Copyright ©1996, American Institute of Aeronautics and Astronautics, Inc.

AIAA Meeting Papers on Disc, January 1996A9618032, AIAA Paper 96-0056

Calculation of multielement airfoil flows, including flap wells

Tuncer CebeciCalifornia State Univ., Long Beach

Eric BesnardCalifornia State Univ., Long Beach

Hsun H. ChenCalifornia State Univ., Long Beach

AIAA, Aerospace Sciences Meeting and Exhibit, 34th, Reno, NV, Jan. 15-18, 1996

A calculation method for multielement airfoils based on an interactive boundary-layer approach using an improved Cebeci-Smith eddy viscosity formulation is described. Results are first presented for single airfoils at low and moderate Reynolds numbers in order to demonstrate the need to calculate transition for accurate drag polar prediction and the ability of the improved Cebeci-Smith turbulence model to predict flows with extensive separation and therefore to predict maximum lift coefficient. Results, in terms of pressure distributions and lift and drag coefficients, are presented for a series of two-element airfoils with flaps or slats. The method is extended to the computation of configurations with flap wells. Results show that the same accuracy can be reached as for faired geometries. The importance of compressibility effects and the turbulence model for stall, and the need to calculate the onset of transition, are demonstrated. Recommendations are made for the preferred approach to predicting the aerodynamic performance of multielement airfoils for use as a practical and efficient design tool. (Author)

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CALCULATION OF MULTIELEMENT AIRFOIL FLOWS,INCLUDING FLAP WELLS

byTuncer Cebeci*, Eric Besnard" and Hsun R Chen***

Aerospace Engineering DepartmentCalifornia State University, Long Beach

AbstractA calculation method for multielement airfoils

based on an interactive boundary-layer approachusing an improved Cebeci-Smith eddy viscosityformulation is described. Results are first presentedfor single airfoils at low and moderate Reynoldsnumbers in order to demonstrate the need to calculatetransition for accurate drag polar prediction and theability of the improved Cebeci-Smith turbulencemodel to predict flows with extensive separation, andtherefore to predict maximum lift coefficient, (c^m^.Results, in terms of pressure distributions and lift anddrag coefficients, are presented for a series of two-element airfoils with flaps or slats. The method isextended to the computation of configurations withflap wells. Results show that the same accuracy can bereached as for faired geometries. A slightcompressibility effect was accounted for byintroducing compressibility corrections to the Hess-Smith panel method. Again, the importance of thecompressibility effects and the turbulence model onstall, and the need to calculate the onset of transition,are demonstrated. Recommendations are then madefor the preferred approach to predicting theaerodynamic performance of multielement airfoils foruse as a practical and efficient design tool.

1. IntroductionIn recent years, there have been significant

accomplishments in computational fluid dynamics.Whereas in the early 1960's calculations performedfor airfoil flows with panel methods and boundary-layer methods were under development for simpleflows, today the calculations are being performedroutinely with Navier-Stokes methods not only forairfoil flows but also for complex aircraft

configurations. Our capabilities in aerodynamic flowshave reached levels which were difficult to imagine inthe early 1960's. Progress has been so great and sorapid that one may even say that computational fluiddynamics has reached, or is very near to reaching, itsmaturity.

Despite these advances, however, there is stillmore to be done in developing design methods forhigh lift configurations. The presence of high andlow Reynolds number flows on various components ofairfoils, including flap wells and significant regions offlow separation near stall conditions as well aspossible merging of shear layers, offer significantchallenges to code developers. The required generalityand accuracy of the code and, equally important, itsefficiency as a design tool, add additional challenges.

The current development of design algorithms forhigh-lift devices follows two approaches. Oneapproach pursues the solution of the Navier-Stokesequations with structured .and unstructured grids.Some of the Navier-Stokes methods used for thispurpose are based on the solutions of theincompressible flow equations [1, 2] while others arebased on the solutions of the compressible flowequations [3]. The incompressible form of theequations employing the numerical procedure ofRogers et al. [1] provides accurate results and allowsthe calculations to be performed efficiently. Thesolution of the compressible equations, on the otherhand, takes a considerable amount of computer time;their convergence rate is slower and, at this time, theyare in the research stage.

