RESEARCH ARTICLE Stereoscopic particle image velocimetry ... · Maxworthy (Maxworthy, 1979; Maxworthy, 1981) discovered the LEV on the wings of a scaled-up model of the hawkmoth Manduca

2017

INTRODUCTIONSeed dispersal distances are a fundamental aspect of plant evolutionand conservation (Howe and Smallwood, 1982; Willson, 1993). Inorder to increase the distance of dispersal, samaras, or winged seeds,descend very slowly by spinning. Mahogany seeds initiateautorotation about their center of mass almost immediately afterbeing released from the host tree by creating a prominent leading-edge vortex (LEV) that is similar to the flow structures that areresponsible for the high lift generated by the wings of hoveringinsects such as fruit flies (Birch and Dickinson, 2003; Fry et al.,2005), hawkmoths (Van den Berg and Ellington, 1997a; Van denBerg and Ellington, 1997b), butterflies (Brodsky, 1991; Willmottet al., 1997), birds (Usherwood, 2009; Usherwood et al., 2005) andbats (Hedenström et al., 2009; Muijres et al., 2008). Ever sinceMaxworthy (Maxworthy, 1979; Maxworthy, 1981) discovered theLEV on the wings of a scaled-up model of the hawkmoth Manducasexta, the attached LEV has been identified as the responsible forthe production of high lift forces and has been subjected toconsiderable investigation (Birch et al., 2004; Bomphrey et al., 2006;Liu et al., 1998; Wu and Sun, 2004).

Two-dimensional (2D) studies have shown that the growth of theLEV begins at the start of translation and continues until the vortexbecomes unstable, detaches from the leading edge (LE) and is shedinto the wake (Dickinson and Götz, 1993). Several studies havebeen performed with the aim of characterizing the unsteadyaerodynamics of insect flight (Brodsky, 1991; Ellington et al., 1996;Grodnitsky and Morozov, 1993; Somps and Luttges, 1985; Thomaset al., 2004). Dickinson et al. (Dickinson et al., 1999) performed

direct measurements of the forces produced by flapping wings andsuggested that the enhanced aerodynamic performance of insectsresults from three distinct, yet interactive mechanisms: delayed stall,rotational circulation and wake capture. Usherwood and Ellington(Usherwood and Ellington, 2002) determined the steadyaerodynamic performance of wings in revolution at low and highReynolds numbers (Re) from 1100 to 26,000 and reported that theiraerodynamics are quite insensitive to variations in both wingmorphology and kinematics, and that aspect ratio has remarkablylittle influence on aerodynamic force coefficients at low to moderateangles of attack. Birch and Dickinson (Birch and Dickinson, 2001)systematically mapped the flow generated by a dynamically scaledmodel insect at Reynolds numbers matching the flows relevant formost insects, and found that the structure of this spanwise flow takesdifferent forms depending on the value of the Reynolds number.Their results demonstrate that flapping wings do not generate a spiralvortex akin to that produced by delta-wing aircraft. Also, they foundthat limiting spanwise flow with fences and edge baffles did notcause detachment of the LEV. Their findings support the hypothesisthat induced downward flow from tip vortices and wake vorticityreduce the effective angle of attack and attenuate the growth of theLEV. Ellington (Ellington, 1984) proposed a scheme to include wingrotation with translation in quasi-steady models. Because the lift ininsect flight was significantly higher than expected on the basis ofquasi-steady aerodynamics, he suggested that important unsteadyflow phenomena play a major role in the force generation process.Dickinson (Dickinson, 1994) investigated rotational parameters bymeasuring forces on the model wings of Drosophila. His results

SUMMARYAn experimental investigation of near field aerodynamics of wind dispersed rotary seeds has been performed using stereoscopicdigital particle image velocimetry (DPIV). The detailed three-dimensional flow structure of the leading-edge vortex (LEV) ofautorotating mahogany seeds (Swietenia macrophylla) in a low-speed vertical wind tunnel is revealed for the first time. The resultsconfirm that the presence of strong spanwise flow and strain produced by centrifugal forces through a spiral vortex areresponsible for the attachment and stability of the LEV, with its core forming a cone pattern with a gradual increase in vortex size.The LEV appears at 25% of the wingspan, increases in size and strength outboard along the wing, and reaches its maximumstability and spanwise velocity at 75% of the wingspan. At a region between 90 and 100% of the wingspan, the strength andstability of the vortex core decreases and the LEV re-orientation/inflection with the tip vortex takes place. In this study, theinstantaneous flow structure and the instantaneous velocity and vorticity fields measured in planes parallel to the free streamdirection are presented as contour plots using an inertial and a non-inertial frame of reference. Results for the mean aerodynamicthrust coefficients as a function of the Reynolds number are presented to supplement the DPIV data.

Key words: aerodynamics, leading-edge vortex, LEV, spiral vortex, rotary seeds, PIV.

