0.9 Figure 416. Vorticity fields (w*) for SFPP1 model.

PAGE 78

78 Figure 417. Spanwise deformation for the SFPP3 wing. Figure 418. Spanwise deformation for SFPP2 wing. Phase () y/h SFPP3 0 30 60 90 120 150 180 210 240 270 300 330 -4 -3 -2 -1 0 1 2 3 4 Phase () y/h SFPP2 0 30 60 90 120 150 180 210 240 270 300 330 -4 -3 -2 -1 0 1 2 3 4

PAGE 79

79 Figure 419. Spanwise deformation for SFPP1 wing. Figure 4 20. Forc e in the streamwise direction for SFPP3 wing using momentum balance method. Phase () y/h SFPP1 0 30 60 90 120 150 180 210 240 270 300 330 -4 -3 -2 -1 0 1 2 3 4 Phase [ ]Fy [mN]SFPP3 wing 0 90 180 270 360 -1 -0.75 -0.5 -0.25 0 0.25 0.5 0.75 1 f/fn = 0.4 f/fn = 0.9

PAGE 80

80 Figure 4 21. Force in the streamwise direction for SFPP3 wing using momentum balance method. Figure 4 22. Force in the streamwise direction for SFPP1 wing using momentum balance method. Phase [ ]Fy [mN]SFPP2 wing 0 90 180 270 360 -1 -0.75 -0.5 -0.25 0 0.25 0.5 0.75 1 f/fn = 0.4 f/fn = 0.9 Phase [ ]Fy [mN]SFPP1 wing 0 90 180 270 360 -1 -0.75 -0.5 -0.25 0 0.25 0.5 0.75 1 f/fn = 0.4 f/fn = 0.9

PAGE 81

81 CHAPTER 5 S UMMARY AND FUTURE WO RK This study carried out experiments on isotropic flexible wings under a plunging motion and involved wings fully and partially supported at the root. The study analyzed the flow, wing structural deformation and forces in order to examine the effects of the flexibility on the aerodynamic performance, and the unsteady mechanisms used to generate the forces. The flexibility was characterized by the effective stiffness parameter, and the wings were studied in a for ward flight environment. The first part of the study consisted of two root mounted wings with varying spanwise flexibility. The conditions tested allowed for an examination of the effects of spanwise flexibility as twist was constrained. As well as being able to compare to studies with different fluid to structural density ratios. The kinematic and scaling parameters were all matched for the first part to assess the dynamic similarity using the effective stiffness. The high inertia of the plunging motion in these experiments caused both models to display significant deformations. The SF3 model showed a coherent vortex tube, with stronger vorticity at locations close to the tip. For some phases a jet like behavior from the vortices was encountered, thus enhancing its thrust production. It also showed flow behavior similar to that of a flapping wing. The SF1 model was too compliant, having large tip root lag. This created a weak vorticity pattern that led to poor aerodynamic performance. Since the behavior was significantly different than the same studies in water, it was concluded that the wing loading, density ratios, and frequency ratios are important when studying flexibility. Matching the kinematic scaling parameters and the effective stiffness did not ensure that the fluid dynamic effects were consistent.

PAGE 82

82 This led to the understanding that the effects of structural resonances should also be considered. The parameter of interest in this case is the frequency ratio, the ratio of plunging (excitation) frequenc y to natural frequency of the material. The second phase of experiments was designed after these results, to include a modal analysis, and flow and deformation measurements for different wing configurations and excitation frequencies. Wings with the same m aterial s were used so that the spanwise deformations could be comparable between experiments. Since the SF wings did not show significant twist, which is linked to the production of thrust, the wing was redesigned to be attached just at a portion of the ro ot. Also in the SF experiments a stiffness parameter in the O(102) was not studied, so it was included in the second set. In addition to these changes, the frequency ratio was added as another parameter in the study. The flexibility is still characterized by the stiffness parameter, but the addition of this parameter was chosen to give more insight into the behavior of the wing under certain conditions. The flow measurements were carried out at frequencies ratios for maximum efficiency and maximum thrust generation as reported by the literature. Results for this set showed that the flow was mostly driven by the spanwise deformation of the wing. As the spanwise deformation increased, so did the strength of the fluidic structures generated. The development of the structures was also found to be a function of the phase lags in the deformation. For cases where the lag between the root and the planes studied were high, a detrimental effect on force production was found. The SFPP wings were still able to generate a LEV when the deformation was not high, but when the wing transitioned from downward to upward motion or vice versa, the LEV was weakened or destroyed. The LEV was also seen present only for about a quarter of the

