-3 0UMCL*SSITIEP H/1 I

IN L11

L.4 1.6

~Ii O KSOLUT*" TEST CHARIfOAL WUAU OF STANWMM 193-A

ARL-A-RO-TM-388 flMl FILE CO-o'-5ssl

q~4.

DEPARTMENT OF DEFENCE

DEFENCE SCIENCE AND TECHNOLOGY ORGANISATIONO AERONAUTICAL RESEARCH LABORATORIES

MEL UOUI4E, vl-:ToRdA

Aerc'odynemics Technical IMern*rj.'Ju.n 368

A NOTE ON TM- A'mHOL'YOAIlC OIESKItJ OF' 71 3N

PARALLEL-S:rX.D AERUFOIL SFf2 1)A5 (U)

N. Pol lock

DTICELECTEf

Approved for public releoseJA 98

ThiL wocrk is copyrigrnt. Apart -cn coy fair dealing, for '.he prpsctf study. rcsEarc!-, criticism or review. or perr.*~t'ed uoider rheCapyrk,.I Act, no, mart ni'v tt repr~duLed Dy uzny prGzt-ss witho'jtv.".ittei pejrmris~Aun. C'3pyrght is hie ietpo isibility of thi DireclorP b-Is'i,~c, 3nd Morke'Ing, A(UP.. Inquiries should be ditrreted to tieA/1-ra~r. ,AfCPS Prc..s Au.tiol'an Goverinmer' P'kltishngp Service,GFO03o,. 34s, Canberra, ACT k60l.

SEPTEMEN 19 87

881 20 U1L

AR-004-551

DEPARTMENT OF DEFENCEDEFENCE SCIENCE AND TECHNOLOGY ORGANISATION

AERONAUTICAL RESEARCH LABORATORY

pAerodynamics Technical Memorandum 388

A NOTE ON THE AERODYNAMIC DESIGN OF THIN

PARALLEL-SIDED AEROFOIL-SECONS (U)

by

N. Pollock

.SUMMARY

There are many situations where parallel,gided aerofoil sections withleading and trailing edge fairings of Iimited hq4Abq ise extent have advantagesover conventional sections,.The desig .of toQae x~conventional sections wasinvestigated using two potential flow plus boundary layer computerprograms. Guidelines for the selectin o'f tli Tending and trailing edge fairingshapes are presented.

0

(C) COMMONWEALTH OF AWFRAILA 1967

POSTAL ADDRESS: Director, Aeronautical Research Laboratory,P.O. Box 4331, Melbourne, Victoria, 3001, Australia

AILt

CONTENTS

NOTATION

1. INTRODUCTION .................................................. 1

2. OUTLINE OF METHOD ............................................ 1

3. ADAPTATION AND VALIDATION OF COMPUTER PROGRAMS ........ 2

4. RESULTS AND DISCUSSIONS ....................................... 2

4.1 Leading Edges ............................................... 2

4.2 Trailing Edges ............................................... 5

4.3 Comparison Between Parallel-Sidedand Conventional Aerofoils .................................... 6

5. CONCLUSION .................................................... 6

REFERENCES ........................................................ 8

APPENDIX ........................................................... 9

FIGURES Accession For

US RA&IDISTRIBUTION DTIC TAB

Unannounced E/Justifieatio

DOCUMENT CONTROL DATAByDistribution/Availability odes

JAvnil and/or-

DIst Special "TIC

°'°'1 '° ° c / ,y

? i~

:*

NOTATION

c Chord of section

CD Drag coefficient = Drag per unit span/pV2 c

CL Lift coefficient = Lift per unit span/kpV2 c

Cp Pressure coefficient = (P-Po)/3koV2

P Local static pressure

PO Free stream static pressure

R Reynolds number based on c

S Trailing edge curvature parameter - see section 4.2

t Section thickness

V Free stream velocity

x Chordwise coordinate

XLE Leading edge fairing length

XTE Trailing edge fairing length

y Coordinate perpendicular to chord

p Free stream density

I"" ~mf~

... I .. . . ..