Received 15 January 2013; Accepted 10 February 2013

The Journal of Experimental Biology 216, 2017-2030© 2013. Published by The Company of Biologists Ltddoi:10.1242/jeb.085407

RESEARCH ARTICLE

Stereoscopic particle image velocimetry measurements of the three-dimensionalflow field of a descending autorotating mahogany seed (Swietenia macrophylla)

E. Salcedo1, C. Treviño2, R. O. Vargas1 and L. Martínez-Suástegui1,*1ESIME Azcapotzalco, Instituto Politécnico Nacional, Avenida de las Granjas No. 682, Colonia Santa Catarina, Delegación

Azcapotzalco, México, D.F., 02250, Mexico and 2UMDI, Facultad de Ciencias, Universidad Nacional Autónoma de México, Sisal,Yucatán, Mexico

*Author for correspondence ([email protected])

THE JOURNAL OF EXPERIMENTAL BIOLOGY

2018

show that axis of rotation, rotation speed and angle of attack duringtranslation are of great importance in the force development duringeach stroke. Sane and Dickinson (Sane and Dickinson, 2002)characterized the effect of wing rotation on the production ofaerodynamic forces by a flapping airfoil and proposed a revised andimproved model that incorporates rotational effects into atranslational quasi-steady model of flapping flight. Lentink andDickinson (Lentink and Dickinson, 2009) performed flowmeasurements and flow visualizations on revolving fly wings byemploying air bubble visualization. Their results indicate that theLEV is stabilized by the ‘quasi-steady’ centripetal and Coriolisaccelerations that are present at low Rossby numbers and result fromthe propeller-like sweep of the wing. Their findings support thehypothesis that the spanwise flow balances the formation of vorticityat the LE by draining it into the tip, and the authors conclude thatforce augmentation through stably attached LEVs represent aconvergent solution for the generation of high lift forces. Lan andSun (Lan and Sun, 2001) numerically investigated the aerodynamicproperties of a wing of relatively small aspect ratio during typicalunsteady rotational motions at low Reynolds number. Their resultsshow that the airfoil in small Reynolds number flow can producea large aerodynamic force, as effective as in large Reynolds numberflow. Bomphrey et al. (Bomphrey et al., 2009) performedexperiments using smoke visualization to describe the flow topologyof free-flying bumblebees and suggested that wing rotation mightplay an important role in the formation of the LEV. Lentink andGerritsma (Lentink and Gerritsma, 2003) studied numerically theaerodynamic performance of plunging airfoils at Re ~100, to assessthe role of airfoil shape, concluding that the thin cambered airfoiloutperformed a thick airfoil with respect to thrust coefficient andpropulsive efficiency. Garmann et al. (Garmann et al., 2012)performed numerical simulations to examine the vortex formation,breakdown and effect of induced angle of attack about a finite-aspect-ratio revolving wing in quiescent flow for a range ofReynolds numbers (200–60,000). The authors determined that forthe Reynolds numbers examined, the overall vortex structureincluding the attachment of a LEV was mostly insensitive totransitional effects despite the apparent vortex breakdown and shearlayer instabilities observed at higher Reynolds numbers. Also,although the LEV was found to weaken with increased angle ofattack, it still remained attached to the wing surface.

Particle image velocimetry (PIV)-based methods have beenextensively used to study the airflows induced by the flapping wingsof animals in free and tethered flight and by fixed mechanical modelflappers. Lu and Shen (Lu and Shen, 2008) studied experimentallythe 3D flow structures and evolution of the LEV on a flapping wingin the hovering condition. Their results showed that the LEV systemis a collection of four vortical elements: one primary vortex andthree minor vortices. Lu et al. (Lu et al., 2006) performed dye flowvisualization and PIV measurements on flapping wings to revealthe detailed features of the LEV region and confirmed the existenceof dual LEVs. Ansari et al. (Ansari et al., 2009) studiedexperimentally the flow around a constant-speed rotating wing anddescribed the flow features of the LEV for two Reynolds numbers(500 and 15,000). The aerodynamic characteristics of autorotatingseeds have been analyzed theoretically and experimentally (Azumaand Yasuda, 1989; Yasuda and Azuma, 1997). Recently, Lentinket al. (Lentink et al., 2009) identified the LEV as the high-lift sourcein rotary seeds and described its detailed flow structure in terms ofvorticity, spanwise flow and vorticity transport in and behind thevortex for spanwise regions at 25, 50 and 75% span. The LEVinvolves LE flow separation that reattaches to the seed and forms

a region of high vorticity concentration. Once the flow fieldseparates at the LE and vortex generation occurs, a large suctionforce accounts for the generation of large lift forces. More recently,Ozen and Rockwell (Ozen and Rockwell, 2012) studiedexperimentally the effects of rotation of a rectangular plate andcharacterized the LEV in relation to the overall flow structure toassess the effects of centripetal and Coriolis forces in the absenceof rotational acceleration effects for Reynolds numbers from 3600to 14,500. Their results show that a stable LEV exists for values ofeffective angle of attack ranging from 30 to 75deg, and that at agiven value of angle of attack, the scale and form of the LEV isrelatively insensitive to Reynolds number.

The aim of the present investigation is to perform a detaileddescription of the flow pattern of autorotating mahogany seeds usingstereoscopic digital PIV (DPIV) and evaluate their aerodynamicperformance. Because the unsteady flow field of wind-dispersedseeds exhibit complex flow structures that feature the formation ofLEVs, results are particularly presented to provide a detaileddescription of the mechanism responsible for its prolongedattachment via the instantaneous 3D velocity field and 2D velocityand vorticity contour maps.