The other approach for developing methods forhigh lift configurations is based on the interactiveboundary layer theory, which involves interactionbetween inviscid and boundary-layer equations [4, 5].In this approach the inviscid flow is often computed

Professor and Chair, AIAA FellowGraduate Student

**•

Professor, AIAA Associate FellowCopyright © 1996 by the American Institute of Aeronautics andAstronautics Inc. All rights reserved

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by a panel method with or without compressibilitycorrections, and the viscous flow is computed by acompressible boundary-layer method. This approachis very efficient but is not as general as the Navier-Stokes approach for more complicated geometries.

Regardless of which approach is used to developa computational tool for high-lift configurations, it isnecessary to include the compressibility effect if thecalculation method employs incompressible flowequations, and to calculate the onset of transition.Both can strongly influence the accuracy of thecalculation method. Experiments on single ormultielement airfoils show that the compressibilityeffect, even at Mach numbers around 0.30, has apronounced effect on the maximum lift coefficient.Similarly the predicted location of transition in thecalculation method is important in properlyidentifying the effects of wind tunnel and flightReynolds numbers. Individual components of multi-element airfoils at wind tunnel Reynolds numbers canexperience relatively lower Reynolds numbers thanthe main airfoil. At chord Reynolds numbers less than500,000, the components can have large separationbubbles, with the onset of transition occurring insidethe separation bubble [6]. As a result, the behavior ofthe flow can be significantly different from thebehavior of the flow on the main airfoil at higherReynolds numbers. Furthermore, the transitionlocation can drastically influence the drag coefficient,and therefore determining the onset of transition iscrucial for predicting drag polars, which are of majorinterest to aircraft designers.

Section 2 describes an interactive-boundary-layerapproach to the calculation of high lift configurationsin two-dimensional flows. It is applied to a variety ofhigh lift systems, including airfoils with flaps andslats, and airfoils with and without flap wells. Resultsare presented and discussed in Section 3. Finally, inview of the present results, a preferred approach forpredicting the flow about multielement airfoils isdiscussed in Section 4.

2. Calculation Method

2.1 Inviscid Method

The inviscid flow field is computed by the HessSmith panel method [7]. Three options were used inthe multielement panel method. As in a single airfoilpanel method, in one option the vorticity strength wastaken to be constant on all panels, and a single valuewas adjusted to satisfy the condition associated with

the specification of circulation. Multielementconfigurations computed with the calculation methodemploying the multielement panel method withviscous corrections showed that, while the resultswere in good agreement with experimental data forconventional airfoils, the results for airfoils with thintrailing edges and/or supercritical airfoils were notTo improve the results, two additional options for thevorticity distribution were incorporated into the panelmethod. One option assumes that vorticity variesquadratically with the surface distance and the secondoption assumes that it varies quadratically in a smallregion near the trailing edge. In this latter option, tobe referred to as the partially parabolic vorticitydistribution option, the size of the region is to bespecified in the panel method. The compressibilitycorrection depends upon the linearized form of thecompressible velocity potential equation and is basedon the assumption of small perturbations and thinairfoils. The correction used in the present panelmethod is based on the Prandtl-Glauert formula asdescribed in [7].

