AIAA-2005-1230

43rd AIAA Aerospace Sciences Meeting and Exhibit10 - 13 January 2005, Reno, Nevada

AIAA 2005-1230

Copyright ©

43rd AIAA Aerospace Sciences Meeting and Exhibit10-13 January 2005, Reno, NV

American Institute of Aeronautics and Astronautics

STALL HYSTERESIS OF AN AIRFOIL WITH SLOTTED FLAP

Kasim Biber*

Istanbul, Turkey 34870

* Engineering Consultant. Mailing Adress: Karliktepe Mah, Serap Sok, No 4/10, Kartal, Istanbul, Turkey. E-mail: kxbiber@yahoo.com, Senior Member AIAA. Copyright 2005 by Kasim Biber. Published by AIAA Inc, with Permission. All Rights Reserved.

AbstractStall hysteresis discovered in wind tunnel

performance of GA(W)-2 airfoil with 25%chord slottedflap is examined further by using the data obtained for lift,pitching moment, surface pressure distribution and hot filmvelocity vector. Test cases include 30 and 40 deg flapdeflections each having an optimum and narrow gap atchord Reynolds number of 2.2 million and Mach number of0.13. The flap optimized to produce the highest Clmax foreach flap angle apparently did not have a proper contourand nose location for the slot flow to function effectively atoff-design conditions. It is shown that suction pressuresover flap, suppressed by thickening wing wake at stall, arenot reversible to their pre-stall values within the decreasingα side of loop. It is suggested that the flap design includethe use of a new flap parameter called slot flow angle todescribe the slot flow orientation and a pressure recoveryfactor to select a proper contour for flap upper surface.

Nomenclaturec = mean chord of flap-nested airfoilCl = lift coefficientClmax = maximum lift coefficientCm = pitching moment coefficientCp = static pressure coefficient, ≡ (p-p∞)/q∞CPmin = minimum pressure coefficientCP@0.95c = pressure coefficient at 95%c upper surfaceCPR = pressure recovery coefficient factorG/c = gap-to-chord ratioO/c = flap overlap-to-chord ratiop = local static pressurep∞ = free-stream static pressureq∞ = free-stream dynamic pressureRe = chord based Reynolds numberx, y = airfoil coordinates; x is along chord lineXf, Yf = flap pivot coordinates; Xf is along airfoil

chord lineα = angle of attack (degree)β = slot flow angle at flap gap location (degree)δ = flap deflection angle (degree)

I. IntroductionStall hysteresis as demonstrated in a wind tunnel is a

phenomenon where the stall inception and stall recovery donot occur at the same angle of attack. If present, it canresult in severe control problems in stall. The hysteresis hasbeen commonly observed1-3 for some single airfoilsoperating at Reynolds numbers below 1 million. At low Re,there is usually a laminar separation bubble thatcharacterizes the flow over airfoils. The bubble contracts insize and trips the boundary layer into turbulent flow withincreasing α. It bursts at stall, and this causes an abrupt fallin Cl. Angle of attack may have to be reduced significantlyfor an attached flow on upper surface. In the process, liftcoefficient is not restored, causing a reduction in Clmax. Thestall hysteresis is sensitive to changes in wind tunnel flowquality and acoustics.2 It decreases in size and eventuallydisappears with Re. However, it is reported by Biber andZumwalt4 that the hysteresis reappears at relatively high Reof 2.2 million for the GA(W)-2 airfoil equipped with 25%cslotted flap.

The hysteresis on the flapped airfoil also occurred inthe stall region and caused in average 25% drop in liftcoefficient. Its size was shown to vary as function of flapangle and gap. Similar results are also reported5 recently inwind tunnel tests of a three-element airfoil but at relativelylow Re of 1 million. In these tests, flap deployment isclearly shown to result in stall hysteresis. Figure 1illustrates the flow field for a typical flap position. There isa slot flow between the boundary layers from cove and flapupper surface. For optimum performance, the slot flowextends downstream so that the boundary layers do notmerge until a location about the flap trailing edge6. The slotflow magnitude is determined by the gap, but its orientationwith respect to main wing varies primarily with overlapsetting. The flap parameters are optimized to obtain the bestairfoil performance. However, this has been traditionallydone with only increasing α. The hysteresis appears to bean off-design phenomenon and occurs only if the airfoil αis lowered from its post stall range. A proper flap settingshould provide a desired performance not only at design but

2005 by Kasim Biber. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission.