PAGE 83

83 cycle The deformation characteristics for the SFPP wings were similar for the same frequency ratios. At the low ratio, the wings showed a small or no lag between the root and the planes analyzed. At the higher ratio, all the wings showed a significant phase lag of about 120. The force results showed that there were mainly two mechanism s that were important for thrust generation. One was higher deformations which lead to higher wing velocities, thus creating a stronger LEV. A caveat to this is that the deformation cannot be too great, as to interf ere with the vortex tubes The other mechanism which is common in all wings is jet like behavior of the vortices. An increase in thrust was seen in all cases when the LEV interacted with the shed TEV, thus pulling the streamwise momentum from the top of th e wing, diagonally down and into the streamwise. In order to fully understand the effect s of flexibility more emphasis needs to be put into understanding the geometric twist of the wings and their structural properties The next step in the study is to ch ange the attachment configuration of the wings, so as to induce more twist. More materials needs to be tested, and a detailed analysis on the twist and spanwise deflections using a Laser Doppler Vibrometer need to be added to the current study. The goal is to find a wing that does not show large phase lag in the spanwise direction, as well as favorable geometric twist for locations closer to the root, and throughout the span. In conjunction with the deformations studies, an analysis on the forces using a force transducer needs to be implemented. The first step in this process would to be able to obtain a tare of the forces. This can be accomplished by placing the flapping mechanism in a vacuum, and obtaining repeatable force measurements. By examining the results, one will be able to assess what contributions

PAGE 84

84 are due to the structure, and what is due to the wing. Once a tare is obtained, it can be used to analyze the aerodynamic forces generated, once the selected wings are tested in a forward flight environm ent. This can also serve to validate the results of the momentum balance approach, to see if the same trends are seen, and how many spanwise planes are required to obtain an accurate force.

PAGE 85

85 LIST OF REFERENCES [1] C. J. Bradshaw and J. Papadopoulos, Bioinspired design of flapping wing micro air vehicles, The Aeronautical Journal vol. 109, no. 2950, pp. 385393, 2005. [2] C. P. Ellington, The novel aerodynamics of insect flight: applications to microair vehicles., The Journal of Experimental B iology vol. 202, no. 23, pp. 343948, Dec. 1999. [3 ] K. D Jones and M F Platzer, Experimental investigation of the aerodynamic characteristics of flapping wing micro air vehicles, in Proc. 41st Aerospace Sciences Meeting, Reno, Nevada Jan. 2003. [4] T. J. Mueller, Fixed and flapping wing aerodynamics for micro air vehicle applications Progress in Astronautics and Aeronautics, AIAA 2001 605 pp [5] P. Wilkins and K. Knowles, Investigation of aerodynamics relevant to flapping wing micro air vehicles, Fluid Dynamics pp. 113, Jun. 2007. [6] Experimental investigation of some aspects of insect like flapping flight aerodynamics for application to micro air vehicles, Experiments in Fluids vol. 46, no. 5, p p. 777798, 2009. [7] G. K. Taylor, M. S. Triantafyllou, and C. Tropea (Eds.), Animal Locomotion. Berlin;Heidelberg: Springer Verlag, 2010, p. 441. [8] S. P. Sane, The aerodynamics of insect flight, Journal of Experimental Biology vol. 206, no. 23, pp. 41914208, Dec. 2003. [9] A. P. Willmott and C. P. Ellington, The Mechanics of Flight in the Hawkmoth Manduca Sexta, The Journal of Experimental Biology vol. 200, pp. 27052722, 1997. [10] I. Faruque and J. Sean Humbert, Dipteran insect flight dynamics Part 1 Longitudinal motion about hover., Journal of Theoretical Biology vol. 264, no. 2, pp. 538552, 2010. [11] P. Henningsson and A. Hedenstrm, Aerodynamics of gliding flight in common swifts., The Journal of Experimental B iology vol. 214, no. 3, pp. 382 93, Mar. 2011. [12] W. Shyy, Y. Lian, J. Tang, H. Liu, P. Trizila, B. Stanford, L. Bernal, C. Cesnik, P. Friedmann and P. Ifju, Computational aerodynamics of low Reynolds number plunging, pitching and flexible wings for MAV applications, Acta M echanica Sinica vol. 24, no. 4, pp. 351 373, Jul. 2008.