2.2 Inverse Boundary Layer Method

Boundary layer equations

The compressible boundary layer equations(mass, momentum and energy) for laminar andturbulent flows are well known and, with thealgebraic eddy viscosity (em) and turbulent Prandtlnumber (Prt) formulation of Cebeci and Smith [7],they can be expressed as follows:

(1)

i^pvir-p.u.rr-+iHGi-hp6.)ir <2>

where T is the temperature, H is the total enthalpygiven by

2

= c.T+— (4)and

pv=pv+pV (5)In the absence of mass transfer, the boundary

conditions for an adiabatic surface areany = 0, u = 0, v = 0, — = 0 (6a)dy

y->oo, u->u.(x),H->H. (6b)In the wake, where a dividing line at y = 0 is

required to separate the upper and lower parts of the

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inviscid flow, in the absence of normal pressuregradient, the boundary conditions at y = 0 become

day=0, — = 0, v = 0 (7)

dy

Solution procedureThe above equations are first expressed in

transformed coordinates. Two sets of transformedcoordinates are used, one for the direct problem whenthe equations are solved for the prescribed pressuredistribution, and the other for the inverse problemwith the external velocity updated during theiterations. The Falkner-Skan transformation is used inthe direct mode and a modified version is used in theinverse mode. Reference 7 presents and discusses thetransformed equations and their solution procedure indetail. The airfoil is divided into upper and lowersurfaces. For each surface, the calculations start at thestagnation point and proceed in the standard mode upto a certain specified x-location. Then, the inversecalculations begin from that location and continue upto the far wake.

Interaction lawThe boundary layer equations become singular at

flow separation and do not allow the calculation ofseparated flows for a prescribed velocity distribution.However, when the external velocity is treated as anunknown, this difficulty can be overcome as discussedin [7J. The external velocity is represented by

ue(x) = ue°(x)+6ue(x) (8)where u° is the inviscid velocity computed by thepanel method and 8ue is the perturbation velocity dueto viscous effects, which is given by the Hilbertintegral

6ue(x) = -x-a (9)

in the interaction region (a, b). Its evaluation isdescribed in detail in [7].

The flow calculations in the flap well regionwhich are similar to those for a backward facing steprequire modifications. A large portion of the flowseparates immediately after the sudden change of theairfoil geometry. The flow reattaches and graduallyrecovers downstream in the flap well region or in thewake. The calculation of such flows is difficult, andpotential theory is not adequate because of thesingularity that occurs at the geometry discontinuityand the strong viscous effects in the separated region.To compute such flows, the interaction law has to be

(5T'=(5')' 1-HDP^-

modified. First, a fairing is placed in the flap wellregion, and the Hilbert integral formulation is used togenerate initial guesses for the displacement thicknessdistribution. Then, the relaxation formula

(10)

where 8* is actually the sum of the distance from thefairing to the flap well cove and the displacementthickness measured from the fairing, is used in theinverse method to replace the Hilbert integralformulation of the external boundary condition. Thenew edge boundary conditions are given by Eq. (6b)and Eq. (10), where u(V and u^ correspond theexternal velocities computed by the boundary layerand inviscid methods, respectively, and CD is arelaxation parameter. At the end of the flap well, thesolution procedure reverts to the Hilbert integralapproach.

Once the boundary layer development iscomputed, the blowing velocity distribution isdetermined from

vB=-(ue.5') (11)and used as a boundary condition in the inviscidmethod. This interactive procedure is repeated untilconvergence of the lift coefficient is achieved.

Turbulence model

An improved version of the algebraic eddy-viscosity formulation of Cebeci-Smith is used here.The eddy viscosity distribution across the boundarylayer is defined by two separate expressions,

S- =

(O, =[o.4y[l-«p- |̂ My.

(O. =4l(u. -

(12)

where0.0168

-1.5 A = 26—i -T (13a)

where F is related to the ratio of the product of theturbulence energy by normal stresses to that by shearstress evaluated at the location where the shear stressis maximum. As discussed in [7], it is given by

where the parameter p is a function ofRt=twA-puV)mtx, which, for tw£0, isrepresented by

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1+2R,(2-R,)1+R,

R.^LO

R.(15)

For TW £ 0, R, is set equal to zero.Also, whereas in the original Cebeci-Smith eddy

viscosity formulation the intermittency expression wasvalid only for zero pressure gradient flows, theexpression in the improved formulation is applicablefor flows with favorable and adverse pressuregradients as well as zero pressure gradient flows. It isbased on Fiedler and Head's correlation [8] and isgiven by

11-erf (16)

where Y and a are general intermittency parameterswith Y denoting the value of y where y = 0.5 and CTdenoting the standard deviation. For details, see [7].