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also at off-design conditions. This requires a throughunderstanding of flap flow field including the slot flow.Smith7 has details of slot flow effects on high lift airfoils,but his discussion does not consider the hysteresis.

Fig. 1 Illustration of slot flow extension over flap.

In this article, the flap flow field has been examinedby using wind tunnel data obtained for CP distribution,velocity vectors and flow visualization in addition to thecompanion publication,4 which has limited data andconcentrates on airfoil force and moment characteristics.Detailed surface pressure distribution data allows thedefinition of a pressure recovery factor for each airfoilelement. Also, attempt is made to guide flap designers byusing the slot flow angle as a new flap parameter. Theprocedure for wind tunnel tests and flap optimization is alsogiven for completeness. The paper is based on the overallexperimental program8 conducted for five test cases offlapped GA(W)-2 airfoil. Flow field data for the sameairfoil is also reported in a separate paper.9

II. Experimental MethodologyA. Wind Tunnel and Test Model

The tests were conducted at Wichita State University(WSU) subsonic wind tunnel with 2.13x 3.05 m (7x10 ft)test section fitted with a 2.13 m high (7 ft) and 0.914 m (3ft) wide two-dimensional inserts,10 which is a closed returntunnel with atmospheric test section static pressure. Thetunnel is equipped with a pyramidal type balance thatmeasures forces and moments with linearized wallcorrections, as an average of 10 readings 0.2 seconds apart.The test model was made of a rectangular wing of 13%cthick GA(W)-2 airfoil with 25%c single-slotted flap,having a reference chord of 0.61 m (2 ft) at flap-nestedposition and a span of 0.914 m (3 ft). The airfoil has itsmaximum thickness of 0.13c at 0.38c and camber of0.0218c at 0.62.8c locations. Along the mid-span of mainwing and flap, there were 69 pressure taps, connected topressure transducers for surface pressure measurements.The model was connected to the external balance systemand pivoted at 0.5c station, considering the tunnelcenterline as horizontal.

B. Test ConditionsTests were made at Re (based on flap-nested mean

chord) of 2.2 x106, dynamic pressure of 1150 N/m2 (24lb/ft2), and Mach 0.13. The test section turbulence level wasless than 1%. Boundary layer transition on main airfoilelement was fixed at 5%c upper and 10%c lower surface byusing 2.4-mm (0.1-in) wide trip strips. The flow two-dimensionality in the test section was evaluated byvisualization of separated flow patterns on the model.Tempera and kerosene flow showed a change in two-dimensional flow character near sidewalls with airfoilstalled. Beyond the stall, a spanwise surface flowcomponent within the separated zone appeared andextended towards the juncture of the model and sidewall,where a vortex pair formed and shed at the model trailingedge. However, this was limited to the outer 25% of thespan. No boundary layer control was employed to reducethe 3-dimensional flow patterns. The sidewall boundarylayer did not have significant effect on the airfoil stallcharacteristics. This was probably due to the relativelyshort upstream length of the sidewalls, 1.06 m (3.5 ft) fromthe model leading edge. Besides tempera and kerosene,tufts were attached to the model upper surface tosupplement the above results.

C. Data Collection and UncertaintyLift, drag and pitching moment were measured for all

test configurations using the tunnel external balance andreduced to coefficient form as Cl, Cd, and Cm. The resultsfor force and moment agree reasonably well with the Ref10 data, but the α range of present tests, −8 deg to about 20deg, was relatively higher. The large α range within tunnelsafety limits allowed the airfoil to be evaluated forhysteresis for both flap-nested and deflected cases. Themodel was initially set to α=0 deg at wind-off and then thetunnel speed was increased to the one corresponding to thetest Re of 2.2x106. Once the airflow was stabilized in thetunnel, α was first decreased to –8 deg and then increasedto a post-stall value following a prescribed schedule havingsmaller intervals near the stall. After reaching its maximum,α was lowered back to –8 deg with the same schedule asbefore without stopping the tunnel to study the hysteresiseffects. The data uncertainties are as follows: for lift, ±0.9Nand ±0.001 (∆Cl), for pitching moment ±0.1N-m and±0.0003 (∆Cm), for pressure transducers ±2.4 N/m2 and±0.004 (∆Cp), for angle of attack ±0.05 deg, and for flapangles ±0.5 deg.

