AO-AJIA 265 ARIZONA UNIV TUCSON ENGINEERING EXPERIMENT STATION F/G 20/4AN EFFECTIVE ALGORITHMI FOR SHOCK-FREE WING DESIGN. (U)JUN St K FUNG. A R SEEBASS, L J DICKSON N0001A-76-C-0IG*

UN4CLASSIFIED TFO-8I-06 " N.

,'ll6lEZ

320

1111I,.oIIIO E

MICROCOPY RESOLUTION TEST CHART

TRANSONIC FLUID DYNAMICS

Report TFO 81-06

K., Y. Fung, A. R. Seebass,L. J. Dickson, C. F. Pearson

AN EFFECTIVE ALGORITHM

FOR SHOCK-FREE WING DESIGN

June 1981~JUN29 1982 L

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fpukbt T':M. wIC; itsdifbibutior. is u.nLttxi

ENGINEERING EXPERIMENT STATIONCOLLEGE OF ENGINEERINGTHE UNIVERSITY OFARIZONATUCSON, ARIZONA 85721

82 06 13

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.TITLE (and Subtitle) 5. TYPE OF REPORT & PERIOD COVERED

SAN EFFECTIVE ALGORITHM FOR SHOCK-FREE

WING. DESIGN 6. PERFORMING ORG. REPORT NUMBER_____TFD 81-067. AUTHOR(s) S. CONTRACT OR GRANT NUMBER(*)

K.-Y. Fung, A. R. Seebass, L. J. Dickson, N00014-76-C-0182and C. F. Pearson

9. PERFORMING ORGANIZATION NAME AND ADDRESS 10. PROGRAM ELEMENT. PROJECT, TASK" oAAREA & WORK UNIT NUMBERSUniversity of ArizonaAerospace and Mechanical EngineeringTucson, Arizona 85720

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Office of Naval Research (code 438) June 1981*' . Arlington, Virginia 22217 28. NUMBER OF PAGES

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University of New Mexico Albuque, que, NM 87131 SCHEDULE

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Wing DesignAirfoil Design

\ I

a, STRACT (Continue ... . ... rove id .e ...... nece y a d Identity by block numbe

This paper reviews the fictitious gas procedure of Sobieczky for findingshock-Tree airfoils and wings. Results for inviscid and viscous flowsfor airfoils and wings are described. The method is applied to a businessjet planform resulting in a wing that should have good low speedcharacteristics as well as an M L/D that is near the maximum achievablefor the wing lift and thickness chosen for the study.

DD IORM 1473 EDITION OF I NOV 65 I5 OBSOLETEI JAN73S/N 0 10 2-014 6601 1

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I AIAAat50

I AIAA-81-1236An Effective Algorithm

Annivery Cebon for Shock-Free WingDesign

K. Y. Fung and A. R. Seebass,University of Arizona, Tucson,AZ; and L. J. Dickson, Universityof Washington, Seattle, WA; andC. F. Pearson, Harvard AeIon,

University, Cambridge, MA

I/ , 0.- 1 T"I .. .

AIAA 14th Fluid and PlasmaI Dynamics Conference1 June 23-25, 1981/Palo Alto, CaliforniaI

IAIAA - 1

I AN EFFECTIVE METHOD FOR SHOCK-FREE WING DESIGN

I I -Y. Fung, A. R. Seebass, L. J. Dickson, and C. F. Pearson

I Abstract

This paper reviews the fictitious gas procedure of Sobieczky forfinding shock-free airfoils and wings. Results for inviscid and viscousflows for airfoils and wings are described. The method is applied to abusiness jet planform resulting in a wing that should have good low

* speed characteristics as well as an M0 L/D that is near the maximumachievable for the wing lift and thickness chosen for the study.

