1-s2.0-S0376042110000023-main

Recent progress in ?apping wing aerodynamics and aeroelasticity

W.Shyy a,n ,H.Aono a ,S.K.Chimakurthi a ,P.Trizila a ,C.-K.Kang a ,C.E.S.Cesnik a ,H.Liu b

a

Department of Aerospace Engineering,University of Michigan,FXB 1320Beal Avenue,Ann Arbor,MI 48109,USA b Graduate School of Engineering,Chiba University,1-33Yayoi-cho,Chiba,Chiba 263-8522,Japan

a r t i c l e i n f o

Available online 13February 2010a b s t r a c t Micro air vehicles (MAVs)have the potential to revolutionize our sensing and information gathering

capabilities in areas such as environmental monitoring and homeland security.Flapping wings with

suitable wing kinematics,wing shapes,and ?exible structures can enhance lift as well as thrust by

exploiting large-scale vortical ?ow structures under various conditions.However,the scaling invariance

of both ?uid dynamics and structural dynamics as the size changes is fundamentally dif?cult.The focus

of this review is to assess the recent progress in ?apping wing aerodynamics and aeroelasticity.It is

realized that a variation of the Reynolds number (wing sizing,?apping frequency,etc.)leads to a change

in the leading edge vortex (LEV)and spanwise ?ow structures,which impacts the aerodynamic force

generation.While in classical stationary wing theory,the tip vortices (TiVs)are seen as wasted energy,

in ?apping ?ight,they can interact with the LEV to enhance lift without increasing the power

requirements.Surrogate modeling techniques can assess the aerodynamic outcomes between two-and

three-dimensional wing.The combined effect of the TiVs,the LEV,and jet can improve the

aerodynamics of a ?apping wing.Regarding aeroelasticity,chordwise ?exibility in the forward ?ight

can substantially adjust the projected area normal to the ?ight trajectory via shape deformation,hence

redistributing thrust and lift.Spanwise ?exibility in the forward ?ight creates shape deformation from

the wing root to the wing tip resulting in varied phase shift and effective angle of attack distribution

along the wing span.Numerous open issues in ?apping wing aerodynamics are highlighted.

&2010Elsevier Ltd.All rights reserved.

Contents

1.

Introduction......................................................................................................2852.Equations and parameters of ?apping wing dynamics ....................................................................

2862.1.Kinematics of ?apping ?ight ...................................................................................

78256f9db9d528ea81c7798derning equations .........................................................................................

2872.3.Scaling laws ................................................................................................2883.Key attribute of unsteady ?apping wing aerodynamics....................................................................

2903.1.Clap and ?ing...............................................................................................

2913.2.Rapid pitch rotation..........................................................................................

2913.3.Wake capture...............................................................................................

2913.4.Delayed stall of leading edge vortex (LEV)........................................................................

2923.5.Tip vortex (TiV).............................................................................................

2933.6.Passive pitching mechanism ...................................................................................2934.Kinematics,wing geometry,Re ,and rigid ?apping wing aerodynamics .......................................................

2944.1.Single wing in forward ?ight condition ..........................................................................

2944.2.Single wing in hovering ?ight condition..........................................................................

2964.3.Tandem wing in forward/hovering ?ight condition.................................................................

2974.4.Implications of wing geometry .................................................................................

2974.5.Implications of wing kinematics................................................................................

2984.6.Surrogate modeling for hovering wing aerodynamics ...............................................................298Contents lists available at ScienceDirect

journal homepage:78256f9db9d528ea81c7798d/locate/paerosci

Progress in Aerospace Sciences

0376-0421/$-see front matter &2010Elsevier Ltd.All rights reserved.doi:10.1016/j.paerosci.2010.01.001Abbreviations:AoA,angle of attack;LEV,leading edge vortex;MAV,micro air vehicle;MTV,molecular tagging velocimetry

n Corresponding author.Tel:+17349360102.

E-mail address:weishyy@78256f9db9d528ea81c7798d (W.Shyy).

Progress in Aerospace Sciences 46(2010)284–327

4.7.Unsteady?ow structures around hawkmoth-like model in hover (301)

4.7.1.Vortex dynamics of hovering hawkmoth (301)

4.8.Effect of the Reynolds number on the LEV structure and spanwise?ow (305)

5.Flapping wing aeroelasticity (307)

5.1.Chordwise-?exible wing structures (308)

5.2.Spanwise-?exible wing structures (313)

78256f9db9d528ea81c7798dbined chordwise-and-spanwise?exible wing structures (316)

6.Conclusions (320)

Acknowledgements (322)

Appendix (322)

References (323)

1.Introduction

Micro air vehicles(MAVs)have the potential to revolutionize our sensing and information gathering capabilities in areas such as environmental monitoring and homeland security.Numerous vehicle concepts,including?xed wing,rotary wing,and?apping wing,have been proposed[1–8].As the size of a vehicle becomes smaller than a few centimeters,?xed wing designs encounter fundamental challenges in lift generation and?ight control.There are merits and challenges associated with rotary and?apping wing designs.Fundamentally,due to the Reynolds number effect, the aerodynamic characteristics such as the lift,drag and thrust of a?ight vehicle change considerably between MAVs and conven-tional manned air vehicles[1–8].And,since MAVs are of light weight and?y at low speeds,they are sensitive to wind gust [1–9].Furthermore,their wing structures are often?exible and tend to deform during?ight.Consequently,the?uid and structural dynamics of these?yers are closely linked to each other.Because of the common characteristics shared by MAVs and biological?yers,the aerospace and biological science commu-nities are now actively communicating and collaborating.Much can be shared between researchers with different training and background including biological insight,mathematical models, physical interpretation,experimental techniques,and design concepts.

In order to handle wind gust,object avoidance,or station keeping,highly deformed wing shapes and coordinated wing–tail movement in the biological?ight are often observed.Under-standing the aerodynamic,structural,and control implications of these modes is essential for the development of high performance and robust?apping wing MAVs for accomplishing desirable missions.Moreover,the large?exibility of the wings leads to complex?uid–structure interactions,while the kinematics of ?apping and the spectacular maneuvers performed by natural ?yers result in highly coupled nonlinearities in?uid dynamics, aeroelasticity,?ight dynamics,and control systems.

Insect wing structures are inherently anisotropic due to their membrane–vein con?gurations,with the spanwise bending stiffness being approximately1–2orders of magnitude larger than the chordwise bending stiffness in a majority of insect species[10,11].In general,the spanwise?exural stiffness scales with the third power of the wing chord,while the chordwise stiffness scales with the second power of the wing chord[10,11]. Insect wings exhibit substantial variations in aspect ratio and con?guration but share a common feature of a reinforced leading edge.A dragon?y wing has more local variations in its structural composition and is more corrugated than the wing of a cicada or a wasp[1,12].It has been shown in the literature[1–3,12]that wing corrugation increases both warping rigidity and?exibility. Furthermore,speci?c characteristic features have been observed in the wing structure of a dragon?y which help prevent fatigue fracture[1,12].The thin nature of the insect wing skin structure makes it unsuitable for taking compressive loads,which may result in skin wrinkling and/or buckling,i.e.,large local deforma-tions that will interact with the?ow.On the aerodynamics side,in a?xed wing set-up,wind tunnel measurements show that corrugated wings are aerodynamically insensitive to the Reynolds number variations,which is quite different from a typical low Reynolds number airfoil[1,4,6,7,12].

As highlighted above,biological?yers showcase desirable ?ight characteristics and performance objectives[1,12–23].The strategies exhibited in nature have the potential to be utilized in the design of?apping wing MAVs[1–8,24–27].In particular,wing ?exibility is likely to have a signi?cant in?uence on the resulting aerodynamics.Based on a literature survey,it was found that several questions in?exible wing aerodynamics have not been adequately addressed in existing literature,among which,the key ones include:(i)How do geometrically nonlinear effects and the anisotropy of the structure impact the aerodynamics character-istics of the?apping wing?(ii)How can?apping?ight be stabilized passively via?exible structures?

Furthermore,even though the rigid wing aerodynamics have been explored in more detail than the?exible wing aerodynamics,several questions still remain,among which,the key ones include:(i)How can the unsteady?ow features be manipulated to enhance performance?As the sizing,?apping kinematics,?apping frequency,and?ight speed vary,which?uid physics mechanisms are important?(ii)How can the observations from high?delity simulations or experimental studies be distilled into reduced order models so that they are fast enough to execute for MAV control development?Since all of the above are not necessarily independent topics,a comprehensive understanding of the role of?apping wing kinematics,aerodynamics,and ?exibility is central to the success of future?apping wing MAV designs.

As evidenced in the references cited,a number of publications exist to address numerous aspects of these issues.Furthermore, recently,many researchers have taken serious efforts in investigating these topics.There seems to be a need to consolidate the fast developing information to help update and bene?t the community. The purpose of this paper is to complement the recent work presented by Shyy et al.[1]to review the recent progress in?apping wing aerodynamics and aeroelasticity at low Reynolds numbers, namely,(O(101)–O(104)).In addition to present established informa-tion,open issues in both aerodynamics/aeroelasticity are highlighted so as to encourage future community-wide efforts.

The rest of the paper is organized as follows:

Flapping wing kinematics,governing equations,and scaling laws are presented in Section 2.Unsteady?ight mechanisms associated with?apping wings and frequently encountered in the literature are described in Section3.A literature survey focusing on?apping wing aerodynamics and aeroelasticity is presented in Sections4and5while emphasizing computational efforts of the authors to highlight selected?apping wing physics.Finally, concluding remarks and areas warranting further study are made in Section6.

W.Shyy et al./Progress in Aerospace Sciences46(2010)284–327285

2.Equations and parameters of ?apping wing dynamics Aerodynamics associated with ?apping wings can be modeled using the unsteady Navier–Strokes (NS)equations.Nonlinear physics with multiple variables (velocity,pressure)and moving geometries are among the aspects of primary interest.Numerous ?apping wing kinematics and scaling parameters related to the ?uid dynamics and ?uid–structure interactions exist.The ?ight regime of each ?yer is characterized by these parameters.

2.1.Kinematics of ?apping ?ight

The kinematics of ?apping ?ight is composed of body and wing movements.As shown in Fig.1,assuming that the wing and body are rigid,the body kinematics can be represented by the body angle (w )(inclination of the body),relative to the horizontal plane (e.g.the ground).The ?apping wing kinematics can be described by three basic positional angles of the wing with the stroke plane (b ):(i)?apping about the x -axis in the wing root-?xed coordinate system described by the positional or stroke angle (f ),(ii)rotation of the wing about the z -axis in the wing root-?xed coordinate system described by the elevation or deviation angle (y ),and (iii)rotation of the wing about the y -axis in the wing root-?xed coordinate system described by the angle of attack (a ).The

stroke plane is de?ned by the wing base and the wing tip of the maximum and the minimum sweep positions.Examples of the time histories of three insects are shown in Fig.2.The time histories of positional angle show approximately ?rst-order sinusoidal curves.The time histories of elevation angle show small amplitude and have twice frequency of main ?apping frequency.On the other hand,the time histories of angle of attack include high frequency component of the ?apping frequency and some of insects show asymmetric patterns per stroke.Moreover,the body angle and the stroke plane angle vary in accordance with the ?ight speed and ?apping wing kinematics of biological ?yers [1,28,29].

