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Low-Reynolds-Number Effects in Passive Stall ControlUsing Sinusoidal Leading Edges

J. L. E. Guerreiro and J. M. M. Sousa

Instituto Superior Tcnico, 1049-001 Lisbon, PortugalDOI: 10.2514/1.J051235

Theobjective of thepresent work isto investigate theapplicationof a sinusoidal leading edge to thedesign of micro

air vehicles. Wind-tunnel tests of wings with low aspect ratios of 1 and 1.5, rectangular planforms, and five distinct

leading edges [four sinusoidal leading edges and onebaseline (straight) leading edge foreach aspectratio]have been

conducted. The Reynolds numbers of 70,000 and 140,000 have been analyzed. For the higher Reynolds number, a

propercombinationof amplitude andwavelength canlead to a substantial increase in lift forangles of attackgreater

than the baseline stall angle. Maximum lift coefficient gains of the order of 45% were achieved by combining both

large amplitude and large wavelength. At the lower Reynolds number, the benefits can be extended to low angles of

attack, leading to a dramatic increase in the range of operation. The results depend strongly on the aspect ratio.

Nomenclature

A = protuberance amplitude, mmAR = aspect ratio, b2=sb = wingspan, mmc = chord, mmCD = drag coefficient, D=

12

V21SCL = lift coefficient, L=

12

V21SD = drag force, NL = lift force, NRe = Reynolds number, Vc=S = wing area, mm2

V1 = freestream velocity, m=s = angle of attack, deg = protuberance wavelength, mm = viscosity, kg=ms

= air density, kg=m3

I. Introduction

T HE interest in micro air vehicles (MAVs) has grownexponentially in recent years motivated by the increasingcapability in miniaturizing the avionics. Equipped with small videocameras, transmitters, and sensors, MAVs are perfect candidates forspecial limited-duration military and civil missions, which mayinclude real-time images of battlefields; detection of biologicalagents, chemical compounds, and nuclear materials; surveys ofnatural disaster areas; and monitoring of forestfires [1,2].

Because of the combination of small dimensions and low speeds,MAVs fly at low Reynolds numbers (Re < 200; 000 [3]). In thisregime, many complicated phenomena take place within boundary

layers. For example, lifting surfaces become susceptible to laminarflow separation, and the laminar bubble, which commonly forms,may have a dramatic effect on the aerodynamic performance. This isa matter of vital importance when a long-term goal is set to develop avehicle with a wingspan of 8 cm that shouldfly at speeds between30to 65 km=h [1], corresponding to a maximum Reynolds numberranging between 45,000 and 100,000 (for unity aspect ratio). In

addition, the stability and control problems associated with the low

moments of inertia, small weight, and wind gusts presents numerouschallenges [3].

The use of classical methods such as synthetic jets, and blowing orsuction, to control stall and increase the range of operation may incertain cases be too energy-consuming for use in MAVs, and theweight penalty on aflight vehicle is prohibitive. Here, we investigatethe application of a passive method inspired by humpback whale(Megaptera novaeangliae) pectoral flippers at moderate to lowReynolds numbers. The humpback whale is extremely agile, and itcan perform admirable turning maneuvers to catch prey [4]. Itspectoral flippers exhibit high aspect ratios (close to 6), being thelongest among the cetaceans, and present an elliptical planform.However, its most notable feature is the unusual leading edge, madeup of severalprotuberances (tubercles), which gives it an appearanceresembling a sinusoidal pattern [5]. Figure 1 shows a photograph ofthe humpback whale and its pectoral flipper. The first wind-tunnelexperiments conducted by Miklosovic et al. [6] used a scale model ofan idealized humpback whale flipper. They showed a delay in thestall angle fromabout 12 to 16 degwhileincreasing themaximum liftand reducing the dragover a portion of the operational envelope. Theinvestigated Reynolds number was about 500,000, estimated to behalf of thevalue of an adult humpback whale.Subsequently, Stanway[7] tested a similar scale model at Reynolds numbersbetween 45,000and 120,000. He also reported a delay in the stall angle; however,increases in maximum lift were found for the higher Reynoldsnumber only. Particle image velocimetry flow visualizationsuggested that two longitudinal counter-rotative vortices are formedat eachprotuberance, in a manner similar to theleading-edge vorticesof a delta wing, by energizing the flow these enabled stall delay.