S I INTODUCTIONThere are a number of advancing technologies that should provide

I about a 40% improvement in transport aircraft fuel efficiency for thepost 757/767 generation of aircraft. These include advances in thepropulsion system, improved operations - including air traffic control-,

d composite materials for primary as well as secondary structures, activeflight control, and supercritical aerodynamics. More than half of thisimprovement will come from the use of composite materials and activeI control, in conjuction with aeroelastic tailoring of the wing structureto suppress flutter. This paper addresses a more modest contributor tothis expected gain, viz., supercritcal aerodynamics. Here we look forimprovements in the "aerodynamic efficiency," M.L/D, of about 5%. Wemust keep in mind that such small improvements are essential inobtaining the composite advance suggested above, and further, that each1% increase in fML/D of a single 300 passenger transport aircraft willI save about S100000 in fuel costs per year 'at present prices.

The goal of maximizing M= L/D requires aircraft wings that haveI shock-free flow over them for as large a Mach number as possible for

fixed lift, thickness, etc. Such flows are mathematically isolated fromone another and have, in the past, been difficult to find. In the late1960s and early 1970s methods for generating airfoils that were shock

I free at supercritical Mach numbers were developed by Nieuwland (1),Bauer, Qarabedian and Korn (2), and Sobieczky (3). These investigationsused different techniques to the same end, and will not be reviewedI here. But even in their most advanced state they did not provide a richselection of airfoils and none could be generalized to threedimensions. The application of these airfoil designs to swept,

I three-dimensional wings, required cut and try modifications of the wingin order to even come close to achieving shock-free flow. But Sobieczky(4), in a brilliant generalization of his earlier approach, saw thatfinding such designs in two dimensions would be routine, and that itseemed this generalization would apply to three-dimensional flows aswell (5). We now know that while this generalization leads to anill-posed boundary-value problem in three dimensions, this causes noserious difficulty for wings of moderate to large aspect ratio (6).

AIAA - 2

I This paper reviews the fictitious gas method of designingshock-free wings, illustrating the procedure with several codes now incommon use in the aircraft industry. The authors know little of the

I overall design process and our focus is more properly on the minormodifications to a wing that is already optimized for low speed andsubcritcal flight. The aerodynamic aspects of the design of commercial

I transports for aerodynamic efficiency have recently been reviewed byLynch (7). We begin with the presumption that the designer has alreadychosen his basic airfoil section and wing planform and that he now

I wishes to maximize the M L/D of the configuration using his existingI computational tools, andwthat only a limited portion of the upper

surface of the wing can be modified to achieve this goal withoutaffecting the airfoil's low speed (CL)mx . For our study we will usethe GA(W)-2 airfoil and the Gates Learjet Century series planform.

AIRFOIL DESIGN

As noted above we begin by choosing a baseline airfoil. The GA(W)-2has good low speed performance as well as some claim to being a

* relatively good supercritical airfoil (8). The numerical algorithmI developed by Melnik (9) for computing the flow past airfoils in the

presence of inviscid-viscous interactions, GRUMFOIL, has had earlydomestic dissemination. Nebeck (10) has modified this code forshock-free airfoil design in the presence of viscous interactions. N.Conley (private communication) reports that a modification of theLearjet wing section to obtain a shock-free flow at a freestream Machnumber of 0.81 and a lift coefficient of CL = 0.50 is desirable if thiscan be done with an airfoil such as the GA(W)-2 which has good lowspeed characteristics. Cosentino (private communication) has addressedthe problem of design for an airfoil Mach number of 0.77 correspondingto a planform sweep of 15.7*. This process is not described here as thedetails may be found in Ref. 5, and our main concern is with wingdesign. With an appropriately chosen baseline airfoil based on theGA(W)-2, Cosentino was able to design an airfoil that was identical tothe GA(W)-2 for the first 9% of its chord in order to retain the goodlow speed performance of the QA(W)-2, but had slight modifications toits upper surface in order to produce shock-free flow. Figure 1compares the flow past the designed airfoil, GA(C)-250, as computed byGRUMFOIL, with that past a GA(W)-2 airfoil that has had its ordinatesreduced to provide an 11.7% thick airfoil rGA(W)-2T3. The design pointis M. = 0.7725 and CL = 0.50 with Re - 6- 106. Figure 2 compares theskin friction and boundary-layer displacement thickness on the twoairfoils; note the small region of separation on the GA(W)-2T which hasled to the lambda shock configuration responsible for the pressuredistribution in Figure 1. We infer from these results that about a 100count drag reduction has been achieved. The GA(W)-2, GA(C)-250, and theI GA(W)-2T airfoils are compared in Figure 3. While there are only minordifferences among the GA(W)-2T and GA(C)-250 airfoils, there are majordifferences in their supercritical performance indicating the greatsensitivity of the flow to very minor changes in the upper surface.Since the GA(C)-250 is identical to the QA(W)-2 for the first 9% of thechord, we expect that it will also have a good low speed (CL)max