The condition used to define yc is the continuityof the eddy viscosity, so that em is defined by (em)(from the wall outward (inner region) until its value isequal to that given for the outer region by (sm)0.

The expression fa models the transition regionand is given by

= l-exp -G(xJdx

-X*)J — (17)

Here xtt denotes the onset of transition and G isdefined by

u« (18)

where C is 60 for attached flows and the transitionReynolds number is R^ = (uex / v),, . In the lowReynolds number range from R c =2xl0 5 toRc = 6 x 103 , the parameter C is given by

C2 = 213 (logR^ -4.7323J (19)The corresponding expressions for the eddy-

viscosity formulation in the wake are

(20)

where (em)u is the eddy viscosity at the trailing edgecomputed from its value on the airfoil and (en)w isthe eddy-viscosity in the far wake given by the largerof

= 0.064u

J(ue-u).dy (21a)

):= 0.064 J(ue-u).dy (21b)

and

y*.with y^ denoting the location where the velocity isminimum.

For high Reynolds numbers, if the flow isattached, the onset of transition is determined byMichel's criterion as described, for example, in [7]. Athigh angles of attack, the flow separates downstreamof the pressure peak before Michel's criterion can besatisfied. Therefore, the onset of transition is chosento coincide with laminar separation.

At Reynolds numbers less than 106, where largeseparation bubbles may be present even at low anglesof attack, it is necessary to calculate the onset oftransition by the en-method as discussed in [7]. Forhigh lift configurations, flaps usually have lowReynolds numbers. Fortunately, the pressuredistribution on the flap upper surface does not varygreatly with angle of attack, and therefore thecomputation of the transition location does not haveto be performed at each angle of attack.

3. Results and Discussions

3.1 Single Airfoils

Before we present a sample of results for high liftconfigurations, it is useful to discuss the role oftransition by examining the results shown in Figs. 1and 2 for two airfoils at high and low Reynoldsnumbers. The results in Fig. 1 are for the NACA0012 airfoil at a chord Reynolds number of 3 x 106.As can be seen, there is a significant differencebetween the calculated lift coefficients in which thetransition location was fixed near the stagnation pointfor all angles of attack or computed. A similarobservation can be made for the drag coefficients.Those calculated with the transition computed show amuch better agreement with experimental data thanthose in which the transition was fixed.

Fig. 2 shows the results for the Eppler airfoil at achord Reynolds number of 200,000. Here, the locationof transition does not play an important role inpredicting lift coefficients (Fig. 2a). However, thecalculations with a fixed transition location can beperformed until a = 13.5°. As before, the dragcoefficients obtained with the transition locationcomputed show better agreement with data than thosewith a fixed transition location (Fig. 2b).

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0.0 3.0 10.0 15.0 20

0.040

0.030

0.020

0.010

0.000

o meaturcmenU

— transition computed— traniitioo it the

leading edge

0.0 0.5 1.0

Fig. 1. Force coefficients for the NACA 0012 airfoil atRe = 3 x 10*, (a) lift and (b) drag.

1.5 r

o measurements- transition calculated•• transition it the leading edge

0.0

(a)-2,0 3.0 8.0 13.0 1S.O

a0.10

0.08

0.06

0.04

0.02

0.00-5.0 0.0 5.0 10.0 15.

a(b)Fig. 2. Force coefficients for the Eppler airfoil at Re '200,000, (a) lift and (b) drag.