Employing a different approach, Miklosovic et al. [8] (at Re 275; 000) and Johari et al. [9] (at Re 183; 000) testedinfinite models in order to study the fundamental nature of theresulting flow from the presence of protuberances. Their results weresubstantially different from those obtained by others in finite scalemodels. An overallincrease in drag wasfound,and the modelswith asinusoidal leading edge were observed to stallfirst. However, the stallbehavior was improved (i.e., it became more gradual) and the liftcoefficients were still higher beyond the point of stall of the baselinemodel (i.e., without tubercles). Tuft visualization [9] showed that theflow separatedfirstat thetroughs betweenthe adjacent protuberanceswhile it was kept attached over the peaks at angles of attack higherthan that of baseline model stall. Another interesting finding fromJohari et al. was that the amplitude of the protuberances had a muchgreater effect on the results than its wavelength.

More recently, Pedro and Kobayashi [10] used a detached eddysimulation formulation to numerically simulate the experience ofMiklosovic et al. [6]. They concluded that the longitudinal vortices

Received 7 March 2011; revision received 7 August 2011; accepted forpublication 12 August 2011. Copyright 2011 by the American Institute ofAeronautics and Astronautics, Inc. All rights reserved. Copies of this papermaybe made forpersonal or internal use, on condition that the copier pay the$10.00 per-copy fee to the Copyright Clearance Center, Inc., 222 RosewoodDrive, Danvers, MA 01923; include the code 0001-1452/12 and $10.00 incorrespondence with the CCC.

Graduate Student, Department of Mechanical Engineering, AvenidaRovisco Pais.Associate Professor, Department of Mechanical Engineering, Avenida

Rovisco Pais. Associate Fellow AIAA.

AIAA JOURNALVol. 50, No. 2, February 2012

461
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not only delayed the trailing-edge separation taking place in theinboard section, where the local Reynolds number was higher(Re > 500; 000), but also prevented the propagation of the leading-edge separation occurring in the outboard section, where the local

Reynolds number was lower (Re < 200; 000), from moving towardthe root.The primary goal of this study is to investigate the applicability of

this solution for stall control to the design of MAVs. Normally, in thedevelopment of these vehicles, the wingspan is a size constraint, sothat low-aspect-ratio (LAR) wings provide the largest wing area forhigher lift. Accordingly, and aiming to achieve the proposedobjective, we use a combination of low-Reynolds-number and LARwings with different leading-edge (sinusoidal) protuberances. Thestudy is based on the direct measurement of the aerodynamic char-acteristics of the wings in a wind tunnel, complemented with smokeflow visualizations.

II. Experimental Apparatus

A. Wing Model ConfigurationDespite its large maximum thickness (17% of the chord length),

the NASA LS(1)0417 profile (Fig. 2) was chosen for this studybecause it hasbeen designed with a large leading-edge radiusin orderto flatten the peak in pressure coefficient in the nose region, thusdiscouraging flow separation and presenting a predictable, docilestall behavior [11]. Although thick airfoils are seldom used on MAVwings, the extra streamlined volume resulting from this choice mayprove to be useful to host electronics without generating additionalcomponent drag.

Ten rectangular wings based on the aforementioned profile werecomputer numerical control machined from Duralumin blocks toensure global accuracy of the airfoil sections and hand polished. Thesurface finish quality, less than 1 m rms in roughness height, wasmeasured with a Mitutoyo SJ-201 profilometer. The models have a

mean chord length of 232 mm, and they can be divided in two setsaccording to their aspect ratio of 1 or 1.5. Each set is formed by thebaseline model and four models with a sinusoidal leading edge,always keeping a constant wing planform area. To define the sinewave,the amplitudesA of0:06c and 0:12c werechosen together withtwo wavelengths of 0:25c and 0:50c. The selected values wereinspired by previous investigations [9] and fall within the range ofvalues associated with humpback whale pectoral flippers. Figure 3illustrates the set of wings with an aspect ratio of 1.5. The models

have been labeled as follows: thefi

rst characters defi

ne the type ofmodel (B for the baseline model and S for a sinusoidal model)and the aspect ratio; thelast characters, separated from theprefix b y a dash and used for the sinusoidal models only, refer to its amplitude

Fig. 1 Humpback whale breaching off the coast of Gloucester,

Massachusetts. Photograph: Mary Schwalm/Reuters; http://www.guardian.co.uk/science/2008/jun/24/animalbehaviour.usa [retrieved

2011].