IAIAA - 3

WING DESIGN

Having selected our baseline airfoil, we now turn to wing design.We use this airfoil in the wing generator code of Sobieczky (11) togenerate the wing input for a three - dimensional computation. We havechosen the FL022 algorithm of Jameson and Caughey (12) for our wingstudies. This code is well accepted by industry and is considerablyfaster than the conservative finite volume code used by Yu (13) to thesame end. We note that while conservative differencing is important in

* the capture of shock waves, our design procedure computes the solutionto an elliptic system and this can be done accurately with anonconservative code. The basic tenets of the procedure have beendescibed elsewhere (6,14). Because the changes we will make to our wing

I sections will be small, we must be careful to be sure they do notbecome obscured in the mapping from the physical plane to thecomputational plane. We have thus included a recomputation of the flow

I field after the design process in the computational variables in orderto verify the results.

We remind the reader that in three-dimensions we solve an ill-posedboundary-value problem, and that any three-dimensional design must beconfirmed by an analysis of the flow past this wing. The results ofthis computation are then compared with an analysis of the original

I wing shape, again using FL022. Here, when there are shock waves presentin the flow, this nonconservative calculation may overestimate theirstrength somewhat; however, the conservative potential approximation isg even worse in this regard.

We begin our study with the candidate wing generated by the winggenerator from the candidate baseline airfoil. Recall that thisbaseline airfoil was derived from the airfoil section of the wing wehave designed to have optimum subcritical performance; it is not theairfoil we have designed to be shock free. We now repeat our fictitious

I gas study with a gas law that is close to that used in the airfoildesign process. For conservative calculations we use a fictitiousdensitypf , that depends on Phe flow speed q in a simple power lawfashion, viz., pf /p = (q*/q) for q > q*, where P < 1, and istypically 0.9. In nonconservative calculat ons we prescribe afictitious sound speed a , where a = q(q/q ) and L > 0. A value ofL = 5 gives results similar to those of P = 0.9. Note that changing L(or P) results in a change in the size of the upper surface of the wingwetted by supersonic flow with the lower values of L (and higher valuesof P) reduce this area because they increase the mass flow through af unit area of the sonic surface.

Our goal, then, is to maximize M.L/D within the constraint that weI maintain the features of the wing that optimized its subcritical

performance. This we do by modifying the baseline airfoil andfictitious gas laws. We may even wish to employ an inverse designprocedure like that of Henne (15) with the fictitious gas in order tohelp locate the fictitious supersonic domain where we wish it on theupper wing surface. Generally, the process of finding such a designrequires several changes in the baseline section definition, additionalchanges in the twist variation to achieve an elliptic loaddistributions and perhaps a half dozen Mach number and angle of attack

AIAA - 4

U changes to determine the maximun M. for which shock-free flow can befound for a given lift. Figure 4 depicts the pressures andcorresponding wing sections for a non-shock-free wing design based onthe GA(W)-2T airfoil. The wing has a lift coefficient of 0.375 at M.0.80 and a nominal thickness of 11.70. Also shown is a shock-freedesign that is derived from this wing that has somewhat less thickness.Figure 5 provides the same results for a wing that is the result of ourshock-free wing design procedure. Here we have taken a baseline that isabout .3% thicker than that desired. The desipned wing has a lift

I coefficient of 0.439 at M = 0.80 and is 11.7 thick. The relativechanges in the section drag coefficients are indicative of the inviscidimprovement in the drag, but the individual magnitudes are obviously

I wrong. For the shock-Free design the boundary layer will obviously notseparate, but this is much less likely for the wing with the GAW)-2Tsection. While these results are given for invisicid flow, they havebeen repeated with the section. boundary-layer displacement thicknessthat, when used with the inviscid algorithm FLO6, gives essentially thesame results as the GRUMFOIL algorithm. Further improvemnts .are nodoubt possible, but these should serve to illustrate the effectiveness

I of the fictitious gas design method.