MATERIALS AND METHODSExperimental setup

Mahogany seeds (Swietenia macrophylla King) were obtained fromthe tropical woods of Veracruz, Mexico. The samples were manuallycollected immediately after they had fallen naturally. Prior to theexperiments, the samples were preserved in a humidifier to preventthe evaporation of moisture. The experiments were carried out in alow-speed, vertical wind tunnel (0.6×0.6×0.5m Plexiglas workingsection) crafted to study the flow and kinematics of descendingmahogany seeds. A schematic diagram of the experimental setupof the vertical wind tunnel and DPIV system is shown in Fig.1.Flow uniformity was achieved by placing flow straighteners at thetunnel’s inlet and outlet sections. The measured turbulence intensityof the free-stream velocity was less than 1%. Free-stream velocitywas adjusted with the terminal velocity of the seeds so that theyspin at a stationary height. The Reynolds number based on the seeds’

The Journal of Experimental Biology 216 (11)

Fig.1. Schematic diagram of the experimental setup. (1) Smoke generator.(2) Turboaxial fan. (3) Variac. (4) Laser. (5,6) CCD cameras mounted onScheimpflug mounts.


20193D flow field of mahogany seeds

terminal velocity (Re=U∞C/ν, where U∞ is upstream uniform free-stream velocity or descent speed, C is the mean chord length of theseed and ν is the kinematic viscosity) ranged from 1474 to 1866,which corresponds to a range of airspeed of U∞=1.2–1.6ms–1.Because samara seeds descend vertically with a small side-slip, inorder to perform measurements at the same spanwise locations, theseeds were initially fixed by means of a 0.3-mm-thick fishing line(Araty Superflex fishing line, Sao Paulo, Brazil) that went throughthe wing’s center of rotation. To verify that the limited degrees offreedom and the friction exerted by the fishing line do not have asignificant influence on the flight kinematics and the angularvelocity of the freely falling seeds, rate of descent, rotational speedand coning angle were compared against those obtained with thesame seeds spinning around a fishing line. As no appreciable changesin the mean values were obtained for any of the samples, it wasassumed that there was no artifact introduced by fixing the seedsto the fishing line. To minimize the scatter of laser light, the seedsand the fishing line were painted mat-black and monochromaticfilters appropriate for the laser wavelength were installed on thelenses to minimize stray light from other sources. The small amountof ink increased the weight of the seeds by an average of 1%. Toreduce errors, the laser and the cameras were kept stationary andthe wind tunnel was mounted on a positioning translation system.By moving it in a direction perpendicular to the laser sheet,measurements at the various spanwise locations of the seed wereaccomplished without displacing the DPIV apparatus.

Image acquisition and data processingVelocity field measurements were performed using a DantecDynamics stereoscopic DPIV system (Skovlunde, Copenhagen,Denmark). The plane was illuminated with a 200mJ double pulseNd:YAG laser (New Wave Gemini, Fremont, CA, USA) at awavelength of 532nm. All measurements were performed usinga pulse separation interval of 50μs. The laser was equipped witha cylindrical lens system that produced a diverging light sheetparallel to the flow direction with a thickness of ~6mm. DantecDynamics software (DynamicStudio version 3.0.69) was used tocontrol the cameras and laser for DPIV data acquisition.Laser/camera synchronization was achieved using an automatedtrigger equipped with a position sensitive infrared detector and adigital delay/pulse generator (Sharp GP2Y0A21, Las Vegas, NV,

USA) so that all image pairs were recorded when the seed wasaligned perpendicular to the laser sheet. Fig.2 illustrates theconfiguration of both cameras, the illuminated plane by the lasersheet and the location of the seed when the pulse generator triggerssynchronized image acquisition and laser pulses. Also, theorientation of the Cartesian rectangular coordinates is shown, withx, y and z in the streamwise, transverse and spanwise directions,respectively. Two 12bit CCD double-frame digital cameras(HiSense MKII, Skovlunde, Copenhagen, Denmark) with aresolution of 1344×1024pixels and equipped with 50mm lenseson Scheimpflug mounts were used to record image pairs. Becausethe size of the seeds varies from one sample to another, thespanwise separations were obtained by displacing the laser sheetto distances that correspond to 0.25R, 0.3R, 0.5R, 0.75R and0.875R, where R is the wingspan (see Fig.3). Measurements werealso taken at the wingbase and the wingtip. Seeding was suppliedfrom a smoke generator (Antari Z-1500II Fog Machine, Taiwan,ROC) placed at the tunnel intake, and seeding quantity wasregulated by monitoring the output from the DPIV system (particlesize 1μm). Because the seeds initiated a rotational motionimmediately after being exposed to a vertical flow, it was possibleto fix the seeds in a specified position of the test section byadjusting the flow speed. By repeating the DPIV measurementsfor 20 samples using 10 sets of 50 image pairs per spanwise sectionfor each seed, instantaneous 3D velocity vectors and 2D velocityand vorticity contours were obtained.