Fig. 2 NASA LS(1)0417 profile. Fig. 3 Set of wing models with AR 1:5.

462 GUERREIRO AND SOUSA
http://www.guardian.co.uk/science/2008/jun/24/animalbehaviour.usahttp://www.guardian.co.uk/science/2008/jun/24/animalbehaviour.usahttp://www.guardian.co.uk/science/2008/jun/24/animalbehaviour.usahttp://www.guardian.co.uk/science/2008/jun/24/animalbehaviour.usa

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(L standing for large amplitude, i.e., 0:12c, and S standing forsmall amplitude, i.e., 0:06c) and the wavelength (analogously, Lfor 0:5c and S for 0:25c). Table 1 lists the dimensions and othergeometric parameters for the wing models used in this investigation.For simplicity, the models with and without protuberances along theleading edge are termed sinusoidal models and baseline models,respectively.

B. Wind Tunnel and Instrumentation

The experiments were performed in the open-circuit wind tunnelof the Department of Mechanical Engineering at Instituto SuperiorTcnico (Fig. 4). This wind tunnel operates in the low-speed(incompressible) flow regime using a blower installed at the inlet, uptoa maximum speed of10 m=s. Tests can beperformed inthe free jetor in a test section with a rectangular cross-sectional area of1:35 0:8 m. Since the present study embraces the three-dimensional flow developing around the wing models, we havechosen to operate in free jet mode, aiming to reduce the need forwind-tunnel corrections dueto blockage. The test section is precededby honeycombs, screens, and a3:1 contraction ratio to minimize thenonuniformity and the turbulence level of the undisturbed stream.Over the range of operating speeds used, the maximum freestreamturbulence intensity is about 0.2%.

The aerodynamic forces (and moments) are transmitted to a six-component Schenck compact balance through a single-strut modelsupport. The values measured by the load cells are acquired using aPREMA 5001 digital multimeter of six half-digits, which comm-unicates with the host computer using the general purpose interfacebus protocol. Scan rates offive channels per second can be executedwith this system.

C. Experimental Procedures and Uncertainties

The experiments were conducted at two Reynolds numbers of70,000 and 140,000, hereinafter termedas the low-Reynolds-numberregime and the moderate Reynolds number regime, respectively. Asthe present work focused on the stall behavior displayed at positiveincidences only, the angle of attack was varied from 0 deg to

30 deg. After this point, the wings were brought back to 0 deg to check if hysteresis was present. For each angle of attack,

approximately 15 to 30 samples were acquired to form the averagevalues ofCL and CD. Flow visualization tests were conducted for theB1.5 and S1.5-LL models at various incidences, using upstreamsmoke injection from a Safex 2001 fog generator with probe NS 1(Dantec, Denmark) and a laser light sheet to illuminate the semispanplan. Still images were captured during the tests employing a SonyDSLR-A200 digital camera.

Wind-tunnel corrections (mainly for weight tares, load componentinteractions, and eventually wall corrections) were applied via

Schenck proprietary software customized for our facility. Adedicated study for the models and operating conditions used herealso allowed us to further correct the data with respect to modelmount interactions.

Aiming to predict the overall 95% confidence limits for CL andCD, we followed the procedure suggested by Coleman and Steele[12]. To estimate theprecision uncertainties, thestandarderror forthemean force coefficients at each angle of attack was calculated andmultiplied by the two-tailed t value (t 2) used for a t distributionand a number of readings (samples) greater than 10. These werecombined with the estimates of the bias errors to predict the overall95% confidence limits. Percentage uncertainties in CL are on theorder of 4% for the moderate Reynolds numbers and 5% for the lowReynolds numbers. Uncertainties in CD are significantly larger,especially forthe low Reynolds numberand loweraspectratio, where

these may be twice as large due to the small magnitude of themeasured forces. For this reason, the results presented here and thesubsequent discussion are essentially based on the lift coefficientvariations with angle of attack. The uncertainty in the angle of attackis estimated to be of the order of 0.2 deg.

III. Results

In this section, we start by presenting the results at a moderateReynolds number (Re 140; 000): first for thewings of aspect ratio1, and next for the wings of aspect ratio 1.5. Then, the results arediscussed and compared. The procedure is subsequently repeated forresults at a low Reynolds number (Re 70; 000).

