Effect of Aspect Ratio on Gurney-Flap Performance
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JOURNAL OF AIRCRAFT Vol. 50, No. 4, July–August 2013
Effect of Aspect Ratio on Gurney-Flap Performance Libin Daniel and Lance W. Traub † ∗
Embry Riddle Aeronautical University, Prescott, Arizona 86301 DOI: 10.2514/1.C032140 10.2514/1.C032140 A low-speed wind-tunnel investigation investigation has been undertaken to establish the effect of wing aspect ratio on Gurneyflapperformance. flapperformance. Character Characterizati ization on is accomplish accomplished ed usinga forcebalanceand flowvisualization flowvisualization.. The Gurney-fla Gurney-flap p lift increm incrementdueto entdueto a shiftin shiftin thezero-li thezero-liftangleof ftangleof attackwasobser attackwasobservedto vedto scalewiththatof scalewiththatof thelift-cu thelift-curveslop rveslopee fordiffere fordifferent nt aspect ratios. As the aspect ratio reduced, a Gurney flap of greater height was required to maximize aerodynamic efficiency. The dependence of aerodynamic parameters (zero-lift angle of attack, minimum drag coefficient, and lift-curve slope) on the Gurney flap s height-to-chord ratio was also examined. ’
0 4 1 2 3 0 C . 1 / 4 1 5 2 . 0 1 : I O D | g r o . a a i a . c r a / / : p t t h | 5 1 0 2 , 4 y r a u n a J n o E G E L L O C D L E I F T S E W & Y R A M N E E U Q y b d e d a o l n w o D
to a delay of the onset of the laminar separation bubble, caused probab probably ly by the end flow flow” [3]. Some Some of the conseq consequen uences ces of wing-t wing-tip ip vortices are a nonlinear lift-curve slope and very high values for the stall angle [4 [4]. The lift generated by low-AR wings can be modeled to be composed of two different sources: linear and nonlinear. The linear linear source source represents represents the presence presence of bound bound circulation circulation.. The nonlinear source embodies the presence of the wing-tip vortices, which cause strong crossflow on the upper surface of the wing, leading to a reduction in pressure and generation of additional lift at moderate and high angles of attack [4 [4]. The lift-curve slope is no longer a constant value for moderate to high angles of attack. An increase in nonlinearity of the lift-curve slope and an increase in the stall stall anglewere anglewere observ observed ed by Torres orres andMueller andMueller [4] witha witha decre decreas asee in aspect ratio. On a slender (delta) wing, such nonlinearity has been associated with the loss of leading-edge (LE) suction [5 [5]. Missio Mission n perfor performan mance ce is direct directly ly relate related d to the maxim maximum um range range and endurance or the payload capabilities of the UAV UAV. An increase in the lift lift capabi capabilit lity y can provi provide de an increa increased sed payloa payload d capabi capabilit lity y. One of the simplest lift augmenting aerodynamic devices is a Gurney flap. A Gurney flap is a small rectangular flap (0.5 to 1.5% of the chord) attach attached ed to the lower lower surfaceof surfaceof a wing/a wing/airf irfoil oil.. It is general generally ly placedat placedat or near the trailing edge of the wing/airfoil and perpendicular to the surface. The Gurney flap functions by increasing the downward deflection of the trailing-edge flow. In essence, it violates the Kutta condition at the trailing edge by creating a finite pressure difference between between the upper and lower lower surfaces. surfaces. The final pressure recovery woul would d then then occu occurr off off surf surface ace,, whic which h is anal analog ogou ouss to a viol violat atio ion n of the the Kutta condition [6 [6]. The Gurney flap increases the effective chord and camber of the airfoil, thereby increasing the circulation. Liebeck [7] suggested suggested a flow pattern pattern in which a virtual virtual cusped cusped trailing trailing edge is formed formed downstr downstream eam of the Gurney Gurney flap from from the shear shear layers layers mergin merging g downs downstre tream am of the flap. flap. It has been been docume documente nted d that that Gurney Gurney flaps, of appropriate height, provide lift augmentation without much effect on drag production [8 [8]. In some cases, a drag reduction has been observed. It has been theorized that if the Gurney flap stays within the boundary layer, no increase in drag is observed [8 [8]. Some of the main benefits of a Gurney flap include no serious structural modificati modifications, ons, no significan significantt drag increase, increase, and significa significant nt lift augmentation. It would be of value to the community to ascertain the effect of aspect ratio on Gurney-flap performance as this is a topic that has receiv received ed little little attent attention ion.. This This study study is a step step towar toward d such such an understand understanding. ing. Moststudies on Gurneyflaps havebeen conducted conducted on airfoi airfoill profil profiles es [6–8]. This This study study focuse focusess on low-a low-aspe spect-r ct-rati atio o AR 3 ( ≤ ) wings, which is consistent with the aspect ratio of small UAVs in operation.