Due to the complexity of the aerodynamics associated with bio-mimicking kinematics (as shown in Figs.1and 2),building a description of the fundamental factors involved can bene?t from simpli?ed models.The simpli?ed models referred to later (Section 4)in the paper remove the rotational (centripetal and Coriolis)aspects while retaining vortex dynamics important in ?apping wing ?ight.While the combination of pitching and translation (versus ?apping about a pivot point)(see Fig.3)of the entire wing are not found in a biological ?yer,the motions used provide a basis for more complex analysis and are feasible mechanical designs.

The motions of the wing can be described by sinusoidal translation (along the X -axis)and pitching (about the Y -axis)with

W.Shyy et al./Progress in Aerospace Sciences 46(2010)284–327

286

the same frequency but not necessarily in phase.Three indepen-dent design variables are introduced:the normalized stroke amplitude with reference to a point of radius of gyration for second moment of the wing (2h a =c mr g )dictating the magnitude of the translation,the pitching amplitude (a a )which then de?nes the angle of attack (a ),and the phase lag (f )which speci?es the timing of the rotation relative to the translation.In synchronized rotation,the rotation takes place at the ends of translation and the leading edge is the same for both the forward and backstroke.Changing phase lag will cause the rotation to start early (advanced rotation)or after the translation has switched direction (delayed rotation).This will affect the angle of attack during subsequent interactions with the wake as well when the wing has achieved maximum translational velocity at the middle of the stroke.

In unsteady ?ows,there is no single angle of attack at each wing section since the ?ow direction varies along the chord as a result of the induced ?ow.Therefore,a very useful quantity known as effective angle of attack is de?ned in the literature for

the case of simple harmonic motion.It is given by the following expression [30,31]:

a e ?tan à1à_h

U 1 !

àa e1Twhere the effective angle of attack a e is measured at reference points of the airfoil,a is the angle of attack,U N is freestream velocity or ?ight velocity,and h is the velocity due to plunge motion,respectively.It may be noted that in the unsteady motion of ?exible

wing structures,the velocities (_h

)not only include the rigid body plunge and pitch motions,respectively but also those due to bending and twist deformations.In such a case,the angle of attack (a )can be de?ned simply as the angle between the line joining the leading and trailing edges of an airfoil section and the direction of freestream.If the structure behaves as a beam,the effective angle of attack will remain the same at each point along the chord (the angle of attack still varies along the chord due to chordwise variation of induced ?ow).It is clearly not the case if the structure behaves like a plate or a shell.Effective angles of attack vary through the chord due to plate-like deformations.The angle at three-quarter chord then may become a representative sectional effective angle of attack [30].Fig.4illustrates the effective angle of attack due to prescribed plunge motion (reference point is three-quarter chord from the trailing edge [31]),and prescribed plunge motion (reference point is the leading edge)with chordwise deformation [32]78256f9db9d528ea81c7798derning equations

The governing equations of ?uid are the unsteady,incompres-sible 3-D NS equations and the continuity equation,which are expressed in vector form as follows:

@U @t tU U r U ?à1r f r p tm r f

r 2

U ;r U U ?0

e2T

where r f is the ?uid density,m is the dynamic viscosity coef?cient,U ?eU V W Tis the velocity vector of the ?uid,t is the time,X ?eX Y Z Tis the position vector of the ?uid based on the inertial frame,r is the gradient operator with respect to X ,and p is the pressure,respectively.

Assuming an isotropic plate-like ?apping wing structure that is loaded in the transverse direction,the governing equations of motion can be written as A s

@2u 0s tA s @2v 0s s te1àn TA s

@2u 0

s ?0e3a T

A s @2u 0@x s @y s te1àn TA s @2v 0@x 2s tA s

@2v 0@y 2s

?0e3b T

D s @4w 0@x 4s t2D s @4w 0@x 2s @y 2s tD s @4w 0@y 4s

àr s h s @2w 0

@t 2?f p e3c T

where u 0,v 0,and w 0are displacement in the x s ,y s ,and z s direction,respectively,of a point on the mid-surface of the plate considered in the x s –y s plane.And,the coef?cients A s =Eh s /(1àn 2)and D s ?Eh 3s =12e1àn 2T

àácorrespond to the extensional and bending stiffnesses,respectively,r s is the density of the plate material,h s is the thickness of the plate,E and n is Young’s modulus of material and Poisson’s ratio,and f p is the distributed transverse load on the plate.The ?rst two equations presented above correspond to the in-plane motion and the last one corresponds to the out-of-plane motion.For the purpose of scaling,only the equation of the out-of-plane motion is con-sidered in Section 2.3.More details of the plate equations are given in Refs.[33,34]

.

Stroke plane

Y

x

Pitch

O

Fig.1.Schematic diagrams of coordinate systems and kinematics of ?apping wing

and body movement.The local wingroot-?xed and the global space-?xed coordinate systems are shown.The local wingroot-?xed coordinate system (x,y,z )is ?xed at the center of the stroke plane (origin O at the wing root)with x direction normal to the stroke plane,the y direction vertical to the body axis,and the z direction parallel to the stroke plane.De?nitions of the positional or stroke angle (f ),the angle of attack (a ),the elevation or deviation angle (y ),the body angle (w ),and the stroke plane angle (b )are indicated in the ?gure.

W.Shyy et al./Progress in Aerospace Sciences 46(2010)284–327287

2.3.Scaling laws

Scaling laws are useful to reduce the number of parameters,to clearly identify characteristic properties of the system under consideration,and to indicate which combination of parameters

becomes important under a given condition.From the view point of ?uid–structure interaction,several dimensionless parameters arise during the non-dimensionalization process of the ?uid and structural dynamics equations using a set of suitable reference scales.Depending upon the problem at hand and the type of equations used to model the physical phenomena involved,the resultant set of scaling parameters could vary.In ?apping wing ?ight,three dimensionless parameters related to the ?uid dynamics,wing kinematics,and three other dimensionless parameters relevant to the ?uid–structure interaction are high-lighted next (see Table 1):

(i)The Reynolds number (Re )represents a ratio between inertial

forces and viscous forces.

Given a reference length (L ref )and a reference velocity (U ref ),the Reynolds number (Re )is de?ned as

Re ?

r f L ref U ref

m

:e4T

In ?apping wing ?ight,since lift and thrust are generated by ?apping wings,the mean chord length of the wing (c m ),is used as the reference length (L ref )and the inverse of the ?apping frequency (1/f )is often utilized as the reference time (T ref ).On the other hand,the reference velocity needs to be selected carefully considering the ?ight conditions and wing kinematics.

In hovering ?ight,and the mean wingtip velocity of the ?apping wing can be used as the reference velocity,written as U ref =U tip =o R ,where o is the mean angular velocity of

the

Fig.2.Time histories of the three angles associated with ?apping wing motion of hovering ?ight for (A)a hawkmoth model [42];(B)a honeybee model [42];and (C)a fruit ?y model [42].Positional/stroke angle,elevation/deviation angle,and angle of attack of the wing are indicated by solid (green),dash-dotted (blue),and dashed (orange)lines,respectively.(For interpretation of the references to color in this ?gure legend,the reader is referred to the web version of this

article.)

Fig.3.Schematics diagram for simpli?ed wing kinematics.The stroke plane angle (b )is equal to zero.The global coordinate system (X ,Y ,Z )is ?xed at the center of the stroke plane with Z direction normal to the stroke plane,the Y direction perpendicular to the wing axis,and the X direction parallel to the stroke plane.a and 2h a =c mr g are the angle of attack and normalized stroke amplitude with reference to a point of radius of gyration for second moment of the wing [16],respectively.

W.Shyy et al./Progress in Aerospace Sciences 46(2010)284–327

288

wing about x -axis (o =2F f ,where F is the full stroke

amplitude,measured in radians)and R is the wing semi-span.Therefore the Reynolds number (Re )for hovering ?ight can be rewritten as Re ?

r f L ref U ref m ?r f A R F fc 2

m

m

;e5T

where the aspect ratio A R =b 2/S ,with the wing planform area

(S )being the product of the wing span (b )and the mean chord length (c m ).Note that the Reynolds number is proportional to the ?ap amplitude,the ?apping frequency,square of the mean chord length,and the aspect ratio of the wing (see Table 2).

In forward ?ight,there are multiple candidates for the reference velocity,for example,the mean wing tip velocity and the forward ?ight velocity (U N ).If the reference velocity

is chosen as the forward ?ight velocity,the Reynolds number

can be represented as Re ?

r f L ref U ref m ?r f c m U 1

m

e6T

In comparison with the Reynolds number based on the mean wing tip velocity,the Reynolds number based on the forward ?ight velocity is proportional to the mean chord length and ?ight velocity,and not related to the ?apping frequency and the ?apping amplitude.

(ii)The Strouhal number (St )describes the relative in?uence of

forward ?ight (U N )versus the ?apping speeds [1].The Strouhal number (St )characterizes the vortex dynamics of the wake and shedding behavior of vortices of a ?apping wing in forward ?ight [1,35].For ?apping wing ?ight,the Strouhal number is de?ned based on the ?apping

frequency,

Fig.4.Illustrations to show effective angle of attack due to prescribed plunge motion and chordwise deformation of (A)a e is the effective angle of attack of an airfoil due to plunge motion (extracted from Ref.[31])(B)a e L :E :and a L.E.are the effective angle of attack for the chordwise ?exible wing case and the angle of attack due to the wing deformation.The effective angle of attack decreases with geometric angle of attack (a L.E.)due to the wing deformation extracted from Ref.[32].

Table 1

Dimensionless parameters and scaling dependency for ?apping wings.Dimensionless parameter

Based on ?apping wing velocity U ref =U tip =A R c m U f Based on ?ight speed U ref =U N Length

Frequency Length Frequency Velocity Reynolds number:Re =q f U ref c m /l c 2m

f

c m Independent U N

Reduced frequency:k =(p fc m )/U ref Independent

Independent c m f U à11Strouhal number:St =(2fh a )/U ref

Independent

Independent c m

f

U à11

Effective stiffness:P 1?D s =eq f U 2ref c 3

m Tc à2m

f

à2

Independent Independent U à21

Effective rotational inertia:P 2?I B =eq f c 5m TIndependent Independent Independent Independent Independent Density ratio:q ?q s =q f

Independent

Independent

Independent

Independent

Independent

Note that D s indicates the ?exural rigidity which is de?ned as the force couple required to bend a structure to a unit curvature.In the case of the isotropic plate,

D s ?Eh 3s =e12e1àn 2

TT.

W.Shyy et al./Progress in Aerospace Sciences 46(2010)284–327289

the travel distance of full ?apping amplitude (R F ),and the speed of forward ?ght,namely,St ?fL ref U ref ?fR F U 1?fA R c m F 2U 1

:

e7T

This de?nition offers a measure of propulsive ef?ciency of

?apping wing ?yer in forward ?ight.

(iii)The reduced frequency (k )provides a better measure of

unsteadiness associated with a ?apping wing than the Strouhal number by comparing spatial wavelength of the ?ow disturbance with the chord length [35].It is de?ned by the angular speed of the ?apping wing (2p f ),mean chord length (c m ),and the reference velocity (U ref ),namely,

k ?

p fc m

U ref

e8T

The reduced frequency based on the mean wingtip velocity can be formulated as k ?

p fc m

ref

?

p

F R

e9T

Note that the reduced frequency is inversely proportional to the ?apping amplitude and aspect ratio of the wing and not related to ?apping frequency.