['1

1. INTRODUCTION

The familiar families of aerofoil sectiorr (see for example Ref.i pervade

all of contemporary aero and hydrodynamic design. They are used for parts of flightor marine systems intended to produce lift with minimum drag. They are also widelyused as basically non-lifting fairings for bluff objects where it is desired to minimisedrag and flow unsteadiness. However there are many circumstances where aconventional aerofoil section is not necessarily the optimum shape for a fluid swept,approximately two-dimensional, object.-,

Where design constraints force the use of very thin sections the smallleading edge radius on conventional aerofoils produces a number of problems (Refs. 2& 3). The maximum lift coefficient is limited by an early leading edge separationand the very high velocity peak near the leading edge at incidence will cause earlyboundary layer transition and increased skin friction drag at some Reynoldsnumbers. In liquid applications cavitation and ventilation will limit the usable lift.In these situations non-conventional section shapes tending to be parallel sided over asignificant portion of their chord could be expected to offer advantages.

Aerofoil sections are a natural choice for fairing bluff objects with largethickness ratio (cross stream dimension/streamwise dimension). The selection of anappropriate aerofoil section is relatively straightforward (Ref.3) since the aerofoilthickness required is almost independent of thickness/chord ratio (Fig.la). For bluffobjects with thickness ratios considerably less than unity the circumscribing aerofoilsection thickness is a strong function of the thickness/chord ratio (Fig.lb) and inmany real situations the optimisation is difficult. For bluff objects of smallthickness it would seem probably that simple leading and trailing edge fairings(Fig.lc) could provide a better compromise than an aerofoil section in somecircumstances.

There are some aerodynamic situations where sections with parallel sidesover a large portion of their chord are necessary to meet their functionalrequirements. An example of this is the "ground board" used for reflection planetesting in a low speed wind tunnel (Ref.4). It was this application which motivatedthe present investigation.

Th6re are also situations where arbitrary rules dictate the use of parallelsided sections where aerofoil sections would otherwise be used. Example of theseare centreboards and rudders of some classes of yachts.

The aim of the investigation reported here is to give some guidance as tothe selection of suitable leading and trailing edge fairings for two dimensional flatplates. The overall thickness/chord ratio range considered is 2% to 6% which coversmost of the practical applications. The invstigation is limited to incompressibleflow in the Reynolds number range W to Walthough the results should be directlyapplicable to sub-critical compressible conditions. .

2. OUTLINE OF METHOD

AA series of fairing shapes was investigated using two readily available

aerofoil analysis computer programs The programs were PROFILE (Refs. 6 & 7) andthe Improved NASA-Lockheed Multielient Airfoil Ana!ysis Program (Ref.8). Bothof these programs were obtained in th rm of FORTRAN source code from theNASA Computer Software Management and-bifaM ation Centre (COSMIC). Theywere chosen for this investigation due to their availabt1ity, adequate ac!i pcy for

i

121

( the present purpose and speed of execution. They are both potential flow programswith a separate boundary layer computation. The NASA program had the capability,to iterate between potential and boundary layer solutions and incorporated arepresentation of the wake.

_.The programs were used as a numerical wind tunnel. A series of shapeswas tested and, based on an analysis of the results and physical reasoning, furthershapes were derived and computed.>, It would have been possible to specify anoptimisation function to be maximised, a series of parameter limits and perform anautomated optimisation using the analysis programs inside an optimisation loop. Thisapproach was not adopted since each potential application requires a completelydifferent optimisation function and the procedure does not give any physical insightinto the reasons for the identification of the optimum design.

3. ADAPTATION AND VALIDATION OF COMPUTER PROGRAMS

Following modifications necessary to adapt the two programs for operationon the ARL ELXSI-6400 computer system (Appendix) they were applied to a widevariety of problems to gain some insight into their capabilities and limitations.Although both codes had areas where they would not produce solutions, or producedobviously erroneous solutions, they behaved satisfactorily on sections of the typestudied in the prese,%t inveqigation (zero camber, thickness chord ratio 2% to 6% andReynolds number 10 to 10-).

