Numerical Investigation of the Aerodynamic and StructuralCharacteristics of a Corrugated Airfoil

Kyle Hord∗ and Yongsheng Lian†

University of Louisville, Louisville, Kentucky 40292

DOI: 10.2514/1.C031135

Previous experimental studies on static, bioinspired corrugated wings have shown that they produce favorable

aerodynamic properties such as delayed stall compared with streamlined wings and flat plates at high Reynolds

numbers (Re � 104). The majority of studies have been carried out with scaled models of dragonfly forewings from

the Aeshna cyanea in either wind tunnels or water channels. In this paper, the aerodynamics of a corrugated airfoil

was investigated using computational fluid dynamics at low Reynolds numbers of 500, 1000, and 2000. A structural

analysis was also performed using the commercial software SolidWorks 2009. The complex vortex structures that

formed in the corrugated airfoil valleys and around the corrugated airfoil are studied in detail. Comparisons are

madewith experimentalmeasurements at different Reynolds numbers andwith simulations of a flat plate. The study

shows that, at lowReynolds numbers, the corrugationdoes not provide anyaerodynamic benefit comparedwith aflat

plate. Instead, the corrugated airfoil generates more drag than the flat plate. Structural analysis shows that the wing

corrugation can increase the resistance to bending moments on the wing structure with reduced thickness and

weight.

Nomenclature

c = chordCD = coefficient of dragCL = coefficient of liftD = dragf = wake vortex shedding frequencyL = liftP = pressureRe = Reynold’s number, �U1c=�St = Strouhal number, �fc=U1� sin�t = timeU = x-component velocityU1 = freestream velocity� = angle of attack� = viscosity� = density

I. Introduction

M ICRO AIR vehicles (MAVs) are small aerial vehicles with atypical wingspan of less than 15 cm, and they weigh less than

90 g. Their flight speed usually ranges between 2 to 10 m=s. Thedevelopment ofMAVs is of great interest to bothmilitary and civilianapplications. MAVs can be used in various scenarios such asreconnaissance, surveillance, targeting, search and rescue, andbiochemical sensing in confined or otherwise hazardous conditions.Their applications are very similar to their larger cousin, theunmanned aerial vehicle (UAV), but MAVs have much smaller sizesand much lower costs. As an example, General Atomics Aero-nautical Systems, Inc.’s, Predator‡UAVs have a cruise speed of about35 m=s, awingspan of 14.8m, and a cost upward of $10million. Thegoal of MAV design is to fit the capabilities of a UAV into a far

smaller aircraft. While there is vast potential for the use of MAVs,there are several challenges that must be overcome.

Because of the MAV’s slow flight speed, the chord Reynoldsnumber across the wing is low: 102–104. At such a low Reynoldsnumber, the flow across the wing is typically laminar. Current MAVdesigns rely on conventional streamlined airfoils for lift generation.However, conventional airfoils are designed to operate at muchhigher Reynolds numbers, greater than 105. The performance ofsmooth airfoils greatly deteriorates once the Reynolds number dropsbelow 105. A reproduction ofMcMasters andHenderson’smaximumlift-to-drag ratio of airfoils through various Reynolds numbers isshown in Fig. 1. The lift-to-drag ratio is the measurement of theeffectiveness of an airfoil that is proportional to the gliding ratio andclimbing ability of the airfoil [2]. For large aircraft, the boundarylayers usually transition to turbulent flow before separation. Theturbulent flow can stay attached through more severe pressuregradients. As the Reynolds number falls below 105, flow approachesthe adverse pressure region as laminar flow. Since laminar flowcannot resist strong an adverse pressure gradient, flow separates aslaminar flow. Laminar flow separation typically leads to prematurestall, dramatic decrease in the lift, and increase in the drag [2]. Tomediate the effects of stalling conditions and the resulting poor lift-to-drag ratio at the low-Reynolds-number region, new airfoil designsmust be created.

Dragonflies are known for their exceptional flying performanceand their gliding ability. Dragonflies are highly maneuverable: theycanfly forward and backward, and they can hover for a long period oftime. These characteristics are very desirable for MAV designs. Thedragonfly genusAeschna is capable of gliding for durations up to 30 swithout an appreciable loss in altitude [3]. Gliding flight, whichrequires no energy expenditure, would prove to be amajor advantageto MAVs in a power-saving technique [4]. Their superior glidingperformance can be attributed to their high-aspect-ratiowings. Ennos[5] and Torres [6] both demonstrated the importance of aspect ratio ingliding flight. Ennos [5] concluded that, as the aspect ratio increases,the gliding ratio will also increase until the profile drag becomesgreater than the induced drag. Torres [6] demonstrated the impor-tance of the aspect ratio and planform design to achieve themaximum gliding ratio.

Dragonflies have some of the highest aspect ratio wings in theinsect world, which contribute to their gliding performance. TheAeshna juncea (hawker dragonfly) was calculated to have an aspect

Received 10 June 2010; revision received 25 October 2011; accepted forpublication 26 October 2011. Copyright © 2012 by K. Hord and Y. Lian.Published by the American Institute of Aeronautics and Astronautics, Inc.,with permission. Copies of this paper may be made for personal or internaluse, on condition that the copier pay the $10.00 per-copy fee to the CopyrightClearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923; includethe code 0021-8669/12 and $10.00 in correspondence with the CCC.