A. Moderate Reynolds Number

1. Wings with Aspect Ratio of 1

Figure 5 shows thelift coefficient variationwith angle of attack forwing models of AR 1. The baseline model CL increasescontinuously at an approximately constant rate up to 21 deg,beyond which it is slightly reduced (stalled). However, after thispoint, further increases in incidence still lead to larger lift values. ThemaximumCL of 0.79 is only reached at the maximum angle of attacktested ( 30 deg) and is approximately 13% higher than the valueat the stall point. For 20 deg, the CL behavior of all sinusoidalmodelsis similar to that of thebaselinemodel, despite thelower valueof the slope dCL=d, which ultimately introduces a penalization inlift coefficient. Still, these models show more favorable stallcharacteristics. The S1-LS model (the one differing more from the

baseline leading-edge geometry) is the first to stall at 20 deg,but it exhibits a more gradual and smoother stall then the baseline

Table 1 Wing model dimensions

Wing C, mm b, mm AR A, mm , mm

B1 232 232 1 S1-LL 232 232 1 0.12 0.50S1-LS 232 232 1 0.12 0.25S1-SL 232 232 1 0.06 0.50S1-SS 232 232 1 0.06 0.25B1.5 232 348 1.5

S1.5-LL 232 348 1.5 0.12 0.50

S1.5-LS 232 348 1.5 0.12 0.25S1.5-SL 232 348 1.5 0.06 0.50S1.5-SS 232 348 1.5 0.06 0.25

Fig. 4 Schematic representation of the experimental setup (dimensions in centimeters). Wing model, support strut, and compact balance are not toscale.

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model. The S1-SL model (the one that deviates less from thebaselineleading-edge geometry) stalls at a much higher angle of attack, 27 deg. The remaining two sinusoidal models do not stallwithin the tested range. In the poststall regime, the most prominentfeature is the penalization in lift introduced by the S1-LS model. Onthe other hand, the S1-LL model shows consistent gains in thisregimebut nonetheless, they arevery small to be consideredrelevant.

Table 2 lists the principal aerodynamic characteristics of this set,namely, the lift coefficient at zeroincidence CL0 , the maximumCL,the angle of maximumCL, and stall angle.

2. Wings with Aspect Ratio of 1.5

The data obtained for the wings with an aspect ratio of 1.5 arepresented in Fig. 6. Again, the baseline model increases CL at anapproximately constant rate up to the angle of stall ( 19 deg),where the maximum CL of 0.78 is reached. In this case, the stall isabrupt and severe. Flow visualization confirmed the occurrence ofleading-edge stall. However, due to the very small height of the

(prestall) separationbubble at this Reynolds number, we were unableto document it clearly; hence, the corresponding photo is not shownhere. Further increases in angle of attack reduce the lift, but for > 24 deg, growth resumes. In addition, aerodynamic hysteresiswasfoundto be present. Thehysteresis loop canbe observed in Fig. 7for the angles of attack lying within the range 17 20 deg.This results in considerable variations in lift coefficient. For example,the lift coefficient at 18 deg in the increasing branch of thehysteresis loop was found to be 55% higher than its correspondingvalue in the decreasing branch.

The sinusoidal models present (average) lift slopes in the linearregion roughly 10% lower than the baseline. Interestingly enough, itis possible to observe that the S1.5-SL model (the one departing lessfrom the baseline leading-edge geometry) shows the highest slope

among the sinusoidal models, while the others remain indistin-guishable. All sinusoidal models stall before the baseline model.However, stall is much smoother and gradual for these. Additionally,its superiority at high angles of attack is unquestionable. Models oflowerwavelength(S1.5-LS andS1.5-SS) behavein a similar fashion;they both stall at 17 deg and, after an initial reduction, the liftcoefficient remains fairly constant. On the other hand, the models of

larger amplitude are the ones that generate superior gains (comparedwith the baseline). For instance, while the lift coefficient of S1.5-LLincreases continuously in the range 19 29 deg, reaching amaximumCL of 0.73 (which is 9% higher than the CL at stall angle),

the model S1.5-SL suffers an abrupt loss at 24 deg. Nohysteresis was found associated with this loss of lift. Also note that,near the upper range of angles of attack studied, the rate of growth oflift is similar for both baseline and higher wavelength sinusoidalmodels.

The aerodynamic characteristics for this set are listed in Table 3.