To gain some indication of the accuracy of the codes in this area theywere compared with experimental results on two 6% aerofoils, the NACA 0006 andNACA 64A006, from Ref.1. The results of these comparisons are plotted in Figs. 2 &

3. It can be seen that for moderate lift coefficients both codes show a similar andacceptable level of agreement with the experimental results. The largest part of thedifference between the two sets of computed results is due to differences in thepredicted boundary layer transition points. The more sophisticated boundary layerand wake treatment in the NASA-Lockheed program did not produce significantlybetter results. The maximum lift coefficient was better predicted by PROFILE thanby the NASA-Lockheed code which consistently gave optimistic values.

Since PROFILE gave better results overall and executed considerablyfaster, it was used for most calculations. However spot checks with the NASA-Lockheed code always showed the same relative performance between differentconfigurations.

All the plotted results presented in this paper were computed usingPROFILE. Since PROFILE objected to parallel-sided profiles a very slightdivergence was incorporated.

4. RESiT8 AND DISCUSION

4.1 Leading Edges

The semi-ellipse (Fig.5) has been the customary choice for a low speednose fairing for a parallel-sided two dimensional section. This selection was based onthe well behaved pressure distribution produced by this shape (Ref.5) and its knownall-round aerodynamically satisfactory behaviour. To investigate the behaviour ofsemi-elliptic leading edges a series of sections with different fineness ratio fairingswere computed. The leading edge shape was given by:

]4

141

The angles of attack for the onset of gross leading edge separation for themodified and elliptic fairings are presented in Fig.8. For low Reynolds numbers thesharper elliptic fairing gives superior results to the modified fairing for small fairinglength. The optimum length for modified fairings at low Reynolds number is large(XLE/t>5). This would be expected since it has been known for many years that lowReynolds number aerofoils require sharp leading edges to avoid early laminarseparation (Ref.9). At high Reynolds number the modified leading edge has anoptimum length of about xLE/t - 3.5 where it gives superior results to an optimumelliptic fairing. At intermediate Reynolds numbers the two fairings have similarmaximum separation free angle-of-attack ranges, but the modified fairing lengthrequired is greater than that for the elliptic fairing.

In situations where cavitation, ventilation or compressibility aresignificant design considerations the minimum pressure coefficient is an importantparameter. The section with the numerically smaller negative pressure peak willhave superior characteristics. For all practical parallel-sided sections the lowestpressure occurs near the leading edge at all angles-of-attack. In Fig.9 the variationof minimum pressure coefficient with angle-of-attack and fairing length is plottedfor a 4% thick section with both leading edge shapes. The results for 2% and 6%thick sections show very similar trends. For angles-of-attack below 4' the ellipticfairing is superior to the modified one. For angles-of-attack above 4" the modifiedfairing is superior to the elliptic one. The apparent superiority of the very shortelliptic fairing at high angles of attack cannot be realised due to prematureseparation.

Where a parallel-sided section is to be used as a ground plane or end plate,the minimum deviation from free stream velocity over the greatest possible portionof the chord is the main design requirement. Although these applications involvenominally zero angle-of-attack they will usually experience induced flow angularityand the performance at small angles will be important. At zero incidence theleading edge fairing creates a positive surface velocity increment (i.e. negativepressure coefficient) which dies away as the flow moves aft until the region ofinfluence of the trailing edge fairing is reached. At incidence the additionalnegative pressure coefficient on the leeward surface will exceed the positiveincrement on the windward surface. The pressure coefficient near the leading edge(say at 0.1c) on the leeward surface gives a good indication of the departure fromfree stream conditions over the major part of the section. In Fig.10 this x/c = 0.1pressure coefficient is plotted against fairing length for both leading edge types andt/c = 4%. The same trends are observed for 2% and 6% thick sections. It can beseen that the modified leading edge is superior to the elliptic one for all leading edgelengths. The modified leading edge shape would therefore be the normal choice for aground board or splitter plate in an aerodynamic experiment.

