NASA Technical Paper - N91CZ · NASA Technical Paper 1865 4. ... twoof which are discussedin this report. First, ifa highmaximum lift inefficient Cl,max can be realized,the wing area

INASA Technical Paper 1865

4.

“

Design and Experimental Results for a

Flapped Natural-Laminar-Flow Airfoil

for General Aviation Applications

Dan M. Somers

Langley Research CenterHampton, Virginia

NASANational Aeronautics

and Space Administration

Scientificend TechnicalInformationBranch

.

1981

INTRODUCTION

Research on advanced-technology’airfoils forhas received considerable attention over the past

general aviation applicationsdecade at the NASA Langley

Research Center.t

The initial emphasis in this research program was on thedesign and testing of turbulent-flow airfoils with the basic objective of pro-ducing a series of airfoils which could achieve higher maximum lift coefficients

+4 than the airfoils in use on general aviation airplanes at that time. For thisseries of airfoils, it was assumed that the flow over the entire airfoil wouldbe turbulent, primarily because of the construction techniques in use (mostlyriveted sheet metal). A summary of this work is presented in reference 1.

.While these new NASA low-speed airfoils did achieve higher maximum lift coeffi-cients, the cruise drag coefficients were essentially no lower than the earlierNACA four- and five-digit airfoils. Accordingly, the emphasis in the researchprogram has been shifted toward natural-laminar-flow (NLF) airfoils in anattempt to obtain lcwer cruise drag coefficients while retaining the high maxi-mum lift coefficients of the new NASA airfoils. In this context, the term“natural-laminar-flowairfoil” refers to an airfoil which can achieve signif-icant extents of laminar flow (?30-percent chord) solely through.’favorable pres-sure gradients (no boundary-layer suction or cooling).

Research on natural-laminar-flow airfoils dates back to the 1930’s at theNational Advisory Ccmmittee for Aeronautics (NACA). (See ref. 2.) The workat NACA was culminated with the 6-series airfoils (ref. 3). The 6-series air-foils were not generally successful as low-drag airfoils, however, because ofthe construction techniques available at the time.

The advent of composite structures has led to a resurgence in NLF research.The initial applications were sailplanes, but recently, a number of poweredgeneral aviation airplanes have been constructed of composites - most notably,the Bellanca Skyrocket II (ref. 4) and the Windecker Eagle (ref. 5). In Europe,powered composite airplanes have also been produced. One such aircraft, theLFU 205, used an NLF airfoil specifically tailored for its mission (ref. 6).

Thus, the introduction of composite construction has allowed aerodynamiciststo design NLF airfoils which achieve, in flight, the low-drag characteristics

. measured in the wind tunnel (ref. 7). The goal of the present research on NLFairfoils at Langley Research Center is to combine the high maximum lift capabil-

P ity of the NASA low-speed airfoils with the low-drag characteristics of the NACAP 6-series airfoils.

> As part of the present research, an NLF airfoil, the NLF(l)-0416, wasdesigned using the method of reference 8 and verified experimentally (ref. 9)in the Langley Lm-Turbulence Pressure Tunnel (LTPT) (ref. 10). Based upon thesuccess of this airfoil and the excellent agreement between the theoretical pre-dictions and the experimental results, a second, more advanced, airfoil wasdesigned using the method of reference 8. An experimental investigation wasthen conducted in the Low-Turbulence Pressure Tunnel to obtain the basic low-

speed, two-dimensionalaerodynamic characteristics of the airfoil. The resultshave been compared with the predictions from the methcd of reference 8.

Use of trade names or names of manufacturers in this report does not con-stitute an official endorsement of such products or manufacturers, eitherexpressed or implied, by the National Aeronautics and Space

SYMBOLS

Values are given in both S1 and U.S. Customary Units.calculations were made in U.S. Customary Units.

CP

c

cc

cd

cd‘

cl

cm

%

h

M

P

q

R

t

2

Administration.

