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A01-16674

AIAA 2001-0859Computational and Experimental Studiesof Asymmetric Pitch/Plunge Flapping -

The Secret of Biological Flyers

Daniel ChasmanSukumar Chakravarthy

kth39 AIAA Aerospace SciencesMeeting and Exhibit8-11 January 2001

Reno, Nevada

(c)2001 American Institute of Aeronautics & Astronautics or Published with Permission of Author(s) and/or Author(s)' Sponsoring Organization.AIAA-2001-0859

Computational and Experimental Studies of Asymmetric Pitch/PlungeFlapping - The Secret of Biological Flyers

by1 9Daniel (Saharon) Chasman and Sukumar Chakravarthy

Abstract Introduction

The unusually high lift, low Reynolds Number,flight regime characteristic of many insect flierscannot be explained using steady-stateaerodynamic principles. Investigators haveproposed novel unsteady fluid mechanisms toaccount for these large aerodynamic forces. Inthe present study, a flat plate was plunged,about its anchored end, with superimposedpitching about the 1/4 chord line at the top andbottom of each plunge motion. Flow fieldswere marked with TiO2, and werephotographed in the absence of a free-streamvelocity. The asymmetric pitching/plungingwing generated a 3-dimensional, vectored,vortex-dominated flow field similar to thatobserved with living insects. Flow fieldvectoring was dependent upon the ratio of thepitch and plunge rotational rates, and only acircumscribed range of ratios resulted incohesive, directed flow structures. Flow fieldvelocity measurements suggest peak forcecoefficients on the order of 10. Theexperimental setting was simulatedcomputationally using the CFD++ Navier-Stokes flow solver in time-accurate mode. Atwo-mesh system is employed. One meshsurrounds the flat plate and is allowed to movethrough a background mesh. This 3-dimensional asymmetric pitch/plungemechanism may be a robust unsteady fluidmechanism for the controlled aerodynamicforce generation observed in some insects andexploitable elsewhere.

Many investigators have attempted tounderstand the enigma of insect flight. Mosthave postulated two-dimensional, steady,potential flow models of viscous, three-dimensional unsteady separated flows(1,2,3,4,5,6). Weis-Fogh (2), for example,proposed his famous two-dimensional inviscidmechanism based on observations that Chalcidwasp clapped the upper surfaces of its wingstogether at the top of an upstroke, and thenflung these wings open about their trailingedges to initiate a downstroke. It was proposedthat the "clap" and "fling" wing motionsgenerated unsteady circulations near the wingsurfaces, and that these circulations were ofsufficient strength to keep high lift forcesacting on the wings throughout the subsequentforward scull motion of the wings withouttaking into account the lift forces generated byplunging or sculling. Theoretical two-dimensional, potential flow models (3) as wellas flow visualizations (4) of the inducedflow/wing interactions supported the hypothesisthat high lift values are produced with thisunsteady mechanism. However, other studiesshow that three-dimensional effects are quiteimportant.

Observations in nature and the lab show thatthe dragonfly, using coordinated motions oftwo pairs of static geometry wings, achievesremarkable aerodynamic performances (10,11).Lift coefficients of 2.3 (2) to 6.1 (12) calculatedfor hovering flight, instantaneous lift forces 6

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times body weight (13) and 15-20 times bodyweight measured during tethered (escape mode)flight (11), are not predicted by steady-stateairfoil theory. The generation of unsteady,separated flows, and nonsteady aerodynamicforce histories, suggest the involvement ofunsteady fluid mechanisms (10,11,13).However, dragonflies do not exhibit "clap" and"fling" wing motions, and it is clear that the liftmechanisms are different from the unsteadymechanisms proposed for the hovering Chalcidwasp. Nonsteady lift generation in thedragonfly has been correlated with spanwisepitching of the wings (2,11,12), downwardplunging of the wings (11), and withcooperative interactions between the fore andaft wing pair (11,12,13).