On the other hand,the reduced frequency based on the forward or cruising ?ight speed can be rewritten as k ?

p fc m

U 1

e10T

The reduced frequency is proportional to ?apping frequency

and the mean chord length,and inversely ?ight speed.The relationship between the Strouhal number and the reduced frequency based on the forward ?ight speed is

St ?A R F p

e11T(iv)The density ratio (r )describes the ratio between the

equivalent structural density and ?uid density.

r ?

r s r f

e12T

(v)The effective stiffness (P 1)describes the ratio between

elastic bending forces and aerodynamic (or ?uid dynamic)forces.

P 1?

Eh 3s

12e1àn 2Tr f U 2ref c 3m

e13T

(vi)If an isotropic shear deformable plate is considered,an

additional dimensionless parameter [33,34],the effective

rotational inertia (P 2),will be

P 2?

I B

r f m

;e14T

where I B is the mass moment of inertia.This describes the ratio between rotational inertia forces and aerodynamic (or ?uid dynamic)forces.

As a summary,assuming that the geometric similarity is maintained,the scaling laws for rigid and ?exible ?apping wing aerodynamics for two sets of reference velocities are listed in Table 1.

Furthermore,in order to understand the effect of the above-scaling parameters on the governing equations,non-dimensional forms of the governing equations are presented based on the reference velocity as follows:

If the ?apping wing velocity is chosen as the velocity scale,then the resulting non-dimensional form of the NS equations and the equation of out-of-plane motion of the isotropic plate are p q t

tU U r ?àr p t1Re r 2

U

e15T

P 1

@4w 0

@x 4s

t2

@4w 0

@x 2s @y 2

s

t

@4w 0@y 4s

!àr h k p

2@2w

@t

2

?p

e16T

where the over-bar designates the dimensionless variable.This form of the equation separates the reduced frequency,the Reynolds number,the density ratio,and the effective stiffness,making it convenient to study the effects of these parameters.For biological ?yers,the ?apping frequency ranges 10–600Hz,and the wing length varies from 0.3to 600mm yielding the Reynolds number from O (104)to O (101)[1,36].In this ?ight regime,unsteady effects,inertia,pressure,internal,and viscous forces are all important.

3.Key attribute of unsteady ?apping wing aerodynamics Natural ?yers utilize ?apping mechanisms to generate lift and thrust.These mechanisms are related to formation and shedding of the vortices into the ?ow,varied wing shape,and structural ?exibility.Therefore,understanding the vortex dynamics,the vortex–wing interaction,and ?uid–structure interaction is very important.A brief introduction to some of the key unsteady mechanisms associated with ?apping wings that are frequently encountered in the literature is given next.Speci?c topics related to the interplay between the

Table 2

Morphological,?ight,scaling,and non-dimensional parameters of selected biological ?yers.Parameter

Chalcid Wasp (Encarsia formosa )Fruit ?y

(Drosophila melanogaster )Honeybee (Apis melli?ca)Hawkmoth

(Manduca sexta )Rufous Hummingbird (Selasphorus rufus )Mean chord length:c m (mm)0.330.78 3.018.312Semi-span:R (mm)0.70 2.3910.048.354.5Aspect ratio:A R 4.24

6.12

6.65 5.39Total mass:M (g)

2.6?10à70.96?10à30.1 1.6

3.4Flapping frequency:f (Hz)370218232.126.141Flapping amplitude:U (rad)

2.09 2.44 1.59 2.0 2.02Mean wing tip velocity:U rip (m/s) 1.08 2.547.38 5.048.66Flight speed:U N (m/s)

0.00.00.00.00.0Normalized stroke amplitude:2h a =c m tip 4.47.48 5.3 5.289.17Normalized stroke amplitude:2h a c mr g 4.4 4.3 3.05 3.04 5.27Reynolds number:Re 23126141258856628Reduced frequency:k

0.355

0.212

0.297

0.296

0.172

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290

unsteady aerodynamics and kinematics,Reynolds number,and wing geometry will be discussed in detail in Section4.

3.1.Clap and?ing

The earliest unsteady lift generation mechanism to explain how insects?y,found by Weis-Fogh[16],was the clap-and-?ing motion of a chalcid wasp,Encarsia formosa.Based on the steady-state approximation,the lift generated by the chalcid wasp was insuf?cient to stay aloft.To explain this,he observed that a chalcid wasp claps two wings together and then?ings them open about the horizontal line of contact to?ll the gap with air.During the?ing motion,the air around each wing acquires circulation in the correct direction to generate additional lift.A schematic of this procedure is shown in Fig.5.As illustrated in Fig.6,Lehmann et al.[37]elucidated this clap-and-?ing mechanism with PIV?ow visualizations and force measurements using a dynamically scaled robotic wing model.Also numerical investigations further demonstrated lift enhancement due to the clap-and-?ing mechanisms at low Reynolds numbers[38–42]. The relative bene?t of clap-and-?ing lift enhancement strongly depended on stroke kinematics and could potentially increase the performance by reducing the power requirements[43,44].The clap-and-?ing mechanism is bene?cial in producing a mean lift coef?cient to keep a low weight?yer aloft:numerous natural?yers,such as hawkmoths,butter?ies,fruit?ies,wasps,and thrips enhance their aerodynamic force production with the clap-and-?ing mechanism [16,45–49].

3.2.Rapid pitch rotation

At the end of each stroke,?apping wings can experience rapid pitching rotation,which can enhance the aerodynamic force generation[50].The phase difference between the translation and the rotation can be utilized as a lift controlling parameter:similar to the Magnus effect,if the wing?ips before the stroke ends,then the wing undergoes rapid pitch-up rotation in the correct translational direction enhancing the lift.This is called the advanced rotation.On the other hand,in delayed rotations,if a wing rotates back after the stroke reversal,then when the wing starts to accelerate it pitches down resulting in reduced lift[50]. In a follow-up study Sane and Dickinson[51]related the lift peak at the stroke ends to be proportional to the angular velocity of the wing using the quasi-steady theory.The numerical studies[1,52] showed an increase in the vorticity around the wing due to rapid pitch-up rotation of the wing led to augmentation of the lift generation.

3.3.Wake capture

The wake capture mechanism is often observed during a wing–wake interaction.When the wings reverse their transla-tional direction,the wings meet the wake created during the previous stroke,by which the effective?ow velocity increases and additional aerodynamic force peak is generated.Lehmann et al.

[37],Dickinson et al.[50],and Birch and Dickinson[53]examined the effect of wake capturing of several simpli?ed fruit?y-like wing kinematics using a dynamically scaled robotic fruit?y wing model at Re=1.0–2.0?102.They compared the force measure-ment data with the quasi-steady approximation then isolated the aerodynamic in?uence of the wake.Results demonstrated that wake capture force represented a truly unsteady phenomenon dependent on temporal changes in the distribution and magni-tude of vorticity during stroke reversal.The sequence of the wake capture mechanism is illustrated in Fig.7.Wang[54]and Shyy et al.[1,55]further elucidated the wake capture mechanism

and

Fig.5.Sectional schematic of wings approaching each other to clap(A–C)and?ing apart(D–F)adopted from Ref.[18]and originally described in Ref.[16].Black lines show ?ow lines and dark blue arrows show induced velocity.Light blue arrows show net forces acting on the airfoil.(A–C)Clap.As the wing approach each other dorsally(A), their leading edges touch initially(B),and the wing rotates around the leading edge.As the trailing edges approach each other,vorticity shed from the trailing edge rolls up in the form of stopping vortices(C),which dissipate into the wake.The leading edge vortices also lose strength.The closing gap between the two wings pushes?uid out, giving and additional thrust.(D–F)Fling.The wings?ing apart by rotating around the trailing edge(D).The leading edge translates away and?uid rushes in to?ll the gap between the two wing sections,giving an initial boost in circulation around the wing system(E).(F)A leading edge vortex forms anew but the trailing edge starting vortices are mutually annihilated as they are of opposite circulation.(For interpretation of the references to color in this?gure legend,the reader is referred to the web version of this article.)

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lift augmentation of the instantaneous lift peak using 2-D numerical simulations.The effectiveness of the wake capture mechanism was a function of wing kinematics and ?ow structures around the ?apping wings [1,37,50,53].A different view on the effect of wake capture existed as well.Jardin et al.[56]used a NACA0012airfoil under asymmetric ?apping wing kinematics such that in the downstroke the interaction of the previously shed wake with the leading edge vortex (LEV)formation was reduced.In the most cases they considered this reduced effect of wake capture led to a closely attached downstroke 78256f9db9d528ea81c7798dpared to a synchronized wing rotation they saw enhanced downstroke aerodynamic loading.

3.4.Delayed stall of leading edge vortex (LEV)

Ellington et al.[57–60]suggested that the delayed stall of LEV can signi?cantly promote lift associated with a ?apping wing.The LEV created a region of lower pressure above the wing and hence it would enhance lift.Multiple follow-up investigations [61–64]were conducted for different insect models,resulting in a better understanding on the role played by the LEV and its implications on lift generation.When a ?apping wing travels several chord lengths,the ?ow separates from the leading and trailing edges,as

well as at the wing tip,and forms large organized vortices known as a leading edge vortex (LEV),a trailing edge vortex (TEV),and a tip vortex (TiV).In ?apping wing ?ight,the presence of LEVs is essential to delay stall and to augment aerodynamic force production during the translation of the ?apping wings as shown in Fig.8[18].Fundamentally,the LEV is generated and sustained from the balance between the pressure-gradient,the centripetal force,and the Coriolis force in the NS equations.The LEV generates a lower pressure area in its core,which results in an increased suction force on the upper surface.Employing 3-D NS computations,Liu and Aono [42]and Shyy and Liu [65]demonstrated that a LEV is a common ?ow feature in ?apping wing aerodynamics at Reynolds numbers O (104)and lower,which correspond to the ?ight regime of insects and ?apping wing MAVs.However,main characteristics and implications of the LEV on the lift generation varied with changes in the Reynolds number,the reduced frequency,the Strouhal number,the wing ?exibility,and ?apping wing 78256f9db9d528ea81c7798dano and Gharib [66]measured the forces generated by pitching rectangular ?at plate at approximately Re =4.0?103and observed the trajectories yielding maximum average lift based on a genetic algorithm.Results showed the optimal ?apping produces LEVs of maximum circulation and that a dynamic formation time that described the vortex formation process of about 4is associated with

production

Fig.7.Illustrations of wake capture mechanism [1,55].(A)Supination,(B)beginning of upstroke,and (C)early of upstroke.At the end of the stroke,(A),the wake shed in the previous stroke denoted by CWV is en route of the ?at plate.As the ?at plate moves into the wake (B and C)the effective ?ow velocity increases and additional aerodynamic force is generated.The color of contour indicates spanwise-component of vorticity.CWV and CCWV indicate clock-wise and counter clock-wise

vortex.

Fig.6.Experimental visualization of clap-and-?ing mechanism by two-wings (M-T)using robotic wing models adopted from Ref.[37].The leading edge of the dorsal wing surface is marked by a white half circle.Fluid ?ow velocities are plotted in color/shades;red/light indicates large velocity magnitudes and arrows represent the velocity vectors at each point in the ?uid;longer arrows signify larger velocities.(For interpretation of the references to color in this ?gure legend,the reader is referred to the web version of this article.)