The design process in the presence of inviscid - viscousI interactions that was successful in two dimensions is, as one would

expect, also successful in three dimensions. We have used the algorithmdeveloped by Stock (16) at Dornier for three-dimensional boundary layercalcuations to provide the boundary layer displacement surface for the

I FL022 computations. The two codes are interfaced with the PABLIMalgorithm of C. L. Streett (private communication). Figure 6 shows -thepressures on the original baseline wing used in the above study with

I those found on the wing designed to be shock free at M. - 0.76 for aReynolds number of 6"10 . We are now in the process of repeating ourinviscid design study to find an equivalent design when invisicd -

* viscous interactions are included.

CONCLUSION

It is clear that the fictitious gas method is capable of providingboth airfoils and wings that are shock free. An experienced practionercan push these designs to the natural barrier that seems to limit the

* maximum Mach number for fixed lift, or the maximum lift for fixed Machnumber, for which shock-free designs are possible. Such studies canalso be carried out successfully in the presence of viscous - inviscid

I interactions. Thus, the method can be used to provide very slightmodifications to an already suitable design to maximize M. L/D. We notethat while a shock-free design point does not maximize this quantity, aI shock-free design need only be used at a very slightly higher Machnumber to achieve what must be near to the maximum possible for a givenlift, Mach number, and thickness.

I Acknowledgement

The authors are indebted to the Air Force Office of Scientific? Research and the Office of Naval Research for their support of this

research. They are also indebted to the NASA Ames Research Center forremote access to their CDC 7600 and for an allocation of computerresources for this and other studies related to NASA's support of theUniversity of Arizona's CFD Traineeships. They wish to thank C. L.Strteett for supplying his PABLIM algorithm for this study and Mr.Leopold of the DFVLR in Gottingen for the graphics for Figure 6.

I3 AIAA -

REFERENCES

1

IINieuwland, G. Y., "Transonic Potential Flow around a Family of Quasi-I elliptical Airfoil Sections," National Aerospace Laboratory, The Netherlands,

TR-T172, 1967.2Bauer, F., Garabedian, P., and Korn, D., "Supercritical Wing Sections III,"

Lecture Notes in Economics and Mathematical Systems, No. 108, Springer, New York

3Sobieczky, H., "Entwurf uberkrittscher Profile mit Hilfe der rheoelektrischenAnalogie," Deutsche Forschungs-und Versuchsanstalt fur Luft-und Raumfahrt ReportDLR-75-43, 1977.

4Sobieczky, H., "Die Berechnung lokaler raumlicher Uberschallfelder," ZAMM,58T, 1978.

5Sobieczky, H., Yu, N. J., Fung, K.-Y., and Seebass, A. R., "New Method forDesigning Shock-Free Transonic Configurations," AIAA J., Vol. 17, No. 7, pp. 722-729, 1979.

6Fung, K.-Y., Sobieczky, H., and Seebass, R., "Shock-Free Wing Design,"AIAA J., Vol. 18, No. 10, pp. 1153-1158, 1980.

'Lynch, F. T., "Commercial Transports-Aerodynamic Design for Cruise Performanceand Efficiency," Douglas Aircraft Company Paper 7026, 1981.

8McGhee, R. J., Beasley, W. D., and Somers, D. M., "Low-Speed AerodynamicCharacteristics of a 13-Percent-Thick Airfoil Section Designed for General AviationApplications," NASA TM X-72697, 1975.

9Melnik, R. E., "Turbulent Interactions on Airfoils at Transonic Speeds--Recent Developments," Computation of Viscous-Inviscid Interactions, AGARD CP No.

291, 1981.

10Nebeck, H. E. and Seebass, A. R., "Inviscid-Viscous Interactions in the NearlyDirect Design of Shock-Free Supercritical Airfoils," Computation of Viscous-InviscidInteractions, AGARD CP No. 291, 1981

11Sobieczky, H., "Computational Algorithms for Wing Geometry Generation, Tran-sonic Analysis and Design," University of Arizona Engineering Experiment Station,Transonic Fluid Dynamics Report TFD 80-01, 1980.