In more recent studies (7, 8) on the dragonfly,Azuma et al. Proposed a computationaltechnique originally developed for predictinglift generated by the rotational motion of rotorblades. The use of momentum theory,however, does not take into account wing-flowinteractions, and effectively "extends" the farwake into the wings, allowing application of anunsteady, time-dependent technique to bothsteady and unsteady cases (9). This resultingdistortion of physical observations introducesinherent problems of helicopter theory (such asviscous effects, vortex buffeting and three-dimensional phenomena) into theunderstanding of dragonfly flight.

To elucidate the influence of individualunsteady components of actual wing motionson the flow field, some investigators havestudied simplified models of insect wingmotion. By driving a thin, vertically-orientedflat plate though a horizontal, sinusoidaloscillation they produced unsteady, two-dimensional, vortex flows which were laminarand stable only within a specific range ofoscillation frequency and amplitude. Withinthis range, changes in stroke amplitude had thegreatest influence on maintaining a cohesivelystructured flow field (17). The flow field

geometry relative to the generation surfacecould be changed by adjusting the angle of theplate away from the vertical (18). Bysuperimposing a rotational pitching motion atthe end of each oscillation half-cycle, two-dimensional, vortex stacking could be directedeither above or below the oscillating plate(19,20). Associated force coefficients wereestimated as high as 5-7. Using a scaled upmechanical model to reproduce dragonfly wingmotions, it was clear that both the ratio ofpitch-to-plunge angular rotational angularrotational rates (14,15), and the wing phaserelations between the fore and aft wings havespecific ranges within which nondestructive,vortex interactions and strong flowdownwashes occur (14,16).

Kinematics: Tethered Dragonfly vs.Mechanical Model. Somps and Luttges (11)provided wing tip kinematics of 21 tethereddragonflies (Libellula Luctuosd) using high-speed photography. The wing motion wasdown and forward during the downstrokes andup and rearward during the upstroke, with anaverage frequency of 28 Hz. Plungingamplitude of the fore wing was 90°, with thelowest wing-tip position 30° below the horizon.Plunging amplitude of the aft wing was 80°with the lowest wing-tip position 40° below thehorizon. Geometric angles of attack (withrespect to the horizon) were between 0° and -10° during the downstroke and between 80°and 90° during the upstroke. Rapid pitchingoccurred at the bottom and top of the wingstrokes. The aft wings led the front pair throughthe stroke with a phase angle difference varyingbetween 50° and 100°.

Additional data describing wing kinematics ofdragonflies (Aeschna junced) tethered in a windtunnel were collected by Reavis and Luttges(13). Two distinct modes were isolated whichpossessed the same basic wing motiondocumented earlier (11). The first modedisplayed a wing beat frequency of 33 to 36 Hz.Stroke amplitude of both wings was over 70°

(c)2001 American Institute of Aeronautics & Astronautics or Published with Permission of Author(s) and/or Author(s)' Sponsoring Organization.

and phase angles between the fore and aftwings were in the range of 90° to 135°. Thesecond mode displayed a higher wing beatfrequency (35 to 39 Hz). The fore wing strokeamplitude was less than 70°, and the wingphase angles were smaller (30° to 90°). Rapidpitching was detected during the midstroke, andat the extremes of the plunging strokes.

In order to simulate most of the wingkinematics of a tethered dragonfly (11), amechanical model was constructed (15,16).The wing stroke amplitude was 80°. The phasedifference between the wings was tested over alarger range than that displayed by live species(90°, 180° and 270°), and the non-pitched angleof attack (during the downstroke) was tested at0°, -30° and -45° with a constant pitchamplitude near 90° (typical to live dragonflies).The wing beat frequency also covered a largerrange compared to that of live dragonflies.Three frequencies were tested: 0.57, 1.00 and1.59 Hz. Based on dimensional analysis, thefirst two were within the range used by livedragonflies. The last frequency was higher.