D. Flap Setting and ParametersWind tunnel tests were made in a test matrix of flap

settings as shown in Table 1. The test matrix includes flap-nested and -deflected 30 and 40 deg cases, each having anoptimum and a narrow gap. The selection of test cases wasbased on the flap optimization studies of Wentz,10

conducted at the WSU in collaboration with NASA. Figure2 shows the geometry of flap setting and parameters. Itincludes the percent-chord Xf and Zf locations of the

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optimum gap for 30 and 40 deg flap deflections. When theflap is nested with the main wing, its quarter-chordaerodynamic center at 0.8125c horizontal and 0.01c verticallocations is considered as the origin of Xf and Zf coordinatesystem. The flap is rotated in this coordinate system foreach flap angle and then translated in first horizontal andthen vertical directions to obtain various gaps.

Table 1: Test matrixCases δ (deg) G/c O/c β (deg)

A 0 0 0 0B 30 0.03 0 21C 30 0.02 0 33D 40 0.015 − 0.01 67E 40 0.0115 − 0.007 55

Fig. 2 Geometric view of flap setting parameters for 30 and 40deg flap deflections.

Flap overlap is referenced to a line normal to the mainwing trailing edge. It is positive for flap nose upstream ofthe reference line and negative for flap downstream of theline. Flap gap is measured as a minimum radius line for acircle centered at wing trailing edge (0.875c) and tangent tothe flap nose. If slot flow is represented in a velocity vectorin its centerline, this vector is considered normal to theminimum radius line. The angle that this vector makes withthe main wing chord line is called a new flap parameter—slot flow angle β. It is in fact physically more significantcompared to other parameters as discussed in subsequentsections.

E. Flap Optimization and EffectivenessIn order to visualize the flap nose position for

optimum gaps, flap optimization reported in Ref 10 ispresented here for 30 and 40 deg flap deflections. Figure 3shows the results for 30-degree flap case. This isconsidered to be a typical landing flap configuration. TheClmax, contours represent various locations of flap nose forgiven flap angle. The loci of these contours produce thehighest Clmax = 3.28, which corresponds to the optimumG/c=0.03, and O/c=0.0. The optimization also conductedfor 40 degree flap, which produced relatively higher

Clmax=3.35, with smaller G/c=0.015 and negative O/c=–0.01 as shown in Fig 4.

Fig. 3 Flap optimization for 30 deg flap with opt gap (case B),from Ref 10.

Fig. 4 Flap optimization for 40 deg flap with opt gap (case D),from Ref 10.

Fig. 5 Flap effectiveness for the airfoil at α=0 deg and Clmaxcondition.

The flap effectiveness for the GA(W)-2 airfoil wasdetermined for the optimum gap settings of 30 and 40 degflap deflections. The additional data for 10 and 20 deg flapdeflections are taken from Ref 10. Figure 5 shows thevariation of incremental Cl with flap angle at zero-α andClmax conditions. The Clmax increases with a rate of 0.1 perdegree of 10 deg flap initially, and then it shows a smallerrate of increase at higher flap deflections and becomesalmost zero at 40-deg flap. The lift coefficient increases atα=0 deg with trends, similar to those in Clmax with a lower

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rate of increase per degree of flap. The flapped airfoilproduces its highest incremental Clmax of 1.7 for 40-degdeflection and Cl of 1.5 at α=0 deg.

III. Results and DiscussionExperiments were made for the test cases described in

Table 1. However in this section, the results are presentedfor test cases B, C and D to have a comparison of flapdeflection as well as gap. Lift and moment data is alsogiven for flap- nested case A. Suction peak and trailingedge CP values are used to define a pressure recovery factoron both main wing and flap. The recovery factor is in turnused to evaluate flow separation on airfoil elements. Hotfilm velocity data is provided only for case B to show slotflow vectors at near stall conditions. Slot flow angle isintroduced as a new flap design parameter.