3.2 Two-element Airfoils without Flap WellA sample of results is presented below for three

two-element configurations without flap wells.Figs 3 and 4 show the results for the MLR 7301

supercritical airfoil/flap configuration. Theexperimental data of Van den Berg and Oskam [9]include pressure distributions at a = 6° and 13.1°, alift curve and a drag polar. A flap of 32% chord wasused at a deflection angle of 20° and with a gap of2.6% chord. The experimental freestream Machnumber was M« = 0.185, and the chord Reynoldsnumber was 2.51 x 10*. Fig. 3 shows a comparisonbetween measured and computed pressuredistributions at a = 6.0° and a = 13.1°, and Fig. 4shows a similar comparison for the lift coefficient anddrag polar. The inviscid flow calculations wereperformed using the partially parabolic vorticityoption, and the viscous flow calculations wereperformed with the onset of transition locationcalculated on the main element and flap. As can beseen from the results in Fig. 4a, the calculated results,including drag, agree well with experimental data.

o MeasurementsCalculations

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4x/c

-2.50.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

(b) X/CFig. 3. Pressure distribution for the NLR 7301supercritical airfoil/flap configuration for (a) a * 6* and(b) a-13.1'.

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3.5 r

(a)0.0

0.10 r

20.0

0.00

(b) 'Fig. 4. Force coefficients for the NLR 7301 airfoil/Hapconfiguration, (a) lift coefficient, and (b) drag polar.

Figures 5 to 9 show the results for two NASAhigh lift configurations tested by Omar et al. [10] fora freestream Mach number of Mo = 0.201 and chordReynolds number of 2.83 x 106. As in the NLR 7301multielement configuration, the inviscid flowcalculations were performed using the partiallyparabolic vorticity option. In addition thecompressibility corrections were made to the inviscidflow using the Prandtl-Glauert formula.

Figure 5 shows the pressure distributions for theairfoil/flap configuration at a = 0.01° and 8.93°. It isseen that the calculated results are in good agreementwith experimental data, although there is somediscrepancy on the upper surface of the flap. Thisdiscrepancy is due to two phenomena, the merging ofshear layers and the inaccurate wake center lineprediction, as shown in Figure 6. It is seen that in theexperiments, the merging occurs at the trailing edgeof the flap for both a = 0° and a = 8°, and that it isnot predicted by the present method. Also, in thepresent method, the wake center line is assumed to bethe dividing streamline merging from the mainelement trailing edge and is closer to the flap uppersurface than the measured one (thick line in Figure

6), which causes a greater predicted flow accelerationon the flap upper surface than the actual acceleration.

oMouurcmenti

-Cp 2.0 -1

-2.00.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

X/c

20.0

16.0

12.0

8.0

4.0

0.0

-4.0

Critical Pretsure Coefficient

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

(b) ^Fig. 5. Pressure distribution for the NASA airfoil/flapconfiguration at (a) a - 0.01* and (b) a » 8.93*.

wake center Una

meuured merging

Fig. 6. Comparison of measured and computed shearlayers for the NASA airfoil/flap configuration, (a) a - 0*and (b) a - 8*.

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Figure 7 shows the lift and drag coefficients forthe same configuration. The lift coefficient is slightlyover predicted due to the discrepancies on the flapupper surface, and similarly the drag coefficient isslightly under predicted. Also, the calculatedincompressible stall angle is rather different from thecalculated compressible one. The critical pressurecoefficient for M» = 0.201 is indicated in Fig. 5b. Ata = 8.93°, the measured stall angle, there exists asmall region of supersonic flow and a shock mayoccur. Even though this shock cannot be predicted bythe panel method, the compressibility corrections thatare applicable at lower angles of attack provide asignificant improvement to the stall prediction.

3.0 r

MeasurementsIncompressibleCompressible

00-10

0.15 r

0 5a

10 15

0.10

Cd

0.05

0.000,0 1.0 2.0 3.0

(b) lFig. 7. Force coefficients for the NASA airfoil/Hapconfiguration, (a) lift coefficient, and (b) drag polar.