∗Graduate Student, Mechanical Engineering Department, 200 SackettHall.

†Assistant Professor, Mechanical Engineering Department, 200 SackettHall. Senior Member AIAA. ‡Data available at http://www.ga-asi.com/ [retrieved 2012].

JOURNAL OF AIRCRAFT

Vol. 49, No. 3, May–June 2012

749

Dow

nloa

ded

by U

NIV

ER

SIT

Y O

F L

OU

ISV

ILL

E o

n N

ovem

ber

4, 2

016

| http

://ar

c.ai

aa.o

rg |

DO

I: 1

0.25

14/1

.C03

1135

ratio of 11.63 and 8.4 for the forewing and hind wing, respectively;the Tipula paludosa (crane fly) has an aspect ratio of 11.3; theEpisyrphus balteatus (marmalade fly) has an aspect ratio of 8.45; theErista listenax (drone fly) has an aspect ratio of 7.15; and theBombuslucorum (white-tailed bumblebee) has an aspect ratio of 6.83 [3,4,7].

Wakeling and Ellington [8] and Zang and Lu [9] both performedobservational studies on the Sympetrum sanguineum dragonfly. Bothconcluded that dragonflies primarily glide at low angles of attack.Wakeling and Ellington [8] also performed a wind-tunnel study ondried wings of the specimen. The wind-tunnel testing suggested thatthe sum of the lift forces produced by the dragonfly’s wingsindividually could not generate enough lift in glidingflight to supportthe weight of the dragonfly. This suggested that fore- and hind winginteractions during gliding flight must be crucial. Zang and Lu [9]then performed a two-dimensional (2-D) numerical study of flatplates in a tandem configuration similar to what is employed bydragonflies. Zang and Lu found that the tandem configurationsignificantly improves the lift generation of the forewing of thedragonfly, and it improves its overall gliding ratio. The sum ofthe new lift forces generated by the wings were found to balance theweight of the dragonfly in gliding flight.

Besides the dragonfly’s gliding ability, another characteristic thatinterests researchers is their corrugated structure. Examining anAeshna cyanea’s forewing reveals a highly corrugated structurewhere the corrugationvaries spanwise and chordwise along thewing.The corrugation provides stiffening of the wing while allowingtorsion to occur [10]. The corrugated wing structure, which does notresemble any traditional streamline airfoil, was originally assumed toperform poorly in gliding flight by producing low lift and high drag.However, several studies have led to multiple conclusions about theuse of the corrugated structure.

Two early wind-tunnel experiments conducted on corrugatedwings by Rees [11] and Rudolph [12] concluded that the corrugationprovides no aerodynamic benefits. However, they both suggestedthat fluid flowing over the corrugation could become trapped insidethe folds. This trapped fluid would either rotate slowly or remainstagnant. Rudolph also noted that the only benefit a corrugated wingwould have over a smooth airfoil is that the corrugation would delayflow separation at higher angles of attack.

Kesel [13] extracted three profiles from the forewing of an Aeshnacyanea. Each profile was taken from a different wingspan distance.The aerodynamic performance was measured at a chord Reynoldsnumber of 7880 or 10,000, depending on the profile used. Keselnoticed vortices that formed in the wing’s corrugation effectivelychanged thewing shape andmade the corrugatedwings behavemorelike a streamlined airfoil. It was found the profiles acted similar toasymmetrical smooth profiles or a flat plate. Kesel concluded that anincrease in lift generation cannot be obtained from the vortex systemfrom random or uniform corrugations but finely tuned corrugationsthrough evolution.

Murphy and Hu [14] studied the aerodynamic characteristics of acorrugated airfoil, taken from an Aeshna cyanea, and compared itwith a streamlined airfoil and a flat plate at chord Reynolds numbersof 58,000 and 125,000. The aerodynamic forces measured showedthat the corrugated airfoil could generate higher lift and delay flow

separation at higher angles of attack compared with the streamlinedairfoil and flat plate. Using a wind tunnel equipped with particleimage velocimetry, they were able to capture images of vortexstructures that formed inside the valleys of the corrugation. It wasdetermined that the peaks of the corrugation promoted the flowtransition from laminar to turbulent, and unsteady vortexes would becaptured in the valleys. These vortexeswould pull the boundary layerto the surface, keeping the flow attached. This allowed the turbulentflow to stay attached through more severe pressure gradients.

Vargas and Mittal [4] numerically studied a corrugated airfoil andfurther compared it with a streamlined profiled version of thecorrugated airfoil and aflat plate at Reynolds numbers of 500 through10,000. The flat plate was found to perform best at low Reynoldsnumbers of less than 5000. Increasing the Reynolds number to10,000, it was found the corrugated airfoil performed better. VargasandMittal concluded that the corrugated airfoil performed best at lowangles of attack. At these angles, the airfoil experienced increases inpressure drag but had a reduction inviscous drag and skin friction dueto the existence of recirculation zones inside the corrugations,leading to a negative shear stress contribution.