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of a maximum-circulation vortex[67,68].Rival et al.[69] investigated experimentally the formation process of LEVs associated with several combinations of pitching and plunging SD7003airfoils in forward?ight using PIV at Re=3.0?104.Results suggested that by carefully tuning the airfoil kinematics,thus gradually feeding the LEV over the downstroke,it was to some extent possible to stabilize the LEV without the necessity of a spanwise?ow.

Tarascio et al.[70]and Ramasamy and Leishman[71] visualized the?ow?elds around a biologically inspired?apping wing at Re=1.0?104by a mineral oil fog strobed with a laser sheet and PIV.They presented the presence of a shed dynamic stall vortex that spans across most of the wing span and multiple shedding LEVs on the top surface of the wing during each wing stroke.Also they provided several observations related to the role of turbulence at low Reynolds numbers.Poelma et al.[72] measured the time-dependent3-D velocity?eld around a ?apping wing at Re=256based on maximum chord.A dynami-cally scaled fruit?y wing in mineral oil with hovering kinematics extracted from real insect movements was used.They presented re?ned3-D structures of LEVs and suggested including the counter-rotating TEVs to get a complete picture for production of circulation.Lu and Shen[73]highlighted the detailed structures of LEVs for a?apping wing in hover at Re=1.6?103. They used phase-lock-based multi-slice digital stereoscopic PIV to show that the spanwise variation along the LEV was time-dependent.Their results demonstrated that the observed LEV systems were a collection of four vortical elements:one primary vortex and three minor vortices,instead of a single conical or tube-like vortex as reported or hypothesized in previous studies [50,57].Recently,Pick and Lehmann[74]used3-D three-components multiple-color-plane stereo PIV techniques to obtain a3-D velocity?eld around a?apping wing.The need for3-D PIV is evident since the critical?ow features in understanding?apping wing aerodynamics,such as LEVs and unsteady wakes behind an insect body,are inherently3-D in 78256f9db9d528ea81c7798dpared to the previous?ndings,they reported similar structure of the LEV but stronger outward axial?ow inside the LEV of up to80%of the

maximum in-plane velocity.On the other hand,Liang et al.[75] presented results based on direct numerical simulation to investigate wake structures of hummingbird hovering?ight and associated aerodynamic performance.They reported that the amount of lift produced during downstroke is about2.95times of that produced in upstroke.Two parallel vortex rings were formed at the end of the upstrokes.There is no obvious leading edge vortex can be observed at the beginning of the upstroke.Although only rigid wing structures were considered,the results were claimed to be in good agreement with PIV measurements of Warrick et al.[76]and Altshuler et al.[77].

3.5.Tip vortex(TiV)

Tip vortices(TiVs)associated with?xed?nite wings are seen to decrease lift and induce drag[78].However,in unsteady?ows, TiVs can in?uence the total force exerted on the wing in three ways(see Figs.8and9):(i)creating a low-pressure area near the wing tip[55,79–81],(ii)an interaction between the LEV and the TiV[55,79–81],and(iii)constructing wake structure by downward and radial movement of the root vortex and TiV[71]. First two mechanisms((i)and(ii))also were observed for impulsively started?at plates normal to the motion with low aspect ratios:Riguette et al.[82]presented experimentally that the TiVs contributed substantially to the overall plate force by interacting with the LEVs at Re=3.0?103.Taira and Colonius[83] utilized the immersed boundary method(IBM)to highlight the 3-D separated?ow and vortex dynamics for a number of low aspect ratio?at plates at different angles of attacks.At Re of 3.0?102–5.0?102.They showed that the TiVs could stabilize the ?ow and exhibited nonlinear interaction with the shed vortices. Stronger in?uence of downwash from the TiVs resulted in reduced lift for lower aspect ratio plates.

For?apping motion in hover,however,depending on the speci?c kinematics,the TiVs could either promote or make little impact on the aerodynamics of a low aspect ratio?apping wing. Shyy et al.[55]demonstrated that for a?at plate with A R=4at Re=64with delayed rotation kinematics,the TiV anchored the vortex shed from the leading edge increasing the lift compared to a2-D computation under the same kinematics.On the other hand, under different kinematics with small angle of attack and synchronized rotation,the generation of TiVs was small and the aerodynamic loading was well approximated by the analogous 2-D computation.They concluded that the TiVs could either promote or make little impact on the aerodynamics of a low aspect ratio?apping wing by varying the kinematic motions[55].

3.6.Passive pitching mechanism

Wing torsional?exibility can allow for a passive pitching motion due to the inertial forces during wing rotation at stroke reversals[84–88].There were three modes of passive pitching motions which were similar to those suggested by rigid robotic wing model experiments[50];(1)delayed pitching,(2)synchro-

F Normal

F Result

F Suction

Lift F Result = F Suction + F Normal

Drag

Fig.8.Leading edge suction analogy adopted from Ref.[18].(A)Flow around the blunt wing.The sharp diversion of?ow around the leading edge results in a leading edge suction force(dark blue arrow),causing the resultant force vector (light blue arrow)to tilt towards the leading edge and perpendicular to free stream.(B)Flow around a thin airfoil.The presence of a leading edge vortex causes a diversion of?ow analogous to the?ow around the blunt leading edge in(A)but in a direction normal to the surface of the airfoil.This results in an enhancement of the force normal to the wing section.(For interpretation of the references to color in this?gure legend,the reader is referred to the web version of this article.)

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nized pitching,and (3)advanced pitching.It was found that the ratio of ?apping frequency and the natural frequency of the wing were important to determine the modes of passive pitching motions of the wing [88,89].If the ?apping frequency was less than the natural frequency of the wing,then the wing experienced an advanced pitching motion,which led to lift enhancement by intercepting the stronger wake generated during the previous stroke [89].Moreover,it was shown for 2-D ?ows,the LEVs produced by the airfoil motion with passive pitching seemed to attach longer on the ?exible airfoil than on a rigid airfoil [88].

4.Kinematics,wing geometry,Re ,and rigid ?apping wing aerodynamics

This section presents a literature survey on ?apping wing aerodynamics using experimental,theoretical,and computational approaches.Selected computational efforts of the authors are used to highlight implications of ?ow structures on the perfor-mance of rigid ?apping wings.Note that the Reynolds numbers shown for hovering studies in this literature review may differ from those in the referenced studies as consistent de?nitions (average wing velocity)are used for the sake of comparison in this paper.

Experimentally,numerous previous efforts on ?ow visualiza-tion around biological ?yers have been made,including smoke visualizations [47,49,90–92]and PIV [76,77,93–101]measure-ments.The advance of such technologies has enabled researchers to obtain not only 2-D but also 3-D ?ow structures around biological ?yers [93,98–101]and/or scaled models [72–74]with reasonable resolution in space.At the same time,measurements of wing and body kinematics have been conducted using high-speed cameras [102–110],laser techniques (a scanning projected line method [111],a re?ection beam method [112],a fringe shadow method [113],and a projected comb fringe method [114]),and a combination of high-speed cameras and a projected comb-fringe technique with the Landmarks procedure [115].Advancement in measurement techniques also enabled quanti?-cation of ?apping wing and body kinematics along with the 3-D deformation of the ?apping wing.Recently,data on the instanta-neous wing kinematics involving camber along the span,twisting,and ?apping motion have been reported (a hovering honeybee

[116];a hovering hover ?y and a tethered locust [117,118],a free-?ying hawkmoth [119]).These efforts help in establishing more complex and useful computational models [120,121].Furthermore,the in-vivo measurement of aerodynamic forces generated by biological ?yers in free-?ight is a very challenging research topic.

Various models have been developed in an effort to under-stand ?apping wing phenomena where the variables are known,controllable,and repeatable.Detailed discussion regarding the experimental and numerical methodologies utilized to examine ?apping wing-related studies is beyond the scope of the current effort.Suf?ce it to say,numerous computational techniques-based moving meshes [122–124]or stationary meshes (cut cell or immersed boundary)[125,126]have been developed.The physi-cal models include NS as well as simpli?ed treatments [127,128].Some of the experimental methods employed are introduced in the paragraph above.

In the following section recent progress regarding rigid ?apping wing aerodynamics is presented.First,studies for forward ?ight will be described.Then studies for hovering ?ight will be presented.Explorations on the implications of wing kinematics and wing shape will be touched upon after that.This will be followed by a highlight focusing on the unsteady aerodynamics of 2-D and 3-D hovering ?at plates,Re =O (102)based on a surrogate modeling approach.Finally,the ?uid dynamics related to the LEV,the TEV,and the TiV will be presented,including the authors’computational efforts to high-light the vortex dynamics of a hovering hawkmoth at Re =O (103)and the effect of Reynolds number (size of ?yers)on the LEV structures and spanwise ?ow.

4.1.Single wing in forward ?ight condition

Von Ellenrieder et al.[129]studied the impact of variation of Strouhal number (0.2o St o 0.4),pitch amplitude (01o a a o 101),and phase angle (651o f o 1201)between pitching and plunging motion on 3-D ?ow structures behind a plunging/pitching ?nite-span NACA0012wing using dye ?ow visualization at Re =164.The results demonstrated that the variation of these parameters had observable effects on the wake structure.However,they observed a representative pattern of the most commonly seen ?ow structures and proposed a 3-D model of the vortex

structure

Fig.9.Drag coef?cients of the aspect ratio 6,and 2plates during a starting-up translation as a function of T (the number of chord lengths the plate has traveled,see de?nition of Ref.[79])adopted from Ref.[79].(A)Overall view;(B)Detailed view of (A).Both (A)and (B)show drag coef?cients for the free tip aspect ratio of 6plate (continuous line)and for the same plate with the tip grazing a raised bottom (dash-dotted line);the dashed line is drag coef?cient for the aspect ratio of 2plate with the tip free.Low aspect ratio of the wing reduces the drag coef?cient signi?cantly due to interactions between a TiV and a LEV.

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behind a plunging/pitching wing in forward?ight.Godoy-Diana et al.[130,131]investigated the vortex dynamics associated with

a pitching2-D teardrop shaped airfoil(2.21o a a o16.91,

0.1o St o0.5)in forward?ight at Re=1.2?103using PIV measurements.Their results illustrated the transition from the von Ka′rma′n vortex streets to the reverse von Ka′rma′n vortex streets that characterize propulsive wakes.Furthermore,the symmetry breaking of this reverse von Ka′rma′n vortex pattern gave rise to an asymmetric wake which was intimately related to the time-averaged aerodynamic force production.Lee et al.[132] numerically investigated aerodynamic characteristics of unsteady force generation by a2-D pitching and plunging5%thick elliptic airfoil with inclined stroke plane at Re=6.8?102.They showed that the thrust was generated due to correct alignment of the vortices at the end of the upstroke and there was a monotonic decrease in thrust as the rotational center of the pitching motion was moved from the leading edge towards the trailing edge (0.1o o0.5).

