Analysis of a Theoretically Optimized Transonic Airfoil

Home , Transonic

NASA Contractor Report 306s

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Analysis of a Theoretically Optimized TransonicAirfoil

M. E. Lores, K. P. Burdges, and G. D. Shrewsbury

CONTRACT NAS2-8697 NOVEMBER 1978 TECH LIBRARY KAFB, NM

00b1772 NASA Contractor Report 3065

Analysis of a Theoretically Optimized Transonic Airfoil

M. E. Lores, K. P. Burdges, and G. D. Shrewsbury LockheedGeorgiaCompa~y Marietta,Georgia

Prepared for Ames Research Center under Contract NAS2-8697

National Aeronautics and Space Administration Scientific and Technical Information Office

1978 Numerical optimization was usedin conjunction with an inviscid, full potent'ial equation, transonic flow analysis computer code to design an upper surface contour fora conventional airfoil to improve its supercritical performance. The modified airfoil was tested in the Lockheed-Georgia Com- pressible Flow Wind Tunnel. The majority of the test was done at eleven million Reynolds number anda four percent tunnel top and bottom wallporosity. A limited amount of testing was done to obtain data at other Reynoldsn umbe rs and wall porosities.

The modified airfoilIs performance was evaluated by comparisonw ith test data for the baseline airfoiland for an airfoil developed by optimization of only the baseline airfoil'sleading edge. While the leading edge modification performed as expected, the upper surface re-designdid not produce all of the expected performance improvements. Although the drag divergence Mach number was increased, the modified airfoil exhibitedmore'drag creep than for the baseline section. This larger drag creep is attributable to the early formulation (at approximately L=.68) of a relatively strong leading edge shock wave.

Theoretical solutions computed using a viscous, full potential equation transonic airfoil code were compared to experimental data for the baselineairfoil and the upper surface modification. These correlations showedthat the theory predicted the baseline airfoil's aerodynamics fairly well,but failed to accurately compute results for the upper surface modification. This failure is shown to be attributable to the inability of the theory to properly treat the thick trailing edge boundary layer associated with the upper surface modification.

Numerical optimization is concluded to offer the means for efficiently designing advanced airfoils. However, until a completely reliable viscous airfoil analysis technique is developed, optimization can be used with confidence only when the character of the viscous flow is significantlyalteredduringnot the optimization process.

ii TABLE OF CONTENTS

Page

SUMMARY ...... i i

INTRODUCT I ON ...... 1

SYMBOLS ...... 4

AIRFOILDESIGN ...... 5 ProblemDefinition ...... 5 NumericalOptimization ...... 6

EXPERIMENTALTESTS ...... 10 Apparatus and TestProcedures ...... 10 Tests andMethods ...... 12

RESULTS AND DISCUSSION ...... 14 C141H7274 Airfoil Aerodynamics ...... 14 Comparison ofAirfoils ...... 15 DesignMethod Evaluation ...... 17

CONCLUDINGCOMMENTS ...... 21

REFERENCES ...... 22

APPENDIX A: PLOTTEDTEST DATA ...... 61

iii

. I NTRODUCT I ON

Efficienttransonic performance continues to bean importantdesign requirementfor manynew aircraft.Specialized airfoils whose contoursare dependentupon design conditions are needed toachieve the desired transonic performance. To designthese airfoils rapidly and effectively,aerodynamicists musthave availableaccurate and easy-to-usetheoretical design methods.The nonlinearityof the partial differential equations that describe transonic flows hashampered thedevelopment of such theoreticaldesign methods. However, advances incomputational fluid dynamics, together with the availability of large and fastcomputers, have resultedin the recent availability of anumber oftransonic design techniques.

Airfoildesign methodscan be categorized as eitherinverse or direct procedures.Inverse methods involve the specification of a desiredpressure distribution and thecalculation of the corresponding airfoil. The need to specify a priori a pressuredistribution that will resultin a physically realisticoptimized airfoil is a disadvantageof inverse procedures. inverse methodshave been formulatedeither by usinghodograph equations or by solving theproblem in the physical plane (e.g., refs. 1 and 2, respectively).Since hodographformulations are applicable only to shock-free flows, they are of limitedusefulness in transonic design. Also, considerable user expertise is requiredto employhodograph design methods. Physical-plane solutions suffer computationaldifficulties in the leading edge regionwhich are usually avoid- edby specifyingthe airfoil geometrynear the leading edge. Sinceproper leading edge designis needed todesign optimized transonic airfoils, this approach limitsthe usefulness of physical plane inverse solutions in transonic designwork.

The above-mentioned difficulties are avoided in direct design methods. inthis design approach, a numericaloptimization algorithm is coupledwith a suitableaerodynamic analysis method todesign airfoils that are in some sense optimizedfor .specific flight conditions. For example, an airfoil contour canbe determined which minimizes drag at a specific lift coefficient withthe pitching-moment coefficient constrained to be withinacceptable limits. Perhaps the most promisingdirect design method is underdevelopment at NASA-Ames byHicks and hisassociates. The method isdescribed and-example designsare discussed in references 3 and 4. Briefly,the method involves coupling a numericaloptimization scheme developedby Vanderplaats (ref. 5) withproven airfoil analysis methods. The abilityto useany theoretical analysis methodand any numericaloptimization'algorithm makes thetechnique very versatile.

Currently,the transonic full potential codedeveloped by Jameson (ref.6) isbeing used toprovide the neededaerodynamic data. Viscous effects, known to be importantin transonic flow calculations, are neglected in Jameson's analysis method. An inviscidaerodynamic module is usedbecause currently availableviscous transonic airfoil analysis programsare not completely reliable, and theyrequire more computationtime than inviscid techniques. Experiencewith applying the procedure to design subsonic airfoils has indi- catedthat aerodynamic performance predicted by inviscid methods will be manifested when a viscousanalysis of the resulting airfoil is performed. Thereis, nevertheless, aneed toexperimentally verify the performance of transonicairfoils designed usingthe inviscid procedure.

Because of its versati lity,Hicks' method should be usefulboth in tran- sonicdesign projects in wh ichperformance improvements inexisting aircraft aresought by airfoilmodif ication, and inprojects in which new airfoils for advanced aircraftare required. The first applicationis being investigated in a projectbeing conducted by Lockheed. Withthe aid of Hicks, Lockheed researchersrecently appl ied the procedure to the redesign of the forward 12% ofthe C-141 airfoilleading edge. Thisapplication was selected because that airfoil exhibits a largedrag creep which might be reducedby a limitedmodi- ficationof the leading edge. Thiswork was successfulin that the predicted dragcreep was reduced tothe same levelobtained by a trial and correction processin which analysis methodswere used toevaluate many candidateleading- edge modifications,but in a fractionof the time.

The airfoil leading-edgedesign using Hicks' method was obtainedby mod ifyingonly the C-141 airfoil uppersurface. In contrast, the airfoils des ignedusing the trial-and-correction procedure involved simultaneous upper

2 and lowersurface modifications. Consequently, Hicks' modification may be easierto incorporate as an aircraft change. Further, because it has a larger leading-edgeradius, Hlcks' airfoil may providebetter low-speed stall charac- teristicsthan either the basic C-141 sectionor the other proposed airfoil modifications.