Recently, Kim et al. [15] performed a numerical study on threedifferent corrugated airfoils with Reynolds numbers of 150, 1400,and 10,000 and angles varying from 0– 40 deg. The study primarilyfocused on the effects of the corrugation on lift. Kim et al. concludedthat the lift was not directly influenced by the Reynolds number andthe corrugation increased the lift through all the angles tested.

Sunada et al. [16] performed water-tunnel tests to study thecharacteristics of 20 wings with the same aspect ratio of 7.25. Theyfound that a 5% camber wing with a sharp leading edge producesbetter hydrodynamic performance, lower drag, and higher lift. Theyalso noticed that the addition of wing corrugation could also improvethe performance of the airfoil. Corrugation was found to be effectivebecause it could increases rigidity, thus allowing for a thinner wingthat was stronger against bending and torsional moments so theairfoil could maintain its profile. Thinner airfoil sections were alsofound to increase the hydrodynamic performance of the airfoil.

Kesel et al. [10] also demonstrated the structure benefits of acorrugated wing through a finite element analysis. They found thatthe wing was stabilized primarily by three-dimensional (3-D) corru-gations. These corrugations dramatically reduced wing deflection bya factor of 20 and reduced stress by 95% compared with a flatter 2-Dwing. Kesel et al. concluded that greater structural stability could beachieved through a corrugated profile while using minimummaterials, thus creating light, strong wings.

The majority of studies carried out have been with scale models ofdragonfly wing sections from the Aeshna cyanea’s forewing at highReynolds numbers of beyond 104. For MAV application, theReynolds number is typically less than 104. It is worthwhile to studythe corrugated airfoil at the low-Reynolds-number region because itsmany favorable characteristics are relevant to MAV designs. In thispaper, a corrugated airfoil taken from an Aeshna cyanea dragonflywas investigated numerically at Reynolds numbers of 500, 1000, and2000. To further understand its structural implication, afinite elementanalysis was performed also.

II. Numerical Method

The Reynolds number in the range of 1000, which is the lowerrange of gliding flight occurring across the wings of the Aeshnacyanea, is the primary focus of this study. In this Reynolds numberrange, flow remains laminar and its behavior is described by theincompressible Navier–Stokes equations:

@u

@t� u � ru��rp

�� �r2u (1)

r � u� 0 (2)

where� is the density,u is the velocity vector,p is the pressure, and�is the kinematic viscosity. The incompressible Navier–Stokesequations are solved with the pressure-Poisson method [17]. The

Fig. 1 Airfoil performance as a function of chord Reynolds

number [1,2].

750 HORD AND LIAN

Dow

nloa

ded

by U

NIV

ER

SIT

Y O

F L

OU

ISV

ILL

E o

n N

ovem

ber

4, 2

016

| http

://ar

c.ai

aa.o

rg |

DO

I: 1

0.25

14/1

.C03

1135

equations are discretized in spacewith second-order-accurate centraldifferences onto a set of overlapping grids. The second-order Crank–Nicolson scheme is used for time integration. The PETSc§ package isused to solve the system of equations. For the Reynolds numbersstudied, the flow was assumed to be laminar with no turbulencemodel employed.

III. Computation Setup

Figure 2 shows the two profiles being tested: a flat plate and acorrugated airfoil. The profile of the corrugated airfoil was takenfrom the forewing of an Aeshna cyanea dragonfly. The originalprofile was developed by Kesel [13] and then taken by Murphy andHu [14], who gave a thickness to the airfoil. The flat plate has roundleading and trailing edges. The flat plate and corrugate airfoil havethe same chord length and thickness of 2% of the chord.

A. Overlapping Grids

An overlapping grid method was used to develop the compu-tational domain. The method employs the use of Cartesian grids as abackground grid and structured body-fitted grids around thecomponents of the domain. This allows for the computationaldomain and its components to bemodeled individually withmultiplesets of grids for accurate representation of the entire domain. Aninterpolation region is created between the overlap of the grids toallow information to pass between them. More information can befound in [18].

B. Grid Sensitivity Analysis

The grid sensitivity analysis would systematically vary thenumber of grid points in the grid domain to investigate the effects ofgrid density on the aerodynamic forces acting on the airfoil. ACartesian grid was used as a background grid, and a body-fitting gridwas used around the airfoil. The background and airfoil grid weresystematically varied to see the changes on the coefficient of lift anddrag. The simulations were run until steady or periodic flow patternsdeveloped, ensuring a convergence criteria of 10�6 was met by thepressure solver for every time step. The time-averaged coefficient oflift and coefficient of drag were then examined.

The coefficients of lift and drag were calculated from the forcehistory of each simulation. The coefficients of lift and drag werecomputed with Eqs. (3) and (4):

cL �L

1=2�U21c

(3)

cD �D

1=2�U21c

(4)

At high angles of attack, periodic vortex shedding was observed inthe study. When that occurred, a time-averaged lift and drag wereused in Eqs. (3) and (4).