A. Hysteresis Effects on Lift and MomentFigure 6 shows Cl and Cm data for flap-nested airfoil

(case A) at both increasing and decreasing sweep of angleof attack. The airfoil has Clmax=1.7 and Cm =–0.0759 atα=16 deg, and Cl=0.4 and Cm=–0.1 at α=0 deg. Fixedtransition allowed 95%c of airfoil upper surface to haveturbulent boundary layer flow. The turbulent flowapparently did not have any bubble induced stall hysteresis.

Fig. 6 Absence of hysteresis in Cl and Cm data for flap-nestedcase A.

Figure 7 shows Cl and Cm data for case B at increasingand decreasing α sweep. The airfoil looses 20% of itsClmax=3.21 with an abrupt stall after α=13.58 deg. Thereappears a value of Cl =2.57, staying almost constant fromα=14.05 to 15.55 deg before another stall. This peculiarbehavior in Cl data was repeatable and better understoodwhen α was lowered back after a few degrees above thesecond stall. When α passes below 14 deg, the liftcoefficient is not restored to its original value (Fig 7), butinstead exhibits a significant loss continuing until α=6.95deg. The lift curve appears to be shifted downward betweenα=6.95 and 14.05 deg, indicating the effect of hysteresis.The Cm data on the other hand shifts upward (becomes lessnegative) in the decreasing side of hysteresis loop.

Narrowing the gap for 30 deg flap (case C) reducedthe α range of hysteresis, as evident from Cl and Cm data inFig 8. The airfoil looses 24.5% of its Clmax=2.95 with anabrupt stall after α=13.04 deg. The post stall Cl=2.24 atα=13.61 remains almost the same until α=15.02 beforeanother stall. The lift coefficient is not restored to itsoriginal value when α decreases below 13.61 deg, at leastnot until α=7.96 deg.

Fig. 7 Stall hysteresis in Cl and Cm data for 30 deg flap withopt gap (case B).

Fig. 8 Stall hysteresis in Cl and Cm data for 30 deg flap withnarrow gap (case C).

Fig. 9 Stall hysteresis in Cl and Cm data for 40 deg flap withopt gap (case D).

Increasing the flap angle to 40 deg (case D) increasedα range of hysteresis significantly as shown in Fig 9. Theairfoil looses 38% of its Clmax=3.905 with an abrupt stall

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after α=13.08 deg. The post stall Cl=2.42 at α=13.61 degremains almost the same until α=15.05 deg before anotherstall. The lift coefficient is not restored to its original valuewhen α decreases below 13.54 deg, not until α=0 deg. For40 deg flap case, the Cm data restores its original value atα=8 deg interestingly earlier than Cl value. It has lowernegative values within the hysteresis loop, possibly due tothe reduction in aft airfoil loading.

B. Hysteresis Effects on CP DistributionKnowing the range of hysteresis loop from force and

moment data, surface pressure distributions were obtainedto study the flow field on airfoil elements for flap cases B,C and D. The measurements were made at α settingsdetermined by α limits and Clmax condition of hysteresisloop in lift curves.

Fig. 10 Cp distribution at α=7, 8, 12, 12.8, 14 and 15.5 deg for30 deg flap with opt gap (case B) with increasing α.

Fig. 11 Cp distribution at α=7, 8, 12, 12.8, 14 and 15.5 deg for30 deg flap with opt gap (case B) with decreasing α.

For 30 deg flap with optimum gap (case B), the Cp

distribution was obtained at α=7, 8, 12, 12.8, 14 and 15.5deg. The data for increasing α side is shown in Fig 10, anddecreasing α side in Fig 11. Comparing these figures, thereis almost no discrepancy seen between the increasing anddecreasing α sides at α limits (7 and 14 deg) of hysteresisloop. The highest discrepancy occurs at α=12.8 deg, whichis around the Clmax angle, as shown in Fig 12. The suctionCP values on main wing are lower for the decreasing side,