Force Measurements of Tethered Dragonflies.Utilizing a three-degree-of-freedom forcebalance, the instantaneous aerodynamic forcesproduced by tethered dragonflies (Aeschnajunced) were correlated to flow visualizationphotographs taken during low speed windtunnel tests (13). The generation of vortexstructures, such as the leading edge vortex,occurs with an increase in lift. Peak lift ofnearly six times the dragonfly body weight wasreported. Changes in wing kinematics resultedin less lift and more thrust, or vice versa. Thedragonfly appears to control and utilizeunsteady separated flows in a manner differentfrom that described by the Weis-Foghmechanism. These experimental results showthat by studying biological models, a betterunderstanding of how to control unsteadyseparated flows is possible.

Fig 1 shows a comparison of the flow produced

by a tethered dragonfly (top) and that of themechanical model (bottom). Both photographsdepict the wings at roughly the same positions.The fore wing is seen at the end of the upstrokeand has a geometric angle of attack near 45°.The aft wing is crossing the zero plunge angle,is moving upward, and shares the samegeometric angle of attack (-45°). The phaseangle between the wings is near 90°. The flowfields elicited by the dragonfly and themechanical model bear striking similarities.

Produced Flows: Tethered Dragonfly Vs.Mechanical Model. During previousinvestigations, the formation of a distinctvortex pair on the bottom surface of the upwardmoving fore wing of the dragonfly has beendocumented (Fig 1). A similar vortex pair wasevident in the same location on the fore wing ofthe mechanical model. A single vortex ofsimilar size was produced under the aft wing inboth cases. The near wake that shed off thesimulated wings was smaller in size and morediffused than that of the tethered dragonfly, butretained the same overall shape. Otherinstances of wing kinematics were visualizedand bore the same close resemblance.

In the present study the motions of themechanical model have been simplified inorder to focus on the influence of pitching andplunging kinematics on the three-dimensionalnature of the induced fluid/wing interactions.

Methods and Materials

Experimental: A distillation of the wingkinematics of the dragonfly and the kinematicsof other insects that utilize unsteady separatedflow, led to the study of the present kinematics.A flat plate (l"x4"xl/32") was plunged upwardand downward about one end using a four-barlinkage mechanism driven by a 1/3 horse powermotor with a 40/1 gear reduction ratio. Large-scale pitching was achieved usingindependently driven rotary solenoids seated inthe spherical bearings of the plate fixed end

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(15). In general, the wing kinematics werecharacterized by ninety degree pitching at theextreme ends of the stroke cycle superimposedinto a pure plunging (-40° to 40°) motion. Thewing was pitched down from 90° to 0° angle ofattack at the beginning of the downstroke, andpitched up from 0° back to 90° at the beginningof the upstroke. This results in a downwardplunging motion at 0° angle of attack and anupward plunging motion at 90° angle of attack.The pitching axis was along the quarter chord,as exhibited by many flying insects. Threewing beat frequencies of 0.57, 1.00 and 1.58 Hzwere tested. These frequencies corresponded tothe values previously used by the fullmechanical model of the dragonfly (15,16).The pitching frequency was held constant atapproximately 8Hz. Pitching / plungingfrequency ratio (FR) values of 14, 8, and 5were obtained by combining the three wingbeat frequencies or plunge rates with theconstant pitch rate. In order to assure three-dimensional observations, three spanwise winglocations were selected for vortex tagging: root,midspan and tip. Application of TiCl4(Titanium tetrachloride is in liquid form. In anexothermic reaction2TiCl4 +4H20 -> 2Ti02 T +8//C11, it breaksto form the highly reflective titanium dioxidesmoke.) to the plate leading edge at theselocations enabled visualization of the inducedflow fields (19). TiOi - tagged flows werephotographed under continuous-source, movielights (5000 candles) using a 16mm Bolexcamera (24, 32 frames / sec; 75mm zoom lens).A dark cloth background separated the drivingmechanisms from the pitching / plunging plate.All tests were conducted in the absence of afree-stream velocity. Nine total test conditions,3 spanwise positions at 3 pitch/plunge ratios,were photographed. These nine test conditionswere evaluated for induced flow cohesiveness,directionality, and velocity.