Nomenclature a0
AR c CD CD min CL CL ∕CD CL max CL 3∕2 CL ∕CD CM Cp h h∕c L∕Dmax Rec a.c.∕c α
α α stall α ZL
Δα ZL
= = = = = = = = = = = = = = = = = = = = =
two-dimen two-dimensiona sionall lift-curve lift-curve slope as a spect ratio chord finite finite wing drag coefficient coefficient finite finite wing minimum minimum drag coefficien coefficient t finite finite wing lift coefficient coefficient finite finite wing lift-to-drag lift-to-drag ratio finite finite wing maximum maximum lift coefficien coefficient t finite finite wing lift-curve lift-curve slope endura endurance nce parame parameter ter finite finite wing pitching pitching moment moment coefficient coefficient center center of pressu pressure re Gurney-f Gurney-flap lap height height ratio of Gurney-flap Gurney-flap height height to chord finite finite wing maximum maximum lift-to-drag lift-to-drag ratio chord chord Reynol Reynolds ds number number aerodynamic aerodynamic center position position relative relative to chord angl anglee of atta attack ck stall stall angle angle of attack attack zero-li zero-lift ft angle angle of attack attack shift in zero-lift zero-lift angle of attack
Introduction
T
HE drivin driving g force force behind behind the ever-i ever-incr ncreas easing ing use of small small unmanned aerial vehicles (UAVs) can be attributed to their utility utility and cost effective effectiveness.The ness.The creation creation of educationaldegrees educationaldegrees that focus on UAVs UAVs supports the ever-increasing demand in this field [1 [1]. Today, oday, UAV UAV usageis diverse, diverse, ranging ranging from military military search and rescue and reconna reconnaiss issanc ancee to urban urban highwa highway y traffi trafficc monito monitorin ring g [2]. The The size size of a UAV is defined by its application. With a focus on localized surveillan surveillance, ce, UAVs UAVs are generally generally diminish diminishing ing in size. However, However, if the wings wings are scaled scaled down, down, the effect effectiv ivee Reynol Reynolds ds number numberss become become very very low. To attain a higher Reynolds number, the wings need a higher chord length. If the wing area is constrained, this implies a lower aspect ratio (AR). Zimmerman Zimmerman [3] obse observ rved ed a redu reduct ctio ion n in the the maxi maximu mum m lift lift coeff coeffici icient ent with with a decreas decreasee in aspect aspect ratio. ratio. Howev However, er, this this trend trend reversed at aspect ratios below 1.5. The effects of a low aspect ratio (belo (below w 1.5) 1.5) includ includee an increas increasee in the maximu maximum m lift lift coeffi coefficie cient, nt, “due Received 2 October 2012; revision revision received 28 January 2013; accepted for publication 1 February 2013; published online 13 June 2013. Copyright © 2013 by Lance W. Traub and Libin Daniel. Published by the American Instituteof Instituteof Aeronautic Aeronauticss andAstronautics,Inc.,with andAstronautics,Inc.,with permissio permission. n. Copies Copies of this paper may be made for personal or internal use, on condition that the copier pay the $10.00 per-copy fee to the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923; include the code 1542-3868/13 and $10.00 in correspondence with the CCC. *Under *Undergra gradua duate te Studen Student, t, Aerosp Aerospace ace and Mechan Mechanica icall Engine Engineeri ering ng Department. † AssociateProfesso AssociateProfessor, r, Aerospaceand Aerospaceand Mechanica Mechanicall Engineeri Engineering ng Department Department.. Member AIAA.
Equipment and Procedure Wind-tunnel tests were conducted in Embry-Riddle ’s 2 by 2 ft blower blower wind wind tunnel tunnel.. This This facilit facility y has a measur measured ed turbu turbulen lence ce intens intensity ity of 0.5% and a jet uniformity better than 99% in the jet core. Forcebalance measurements were undertaken using a six-component NK 1217
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flaps were attached to the pressure side trailing edge using tape that spanned the length of the flap, as shown in Fig. 2. The length of the side that was attached to the trailing edgewas keptconstant for all the cases at 0.25 in. Each Gurney flap spanned the respective model. Wind-tunnel tests were carried out for ARs of 1, 2, and 3 and for Gurney flap heights of 1, 2, and 4% of the chord along with a clean configuration case. The Rec was kept at 2.5 × 105 for each test case by setting a test section velocity of 35 m ∕s. This resulted in a total of 12 different test cases. A repeatability test was also carried out for an AR of 3 and Gurney-flap height of 4%. The pitching moment reference location was the quarter chord.