There is little to suggest that leading edge fairing shapes intermediatebetween the elliptic and zero curvature at tangency types would have significantadvantages. However for particularly demanding specific applications they may beworth investigating.

[3J

y = 1 -(XLE x) 2

L

where the variables are defined in Fig.4

For the trailing edge a simple quadratic fairing was used (Fig.6). Theshape was given by:

with xTE=4 . y =± (1- (x - c + xE) 2 )

Since premature leading edge separation is one of the major problems withthin sections, the effect of section thickness and elliptic leading edge fineness ratioon angle of attack for significant separation was investigated. The results are shownin Fig.7. Boundary layer separation very near the trailing edge was predicted for allangles of attack where the leading edge flow remained attached. However this hadno effect on the predictions of leading edge separation since there was no iterativesolution of boundary layer and potential flow. The pressure distribution calculatedand used in the prediction of leading edge separation was that for an attachedtrailing edge flow.

The differences between the predicted separation angles of attack forgeometrically similar leading edges on different thickness sections are due partly tothe differences in Reynolds number based on a characteristic leading edge fairingdimension and partly on the effect of the trailing edge on the leading edge pressuredistribution. No attempt to separate these two effects was made. However as wouldbe expected there is a clear trend for the thicker sections to retain attached flow tohigher angles of attack.

For most of the cases computed there is a maximum separation free angleof attack for leading edge fairing lengths in the range 2<xLE/t<3 with earlierseparation for longer and shorter fairings. This suggested two different separationmechanisms and an examination of the computations showed that for long fairingsthe separation occurred on the small radius-of-curvature nose, while for shortfairings the separation occurred on the shoulder where the fairing was tangent to theparallel-sided part of the section. The maximum separation angle-of-attackoccurred at the transition between these two states. Some of the separations wereclearly laminar, some turbulent and some indeterminate. From Fig.7 it is evidentthat if an elliptic leading edge fairing is used a XLE/t value of 2 will give the largestangle-of-attack range under most conditions.

The elliptic leading edge results suggested the possibility of greater angle-of-attack ranges if one of the separation modes could be suppressed. To explore thispossibility a modified leading edge profile with zero curvature at the point oftangency between fairing and section was investigated. The shape (Fig.5) wasnecessarily blunter than an elliptic one of the same length and was given by:

t 8v(x 2x X2

y - 2 3vxLE XLE 3xIE

LB... . . . .

151

4.2 TraiIiDg FIMes

As for the leading edge fairing, the first requirement of the trailing edgefairing is the elimination or minimisation of separation. Section drag would probablybe the most appropriate parameter to assess the seriousness of trailing edgeseparation. However neither of the analysis methods used gave a good estimate ofdrag in the presence of separation so the y coordinate of the separation point dividedby the total section thickness was adopted. This gives some indication of the wakethickness.

The variation of separation point coordinate with trailing edge length for aquadratic fairing on a 4% thick section at zero incidence is shown in Fig.11. Similarresults are obtained for other thickness ratios and the separation points arerelatively insensitive to angle of attack. Separate curves for laminar and turbulentapproach boundary layers are presented. For rost parallel sided sections atincidence with chord Reynolds numbers less than 10T the windward surface boundarylayer is laminar at the start of the trailing edge fairing and the leeward surface layeris turbulent. At zero incidence for Reynolds numbers not greatly exceeding 10,

both boundary layers will be laminar if xLE/t >3 for elliptic leading edge fairings, orxLl/t>4 for modified fairings. It is evident from Fig.11 that trailing edge fairingle1gth of around 6t are required to obtain attached flow with a turbulent approachboundary layer and even longer fairings with laminar layers. As would be expectedlonger fairings always give superior results to shorter ones.