3. Discussion

It may be concluded that, for the wings with an aspect ratio of 1,there is no significant advantage in modifying the geometry of theleading edge, as differences were small. This is due to the absence ofa true stall behavior in the baseline model; the lift is only reducedabout 6% and, subsequently, the previous increase with incidenceresumes. In fact, the lift coefficient of all wings was always seen

increasing at high angles of attack. This trend can be typically foundin LAR wings [13,14]; it is associated to the augmented intensity oflow pressure on the upper surface of the wing asa consequence of thetip vortices. For LAR wings, these vortices can have a dominanteffect in the aerodynamic characteristics at high angles of attack.Torres and Mueller [14] alsoshowed, bymeans offlow visualization,that the tip vortices energize the flow near the wingtips, limiting theseparation bubble to the inboard section of the wing. So, thisprevalent effect may explain the fast recovery of the baseline modelfrom stall and the continuous increase of lift for all models at highangles of attack. The lift coefficient of the S1-LL model normalizedby the lift coefficient of the baseline model (CLS1LL=CLB1 ) is plottedin Fig. 8, demonstrating the superiority of the baseline model in mostof the investigated range of angles of attack.

On the other hand, if the aspect ratio of the wings increases, theimpact of the tip vortices on the upper wing surface is expected todecrease. This is in consonance with the observation that the baselinemodel of aspectratio 1.5presents a completely distinct stall behavior.The abrupt and severe stall causesa reduction of the lift coefficient of32% (from its maximum value). In the poststall regime, a propercombination of protuberances amplitude and wavelength (namely,

Fig. 5 CL vs for the wing models with AR 1 atRe 140; 000.

Table 2 Aerodynamic characteristics of the wings

with AR 1 atRe 140; 000

Wing CL0 CLmax CLmax , deg stall, deg

B1 0.120 0.79 30 21S1-LL 0.142 0.82 30

S1-LS 0.136 0.75 30 20S1-SL 0.143 0.78 27 27S1-SS 0.140 0.79 30

Fig. 6 CL vs for the wing models with atAR 1:5 atRe 140; 000.


with AR 1:5 atRe 140; 000


B1.5 0.176 0.78 19 19S1.5-LL 0.178 0.74 29 16

S1.5-LS 0.175 0.68 17 17S1.5-SL 0.188 0.74 17 17S1.5-SS 0.173 0.69 17 17


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large amplitude and large wavelength) lead to significantimprovements over the baseline model. The normalized liftcoefficient of the S1.5-LL model is also plotted against angle ofattack in Fig. 8 for comparison purposes. At this higher aspect ratio,maximum gains in of the order of 45% can be achieved with amaximum loss of about 2025%.

The results obtained for the wings with a larger aspect ratio alsoshow that both amplitude and wavelength play a major role in thebehavior of the lift coefficient, especially at high angles of attack. Fora two-dimensional experiment, the investigations made by Johari

etal.[9] showed that thewavelengthplayeda minor role. However, ifwe compare the data evolution of S1.5-SL and S1.5-SS, largedifferences can be appreciated in the poststall regime. We also notedthat the lift slope at high angles of attack (approaching 30 deg) iscomparable in both these two sinusoidal models and the baselinemodel. This may suggest that they share a common mechanism,which might be responsible for such correspondence. Concerningthe baseline model, it appears reasonable to assume that successiveincreases in incidence would increase the pressure differencebetween suction and pressure sides, thus intensifying the tip vorticesto a point that the trend of lift decrease would be reversed. After acertain threshold in angle of attack (here, approximately 24 deg), the flow around the wing would be dominated by tipvortex structures and the lift would grow once more continuously.However, in the case of the sinusoidal models, an additional entity is

shaping the lift curve, namely, the vortices generated by the leading-edge protuberances (allowing the CL to remain at a higher level afterstall), together with the tip vortices and the inevitable resulting

interaction, which seem to be particularly favorable for the S1.5-LLmodel.

B. Low Reynolds Number

1. Wings with Aspect Ratio of 1

The evolutions of the lift coefficient with angle of attack for all thewings with aspect ratio 1 operating at low Reynolds numbers arepresented in Fig. 9. It is clearly observed that the wing models withprotuberances along the leading edge have the potential to generatelarge lift benefits across therange of angles of attack,especially in therange 0 5 deg.