The Hicks'modification to the C-141 airfoil leading-edge,as well as the basic C-141 section, havebeen testedin the LockheedCompressible Flow Wind- Tunnel (CFWT) attransonic speedsunder an internal Lockheed research program. Airfoilsurface pressure distributions and theattendant forces and moments were obtainedfor an extensiverange of Mach numbersand lift coefficients. These datasubstantiated the theoretically predicted performance improvements resultingfrom numerical optimization. The windtunnel test data showed that a 7% improvement in (ML/D) may have resultedfrom the modification of the upper surfaceof the forward 12% ofthe airfoil. In addition to producing an effic- ientairfoil modification, numerical optimization required about half the computation time and resultedin a25% reductionin engineering hours when compared to a conventionaltrail-and-correction approach.

The purpose of the workreported herein was to determine the applicability ofnumerical optimization in an extensiveredesign of a conventionalairfoil to improve itssupercritical performance. The problemselected was there-contour ingof the entire upper surface of the baseline C-141A wingairfoil section. Thisproblem was selected because the availability of the workalready done on the C-141 airfoil uppersurface leading-edge modification premitted an efficient comparison of the use of numericaloptimization for limited and extensiveair- foilmodification.

Inthis report, the aerodynamic design of the upper surface modification usingnumerical optimization is discussed, the wind tunnel model design and testare described, the redesigned airfoil performance is compared withthat ofthe baseline and modifiedleading-edge airfoils, and thedesign procedure is evaluated.

Forreasons which will become apparent,the upper surface modified airfoil will be referredto as C141H7472.The baselineairfoil and theoptimized

V optimizationdesignvariables

z coordinatenormal airfoilto chord line, cm (in.) a geometricangle airfoilof chord 1 ine,degrees

Y specificratio ofheats

T windtunnelporosity,wall %

Subscripts:

t.e. trailingt.e. edge

T transitionlocationstrip

0 normalforcezero

1 tunnelstation one chordlength downstream of model m denotesfreestream conditions

Abbreviations:

CFWT LockheedCompressible Flow Wind Tunnel

1, 1.5. lowersurface

u, U.S. uppersurface

L.E. 1 ead i ng edge

AIRFOIL DESIGN

ProblemDefinition

The design objective of this study was tominimize the cruise drag of the

basel ine C-141 airfoil, and toincrease the ! dragdivergence Mach number at cruise 1 ift. The section Mach numberand lift coefficientcorresponding to a i rplane cruiseconditions are .72 and .57, respectively.In order to have a direct comparison withthe leading-edge upper surface modification of the base 1 ine airfoil designedby Lockheed and Ames, theairfoil modification was restrictedto the uppersurface. Geometric cqnstraints imposedon theairfoil modification were thatthe thickness-to-chord ratio not bereduced and that

5 theairfoil leading-edge retain at least the same degree ofbluntness. The lattercondition was imposed to avoid potentially poor airfoil stall characteristics.

NumericalOptimization

The airfoil uppersurface contour needed toattain the design object i ve was determinedusing the previously discussed NASA-Ames aerodynamic numer ical optimization scheme.

Design pointdefinition. - Sincethe optimization scheme used an inviscid transonic method toprovide aerodynamic data required during the optimization process,the first stepin the design study was todetermine an inviscid designcondition. The underlyinghypothesis in this inviscid optimization is that improvements made atthe inviscid design conditions will be realizedin a viscousflow.

b The invisciddesign condition was determinedby first computing a viscous solutionusing the NYU transonicflow analysis routine (ref. 1) forthe baselineairfoil (C141-1) atcruise conditions. Since the evaluation of the optimizedairfoil would bedone usingwind tunnel data, the solutions were computed atthe tunnel Reynolds number.Thus, thefollowing conditions were specifiedin performing the viscous calculations:

Cn = -57 ~m = .72 RN = 11 X lo6 x/c = .10

The resultsof these calculations are shown infigure 1 where theyare compared withexperimental data. The agreementbetween theory and experiment shown here is fair,with the major discrepancy being the slightly more aft theoretical shock location.Since recent work by Blackwell, et al., reported inreference 7 shows thestrong dependence of shock locationto wall porosity

6 c

and since the theoretical calcualtions are done with free-air boundary con-

dit ilons, no attempt was made to seek better theory-to-experiment agreement.

The viscous solution indicated that the airfoil angle of attack to achiseve the above conditions was approximately two degrees. The assumption was made that the lift loss due to viscosity for the optimized airfoil would be about the same as for the baseline airfoil. The inviscid design point was thus defined to be:

M, = .72 a = 20

Design object&. - The design objective (i.e., the parameter to be minimized at the design point) for this study was wave drag minimization at the design point. In an attempt to increase MDD, and at the same time avoid a point optimization which would be reflected in a local bucket in the Cd variation with Mach number, a secondary design objective was to reduce Cdw at .74 Mach number. This second design objective was introduced as a constraint in the optimization scheme, and its imposition is discussed in the following section. Consequently, the objective function in the minimization scheme was:

OBJ = Cdw(a = 2O, M, = .72)

Design constraints. - Four constraints were imposed during the optimization scheme:

(1) Z upper /C (X/C = .5) > .074 (2) Z upper /C (X/C = .005) > .01 (3) Cn > -85 (4) cdw (a = 2O , M, = .74) > -0020

The first constraint was imposed to ensure that the optimized airfoi 1 was at least as thick as the baseline section. An arbitrary nose bluntness was forced by the second constraint. The third constraint was required in an a t tempt to ensure that when viscous effects were taken into account, the airfoi 1 would

7 produce atleast the desired cruise lift. The finalconstraint enforces the secondarydesign objective by requiring Cdw at M, = .74 beless than 20 counts. The 20-countlevel was selectedto be compatib le with the drag at M, = .72 to produce a flat Cdw versus M, curveat Cn = .57

Designvariables. - Properselection of design variables is imperative if thedesign objective is to be efficientlyattained in numerical optimization. Inthe leading-edge modification study a singlepolynomial representation of theforward 12% of theupper surface was used. Inthat case,the design variables(i.e., the parameters perturbed during the optimization scheme) werethe coefficients of thepolynomial and/or the exponents on the polynomial terms. Thisapproach proved to be successfulbecause only a fewterms were required to achieve sufficient design flexibility andhence computation timeswere small.

However,numerous polynomialswould be requiredto provide an entire upper surfaceparameterization with adequate design flexibility with each polynomial maintaingordinate and at least first derivative continuity at the matchpoin-ts. Such anapproach would not only be complex, it wouldalso be computationally expensive.Therefore, an alternativeairfoil parameterization schemewas used inthis study. Thescheme was developedby Ames researchers and it involves the use ofperturbation shape functionsto distort the upper surface contour ofthe baseline airfoil. The shape functionsused in this work are shown in figure 2 withtheir defining equations. In this case, thedesign variables arethe pre-multiplying coefficients which determine the magnitude of the in- dividual shape functions. These pre-multiplying(or participation) coefficients areadjusted by the optimization scheme untilthe design objective is met with- outviolating the constraints. Thus, twelve(12) geometric design variables wereused inthis study. An additionaldesign variable, the angle of attack (a), was tried and found to beunnecessary.

Airfoil nomencalture. - Sincethe upper surface modification was developed withthe objective of reducing the drag of thebaseline C-141 airfoil at .72- and .aMach numbers,and sinceperturbation shape functionswere developed by -Hicks at NASA-Ames, the resulting airfoil will be referred to as C141H7472. For thepurposes ofthis report, the baseline section will be called C141-1.

8 Since the optimized leading edge was the sixthin a series of leading edges designed for the baseline section, this airfoiis called C141-6.

Optimization results. - The numerical opt mization was doneby starting with the baseline airfoil ata = 2O and comput ng solutions for M, = .72 and M,,, M,,, = -74 for the perturbations of the design variablesuntil the design objective and the four constraints were met. The initialand final inviscid pressure distributions forMoo = 0.72 and MOD = .74 for the C141-1 and the C141H7472 airfoils are shown in figure 3. The amelioration of the inviscid flow field and the attendant reduction in wave drag resulting from numerical optimization is evident in these data.