Computational: Navier-Stokes flow solvercalled CFD++ is being used for thecomputational studies. CFD++ is based on the

principles of unified-grid and unified-physicscovering a broad range of physics. Some of thefeatures utilized specifically for the currenteffort are enumerated here. CompressibleNavier-Stokes equations were solved alongwith nonlinear k-epsilon turbulence model.The low-speed specialization is based on apreconditioning approach. A dual-timestepping strategy is employed for ensuring timeaccuracy. An algebraic mulit-grid procedure isused for converging the internal relaxationiterations within each time step. An oversetmesh approach is used. A block of mesh cellsis attached to the moving plate. For studieswith a single plate, it is sufficient to have thismesh extend sufficiently far away and thewhole mesh is treated as rigidly attached to themoving plate. To prepare for later studies, anoverset approach is also being tested where themesh block attached to the plate is smaller insize and it is embedded in a background mesh.The inner mesh floats within the backgroundmesh. The full paper will include more detailsand results.

Results

Experimental: Fig. 2 shows Typicalvisualization sequence of the flow produced bythe square wing for FR=8. The first half of thecycle, sequence of frames 1 through 5,represents the downstroke. The upstroke isseen in the sequence of frames 6 through 10.Each of the episodes is shown at three spanlocations, simultaneously.

Produced Flows: Representative sequences ofthe flow structures at root, midspan and tiplocations, which were generated by thekinematics of the present model, are providedin Fig. 2. Frame 1 shows the wing immediatelyafter the pitching down has occurred. A vortexstructure is seen on the trailing edge across allspanwise position. While the midspan positionin the center column shows the larger structure,the root position shows a smaller vortexstructure. The column showing tip position

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reveals the development of a vortex structureafter it sheds off the wing (frames 1 through 5).This sequence, represent history of one vortexappears to be associated with the pitching downmotion. Frame 3 shows a vortex over thedownward plunging wing across all spanwiselocations. This vortex continues to grow inframes 3 through 5. The midspan columnshows similar development of a downwardplunging vortex structure. The root positiondisplays a rather small and somewhat diffusedvortex structure.

In frames 6-10, the flow structures generatedduring the upstroke motion are isolated. Frame7 shows the wing immediately after pitching upto 90° angle of attack. At this point in thecycle, the midspan position shows thedownward plunging vortex to rotate and bedisrupted by the upward moving wing.Moreover, a small cohesive vortex is sheddingdown and away from the wing. This vortex isseen in all three span positions and is producedby the pitching up wing. The next frames showthe pitching-up vortex stagnating in thelower/left corner of the frames. Frame 8 (allspan positions) shows the wing, as it plungesupward, in the middle of the stroke. A clearslip-stream is forming, following the movingwing path. Frames 9, 10 and 1 through 3 showthe upward plunging vortex structuredeveloping into a vortex street. The largerstructure is seen at midspan and the smallest atthe root. Over the complete stroke cycle, fourdifferent vortex structures were identified, eachare associated with one of the four principalkinematic elements (i.e. pitching-down,downward plunging, pitching-up and upwardplunging).

Fig.3 summarizes the flow visualization results.Schematics of the visualizations of the elicitedflows at the three span positions werecondensed into a single three-dimensionaloccurrence by drawing the wing and elicitedflows in isometric perspective. Each of thefour rows depicts the wing during a

representative instant of the four kinematicelements: pitching-down, downward plunging,pitching-up and upward plunging. Typicalvortex structures that are associated with eachof the kinematic elements are shown beinggenerated by the moving wing. Two to four"older" vortex structures produced duringprevious cycles are shown spatially distributedfor three FR values, 14, 8, and5.

The vortex dynamics of all the vortex structuresdiffers little for the three FR cases (Figures2,3). All the produced vortex structures shedfirst with a jet-like formation, slow down, andthen stagnate at the far wake region. Oncestagnant, these vortex structures grow, crowdinto older structures and finally dissipate. AtFR=14, the vortex structures travel to greaterdistances than lower FR values. Lower FRvalues display smaller, more cohesive vortexstructures that crowd sooner.