)

Measurements and

+A

Pz - Pmpressure coefficient,

~m

airfoil chord, cm (in.)

section chord-force coefficient, @P d(:)

section profile-drag coefficient, ~~ cd, ‘~)

point drag coefficient (ref. 11]

section lift coefficient, Cllcos a - cc sin a

section pitching-munent coefficient about quarter-chord point,

-$4-‘“2’)‘(:)+$43‘(:)$ ()

xsection normal-force coefficient, - (2Pd -

c

vertical height in wake profile, cm (in.)

free-stream Mach number

static pressure, Pa (lbf/ft2)

dynamic pressure, Pa (lbf/ft2)

Reynolds number based on free-stream conditions and airfoil chord

airfoil thickness, cm (in.)

.

.i

,

x airfoil abscissa, cm (in.)

z airfoil ordinate, cm (in.)

cl angle of attack relative to chord line, deg

6f flap deflection, positive downward, deg

f Subscripts:

1 local point on airfoil, .

max maximum

min minimum

w free-stream omditions

Abbreviations:

1s lower surface

LTPT Langley Low-Turbulence Pressure Tunnel

NLF natural laminar flow

us upper surface

AIRFOIL DESIGN

OBJECTIVES AND CONSTRAINTS

The target application for this airfoil is a high-performance, single-engine, general aviation airplane. This application requires low sectionprofile-drag coefficients Cd at a Reynolds number R of about 9 x 106 forthe cruise section lift coefficient (CZ = 0.2) as well as for the climb sectionlift coefficients (cl = 0.5 tO l.O)O

Two primary objectives were identified for this airfoil. The first o’bjec-. tive was to design an airfoil which would produce a maximum lift coefficient

cj,max, atR= 3 x 106 comparable to those of the NASA low-speed series air-foils. (See ref. 1.) A requirement related to the first objective was thatjCI,max not decrease with transition fixed near the leading edge on both sur-faces.. This means that the maximum lift coefficient cannot depend on theachievement of laminar flow. Thus, if the leading edge of the wing iscon-taminated by insect remains, etc.~ ‘he Cz,max should not decrease. Thisrequirement is set by safety considerations relating to stall and, therefore,to landing speeds. The second objective was to obtain low profile-drag coeffi-cients cd fran the cruise lift coefficient c1 of 0.2 to about 1.

3

Three constraints were placed on this airfoil design in order to make itcompatible with existing aircraft designs. First, the airfoil thickness t/cmust be 15 percent. Secondr the pitching-mcnent coefficient ~ should be nomore negative than -0.05 at the cruise lift coefficient (CZ = 0.2). Third, theairfoil must incorporate a simple flap having a chord equal to 25 percent ofthe airfoil chord c.

PHILOSOPHY r

Given the previously discussed objectives and constraints, certain chara~teristics of the design are evident. The following sketch illustrates the

.+desired c1 - cd curve, which meets the goals for this design:

.1.8 -

1.0 —

0.2 —

cd

Sketch 1

The desired airfoil shape can be related to the pressure distributions which occurat the various lift oaefficients shown in the sketch. Point A is the cruise con-dition (cl = 0.2, R“= 9 x 106). The value of cd for this point is determinedby the extents of hminar flow on the upper and lower surfaces. There is littleaerodynamic advantage in achieving low drag below c1 = 0.2. This is especiallyimportant if high maximum lift must be obtained (pointC). However, in anattempt to insure a low-drag coefficient at the cruise lift coefficient(cl = 0.2) despite contour deviations due to construction tolerances, the lower -limit of the low-drag range was extended downward to ci = 0.1. Notice that the .drag at point B (CZ = 1.0) is not quite as low as at point A (cl = 0.2). This .feature is quite important because it shows that the transition point on theupper surface moves slowly and steadily toward the leading edge with increasing .Czr as opposed to the sudden forward junp characteristicof the NACA 6-seriesairfoils. This feature leads to an airfoil with a relatively blunt leading edgewhich, in turn, should produce a high maximum lift inefficient as well as goodflap effectiveness.