In a recent study, Granlund et al. [19] showed the effects smalldomain sizes have on the coefficient of lift in water channels. Theyfound the coefficient of lift increased by a factor of 2 when thedomain was halved in size. This effect, however, was not prominentuntil high angles of attack. Tomitigate this effect, the top and bottomwalls of the computational domainwere set to inflowboundaries, andtwo domain sizes were tested.

At 20 deg, the corrugated profile was tested with 10c � 10c and20c � 20c domains. The time-averaged coefficients of lift for bothcases were 0.948 and 0.952, respectively. The time-averaged coeffi-cients of drag were 0.441 and 0.439, respectively. The relativelysmall difference in the force coefficients show that any staticblockage effect in the computational domain was minimal, thusallowing for a smaller 10c � 10c domain to be used.

The grid sensitivity analysis for the corrugated profile wasperformed at an angle of attack of 8 deg. The convergence of lift anddrag is reported in Table 1. At this angle of attack, no vortex sheddingwas observed. It seemed that a grid with 600 lines in the circum-ferential direction and 200 lines in the radial direction (600 � 200)was required. Upon examining the flowfield, it was observed that thewake velocity was quickly damped out as it passed into coarser gridsin the wake region. It was determined that an additional grid in thewake region would be required to capture any vortex structuresgenerated at higher angles of attack. Figures 3a and 3b show the oldoverlapping grid scheme and the newgrid scheme (with added grid inthe wake region) with respective velocity contours. It was clear thatthe added trailing-edge grid better resolved the flow structure in thewake. This additional trailing grid reduced the overall sensitivity ofthe grid to changes in grid density. Thus, the requirement on theairfoil grid could be reduced with the addition of the trailing-edgegrid. From the grid sensitivity analysis, it was found a 400 � 100airfoil grid and a 200 � 100 trailing-edge grid would accuratelyrecreate the necessary grid scheme to produce valid results andpreserve the flowfield. The grid spacing along the surface of thecorrugated profile was approximately 0:0014c. Without the trailing-edge grid, it would require a 600 � 200 airfoil grid. The same processwas performed on the flat plate as the corrugated airfoil. It was foundthat a grid with a 300 � 100 body-fitted grid with a 200 � 50 trailinggridwas sufficient. The grid spacing along the flat platewas 0:0025c.

C. Suitability of a Two-Dimensional Simulation

Given the complex corrugated nature of a dragonfly wing, it isreasonable to question the suitability of a 2-D study. The varyingspanwise corrugation would, in theory, induce complex 3-D flowphenomena that could influence the lift and drag generation of thecorrugated profile. A 3-D periodic spanwise grid was generated tostudy the 3-D effects of the corrugation. The wing’s aspect ratio wasequal to 1, and the angle of attack was varied from 0 to 12 deg. Thetime-averaged coefficient of the lift and dragwere compared with the2-D cases. It was found that, for all cases, the lift and drag varied onlyby a maximum of 8%. Upon further investigation, it was found thedifference in the force coefficients resulted from a variation in gridgeneration, and therewas no velocity parallel to the span of thewing.Thus, it was concluded that the 2-D simulation was sufficient.

IV. Results

A. Effect of Angle of Attack

The effect of angle of attack on aerodynamic forces wasinvestigated. The chord Reynolds number remained 1000. Forcomparison, the calculated coefficients of lift were plotted againstexperimental data from Kesel [13] at a Reynolds number equal to10,000 and numerical data fromKim et al. [15] at a Reynolds numberequal to 1400, in Fig. 4a. Since vortex shedding occurred at modestangles of attack, the results plotted are the time-averaged coefficient

Fig. 2 Test airfoil profiles.

Table 1 Grid sensitivity analysis of corrugated profile and

flat plate with trailing grid at a Reynolds number of 1000

Corrugated profile Flat plate

Airfoil grid Background �CL �CD �CL �CD

200 � 50 160 � 160 0.447 0.192 0.655 0.159300 � 50 160 � 160 0.465 0.176 0.607 0.148300 � 100 160 � 160 0.469 0.181 0.588 0.144400 � 100 160 � 160 0.472 0.179 0.586 0.143500 � 100 160 � 160 0.474 0.178 0.584 0.143

§Data available at http://www.mcs.anl.gov/petsc/petsc-as/ [retrieved2012].

HORD AND LIAN 751

Dow

nloa

ded

by U

NIV

ER

SIT

Y O

F L

OU

ISV

ILL

E o

n N

ovem

ber

4, 2

016

| http

://ar

c.ai

aa.o

rg |

DO

I: 1

0.25

14/1

.C03

1135

of lift and drag. The numerical prediction was very close to theexperimental data at low angles of attack (�� 4 deg). Because ofthe disparity of Reynolds number used, the closeness seems toindicate the lift was not sensitive to the Reynolds number at lowangles of attack. At modest angles of attack, there is a disagreementbetween Kim et al.’s data and the numerical data. The numericalsimulation predicts a lower lift coefficient than the experimental dataof Kesel [13] at a high Reynolds number and with Kim et al.’s [15]measurement. The deviation from Kim et al.’s simulation may beexplained by the corrugate profile they used. While their profile wasidentical, the profile thickness was much thinner. As previouslystated, Sunada et al. [16] noted that thinner profiled airfoils achievehigher lift. One reason for the high lift in both the numerical

simulation and Kim et al.’s [15] data is, at a low Reynolds number,viscosity plays an important role andflow remains attached. Thus, noobvious stall was observed over the range studied.