PAGE 86

86 [13 ] W. Shyy, H. Aono, S. K. Chimakurthi, P. Trizila, C. K. Kang, C. E. S. Cesnik and H. Liu Recent progress in flapping wing aerodynamics and aeroelasticity, Progress in Aerospace Sciences vol. 46, no. 7, pp. 284327, Oct. 2010. [14] C. k won Kang, H. Aono, C. E. S. Cesnik and W. Shyy Effects of Flexibility on the Aerodynamic Performance of Flapping Wings, Journal of Fluid Mechanics, vol. 689, pp. 3274, 2011. [15] M. Keenon, K. Klingebiel, H. Won, and A. Andriukov, Development of the Nano Hummingbird: A Tailless Flapping Wing Micro Air Vehicle, in Proc. 50th AIAA Aerospace Sciences Meeting, Nashville, Tennessee, Jan. 2012. [16 ] G. C. H. E. de Croon, K. M. E. de Clercq, R. Ruijsink, and B. Reme s, Design, aerodynamics, and visionbased control of the DelFly, International Journal of Micro Air Vehicles vol. 1, no. 2, pp. 7198, 2009. [17] R. J. Wood, The First Takeoff of a Biologically Inspired At Scale Robotic Insect, IEEE Transactions on Robotics vol. 24, no. 2, pp. 1 7, 2008. [18 ] P. Zdunich, D. Bilyk, M. MacMaster, D. Loewen, J. DeLaurier, R. Kornbluh, T. Low, S. Stanford and D. Holeman, Development and Testing of the Mentor Flapping Wing Micro Air Vehicle, Journal of Aircraft vol. 44, no. 5, pp. 17011711, 2007. [19] S. S. Baek and R. S. Fearing, Flight Forces and Altitude Regulation of 12 gram I Bird, Electrical Engineering, pp. 454460, 2010. [20] T. L. Hedrick, J. R. Usherwood, and A. A. Biewener, Low speed maneuvering flight of the rosebreasted cockatoo (Eolophus roseicapillus). II. Inertial and aerodynamic reorientation., The Journal of Experimental B iology vol. 210, no. 11, pp. 191224, Jun. 2007. [21] B. Y. C. R. Betts and R. J. Wootton, Wing Shape and Flight Behaviour in Butterflies ( Lepidoptera: Papilionoidea and Hesperioidea): A preliminary analysis Journal of Experimental Biology vol. 138, pp. 271 288, 1988. [22] C. K. Kang, H. Aono, C. E. S. Cesnik, and W. Shyy, Effects of flexibility on the aerodynamic performance of flapping wings, Journal of Fluid Mechanics vol. 689, pp. 3274, Nov. 2011. [23] R. J. Wootton, Leading Edge Section and Asymmetric twisting in the wings of flying butterflies Journal of Experimental Biology vol. 180 pp. 105117, 1993. [24] S. A Combes, Flexural stiffness in insect wings I. Scaling and the influence of wing venation, Journal of Experimental Biology vol. 206, no. 17, pp. 29792987, Sep. 2003.