because the flap apparently does not provide the necessarydownwash, and therefore the circulation, for the main wingas it does while increasing the angle of attack. For bothsides of loop, suction CP on main wing shows a dramaticfall after its peak value at near leading edge. The dramaticfall is followed by a short step between 5% and 7.5% chordlocations where the transition is fixed on upper surface. Thetrip strips apparently produced a short bubble to trip theflow. This was also evident from surface flowvisualizations. At low α setting, the aft portion of flap hasnearly constant CP distribution, as in Fig 10. The start ofconstant CP is considered to be the location for flowseparation, as evidenced in correlation to the flowvisualization studies. The region of separated flow on flapdecreases with increasing α settings and almost disappearsat α=12.8 deg prior to the stall. This is considered to be atypical feature of flaps designed to maximize the Clmax ofairfoil system.10 At post stall α=14 deg, suction CP valueson flap are flattened, indicating a leading edge stall. Theflatness on flap moves upstream onto the main wing, and athigher α=15.5 deg, it leads to a massive flow separation.When α is lowered back from 14 deg, the flow on flapremains stalled until α=7 deg where the airfoil lift isrestored to its value obtained with increasing α. In otherwords, the suppressed CP values on flap under the influenceof thickening wing wake after the first stall are evidentlynot returned to their pre-stall values until a significantreduction in α.

Fig. 12 Hysteresis effect in Cp distribution at α=12.8 deg for 30deg flap with opt gap (case B) with increasing and decreasingα.

For 30 deg flap with narrow gap (case C), the Cp

distribution was obtained at α=8, 10, 12, 12.8, 14 and 15.5deg. The data for increasing α side is shown in Fig 13 anddecreasing side in Fig 14. Unlike the optimum case B, thesuction CP values on flap do not show a separated region atpre-stall α=8 deg, and they stay almost the same untilα=12.8 deg. This corresponds to the lift curve roundingnear Clmax condition (see Fig 8). The data shows almost nodiscrepancy at α=8 deg while it shows some at α=14 deg.The highest discrepancy between the increasing anddecreasing α sides occurs at α=12.8 deg, as shown in Fig15. As α increases to 15.5 deg, the flow separation moves

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upstream on main wing, but not enough to cause a leadingedge stall.

Fig. 13 Cp distribution at α=8, 10, 12, 12.8, 14 and 15.5 deg for30 deg flap with narrow gap (case C) with increasing α.

Fig. 14 CP distribution at α=8, 10, 12, 12.8, 14 and 15.5 deg for30 deg flap with narrow gap (case C) with decreasing α.

Fig. 15 Hysteresis effect in Cp distribution at α=12.8 deg for 30deg flap with narrow gap (case C) with increasing anddecreasing α.

For 40 deg flap with optimum gap (case D), the Cpdistribution was obtained at 1, 2, 12, 12.8, 14 and 15.5 deg.The data for increasing α side is shown in Fig 16 anddecreasing side in Fig 17. The CP data shows the highestdiscrepancy between the increasing and decreasing α sidesat α=12.8 deg (see Fig 18), and almost no discrepancy at αlimits (2 and 14 deg) of loop. Notice that the correspondinglift curve in Fig 9 shows the lower end of hysteresis loop atα=0 deg. The start of hysteresis for this case would bebetter shown with selecting another α setting (say 3 deg).

The flow separation on flap disappears as α settingincreases from 2 to 12 deg, leading to the highest Clmaxcondition.

Fig. 16 Cp distribution at α=1, 2, 12, 12.8, 14 and 15.5 deg for40 deg flap with opt gap (case D) with increasing α.

Fig. 17 Cp distribution at α=1, 2, 12, 12.8, 14 and 15.5 deg for40 deg flap with opt gap (case D) with decreasing α.

Fig. 18 Hysteresis effect in Cp distribution at α=12.8 deg for 40deg flap with opt gap (case D) with increasing and decreasingα.

CP distributions at each α setting were integrated tofind individual lift contribution from wing and flapcomponents. The integration was made by the trapezoidalmethod in chord-line intervals given with airfoilcoordinates. Considering all test cases, the integrated Clwas very close to or at most 4% higher than thecorresponding balance Cl.

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Fig. 19 Cl values from integrated CP distributions on wingalone, flap alone and wing + flap for case B with increasingand decreasing α.

Fig. 20 Cl values from integrated CP distributions on wingalone, flap alone and wing + flap for case C with increasingand decreasing α.

Fig. 21 Cl values from integrated CP distributions on wingalone, flap alone and wing + flap for case D with increasingand decreasing α.