Anderson et al.[133]considered harmonically oscillating NACA0012airfoils in a water tunnel to measure the thrust.After a parametric study(01o a a o601,0.25o h a/c m o1.0, 301o f o1101)to?nd the optimum?ow condition for the thrust generation(a a=301,h a/c m=0.75,f=751)at Re=4.0?104and St=0.05–0.6,they proceeded to show the presence of a reverse von Ka′rma′n vortex street formed by the vortices shed from the leading and trailing edges for St in range of0.3and0.4at Re=1.1?103.Triantafyllou and co-workers[134–136]performed parametric investigations using experiments on the performance of a pitching/plunging NACA0012airfoil in forward?ight at Re between2.0?104and 4.0?104,and St between0.1and0.45. Systematic measurements of the?uid loading showed a unique peak ef?ciency of more than70%for optimal combinations of the parameters(e.g.h a/c=0.75,a a=151,and f=901at St=0.25gives an ef?ciency of73%)and observed that higher thrust can be expected when increasing the Strouhal number and/or the maximum of the angle of attack.Then a parametric range where the ef?ciency and high thrust conditions were achieved together would fall in the parameter domain they 78256f9db9d528ea81c7798di and Platzer[137]used LDV and dye injection techniques to visualize the velocity?eld and the wake structures of an oscillating NACA0012airfoil in water at Re ranging from5.0?102to2.1?104.The transition from drag to thrust was seen to depend on the non-dimensional plunge velocity (kh a which is proportional to St),i.e.for kh a40.4the considered airfoil was thrust-producing.Cleaver et al.[138]performed force and supporting PIV measurements on a plunging NACA0012airfoil at a Reynolds number of1.0?104,at pre-stall,stall,and post-stall angles of attack.The lift coef?cient for pre-stall and stall angles of attack at larger plunge amplitudes showed abrupt bifurcations with the branch determined by initial conditions.With the frequency gradually increasing,very high positive lift coef?cients were observed,this was termed mode A.At the same frequency with the airfoil impulsively started,negative lift coef?cients were observed,this was termed mode B.The mode A?ow?eld is associated with trailing edge vortex pairing near the bottom of the plunging motion causing an upwards de?ected jet,and a resultant strong upper surface leading edge vortex.The mode B?ow?eld is associated with trailing edge vortex pairing near the top of the plunging motion causing a downwards de?ected jet,and a resultant weak upper surface leading edge vortex.The bifurcation was not observed for plunge small amplitudes due to insuf?cient trailing edge vortex strength,nor at post-stall angles of attack due to greater asymmetry in the strength of the trailing-edge vortices, which creates a natural preference for a downward de?ected mode B wake.

Lewin and Haj-Hariri[139]conducted2-D numerical investiga-tions for?uid dynamics associated with elliptic-like plunging airfoils at Re=5.0?102and compared and contrasted the?ndings with ideal?ow theories.They mentioned that for high-frequency plunging,the vorticity was shed primarily from the trailing edge, and therefore better matched the inviscid models.Though for high kh a the LEV and its secondary vortices were occasionally shed into the wake,which would differentiate the physics from those found in inviscid models.The monotonic trend found in ideal?uid models of ef?ciency decreasing as reduced frequency increases, was not seen in the numerical models where the maximum ef?ciency was found for an intermediate range of reduced frequencies.Lua et al.[140]experimentally examined the wake structure formation of a2-D elliptic airfoil undergoing a sinusoidal plunging motion at Re=1.0?103and k=0.1–2.0.The results showed the type of wake structure produced depends on not only the reduced frequency,but also the normalized stroke amplitude. Bohl and Koochesfahani[141]focused on quantifying,via MTV,the vortical structures in the wakes of a sinusoidally pitching NACA0012airfoil with low pitching amplitude,a a=21,at Re=1.3?104.The reduced frequency was set to a relatively high range,between4.1and11.5,to generate thrust.They found that the transverse alignment of the vortices switched at k=5.7,i.e.the vortices of positive circulation switched from below to above the vortices of negative circulation.The mean streamwise velocity pro?le herewith changed from velocity de?cit(wake)to velocity excess(jet).However,this switch from the vortex array orientation could not be used to determine the crossover from drag to thrust. Von Ellenrieder and Pothos[142]conducted PIV measurements behind a2-D plunging NACA0012airfoil,operating at St between 0.17and0.78,and Re=2.7?104.Their results showed that for Strouhal numbers larger than0.43,the wake became de?ected such that the average velocity pro?le was asymmetric about the mean heave position of the airfoil.Jones and Babinsky[143] studied the?uid dynamics associated with a three-dimensional 2.5%thick waving?at plate.The spanwise velocity gradient and wing starting and stopping acceleration that exist on an insect-like ?apping wing are generated by rotational motion of a?nite span wing.The?ow development around a waving wing at Re=6.0?104 was studied using high-speed PIV to capture the unsteady velocity ?eld.Vorticity?eld computations and a vortex identi?cation scheme reveal the structure of the3-D?ow-?eld,characterized by strong leading edge and tip vortices.A transient high lift peak approximately1.5times the quasi-steady value occurred in the ?rst chord-length of travel,caused by the formation of a strong attached leading edge vortex.This vortex then separated from the leading edge resulting in a sharp drop in lift.As weaker leading edge vortices continued to form and shed lift values recovered to an intermediate value.They also reported that the wing kinematics had only a small effect on the aerodynamic forces produced by the waving wing if the acceleration is suf?ciently high.Calderon et al. [144]presented an experimental study on a plunging rectangular wing with aspect ratio of4,at low Reynolds numbers of1?104–3?104.Time-averaged force measurements were presented as a function of non-dimensional frequency,alongside PIV measure-ments at the mid-span plane.In particular,they focused on the effect of oscillations at low amplitudes and various angles of attack. The presence of multiple peaks in lift was identi?ed for this3-D wing,thought to be related to the natural shedding frequency of the stationary wing.Wing/vortex and vortex/vortex interactions were identi?ed which may also contribute to the selection of optimal frequencies.Lift enhancement was observed to become more notable with increasing plunging amplitude,to lower reduced frequencies,with increasing angle of attack.Despite the highly3-D nature of the?ow,lift enhancements up to180%were possible.

Under Research and Technology Organization(RTO)arrange-ment of the North Atlantic Treaty Organization(NATO)there was

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a community-wide effort organized,which offered a wide range of experimental and computational data for both SD7003airfoil and?at plate,with kinematics promoting different degrees of ?ow separation.The detailed information can be found in[145]. Here we present samples of the information collected in this group endeavor.Ol et al.[146]compared PIV?ow?eld measurements of a pitching and plunging SD7003airfoil at Re=6.0?104,k=0.25,and St=0.08with computed result by Kang et al.[147].They considered two kinematic motions,a shallow-stall case and a deep-stall case where the maximum effective angle of attack was larger than the former case.In the shallow-stall case where the?ow was moderately attached overall,the computed result was able to approximate the?ow?eld measured using PIV well.For the deep-stall case the?ow separated just before the middle of the downstroke(i.e.maximum effective angle of attack).The numerical solution showed vortical struc-tures similar to the PIV,but at a later phase of motion.However, the instantaneous lift over a motion cycle obtained from both methods compared well,indicating that the differences in details of the?ow structures do not necessarily lead to large differences in the forces integrated over the airfoil,as long as the large-scale ?ow structures remain similar.

For Re(104)and higher,turbulence in?uences the development of the?ow structures and forces.Ol et al.[145],Baik et al.[148] investigated the?uid physics at Re=O(104)of a pitching and plunging SD7003airfoil and?at plate,experimentally using PIV focusing on the second-order turbulence statistics.They observed laminar boundary layer and laminar-to-turbulence transition.In a companion paper Kang et al.[147]used RANS computations with SST turbulence model[149]to simulate the same cases[146]to investigate the implications of the turbulence modeling.By limiting the production of turbulence kinetic energy they observed that leading edge separation was dependent on the level of eddy viscosity for the SD7003airfoil,and hence turbulence,in the?ow. Regarding the computed lift,they concluded that the large scale vortical structures in the?ow were the contributing factors.Baik et al.[150]conducted an experimental study of a pitching and plunging?at plate at Re=1.0?104constrained to motions enfor-cing a pure sinusoidal effective angle of attack.The effect of non-dimensional parameters governing pitching and plunging motion including Strouhal number(St),reduced frequency(k),and the plunge amplitude(h a)was investigated for the same effective angle of attack kinematics.The formation phase of the LEV was found to be dependent on k:the LEV formation is delayed for higher k value. It was found that for cases with the same k the velocity pro?les normal to the airfoil surface closely follow each other in all cases independent of pitch rate and pivot point effect.Of course,even though the?ow structures with constant k seemed little affected by Strouhal number and plunging amplitude,the time history of forces along the horizontal(thrust)and normal(lift)directions can be substantially altered because the geometric angle-of-attack, viewed from the ground.

Visbal et al.[151]computed the unsteady transitional?ow over a plunging2-D and3-D SD7003airfoil with high reduced frequency(k=3.93)and low plunge amplitude(h a/c m=0.05)using implicit large Eddy simulations at Re=1.0?104and4.0?104.The results showed that the generation of dynamic-stall-like vortices near the leading edge was promoted due to motion-induced high angles of attack and3-D effects in vortex formation around the wing.Radespiel et al.[152]compared the?ow?eld over a SD7003 airfoil with and without plunging motion at Re=6.0?78256f9db9d528ea81c7798ding a NS solver along with the linear stability analysis to predict transition from laminar-to-turbulent?ow,they concluded that transition and turbulence can play an important role in the unsteady?uid dynamics of?apping airfoils and wings at the investigated Reynolds numbers.4.2.Single wing in hovering?ight condition

Ellington and co-workers[57–60,62,103,104]did pioneering research on?apping wing aerodynamics at Re=4.0?103–7.0?103.They built a scaled-up robotic hawkmoth wing model and visualized the?ow?eld of hovering hawkmoth wing movements[57–60,62,103,104]using smoke visualization tech-niques.They observed that the presence of the LEV at high angle of attack during the downstroke,and suggested that‘delayed stall’of the LEV was responsible for high lift production by hovering hawkmoths(see Section 3.4).Dickinson and co-workers [21,22,37,50,51,72,153–159]made original contributions to the understanding the?apping wing aerodynamics at lower Reynolds number regimes(Re=1.0?102–1.5?103).They utilized a dyna-mically scaled robotic fruit?y model wing in an oil tank and conducted systematic experiments to relate the prescribed simpli?ed?y-like kinematics to the resulting aerodynamic forces. They categorized the aerodynamic loading into three parts:forces due to(i)translation(delayed stall of the LEV[50,72,153–155], (ii)rotation[50,51,156–157],and(iii)interaction with the wakes (wake capture[50,55]).Furthermore,Fry et al.[158]investigated the aerodynamics of hovering/tethered fruit?ies using a dyna-mically scaled robotic fruit?y wing model at Re=1.2?102. Altshuler et al.[159]studied the aerodynamics of a hovering honeybee using a dynamically scaled robotic honeybee wing model at Re=1.0?103.Their results showed that aerodynamic force enhancement due to wake capturing and rotational forces were important in both fruit?y and honeybee hovering.Sunada et al.[160]measured?uid dynamic forces generated by a bristled wing model with four different wing kinematics using scale-up robotic wings at Re=10.The results demonstrated that?uid dynamic forces acting on the bristled wing were a little smaller than those on the solid wings.

Nagai et al.[161]used a mechanical bumblebee wing model and measured the resulting forces with strain gauges and?ow structures using PIV for a hovering and forward?ight at Re=O(103).The comparison between the experimental results and the numerical solutions,computed using a3-D NS code, showed good agreement quantitatively in forces and qualitatively in?ow structures.For the forward?ight the relevance of the delayed stall mechanism depended on the advance ratio.They observed that the LEV hardly appeared during upstroke at high advance ratios(over0.5).