PAGE 87

87 [25] T. L. Daniel and S. A. Combes, Flexible wings and fins: bending by inertial or f luid dynamic forces?, Integrative and comparative biology vol. 42, no. 5, pp. 10449, Nov. 2002. [26] S. A Combes, Into thin air: contributions of aerodynamic and inertial elastic forces to wing bending in the hawkmoth Manduca sexta, Journal of Experi mental Biology vol. 206, no. 17, pp. 29993006, Sep. 2003. [27] W. Shyy and H. Liu, Flapping Wings and Aerodynamic Lift: The Role of Leading Edge Vortices, AIAA Journal vol. 45, no. 12, pp. 28172819, Dec. 2007. [28] J. Tang, D. Viieru, and W. Shyy, E ffects of Reynolds Number and Flapping Kinematics on Hovering Aerodynamics, AIAA Journal vol. 46, no. 4, pp. 967976, Apr. 2008. [29] M. S. Triantafyllou, G. S. Triantafyllou, and D. K. P. Yue, Hydrodynamics of Fishlike Swimming, Annual Review of Fluid Mechanics vol. 32, pp. 3353, Jan. 2000. [30] Z. J. Wang, Vortex shedding and frequency selection in flapping flight, Journal of Fluid Mechanics vol. 410, pp. 323341, 2000. [31] R. F. Huang, J. Y. Wu, J. H. Jeng, and R. C. Chen, Surface flow and vor tex shedding of an impulsively started wing, Journal of Fluid Mechanics vol. 441, no. 1, pp. 265292, 2001. [32] G. K. Taylor, R. L. Nudds, and A. L. R. Thomas, Flying and swimming animals cruise at a Strouhal number tuned for high power efficiency, Na ture vol. 425, no. 6959, pp. 707 711, 2003. [33] G. S. Triantafyllou, M. S. Triantafyllou, and M. A. Grosenbaugh, Optimal thrust development in oscillating foils with application to fish propulsion, Journal of Fluids and Structures vol. 7, no. 2, pp. 205 224, 1993. [34] M. S. Triantafyllou, G. S. Triantafyllou, and R. Gopalkrishnan, Wake mechanics for thrust generation in oscillating foils, Phys Fluids A vol. 3, no. 12, p. 28357 1991. [35] J. M. Anderson, K. Streitlien, D. S. Barrett, and M. S. Tri antafyllou, Oscillating foils of high propulsive efficiency, Journal of Fluid Mechanics vol. 360, no. 1, pp. 4172, 1998. [36] D. Read, Forces on oscillating foils for propulsion and maneuvering, Journal of Fluids and Structures vol. 17, no. 1, pp. 1 63183, 2003.

PAGE 88

88 [37] L. Guglielmini, A simple model of propulsive oscillating foils, Ocean Engineering, vol. 31, no. 7, pp. 883899, 2004. [38] S. Heathcote and I. Gursul, Flexible Flapping Airfoil Propulsion at Low Reynolds Numbers, AIAA Journal vol. 4 5, no. 5, pp. 10661079, May 2007. [39] S. Heathcote, Z. Wang, and I. Gursul, Effect of spanwise flexibility on flapping wing propulsion, Journal of Fluids and Structures vol. 24, no. 2, pp. 183199, Feb. 2008. [40] B. K. Ohmi and M. Coutanceau, Vortex formation around an oscillating and translating airfoil at large incidences, Journal of Fluid Mechanics vol. 211, pp. 3760, 1990. [41] K. Ohmi, M. Coutanceau, O. Daube, and T. P. Loc, Further experiments on vortex formation around an oscillating and t ranslating airfoil at large incidences, Journal of Fluid Mechanics vol. 225 p p 607 630, 1991. [42] C. kwon Kang, H. Aono, S. Carlos, and W. Shyy, A Scaling Parameter for the Thrust Generation of Flapping Flexible Wings, in Proc. 49th AIAA Aerospace S ciences Meeting, Orlando, Florida, Jan. 2011 [43] J. M. Rausch, L. P. Bernal, C. S. Cesnik, W. Shyy, and L. Ukeiley, Fluid Dynamic Forces on Plunging SpanwiseFlexible Elliptical Flat Plates at Low Reynolds Numbers, in Proc. 41st AIAA Fluid Dynamics Hon olulu, Hawaii, Jun. 2011. [44] D. Ishihara, T. Horie, and M. Denda, A twodimensional computational study on the fluidstructure interaction cause of wing pitch changes in dipteran flapping flight., The Journal of Experimental B iology vol. 212, pp. 110, Jan. 2009. [45] B. Thiria and R. Godoy Diana, How wing compliance drives the efficiency of self propelled flapping flyers, Physical Review E vol. 82, no. 1, pp. 1 4, Jul. 2010. [46] J. M. Rausch, Y. S. Baik, L. P. Bernal, C. E. S. Cesnik, and W. Shyy, Fluid Dynamics of Flapping Rigid and SpanwiseFlexible Elliptical Flat Plates at Low Reynolds Numbers, in Proc. AIAA 40th Fluid Dynamics Conference and Exhibit Chicago, Illinois, Jul. 2010. [47] D. Ishihara, Y. Yamashita, T. Horie, S. Yoshida, and T. Niho, Passive maintenance of high angle of attack and its lift generation during flapping translation in crane fly wing., Journal of Experimental Biology vol. 212, no. 23, pp. 38823891, 2009.