The pitching-down vortex conforms to the wingcontour while being generated (Fig.3). Uponshedding, this three dimensional vortex pairbends outward at the center. After shedding,the vortex structure is condensed into amushroom shaped vortex. An "older" structureis seen growing, and opening up to form avortex ring. Generally, the pitching-downvortex sheds rearward.

The downward plunging vortex structure iscomposed of multiple vortices (Fig.3). Theinitial wake structure sheds forward at FR = 14,and sheds rearward at FR = 5. FR = 8 displaysa moderate rearward shedding. The large, mainvortex of this structure sheds only when thewing starts to pitch up. The pitching-up wingforces the vortex produced by the downwardplunging to rotate counterclockwise. Thepitching-up vortex displays growth, sheddingand formation that is very similar to that of thepitching-down vortex. The sheddingdownward, however, follows the direction ofthe edge of the wing at the end of the pitching-up (90°). The upward plunging vortex structure

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is also a multi-vortex structure. FR = 14 showsa viscous shear flow that ends in a smooth helixof tip vortex. The older structure is seenshedding upward and forward. FR = 8 shows aseries of three vortex filaments that intertwinewith the wing tip vortex helix. Two oldervortex structures are seen shedding rearward inthe form of vortex pairs. The associated tipvortices, partially disrupted by the movingwing tip, are stagnating close to the lowerportion of the tip trajectory. FR = 5 shows aneven more developed vortex street composed ofmany small cohesive filaments that intertwinewith the tip vortex. Older vortex structuresshed rearward as a whole.

the notations and arrangement used in Fig. 3are repeated in Fig.4A. The flow structures arefurther simplified. Each flow structure isassigned a symbol that characterizes thestructure. In addition, the following parametersare quantified based on the visualization data.The time history of each motion element isdenoted by T and is displayed at the top rightcorner of each test condition. The averagevortex structure diameter is denoted by d and isexpressed in terms of the chord length c (topleft). The vectorial properties of the vortexstructures are expressed by the direction of thevortex structures (())) with respect to X-axis andby the average displacement rate (V) expressedin terms of chord per second (bottom left). Thelocal aerodynamic force coefficient that wasderived from the momentum theorem (19,20) isused as well. This ratio ( c f ) is defined by

Cf = V2d2/4x(fa))2 -A. Where A=c-b is thewing area; f is the motion element frequencyand cois the motion element amplitude (a)is

-c-a/360 for pitching and -b-j3/360 for

plunging). Cf is displayed at the bottom rightcorner of each test condition.

The values and direction of the overallaerodynamic force coefficient (Cf) are shown inFig. 4B for the three FR test conditions. These

values and directions were obtained throughtime averaging and vector addition. All testsshow Cf values larger than 1.00. The directionof the overall force is defined with respect tothe horizon. Forward sense or X-axis directionis to the right of the frames.

The local aerodynamic force coefficient (Fig.4A) is the ratio between the forces of theproduced vortex structure and those of therelated forcing function (see above). Ingeneral, the minimal values of Cf areencountered at FR = 5 and maximal values areencountered at FR = 8. Moreover, minimalvalues of Cf are also found for vortex structuresproduced by the pitching-up and the downwardplunging motions while the maximal values arefound for vortex structures produced by thepitching-down and the upward plungingmotions.

The overall force of all the vortex structures(Fig. 4B), at FR = 5, acts on the wing forwardand down, while at FR =14, this combinedforce acts on the wing backward and up. Onlyat FR = 8, that also displays the maximal Cfvalue of 4.18, does the overall force act on thewing up and forward.

Four vortex structures are produced by fourelements of the wing kinematics. The pitchingmotions produce a single vortex ring per cycle,while the plunging motions produce multi-vortex structures. Three dimensionally, thepitching vortices are most dominant along themidspan. The plunging vortex structures,clearly, are weak at the root, and maximal atthe tip. Maximal overall aerodynamic forceoccurs at FR = 8. This test condition alone,displays both lift and thrust.