Results and Discussion 0 4 1 2 3 0 C . 1 / 4 1 5 2 . 0 1 : I O D | g r o . a a i a . c r a / / : p t t h | 5 1 0 2 , 4 y r a u n a J n o E G E L L O C D L E I F T S E W & Y R A M N E E U Q y b d e d a o l n w o D
Fig. 1 CAD drawings (in inches) and model image showing spanwise extents of the removable panels.
biotechnical sting balance. A dedicated interface coded in Visual Basic 6 was written for this balance. Balance output voltages were digitized using a National Instruments 16 bit A/D board. Voltages were converted to loads using an internal calibration matrix. Each presenteddata point is theaverage of 5000 readings. Uncertainties for the lift, drag, and pitching moment coefficients were estimated as 0.01, 0.005, and 0.01, respectively. The reference area used to obtain the aerodynamic coefficients corresponded to the wing’s projected area. The model’s angle of attackwas setand measured using a feedback loop in conjunction with a Midori angle sensor. Angle-of-attack repeatability was established as better than 0.1 deg. Wall corrections were notapplied as thetestswere comparative in nature. Wind-tunnel testing was conducted at a freestream velocity of 35 m∕s, yielding a Reynolds number of 2.5 × 105 based on the reference chord lengthof 0.127 m. During testing, the models were pitched from −6 to 28 deg in 2 deg increments. The variable-aspect-ratio wind-tunnel model was rapid prototyped from acrylonitrile butadiene styrene using Embry-Riddle’s rapidprototyping facilities, as shown in Fig 1. The airfoil section was a S8036 with a thickness of 16%. Gurney flaps as shown in Fig. 2 were constructed using thin brass shim stock and were bent and cut to shape using a metal bender and shear. The angle was kept as close to 90 deg as possible to maintain commonality with other studies. The
Repeatability plots for AR 3 anda Gurney-flap heightof 4% are shown in Fig. 3. The repeatability is seen to be good. The baseline configuration refers to that with no Gurney flap (h∕c 0% ). For all cases, lift augmentation is observed with the incorporation of the Gurneyflap, as shown in Fig. 4. A negative shift in the zero-lift angle of attack suggests that the Gurney flap adds camber to the airfoil profile. However, unlike a normal trailing-edge flap, no significant impact is observed on the stall angle. The lift-curve slope for the Gurney-flap configurations is observed to be higher than that of the baseline configuration. A Gurney flap violates the Kutta condition at the trailing edge and reduces the adverse pressure gradient on the suction surface [9]. This may reduce the uppersurface boundary-layer displacement thickness leading to a reduced decambering effect, at moderate angles of attack [10]. Additionally, the thinning of the lower-surface boundary layerwith α maymake the Gurney flap more effective with incidence [9]. The lift curves for AR 1 are notably nonlinear. This can be attributed to thevortex lift produced from the side-edge sheets [5]. It is also of note that the AR 1 wing didnot stall forany configuration. This ischaracteristic of low-AR wings [3,4]. The effect of the Gurney flap on drag depends on the height of theGurney flap [7], as shown inFig. 5. The dashedline represents the drag-due-to-lift component assuming elliptical loading, in which the Oswald efficiency factor is assumed to be 1, for h∕c 0%. It can be seen that themajorityof thedrag is this drag-due-to-lift componentas 1.4
AR = 3 h/c = 4%
1.2 1.0 L
0.8
C 0.6
0.4 0.2 0.0 -5
0
5
10 α
0.0
15
20
,deg
-0.1 m
C
-0.2
-0.3 0.4
RUN 1 RUN 2
0.3 D
C 0.2
0.1 0.0 0.0
0.2
0.4
0.6
0.8
1.0
CL Fig. 2
Gurney flap on the wing model with AR
1.
Fig. 3
Data repeatability.
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0.3
1.4 1.2
AR=3
AR=3
1.0
0.2
0.8 D
L
C 0.6 0.4
C
0.1
0.2
100% LE Suction
0.0 -0.2
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AR=2
1.0
0.3
h/c=4% h/c=2% h/c=1%
AR=2
h/c=0%
0.8 L
D
C 0.6
0 4 1 2 3 0 C . 1 / 4 1 5 2 . 0 1 : I O D | g r o . a a i a . c r a / / : p t t h | 5 1 0 2 , 4 y r a u n a J n o E G E L L O C D L E I F T S E W & Y R A M N E E U Q y b d e d a o l n w o D
C 0.2
0.4
h/c=4%
0.2
0.1
h/c=2%
0.0
h/c=1%
-0.2 1.4
0.0 0.6
h/c=0%
1.2
0.5
1.0
AR=1
0.4
0.8 L
AR=1
D
C 0.6 0.4
C 0.3
0.2
0.2 0.1
0.0 -0.2 -5
0
5
10
15
20
25
0.0 -0.2 0.0
30
, deg
α
Fig. 4
Effect of Gurney-flap height and aspect ratio on lift coefficient.