PAGE 89

89 [48] S. Ramananarivo, R. Godoy Diana, and B. Thiria, Rather t han resonance, flapping wing flyers may play on aerodynamics to improve performance., in Proc. National Academy of Sciences of the United States of America, vol. 108, no. 15, pp. 59649, Apr. 2011. [49] S. Michelin and S. G. Llewellyn Smith, Resonance and propulsion performance of a heaving flexible wing, Physics of Fluids, vol. 21, no. 7, p p 071902:1 15 2009. [50] H. Masoud and A. Alexeev, Resonance of flexible flapping wings at low Reynolds number, Physical Review E vol. 81, no. 5, pp. 15, May 2010. [51] P. Wu, P. Ifju, and B. Stanford, Flapping Wing Structural Deformation and Thrust Correlation Study with Flexible Membrane Wings, AIAA Journal vol. 48, no. 9, pp. 21112122, 2010. [52] S. E. Spagnolie, L. Moret, M. J. Shelley, and J. Zhang, Sur prising behaviors in flapping locomotion with passive pitching, Physics of Fluids, vol. 22, no. 4, p. 041903, 2010. [53 ] J. Zhang, N Liu, and X Lu, Locomotion of a passively flapping flat plate, Journal of Fluid Mechanics vol. 659, no. 1, pp. 4368, 2010. [54] M. Vanella, T. Fitzgerald, S. Preidikman, E. Balaras, and B. Balachandran, Influence of flexibility on the aerodynamic performance of a hovering wing., The Journal of Experimental Biology vol. 212, no. 1, pp. 95105, Jan. 2009. [55] S. Heathc ote, I. Gursul, and D. Martin, Flexible Flapping Airfoil Propulsion at Zero Freestream Velocity, AIAA Journal vol. 42, no. 11, pp. 21962204, 2004. [56] S. Heathcote and I. Gursul, Flexible Flapping Airfoil Propulsion at Low Reynolds Numbers, AIAA Jou rnal vol. 45, no. 5, pp. 10661079, May 2007. [57] L. Zhao, Q. Huang, X. Deng, and S. Sane, The effect of chordwise flexibility on the aerodynamic force generation of flapping wings: Experimental studies, Proc. IEEE International Confer ence on Robotics and Automation, Kobe, Japan, May 2009, pp. 42074212. [58] A. M. Mountcastle and T. L. Daniel, Aerodynamic and functional consequences of wing compliance, Experiments in Fluids vol. 46, no. 5, pp. 873 882, 2009. [59 ] H. Aono, S. K. Chimakurthi, P. Wu, E. Sallstrom, B. Stanford, C.E.S. Cesnik, P. Ifju, L. Ukeiley and W. Shyy A computational and experimental study of flexible flapping wing aerodynamics, in Proc. 4 8th AIAA Aerospace Sciences M eeting, Orlando, Florida, Jan. 2010.