The quadratic fairing shape considered up to this point was selected sinceit was the simplest that would meet the required conditions of tangency with thebasic section and zero trailing edge thickness. To investigate the effect of fairingshape in more detail a cubic expression was used with the slope at the trailing edgeas an additional parameter.The shape was given by:

X2 X3

y ± (1+ ( 2 S-3)--- + 2 (1-S) -i-

where x, = x - c + xU

Slope at x = cand S =

Slope at x = c for quadraticfairing of same xTE

For S - 1 the cubic shape reduces to the earlier quadratic form and for S 0.75 thespecial case of zero surface survature at the trailing edge results. For S<0.75 thefairings have concave regions.

In Fig.12 the variation of trailing edge separation y coordinate is plottedagainst the slope parameter for a 4% thick section with an xTE = 4t cubic fairing.Similar results are obtained for other thicknesses and trailing edge lengths. For alaminar approach boundary layer a minimum in y occurs for values of S between0.75 and 1.0. For a turbulent layer y reduced mZnotonically with reducing S. Forgeneral use the zero curvature S 0.9hape appears to be a good choice.

. .. . ..

161

As noted previously the major requirement for sections for ground boardand splitter plate applications is the minimum deviation from free stream velocity(c = 0) over the greatest chordwise extent. The fairing required to provide trailingedge closure inherently produces a local flow acceleration which has some upstreaminfluence. The shorter the trailing edge fairing the further downstream thisacceleration occurs, but the greater its magnitude. The result of these conflictingreffects for a specific trailing edge fairing is shown in Fig.13. Very short fairingsshow definite superiority in this particular situation and this result appears to befairly general from the calculations conducted. Short fairings could have significantseparation and the truncation of the section to produce a bluff base could give goodresults in some circumstances.

4.3 Comparison Between Paralel-Side and Conventional Aerofoils

To provide some insight into their relative performance, a conventionaland a parallel-sided section were compared. A thickness/chord ratio of 4% waschosen and a scaled thickness NACA 64006 profile was used as the conventionalreference aerofoil. Although in principle NACA 6-series sections can not be simplyscaled, the section produced had a satisfactory pressure distribution and wasconsidered to be representative of good modern practice. On the basis of theinvestigations reported above a parallel-sided section with a 4t long modified leadingedge fairing and a 5t long, S = 0.75, cubic trailing edge fairing was selected forcomparison. The two section shapes are compared in Fig.14. It can be seen that theparallel-sided section has considerably greater cross section area and would haveeven greater strength (first moment of area) and stiffness (second moment of area)than the conventional section.

Comparative lift-drag curves are plotted in Fig.15. At a Reynolds numberof 105 both sections have a similar maximum lift ang the conventional section hasconsistently lower drag. At a Reynolds number of 10 the parallel-sided section hasapproximately double the maximum Iit, but higher drag than the conventionalsection. At a Reynolds number of 10' the parallel-sided section has more thandouble the maximum lift of the conventional section and lower drag at liftcoefficients above 0.15. The rise in drag at low lift appears to be a genuine effectassociated with the movement of the transition points.

It is clear that conventional section shapes are not necessarily theoptimum shape for very thin aerofoils.

5. CONCLUION

There are many situations in which parallel-sided sections with leading andtrailing edge fairings of limited chordwise extent have advantages over conventionalsections. A numerical investigation into the design of this type of profile wasundertaken using the Improved NASA-Lockheed Multielement Airfoil AnalysisProgram and the Eppler program PROFIW . A section thickness range of 2% to 6%and a Reynolds number range of 10) to 10' were covered.

The main conclusions were:

a. For a conventional semi-elliptic leading edge fairing a maximum angleof attack range is realised for a fairing length to thickness ratio ofapproximately 2.

171

b. For many applications a leading edge fairing with zero curvature atthe point of tangency has advantages over an elliptic fairing.

c. Trailing edge fairings defined by a cubic function with zero curvatureat the trailing edge have favourable characteristics.

d. For ground board or splitter plate applications in aerodynamic testing,the shortest practical leading and trailing edge fairings should beused.