Computational: Fig. 5 shows that the residualpattern is generally low and unchanged overseveral cycles. This trend indicates that thesolution is stable. Fig. 6 provides the forcecalculations over more than two and a halfcycles. The plot depicts the time variation of

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Lift, Thrust and a spanwise force vary duringthe change from one motion to the next by thefour motion elements of the wing kinematics.

The last figure compares the computationallysimulated produced flows to that smoke-visualized in Fig. 2. Fig. 7 mimics thesequence and format of Fig. 2. Similarly, thedownstroke motion in three locations (i.e., root,midspan and tip) is displayed separately fromthe upstroke in plate 7a and 7b, respectively.Each sequence consists of five frames.Although the flow is less perturbed, the fineflow structures as well as the moving wing areeasily followed.

Conclusions

The present asymmetric pitch/plunge modelcorroborated well with previous studies ofdragonfly wing kinematics model (14, 15, 16)and simple plunging or pitching plate models(17,19,20). A simple plunging plate model (17)has shown that stroke amplitude is critical inyielding constructive interference whileminimizing complete flow separation. Theplunging motions of the square wing used inthis study automatically account for variation inplunging stroke amplitude since the amplitudeis almost zero at the wing root and is maximumat the wing tip. The ensuing vortex protectionshows minimum sized vortices at the wing tip.Such three-dimensional vortex dynamicsbetween pitching and plunging vortices arecircumvented by the dragonfly fore winggeometry which controls both pitching andplunging vortices to develop around the windmidspan (14).

The asymmetric pitch/plunge model shows thata limited range of parameters exists for thevortices to constructively interfere. The simpleproduction of pressure gradient and vorticitysupport of same separated flows, matched suchthat lower value dynamic variables yield littlecohesive vortex structure and higher valuedynamics yield vortices that form successively

and interfere with each other. In present test,this range is limited to FR = 8 where the overallaerodynamic force coefficient (Cf) was 4.18and formed an angle of 15° with the horizonsuch that lift and thrust act accordingly. Tiltingthe plunging plane by 30° (typical to thedragonfly wing kinematics) causes the overallaerodynamic force to form 45° with the horizonsuch that the lift equals the thrust as displayedby escaping dragonflies (14).

Vortices produced in this study by combinedpitching and plunging motions resemble thosepreviously produced by separate simplepitching or simple plunging. The overalleffects, however, are quite different. Withinthe tested range of FR, combined motionsproduced vectored vortices that vary indirection and intensity with FR values.Changes in vortex-vortex interactions andwing-vortex interactions cause changes indirection and intensity of the produced flowfield.

Although two-dimensional analysis shows thata pitching vortex pair develops evenly fromroot to tip, three-dimensional analysis shows asingle vortex ring develops and grows awayfrom the wing midspan. While the pitching-down motion produces a vortex ring possessingthe maximal value of the local aerodynamicforce coefficient (Cf = 8.7), pitching-upproduces a vortex ring possessing minimalvalues (Cf = 0.5) for two FR tests (14 and 5). Areversed trend is displayed by plunging vortexstructures. Upward plunging produces a vortexpossessing a maximal Cf value of 0.5.

The pitch/plunge model provides anasymmetric flapping kinematics consisting offour motion elements. Each of the motionelements contributes to the overall dynamicforce produced throughout the cycle. Thisunsteady separated flow model does not requirea "Weis-Fogh"-type mechanism as proposedfor the Chalcid wasp (2). The Chalcid waspdisplays typical pitch/plunge wing kinematics

(c)2001 American Institute of Aeronautics & Astronautics or Published with Permission of Author(s) and/or Author(s)' Sponsoring Organization.

tilted by approximately 80° with respect to thehorizon such that plunging becomes sculling.FR value for the kinematics of the Chalcidwasp is about 8 (2). Based on the presentmodel, the overall aerodynamic force for such atilted plane is directed mostly for lift and the"clapping" motion is but the pitching-downmotion element at the end of maximum(^sculling) stroke. Initial analysis of the wingkinematics of other flying insects indicates thatmany (Odonata, Lineata, Dipetra, etc.) mayuse the pitch/plunge mechanism.