Figures 19, 20 and 21 show Cl variation with αsettings for all three-flap cases studied. For all cases, flap Cl

stays about constant for both increasing and decreasing αsides of hysteresis loop. Its addition shifts the wing Cl

upward to build up total airfoil Cl. When α=12.8 deg, flapCl is only 13.1%, 11.8% and 12.5% of total airfoil Cl for

case B, C and D, respectively. The data shows that the flapCl is not very sensitive to changes in α until the stall, butthe main wing is, and it is similar to that on single airfoils.Flap apparently has the effect of boosting the circulation ofthe main wing, which has the majority of total airfoil Cl.The circulation on the main wing in turn effectively reducesthe flap α, as well as the velocities on its surface and hencereduces its lift.7

C. Recovery Factor on CP DistributionsCP distributions on upper surface of airfoil elements

exhibited a suction peak followed by a region of recoveryto a pressure value near the trailing edge. The region ofpressure recovery is of critically importance for its stronginfluence on flow separation. For practical uses, it isdefined in Ref 11 by a coefficient factor as follows:

The pressure recovery coefficient, CPR is in factderived from the canonical pressure coefficient describedby Smith.7 Here, CPmin and CP@0.95c are the pressurecoefficient values at the point of minimum pressure and thepoint of maximum pressure recovery, respectively. Thepoint of maximum pressure recovery was assumed to be at95%c location of airfoil elements, corresponding to portlocations at 0.775c for wing and 0.975c for flap. Thesepressure coefficient values were determined from CP

distributions and plotted against α to see their changes onmain wing and flap.

Fig. 22 Peak suction CP values on wing and flap for case Bwith increasing and decreasing α.

Peak suction pressure coefficient, CPmin on both wingand flap are shown in Fig 22 for optimum gap case of 30deg flap. It corresponds to the location for the maximumvelocity or start of pressure rise on each airfoil element.Wing CPmin has a maximum of –14.9 at α=12.8 deg,followed by 25% drop with stall. It does not reach itsoriginal CPmin value for the decreasing α side until α islowered from 14 deg all the way to 7 deg, as in thecorresponding lift curve. The flap CPmin is apparentlysuppressed by the boundary layer wake from main wingand shows no sensitivity to changes in α until the stall. It

min

min95.0@

1 P

PcPPR C

CCC

−

−=

AIAA-2005-1230has a value of –2.95 at α=12.8 deg, followed by a drop to –1.12 at α=14 deg, and stays at about this low for decreasingα side of loop. The flap CPmin is in fact located slightlydownstream of main wing trailing edge where the wakeflow having the suction CP@0.95c is discharged into the slotflow region.

Fig. 23 CP values at 0.95c of wing and flap upper surface forcase B with increasing and decreasing α.

Fig. 24with in

Pboth wCP@0.9

stall. 0.873decreaα and–0.70approdecreaα=8 d

Pthe CPon boCPR indeg, decrea0.67 a0.18 a

the flapped airfoil Clmax. When α is lowered from 14 deg,the flap CPR values show a large discrepancy from those ofthe increasing α side. This type of behavior in wing andflap CPR values was also observed in plots of recoveryfactor for narrow gap case C and higher flap angle case D,as shown in Figs 25 and 26 respectively. These flap gapcases B, C and D are compared in Fig 27 for onlyincreasing α side. Wing CPR values are nearly independentof flap setting and appear to depend primarily on α, eventhough lift coefficient and minimum CP values are stronglyinfluenced by the flap deflection. Flap CPR values howevershows variations with α prior to the stall. Case D has thehighest values, but maintains the same slope as case B.Case C shows a decreasing trend in slope until the stall.

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Pressure recovery factors on wing and flap for case Bcreasing and decreasing α.

ressure coefficient at 95%c upper surface, CP@0.95c oning and flap is shown in Fig 23 for case B. Wing

5c value are not sensitive to changes in α until theIt is –1.239 at α=12.8 deg, followed by a drop to – at α=14 deg. Flap CP@0.95c value on the other handses slightly (becomes less negative) with increasing

becomes –0.111 at α=12.8 deg followed by a jump to6 at α=14 deg. The wing and flap values apparentlyach to each other with the stall. They get closer forsing α side and have a common value of –0.783 ateg before each going back to its original value.ressure recovery factor, CPR correlates the CPmin to

@0.95c through its definition shown above. Its variationth wing and flap is shown in Fig 24 for case B. Wingcreases from 0.75 at α=7 to a maximum 0.86 at α=14and shows no significant difference from thesing α side. Flap CPR on the other hand goes fromt α=7 to 0.71 at α=12.8 and then drops sharply tot α=14 deg. Its maximum occurs simultaneously with

Fig. 25 Pressure recovery factors on wing and flap for case Cwith increasing and decreasing α.