The use of relatively simple potential flow and boundary layer programs asa "numerical wind tunnel" was found to be a valuable design technique allowing awide range of shapes to be investigated at low cost.

a

[8]

REFERENCES

1. I.H. Abbott & Theory of Wing Sections.A.E.Von Doenhoff Dover Publications N.Y. 1959

2. S.F. Hoerner & Fluid-Dynamic Lift.H.V. Borst Hoerner Fluid Dynamics N.J. 1975

3. S.F. Hoerner Fluid-Dynamic DragHoerner Fluid Dynamics N.J. 1965.

4. W. Rae & Low Speed Wind TunnelA. Pope Testing 2nd Edition. Wiley 1984

5. J.L. Hess & Calculation of Potential FlowA.M.O. Smith About Arbirtary Bodies.

Progress in Aeronautical SciencesVol. 8. D.Kuchemann Ed.Pergamon Press. 1967.

6. R. Eppler & A Computer Program for the DesignD.M. Somers and Analysis of Low-Speed Airfoils.

NASA Tech. Memo. 80210. 1980.

7. R. Eppler & Supplement to: A Computer ProgramD.M. Somers for the Design and Analysis of

Low-Speed Airfoils.NASA Tech.Memo.81862. 1980

8. G.W. Brune & An Improved Version of theJ.W. Manke NASA-Lockheed Multielement Airfoil

Analysis Computer Program.NASA CR-145323. 1978.

9. F.W. Schmitz Aerodynamics of the Model Airplane,Part 1 - Airfoil Measurements. 1942Redstone Scientific InformationCentre, Translation RSIC-721.

dILi

191

APPENDIX

Modification to Programs for use on ARLELXSI 6400 computer system

In program PROFILE the 5th parameter in the call to subroutine GAUSS insubroutine PANEL was a constant. Not surprisingly when GAUSS tried to change thevalue of this parameter an error was generated. The solution adopted was to replacethe constant in the call with a dummy variable initialised to the appropriate value(0.) prior to the call. To avoid floating overflows when computing thin sections the+DOUBLE compiler switch (64 bit precision) was used.

The modifications to the NASA-Lockheed program were more extensive.Due to the effectively unlimited virtual memory size of the ELXSI the overlaystructure of the code was removed by treating the overlay calls as subroutine calls.The code used a dynamic storage system which relied on operating system specificcapabilities which were not readily simulated on the ELXSI. The solution adoptedwas to define a large (60 000) one dimensional array and EQUIVALENCE-ing allvariables stored in dynamic storage to this array. The function LOCF alwaysreturned the value 1. The statement SAVE LOCB, IPA was added to subroutineDYNSET and SAVE THTFIX was added to subroutine BLTRAN. The assemblylanguage matrix manipulation routines VIP and VIPD were replaced with FORTRANtranslations. Many other minor changes were made to bring the code up to currentFORTRAN standards. After operating the code for some time it was found thatalthough boundary layer transition following laminar separation was correctlypredicted, natural transition never occurred. The problem was traced to theinconsistent dimensioning of array A in routines BLTRAN, POINT and SLOPE. Theeffect was to overwrite the local switch variables KON and KCH in BLTRAN. Thesolution adopted was to DIMENSION array A(4) in BLTRAN. The use of the+DOUBLE compiler switch overcame occasional errors in the boundary layerroutines.

The fixed input formats in both codes were converted to free format tosimplify the preparation of data files.

k~ ~ ~ ~ ~ ~ ~ ~~-- ---- .. .............................. ..

a. High thickness ratio object -NACA 64 series sections

b. Moderate thickness ratio object-NACA 64 series sections

c. Moderate thickness ratio object-simple leading and trailing edge fairings

FIG. 1. AERODYNAMIC FAIRINGS FOR BLUFF OBJECTS

0.009

0.008

R e 6 x 10 6J

CD

0.004

0.00Eprmet(rf15C08

0.003

- - -Multielement C L max =1.4

0.002-- .~Profile CL a = 0.9

0.001

00.1. 0.2. 0.3 0.4 0.5 0.6 0.7 0.8

CL

FIG. 2. COMPARISON BETWEEN COMPUTATION AND EXPERIMENT-NACA 0006

0.008

0.007

0.003 -o-- -Eprmn (e )C a .