Comparisons of2-D computational simulations of an elliptic airfoil in hover against3-D experimental data of the fruit?y model[50]were performed by Wang et al.[162].They concluded that2-D computed aerodynamic forces were good approxima-tions of3-D experiments for the advanced and symmetrical rotation cases considered in their study.Lua et al.[163] experimentally investigated the aerodynamics of a plunging2-D elliptic airfoil at Re between6.6?102and2.7?103.The results showed that the?uid inertia and the LEVs played dominant roles in the aerodynamic force generation,and time-resolved force coef?cients during plunging motion were found to be more sensitive to changes in pitching angular amplitude than to Reynolds number.Wang[164–166]carried out2-D numerical investigations on the vortex dynamics associated with a plunging/ pitching elliptic airfoil at Re=O(102)–O(104).The result showed a downward jet of counter rotating vortices which were formed from LEVs and TEVs.Bos et al.[167]performed2-D computational studies examining different hovering kinematics:simple harmo-nic,experimental model[50],realistic fruit?y[158],and modi?ed fruit?y.The results showed that the realistic fruit?y kinematics lead to the optimal mean lift-to-drag ratio compared to other kinematics.Also they concluded that in the case of realistic fruit ?y wing kinematics,the angle of attack variation increases the

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aerodynamic performance,whereas the deviation levels the forces over the?apping cycle.Kurtulus et al.[168]obtained a?ow?eld over a pitching/plunging NACA0012airfoil in hover at Re=1.0?103experimentally and numerically.A2-D computation was compared to a pitching and plunging airfoil in water tank. They found that the more energetic vortices which were the most in?uential?ow features on the resulting forces were visible.

Hong and Altman[169,170]investigated experimentally the lift generation from spanwise?ow associated with a simple ?apping wing at Re between6.0?103and1.5?104.The results suggested that the presence of streamwise vorticity in the vicinity of the wing tip contributed to the lift on a thin?at plate?apping with zero pitching angle in quiescent air.Isaac et al.[171]used both experimental and numerical methods to investigate the unsteady?ow features of a?apping wing at Re between5.1?102 and5.1?103.They showed a feasible application of the water treading kinematics for hovering using insect/bird-like cambered wings.

4.3.Tandem wing in forward/hovering?ight condition

Aerodynamics associated with dragon?ies differs from other two-winged insects because forewing and hindwing interactions generate distinct?ow features[12].Sun and Lan[172]studied the lift requirements for a hovering dragon?y using a3-D NS solver with overset grid methods.They showed that the interaction between the two wings was not strong and reduced the lift compared to single wing con?guration,however,large enough to stay aloft.Yamamoto and Isogai[173]conducted a study on the aerodynamics of a hovering dragon?y using a mechanical?apping apparatus with a tandem wing con?guration and compared the time history of forces obtained from a3-D NS solver.The force comparison showed a good agreement and the results suggested that the phase difference between the?apping motions of the fore-and hind-wings only had small in?uence on the time averaged forces.

Lehmann[44]and Maybury and Lehmann[174]investigated the effect of changing the fore-and hindwing stroke-phase relationship in hover on the aerodynamic performance of each ?apping wing by using a dynamically scaled electromechanical insect wing model at Re of approximately 1.0?102.They measured the aerodynamic forces generated by the wings and visualized?ow?elds around the wings using PIV.Their results showed that wing phasing determined both mean force produc-tion and power expenditures for?ight,in particular,hindwing lift production might be varied by a factor of two due to LEV destruction and changes in the strength and the orientation of the local?ow vector.Lu et al.[175]showed physical images revealing the?ow structures,their evolution,and their interactions during dragon?y hovering using an electromechanical model in water based on the dye?ow visualization.Their results showed a delayed development of the LEV in the translational motion of the wing.Furthermore,in most cases,forewing–hindwing interac-tions were detrimental to the LEVs and were weakened with increase of the wing–root spacing.For a dragon?y in forward ?ight,the conclusions from Wang and Sun[176]were similar in that the forewing–hindwing interaction was detrimental for the lift,but suf?cient to support its weight.They suggested that the downward-induced velocity from each wing would decrease the lift on other wings.

Dong and Liang[177]modeled dragon?y in slow?ight by varying the phase difference between the forewing and hindwing and investigated the changes of aerodynamic performance of hindwings.They found that the performance of forewings is not affected by the existence of hindwings;however,hindwings have obvious thrust enhancement and lift reduction due to the existence of forewings.For slow?ight,by decreasing the phase angle difference,hindwings will have larger thrust production, slight reduction of lift production,and larger oscillation of force production.Independently,Warkentin and DeLaurier[178]did a series of wind-tunnel tests on an ornithopter con?guration consisting of two sets of symmetrically?apping wings of batten-stiffened membrane structures,located one behind the other in tandem.It was discovered that the tandem arrangement can give thrust and ef?ciency increases over a single set of ?apping wings for certain relative phase angles and longitudinal spacing between the wing sets.In particular,close spacing on the order of1chord length is generally best,and phase angles of approximately07501give the highest thrusts and propulsive ef?ciencies.Again,referring to other reported studies involving rigid and?exible wings,the aerodynamics and aeroelasticity associated with wing–wing interactions need to be further studied.In another study,Broering et al.[179]numerically studied the aerodynamics of two?apping airfoils in tandem con?guration in forward?ight at a Reynolds number of104.The relationship between the phase angle and force production was studied over a range of Strouhal numbers and three different phase angles,01,901and1801.In general,they found that the lift, thrust and resultant force of the forewing increased compared to those of the single wing.The lift and resultant force of the hindwing was decreased,while the thrust was increased for the0 phase hindwing and decreased for the90and180phase hindwings.The lift,thrust and resultant force of the combined fore and hindwings was also compared to the case of two isolated single wings.In general,the0phase case did not noticeably change the magnitude of the resultant force,but it inclined the resultant forward due to the decreased lift and increased thrust. The90and180phase cases signi?cantly decreased the resultant force as well as the lift and thrust.Clearly,more work is needed to help unify our understanding of the wing–wing interactions as function of the individual and relative kinematics and dimension-less?ow and structure parameters.

Wang and Russell[180]investigated the role of phase lag between the forewing and the hindwing further by?lming a tethered dragon?y and computing the aerodynamic forces and power.They found that the out-of-phase motion in hovering uses almost minimal power to generate suf?cient lift to stay aloft and the in-phase motion produce additional force to accelerate in takeoffs.Young et al.[181]investigated aerodynamics of the ?apping hindwing of Aeschana juncea dragon?y using3-D computations at Re between1.0?102and5.0?104.The?apping amplitude observed,34.51,for the dragon?y maximized the ratio of mean vertical force produced to power required.Zhang and Lu [182]studied a dragon?y gliding and asserted that the forewing–hindwing interaction improved the aerodynamic performance for Re=O(102)–O(103).

4.4.Implications of wing geometry

Lentink and Gerritsma[183]considered different airfoil shapes numerically to investigate the role of shapes in forward?ight on the aerodynamic performance.They computed?ow around plunging airfoils at Re of O(102)and concluded that the thin airfoil with aft camber outperformed other airfoils including the more conventional airfoil shapes with thick and blunt leading edges.One exception was the plunging N0010which due to its highest frontal area had good 78256f9db9d528ea81c7798dherwood and Ellington[184]examined experimentally the effect of detailed shapes of a revolving wing with planform based on hawkmoth wings at Re=5.0?103.The results showed that detailed leading

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edge shapes,twist,and camber did not have substantial in?uence on the aerodynamic performance.In a companion paper Usher-wood and Ellington[185]examined experimentally the effect of aspect ratio of a revolving wing with the same hawkmoth planform[184]adjusted to aspect ratios ranging from4.53to 15.84with corresponding Re of1.1?103–2.6?104.The results showed the in?uence of the aspect ratio was relatively minor, especially at angle of attack below501.Luo and Sun[186] investigated numerically the effects of corrugation and wing planform(shape and aspect ratio)on the aerodynamic force production of model insect wings in sweeping motion at Re=2.0?102and3.5?103at angle of attack of401.The results showed that the variation of the wing shape almost unaffected the force generation and the effect of aspect ratio was also remarkably small.Moreover,the effects of corrugated wing sections in forward?ight were studied in numerical simulations [187,188]and a numerical–experimental approach[189].The results demonstrated that the pleated airfoil produced compar-able and at times higher lift than the pro?led airfoil,with a drag comparable to that of its pro?led counterpart[187].

Altshuler et al.[190]tested experimentally the effect of wing shape(i.e.with sharpened leading edges and with substantial camber)of a revolving wing at Re between5.0?103 and 2.0?104.Their results demonstrated that lift tended to increase as wing models become more realistic as did the lift-to-drag ratios Ansari et al.[191]used an inviscid model for hovering ?apping wings to show that increasing the aspect ratio,wing length,and wing area enhances lift.Furthermore,they suggested that for a?apping wing MAV,the best design con?guration would have high aspect ratio,straight leading edge,and large wing area outboard.The pitching axis would be then located near the center of the area in the chordwise direction to provide the best compromise for shedding vortices from the leading and trailing edges during the stroke reversal.Green and Smith[192]examined experimentally the effect of aspect ratio and pitching amplitude of

a pitching?at plate in forward?ight at Re between3.5?103and

4.3?104and aspect ratios of0.54and 2.2

5.They measured unsteady pressure distributions on the wing,and compared to the PIV measurements of the same setup[193].They concluded that the3-D effects increased with decreasing aspect ratio,or when the pitching amplitude increased.

Kang et al.[147]investigated the airfoil shape effect at Re=O(104)by comparing the?ow?eld around pitching and plunging SD7003airfoil and?at plate using PIV[148],and CFD in forward?ight.It was observed that for the?at plate the?ow was not able to make turn around the sharper leading edge of the?at plate and eventually separated at all phases of motion.The?ow separation led to larger vortical structures on the suction side of the?at plate hence increasing the area of lower pressure distribution on the?at plate surface.From the time history of lift,available for the CFD,it was seen that for the?at plate these vortical structures increased the lift generation compared to the SD7003,which had a blunter leading edge.

4.5.Implications of wing kinematics

A primary driver of the unsteady aerodynamics in?apping wing?ight is the wing motions.Yates[194]suggested that the choice of the position of the pitching axis may enhance performance and control of rapid maneuvers and thus enable the organism to more adeptly cope with turbulent environmental conditions,to avoid danger,or to more easily capture food.The instantaneous?uid forces,torques,and rate of work done by the propulsive appendages were computed using2-D unsteady aerodynamic theories.For a prescribed motion in forward?ight,the moment and power were further analyzed to?nd the axes,for which the mean square moment was minimal,the mean power to maintain the moment was zero,the mean square power to maintain moment was a minimum,and the mean square power to maintain lift equaled the mean square power.Sane and Dickinson [51]investigated the effect of location of pitching axis on force generation of the?apping fruit?y-like wing in the?rst stroke using a scaled-up robotic wing model.They estimated the rotational forces based on the quasi-steady treatment and blade element theory.The results showed that rotational forces decrease uniformly as the axis of rotation moves from the leading edge towards the trailing edge and change sign at approximately three-fourths of a chord length from the leading edge of the wing[50].