12Jameson, A. and Caughey, D. A., "Numerical Calculations of the Transonic FlowPast a Swept Wing," NASA CR-153297, 1977.

AIAA - 6

S13Yu, N. J., "An Efficient Transonic Shock-Free Wing Redesign Procedure usinga Fictitious Gas Method," AIAA J., Vol. 18, No. 2, pp. 143-148, 1980.

14Raj, P., Miranda, L. R., Seebass, A. R., "A Cost-Effective Method for Shock-Free Supercritical Wing Design," AIAA Paper 81-0383, AIAA 19th Aerospace SciencesMeeting, St. Louis, January 1981.

15Henne, P. A., "Inverse Transonic Wing Design Method," J. Aircraft, Vol. 18,No. 2, pp. 121-127, 1981.

16Stock, H. W., "Integral Method for the Calculation of Three-Dimensional

j Laminar and Turbulent Boundary Layers," (translation of Dornier Report), NASA TM75320, 1978.

I This paper is declared a work of the U.S.Government and therefore is in the public domain.

Released to AIAA to publish in all forms.

1

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FGure-2 3. I Cmaind GAC) 5 the airfoils.

N Ww LNCG C L 0.4255 -0 2-.042 4

A x ) x x OL W',ENC, CL 0.4226, CD -,.C ,. = -0.t35

TIP 0 "

lX )

C., x

CPU

ot N

Figure 4. Pressures and wing section shapes fora wing derived from the GA(W)-2T airfoil and a shock-free design that results from this airfoil when usedas a baseline. The lift coeficient of the non-shockfree wing is 0. 430 and the wing root is 11. 7 per centthick. The lift coefficient for the shock-fr.. wingis 0.364 and this wing is about 11.4 per cent thick.The wing p'anfcrm is shown at the end of the Figure.

NEW '.,LNG. CL = .4S,04 CS "-26 CM1 -0"3

x x x " x OL6C WING. CL =- 0.A5AS, CD C' .COLZ. C." = -0. .5ZS

I-0..jCP '

X, XC,~

Figur~e 4. Pr~essures and wing section shapes fora wing derived from the GA(W)--2T airfoil and a shock-free design that results from this airfoil when usedas a baseline. The lift coeficient of the non-shockfree wing is 0.430 and the wing root is 11.7 per centthick. The lift coefficient for the shock-free wingis 0.364 and this wing is about 11.4 per cent thick.The wing planform is shown at the end of the Figure.

Figure 4 (continued).

rl4S 2.14

7ILNE W W IN G . C L = 1 .44 3 4 . , : . 2 , , , - .3

x x xxx OLD WtLNO-. CL = C.4533. CC .O2 C C'" -0 .1455

x

Fiur 4. Prs"re an igseto"hae oa 0 wing deie frmth,--2 irolan sok

0TP ,2 . 710J4

free design that ,

Figure 4. Pressures and wing section shapes foa wing derived from the GA(W)-2T alerfoil and a shock-free design that results from this airf#oil when useda s a baseline. The lift coeficimnt of the non-shockfree wing is 0. 430 and the wing root is 11. 7 per centthick. The lift coefficient for the shock-free wingis 0. 384 and this wing is about 11. 4 per cent thick.Thu wing planform is shown at the end of the igure.

Figure 4 (continued).

NEW WING, CL = C."573. CO =-C.CSC. SM = -O.1452

x x x x x OLC [N,.. CL = C 63 . C = .CCS53 CM = 1535

CPt4

-0.4'J'.,9- ' .,,,

C,

C.CC

*C 4C?

Figure 4. Pressures and wing section shapes fora wing derived from the GA(W)-2T airfoil and a shock-free design that results from this airfoil when usedas a baseline. The lift coeficient of the non-shockfree wing is 0.430 and the wing root is 11.7 per centthick. The lift coefficient for the shock-free wingis 0.364 and this wing is about 11.4 per cent thick.The wing planform is shown at the end of the Figure.

Figure 4 (continued).