For each image pair captured, 32×32pixel interrogation areaswith 50% vertical overlap and 25% horizontal overlap were used.An adaptive-correlation PIV algorithm with five high-accuracysubpixel refinement steps yielded a 55×63 array of vectors. Datavalidation was carried out using peak validation with a minimumpeak height relative to peak 2 of 1.15. Local neighborhoodvalidation was performed using a moving average validationalgorithm with an acceptance factor of 0.12. A 3×3 filter was usedto smooth the vector fields in order to clearly define theinstantaneous 3D flow structures. Deleted values were filled usingan interpolation method based on the surrounding vectors from a3×3 nearest neighbor matrix, resulting in an average percentage ofspurious vectors of roughly 2%. The computed 3D vector andvorticity fields for each spanwise location were displayed usingTecplot 360 (Bellevue, WA, USA).

18 deg

Camera 1Camera 2

17 deg

y, Uφ

x, U

z, W

Fig.2. Upper view of the test section of the wind tunnelillustrating the laser/camera configuration and orientation ofthe Cartesian rectangular coordinates with x, y and z in thestreamwise, transverse and spanwise directions,respectively. For each spanwise region, the origin of the z-axis corresponds to the centre of the laser sheet. U,velocity in the x-direction; Uϕ, velocity in the tangentialdirection; W, velocity in the z or spanwise direction.


2020

Geometry and kinematicsThe geometry and kinematics of rotary seeds have been describedpreviously (Azuma and Yasuda, 1989; Greene and Johnson, 1990;Minami and Azuma, 2003; Yasuda and Azuma, 1997). Tocharacterize representative kinematics, images of the rotary seedsspinning at a stationary height during free fall were recorded usinga high-speed digital camera (Redlake, HG-100K/HG-LE, Pasadena,CA, USA) at a frame rate of 250framess–1, as this was sufficientto resolve the rotational motion of the seeds. Images were capturedon a homogeneously illuminated white background to obtain goodcontrast. The coning angle (γ) was computed from static images inwhich the seeds lie orthogonal to the camera direction. Because the

seed’s dimensions along the spanwise direction are known, theconing angle was inferred using the projected length of the seed’stotal length along the horizontal plane (Varshney et al., 2012). Anaccurate spinning rate of autorotation was inferred by measuringthe elapsed time between consecutive images where the seed liesorthogonal to the camera direction. Table1 shows the measuredgeometry and kinematics of the seeds. Results are displayed asmeans ± s.d., and the sample size was N=20.

RESULTSInstantaneous 3D flow structure

When displaying 3D flows in the plane, the flow structure variesdepending on the location of the observer relative to the wing. Forall of the images shown, the origin is located at the lower rightcorner, as in Fig.2. For all spanwise locations, the origin of the z-coordinate is located at the central part of the plane illuminated bythe laser sheet, where z is positive in the direction towards thewingbase and negative in the direction towards the wingtip. Velocityand vorticity contours are displayed in the x–y plane located at z=0,and they are a 2D projection of the real 3D vectors using velocitycomponents in the plane of interrogation. For all images presented,the brown contour denotes the size and location of the wing sectionwithin the flow. Red/yellow coloration represents positive vorticityor clockwise fluid rotation, while blue/purple coloration indicatesnegative or counterclockwise rotation. Here, green regions reflecta lack of rotational motion.

Fig.4 shows the instantaneous vector map and velocity andvorticity fields at the wingbase. Note that for this spanwise regionthe laser light sheet does not illuminate the region below the LEwhen the pulse generator triggers synchronized image acquisitionand laser pulses. Therefore, a mask has been applied to the regionwith bad stereoscopic PIV correlation. The free-stream flowdirection is vertical upwards and parallel to the x–y plane (upperleft image), and the unperturbed free stream can be seen at the lowerleft and right corners of the latter. Although the spanwise velocityat this position is over 1ms–1, which is plenty for flow separationunder the right conditions, no flow separation occurs on top of theairfoil and therefore no LEV exists for this spanwise region.However, it can be seen that the sheer layers above the LE and thetrailing edge (TE) of the airfoil serve as a vorticity source, becausetwo regions of relatively small vorticity with opposite-sign rotationare generated (lower right image). However, although their sizesare relatively similar, the left-hand clockwise vorticity on top of theLE is stronger than the right-hand counterclockwise vorticity on top


R (wingtip)

Wingbase

0.875R

0.75R

0.5R

0.3Rl

0.25R

Rw

RD

A B

Fig.3. Spanwise positions along the wing for flow measurements. Here, Ris the distance from the wingbase to the wingtip, RW is the distance fromthe seed’s center of rotation to the wingbase, RD is the distance from theseed’s center of rotation to the wingtip and l is the total wingspan. A and Billustrate the lower and upper plan views of the seed, respectively.