Figures 8 and 9 show the results for a slat/airfoilconfiguration. Figure 8 presents a comparisonbetween measured and calculated pressuredistributions at 26.88°. While the agreement isexcellent for the slat, the pressure peak on the mainairfoil is slightly under-predicted. Figure 9 shows thelift and drag coefficient comparisons for the sameconfiguration. The agreement with data is excellentup to stall for the lift coefficient and the drag polar ispredicted satisfactorily. The computed maximum liftcoefficient and stall angle are 2.88 and 27.5°,respectively, and the measured ones are 2.90 and

26.9°. This gives a 0.7% error for the maximum liftcoefficient and an error of 2.2% for the stall angle.

18.0 r

14.0

10.0

6.0

2.0

-ZO

-Cp

-0.2 0.0 0.2 0.4 0.6 0.8 1.0x/c

Fig. 8. Pressure distribution for the NASA slat/airfoilconfiguration at a = 26.88*.

3.0 r

2.0

1.0

0.0

Skt

10.0 15.0 20.0a

23.0 30.0

0.130

0.125

0.100

0.075

0.050

0.025

n tm\

-

o Mc»urananti—— Cilcubtion

3

- ° o)

r ^^S^

0.0 1.0 ZO 3.0

(b) *Fig. 9. Force coefficients for the NASA slat/airfoilconfiguration, (a) lift coefficient and (b) drag polar.

3.3 Two-element Airfoil with Flap WellThe method described in Section 2 was applied to

an airfoil/flap configuration tested by Omar et al. [10]similar to that of the previous section, but comprisinga flap well cove to illustrate the applicability of themethod to airfoils with flap wells.

As mentioned in Section 2, the calculations areperformed in several steps. First, a fairing is assumedin the flap well region. Inviscid calculations are thenperformed for this faired geometry and an external

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velocity distribution is obtained. The boundary layerequations are solved over the airfoil for this pressuredistribution with the Hilbert integral inverseformulation of Section 2 so that an initialdisplacement thickness in the flap well region can beobtained. Then, in the flap well cove, the inverseformulation employing the relaxation formula of Eq.(10) is used starting with this initial displacementthickness distribudon added to the distance from theflap well cove to the fairing. After several iterations, anew displacement thickness distribution in the flapwell cove is determined. The correspondingdistribution over the faired airfoil is calculated andsimulated into the inviscid method with the blowingvelocity. As in the cases without flap well, severalinviscid/viscous iterations are performed untilconvergence.

Figure 10 presents the geometry in the flap wellregion and the fairing used for the calculations.Results in terms of computed displacement thicknessare shown for a = -8.11° and a = 8.59°. As expected,the recirculation region is much greater for a = -8.11°than for a = 8.59°. Figure 11 presents thecorresponding skin friction coefficient variation in theflap well region and demonstrates the ability of themethod to compute large regions of separated flow.

Fig. 10. Computed displacement thickness in the flapwell region for (a) a - -8.11* and (b) a = 8.59 *.

Figure 12 shows a comparison of measured andcomputed pressure distributions in the neighborhoodof the flap well cove and on the flap for a = -8.11°, a= -0.02° and a = 8.59°. Comparing measurementswith those for a smooth geometry (Fig. 5), it is seenthat the presence of the recirculating flow essentiallycauses an almost constant pressure distribution in theflap well cove and increases the flow velocity in thevicinity of the flap leading edge.

o.oio

0.005

Cf

0.000

-a 005

a--8.11a-8.59

dementtrailing edge

0.65 0.70 0.75 O.K 0.85x/o

Fig. 11. Computed skin friction coefficient in the flapwell region for a - -8.11* and a - 8.59 *.

Cp

° measurementswith flap weflcalc.

•••••- without flap well calc.