Comparing the predicted numerical drag coefficient (Fig. 4b) toKim et al.’s [15] numerical and Kesel’s [13] experimental results, itwas seen that the predicted numerical dragmatches closely with Kimet al.’s [15] results. Again, the numerical data show a deviation fromwith a higher predicted drag. This can be attributed to a moreprominent viscous effect at lower Reynolds numbers. Comparisonwith the flat plate is shown in Figs. 4c and 4d. The corrugated airfoiland the flat plate produce very similar lift at almost all the angles ofattack, which was consistent with Kesel’s [13] findings. Thecorrugated profile produced slightly higher drag than the flat plate,

Fig. 3 U velocity component contour a) without a trailing grid, and b) with a trailing grid.

Fig. 4 Numerical results of corrugated profile plotted against published data (Figs. 4a and 4b) and numerical results of the flat plate at a Re of 1000(Figs. 4c and 4d).

752 HORD AND LIAN

Dow

nloa

ded

by U

NIV

ER

SIT

Y O

F L

OU

ISV

ILL

E o

n N

ovem

ber

4, 2

016

| http

://ar

c.ai

aa.o

rg |

DO

I: 1

0.25

14/1

.C03

1135

reducing its gliding ratio as seen in Fig. 4d. The corner seen in the liftof the flat plate between angles of 10 and 12 deg cannot be attributedto a hysteresis in the simulation. Each simulationwas conductedwitha static angle of attack. This corner does not appear in the drag due toviscous forces mainly contributing to the drag as opposed to pressureforces that mainly contribute to lift at this low angle of attack.

B. Effect of Reynolds Number

The effect of the Reynolds number was also investigated. Theresults of the Reynolds numbers of 500 and 2000 were comparedwith the previous results. As previously discussed, Wakeling andEllington [8] showed that dragonflies glide predominately at lowangles of attack. Thus, for the cases for the Reynolds numbers of 500and 2000, the angle of attack was only varied from 0 to 20 deg. Theresults of the force coefficients for the corrugated airfoil are shown inFig. 5a. At low angles of attack, � � 12 deg, lift remained relativelyunchanged. At higher angles, � > 12 deg, lift grew with theReynolds number. As the Reynolds number increases, viscouseffects become less prominent, and drag decreases. The decrease indrag increases the gliding ratio, as seen in Fig. 5b.

Similar results were seenwith the flat plate. The results of the forcecoefficients are shown in Fig. 6a. As the Reynolds number increased,the lift remained constant for low angles of attack, � � 12 deg. Athigher angles, lift increased with the Reynolds number. Like thecorrugated profile, drag decreased with an increasing Reynoldsnumber due to the lessening of viscous forces. Unlike the corrugatedprofile, the reduction of drag led to a large growth in the gliding ratio;see Fig. 6b.

C. Effects of Leading Edge

Observing the stark differences in gliding ratios between thecorrugated profile and flat plate at the various Reynolds numbers, itwas plausible to assume the differences in the leading- and trailing-edge geometries of both profiles may have played a part. To analyzethe effect the leading- and trailing-edge geometries had on the forcecoefficients, a rounded edge flat plate was compared with a flat platewith squared edges. Both flat plates were simulated at Reynoldsnumbers of 500, 1000, and 2000, with the angle of attack beingvaried from 0 to 20 deg.

In Figs. 7a and 7b, therewas little difference observed between thetwo edge types in terms of the force coefficients at Reynolds numbersof 500 and 1000. When the Reynolds number was equal to 2000(Fig. 7c), the differences between the lift and drag of the two profileswere beginning to diverge. The square edgewas producing 3%morelift and drag on average compared with the rounded edge. It wasconcluded that the edge geometry had little impact at these lowReynolds numbers. Kunz [20] came to a similar conclusion; it wasfound when the Reynolds number was less than 6000 and the edgegeometry was not a dominating factor in force production.

D. Effects of Corrugation

Examining the streamlines around the corrugated airfoil, at aReynolds number of 1000, it was found that near-stagnant rotatingflowwas trappedwithin the valleys of the corrugation. Because of thetrapped vortices, the corrugated airfoil acted like a thick smoothairfoil. This is similar to what was seen in [4,11,12,14]. For visualaid, the virtual profile was outlined in Fig. 8. The illustration shows

Fig. 5 Effect of Reynolds number on the corrugated profile at various angles of attack: a) coefficient of lift (closed symbol) and drag (open symbols), and

b) gliding ratio.

Fig. 6 Effect of Reynolds number on the flat plate at various angles of attack: a) coefficient of lift and drag, and b) gliding ratio.