Table1. Geometrical and kinematic characteristics of mahogany seeds (Swietenia macrophylla)

Parameter Mean ± s.d. (N=20)

Mass of wing, M (g) 0.632±0.0535Planform area, S (cm2) 17.6±2.4Total wingspan, l (cm) 9.27±0.557Distance from the seeds’ center of rotation to the wingtip, RD (cm) 7.63±0.458Disc area swept by rotating wing, ASD (cm2) 162±20Solidity, S/ASD 0.1095±0.0156Aspect ratio 4.06±0.31Mean chord length, C (cm) 2.29±0.12Wing loading based on the planform area, WL (Nm–2) 3.56±0.4Wing loading based on the disc area, WLD (Nm–2) 0.39±0.0359Coning angle, γdeg 20±2Rotation speed (rads–1) 44.82±0.94Vertical speed (ms–1) 1.45±0.10Advance ratio 1.44±0.13Tip angle of attack (deg) 18±2



U (m s–1)

W (m s–1) ω (s–1)

Uφ (m s–1)

Fig.4. Instantaneous flow pattern at the wingbase and velocity and vorticity contour plots. The images show from top to bottom and left to right the 3Dvelocity vectors, and U, Uϕ and W velocity (ms–1) and vorticity ω (s–1) fields, respectively. LE, leading edge; TE, trailing edge.

U (m s–1)

W (m s–1) ω (s–1)

Uφ (m s–1)

Fig.5. Instantaneous flow pattern at 0.25R. The images show from top to bottom and left to right the sectional streamlines, and U, Uϕ and W velocity (ms–1)and vorticity ω (s–1) fields, respectively. The dotted red circle highlights the size and location of the leading-edge vortex (LEV) core.


2022

of the TE. The two regions of vorticity located at the upper rightcorner of this image illustrate how vorticity from a previousrevolution is shed into the wake.

Fig.5 shows how for a spanwise location of 0.25R, the flowseparates at the LE and a small LEV appears above the airfoil.Here, a mask has been applied at the lower left region of thevelocity and vorticity contours, as noise from the PIV signal thatis coming from the scattered laser light reached a peak at thisspanwise location. Nonetheless, the detailed flow structure is wellresolved above the airfoil. For clarity, instead of displaying theinstantaneous 3D velocity vectors, the corresponding sectionalstreamlines are depicted (upper left image) spiraling into acritical point, which is a discernible distinction for the presenceof the LEV, with its core highlighted by the red dotted line. TheLEV core refers to the region of the curve demarcated by limitcycles defining the LEV trajectory. A slight increase in the regionof clockwise vorticity on top of the LE and a dramatic drop inthe region of counter-clockwise vorticity next to the TEdemonstrate that flow separation at the LE creates and feedsvorticity to the LEV. A strong spanwise flow towards the seedtip has been measured. The resulting flow strain ∂W/∂Z close to

100s−1 stretches the LEV, thus increasing the LEV intensity anddecreasing its size, promoting the LEV to be maintained at theseed’s upper surface. This velocity gradient in the spanwisedirection is mainly generated by the centrifugal force of thespinning seed.

Fig.6 displays the instantaneous flow pattern and theinstantaneous velocity and vorticity contour plots at a spanwiselocation of 0.5R. For this spanwise region, a well-defined LEV islocated on top of the airfoil. Here, the W velocity component abovethe LE is more than twice the value of the free-stream velocity.Also, a region of concentrated vorticity is consistent with a growingLEV, and an excellent match between the location of the maximumout-of-plane vorticity in the local flow field and the location of themaximum spanwise velocity was found. Inspection of theinstantaneous velocity vectors and contour plots readily reveals thatthe influence of the spanwise flow through a spiral vortex extendsto a region downstream with respect to the free stream, as can beseen from the U velocity contour plot (top middle image).

Fig.7 shows the instantaneous 3D velocity vector field, theinstantaneous sectional streamlines, and the instantaneous velocityand vorticity fields at 0.75R. For this spanwise region, the size of


U (m s–1)

W (m s–1) ω (s–1)

Uφ (m s–1)

Fig.6. Instantaneous flow pattern at 0.5R. The images show from top to bottom and left to right the 3D velocity vectors, and U, Uϕ and W velocity (ms–1)and vorticity ω (s–1) fields, respectively.



the LEV core, highlighted by the dotted red line, reaches a maximumand extends to approximately the size of the wing chord. Again,the largest value of the spanwise velocity (normal to the laser sheet)is observed below the core axis. Hence, the spanwise pressuredistribution is affected accordingly, causing the lift force to reacha maximum at the outer third of the wing. This supports Norberg’sanalysis of Acer platanoides (Norway maple) samaras, where themaximum lift force measured is located in the region thatcorresponds to the outer third of the wingspan (Norberg, 1973).

The instantaneous flow pattern at 0.875R is shown in Fig.8.Again, the instantaneous 3D velocity vector field, the instantaneoussectional streamlines, and the U, Uϕ and W velocity and vorticityfields are displayed. For this spanwise region, the sectionalstreamlines (upper middle image) spiraling into a critical pointdemonstrate that the LEV is still bound to the wing surface.However, despite its reduction in size and less coherent structure,the flow keeps separating at the LE creating vorticity. Although itssize is smaller than for 0.75R and the magnitude of the spanwiseflow starts to drop, its value is still up to twice the value of the free-stream velocity. Also, the reduction in the size of the LEV corehighlighted by the red dotted line (upper middle image) affects thevorticity field accordingly, and its value increases when comparedagainst its value for 0.75R.