PAGE 90

90 [60] D. K. Kim, J. H. H an, and K. J. Kwon, Wind tunnel tests for a flapping wing model with a changeable camber using macrofiber composite actuators, Smart Materials and Structures vol. 18, no. 2, p. 24008, 2009. [61] H. Aono, S. K. Chimakurthi, C. E. S. Cesnik, H. Liu, and W. Shyy, Computational modeling of spanwise flexibility effects on flapping wing aerodynamics, in Proc. 47th AIAA Aerospace Sciences Meeting, Orlando, Florida, Jan. 2009. [62] M. Hamamoto, Y. Ohta, K. Hara, and T. Hisada, Application of fluid structure i nteraction analysis to flapping flight of insects with deformable wings, Advanced Robotics vol. 21, no. 1, pp. 1 21, 2007. [63] S. K. Chimakurthi, J. Tang, R. Palacios, C. E. S. Cesnik, and W. Shyy, Computational Aeroelasticity Framework for Analyzing F lapping Wing Micro Air Vehicles, AIAA Journal vol. 47, no. 8, pp. 18651878, 2009. [64] R. Albertani, P. Khambatta, A. Hart, L. Ukeiley, M. Oyarzun, L. Cattafesta and G. Abate, Validation of a Low Reynolds Number Aerodynamic Characterization Facility, in Proc. 47th AIAA Aerospace Sciences Meeting, Orlando, Florida, Jan.2009. [65] AnnaVandenhoeck Ring, LaVision GmbH. Gottingen, Germany. [66] J. C. R. Hunt, A. A. Wray, and P. Moin, Eddies, streams, and convergence zones in turbulent flows, in Center for Turbulence Research Proc. Summer S chool P rogram 1988, pp. 193 208. [67] E. Sallstrom, L. Ukeiley, P. Wu, and P. Ifju, Aerodynamic Forces on Flexible Flapping Wings, in Proc. 49th AIAA Aerospace Sciences, Orlando, Florida, Jan. 2011 [68] E. Sallstrom Flow Field of Flexible Flapping Wings, PHD Dissertation, University of Florida, Gainesville, FL, 2010. [69] A. K. Prasad and R. J. Adrian, Stereoscopic Particle Image Velocimetry Applied to Liquid Flows, Experiments in Fluids vol. 15, no. 1, pp. 49 6 0, 1993. [70 ] R. Hartley and A. Zisserman, Multiple view geometry in Computer V ision ," Cambridge: Cambridge University Press, 2000, p. 624. [71] M. F. Platzer, K. D. Jones, J. Young, and J. C. S. Lai, Flapping Wing Aerodynamics: Progress and Challenges, AIAA Journal vol. 46, no. 9, pp. 21362149, Sep. 2008.

PAGE 91

91 [72] K. D. Jones and M. F. Platzer, Bio Inspired Design of Flapping Wing Micro Air Vehicles An Engineers Perspective, in Proc. 44th AIAA Aerospace Sciences Meeting and Exhibit Reno, Nevada, Jan. 2006. [73] M. Bozkurttas, H. Dong, R. Mittal, P. Madden, and G. V. Lauder, Hydrodynamic Performance of Deformable Fish Fins and Flapping Foils, in 44th AIAA Aerospace Sciences Meeting and Exhibit Reno, Nevada, Jan. 2006.

PAGE 92

92 BIOGRAPHICAL SKETCH Diego Gustavo Campos was born in Miami, Florida. He has always had a passion for airplanes, rockets and anything that flies. Every time he had the chance to be in a plane, he would fight for the window. Not to see the ground below, but to be able to stare at th e wing, and all its mechanism s as it flew. Secretly he still does it. As a little kid, his dream was to become an astronaut and work for NASA. He moved to Guatemala when he was 5, but moved back to Miami to finish high school, and be able to pursue a degree in aerospace engineering. He received his bachelors degree in aerospace engineering from the University of Florida in 2010. He then enrolled in the masters program at UF in the fall of 2010, where he studied biologically inspired flexible wings under t he direction of Dr. Lawrence Ukeiley. He plans to graduate in May of 2012 and pursue a career in industry. His lifelong goal is to take part in the design and analysis of the next generation commercial aircraft.