HORD AND LIAN 753

Dow

nloa

ded

by U

NIV

ER

SIT

Y O

F L

OU

ISV

ILL

E o

n N

ovem

ber

4, 2

016

| http

://ar

c.ai

aa.o

rg |

DO

I: 1

0.25

14/1

.C03

1135

the virtual profile around the corrugation comparedwith the flat plateat various angles of attack. The virtual profile was drawn throughvisual inspection ofwhere the velocity near the airfoil becamegreaterthan 0:1U1. As the angle increased, the increase in virtual profilethickness of the corrugated airfoil increased the pressure drag. Theflat plate does not showavirtual profile thickness until approximately8 deg.When the angle is less than 8 deg, the flow sticks to the surfaceof the flat plate, increasing viscous drag, yet pressure drag is reduced.Flow across the corrugated profile conveys across the slowly rotatingflow in the valleys, which results in the formation of the virtualprofile. The rotating flow in the valleys results in the production ofnegative viscous drag that reduces the total drag caused by shear.Because of the large separation of flow across the corrugated profile,there is a large increase in pressure drag compared with the flat plate.

At 8 deg, the coefficient of drag for the corrugated airfoil and theflat plate were 0.156 and 0.141, respectively. The viscous drag made

up only 17% of the total drag on the corrugated airfoil, while theviscous drag made up 30% of the drag on the flat plate. Thiseffectively shows that the corrugated airfoil can lower viscous drag.However, because of the thick virtual profile produced by the trappedvortices, the pressure drag on the corrugated airfoil was 1.34 timeshigher than the flat plate’s pressure drag. This increase in dragreduces the lift-to-drag ratio. Both the flat plate and the corrugatedairfoil produced peak lift-to-drag ratios �CL=CD�max around 6 deg.The peak lift-to-drag ratio of the flat plate and the corrugated airfoilwere 4.3 and 3.3, respectively.

E. Stability of the Corrugated Airfoil

At angles greater than 12 deg, both the corrugated profile and theflat plate began to exhibit vortex shedding. The vortex sheddingcauses both lift and drag to oscillate on the airfoils. The Strouhalnumber of the vortex shedding at different angles of attack is plottedin Fig. 9a, which was found using Eq. (5):

St� sin�fc

U1(5)

Overall, the Strouhal number remains constant as the angle ofattack increases, which is consistent with the observation that theStrouhal number over a blunt body is approximately 0.2. Thecorrugated profile and the flat plate demonstrate similar vortexshedding patterns at high angles of attack, indicating both of thembehave like a blunt body. Figure 9b plots themaximumandminimumlift at each angle of attack for the corrugated profile and flat plate.Comparing Figs. 9a and 9b, it can be seen again how the corrugatedprofile acts very similar to the flat plate, even in lift oscillation. Thelift history shown in Fig. 10 illustrates the similarities of the sheddingfrequency and lift oscillations in both the flat plate and corrugatedairfoil at 20 deg. In Fig. 11, snapshots are shown of the vorticitycontours of both airfoils at 20 deg. The snapshots were taken at thetime instants corresponding to maximum and minimum lift. It isimportant to note that the corrugation does not seem to affect theshedding frequency.

F. Viability of Corrugated Airfoil

The numerical simulations have demonstrated that the corrugatedairfoil acts similar in lift production as aflat plat; however, it producesmore drag, which agrees with Kesel [13]. This increase in drag isbecause the near-stagnate rotating vortices make the corrugatedairfoil function like a thick streamlined airfoil. Because of its highpressure drag, the corrugated airfoil actsmuch like a cambered airfoilat angles of attack greater than zero. The increase in pressure drag ispartially offset by the decrease in viscous drag due to the negativeshear stresses in the valleys, leading to a net increase of total drag.This increase in drag reduces the lift-to-drag ratio significantly. Thecorrugated profile has also exhibited similar vortex sheddingfrequencies and lift oscillation amplitudes as the flat plate. This

Fig. 7 Coefficient of lift and drag polar plots at various Reynolds numbers. The open square represents the square leading edge, and the open circle

represents the round leading edge.

Fig. 8 Steady flow streamline visualization around the corrugated

profile. Virtual profile represented by dotted line.

754 HORD AND LIAN

Dow

nloa

ded

by U

NIV

ER

SIT

Y O

F L

OU

ISV

ILL

E o

n N

ovem

ber

4, 2

016

| http

://ar

c.ai

aa.o

rg |

DO

I: 1

0.25

14/1

.C03

1135

evidence seems to indicate that the corrugated airfoil is not intendedfor aerodynamic improvement but instead for structural benefits, aspreviously hypothesized by other researchers [11,12].

V. Structural Analysis

A. Structural Setup

The structural simulation performed here was similar to Keselet al.’s [10] finite element analysis of the structural benefit of theAeshna cyanea forewing. Instead of reconstructing the forewing ofthe Aeshna cyanea, it was decided to create a 3-D homogeneousprofile of the wingspan to test the structural properties of thecorrugated profile. The corrugated wingspan was compared with aflat plate wingspan. Each wing was created using the SolidWorks2009 [21] designer, and then it was tested using the program’s ownstructural simulation tools.