Fig.9 shows the instantaneous 3D velocity vectors, and the U,Uϕ and W velocity and vorticity contours at the wingtip. Here,

the wingtip is located at the region with the largest value of thetangential velocity component, which in this case corresponds to2.7ms–1. The instantaneous velocity vectors illustrate how forthis spanwise location, no LEV is present at the wingtip,suggesting that the LEV re-orientation/inflection into the tipvortex takes place in a spanwise region between 0.9R and thewingtip. This is supported by the displayed velocity and vorticitycontours at the wingtip, as there is no sign of a long trail ofvorticity in the seed’s wake and the instantaneous velocity vectorsshow that the free stream is only perturbed by the wingtip at thislocation.

Flow structure in an inertial frameIn this subsection, the flow patterns for each spanwise locationshown previously are displayed using a non-inertial frame. In orderto show the flow structure in an inertial frame, the non-inertial frameis transformed to an inertial frame by adding the local rotationalvelocity of the wing at each spanwise location. In this way, thevortical flow structure is obtained for stationary wing experiments.It should be noted that both the W velocity and vorticity fields remainunchanged when using an inertial frame.

Fig.10 shows the instantaneous flow field and contour maps atthe wingbase. Here, a slight deflection of the instantaneous velocitypattern is observed due to an increase in the local rotationalvelocity.

U (m s–1)

W (m s–1) ω (s–1)Uφ (m s–1)

Fig.7. Instantaneous flow pattern at 0.75R. The images show from top to bottom and left to right the 3D velocity vectors, sectional streamlines, and U, Uϕand W velocity (ms–1) and vorticity ω (s–1) fields, respectively. The dotted red circle highlights the core of the LEV.


2024 The Journal of Experimental Biology 216 (11)

U (m s–1)

W (m s–1) ω (s–1)Uφ (m s–1)

Fig.8. Instantaneous flow pattern at 0.875R. The images show from top to bottom and left to right the 3D velocity vectors, sectional streamlines, and U, Uϕand W velocity (ms–1) and vorticity ω (s–1) fields, respectively. The dotted red circle highlights the core of the LEV.

U (m s–1)

W (m s–1) ω (s–1)

Uφ (m s–1)

Wingtip

Fig.9. Instantaneous flow pattern at the wingtip. The images show from left to right the 3D velocity vectors, and U, Uϕ and W velocity (ms–1) and vorticity ω(s–1) fields, respectively.



U (m s–1)

W (m s–1) ω (s–1)

Uφ (m s–1)

Fig.10. Instantaneous flow pattern at the wingbase and velocity and vorticity contour plots using an inertial frame. The images show from top to bottom andleft to right the 3D velocity vectors, and U, Uϕ and W velocity (ms–1) and vorticity ω (s–1) fields, respectively.

U (m s–1)

W (m s–1) ω (s–1)

Uφ (m s–1)

Fig.11. Instantaneous flow pattern at 0.25R in an inertial frame. The images show from top to bottom and left to right the 3D velocity vectors, and U, Uϕ andW velocity (ms–1) and vorticity ω (s–1) fields, respectively.


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Fig.11 shows the instantaneous flow field at 0.25R. Comparingthese results with those in Fig.5, an increase in rotation relative totranslation affects the pattern accordingly, generating circulatoryforces above the wing, which in turn enhance spanwise flow.

The flow pattern at 0.5R in an inertial frame is shown in Fig.12.Clearly, a remarkable change in the flow pattern is observed, whereasthe value of the local rotational velocity matches the value of thefree-stream velocity with a consequent increase in the total velocitydefined in the following subsection. Hence, the incoming flow ofthe free stream no longer has an upward direction. Instead, theinstantaneous 3D velocity vectors in the upper left image of Fig.12have an orientation of ~45deg with respect to the horizontal. Also,clockwise fluid rotation reaches a maximum at the LEV core, whichcoincides with the location of the maximum spanwise velocity.

The instantaneous 3D velocity vector field, velocity and vorticityfields at 0.75R in an inertial frame are shown in Fig.13. For thisspanwise region, a very well-defined vortex core that reaches itsmaximum stability is defined by the spiraling flow pattern. It is tobe noted that the size and strength of the vortex core at this spanwiselocation are consistent with the maximum measured value of thetipward spanwise flow above the airfoil, which is three times thevalue of the free-stream velocity. Also, it is observed that an increasein the size of the LEV core and a decrease in the value of positivevorticity take place. By inspecting the measured flow pattern at eachspanwise location, it is clear that a gradual increase in the size,strength and structure of the LEV along the length of the wingconfirm that the LEV structure is that of an outboard spiralingstraight cone pattern.

The instantaneous 3D velocity vector field, velocity and vorticitycontours at 0.875R in an inertial frame are shown in Fig.14. Here,the rotation of speed at the LEV core slows down, its strength andstability become weaker, and a decrease of the spanwise velocityis observed. In Fig.15, the measured flow at the wingtip in an inertialframe shows how the local rotational velocity is maximum, reachinga value of almost three times the free-stream velocity.