Fig. 26 Pressure recovery factors on wing and flap for case Dwith increasing and decreasing α.

The recovery factor CPR in general has a critical valuefor which separation first develops. The critical value(shown in Fig 27) is about 0.72 on flap, experiencing theabrupt stall at α=12.8 deg earlier than the main wing, whichhas its peak 0.86 at α=14 deg. The critical CPR correspondsto a maximum pressure recovery at 95%c location. It can infact be used as a design parameter as suggested in Ref 11.For an inverse airfoil design, CP distribution is typicallymodified according to design specifications. With themodification, the CPmin and CP@0.95c values could be set toproduce the desired CPR value. In this way, airfoil contouris also changed. The changes in airfoil contour may resultin favorable effect on separation and stall, but not enough

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to alleviate the hysteresis problem in flapped airfoil. Thereis also the effect of slot flow that appears significant, asdiscussed in the subsequent section.

Fig. 27 Comparison of pressure recovery factor for case B, Cand D on wing and flap. Increasing α sweep only.

Fig. 28 Hot film velocity vectors on flap flow field for case B.

D. Slot Flow OrientationSlot flow orientation was studied by using oil dot flow

visualization and hot film probe measurements.8,9 Figure 28shows the hot film velocity vectors of flap region for case Bat α=12.8 deg. The hot film data were obtained for given αafter settling the test flow produced by increasing air speedin the tunnel. Boundary layer and wake deficits are clearlyvisible on the velocity profiles. The vector data representthe resultant of horizontal and vertical velocity components.They are relatively high at flap trailing edge and inclineddownward, however inclined upward for the region of slotflow as depicted at the first survey station above the flapleading edge. The hot film data was taken as much as6.35mm away from surface for probe safety. The slot flowwas also visualized by oil dots located at one-25.4mmsquare grid points of a splitter plate about one-chord long(not to confuse with the pressure plate also used in theexperimental program8). The plate was large enough tocover the separated flow field and wake of airfoil elements.Oil flow pattern and velocity vectors were in agreement toshow the upward inclination of slot flow with respect to thefree stream flow. This type of flow inclination in velocities,perhaps at a smaller degree, can also be seen on otherpublished data.12,13

The flow field data clearly show that the slot flowtends not to follow the flap nose curvature closely, because

of an upward inclination. The inclination was higher for 40deg flap case with its nose position shown in Fig 4. The slotflow angle β is in fact a measure of this inclination asshown in Fig 2 and sensitive to changes in overlap andcontour of flap nose. It was computed for various flap pivotlocations producing the same gap as the optimum for eachflap deflection. The calculated β values geometrically seemto correlate with the orientation of slot flow determined byhot film velocities above the flap nose.

Fig. 29 Variation of flap pivot locations with slot flow angle βfor 30 and 40 deg flap with opt gaps (cases B and D,respectively).

Figure 29 shows β variation with Xx (%) and Zf (%)flap pivot locations for 30 and 40 deg deflections. Theoptimum flap settings shown with Fig 2 have positive βvalues for both flap deflections. The angle β is 24.4 deg forδ=30 deg and 31.1 deg for δ=40 deg flap case. When β=0deg, Xf =9.5% and 10.2% and Zf=4.0% and 3.4% for δ=30and 40 deg flap respectively. Both zero and negative βvalues would result in some flap overlap, for which the slotflow would be directed over the flap. The inclined slot flowwould in fact promote favorable pressure gradients on theflap upper surface, and hence delay possible flowseparation. However, increasing overlap, the flap nose getscloser to the cove separation bubble, and this may reducethe effective gap size due to the presence of boundarylayers. This requires gap optimization conducted as close toflight Reynolds number as possible. Also, the overlappedsection of flap nose does not produce suction pressure, butprovide a passage for the slot flow.