NEW IW!NG. CL M.A51C. CO =-O.CC55, CM 019

x x x x x OLO WING, CL = 0.4579. CO -0.00CC7. C= -0.!715

x

c P

I.

p

CF

Figure 4. Pressures and wing section shapes fora wing derived from the GA(W)-2T airfoil and a shock-free design that results from this airfoil when usedas a baseline. The lift coeficient of the non-shockfree wing is 0.430 and the wing root is 11.7 per centthick. The lift coefficient for the shock-free wingis 0.364 and this wing is about 11.4 per cent thick.The wing planform is shown at the end of the Figure.

L I

I ~-NEW WING, CL = C3995, CO =-.0=75. 1CM =-0.1424x x x x x OL' WING. CL = 0.4075. C0 -0.3 , C . M -0.1572

! X X

I C

CC?-0: aA -05mI STPC'cT 1 .35

Figure 4. Pressures and wing section shapes fara wing derived from the A(W)-2T airfoil and a shock-free design that results from this airfoil when usedas a baseline. The lift coeficient of the non-shockfree wing is 0. 430 and th. wing root Is 11.7 per centthick. The lift coefficient for the shock-free wingig 0. 384 and this wing is about 11.4 pe cent thick.The wing planom is shown at the end o the Figure.

Figure 4 (continued).

NEW WINcG. CL = 0.3095. CO =-C.0131. CM -0.1219

x x x x x OLD WING. CL 0.3!55, CD = -0.0104. CM -0.1295

cP x

CPP

S.PANST =2.35IN"

t.t

IC?

Figure 4. Pressures and wing section shapes fora wing derived from the QA(W)-2T airfoil and a shock-free design that results from this airfoil when usedas a baseline. The lift coeoficient of the non-shockfree wing is 0.430 and the wing root is 11.7 per centthick. The lift coefficient for the shock-free wingis 0.364 and this wing is about 11.4 per cent thick.The wing planform is shown at the end of the Figure.

Figure 4 (continued).

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x x x x X OL' IN'. CL = 0.4451. C7 -0n.3 C -3

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-0 .41C C

C'

:I

Figure 5. Pressures and wing section shapes for aa wing derived fram the baseline airfoil that gavethe GA(C)-250 shock-free airfoil. Also shown are thepressures on this baseline airfoil. The lift coef-ficent of the shock-free design is 0.439; that forthe baseline wing is 0. 447. The proper comparisonhere is between this shock-free design and the oldwing of Figure 4. These wings have the same thick-ness and nearly the same lift coefficient.

NEW WINC, CL = 0.4655. C, :-0..C02, C -0.=CM CX x x x x QLD WING. CL 0.4717. CD: -0.C7. :M -0.153

-o.4s " -0c1

Figure 5. Pressures and wing section shapes for a

a wing derived from the baseline airfoil that gave

the GA(C)-250 shock-free airfoil. Also shown are the

pressures on this baseline airfoil. The lift coef-ficent of the shock-free design is 0.439; that for

the baseline wing is 0. 447. The proper comparison

here is between this shock-free design and the old

wing of Figure 4. These wings have the same thick-

ness and nearly the same lift coefficient.

Figure 5 (continued).

I NEW WINc-, CL = C A621. CO :=0C20.0 C3

x x x x x OLC WINC-. CL = .4633. CO = 0.C057. ' -0.1449

I CP

I -oci.,PNST :O.7S94.

I

I

Figure 5. Pressures and wing section shapes for aa wing derived from the baseline airfoil that gavethe GA(C)-250 shock-free airfoil. Also shown are thepressures on this baseline airfoil. The lift coef-ficent of the shock-free design is 0. 439; that forthe baseline wing is 0. 447. The proper comparisonhere is between this shock-free design and the oldwing of Figure 4. These wing.s have the same thick-ness and nearly the same lift coefficient.

Figure 5 (continued).

NEW W, . CL = ,.72,. CD -0. 7 CM = -0.1455

x x x x x OLC ,,NZ-. CL = 0.$8C5 CO 0.,0025. CM -0. 25 1

I 8I cP

c.u

90%

Figur"e 5. Preossur'es and wing sectcion shapes for" aa wing deri ved fr-om the baseli.ne air-foil that gavethe GA(C)-25O shock-fr ee air-foil. Also shown ar'e thepr'essur-es an this baseline airfoil. The lift €oef-fi.cent of t;he shock-free design is 0. 439; that; forthe baseline wing is 0. 447. The pr'oper" compari sonher'e is between this shock-fr'*e design and the oldwing of Figure 4. These wings have the same t;hick-nest and nearly the same lift coefficient.