Ansari et al.[195]studied the effects of wing kinematics on the aerodynamic performances of insect-like?apping wings in hover based on non-linear unsteady aerodynamic models.They found that the lift and the drag increased with increasing?apping frequency,stroke amplitude,and advanced wing rotation.How-ever,such increases were limited by practical considerations. Furthermore,the authors mentioned that variations in wing kinematics were more dif?cult to implement mechanically than variations in wing planform.Hsieh et al.[196]investigated the aerodynamics associated with the advanced,delayed,and sym-metric rotation and decomposed the lift coef?cients in terms of the lift caused by vorticity,wing velocity,and wing acceleration. The results suggested that while the symmetric rotation had the most lift due to vorticity on the surface of the wing and in the ?ow,the maximum total lift is found with advanced rotation. Oyama et al.[197]optimized for the mean lift,mean drag,and mean required power generated by a pitching/plunging NACA0012airfoil in forward?ight using a2-D NS solver at Re=103.The multi-objective evolutionary algorithm was used to ?nd the pareto front of the objective functions(i.e.by considering the reduced frequency,plunge amplitude,pitch amplitude,pitch offset,and phase shift as the design variables).They found that the pitching angle amplitude(between351and451)was optimum for high-performance?apping motion and the phase angle between pitch and plunge of about901.In addition,the reduced frequency was a tradeoff parameter between minimization of required power and maximization of lift or thrust where smaller frequency leads to smaller required power.

4.6.Surrogate modeling for hovering wing aerodynamics

Numerous studies,including Wang et al.[162]and references cited above,reported similarities as well as differences in aerodynamics and?ow structures between2-D and3-D?apping wings.There is a need for establishing a comprehensive frame-work to address these matters.From a vehicle development perspective,since3-D Navier–Stokes simulations are expensive to run,if2-D simpli?cations can adequately reproduce the main aerodynamic features of3-D?apping wing,naturally,the needed data can be generated much more economically.Trizila et al. [198,199]used surrogate modeling techniques[200–202]to investigate a large number of hovering wing cases to develop surrogate models for time averaged lift and thrust.They identi?ed regions where2-D and3-D results(time averaged lift and thrust) were comparable,as well as those that were substantially different.Furthermore,based on the guidance from the surrogate models,they probed the?uid physics associated with2-D and 3-D cases,and were able to highlight the roles played by the LEV and TiVs in unsteady aerodynamics.The impact on lift from the2-D/3-D unsteady mechanisms is detailed further in the subsequent sections.

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The?apping wing scenario is simpli?ed to better identify and understand the competing interactions and in?uences.The wing is modeled as a?at plate with2%thickness with respect to the chord;for the?nite wing,the aspect ratio is4.The mid-span cross-section of the3-D model is used for the2-D simulation. Simpli?ed wing kinematics are employed(see Section2.1)and the mid-chord of the rigid airfoil is selected as the pitching axis.It was shown the position of the axis about which the wing pitches will in?uence the aerodynamics[50,51,194,195,197]and Section4.5.The results shown will not be independent of this choice of rotation(which is beyond the scope of the study presented),however,the understanding of the most prominent features will be relevant to?apping?ight in general.The three kinematic parameters(or the design variables in surrogate modeling),h a(plunge amplitude),a a(pitch amplitude),and f (phase lag between pitching and plunging motion)can be varied independently.

The range of the design variables is as follows.The normalized stroke amplitude is representative of a range of?apping wing ?yers:2:0o2h a=c m r

g

o4:0.Details on pitch amplitude and phase lag are not as plentiful in the literature,so cases are chosen with low angles of attack(AoA min=101;high pitching amplitude)and high angles of attack(AoA min=451;low pitching amplitude): 451o a a.o801.The bounds on phase lag are chosen symmetric about the synchronized hovering:601o f o1201Although de-layed rotation is not a focus of many studies found in literature, due to its reduced ability to generate lift compared to its normal hovering and advanced rotation brethren in2-D?ow,it will be shown that the interaction of a TiV with a LEV for a delayed rotation case can exhibit prominent3-D effects bene?cial to the wing’s lift performance.

A Navier–Stokes solver[203]is used to obtain the time-dependent?ow solution.Due to the kinematic constraints there are only two relevant non-dimensional groups in the incompres-sible case.The plunging amplitude to chord ratio,2h a=c mr

g

,and the Reynolds number:since Re is being held constant(for a?xed medium)the plunging amplitude and?apping frequency are not independent.The Reynolds number,based on the average tip velocity,is equal to65,which is similar to the fruit?y,Drosophila melanogaster.The reduced frequency,k,contains the same information as the normalized stroke amplitude(see Section2.1).

The surrogate modeling tools[200–202],trained with CFD data (order of days to obtain the results for one training point),are used to ef?ciently evaluate off design points(in a fraction of a second),global trends across the design space,kinematic variables’sensitivity,and tradeoffs between lift and power.The quantities of interest,the objective functions in the surrogate modeling nomenclature,are mean lift coef?cient,C L,and an approximation of the power required over the stroke cycle.For more details on the implementation and error quanti?cation the reader is referred to Refs.[198,199](Fig.10).

Fig.11shows iso-surfaces of the mean lift coef?cient where each axis corresponds to one of the kinematic parameters,i.e.h a, a a,or f.Fig.11(A),(B),and(C)correspond to the2-D lift,3-D

lift,

Fig.10.Effect of TiVs on lift generation associated with a pitching/plunging?at plate(A R=4)at the middle of stroke adopted from Ref.[54].(A)Delayed rotation case (2h a=c mr

g

?2:0,a a=451,and f=601);(B)Synchronized rotation case(2h a=c mr g?3:0,a a=801,and f=901).Note that solid and dashed lines in(A-2)and(B-2)indicate the results from the three-and two-dimensional wings,respectively.

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and difference between the two,respectively.Observations that are immediately apparent are that kinematic combinations with low a a (high AoA)and advanced rotation (high f )have the highest mean lift in 2-D and 3-D.This result qualitatively agrees with the results of Wang et al.[162]and Sane and Dickinson [51].Due to the non-monotonic response in phase lag found in the 2-D lift response at high pitching amplitudes (see Fig.11(A)),there are two regions where there is low,and possibly negative,mean lift generation.The ?rst region is de?ned by low plunge amplitudes (low 2h a =c mr g ),low AoA (high a a ),and advanced rotation (high f ).The second region is de?ned by low AoA (high a a ),and delayed rotation (low f )and is where the 3-D kinematics also generate low mean lift values.

A variable’s sensitivity is directly related to the gradients along the respective design variables,while a more quantitative measure is the global sensitivity analysis;these measures are examined in Trizila et al.[198,199].It is seen that the gradients along the a a and f axes are much more signi?cant than that along the normalized stroke amplitude (2h a =c mr g ).(Note:Lua et al.[163]

?nd the effect of Re is noticeably smaller than that of a a on the mean lift.)With these observations,the trends seen as a variable is varied are more clearly illuminated,but also the associated limitations are just as apparent.For example,advancing the phase lag is bene?cial in 2-D except when at high a a ;in 3-D there is no such exception within the bounds 78256f9db9d528ea81c7798dparisons with Sane and Dickinson’s experiments [51]show qualitative agree-ment in the trends in mean lift as a function of a a and f within the common ranges,with the noticeable difference in setups being the current study using pure translation to represent the plunge whereas the experimental study ?aps about a pivot point.

The difference between 2-D and 3-D lift may raise the question about areas of the design space for which 2-D computations may suf?ciently approximate their analogous 3-D counterparts or where there are substantial 3-D effects which would preclude such a comparison.In order to illustrate comparable 2-D and 3-D cases,a training point for which the full CFD solution was simulated was chosen from the region showing similar mean lift.Fig.12presents the time history of lift for a synchronized

rotation

Fig.11.Iso-surfaces of the time averaged lift achieved over the entire design space of kinematic combinations evaluated:(A)2-D model;(B)3-D model;and (C)the difference between the two models.Note the magnitude of the discrepancy being a noticeable fraction of the values of lift.The blue region in (C)denotes kinematics for which the 2-D lift is higher than the equivalent 3-D kinematics.Likewise the yellow/red region denotes higher 3-D mean lift.(For interpretation of the references to color in this ?gure legend,the reader is referred to the web version of this article.)

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300

case with generally low AoA (2h a =c mr g ?3:0;a a ?801;f ?901).The ?gure shows not only good agreement for this case in the mean or time averaged sense,which can be deduced from the surrogate models,but also instantaneously.Fig.13shows little variation in the spanwise vortex dynamics encountered by each wing cross-section.This is accomplished by way of an iso-surface of the quantity Q ,a measure of rotation which separates out the shear and is de?ned in [204],colored by the spanwise vorticity.In this con?guration the LEV will be red/yellow,the TEV blue,and the TiV green.Next to the ?ow ?eld shots are plots of the spanwise lift at the selected time instances which also show decent agreement between 2-D and 3-D.The variation that is present is generally con?ned locally to the tips,though the magnitude is small.The TiVs are most prominent at the end of translation,but as seen from the spanwise distribution of lift,are limited in in?uence.Note that other 2-D and 3-D cases agreed in the mean sense,but instantaneously differed and this situation is explored further in Trizila et al.[198,199].

In contrast to the case illustrated above,another set of kinematics chosen for which the 2-D and 3-D surrogate models did not exhibit such agreement.Fig.14illustrates a delayed rotation case with high AoA (2h a =c mr g ?2:0;a a ?451;f ?601),where the 2-D and 3-D cases show noticeable differences in the instantaneous lift.The source of these differences is better illustrated in Fig.15.The spanwise variation in the vortex dynamics is seen in the plots of the ?ow ?eld as well as in the lift distribution across the span of the wing.Once again the iso-surface connected to the wing can be distinguished by the LEV (red and yellow),the TEV (blue)and the TiV (green).The TiV has noticeable impact on the resulting ?ow features and aerodynamic loading.First,the distribution of lift due to pressure shows a local peak at the tips which is a force enhancement over the 2-D counterpart.There also appears to be an LEV anchoring mechanism,which keeps the LEV attached over a portion of the span near the wing tip thereby increasing the lift farther inboard.The net effect of the tip vortices is a substantial increase in performance for this set of kinematics.

In Trizila et al.[198,199]the design space was more thoroughly explored.A conclusion that is not apparent from the steady-state aerodynamics is that TiVs can be utilized to increase performance in the context of low Re ?apping wing ?ight.Due to the competing effects the TiV introduce,the role the TiV plays can vary from case to case (i.e.its mere presence does not guarantee a performance increase).The TiV can introduce a low-pressure region on the upper wing surface and anchor the LEV,which would have otherwise been shed.On the other hand,it can also induce downwash thereby reducing the effective angle of attack and consequent lift.

4.7.Unsteady ?ow structures around hawkmoth-like model in hover There are a number of computational studies of realistic wing con?gurations of a hornet [205],a bumblebee [206,207],a hawkmoth [42,61–64,79,208],a honeybee [42],a drone ?y [209],a hover ?y [210],a fruit ?y [42,52,80,81,211,212],and a thrips [42]accompanied by appropriate wing kinematics.Moreover,references cited throughout the literature review have elucidated aspects of the unsteady vortical ?ow phenomena by way of dynamically scaled robotic wings and biological ?yers.In order to expand our knowledge about the LEV mechanisms and unsteady 3-D ?ow features associated with a biological ?yer-like ?apping model,a numerical study on the aerodynamics and vortex dynamics around a realistic hawkmoth model with complex ?apping wing motions is discussed and highlighted in this subsection.