The C141-1 and C141H7472 airfoil geometries are shownin figure 4 and the coordinates of the C141H7472 airfoil are listed in table I. Evident in this figure is the attempt by the optimization code to use aft-camber to achieve the design objective. Since the lower surface was fixed, the only way in- to corporate aft-camber was to"hump" the upper surface at about 75% chord.

The aft hump leads to a strong adverse pressure gradient on the upper surface near thetrailing edge which conceivably could havea catastrophic effect on the boundary layer. This possibility was examined by computing the viscous flow about both airfoils using theNYU 2-D transonic airfoil program. The results of these calculations are shownin figure 5 where inviscid and viscous results for theai rfoi 1s at ct = 2O and M, = .72 and Moo = .74 are shown. The separation point predicted by the Nash-Macdonald (ref. 1) criteria used in the NYU program are flagged in the pressure distributions. Separation is predicted to occur on both airfoils, with the separation point being further forward on the C141H7472 airfoil. The default procedure of theNYU program for treating trailing-edge separations was used in these calculations. (The procedure is described in detail in reference 1.) Using the default procedure, the program predicts that both airfoils will have about the same drag, despite the apparent shock-free flow associated with the modified airfoil.

The lift loss due to viscosity is also evidentin the results shown in figure 5, and it is larger than estimated. Consequently, the airfoils have to operate at an angle of attack greaterthan 2O to achieve a Cn = .57.

9 The decision wasmade at this point to test the C141H7472 airfoil despite thepredictions of flow separation and theuncertainty in the actual viscous designcondition. This decision wasmade because ofthe belief that test data were neededtoprovide guidance for future applicationsofnumerical optimization. The model design and windtunnel test are discussed in the next section of this report .

EXPERIMENTALTESTS

Apparatusand Test Procedures

Model. - A two-dimensional model ofthe C141H7472 airfoil was fabricated from 17-4PH stainlesssteel in accordance with the coordinates given in table I. The modelhas a chordof 17.. 78 cm (7.00in.) andaspan of 50.80 cm (20.00 in.). The model completely spans thetwo-dimensional test section and is supportedfrom the side walls by means of tangs. A photograph ofthe model installedin the LockheedCompressible Flow Wind-Tunnel is shown infigure 6.

The model was instrumentedwith fifty-three (53) static-pressure measuring orifices: 27 on theupper surface and26 on thelower surface. The orifices were locatednear the mid-span of the modeland weremounted flush andnormal tothe local contour. The measured orificelocations are listed in table II.

The model contour was checkeddimensionally using a template and feeler gage. Discrepanciesfrom the design contour were mostlywithin k.025 mn (.001 in.)with some areasreaching deviations of k.050 mm (.002in.). The airfoil surface was polishedto conventional transonic model surfacefinish of less than .4 microns(15 microinches). Spanwise twist andwarp ofthe model were found to be nil.

Testfacility. - The model was testedin the Lockheed CRJT. Reference 8 contains a completedescription of this facility. The tunnel is ofthe blow- down type,exhausting directly to the atmosphere. The airstorage capability is 368 m3 (13,000 ft3) at 4.13 x lo6 N/m2 (600psia). A sleeve-typecontrol

L valveaccurately maintains the settling chamber stagnationpressure at selected pressureless than or equal to the 1.72x lo6 N/m2 (250psia) maximum and at mass flowrates less than 1089 kg/sec. (2400 lb/sec.).

The testsection is 50.8 cm (20.0 in.)wide by 71.2 cm (28.0 in.)high by 183 cm (72.0in.) long and is enclosedin a 3.7 m (12.0 ft.) diameterplenum chamber. Forthe model tested,the tunnel height to model chordratio is 4.0 and thetunnel span to model chordratio is 2.9. ModePblockage was 3 percent ofthe test section cross sectional area. The top and bottomwalls of the two- dimensionaltest section have variableporosity capability (from 0 to lo%), obtainedby sliding two parallel plates with .635 cm (.250in.) diameter holes slanted 60 degreesfrom the vertical. The2-D testsection side walls are not porous.

Wake surveyrake. - The fixed wake-surveyrake used for section drag measurements isdescribed in figure 7 and shown installedin the tunnel in figure 6. Thewake rake was mounted atthe tunnel centerline one chordlength behind theairfoil model. The rake hasa totalof 90 total headmeasurement tubes and fourstatic pressure tubes. The tubesare .15 cm (.06in.) in diameter. Thewake rake hasbeen calibrated in thetunnel without amodel present.

Datahave been obtainedin prev iousCFWTairfoi1tests similar to that conductedherein with the wake rake installed andremoved todetermine its influence on theflow overthe airfoil. These unpublisheddata indicated the wake rake hadneg ligible effects on thenormal-force coefficient, the pitching-momentcoeff icient, and theairfoil pressure distribution.

Instrumentation. - Measurements of the static pressures on the airfoil surfaces and the wake rakepressure were made using electronically actuated pressurescanning valves. The full-scale range ofthe quarter-percent accuracy forthe wind tunnel conditions tested: wake rake - 28.6 dynes/cm2 (k12.5 psi); and airfoilpressures k34.4 dynes/cm2 (250.0 psi). CEC forcebalance pressuretransducers wereused inconjunction with CEC servoamplifiers to provide a precise measurement ofthe atmospheric pressure, stagnation pressure, and testsection static pressure to .025% ofthe transducer capability: 6.89~ lo5 N/m2 (100.0 psi)for the test section static and 1.38~10~N/m2 (200.0 psi)

11 forstagnation pressure. These transducersallow determination of the test section Mach number to a accuracy of 5.001 atthe higherst stagnation pressure.

Angle of attack was measured with a calibratedpotentiometer operated by the angle of attack drive mechanism.

Raw pressuredata were recorded on magnetic tape utilizing theCFWThigh speed dataacquisition system.

Test and Methods

Testconditions. - The aerodynamic characteristicsof the C141H7472 airfoil wereinvestigated over a widerange oftest conditions. The angleof attack of the airfoil was variedfrom 0 to 5 degreesand the Mach number range investigated was from 0.45 to 0.78.Tests were conducted at nominalReynolds numbers basedon airfoil chord of 4 and 11 mi 11 ion. The majorityof the tests was conductedfor a wind-tunnelporosity of 4%. Limiteddata were obtained over a wallporosity range of 2 to 6% to ascertain the sensitivity of the new airfoilto this parameter. These resultsare included in Appendix A.

Datareduction. - The staticpressure measurements atthe airfoil surface werereduced tostandard pr essurecoeff icients andthen machine integrated to obtainsection normal-force and section pitching-momentcoefficients about the quarterchord using the fol lowingequat ions :

1 .. .. = I (cp2 - 0

Sectionprofile drag measurementswere computed from the wake surveyrake measurementsby the method ofreference 9 utilizingthe following equations:

12 and

The ,ked is a correctionfor the wake raketotal head tubedisplacement effect when in a transversevelocity gradient. This correction is discussed inreference 9 and is given by

Transition. - Forthe Reynolds number testsof 4 million, boundarylayer transition was fixed. The airl'oil was investigatedwith roughness particles located on bothsurfaces at 0.05 C. The roughnessheight was 0.00039 C and was. selectedaccording to the criteria of reference 10. The roughness strips were 0.13 cm (0.05 in.)wide and consistedof Ballotini glass beads setin a plasticadhesive.