Measurement of aerodynamic performanceThe seeds’ mean vertical or thrust coefficients were estimated byrelating their terminal velocity to their mass. The relative or totalvelocity is defined as UT=(U∞

2+Uϕ2)1/2, where U∞ is the descent

speed, Uϕ is the local rotational or angular velocity (Uϕ=Ωrcosγ,where Ω is the angular velocity and r is the local radial distancefrom the wingbase). Let β be the angle between the horizontal andthe relative velocity direction of the flow. Then:

where the velocity ratio is λ=ΩRDcosγ/U∞ and ξ is defined as ξ=r/RD.Here, RD is the distance from the seed’s center of rotation to thewingtip. Therefore:

For a given differential blade section Cdr, where C(r) is the chord,the following relationships are obtained:

δT = (δLcosβ + δDsinβ) cosγ, (3)

δLsinβ – δDcosβ = 0. (4)

Here, δL, δD and δT are the lift, drag and thrust (vertical) forces,respectively. From Eqn4, δD/δL=tanβ=1/λξ. From Eqn3, then:

β = Ω γ

+Ω γ= λξ

+ λ ξ∞

r

U rcos

cos

cos 1. (2)

2 2 2 2 2 2

β =Ω γ

=λξ

∞Ur

tancos

1, (1)

Therefore:

where ρ is fluid density, CL is the local lift coefficient. The totalthrust is then:

where ε=RW/RD, with RW being the distance from the seed’s centerof rotation to the wingbase (see Fig.3). Introducing the mean valuesof the lift coefficient and the wing chord length, respectively:

with:

and

thus:

where cL and c are the normalized local lift coefficient and chord,respectively.

From Eqn5:

where:

The thrust coefficient CT is defined as:

CT = cosγCLCI(λ) , (15)

from the measurements:

where Mg is the weight of the seed. Then, the definition of the thrustcoefficient involves only the descending velocity. Once the thrustcoefficient is known, the lift coefficient can be obtained using Eqn15.Fig.16 shows the measured thrust coefficients based on the wingplanform area as a function of the Reynolds number. Here, the seeds’measured mean thrust coefficients range from 0.43 to 0.91.

=ρ ∞

CMg

CR U

2, (16)T

D2

∫( )λ = λε

ξ + λ ξ +λ ξ

⎛

⎝⎜

⎞

⎠⎟ ξ

εI cc

(1– )1 1

1d . (14)

2

1L

2 22 2

( )= γ ρ λ = ρ∞ ∞T C C R U I C C R Ucos

2

2 , (13)L D

2T D

2

∫ ∫ξ = ξ = − εε ε

c cd d 1 , (12)L

1 1

∫= γ ρ λ ξ + λ ξ +λ ξ

⎛

⎝⎜

⎞

⎠⎟ ξ∞

εT U R C Ccos

21 1

1d , (7)2

D1

L2 2

2 2

∫=− ε

ξε

C C1

1d , (8)L L

1

∫=− ε

ξε

C C1

1d , (9)

1

=− ε

CC

c1

, (10)LL

L

=− ε

CC

c1

, (11)

( )δ = δ β γ + β

= δ γ λξ

+ λ ξ+

λ ξ

⎛

⎝⎜

⎞

⎠⎟

T L

L

cos cos 1 tan

cos1

11

. (5)

2

2 2 2 2

δ = γ ρ λξ + λ ξ +λ ξ

⎛

⎝⎜

⎞

⎠⎟ ξ∞T C CR Ucos

21 1

1d , (6)L D

2 2 22 2




U (m s–1)

W (m s–1) ω (s–1)

Uφ (m s–1)

U (m s–1)

W (m s–1) ω (s–1)

Uφ (m s–1)

Fig.12. Instantaneous flow pattern at 0.5R in an inertial frame. The images show from top to bottom and left to right the 3D velocity vectors, and U, Uϕ andW velocity (ms–1) and vorticity ω (s–1) fields, respectively.

Fig.13. Instantaneous flow pattern at 0.75R, velocity and vorticity contour plots in an inertial frame. The images show from top to bottom and left to right the3D velocity vectors, and U, Uϕ and W velocity (ms–1) and vorticity ω (s–1) fields, respectively.


2028 The Journal of Experimental Biology 216 (11)

U (m s–1)

W (m s–1) ω (s–1)

Uφ (m s–1)

U (m s–1)

W (m s–1) ω (s–1)

Uφ (m s–1)

Wingtip

Fig.14. Instantaneous flow pattern at 0.875R, velocity and vorticity contour plots in an inertial frame. The images show from top to bottom and left to rightthe 3D velocity vectors, and U, Uϕ and W velocity (ms–1) and vorticity ω (s–1) fields, respectively.

Fig.15. Instantaneous 3D flow pattern, velocity and vorticity contour plots at the wingtip in an inertial frame. The images show from top to bottom and left toright the 3D velocity vectors, and U, Uϕ and W velocity (ms–1) and vorticity ω (s–1) fields, respectively.