The best location for landing flap has beentraditionally obtained by finding a location for flap nosethat results in the highest maximum lift coefficient. It issuggested here that the flap be optimized with considerationof hysteresis effects by using the additional flap parameterβ to determine the slot flow orientation. For each flap angleand gap setting, there seems to be an optimum β value thatresults in significant reduction if not elimination ofhysteresis effects. The optimum β value can be determinedwith further research and hence requires wind tunnel testsof this kind.

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IV. ConclusionsHysteresis effects discovered in wind tunnel

performance of flapped-GA(W)-2 airfoil is furtherexamined by using the data obtained for CP distribution andhot film velocity vector in addition to force and momentcharacteristics reported earlier. Based on the results ofexperiments, the following concluding remarks can bedrawn:

1) Flow separation present on flap at low α disappearsat Clmax condition. Flap CP distribution under the influenceof main wing wake is not sensitive to changes in α untilstall. With the first stall, flap suction pressures aresuppressed by thickening of main wing wake. Thesuppressed pressures are apparently not reversible to theirpre-stall values until angle of attack is loweredsignificantly.

2) Pressure recovery on airfoil elements can bedescribed by a coefficient factor. Peak value for therecovery factor occurs on flap simultaneously with theflapped airfoil Clmax. The limiting separation value for therecovery factor, considered as a design parameter, can beused to modify CP distribution for desired flap contour.

3) Slot flow velocities with an upward inclinationindicate a reduction of circulation effect over the mainwing. The slot flow orientation described by a new flapparameter β, is more sensitive to changes in flap positionand contour.

4) It is suggested that the flap design include theuse of slot flow angle to describe the slot flow orientationand limiting pressure recovery factor to select a propercontour for flap upper surface.

V. References1 Mueller, T.J., "Low Reynolds Number Vehicles,"AGARDograph No. 288, February 1985.2 Marchman, J. F., “Aerodynamic Testing at Low ReynoldsNumbers,” Journal of Aircraft, Vol. 24, No.2, Feb 1987,pp. 107-114.3 Biber, K., "An Overview of Steady and Dynamic AirfoilPerformance," SAE Paper 93-1228, General AviationTechnology Meeting, May 9-11, 1993.4 Biber, K. and Zumwalt, G. W., "Hysteresis Effects onWind Tunnel Measurements of a Two-Element Airfoil,"AIAA Journal, Vol.31, No.2, Feb. 1993, pp.326-330.5 Landman, D. and Britcher, C. P., “ExperimentalInvestigation of Multielement Airfoil Lift Hysteresis due toFlap Rigging,” Journal of Aircraft, Vol. 38, No. 4, July-August 2001, pp. 703-708.6 Foster, D.N., Irwin, H.P.A. and Williams, B.R., “TheTwo-Dimensional Flow Around A Single Slotted Flap,”R.A.E. R&M, 3671, Sept. 1971.7 Smith, A.M.O., “High-Lift Aerodynamics,” Journal ofAircraft, Vol. 12, No 6, June 1975, pp501-530.8 Biber, K. and Zumwalt, G.W, “An Experimental Study ofa Two-Element Airfoil with Large Separation, AIAA Paper92-0267, 30th Aerospace Sciences Meeting, Reno, NV, Jan.1992.

9 Biber, K. and Zumwalt, G. W., "Flow FieldMeasurements on a Two-Element Airfoil with LargeSeparation," AIAA J, Vol. 31, No. 3, March 1993, pp. 459-464.10 Wentz, W. H., jr., "Wind Tunnel Tests of the GA(W)-2Airfoil with 20% Aileron, 25% Slotted Flap, 30% FowlerFlap and 10% Slot-Lip Spoiler," NASA CR-145139, 1977.11 Wentz, W.H., Jr., “Use of Simplified Flow SeparationCriteria for Slotted Flap Design,” SAE Paper 77-0481,Business Aircraft Meeting, Wichita, KS, March 29-April 1,1977.12 Braden, J.A., Whipkey, R.R., Jones, G.S., and Lilley,D.E., Experimental Study of the Separating ConfluentBoundary Layer,” Vol. I, Summary, NASA CR 3655; Vol.II, Experimental Data, NASA CR-166018, March 1983.13 Wentz, W.H., Jr and Ostawari, C., “Additional FlowField Studies of the GA(W)-1 Airfoil with 30-PercentChord Fowler Flap Including Slot-Gap Variations,” NASACR 3687, May 1983.