For theReynolds number tests of 11 million no transitionstrips were uti 1 ized.

Tunnelwall effects. - The effectof the tunnel walls on the twodimen- sionality of theflow is consideredto be small.This statement is supported bymeasurements reportedin reference 11 on thebaseline C-141 airfoilwith a similartest arrangement. These resultsindicated very little variation of thepressure coefficient across the rodel span forvarious flow conditions. The conclusion was furthersubstantiated by observationof oil flow patterns atthe airfoil-wall intersction. Disturbances in this juncture were confined to a verysmall regions.

Standardsubcritical wind-tunnel boundary corrections (normal-force interference and blockage ) havebeen calculatedfor this test using the method of reference 12. Recent studies(ref. 7) have shown, however, this method to be

13 generally inadequate at transonic speeds. As a result, these corrections have not be applied to the data presented herein.

RESULTS AND DISCUSSION

A complete set of basic aerodynamic force and moment data as well as surface pressure distributions for the C141H7472 airfoilat a Reynolds number of 11 million and wind-tunnel wall porosity of4% is contained in Appendix A. These data will form the basis for assessing the modified airfoil performance to be discussed below, and unless stated otherwise all data will be for these conditions. Appendix A also contains limited data fora Reynolds number of 4 million, wind-tunnel wall porosity data from2 to 6%.

The evaluation of the performanceof the C141H7472 airfoil will be made by compar i ng test data for this airfoi1 with data obtained in a recent test of the C141- 1 and C141-6 airfoils. Fo llowing this airfoil performance evaluation, the efficacy of the design procedure will be examined.

C141H7472 Ai rfoi1 Aerodynamics

The experimenta 1 data obtained from the C14 1H7472 airfoil model in the Lockheed-Georg ia CFWT are discussed in this section. This discussion is fol- lowed by a rev iew of the aerodynamic forces resulting from the surface pressures.

Airfoi 1 pressures. - The variation w ith free stream Mach number of the surface pressure distributionsat the design normal force coefficient of0.57 can be seen in the data shown in figure 8 . A number of conclusions can be drawn from these results. First, the airfoil does not have the aft-loading associated with the cusped region ofa modern supercritical airfoil. In fact, there is a small negative lift region covering the last ten percent chord. This lack of aft loading is attributable to the modification of only the upper surface. Since the lower surface could not deform, the amount ofaft camber that could be designed into the airfoil was limitedby geometric constraints.

14 The only way to induce any aft-loading was thus"hump" to the rear upper surface; a design change which was doneby the optimization design code.

The airfoil hasa substantial suction peak which becomes supersonic at about 0.6 Mach number. The supersonic region increases in size with increasing Mach number, and is terminated bya fairly strong shock wave for Mach numbers greater than about 0.64. The maximum shock strength prior to drag divergence is reached at a free stream Mach number of 0.68. In this case, the local Mach number ahead of the shockis 1.26, and the shock induces a localized separation bubble at the footof the shock.

The variations with free stream Mach number of shock strength and location are summarized in figure 9. The shock movemer?t is orderly, with the shock first forming at M, = 0.60 at about 2% chord, and moving aft to approximately 55% chord at Mm = 0.78. The rapid increase in shock strength at about0.68 Mach is evident in this figure. This early formation ofa strong shock wave can be expected to have detrimental effect on airfoil drag characteristics.

Airfoil forces. - The airfoil drag coefficient variation with Mach number for Cn = 0.57 is shown in figure 10. These data exhibit a substantial drag increase in range of M, = 0.60 to 0.72. This rapid and undesirable drag increase is no doubt caused by the formation of the relatively strong leading edge shock discussed in the preceeding section. From M, = 0.72 to M, = 0.76 the airfoil drag remains fairly constant. This result is interesting since a "flat" Cd vs M, curve in this Mach range was one of the airfoil design goals. For Mach numbers greater than 0.76, the airfoil experiences the onset rapidof drag rise associated with the increasing strength of the shock wave.

Comparison of Airfoils

Airfoil C141H7472 was designed at an inviscid condition which was expected to produce a minimum wave drag airfoil ata normal-force coefficient of0.57. In this section, the performance of this airfoil at its design point relative to both the C141-1 and C141-6 airfoils is evaluated. The variation of measured drag with Mach number for the three airfoils Cnat = 0.57 is shown in figure 11. The following observations can be made form these data:

15 1. Airfoil C141H7472 has a higherdrag divergence Mach number than either of the other two sect ions.

2. For Mach numbers lessthan MDD forthe C141-1 airfoil,the C141H7472 airfoil has substantially more drag.

3. The leading-edgemodification to the baseline airfoil (C141-6) reduces thesupercritical drag and increases MDD relativeto the baseline airfoil (C141-1).

The reasons for theseresults canbe deduced fromthe chordwise pressure distributions shown infigure 12. For M, = 0.55, theflows are subcritical, and inthe absence of any indicationsof flow separation, the higher drag of themodified airfoil is probably attributable to its blunt trailing edge. The rapiddrag increase of the airfoil C141H7472 atapproximately M, = 0.68can be seen to bedue tothe formation of a strongleading-edge shock wave which does notappear on either of the other two airfoils. TheMach number upstream of theshock wave isapproximately, 1.26 at M, = 0.68and Cn = 0.56.

As Mm increases and thedesign Mach numbers areapproached, the pressure distributions show thatthe shockon airfoil C141H7472moves downstream,and decreases instrength. At the same time, a shock wave formson the other two airfoils, and increasesrapidly in strength. This behavior results in the increased MDD associatedwith the C141H7472 airfoil.

Not directly anoutcome ofthis study, but nevertheless of interest, is theperformance ofthe airfoil with the leading-edge mdification (C141-6) near its designpoint. When compared withthe baseline airfoil (C141-1), the leading-edgemodification produces significantly more leading-edgesuction (fig. 12).Also, the suction peak isfollowed by a nearlyisotropic re- compression.This behavior results in the avoidance of the premature shock formationwhich occurred when theentire upper surface was modified. An inter- estingquestion, and onewhich remains to be definitely answered, is the fail- ureof the optimization scheme to find a leading-edgegeometry which would produce a similarisentropic compression when theentire upper surface was

16 modified. Perhaps the different results are attributableto the use of differ- ing shape functions in the optimization scheme.

The airfoil C141H7472 did not perform as expected atCn = 0.57. The preliminary theoretical analysis discussedin the airfoil design section indicated that the normal-force loss dueto viscosity might have been underestimated in establishing the inviscid designpoint. Consequently, the airfoil C141H7472 might be expectedto perform better at a reduced normal-force coefficient. However, the drag variations with Mach number for the three airfoils at Cn = 0.50 exhibit the same general characteristics as theydid at Cn = 0.57, as evidencedby the data on figure 13.

Design Method Evaluation

The experimental data comparisons discussed above show that the upper surface modification increasedM, at the expenseof more drag creep, and that in fact the C141H7472 airfoil's drag at theM, = 0.72 and M, = 0.74 design points was larger than that of the baseline airfoil. This less than satis- factory airfoil performance wasnot a result of the failure of numerical optimization, because the optimizationdid reduce the design objective,inviscid Cd,. This fact is evidenced by figure 3 where the inviscid pressure distributions forboth airfoils at the design conditions were shown.

The lack of performance by the C141H7472 airfoil, then, must be due to adverse viscous effects which werenot taken into account. The effects of viscosity on airfoil performancewereexamined by computing solutions using the viscous NYU program (ref. 1) for both the baseline and the modified airfoils and comparing the solutions with experimental data. The solutions were computed using the non-conservative optionin the NYU code, and employing the program in more-or-less "cook book" form. However, the boundary layer dis- placement effects had to be drastically under-relaxed, and two inviscid iterations were done between boundary layer calculationsto permit a more stable convergence process.