opposed to airfoil pressure drag. The 1% Gurney-flap configurations have a lower minimum drag than the baseline configurations (yieldinga drag curve lowerthan that for 100% leading-edgesuction) for AR 2 and3. This could be attributed to theheight of theGurney flap being less than that of the boundary-layer thickness. Also, the Gurney-flap configurations are at a lower angle of attackas compared to the baseline configuration for the same lift coefficient. This may result in a sectional pressure drag benefit. However, a drag penalty is observed for a 4% Gurney-flap configuration. This may be due to an increase in the base drag because a 4% Gurneyflap probably does not stay within the boundary layer. The 4% Gurney flap’s drag penalty is observed to diminish with a reduction in the aspect ratio, as shown in Fig. 5. With a reduction in aspect ratio, the spanwise pressure gradients are more pronounced. Consequently, the flowfield near the trailing edge for a small-aspectratio wing could be highly three dimensional. Three-dimensional (3-D) disturbances have been observed to lead to a decrease in the drag values for Gurney-flap configurations as observed by Meyer et al. [11]. Gurney flaps on an airfoil have been associated with the periodic shedding of a von Karman vortex street [12]. At low aspect ratios, this three dimensionality of the flow may serve to disrupt the periodic shedding fromthe Gurney flap, leading to a decrease in base drag. Figure 6 summarizes longitudinal moment-based characteristics. The effect of the Gurney flaps on the pitching moment coefficient is shown in Fig. 6a . A cambering effect due to the Gurney flap can be observed in all the cases. The nose-down pitching moment magnitude increases with an increase in the Gurney-flap height, a characteristic of an increase in camber. With greater aspect ratios, a reduction is observed in the change of the pitching moment curve slope (dCm ∕dCL ) with flap attachment. A more negative pitching moment curve slope is indicative of the rearward movement of the aerodynamic center. For AR 1, nonlinearity in thepitchingmoment is observed.This can be attributed to the vortex lift from the wing-tip sheets, which varies with sin2 α [13]. The increase in loading due to a Gurney flap
0.2
0.4
0.6
0.8
1.0
1.2
1.4
CL Fig. 5
Effect of Gurney-flap height andaspect ratio on drag coefficient.
would increase thegradient in the spanwise load distribution near the wingtips and, thus, the strength of the trailing vorticity. Figure 6b shows the correlation between the pitching moment and lift coefficient increments for a given α , a dependence theoretically established in [14] for an airfoil. The increment is with respect to h∕c 0% . As seen, the correlation with the sectional thin airfoil theory results of Liu and Montefort [14] (denoted as “TA” where ΔCL − 4ΔCm ) improves as AR increases, a consequence of the diminishing impact of 3-D effects on the location of the wing ’s aerodynamic center, as will be clarified. Figures 6c and 6d present the calculated location of the wing’s center of pressure and aerodynamic center (a.c.). The addition of the flap is seen to movethe center of pressure aft for all ARs compared to h∕c 0% . For a given flap dimension, the center-of-pressure location is weakly affected by AR for moderate to high CL . The Cp initially moves forward rapidly at low CL andthen levelsoff at higher loadings. The aerodynamic center, Fig.6d, shows a moderate aft shift with the addition of the Gurney flap. The height of the flap does not appear to have a marked impact on the a.c. location. Note that, for AR 1 , the a.c. moves progressively back with increasing CL . This is shownwith greater clarity when thea.c. is presentedas a function of the angle of attack. Also, for AR 1 and 2, h∕c 0% shows an a.c. location in front of thequarter chord (the momentreference), whereas for h∕c > 0, thea.c. is located aftof thequarter chord.Accounting for the a.c. deviation from the quarter chord and its movement (i.e., multiplying this deviation by CL accounting for the sign of the imposed moment) yielded a correction to themoment incrementdata, shown in the right-hand-side plot of Fig. 6b. As seen, the correlation with the two-dimensional theory of Liu and Montefort [14] is improved. The lift-to-drag ratio and the endurance parameter are shown in Figs. 7 and 8. It canbe observed that the 1% Gurney flap provides the highest lift to drag ratio and endurance parameter value for aspect ratios of 2 and 3. For AR 1, a 2% Gurney flap provides a slightly higher value for the lift-to-drag ratio and endurance parameter than the 1% Gurney flap. This is due to the small CD min penalty observed
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0.0
-0.1 m
C
-0.2 AR=3 -0.3 0.0
-0.1 m
C
h/c=4%
-0.2 AR=2
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h/c=2% h/c=1%
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C
-0.2
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-0.3 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 CL
a)
0.9 0.8 0.7 e 0.6 g n 0.5 a h C0.4 L C0.3 0.2 0.1 0.0 0.9 0.8 0.7 e 0.6 g n 0.5 a h C0.4 L C0.3 0.2 0.1 0.0 0.9 0.8 0.7 e 0.6 g n 0.5 a h C0.4 L C0.3 0.2 0.1 0.0 -0.12
TA Theory h/c=4% h/c=2%
AR=3
h/c=1%
AR=2
AR=1
-0.09
-0.06 -0.03 CMChange
0.9 AR=2 0.8 0.7 e g 0.6 n a 0.5 h C0.4 L C0.3 0.2 0.1 0.0 0.9 Data corrected for AR=1 a.c. movement 0.8 0.7 e 0.6 g n 0.5 a h C0.4 L C0.3 0.2 0.1 0.0 -0.12 -0.09 -0.06 -0.03 0.00 CMChange
b) 2.0
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c)
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4 α
8 , deg
12
16
d)
Fig. 6 Effectof Gurney-flap heightand aspectratioon longitudinalmoment-based characteristics: a) pitching moment, b) momentincrement, c) centerof-pressure location, and d) aerodynamic center location.