0.002 - ----- Multielement C L a= 0.95

001-Profile CL max = 0.75

0 0.1 0. 2 0. 3 0.4 0.5. 0.6 0.7

CL

FIG. 3. COMPARISON BETWEEN COMPUTATION AND EXPERIMENT-NACA 64A006

y t

[ LE t

C-

FIG. 4. BASIC DIMENSIONS OF SECTION

\ ' . . Ellptic

FIG. 5. LEADING EDGE SHAPES x LE /t= 2.5

Cubic (zero curvature at T.E.)

Quadratic

FIG. 6. TRAILING EDGE SHAPES x TE /t = 5.0

4i

0

dP

II -

o o

L <IlI 0 C i,- pI '--4

ox0

0 x O E-4

dP 0x

00

.(0

-04

d4~ 0

II o 0

Cd4 0 0 x' 1 J -

uoT peRdas ti

t

C*I

+L

- /

w 1

+ 0

E- 0

0 u0

> x

43 /

- E-

U -4CL4I

4-' I / (4

co *n 0

/ Oliva u

IU

z

Ci4

CDl Ln D

00O0

-- U

E- 7

U

Oo 4

' />II x

/ 41

r4~

0

AllC

-' a e mlm li m N mm m m m H

tic = 4%

------------------Elliptic leading edge

-'Modified leading edge

-0.8

-0.7-/

-4 -0.6

x4 -0.5

-0.

w0 0.

-03

-0.0

-0.2. --0

-0.1

-01 X/c 0.1

1 2 3 4 5 6

x LE/t

FIG. 10. VARIATION OF PRESSURE COEFFICIENT AT x/c =0.1

WITH LEADING EDGE SHAPE

~--~--Laminar boundary layer

Turbulent boundary layer

0.4

0.3

y SEP N

0.11-

01112 3 4 5 6

0.4 -xTE

0.3

Y SEPt

0.2

R 106

0.2-

0.1

R = 10O7

1 2 3 4 5 6x TE

FIG. 11. VARIATION OF Y COORDINATE OF SEPARATIONWITH TRAILING EDGE LENGTH - QUADRATIC

TRAILING EDGE, tic - 4S

- ------ Laminar boundary layer

- J Turbulent boundary layer

0.4

0.3P

YSEP / -#

0.2 + . + s $ R = 10 5

0.21-l0

0.1!

01 1 2

s.

0.3 -

YSEP

0. 2 4t -=10 6

0.1

1 2

0 1 S 2

FIG. 12. VARIATION OF y COORDINATE OF SEPARATIONWITH TRAILITY EDGE SLOPE PARAMETER S -CUBIC TRAILING EDGE XTE- 4t, tic = 4%

cp

-0.10.

-* FIG. 13. VARIATION OF PRESSURE COEFFICIENT AT x/c -0.8WITH TRAILING EDGE LENGTH- QUADRATICTRAILING EDGE, tic -4%, a 00

.... .....