The baseline model CL increases with an unmistakably variablegrowthrateup tothe angle of stall, 19 deg. Similar to thestudiesperformed at moderate Reynolds numbers, lift values recoverimmediately after stall (with a reduction in CL of only 5%), and thelift coefficient keeps increasing toward the maximum investigatedangle of attack. The peak of 0.75 is 36% larger than the value at thestall angle.

The sinusoidal models show, in addition to the higher CL at lowangles of attack, a more linear evolution of the lift coefficient beforethe angle of stall of the baseline model. In line with previous results,the model with the large amplitude and large wavelength of theprotuberances displays notable aerodynamic characteristics, and aminimal lift penalty with respect to the baseline model can only befound in the range 10 15 deg. This is a consequence of thelower average slope in the prestall regime, but the superiority isnonetheless evident. The S1-LS model exhibits the lowestperformance amongthe sinusoidal models, revealing the consistenceof these data with that previously discussed.

Table 4 summarizes the aerodynamic characteristics obtained forthis set of measurements.

2. Wings with Aspect Ratio of 1.5

The lift coefficient for the wings with aspect ratio 1.5 is plotted inFig. 10 as a function of angle of attack. Again, the sinusoidal modelsshow the potential to generate large lift benefits, most notably for0 5 deg and 17 30 deg. Once more, the baselinemodel CL is seen increasing in a nonlinear fashion up to the angle ofstall at16 deg,where the maximumCL of 0.64is reached. The abrupt

Fig. 7 CL vs for the B1.5 wing model atRe 140; 000 showing the

hysteresis loop.

Fig. 8 S1-LL lift values normalized by B1 lift values and S1.5-LL liftvalues normalized by B1.5 lift values, atRe 140; 000.

Fig. 9 CL vs for the wing models with AR 1 atRe 70; 000.


with AR 1 atRe 70; 000


B1 0:007 0.75 30 19S1-LL 0.143 0.82 30

S1-LS 0.121 0.70 30 20S1-SL 0.093 0.77 30 S1-SS 0.130 0.76 30


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stall causes a reduction in lift coefficient of approximately 32%.However, no aerodynamic hysteresis was found at this lowerReynolds number. A confirmation that stall was indeed abrupt wasprovided by theflow visualization portrayed in Figs. 11 and 12 . Just

before stall, a separation bubble is observed in the leading-edgeregion. After stall, this separation bubble has burst and the flow iscompletely separated over the upper surface of the wing. Then,values are seen increasing up to 21 deg, where a furtherreduction takes place. For 25, the evolution is quite similar tothe one at the higher Reynolds number, previously depicted in Fig. 6.

The sinusoidal models present a lower (average) lift slope(although more constant) before the stall angle. The S1.5-SL showsthe highest lift slope among the models with protuberances. The stallis more gradual and less severe, leading to an improved performancein the poststall regime. Whereas at the higher Reynolds numbers, allsinusoidal models stalled first, at low Reynolds numbers, only the

S1.5-LL stalls before the baseline model, namely, at 15 deg. Inthe poststall regime, the lift coefficient evolutions with angle ofattack are identical to those obtained forthe higherReynolds number.

The aerodynamic characteristics for this set of measurements arelisted in Table 5.

3. Discussion

In contrast with the conclusions drawn from the experimentscarried out at moderate Reynolds numbers, the latter data indicatethat, for wings with an aspect ratio of 1 operating at low Reynoldsnumbers, it is advantageous (in terms of lift coefficient) to use asinusoidal leading edge. The lift force produced by the model with

larger amplitude and larger wavelength protuberances is larger thanthat produced by thebaselinethroughout thewhole range of anglesofattack. In Fig. 13, the normalized lift coefficient of this model isplotted against the angle of attack for 10 deg. The graph isrestricted to 10 deg because of the large relative differencebetween the CL values in both sets at low angles of attack (to bediscussed next), which would otherwise preclude a properrepresentation of the data. The results for the higher Reynoldsnumber are also plotted in Fig. 13 to enrich the analysis and betterillustrate the differences between the two regimes. Maximum gainsof the order of 25% in lift can be obtained for 10 deg.