0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2Xfc

Cp

0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2X/c

Cp

0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2(c)

Fig. 12. Comparison of measured and computedpressure distributions hi the flap well neighborhood for(a) a - -8.11*. (b) a - -0.02* and (c) a - 8.59 *.

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Figure 12 shows that flap well results are betterthan those obtained with the fairing which ignoredthe presence of the flap well. On the main element,while the agreement is satisfactory for a = -8.11°, theregion of recirculating flow is under predicted for a =-0.02° and a = 8.59°. This may be due to severalfactors, such as the inappropriateness of theinteraction law and of the turbulence model for suchrecirculating flows. Work is in progress to improvethe results. However, the pressure distribution on theflap upper surface, in particular close to the leadingedge, is satisfactory, which suggests that thedisplacement thickness prediction is accurate near thetrailing edge of the main element.

Lift and drag coefficients were computed but arenot shown here since they are essentially the same asfor the case without flap well (Fig. 7).

4. Concluding Remarks

An interactive boundary-layer method with animproved Cebeci-Smith eddy viscosity formulation isused to calculate the aerodynamic performancecharacteristics of high lift devices. The results showgood agreement with measurements for a variety ofmultielement airfoils comprising slats, main elementand flaps. The method has also been extended to thecomputation of airfoils with flap wells, and the resultsshow the same overall level of accuracy. In general,the predictions are excellent for relatively low anglesof attack and very satisfactory up to stall. The studyshows that the onset of transition location plays asignificant role in predicting drag and that itscalculation must be a part of the computationalmethod. The study also shows that for some flowsmerging of shear layers takes place and, since thepresent method does not account for this merging, thecalculated results near stall conditions, whilesatisfactory, are not as good as those at lower anglesof attack.

The stall prediction is satisfactory for most cases.However, when the pressure peak on the mainelement reaches values close to or greater than thecritical pressure coefficient, a truly compressibleinviscid method, such as a full potential or Eulermethod, should be coupled with the presentcompressible boundary layer method in order tocompute stall with reliability. Work is in progress toincorporate these capabilities, including the mergingof shear layers.

References1. Rogers, S.E., Wiltberger, N.L. and Kwak, D.,

"Efficient Simulation of Incompressible ViscousFlow Over Single- and Multielement Airfoils,"AIAA Paper No. 92-0405,1992.

2. Rogers, S.E., "Progress in High-Lift AerodynamicCalculations," AIAA Paper No. 93-0194, Jan.1993.

3. Valarezo, W.O. and Mavriplis, D.J., "Navier-Stokes Applications to High-Lift Airfoil Analysis,"AIAA Paper No. 93-3534, Aug. 1993.

4. Cebeci, T., "Calculation of Multielement Airfoilsand Wings at High Lift," AGARD ConferenceProceedings 515 on High-Lift Aerodynamics,Paper No. 24, Banff, Alberta, Canada, Oct. 1992.

5. Cebeci, T., Besnard, E. and Messie, S., "AStability/Transition-lnteractive-Boundary-LayerApproach to Multielement Wings at High Lift,"AIAA Paper No. 94-0292, Jan. 1994.

6. Cebeci T, "Essential Ingredients of a Method forLow Reynolds-Number Airfoils," AIAA Journal,Vol. 27, pp. 1680-1688, 1983.

7. Cebeci, T., An Engineering Approach to theCalculation of Aerodynamic Flows, to bepublished, 1996.

8. Fiedler, H. and Head, M.R., "IntermittencyMeasurements in the Turbulent Boundary Layer,"J. Fluid Mech., Vol. 25, Part 4, pp. 719-735, 1966.

9. B. Van den Berg and B. Oskam, "Boundary LayerMeasurements on a Two-Dimensional Wing withFlap and a Comparison with Calculations,"AGARD CP-271, Sept. 1979.

10. E. Omar, T. Zierten and A. Mahal, "Two-Dimensional Wind Tunnel Tests of a NASASupercritical Airfoil with Various High LiftSystems," NASA CR-2215, 1977.

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