Figs.16and 17show the morphological and wing kinematics models of a realistic hawkmoth 78256f9db9d528ea81c7798dputations are performed using ‘‘a biology-inspired dynamic ?ight simulator [81,213]’’.This framework is capable of simulating an insect with realistic wing–body morphologies and ?apping-wing/body kinematics.Detailed descriptions of the computational modeling can be referred to in Refs.[64,79,208,213].

4.7.1.Vortex dynamics of hovering hawkmoth

Iso-vorticity-magnitude surfaces around a hovering hawkmoth at nine-time instants in a ?apping cycle are shown in Fig.18.The contour color on the iso-vorticity-magnitude surfaces in Fig.18indicates the magnitude of the normalized helicity density,which is computed by projecting the spin vector of a ?uid element onto its momentum vector,being positive (red)if these two vectors point in the same direction and negative (blue)if they point to the opposite direction.This quantity can be useful for illustrating helical vortex structures.One aim of the study is to correlate the time histories of the aerodynamic loadings with the dominant ?ow features [214].As such,the time histories of the aerodynamic forces on the wings and body are plotted in Fig.19:(A)vertical (lift)force,and (B)horizontal (drag or thrust)force,respectively.4.7.1.1.Flow structures during downstroke.In the ?rst half of the downstroke (see Fig.17),Fig.18A-1,a horseshoe-shaped vortex is generated by the initial wing motion of downstroke.Poelma et al.[72]showed a similar three-dimensional ?ow structure around an impulsively started dynamically scaled ?apping wing using PIV.The horseshoe-shaped vortex is composed of three vortices,namely,a LEV,a TEV,and a TiV,and it grows in size as the translational and angular velocity of the wing increases.In par-ticular,the radii of the LEVs and the TEVs expand from the wing root to the wing tip,resulting in a 3-D vortex structure.These vortices produce a low-pressure region in their core and on the upper surfaces of the wing (Fig.20(1))when they are attached.Lift forces shows a peak at the corresponding time instant (Fig.19(A)and Fig.17(b)).Therefore,this would imply that the LEVs,

the

Fig.12.The 2-D (solid:red)and 3-D (dashed:black)lift coef?cients for the kinematic parameters,2h a =c mr g ?3:0;a a ?801;f ?901.This case is synchronized rotation and representative for the cases that show very good agreement between the 2-D and the 3-D (A R =4)calculations in the time averaged as well as the instantaneous sense.(For interpretation of the references to color in this ?gure legend,the reader is referred to the web version of this article.)

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TEVs,and the TiVs enhance the lift force generation in hovering

?ight of the hawkmoth.It is seen that the TEVs generated by the

right and left wings meet at the rear body (Fig.18A-2),resulting in an interaction with each other.These vortex–vortex and vortex–body interactions lead to more complex vortical features around the hovering hawkmoth than the 2-D ?ow structures

seen Fig.13.The lift per unit span (right column)and iso-Q surface (Q =0.75)(left column)colored by spanwise vorticity magnitude for ?ow ?elds over half the wing associated with the kinematic parameters,2h a =c mr g ?3:0;a a ?801;f ?901at t /T =0.05,0.25,and 0.45.Note that solid and dashed lines indicate the results from the three-and two-dimensional wings,respectively.The spanwise variation in forces is examined with the 2-D equivalent (redline)marked for reference.The spanwise variation is limited.(For interpretation of the references to color in this ?gure legend,the reader is referred to the web version of this article.)

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302

around pitching/plunging airfoils.During the mid-downstroke (see Fig.17(c)),the TEVs are mostly shed from the wings while the TEVs stay attached on the body.Moreover,the shed TEVs stay connected to the TiVs (Fig.18A-3).Of the three vortex structures,the LEVs produce the largest and strongest area of low pressure on the wing surface (Fig.20(2)).Immediately after that,the LEVs begin to break down at a location approximately 70–80%the span of the wing length.The LEV,the TiV,and the shed TEV together form a doughnut-shaped vortex ring around each wing (Fig.18A-4).Recent experimental visualization studies showed similar vortex ring structures around a hovering hummingbird [77],during slow forward ?ights of a bat [99,100],and a free-?ying bumble bee [92].Looking at the structure of the doughnut-shaped vortex ring close to the wing tip,the vortical structure is twisted (rolled-up)behind each wing,which results from an interaction between the broken-down LEV and the shed TV (Fig.18A-4).This helps to illustrate the rich complexity of 3-D interactions experienced in ?apping wing ?ight.

Continuing on,during the second half of the downstroke (see Fig.17(d)),the TiVs enlarge gradually.Eventually,when the wings approach the end of the downstroke,the LEVs and the TiVs weaken and begin to detach from the wings.An additional vortex is observed around the wing root and connects with the shed TEV (Fig.18A-5).The doughnut-shaped vortex rings of the wing pair break up into two circular vortex rings,eventually forming the far-?eld wake below the hawkmoth.Two small vortex rings of the wing pair near the wing root are observed to join the two circular vortex rings (Fig.18A-6).The weakening of the low-pressure area on the wing surface due to separation of the vortices leads to a smaller aerodynamic force acting on the wing and the high angle of attack of the wing leads to high thrust but low lift generation (Fig.20(3)).During most of the downstroke,the doughnut-shaped vortex ring pair has an intense,downward jet-?ow through the ‘‘doughnut’’hole,which forms the downstroke downwash.

In the ?rst half of the supination (see Fig.17(e)),occurring near the end of the downstroke,as the ?apping wing slows down,the attached vortices (the LEVs and the TiVs)are shed from the

wings.At this time instant,a pair of downstroke stopping vortices is observed wrapping around the two wings (Fig.18B-1).When the ?apping wings begin to pitch quickly about the spanwise axis,a pair of upstroke starting vortices is detected around the wing tip and the trailing edge (Fig.18B-2).

4.7.1.2.Flow structures during upstroke.In the second half of the supination (Fig.17(f)),TEVs and TiVs associated with the be-ginning of the upstroke are generated when the ?apping wings accelerate rapidly.The downstroke wakes of the circular vortex rings are subsequently captured (Fig.18B-3),but a correlation with the time history of lift shows a relatively minor impact.The idea of wake capture has been documented many times [1,36,43,44,50,55,56]and Section 3.4.The point here is that the role it plays in the lift generation can vary depending on the context.Dickinson et al.[50]experimented with 3-D ?apping kinematics at lower Re ,i.e.O (102),which showed a signi?cant contribution to lift from the wake capturing.In contrast,in the present study,the hovering hawkmoth-like wing kinematics at a Re of 6.3?103do not show a prominent wake capturing me-chanism in the lift histories.Another study [81]looking at fruit ?y wing motions at Re O (102)also demonstrated a situation where the wake capturing had little impact on the aerodynamic loading.While still in the ?rst half of the upstroke (Fig.17(g)),when the ?apping wings begin to accelerate upward,the TEVs and TiVs are shed from the two wings (Fig.18C-1).The TiVs are continually regenerated and fed while the LEV generation is initiated.To-gether with the TEVs,the LEVs and TiVs form a horseshoe-shaped vortex pair wrapping each wing.Similar to what is seen during the downstroke,the horseshoe-shaped vortex grows and evolves into a doughnut-shaped vortex ring for each wing.Root vortices are also detected at this stage and join the vortex ring as illu-strated in Fig.18C-2.The dif?culty in clearly demarcating and expressing the relevant phenomena is a direct consequence of the 3-D nature of the vortex structures and their subsequent inter-actions .Note that due to asymmetric variation of angle of attack between the upstroke and downstroke,the LEVs generated in the upstrokes are smaller than those in the downstrokes.In the sec-ond half of the upstroke (Fig.17(h)),the doughnut-shaped vortex rings elongate and deform while maintaining their ring-like shape (Fig.18C-3).During most of the upstroke,the downwash induced through the hole of each vortex ring is observed to be similar to that of the downstroke,despite the asymmetric forward and backstroke kinematics.

During early pronation (Fig.17(i))at the end of the upstroke,the attachment points of the shed TiV move slightly (approxi-mately 10–20%of the wing length)from the wing tip to the wing root during the course of the upstroke due to the wing movement (Fig.18D-1).Concurrently,the stopping vortices are observed wrapping around each wing (Fig.18D-1).As the wings begin to rotate quickly,the upstroke stopping vortices are shed from the trailing edge and the downstroke starting vortices are detected at the leading edge and wing tip.Thereafter,the upstroke doughnut-shaped vortex rings are shed downward,breaking up into two vortex wake rings;the root vortices are also shed,forming a single vortex ring under the body (Fig.18D-2).During late pronation (Fig.17(a)),at the end of the upstroke and beginning of the downstroke,starting vortices are observed around the leading and trailing edges and wing tip (Fig.18D-3).

4.7.1.3.Flight energetics.As to the aerodynamic force generation,two peaks in the lift force are predicted during each stroke for a hovering hawkmoth (see Fig.19).Considering the correlation between the aerodynamic forces and the key unsteady ?ow fea-tures associated with ?apping wings discussed in Section 3,

the

Fig.14.The 2-D (solid:red)and 3-D (dashed:black)lift coef?cients for the delayed rotation and high AoA case governed by the kinematic parameters,2h a =c mr g ?2:0;a a ?451;f ?601.Here the difference between 2-D and 3-D (A R =4)calculations is signi?cant during translational phase of the wing motion.(For interpretation of the references to color in this ?gure legend,the reader is referred to the web version of this article.)

W.Shyy et al./Progress in Aerospace Sciences 46(2010)284–327303

delayed stall of the LEV and contributions from the TEV and TiV

are responsible for the ?rst lift peak.The second peak is likely to

be associated with a contribution from the rapid increase in

vorticity [1,52]as the wing experiences a fast pitching motion.

Relevant to estimates of energy consumption in natural ?yers and

control applications in MAV design/construction,the computed

time histories of the aerodynamic torques are plotted in Fig.21

(A)rolling,(B)pitching and (C)yawing,respectively.Note that the

term ‘total wing’in Fig.21is the sum of the torques of the right and left wings.Two of the aerodynamic torques are relatively comparable,the aerodynamic rolling (ART)and yawing (AYT)torques of the two wings (‘total wing’)are much smaller than those of the aerodynamic pitching torque (APT).The time-varying total ART and total AYT are mostly zero over a ?apping cycle because of the symmetrical ?apping motion of the left and right wings and therefore the averaged total ART and AYT become approximately zero (Fig.21(A)and (C)).On the other hand,the APT of the two wings varies over a range,from à0.6?10à3

to Fig.15.The lift per unit span (right column)and iso-Q surfaces (Q =0.75)(left column)colored by spanwise vorticity over half of the wing using the kinematic parameters,2h a =c mr g ?2:0;a a ?451;f ?601at t /T =0.05,0.25and 0.45.Note that solid and dashed lines in (A-2)and (B-2)indicate the results from the three-and two-dimensional wings,respectively.The spanwise variation in forces is examined with the 2-D equivalent (redline)marked for reference.The TiV leads to increased lift in their immediate region as well as anchor the vortex shed from the leading edge.(For interpretation of the references to color in this ?gure legend,the reader is referred to the web version of this article.)

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