The ag reement between theoret 1ica drag predictions and experimental re- sul ts is in genera 1 poor for both the base1 ine and the modified airfoil as demonstratedby the data shown in figure 14.The followingobservations can be made fromthese data:

1. MDD is predictedto within 004 Mach number for both airfoils. 2. The shape ofthe drag curve for the base1 ine airfoil is fairly we1 1 predicted,but is underestimated by approximately 10 counts. 3. Boththe level and the shape ofthe C141H7472 airfoil'sdrag curve are rnispredicted by theory.In particular, the early drag rise occurring at M, = 0.68 is missed inthe theoretical calculations.

The reasons forthe failure of the NYU viscoustransonic codecan be deducedby comparingtheoretical and experimentalpressure distributions at the sameMach numberand 1 ift coefficient. These dataare shown forthe C141-1 and C141H7472 airfoilsin figures 15 and 16, respectively.

The results shown infigure 15 indicatethat the C141-1 airfoilpressure distributionsare fairly well predicted by theory, with the major discrepancies beingthe shock location, trailing edge pressurerecovery, and thelower sur- facepressure level. The failure to properly compute thetrail ingedge pressure recoveryis probably due tothe large (approximately 20 degrees) trail ing-edge includedangle which produces a thick boundarylayer. The NYU codeuses a conventional(albeit adjusted) boundary layer methodwhich is notapplicable tothick boundarylayers. The impropercalculation of the trailing edge flow causeserroneous resultselsewhere, as manifestedby the incorrect shock wave and lowersurface pressures.

Dispitethe fact that the theoretical shock wave isstronger than the experimental shock, the NYU programpredicts a lowerdrag level than recorded inthe test. Drag predictionusing this code,then, isprobably too uncertain for use innumerical optimization, even when thegeneral character of the airfoilpressure distribution is fairly well predicted.

The theoreticalpressures for the C141H7472 airfoil bear little resembl- ance totheir experimental counterparts, asevidenced by the results shown in figure 16. At Mm = 0.72, theentire character of the leading edgeshock is missed,while at MOD = 0.74, a dualshock is predicted when only oneshock

18 occurred.In both cases, the trailing edge pressurerecovery is over-predicted; evenmore so thanfor the baseline airfoil. Also, the lower surface pressures areunder-predicted, but not quite to the same degreewhich they were missed forthe C141-1 airfoil.

Solutionsfor the C141H7472 airfoil were also computed atoff-design conditions, and results for Mm = 0.45 and Mm = 0.78 are shown in figures 17 and 18, respectively(both solutions are for Cn = 0.57). For thesubcritical M, = 0.45 condition, agreementbetween theory and experimentis good, exceptfor the aforementionedtrailing edge pressurerecovery. At M, = 0.78, theshock wave has moved aftto approximately 55% chord, and thesupersonic re-expansion which occurredin the M, = 0.72and 0.74 solutionsis not predicted. Although agreement here is betterthan at the design conditions, it is notsufficiently accuratefor airfoil optimization. In fact, drag predictions are relatively accurateonly for subcritical flows for the C141H7472 airfoil.

All ofthe discrepancies are probably attributable in the main to improper modeling ofthe viscous trailing edge flow.This failure is accentuatedfor the C141H7472 airfoil because the "hump" inthe upper surface produces a strong adversepressure gradient near the trailing edge. The resultinggradient produces a thicker boundarylayer than can be predicted by simpleboundary layer theory.This thick boundary layer produces a reduced trailing edge pressure recovery when compared tothe baseline airfoil; a resultwhich is not predict- edby theory.

Experiencesboth at Lockheed and elsewherehave shown the NYU code to yieldreliable transonic results for other airfoils. Consequently, alternate reasons for the failure to predict the C141H7472 airfoil's aerodynamicswere explored.

One possibility examined was windtunnel wall interference. Previous testsin the CFWT (includingthe baseline airfoil tests) indicate that 4% porositybest simulates free-air conditions. Was it possible, however, that goodagreement could be attained between theory and experiment forthe C141H7274 airfoilusing a differentwall porosity? This question was answeredby using thelimited variable porosity data taken in this test, and comparing them with theoretical solutions at the same lift coefficients. The result of this side-study was that good agreement could not be found for any porosity(2% to 6%) investigated.

A second possibility for the disagreement might be the failure of the invisci d flow region nonconservative formulation. This possibility was explored by computing some solutions using the quasi-conservative differencing scheme option included in the NYU code. This study was done becausea con- servat i ve problem formulation is known to be correct for flows with shock waves. Consequently there wasa need to determine if the use of sucha formulation would improve the data correlations for the modified airfoi1. The results of this study are summarizedin figure 19 where nonconservativeand quasi-conservative solutions are compared with experimental data formd- the ified airfoil at the design points. As these comparisons show, the theoretical solutions are similar,and neither agrees well with test data. The fundamental problem of the failure to accurately compute the trailing edge flow is evident in both solution techniques.

An attempt was made to forcea match between theory and experiment by varying the theoretical angle of attack and/or free stream Mach number. The comparisons were made for experimentalCn = 0.57 and M, = 0.72,0.74, and 0.78. Theoretical solutions were computed using both conservative and nonconservative differencing. The results of that investigation are summarized in figure 20. The improved correlation is evident in these data; however, the improvement was obtained for substantially different theoreticallift coefficients and free stream Mach numbers. Of interest is the close agreement between theoretical and experimental angle of attack. This result implies that the good correlation on shock strengthand position was probably obtained because the airfoil was at the same effective attitudein both the theoretical calculationsand experiment. The trailing edge flow is still not correctly predicted, and the erroneous drag predictions remain.

This attainment of the better theory/experiment correlation required,of course, a priori knowledge of the experimental results. Such a requirement obviously cannot be placed on an airfoil design methodology. Hence, theob- servation can be made that an improved transonic viscous airfoil method is

20 required to make airfoil design practical and reliable. The most needed improvement seems to be a better trailingedge flow formulation.

CONCLUDING COMMENTS

An upper surface for a conventional airfoil section has been designed using numerical optimization to improve the airfoil's supercritical performance. The modified airfoil (C141H7472) was tested in the Lockheed-Georgia Compressible Flow Wind Tunnel. The performance of the modified airfoil was evaluated by comparisons with test data forboth the baseline conventional section (C141-1) and an airfoil development by modificationof only the baseline airfoil's leading-edge (C141-6). An evaluation of the design procedure was then made by comparing theoretically predicted airfoil aerodynamics with experimental results. The salient results of the study are summarized below:

1. The airfoil with modified upper surface (C141H7472) increasedMDD relative to the base1 ne airfoil (C141-1) at the expense of larger drag creep which is attributable to the premature formationof a relatively strong shock wave.

2. Numer i ca optimization did produce an airfoil with reduced inviscid wave drag. However, viscous analysis failed to predict either the premature shock formation or the airfoil's drag level.

3. The failure of the viscous airfoil analysis methodin this application is probably due to the inability of the method to compute the thick boundary layer resulting from the strong adverse pressure gradient occurring over the trail ing-edge regionof airfoil C141H7472.

4. The use of a quasi-conservative formulationin lieu of the standardnon- conservative schemedid not have a significant effecton the useability of the theoretical results.

5. The concept of numerical optimization offers an efficient and versatile method for aerodynamic design. However, inviscid optimization shouldbe restricted to limited modifications whichdo not significantly affect the

21 viscous flow (e.g., the leading-edge re-design study briefly discussed herein), or to airfoil designs for which viscous effects are well-understood.