This outline of the desired section characteristics is not sufficient todesign the airfoil, however, primarily because of the variable introduced by

4

the flap and the unconstrained extents of laminar flow on the upper and lowersurfaces. In order to evaluate the effects of these variables, it is helpfulto examine the design goals with respect to overall aircraft performance. Forthis airfoil, th primary goal is a reduction in wing parasite drag. This goalcan be achieved in a number of ways, two of which are discussed in this report.First, if a high maximum lift inefficient Cl,max can be realized, the wingarea can be reduced relative to a wing with a lower Cz,max* This conclusion isbased on the assumption that both aircraft must achieve the same minimum speed.

i Second, if the amount of laminar flow on one or both surfaces can be extended,the minimum profile-drag coefficient cd,min will be reduced. Further analysisindicates that by maximizing cl,maxicd,min~ the win9 parasite drag is minimized.. . Unfortunately, a reduction in cd,min through the extension of the amount oflaminar flow on the upper surface generally results in a reduction in cz,max.(See ref. 3.) By trial and error, it was determined that Cl,maxicd,min would

. be maximized for this application if the extent of laminar flm was about 0.4con the upper surface and about 0.6c on the lower surface.

The effect of the flap on the design can be evaluated by examining the con-straint on the pitching-manent coefficient (~,cruise Z -0.05). The objective

/ of a high maximum lift coefficient is in conflict with the pitching-manent con-straint. For this design, the flap can be used to alleviate this conflict byemploying negative (up) flap deflections. This concept allows an airfoil to bedesigned which has a fairly large amount of camber (conduciveto a high c~,max)but retains the ability to achieve a low pitching-mcment coefficient at thecruise lift coefficient (cl = 0.2). This concept has the added advantage that,by deflecting the flap up or down, the low-drag range can be shifted to lower orhigher lift coefficients, respectively. (See ref. 12.) Based upon experiencewith other airfoils, the negative flap deflection df was limited to -1OO.

Fran the preceding discussion, the pressure distributions along thec1 - cd curve from points A to B in sketch 1 can be deduced. The pressure dis-tribution for a flap deflection of 0° at a lift coefficient of about 0.7 (i.e.,between points A and B) should probably resable sketch 2.

rus

.

●

a

cP

+

I 1 I I

o 0.4 0.6 1.0

x/c

Sketch 2

.

For the reasons previously stated, a favorable pressure gradient on the uppersurface is desirable up to x/c = 0.4. Aft of 0.4c on the upper surface, ashort region of slightly adverse pressure gradient is desirable to pranote theefficient transition from Iaminar to turbulent flow (ref. 13). Thus, the ini-tial slope of the pressure recovery is relatively shallow. This short region isfollowed by a steeper concave pressure recovery which produces lcxwerdrag andhas less tendency to separate than the mrresponding linear or convex pressurerecovery (ref. 13). The proposed pressure recovery, although concave, does notapproach the extreme shape of a Stratford recovery (ref. 14). The Stratford Precovery is not appropriate for an airfoil which must operate over a range oflift coefficients and Reynolds numbers (ref. 15).

,

For the reasons previously stated, a favorable pressure gradient on the.

lower surface is desirable up to x/c = 0.6. A rather abrupt and very steep con-cave pressure recovery is introduced aft of 0.6c, which results in a large .amount of aft camber. This camber, although limited by the pitching-mcxnentcon-straint (Cm,cruise ~ -0.05 with ~ = -10°), helps produce a high maximum liftcoefficient.

For point A (cz = O.2) in sketch 1, the pressure distribution should resereble sketch 3. For this lift coefficient, the flap is deflected up 100. Along

cP

+ 1 I I Io 0.4 0.6 1.0

x/c

Sketch 3

the lower surface, the pressure gradient is initially adverse, then zero, andthen increasingly favorable. Basitally, this concept is to transition as theStratford pressure remvery (ref. 14) is to separation. The concept was sug- -gested by Richard Eppler of the University of Stuttgart, Stuttgartr West GeLmany. .

For point B (C2 = 1.0) in sketch 1, the pressure distribution should resem- “ble sketch 4. For this lift coefficient, the flap is deflected down 100. Afavorable pressure gradient on the upper surface to x/c = 0.4 and a zero pres-

.

sure gradient on the lower surface to x/c = 0.6 is expected to result in lowdrag, albeit at the lower limit of the low-drag range for this flap deflection.

6

CP

+, I I I I

o 0.4 0.6 1.0

Sketch 4

It should be noted that the cruiseflap concept may not be optimum for allapplications. If the construction tolerances at the flap hinge are not suf-ficiently tight, lift and drag penalties due to a disturbance to the turbulentboundary layer ‘maybe sufficient to offset the advantages of this concept. (Seeref. 16.)