for the2% Gurneyflap coupled with lift augmentation. A 4% Gurney flap generally provides attenuated performance. This can be attributed to the drag penalty associated with this flap. The 1% Gurneyflapleads toan increase of13, 19, and 17% and anincreaseof 4, 12, and 9% in the maximum lift-to-drag ratio and the maximum endurance parameter for aspect ratios of 1, 2, and 3, respectively, compared to the baseline configuration. The minimum drag coefficient benefit of some flap configurations yields Gurney 3∕2 geometries with C L ∕CD and C L ∕CD ratios greater than that with 100% suction (which are based on CD min for h∕c 0% ).
Thevariation of themaximum lift-to-drag ratio versusthe Gurneyflap height-to-chord ratio is shown in Fig. 9. The greatest increase is observed for a 1% Gurney flap. The drag penalty associated with the 4% Gurneyflap reduces itsmaximum lift-to-drag ratio. It is observed to be comparable to the baseline configuration. For an aspect ratio of 3, a 1% Gurney flap has a greater maximum lift-to-drag ratio than a 2% Gurney flap. However, as the aspect ratio is reduced, the 2% Gurney flap is observed to be comparable to the 1% Gurney flap. Within the realm of the data collected in this experiment, it can be suggested that, with a reduction in aspect ratio, the height of the
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14
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) D / L (
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h/c=4%
2
h/c=2%
0 6
h/c=1%
6
4
h/c=0%
AR=1
0
1
2
4
Fig. 9
D
3
4
h/c, %
100% LE Suction
Effect of Gurney-flap height on maximum lift-to-drag ratio.
C / L 2 C
0
6
-2 0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
CL Fig.7
Effectof Gurney-flapheight andaspect ratioon lift-to-dragratio.
Gurney flap that provides the greatest lift-to-drag ratio is observed to increase. Liu and Montefort [14] suggest a “benefit ” parameter, which evaluates the performance of an aerodynamic effecter accounting for its impact on both the lift and drag. The relation is given by 10
AR=3
8 D
6 C /
g , n i g r a M t i f e n e B
g , n i g r a M t i f e n e B
g , n i g r a M t i f e n e B
0
AR=2
6 D
4
C
2
h/c=1%
AR=2
5 4 3 2
h/c=4%
1
h/c=2%
0
h/c=1% AR=1
5 4 3 2 1 0 0
5
10 α
Fig. 10
15
20
, deg
Effect of Gurney-flap height and AR on the benefit margin.
h/c=0%
AR=1
100% LE Suction / 3 L
0
h/c=2%
D
C / 2
1
-1
h/c=4%
0 4
2
-1 6
2
/ 3 L
3
6
C 4
C / 2
AR=3
4
-1
2 / 3 L
8
5
g
− 6 ΔCD 9 ΔCL 7 CD 7 CL
(1)
2
C
0
0.0
0.2
0.4
0.6
0.8 CL
1.0
1.2
1.4
Fig. 8 Effect of Gurney-flap height and aspect ratio on endurance parameter.
where thedifferencesare with respect toh∕c 0%. A g value greater than zero indicates a net benefit. As seen in Fig. 10, flap heights of 1 and 2% show a net benefit, which decreases with incidence. The 4% flap, despite its significant lift increment, is hampered by its drag penalty such that g is greater than zero for low to moderate incidence only. In this study, the stall angle is defined as the angle in which the lift coefficient has an identifiable maximum. For a Gurney-flap height of
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25
0.04 AR=3 AR=2 AR=1
20 0.03
15 g e d , L L A T S
C
Stall Angle
α
AR=3
10
AR=2
0 4 1 2 3 0 C . 1 / 4 1 5 2 . 0 1 : I O D | g r o . a a i a . c r a / / : p t t h | 5 1 0 2 , 4 y r a u n a J n o E G E L L O C D L E I F T S E W & Y R A M N E E U Q y b d e d a o l n w o D
n i m D 0.02
5
1.4 1.2 1.0 L0.8 C 0.6 0.4 0.2 0.0 -0.2
0.01
-5
0
5
10 α
15
20
25
30 0.00
, deg
0
0 0
1
2
3
Fig. 13
AR=3 AR=2 AR=1
-2
) g e d ( L Z α ∆
-4
-6 0.05
0.10
(h/c)
Fig. 12 attack.