6. Research should be devoted to developing an improved two-dimensional transonic viscous flow method. If such a method were available, its use with numerical optimization would providea means for the efficient design of advanced transonic ai 1 rfois.

REFERENCES

1. Bauer, F.; Garabedian, P.; Korn, D; and Jameson, A.: Supercritical Wing Sections II. Lecture Notes in Economics and Mathematical Systems, Vo 1. 108, Springer-Verlag, New York, 1975. 2. Carlson, L. A.: Transonic Airfoil Design Using Cartesian Coordinates NASA CR-2578, December 1975. 3. Hicks, R. M. and Vanderplaats, G. N.: Design of Low-Speed Airfoils by Numerical Optimization. SAE Business Aircraft Meeting, Wichita, April 1975. SAE Paper 750524. 4. Hicks, R. M.; Mendoza, J. P.; and Bandettini, A.: Effects of Forward Contour Modification on the Aerodynamic Characteristicsof the NACA 64:-212 Airfoil Section. NASA TM X-3293, Sept. 1975. 5. Vanderplaats, G. N.: CONMIN-A Fortran Program for Constrained Function Minimization - User's Manual. NASA TM X-62282, Aug. 1973. 6. Jameson, A.: Iterative Solution of Transonic Flows Over Airfoils and Wings. Comm. Pure Applied Mach, Vol. 27, 1974. 7. Blackwell, J. A., Jr.; Pounds, G. A.: Wind-Tunnel Wall Interference Effects on a Supercritical Airfoil at Transonic Speeds. JomaZ of Aircraft, Vol. 14, No. 10, pp. 939-935, October 1977. 8. Pounds, G. A. and Stanewsky, E.: The Research Compressible Flow Facility, Part 1: Design. Lockheed Engineering Report ER-9219-1, October 1967. 9. Pankhurst, R. C. and Holder, E. W.: Wind-TmneZ Technique. Sir Isaac Pitman and Sons, Ltd., London, p. 276, 1965. 10. Braslow, Albert L. and Knox, Eugene C.: Simplified Method for Determining of Critical Height of Distributed Roughness Particles for Boundary Layer Transit ion at Mach Numbers from0 to 5. NACA TN 4363, 1958.

22 11. Pounds, G. A.: An Initial Two-Dimensional WallInterference Investigation in a Transonic Wind Tunnel withVariable Porosity Test Section Walls. AlAA Paper No. 72-1011, September 1972. 12.Garner, H. C. ; Rogers, E. W. E.; Acum, W. E. A.; and Maskell, E. C.: Subsonic Wind-Tunnel WallCorrect ions. AGARDograph 109,October 1966. TABLE 1. - DESIGNORDINATES FOR C141H7472 AIRFOIL

UPPERSURFACE LOWER SURFACE ~- x/c z/c x/c z/c x/c z/c

.ooooo .ooooo .35000 .07070 .ooooo .ooooo .00020 -00489 .37500 .07185 .0024 1 .00781 .00040 .00625 .40000 - 07277 .00961 .01527 .00060 .00724 .42500 .07347 .02153 .02192 .00080 .00804 .45000 - 07395 .03806 .02735 .00 100 .00874 .47500 .07421 .05904 .03228 .00200 .01133 .50000 .07426 -08427 .03664 .00300 .01320 .52500 .07410 . 1 1349 .04016 .00400 .01471 .55000 .07374 .14645 .Ob287 . 0 1000 .(I2069 - 57500 .07318 .18280 .Ob51 6 .02000 .02653 .60000 - 07239 .22221 .Ob697 .03000 - 03059 .62500 .(I7135 .26430 .04820 .04000 .03385 .65000 .07002 .30866 .Ob895 .05000 .03664 .67500 .06834 .35486 .Ob928 .06000 .03911 - 70000 .06624 .bo245 .Ob89 1 .07000 .Ob1 33 .72500 .06366 .45099 .04784 .08000 .a4337 ,75000 .0605 1 .50000 .04619 .10000 .Ob698 .77500 .05672 .5490 1 .Ob398 .12500 .05083 .80000 .05222 * 59755 .Oh093 .15000 .05414 .82500 .04698 .64514 .03717 .17500 .05704 .85000 .Ob1 08 .69134 .03314 .20000 .05963 .87500 .03476 73570 .02927 .22500 .06197 .90000 .02840 .77779 .02524 .25000 .06410 .92500 .02240 .81720 .02140 .27500 .06604 .95000 .0 1673 * 85355 .01769 .30000 .06779 -96000 .(I1446 .8865 1 .01410 .32500 -06934 .97000 .01214 .91573 .o 1072 .38000 .00978 .94096 .00765 1 .ooooo .00500 .96 194 .00498 .97847 .(IO278 .99039 .00122 .99759 .00030 1 .ooooo .ooooo

24 TABLE II. - AIRFOIL C141H7472 PRESSURE ORIFICELOCATIONS

UPPERSURFACE LOWER SURFACE

TUBENO. x/c TUBE NO. x/c

1 0.0 28 .0144 2 .0145 29 .0289 3 .0294 30 .0447 4 .0446 31 .0597 5 ,0629 32 .0751 6 .0750 33 .0994 7 -1000 34 .1497 8 .1500 35 .1996 9 .200 1 36 .2494 10 .2497 37 .3000 11 ,3000 38 .3497 12 .3506 39 .3993 13 .bo00 40 .4487 14 .4493 41 .4986 15 .SO0 1 42 .549 1 16 .5493 43 .5996 17 ,5997 44 .6495 18 .6500 45 .6986 19 .699 1 46 .749 1 20 .7506 47 .799 1 21 - 7994 48 .8483 22 .a497 49 .8996 23 .8994 50 .9490 24 .9500 51 .9639 25 .9643 52 .9799 26 ,9794 53 .9940 27 .9956

25 DATA Cn 'd RN

UTEST .72 .566 .0097 3.3O 11 x 1 06 THEORY570 .72 .0088 2.20 11 x 1 06

Figure 1. Design point theoretical and experimental pressures for the base1 ine ajrfoi1 (C141-1).

26 EXPONENTTABLE

a 1.943358 9 3.106283 10 6.578813

x/c

Figure 2. Upper surface modification airfoil parameterization.

4 -1.6 -1

-1.2 -1

-.8

CP cP -.4

.8 0 .2 .4 .6 0 .2 .4 .6 .8 1 .,o x/c x/c

Figure 3. Airfoil C141H7472 invisciddesign pressures (a= 2'). BASELINE AIRFOIL - Cl41-1

UPPER SURFACE MODIFICATION - C141H7472

Figure 4. Comparison ofairfoil geometries.

N ul W 0 -1.6 -1.6 rI"

-1.2 -1.2

- .8 -.8

cP cP -.4 -.4

C 0

.E .8 0 ,4 .6 .8 1 .o 0 .2 4 .6 8 1 .o x/c x/c

CONDITIONS: Mm = 0.72, RN = 11 x lo6

Figure 5. Inviscid and viscouspressures on the baseline and modified airfoils at a=2O (Continued). -1 -1.6

-1 -1.2

-.8

-.4

cP O

.8 0 .4 .6 1 .o .2 .4 .6 .8 1 .o .2 .8 x/c x/c CONDITIONS: M,=.74, RN = 11 x106

Figure 5. Concluded. Figure 6. Wind tunnel model installation. TOP VIEW

4 STATIC TUBES

90 TOTALHEAD TUBES

] I 0285~SPACING

1I 0142~SPACING 7

W W -2,4

-2,o

-,4

x/c

Figure 8. - Airfoil pressure distribution, Cn=.57, R~=11x1O6, x/CT = free.