Acknowledgement

Supported in part by AFOSR grant F49620-84C-0065 and by ONR grant N00014-85K-0053. Dr. Mark Kliss and Dr. Chris Sompsassistance in the experimental work and initialproof reading is highly appreciated. This paperis dedicated to Professor Marv Luttges whopassed away in April of 1994.

References

1. M.F.M. Osborne, J.Exp. Biol 28, 221(1951)

2. T Weis-Fogh, ibid, 59, 169 (1973)

3. M.JJLighthill, J.Fluid Mech. 60, 1 (1973)

4. T.Maxworthy, J. Fluid Mech 93, 47 (1979)

5. M. Jensen, Phil.Roy.Soc. London, Ser.239,511-52(1956)

6. W. Nachtigall, in Insect in Flight (McGraw-Hill, New York, 1974)

7. A. Azuma and T.Watanabe, J.Exp.Biol.137, 221-252 (1988)

8. A. Azuma and K.Kawachi, J.AIRCRAFT,16, 6-14 (1979)

9. A. Azuma, S. Azuma, I. Watanabe andT.Furuta, J.Exp.Biol. 116, 79-107 (1985)

10. M.WJLuttges, C.Somps, M.Kliss, M.Robinson, in Proceedings of Workshop onUnsteady Separated Flow, M.Francis andM.W.Luttges, Eds. (Colorado AssociatedUniversity Press, Boulder, 1984), 127-136

11. C.Somps and M.W.Luttges, Science 228,1326 (1985)

12. R.A. Norberg, in Swimming and Flying inNature (Plenum, New York, 1975), 2, 763-781

13. M.A.Reavis and M.W.Luttges, Proceedingsof the AIAA Aerospace Sciences Meeting,AIAA-88-0330 (1988).

14. D.Sarahon and M.W. Luttges, ibid, AIAA-89-0832

15. Ibid, AIAA-88-0569 (1988)

16. Ibid, AIAA-87-0121 (1987)

17. M.Kliss, C.Somps, M.W.Luttges,J.Theor.Biol. 136, 209 (1989)

18. M.W.Luttges in Frontiers in Fluid Mech.M.Gad-el-hak (Ed.), Springer-Verlag, InPress

19. P. Freymuth, in Proceedings of theConference in Notre Dame, T.J. Muller(Ed.), 231-245, Springer-verlag, New York,(1989)

20. P. Freymuth, in Experiments in Fluids,Springer-Verlag, In Press

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Fig 1 Flow Field Generated By Live Dragonfly (above) vs. Mechanical (below @ 7:1 scale)

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FR-8 Downstroke

Root Mid TipFigure 2a Visualization sequence during downstroke

10

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F.R-S Upstroke

Figure 2b Visualization sequence during upstroke

11

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Fl: 14

Down

FitcMnf-Up

Upward

Fig. 3 3-D schematics of the three test conditions

12

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FK 14Wing

A

B

C/-2J

sec

£=265* i| A?¥«3.Sc/s C^OJ

V=2.5e/s

Fig. 4 Numerical analysis of the experimental test results

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1EOT

IE-1 -

w09ccx§

1E-2-

1E-3-IZOO

t.3426-03-

•r -1.342e-03-

Residual Plot (Normalized)

—•mass«—»x - momentum*— y-iiipnieintum

z-momenUim

400 600iterations

800 1000

Fig. 5 Residual pattern over three cycles

Fluxes, Forces, and Moments

2)00 50Q GOOiterations

700 800

Fig. 6 3-Dimentional Force Calculations

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FR=8 Root Mid

Fig. 7a CFD Simulation During Downstroke

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FR=8 Root Mid

Fig. 7b CFD Simulation During Upstroke

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