3
4
Effect of Gurney-flap height on minimum drag coefficient.
Effect of Gurney-flap height on stall angle.
0
0.00
2
h/c, %
4
h/c, % Fig. 11
1
0.15
0.20
0.5
all three cases are observed to have a similar slope, as shown in Fig. 12. The minimum drag coefficient also reduces with an increase in the aspect ratio, as shown in Fig 13. This is corroborated by the data obtained by Zimmerman [3]. An explanation by Zimmerman suggests a penalty associated with tip drag. As the aspect ratio decreases, the penalty due to tip drag contributes more toward the total drag. Becausethe tipdrag values do notchange with aspectratio, at a lower aspect ratio, the total drag coefficient obtained is higher. A reduction in minimum drag coefficient is obtained for the 1% Gurney-flap configuration, as shown in Fig. 13, supporting the inference that it lies withinthe boundary layer anddoes notcontribute significant base drag. For Gurney-flap heights greater than 1%, the slope of the line increases with an increase in aspect ratio. A similar increase in the minimum drag coefficient was observed by Traub for an annular wing equipped with a Gurney flap [15]. Two different theoretical approaches were used to estimate the liftcurve slope for the clean configurations. The Lamar code [17] and Helmbold’s equation [13] were used to obtain the percent difference in the computed and experimental lift-curve slopes. The lift curve for a small-AR wing can be calculated using a simplified equation dueto Helmbold [13]:
Effect of Gurney-flap height on normalized zero-lift angle of
CL α
less than 2%, the stall angle is observed to remain unaffected compared to the baseline configuration as shown in Fig. 11, as initially observed by Liebeck [7]. The 4% Gurney flap reduces the stall angle. A Gurneyflap leads to a higher leading-edge suction peak anda lower adverse pressure gradient [9].A4%Gurneyflapmaylead to such an increase that theadverse pressure gradient is notattenuated [9]. Thezero-lift angle of attack wascalculated by extrapolating thelift curve. Data points from −4 to 4 deg were used for the extrapolation. Because the lift curve was observed to be nonlinear for AR 1, a second-degree polynomial fitwas used to obtainthe zero-lift angle of attack. For theremainingcases, a linear curve fit wasused. An almost linear decrease in the zero-lift angle of attack is observed with an increase in the Gurney-flap height, as shown in Fig. 12. A dependency upon h∕c as well as upon h∕c has been documented [14–16]. This behavior is seen to be preserved for finite-AR wings and Gurney flaps of moderate length. The aspect ratio does not seem to affect the change in zero-lift angle of attack significantly because
p
1
a
0 a0 2 1∕2 π AR
(2)
a0 π AR
Table 1 Comparison of computed and experimental lift-curve slopes CL values, 1 ∕ deg
AR1 AR2 AR3 Experimental 0.0259 0.0426 0.0555 Helmbold’s equation 0.0259 0.0454 0.0587 Lamar code 0.0259 0.0442 0.0598 α
Table 2 Percent difference between computed and experimental lift-curve slopes.
Method Helmbold’s equation Lamar code
AR1, %
AR2, %
AR3, %
0 0
6.57 3.75
6.72 7.74
DANIEL AND TRAUB
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increase in Gurney-flap height, a moderate increase in the lift-curve slope is also observed. This increase in lift-curve slope can be considered to be a viscous effect due to the relative displacement thickness of the upper and lower surfaces and the thinning of the pressure side boundary layer with α , as explained before [10]. The thinning of the boundary layer on the pressure side also makes the Gurney flap more effective, as the angle of attack increases [9]. The observed variationin the lift-curve slope is small, as presented in Fig. 14. For a given shift in the zero-lift angle of attack, the change in the lift coefficient can thus be computed as ΔCL C Lα α ZLh
∕c0
0 4 1 2 3 0 C . 1 / 4 1 5 2 . 0 1 : I O D | g r o . a a i a . c r a / / : p t t h | 5 1 0 2 , 4 y r a u n a J n o E G E L L O C D L E I F T S E W & Y R A M N E E U Q y b d e d a o l n w o D
Fig. 14
Effect of Gurney-flap height on lift-curve slope.