34 -2,o

-1,6

-1,2

-,8

-,4

,8 x/c

Figure 8. Continued.

35 -2,Q

-112

-,4

x/c

Figure 8. Continued.

36 -2.4

-2,o

x/c

Figure 8 Concluded.

37 I4

I 76 I 60 .64 I 68 I 72 80 Mw

I4 x/cs

I I 68 I 72 I 76 80 I 6,O I 64 r1 W Figure 9. - Effect of Machnumber on airfoil shock characteristics at C,=.57, R~=11x106, X/CT=free. I020

I 016

[d I012

I008

I 44 I43 I 52 I 56 I 60 I 64 I 68 I 72 I 76 I 80

F1 m

Figure 10. - Effect of Machnumber on drag coefficient, Cn = .57, R~=llx106, X/CT=free. P 0

Figure 11. Comparison of measured airfoil performances at Cn=O.57, R~=11xl0q SYMBOL A I RFO I L Cn cd Cm A C141-1 -567 .0092 -.Ob33 0 C141-6 -531 -0090 -.Ob06 El C1417472 -569 .0096 -.Ob17

.1 .2

-.8

-.4

0 C P

.8 0 .2 .4 .6 .8 1 .o x/c

Figure12. Comparison of measured airfoilpressures, RN = 11 x106.

41 -1.6

-1.2

-.8

- .4

.8 0 .2 .4 .6 .8 1 .o x/c

Figure 12. Continued.

42 SYMBOL A IRFO IL Cn cd cnl A C141-1 ,562 .0097 -.Ob31 0 C141-6 . .579 .0095 -.0373 C.1417472 .558 .0116 -.0333

-1.6 , ...... - .-...... ,.. - . .,-.., ....:...:; ! 'I ': .! " __ ~ ._...... - '! . , .. ., ., ...... ,., -1 .2

-.8

-.4

.8 0 .6 .2 .4 .8 1 .o x/c

F i gure 12. Continued.

43 SYMBOL A I RFO I L C" cd cm A C141-1 -566 .OlOl -.0413 0 C141-6 -546 .0095 -.Ob13 El C1417472 .571 .0121 -.0322

0 .2 .4 .6 .8 1 .o x/c

Figure 12. Continued.

44 SYMBOL AIRFOIL Cn ‘d cm A C141-1 .566 .0109 -.0490 0 C141-6 .569 .0099 -.Oh30 El C1417472 -572 .0120 -.0333 -1.6

-1.2

-.8

-.4

x/c

Figure 12. Continued.

45 SYMBOL A I RFO I L ‘d Cn cm A C141-1 .557 .O139 -.056j 0 C141-6 .61O .O147 -.0568 a C1417472 .563 .0120 -.0367

0 .2 .4 .6 .8 1 .o x/c

Figure 12.Continued.

46 I

SYMBOL A I RFO I L Cn cd Crn 0 C141-1 .546 .O218 -.Of552

0 C1417472 .577 .0160 -.0455 -1.6 ......

-1.2

-.a

-.4

.8 0 .2 .4 .6 .a 1 .o x/c

Figure 12. Concluded.

47 I

Figure 13. Measured airfoil performance at Cn=0.50. Figure 14. Theoretical and experimental drag for the baseline and upper surface modification. -1

0 .2 .4 .6 .8 1 .o x/c

Figure 15. Baseline airfoil theoretical and experimental pressures at C,=O.57.

50 C 'P

x/c

Figure 15. Concluded. -1.6

-1 .2

-.8

.a 0 .2 .4 .6 .8 1 .o x/c

Figure16. Airfoil C141H7472 theoretical and experimental pressures at C, = 0.57. 0 .2 .4 .6 .8 1 .o x/c

Figure 16. Concluded.

53 -1 .6

-1 .2

-.8

C 'P

-.4

.8 0 .2 .4 .6 .8 1 .o x/c

Figure 17. Comparison of airfoil C141H7472 pressures at subcritical conditions (C,= .57, Mm= ,451

54 -1.6

.- ...... ': ,I. -1 .2 ,I_. .i . 4...... I...... i. .. .I . .._.I. . . -.8 ..- ...... - ,..... cP I. ..

- .4 ..". * .."..

...... 0

I i .4 ...!

.8 0 .2 .4 .6 .8 1 .o x/c

Figure 18. Comparison of airfoil C141H7472 pressures near 'drag d ivergence (Cn = .57, M, = .78)

55 -1 .6

-1 .2

- .8

0 .2 .4 .6 .8 1 .o x/c

Figure 19. Comparison of theoretical solutions with experimental data for airfoil C141H7472 at Cn = 0.57

56 -1.6

-1 .2

-.8

cP -.4

x/c

Figure 19. Concluded.

57 "-. ..I I I II I I

SYMBOL DATA MACH a C" 'd

0 EXP. .72 3.0 0.57 .0121 NON-CONS. .72 3.0 0.69 .OO96 "- QUASI-CONS. .71 3.0 0.65 .0080 -1

-1

0 .2 .4 .6 .8 1 .o x/c Figure 20. Airfoil C141H7472 theoretical and experimental pressure match.

58 SYMBOL DATA MACH a cd

0 EXP 0.74 0.572.77 .oi 20 NON-CONS. 0.73 2.75 0.66 .0089 "- QUASI-CONS. 2.750.725 0.68 .0092

C'P

x/c

Figure 20. Continued.

59 SYMBOL DATA MACH a C" 'd

0 EXP 0.58.78 2.5 .0160 - NON-CONS. .75 2.4 0.65 .0089 - - - QUAS I -CONS. .76 2.5 0.60 .0138

-1 .6

-1 .2

-.E

0 C'P

.8 0 .2 .4 .6 .8 1 .o x/c

Figure 20. Concluded.

60 APPENDIXA: PLOTTEDTEST DATA

Resultsfrom Lockheed-Georgia Comressible Flow Wind TunnelTest 029 are detailedin plotted form in this appendix. The aerodynamic forcecoefficients for ai rfoi 1 C141H7472 are shown in figures A1 through A9 for the basic test conditionsof RN = 11 x IO6, T = 4%, and freetransition. Figures A10 through A13 containthe aerodynamic coefficients for RN = 4x lo6, T = 4%, and transition fixed at 5% chord.

The chordwisepressure distributions are shown forthe basic test con- ditionsin figures A14 through A29, and for RN = 4x lo6 infigures A30 through A36. Figures A37 and ~38contain the chordwise pressure distributions for wall porositiesof 2%, 3%, 4%, 5%, and 6%.

61 (r N 1.0

.6 c"

4 6 .010 .014 .O18 .022 -.04 -.O 8 a 'd cm Figure AI. - Airfoilforce data for M=O.45, R~=11x106, x/C~=Free 1.0

n -0 2 4 6 .a0 .014 .O 18 .O22 -.04 -.OS a ‘d m -r

1.0

.6 c”

4 6 .010 .014 .022 -.04 -.O 8 a ‘d ~i~~~~~3. - Airfoil force data for M=0.60, R~=11x106, X/CT=Free 1.0

.6 cn

c 2 4 6 .010 .014 .O 18 .022 -.04 -.08 ‘d Figure Ab. - Airfoil force data for M=0.64, RN= 11 x106, x/C~=Free 0 0

1.0

.6 c"

4 6 .010 .014 .O18 .022 -.04 a 'd 1.0

.6 c"

0 0 2 4 6 .010 .014 .O18 .022 -.04 -,OS -32 a 'd cm Figure A6 . - Airfoilforce data for M=0.72, R~=llx106, x/C~=Free cn co

1.o

.6 c”

6 .010 .O18 .022 -.04 -32 E

1.0

.6 c"

0 2 4 6 .010 .014 .O18 .022 -.04 -.OB a 'd m u3 Figure A8 . - Airfoi 1 force data for M= 0.76, RN = 11 x 1 06, X/CT = Free v 0

1.o

a 'd P

1.0 !I

i .8 'I

I I

.6 L I ! ! cr-l i !