DISCUSSIONIn this work, the detailed flow structure of the LEV of descendingautorotating mahogany seeds (S. macrophylla) has been revealedthrough stereoscopic DPIV with high spatial resolution. Flowmeasurements have been performed to quantitatively measure theairflow and assess the underlying flow structures and spiraling natureof the LEV. Our experimental findings demonstrate that the LEVis responsible for the generation of strong spanwise flow above theairfoil, which in turn produces a steep increase in the pressuredifferential across the wing, enhancing lift generation. Results showthat the separated boundary layer at the LE rolls up to form theLEV. The latter has a conical straight shape and increases in sizealong the spanwise direction, starting at 0.25R and reaching itsmaximum stability and spanwise velocity at 0.75R. At a wingspanregion between 0.9R and the wingtip, the strength and stability ofthe vortex core decreases and the LEV is reoriented into the tipvortex, thus convecting away the vorticity. We observed that for allwingspan regions demarcated by a stably attached LEV, all of thevelocity and vorticity plots show a peak of local spanwise velocityand vorticity at the LEV core. We have shown that the LEV hastwo different regions, each with distinguished features. One is thevortex core (with a large spiral structure) and the other is an outervortex region with small spanwise flow. Based directly on themeasurements of the 3D flow field, the aerodynamic performanceof mahogany seeds in autorotational flight during optimal flightconditions has been correlated with the aerodynamic force theyproduce, which allows an understanding of the role of the LEV inthe lift-generation process associated with strong spanwise flowtowards the wingtip. The measured mean thrust coefficients werecalculated as the average of the corresponding instantaneous forcesover the entire wing, and our data reveal that the measuredaerodynamic forces yield results that are very similar to those ofother autorotating seeds.

ConclusionsIn the present study, the airflow of autorotating mahogany seeds(S. macrophylla) was quantitatively measured using stereoscopicDPIV. In addition, evaluation of their aerodynamic performance hasbeen presented. The results of the present study show that high flowstrain and strong spanwise flow within the LEV core, with velocitiesas high as 148% of the wingtip speed, are responsible for augmentinglift forces. Based on the measured flow patterns, the followingconclusions can be drawn:

1. No LEV is present at the wingbase.2. At 0.25R, the flow separates at the LE, a region of positive

(clockwise) vorticity is generated, the LEV appears above the airfoil,and the separated flow reattaches close to the TE.

3. The LEV increases in size and strength while spiraling outwardtowards the wingtip with a straight cone pattern, which is responsiblefor enhancing lift generation. The strong flow strain in the spanwisedirection stretches the LEV, thus increasing its intensity andpromoting the attachment of the latter against the airfoil.

4. The LEV core and spanwise velocity reach a plateau at 0.75Rand decrease in size and strength at 0.875R.

5. In a spanwise region between 0.9R and the wingtip, the LEVis reoriented into the tip vortex.

LIST OF SYMBOLS AND ABBREVIATIONSASD disc area swept by rotating wingc normalized local chord lengthC mean wing chord lengthcL normalized local lift coefficientCL local lift coefficientCT mean thrust of vertical force coefficient based on the wing

planform areaD dragDPIV digital particle image velocimetryg gravitational accelerationl wingspanL liftLE leading edgeLEV leading-edge vortexM wing massPIV particle image velocimetryr local radial distance from the wingbaseR distance from the wingbase to the wingtipRD distance from the seed’s center of rotation to the wingtipRe Reynolds number based on the mean wing chord lengthRW distance from the seed’s center of rotation to the wingbaseS wing planform areaT thrustT mean thrust forceTE trailing edgeU velocity in the x-directionU∞ upstream uniform free-stream velocity (descent speed)UT relative speed of wing element or total velocityUϕ velocity in the tangential directionW velocity in the z-directionWL wing loading based on the planform areaWLD wing loading based on the disc areax, y, z Cartesian coordinate systemβ angle between the horizontal and the relative velocity direction

of the flowε RW/RDγ coning angleν kinematic viscosityξ r/RDρ fluid densityσ solidityω out-of-plane vorticity (normal to the x–y plane)Ω rotational speed or spinning rate

ACKNOWLEDGEMENTSThe authors gratefully thank Systelectro S.A. de C.V. for providing technicalassistance with the DPIV system. The authors would like to express their sincerethanks to Ruben Mil and Uriel Suárez for their assistance in the experimental tests.

AUTHOR CONTRIBUTIONSE.S. built the wind tunnel and manually collected the seeds. E.S. and L.M.-S.designed the study and performed all the experiments. E.S. and L.M.-S.assembled output data. L.M.-S. and C.T. analyzed and interpreted data. L.M.-S.,C.T. and E.S. wrote the paper. R.O.V. gave conceptual advice. L.M.-S. and C.T.supervised the project.

1.0

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.21200 1300 1400 1500 1600

Re

CT

1700 1800 1900 2000

Fig.16. Measured thrust coefficients versus the Reynolds number.


2030

COMPETING INTERESTSNo competing interests declared.

FUNDINGThis research was supported by the Secretaría de Investigación y Posgrado,Instituto Politécnico Nacional [grant 20100033].

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RESEARCH ARTICLE Stereoscopic particle image velocimetry ... · Maxworthy (Maxworthy, 1979; Maxworthy, 1981) discovered the LEV on the wings of a scaled-up model of the hawkmoth Manduca