B. Material Properties and Modeling

To model a dragonfly’s wing, the 3-D wing will be given theproperties of chitin. Eachmodel was assumed to have amaterial with

an isotropic nature. The properties of chitin were taken from Kesel[13], which list the Young’s modulus as 6:1 GN=m2 and an assumedPoisson’s ratio of 0.25. Each model was then subjected to a pressureload of 4:061 � 10�6 GN=mm2, which provides a homogenouswing loading that approximates the weight of the dragonfly.

Several models of the corrugation and flat plate were created,varying the percent thickness of each from 1 to 6%. Each wing had achord length of 1 cm and a span of 4 cm,which are approximations ofthe dimensions of the Aeshna cyanea forewing; Fig. 12 shows asample of the models produced.

The maximum displacement of the various profile thicknesses ofthe flat plate and corrugated profile were measured. Figure 13agraphs the displacement of each thickness. The flat plate shows littleresistance to displacement at its thinnest thickness. The 1% flat platedeflects approximately 2.5 mm under load. However, the corrugatedprofile demonstrates a much higher rigidity in comparison. Itsdeflection was 35 times lower than the flat plate. Past a 3% thickness,the flat plate shows little improvement on deflection reduction, whilethe corrugated wing shows little to no change.

A similar trend is seen with the average stress across the wings, aspreviously seenwith the deflection. The flat plate showsmuch higheraverage stress at lower thicknesses, but past 3%, the reduction ofstress decreases slower as the thickness increases. Figure 13b graphsthe average stress on each wing. At 1%, the corrugated wing showseight times less average stress than the flat plate. The corrugation

Fig. 9 Vortex shedding dynamics for both the corrugated airfoil and the flat plate where examined: a) Strouhal number of wake shedding frequency,

and b) oscillating coefficient of lift of corrugated airfoil and the flat plate. Closed symbols represent CLmax, and open symbols represent CLmin.

Fig. 10 Force history of flat plate and corrugated airfoil at 20 deg.

Fig. 11 Vorticity contours of the corrugated airfoil (left) and flat plate (right) at 20 deg after periodic flow has been established.

Fig. 12 Flat plate and corrugated wing models used.

HORD AND LIAN 755

Dow

nloa

ded

by U

NIV

ER

SIT

Y O

F L

OU

ISV

ILL

E o

n N

ovem

ber

4, 2

016

| http

://ar

c.ai

aa.o

rg |

DO

I: 1

0.25

14/1

.C03

1135

again shows its superior ability to handle loading more efficientlythan the flat plate without increasing the thickness of the wing. Likethe deflection trend, the normalized stress ratio also begins to fall asplate thickness increases.

VI. Conclusions

Numerical simulations were performed to understand theaerodynamic and structural characteristics of a corrugated airfoil.The aerodynamics was studied by solving the incompressibleNavier–Stokes equations on an overlapping grid, while the structurecharacteristics were investigated using commercial softwareSolidWorks 2009. It was observed that the corrugated airfoilproduces similar lift as a flat plate, but at peak gliding ratios, itproduces more drag. This increase in drag is due to the higherpressure drag resulting from the thicker virtual streamlined profilecreated by the stagnant vortices trapped in the valley. The higherpressure drag is partially offset by the negative shear stresses from therotating vortices. The lift oscillations of both the flat plate and thecorrugated profile were identical with similar vortex sheddingfrequencies at higher angles of attack. This shows that the corru-gations do not interfere with the vortex shedding. However,compared with a flat plate, the flat plate produces more favorableaerodynamic characteristics. Overall, the aerodynamic analysisshowed that the selected corrugated profile provides no advantages interms of stall delay or lift generation. This conclusion is contrary toother studies at much higher Reynolds numbers.

Investigating the structural properties of the corrugated wing andflat plate showed that, under a static loading, the corrugatedwingspan had superior performance compared with the flat plate interms of bending resistance. The study showed that the corrugatedwing can reduce deflection and stress on thewing. It would take a flatplate with three times the thickness to perform as well as thecorrugated wing. By using corrugation, it has been shown thatincreased structural rigidity can be obtained with minimum increasein materials.

These two studies provide strong evidence that the corrugatedprofile is primarily used for structural support in gliding flight at lowReynolds numbers. It provides similar lift, higher drag, and vastlymore rigid lift surface.

Acknowledgments

This work is partially support by a grant from the KentuckyScience and Engineering Foundation and by an Intramural ResearchIncentive Grant from the Office of the Executive Vice President forResearch at the University of Louisville.

References

[1] McMasters, J. H., and Henderson, M. L., “Low Speed Single ElementAirfoil Synthesis,” Technical Soaring, Vol. 6, No. 2, 1980, pp. 1–21.

[2] Gad-el-Hak, M., “Micro-Air-Vehicles: Can They Be ControlledBetter?,” Journal of Aircraft, Vol. 38, No. 3, 2001, pp. 419–429.doi:10.2514/2.2807

[3] Brodsky, A. K., “Flight and Behavior,” The Evolution of Insect Flight,1st ed., Oxford Univ, Press, New York, 1994, pp. 66–76.

[4] Vargas,A., andMittal, R., “AComputational Study of theAerodynamicPerformance of a Dragonfly Wing Section,” 2nd Flow ControlConference, Portland, OR, AIAA Paper 2004-2319, 2004.