0 C 2 4 6 .010 .014 .O 18 .022 -.04 -.O 8 a 'd

U d Figure A10 - - Airfoil force data for M=0.72, R~=4~10~,X/CT=.O~ "0 2 4 6 .010 .014 .O 18 .O22 -.04 -.OS a 'd 1. . crn .f

.E c"

w W Figure ,412 . - Airfoil force data for M= 0.76, RN= 4x lo6, X/CT= .05 4 &

1.0

.6 c”

a ‘d

Figure A13. - Airfoil force data for M=O.78, RN=~x~O~,X/C,= .05 -2.4

-200

-1,6

-,4

I8 "L_. c1 " .- 4 5i1 -2,o

-1,6

-1,z

-,8

-,4

6 Figure A15 .- Airfoil PressureDistribution for M = 0.55, RN = 11 X 10 , X/C, = Free

76 -2,4

-2,o

-1,6

-1,z cP

-,8

-,4

I Figure A16 .- Airfoil Pressure Distribution for M=0.60, RN= 11 x 106, X/C, = Free 77 -2,4

-2,o

-1,6

-1,2

-,8

-,4

6 A17.-Airfoil Pressure for M = 0.60, R = 11 X , Figure Distribution N 10 X/C, = Free 78

1 -2,4

-2,o

-1,6

Figure A18.- AirfoilPressure Distribution for M=O.64, R~=11X106, X/C, = Free 79 -2,4

-2,o

-116

-1,2

Figure A19.- AirfoilPressure Distribution for M = 0.64, R = 11 x 106 , N X/C, = Free

80 -2,4

-zoo

-1,6

-1,z

CP -,8

-,4

FigureA20.- Airfoil Pressure Distribution for M=0.68, R~=llxlO~, X/CT = Free

81 -z14

-2,o

-116

-1,2

cP -,8

-,4

6 FigureA21.- Airfoil Pressure Distribution for M = 0.68, RN = 11 X 10 , X/C, = Free

82 -2,4

-2,o

-1,6

-1,z

-,4

X/CT = Free 83 -2,4 ",

-2,o

-1,6

-1,z

-,3

-,4

6 Figure A23.- Airfoil Pressure Distribution for M = 0.72, RN = 11 x 10 X/C, = Free

84 -2,4

-2,o

-1,6

-1,z cP -,8

-,4

Figure A24 .- Airfoil Pressure Distribution for M=0.74, R~=11X lo6, X/CT = Free 85 -2,o

-1,6

-1,2

-18

-I 4

86 -2,o

-,4

Figure A26,- AirfoilPressure Distribution for M=0.76, R~=11x106, X/CT = Free a7 -2,o

-116

-112

-,8

-,4

6 Figure A27.- AirfoilPressure Distribution for M = 0.76, RN = 11 x 10 , X/C, = Free 88 -2,4

-2,o

-1,6

Figure A28.- Airfoil Pressure Distribution for M=0.78, R~=11x106, X/CT = Free -2,o

-1,6

-1,z

-,8

-,4

6 Figure A29.- AirfoilPressure Distribution for M = 0.78, RN = 11 x 10 , X/C, = Free -2,o

-116

-1,z

-18

-,4

Figure~30.- Airfoil Pressure Distribution for M=0.72, R~=4~10~, X/CT= .05 91 -2,4

-2,o

-1,6

-1,2

-,8

-,4

Figure A31 .- Airfoil PressureDistribution for M=0.74, Qq=4x106, X/CT = .05

.. -2,4

-2,o

-1,6

-1,2

-,8

-,4

1 Pressure Distribut .05 Figure A33 .- Airfoil Pressure Distribution for M=0.76, RN=~Xlo6, X/CT = .O5

94 -L6

-,4

6 Figure A34 .- AirfoilPressure Distribution for M = 0.76, RN = 4 X 10 , X/C, = .05 95 -2,4

-2,o

-,4

Figure A35.- AirfoilPressure Distribution for M=0.78, RN=~X~O~, X/C, = .05 -2,4

-20

-1,6

-1,z

-,8

-,4

6 Figure A36.- Airfoil Pressure Distribution for M = 0.78, RN = 4 X 10 , X/C, = .05 97 -1

-1

-,4

Figure A37.- Effectof WindTunnel Wall Porosityon Airfoil Pressure 6 Distribution, M = .74, RN = 11 x 10 , ct = 3.85 .

98 -2,4

-2,o

-,4

Figure A38.- Effect of Wind Tunnel Wall Porosity on Airfoil Pressure 6 Distribution, M = .74 RN = 11 x 10 , c1 = 3.85.

i . .." "" ~. ". -i- . .. 1. ReportNo. 2. Government Accessionr-RIipp;'nt's-Cxalcq No. No. NASA CR-3065 . .. . . -.- ...... ~ ." 4. Titleand Subtitle I 5. Repon Date ANALYS I S OF A THEORET I CALLY OPT I MI ZED TRANSON IC AI RFO I L

~ "- ~~ 1 -~.~ 7. Author(s1 Report Organlzation 8. Performing No. M. E. LORES, K. P. BURDGES, G. D. SHREWSBURY LG78ER0212

~~ ~ 9. Performing Organization Name and Addres

LOCKHEED-GEORGIA COMPANY 11.Contract or Grant No. MARIETTA, GEORGIA NAS2-8697

~ 13. TypeReponof and Period Covered 12. Sponsoring Agency Nameand Address

NATIONALAERONAUTICS AND SPACE ADMINISTRATION 14. Sponsoring Agency Code WASHINGTON, D. C. 20546

15. SupplementaryNotes AMESRESEARCH CENTER, NASA, TECHNICALMONITOR - RAYMOND M. HICKS

~ ~~~~~ ~ 6. Abstract Numericaloptimization was used inconjunction with an inviscid,full potential equation,transonic flow analysis computer code todesign an uppersurface contour for a conventionalairfoil to improve its supercritical performance. The modified airfoil was testedin the Lockheed-Georgia Compressible Flow WindTunnel. The modified airfoil's performance was evaluatedby comparison with test data for the baseline airfoil and for an airfoil 'developedby optimization of leading edge ofthe baseline airfoil.While the leading edge modificationperformed as expected,the upper surface re-designdid not produce a1 1 ofthe expected performance improvements. A1 thoughthe dragdivergence Mach number was increased,the modified airfoil exhibited more drag creepthan the baseline section. This larger drag creep is attributable to the early formulation(at approximately M, = .68) of a relativelystrong leading edgeshock wave.

Theoreticalsolutions computed using a fullpotential, transonic airfoil code correctedfor viscosity were compared toexperimental data for the baseline airfoil and theupper surface modification. These correlations showed thatthe theory pre- dictedthe aerodynamics of the baseline airfoil fairly well, but failed to accurately compute dragcharacteristics for the upper surface modification. This failure is showr to be attributableto the inability of the theory to properly treat the thick trailing edgeboundary layerassociated with the upper surface modification.

7. Key Words (Suggested by Author(sl1 18. Distribution Statement airfoils,supercritical Unlimited

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