where a0 is the theoretical lift-curve slope, often assumed to be 0.11 deg−1 or 2π rad−1. Helmbold’s equation was chosen because it is valid for all relevant ARs. Tables 1 and 2 give the CL values obtained and the percent differencewhen compared to the experimental results. The difference did not exceed 8%. The variation in the lift-curve slope with Gurney-flap height, as compared to the baseline configuration, is shown in Fig. 14. With an α
6
1.2
AR=1
0.8
D
AR=1
4
C / L C
L
C0.6 0.4
2
0.2 0.0 0 0.0
-0.2 -5
0
5
10 α
15
20
25
30
0.2
0.4
0.6
0.8
1.0
1.2
1.4
CL
, deg
1.4 8
1.2 1.0 L
6 AR=2
0.8
D
C0.6 0.4
4
C / 2 L C
0
0.2
AR=2
-2
0.0 -0.2 -5
0
5
10 α
1.4 1.2
15
20
25
-4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 CL
30
, deg
12 10
AR=3
1.0 0.8
D
L
8
C / L 6 C
C0.6 0.4
AR=3
4
0.2
2
0.0 -0.2
0 -5
0
5
10 α
Fig. 15
15
, deg
20
25
30
α ZL h∕c
(3)
This shows that, with an increase in the AR, the change in the lift coefficient, for a given Gurneyflap, increases because of a larger liftcurve slope. This may be observed in Fig. 4. With an increase in the aspect ratio, the lift augmentation of the Gurney flap, at a given angle of attack, increases. Consequently, the effect of a Gurney flap may be estimated using sectional data to ascertain α ZL in conjunction withthe finite wing’s lift-curve slope. Forall the clean configuration cases, at the angle for the maximum lift-to-drag ratio,a deflection is observed in thelift curve,as shown in Fig. 15. This deflection coincides with the angle or CL in which CL ∕CD max is achieved. A study by Lee and Pereira [18] infers that, at the maximum lift-to-drag ratio, the axial tip vortex switches from being a wakelike to a jetlike vortex. It may thus be inferred in this study that the vortex lift becomes more predominant after the tip vortex switches to a jetlike vortex structure. To further understand the dependency of aspect ratio on the Gurney-flap performance, flow visualization was performed using a mixture of titanium dioxide, linseed oil, and paraffin at angles of attack of 2 and 10 deg. An AR 2 clean configuration and a 2%
1.4 1.0
−
0.0
0.2
0.4
0.6
0.8
CL
Angle in which vortex switches from wakelike to jetlike.
1.0
1.2
1.4
1224
DANIEL AND TRAUB
h/c=0%
Attached Laminar Flow
h/c=2%
Wing tip
Laminar Separation Bubble
=2º
α
Attached Turbulent Flow
0 4 1 2 3 0 C . 1 / 4 1 5 2 . 0 1 : I O D | g r o . a a i a . c r a / / : p t t h | 5 1 0 2 , 4 y r a u n a J n o E G E L L O C D L E I F T S E W & Y R A M N E E U Q y b d e d a o l n w o D
a)
c)
Attachment Line
Tip Vortex induced sidewash Separation Line =10º
α
b)
d)
Fig. 16
TiO2 flow visualization pictures for AR
Gurney-flap configuration were used for the flow visualization. With an increase in the angle of attack, a forward shift in the bubble is observed, as shown in Figs. 16a and 16b. Unusually, the bubble seems to increase in size as well. Side-edge vortices are also observed to be larger with more pronounced sidewash, yielding to a stronger crossflow over the wing. The Gurney flap is observed to strengthen the crossflow over the wing, as shown in Figs. 16a and 16c. This can be observed by the stronger tip-vortex-induced sidewash and a more pronounced attachment line for Gurney-flap configurations. This further implies that the increased loading due to a Gurney flap intensifies the side-edge vortices. Similar trends were observed for aspect ratios of 1 and 3, as well.
IV.
Conclusions
A low-speed wind-tunnel investigation was undertaken to explore the effect of aspect ratio on the aerodynamic characteristics of a Gurney flap. At a given angle of attack, the lift augmentation due to the flap increased with aspect ratio. It was seen that the Gurney flap lift increment, referenced to the shift in the zero-lift angle of attack, scales well with the lift-curve slope change due to aspect ratio. The increase in the lift-curve slope and the shift in the zero-lift angle of attack due to a Gurney flap were independent of the aspect ratio. The drag penalty due to a large Gurney flap was observed to reduce with aspect ratio.The shift in zero-lift angle of attack wasobservedto have a h∕c dependency. The height of the most aerodynamically efficient Gurney flap was noted to increase as the aspect ratio decreased.
p
Acknowledgments The authors would like to thank the associate editor and reviewers, whose comments and suggestions improved the clarity and focus of this article.