[5] Ennos, A. R., “The Effect of Size On the Optimal Shapes of GlidingInsects and Seeds,” Journal of Zoology, Vol. 219, 1989, pp. 61–69.doi:10.1111/j.1469-7998.1989.tb02565.x

[6] Torres, G. E., “Aerodynamics of Low Aspect Ratio Wings at LowReynolds Numbers with Applications to Micro Air Vehicle Design,”Ph.D. Dissertation, Department of Aerospace and MechanicalEngineering, Univ. of Notre Dame, Notre Dame, IN, 2002.

[7] Ellington, C. P., “The Aerodynamic of Hovering Insect Flight: I. TheQuasi-Steady Analysis,” Philosophical Transactions of the Royal

Society Series B, Biological Sciences, Vol. 305, No. 1122, 1984,pp. 1–15.doi:10.1098/rstb.1984.0049

[8] Wakeling, J.M., andEllington, C. P., “DragonflyFlight I.Gliding Flightand Steady-State Aerodynamic Forces,” Journal of Experimental

Biology, Vol. 200, 1997, pp. 543–556.[9] Zang, J., and Lu, X., “Aerodynamic Performance due to Forewing and

Hindwing Interaction in Gliding Dragonfly Flight,” Physical Review,Vol. 80, 2009, Paper 017302.doi:10.1103/PhysRevE.80.017302

[10] Kesel, A., Philippi, U., and Nachtigall, W., “Biomechanical Aspects ofInsect Wing: An Analysis Using the Finite Element Method,”Computers in Biology and Medicine, Vol. 28, 1998, pp. 423–437.doi:10.1016/S0010-4825(98)00018-3

[11] Rees, C. J. C., “Aerodynamic Properties of an InsectWing Section and aSmooth Aerofoil Compared,” Nature, Vol. 258, Nov. 1975, pp. 141–142.doi:10.1038/258141a0

[12] Rudolph, R., “Aerodynamic Properties of Libella Quadrimaculata L.(Anisoptera. Libelludidea), and the Flow Around Smooth andCorrugated Wing Section Models During Gliding Flight,” Odonato-

logica,Vol. 7, 1987, pp. 49–58.[13] Kesel, A., “Aerodynamic Characteristics of Dragonfly Wing Sections

Comparedwith Technical Aerofoils,” Journal of Experimental Biology,Vol. 203, 2000, pp. 3125–3135.

[14] Murphy, J., and Hu, H., “An Experimental Investigation on a Bio-Inspired Corrugated Airfoil,” 47th AIAA Aerospace Sciences MeetingIncluding the New Horizons Forum and Aerospace Exposition,Orlando, FL, AIAA Paper 2009-1087, 2009.

[15] Kim, W., Ko, J., Park, H., and Byun, D., “Effects of Corrugation of theDragonfly Wing On Gliding Performance,” Journal of Theoretical

Biology, Vol. 260, No. 4, 2009, pp. 523–530.doi:10.1016/j.jtbi.2009.07.015

[16] Sunada, S., Yasuda, T., Yasuda, K., and Kawachi, K., “Comparison ofWing Characteristics at Ultralow Reynolds Number,” Journal of

Aircraft, Vol. 39, No. 2, 2002, pp. 331–338.doi:10.2514/2.2931

[17] Henshaw, W. D., “A Fourth-Order Accurate Method for theIncompressible Navier–Stokes Equations on Overlapping Grids,”Journal of Computational Physics, Vol. 113, No. 1, 1994, pp. 13–25.

Fig. 13 Structural characteristics of both wings with varying thickness: a) maximum displacement of models, and b) average von Mises stress.

756 HORD AND LIAN

Dow

nloa

ded

by U

NIV

ER

SIT

Y O

F L

OU

ISV

ILL

E o

n N

ovem

ber

4, 2

016

| http

://ar

c.ai

aa.o

rg |

DO

I: 1

0.25

14/1

.C03

1135

doi:10.1006/jcph.1994.1114[18] Henshaw, W. D., “Ogen: An Overlapping Grid Generator For

Overture,” Lawrence Livermore National Lab., TR UCRL-MA-132237, Livermore, CA, 1998.

[19] Granlund, K., Ol, M., Garmann., D., and Visbal, M., “Experiments andComputations on Abstractions of Perching,” 40th Fluid Dynamics

Conference, Chicago, IL, AIAA Paper 2010-4943, 2010.[20] Kunz, P. J., “Aerodynamics and Design for Ultra-Low Reynolds

Number Flight,” Ph.D. Dissertation, Dept. of Aeronautics andAstronautics, Stanford Univ., Menlo Park, CA, 2003.

[21] SolidWorks 2009, x64 Ed. SP3.0, Dassault Systèmes Americas Corp.,Waltham, MA, 2009.

HORD AND LIAN 757

Dow

nloa

ded

by U

NIV

ER

SIT

Y O

F L

OU

ISV

ILL

E o

n N

ovem

ber

4, 2

016

| http

://ar

c.ai

aa.o

rg |

DO

I: 1

0.25

14/1

.C03

1135