C-4rk

I'0

/ '4

$4 <

0 0

0 9: F. 0Io -I z 0

pl I 4

10 go

N 4 '0* 9 ,

FA of

---- ~-Scaled NACA 64006i

- --- Modified leading edge x LE 4t

S = 0.75 trailing edge x TE= 5t

0.0151

0.014 - *

CD 0.0131

DII

0.0111

0.0101

0.009[ 1 L I I

0; 0.11 0.2; 0!31 0.41 0.51 0.61 0.7 0.8' 0.9 1.0

o.010L CLI

0.0091 -

0. 0081 1ol

0. 0071D0 6

0.006, - 10

0.0051-

0.0041/

0.003401 0.11 0.2 0.31 0.4, 0.51 0.6' 0.7 0.8 0.9 1.0

0.010 -L

0.009;

0.0081- A/

C D 0.00711 -r-* WeR 1

0. 006 .,.-R10

0.005

0.00 I0, 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 1.0

C 1

FIG. 15. COMPARISON BETWEEN CONVENTIONAL AND

PARALLEL SIDED SECTIONS t/c =4%

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GERMANYFachinformationszentrum: energie, Physic, Mathematik GMBH

INDIACAARC Coordinator AerodynamicsDefence Ministry, Aero Development Establishment, LibraryHindustan Aeronautics Ltd, LibraryNational Aeronautical Laboratory, Information Centre

JAPANNational Aerospace LaboratoryInstitute of Space and Astronautical Science, Library

NETHERLANDSNational Aerospace Laboraotry (NLR), Library

NEW ZEALANDDefence Scientific Establishment, Library

SWEDENAeronautical Research Institute, LibrarySwedish National Defence Research Institute (FOA)

SWITZERLANDF + W (Swiss Federal Aircraft Factory)

UNITED KINGDOMMinistry of Defence, Research, Materials and CollaborationCAARC Coordinator Aerodynamics

Royal Aircraft EstablishmentBedford, LibraryPyestock, Director

National Physical Laboratory, LibraryNational Engineering Laboratory, LibraryBritish Library, Document Supply CentreAircraft Research Association, LibraryBritish Maritime Technology LtdMotor Industry Research Association, DirectorBritish Aerospace

Kingston-upon-Thames, LibraryHatfield-Chester Division, Library

British Hovercraft Corporation Ltd, LibraryShort Brothers Ltd, Technical Library

UNITED STATES OF AMERICANASA Scientific and Technical Information FacilityUnited Technologies Corporation, LibraryLockheed-California CompanyLockheed Missiles and Space CompanyLockheed GeorgiaMcDonnell Aircraft Company, Library

Spares (10 copies)TOTAL (103 COPIES)

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AR0451J AR-EOT-8 SEPTEMBER 1987 DST 85/025

4. Triyl a. 8EUITYi CLa.1fl*O S. Oft. 01

A NOTE ON THE AERODYNAMIC PL ACEavlIl SXATI~w ad0 1E. SEW". Cmuumn&w. 24DESIGN OF THIN PARALLEL-SIDED aw a 10103M.

AEROFOIL SECTIONS (U) MJEMJL.INo.'I '

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AERONdAUTICAL RESEARCH LABORATORIES SCR

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14. OECIPTOI 15. la W6ECTCA1109

AirfoilsAerodynamic characterists .DRDA SubjectComputational fluid dynamics Category

0051A0046B

There are many situations where parallel-sided aerofoil sections with leadingand trailing edge fairings of limited chordwise extent have advantages over

* conventional sections. The design of these unconvrentional sections wasinvestigated using two potential flow plus boundary layer computerprograms. Guidelines for the selection of the leading and trailing edge

* fairing shapes are presented.

! UNCLASSIFIED

THIS PAGE IS TO BE USED TO RECORD IWORKATION WHICH IS REQUIRED BY THE ESTABLISHMENT FORITS OWN USE B UT WIICH MILL NOT BE ADDED TO THE DISTIS DATA UNLESS SPECIFICALLY REQUESTED.

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p AERONAUTICAL RESEARCH LABORATORIES, MELBOURNEh

3. owT Usw No MW Is. Cwt cow 2. TIE W VaS NO PVeUW cOMM

Aerodynamics Technical 54 5006Memo 388

21. VougutI pMONG t

1. PROFILE

2. IMPROVED NASA-LOCKHEED MULTIELEMENT AIRFOIL ANALYSISPROGRAM

2. 5T*LIIWTM Fff.

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