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2
(flow is from top to bottom).
Concepts at the Undergraduate Level: One Approach,” AIAA Atmospheric FlightMechanics and Exhibit , AIAA,Austin, TX,11 –14 Aug. 2003; also AIAA Paper 2003-5619. [2] Ro, K., Oh, J., and Dong, L., “ Lessons Learned: Application of Small UAV for Urban Highway Traffic Monitoring,” 45th AIAA Aerospace Sciences Meeting and Exhibit , AIAA, Reno, NV, 8 –11 Jan. 2007; also AIAA Paper 2007-596. [3] Zimmerman, C. H., “Characteristics of ClarkY Airfoils of Small Aspect Ratios,” NACA TR-431, 1933. [4] Torres, G. E., and Mueller, T. J., “Aerodynamic Characteristics of Low Aspect Ratio Wings at Low Reynolds Numbers,” Fixed And Flapping Wing Aerodynamics For Micro Air Vehicles Applications , edited by Mueller, T. J., Progress in Aeronautics and Astronautics, Vol. 195, AIAA, Reston, VA, 2001, pp. 115 –139, Chap. 7. [5] Polhamus, E. C., “Predictions of Vortex-Lift Characteristics by a Leading-Edge-Suction Analogy,” Journal of Aircraft , Vol. 8, No. 4, 1971, pp. 193–199. doi:10.2514/3.44254 [6] Traub, L. W., and Agarwal, G., “Aerodynamic Characteristics of a Gurney Flap at Low Reynolds Numbers,” Journal of Aircraft , Vol. 45, No. 2, 2008, pp. 424 –429. doi:10.2514/1.28016 [7] Liebeck,R. H., “Designof a SubsonicAirfoilsfor High Lift,” Journal of Aircraft , Vol. 15, No. 9, 1979, pp. 547 –561. doi:10.2514/3.58406 [8] Gigue’re, P., Dumas, G., and Lemay, J., “Gurney Flap Scaling for Optimum Lift-to-Drag Ratio,” Journal of Aircraft , Vol. 35, No. 12, 1997, pp. 1888–1890. [9] Maughmer, M. D., and Bramesfeld, G., “Experimental Investigation of Gurney Flaps,” Journal of Aircraft , Vol. 45, No. 6, 2008, pp. 2062–2067. doi:10.2514/1.37050 [10] Traub, L. W., andAgarwal,G., “Exploratory Investigation of Geometry Effects on Gurney Flap Performance,” Journal of Aircraft , Vol. 44, No. 1, 2007, pp. 351 –353. doi:10.2514/1.28385 [11] Meyer, R., Hage, W., and Bechert, D. W., “ Drag Reduction on Gurney Flaps by Three-Dimensional Modifications,” Journal of Aircraft , Vol. 43, No. 1, 2006, pp. 132 –140. doi:10.2514/1.14294 [12] Jeffrey, D., Zhang, X., and Hurst, D. W., “Aerodynamics of Gurney Flapson a Single-ElementHigh-Lift Wing,” Journal of Aircraft , Vol.37,
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No. 2, 2000, pp. 295 –301. doi:10.2514/2.2593 [13] Thwaites, B., Incompressible Aerodynamics , Dover, New York, 1960, p. 341. [14] Liu, T., and Montefort, J., “ Thin-Airfoil Theoretical Interpretation for Gurney Flap Lift Enhancement,” Journal of Aircraft , Vol. 44, No. 2, 2007, pp. 667–671. doi:10.2514/1.27680 [15] Traub, L. W., “ Effect of Gurney Flap on Annular Wings,” Journal of Aircraft , Vol. 46, No. 3, 2009, pp. 1085 –1088. doi:10.2514/1.43096
0 4 1 2 3 0 C . 1 / 4 1 5 2 . 0 1 : I O D | g r o . a a i a . c r a / / : p t t h | 5 1 0 2 , 4 y r a u n a J n o E G E L L O C D L E I F T S E W & Y R A M N E E U Q y b d e d a o l n w o D
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[16] Cavanaugh, M. A., Robertson, P., and Mason, W. H., “WindTunnel Test of Gurney Flaps and T-Strips on an NACA 23012 Wing,” 25th AIAA AppliedAerodynamics Conference , AIAA,Miami, FL,25 –28 June 2007; also AIAA Paper 2007-4175. [17] Lamar, J. E., “ Extension of Leading-Edge Suction Analogy to Wings with Separated Flow Around the Side Edges at Subsonic Speeds,” NASA TR-R-423, Oct. 1974. [18] Lee, T.,and Pereira,J., “Nature of Wakelike and Jetlike Axial Tip Vortex Flows,” Journal of Aircraft , Vol. 47, No. 6, 2010, pp. 1946 –1954. doi:10.2514/1.C000225
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