Figure 5 (coninued).

a inLerve.ro.t.b.ein.a oi ta gv

SI

NEW I NG 'C C .4140. CC =-O . .,., . = r - .X X X X X CL NCf"LC'5.CC -CS3 'z-Ot6,, .. x[ , = x. 2 G x. , = - 0 . ,, w 3 , C I = - 0 .- t 5 55

!C "

-- :

01

Figure 5. Pressures and wing section shapes for aa wing derived from the baseline airfoil that gavethe GA(C)-250 shock-free airfoil. Also shown are thepressures on this baseline airfoil. The lift coef-ficent of the shock-free design is 0.439; that forthe baseline wing is 0. 447. The proper comparisonhere is between this shock-free design and the oldwing of Figure 4. These wings have the same thick-ness and nearly the same lift coefficient.

Figure 5 (continued).

Z'

NEW WING. CL =. A . 0 -,-,7 CM =-1637

x x x x x OLC WINC, CL = .47-. CO75 -C.,, . Cl -

Ii

Cpr

tP=7~ I .571

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I YW : 0 .0: =

1 o0°

Figure 5. Pressures and wing section shapes for aa wing derived from the baseline airfoil that gavethe GA(C)-250 shock-free airfoil. Also shown are thepressures on this baseline airfoil, The lift coef-ficent of the shock-free design is 0. 439; that forthe baseline wing is 0. 447. The proper comparisonhere is between this shock-free design and the oldwing of Figure 4. These wings have the same thick-ness and nearly the same lift coefficient.

Figure 5 (continued).

I

I NEW NG, C -- 0.321. 3. =-0.0., C -0,125x x x x x OLC WIJNG, CL = C3309. CC -C.0139. :I -C1305

C,I cPC?..

I

Figure 5. Pressures and wing section shapes for aa wing derived from the baseline airfoil that gavethe GA(C)-250 shock-free airfoil. Also shown are thepressures on this baseline airfoil. The lift coef-ficent of the shock-free design is 0. 439; that forthe baseline wing is 0. 447. The proper comparisonhere is between this shock-free design and the oldwing of Figure 4. These wings have the same thick-ness and nearly the same lift coefficient.

Figure 5 (concluded).

/ . . . - . . . ' =

r-* -C. Zx Miq M .Z.AC" .7S T%4. am v VC -.- 2

.- .3. .Z S 618 -U- =9 a,:-I7 Sir

1 7 1

- - ~ . ._- ico

-' c I-.i -. I~

40

4 Cy4

Figure 6. Winwg planform, section pressures, and section shapes for a -Wing thatwas designed to be shock fro# in the presence of inviscid-viscous interactionsesing FL022 and the Stock 3D boundary - layer algorithm coupled by Stratte'sILIM algorithm.

__

IC%. 62 vc .22 V v 1 . -.. 222

* :.. .~ ~ .177~

v~ae~~,~.*s ; -. . 3*. -;

artM

Ii4

aq , ! .Zj li - r j 4CS V " . 31 S !5 .3 Si VT NG

4AC~ - .923 A w s A _9 .!7 .%IA &:F ? -r-am V3 *_=- A Aft:1x

I-

to(Ip R eil

. 9 1 ~~ ~ ~ i g r 6 ( c o n t i n u e d ) ! ' ~ S. 3 / '5 3 S a ' i t

f *V~~~~~%-. ---20S ~ 6 ' - -A ' --'A ....... ~

I. 71. .=dRV t-

Mr Xs I

35'!3.31 3 21!3.31 SWEvT 4LNS 9'58 S!53 d~dI

m- --60 .as - .=a =. t - C.- A .a - .m3021

C-23

*10

Figure 6 (continued).

ti .,Z A.,s J -= . t

I"

Figu'e 6 (concluded).

v0*1vo "-',