Based on thedata presented before in Figs. 9 and 10 , relative gainsin lift at low angles of attack are expected to be much higher. Aimingto determine the cause of such drastic differences between the twoinvestigated Reynolds number regimes, in Figs. 14 and 15, we plot

thelift coefficient asa function ofangle ofattack at moderate and lowReynolds numbers for the baseline and S1-LL models, respectively.It can be seen that the reduction in Reynolds number leads to asubstantial performance deterioration of the baseline model(particularly at low angles of attack), whereas the S1-LL modelseems to be remarkably insensitive to the Reynolds numbervariation. Behind this unexpected behavior, we have identified aregion of separated flow near the trailing edge of the baseline modeloperating at Re 70; 000, which is much smaller or evennonexistent in the sinusoidal models. This matter is later analyzed inmore detail with the aid offlow visualization for the models with anaspect ratio of 1.5.

Fig. 10 CL vs for the models with AR 1:5 atRe 70; 000.

Fig. 11 Flow visualization for the B1.5 model at 16 deg. Note theapproximate location of the separation point denoted by S and the

wing section contour at the visualization plane.

Fig. 12 Flow visualization for the B1.5 model at 17 deg. Note the

approximate location of the separation point denoted by S and thewing section contour at the visualization plane.

Table 5 Aerodynamic characteristics of the wingswith AR 1:5 atRe 70; 000


B1.5 0.021 0.64 16 16S1.5-LL 0.161 0.65 27.5 15S1.5-LS 0.158 0.62 16 16S1.5-SL 0.101 0.63 16 16S1.5-SS 0.154 0.63 16 16

Fig. 13 S1-LL lift values normalized by B1 lift values atRe 70; 000and 140,000.


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The performance deterioration of the baseline model with anaspect ratio of 1 also translates into a lower stall angle. Interestinglyenough, the maximum CL is only reduced 5%, which may beassociated to the higher average lift slope after the stall angle.Nevertheless, such behavior is likely to be a consequence of theincreased coherence of the tip vortices at low Reynolds numbers[15].

For the wings with an aspect ratio of 1.5, the baseline model is alsomore sensitive to the Reynolds number reduction, as can beconcluded by comparing Figs. 16 and 17 . The former shows CL vs

at moderate and low Reynolds numbers for the baseline model, andthe latter shows these results for the S1.5-LL model. The liftcoefficient of the baseline model is reduced, mainly in the range

0 5 deg, analogous to the observations made at the loweraspect ratio. Now, this is easily understood by analyzing andcomparing Figs. 18 and 19 , which illustrate the behavior of theboundary layer at 3 deg, for moderate and low Reynoldsnumbers, respectively. The immediate conclusion is that, in bothcases, the boundary layer separates in the aft section of the wing.However, at moderate Reynolds numbers, it reattaches to the surfaceforming a recirculation bubble, while at low Reynolds numbers, theseparated shear layer can no longer reattachto thewing surface. Flowvisualization of the S1.5-LL model still showed the formation of a

Fig. 14 CL vs for the B1 wing model atRe 70; 000 and 140,000.

Fig. 15 CL vs for the S1-LL wing model atRe 70; 000 and 140,000.

Fig. 16 CL vs for the B1.5 wing model atRe 70; 000 and 140,000.

Fig. 17 CL vs for the S1.5-LL wing model at Re 70; 000 and140,000.

Fig. 18 Flow visualization for the B1.5 wing model atRe 140; 000

and 3 deg. Note the approximate locations of the separation andreattachment points denoted by S and R, respectively, and the wingsection contour at the visualization plane.

Fig. 19 Flow visualization for theB1.5 wing model atRe 70; 000and

3 deg. Note the approximate location of the separation pointdenoted by S and the wing section contour at the visualization plane.


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[9] Johari, H., Henoch, C., Custodio, D., and Levshin, A., Effects ofLeading-Edge Protuberances on Airfoil Performance, AIAA Journal,Vol. 45, No. 11, 2007, pp. 26342642.doi:10.2514/1.28497

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F. CotonAssociate Editor

http://dx.doi.org/10.1063/1.1688341http://dx.doi.org/10.2514/1.30303http://dx.doi.org/10.2514/1.28497http://dx.doi.org/10.2514/3.12742http://dx.doi.org/10.2514/1.439http://dx.doi.org/10.2514/1.40615http://dx.doi.org/10.2514/1.40615http://dx.doi.org/10.2514/1.439http://dx.doi.org/10.2514/3.12742http://dx.doi.org/10.2514/1.28497http://dx.doi.org/10.2514/1.30303http://dx.doi.org/10.1063/1.1688341

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