EXECUTION

Given the pressure distributions for c1 = 0.2, c1 = 0.7, and c1 = 1.0,the design of the airfoil is reduced to the inverse problem of transformingthe pressure distributions into an airfoil shape. The method of reference 8 wasused because it is ideal for handling multipoint designs, i.e., designs wheremore than one angle of attack must be considered. This method was also chosenbecause of its capability to analyze flap deflections and because of confidencegained during the design, analysis, and experimental verification of theNLF(l)-0416 airfoil (ref. 9).

The inviscid pressure distributions computed by the method of reference 8for c

i= 0.7 (df = 00), c1 = 0.2 (df =-100), and

T;: ;e;;!ti;~fs;a~e~)a;~eshown zn figures l(a), l(b), and l(c), respectively.shown in figure 2 and the coordinates with 0° flap deflection are presented intable I. The designation, NLF(I)-0215F, follows the form:

●

Application Airfoil number t/ccl,design —

# Natural &aminar glow ~ 0.2 0.15.- —

.

The second “F” designates “flapped.” For this airfoil, CZ,design is definedas the cruise lift coefficient. It must be emphasized, however, that this in noway implies that this airfoil was designed at only one point, clrdesignt● all ofthe objectives and constraints were considered.

7

WIND TUNNEL

The Langley Low-Turbulence Pressure Tunnel (LTPT) is a closed-throat,single-returntunnel which can be operated at stagnation pressures from 3 to

1000 kpa (OC03 to lo atm). (See ref. 10.) The minimum unit Reynolds numberis approximately 3.9 x 104 per meter (1.2 x 104 per foot) at a Mach number of0.05, whereas the maximum unit Reynolds number is approximately 4.9 x 107per meter (1.5 x 107 per foot) at a Mach number of 0.23. The maximum tunnel-

.

emptytest-section Mach number of 0.46 occurs at a stagnation pressure ofabout 100 kPa (1 atm). ,.

The test section is 91.44 cm (36.00 in.) wide by 228.6 cm (90.00 in.) high.Hydraulically actuated circular plates provide positioning and attachment forthe two-dimensionalmodel. The plates, 101.6 cm (40.00 in.) in diameter, are -flush withmounted to

the tunnel sidewalls and rotate with the model. The model ends wererectangular model attachment plates, as shown in figure 3.

MODEL

The forward portion of the wind-tunnel model of the NLF(l)-0215F airfoilconsisted of an aluminum spar surrounded by plastic filler with two thinlayers of fiberglass forming the aerodynamic surface. The flap was constructedof aluminum and was attached to the forward portion of the model by aluminumbrackets. These brackets were shaped so as to simulate 0°, -10°, and 10°deflections of a sealed, center-hinged, simple flap. (See fig. 4.) The loca-tion of the flap-hinge point was x/c = 0.7500, z/c = 0.0328. The model hada chord of 60.960 cm (24.000 in.) and a span of 91.44 cm (36.00 in.). Upper-and lower-surface orifices were located 7.62 cm (3.00 in.) to one side ofthe midspan at the chord stations listed in table 11. Spanwise orifices werelocated in the upper surface only in order to monitor the two-dimensionalityof the flow at high angles of attack. All the orifices were 1.0 mm (0.040 in.)in diameter with their axes perpendicular to the surface. The model surfacewas sanded with No. 600 dry silicon carbide paper to insure an aerodynamicallysmooth finish. The steps and gaps between the brackets and the forward portionof the model and between the brackets and the flap were eliminated by filling.The model contour accuracy was generally withinmined by measurement.

WAKE RAKE

fO.05 mm (0.002 in.) as deter-

.

A fixed wake rake (fig. 5) was cantilevered from the tunnel sidewall at the.

model mids~n and 1.0 chord downstream from the trailing edge of the model. The .

wake rake employed 91 total-pressure tubes, 0.152 cm (0.060 in.) in diameter, and5 statiepressure tubes, 0.318 cm (0.125 in.) in diameter. The total-pressuretubes were flattened to 0.102 cm (0.040 in.) for a length of 0.61 cm (0.24 in.)from the tips of the tubes. Each statimpressure tube had four flush orificeslocated 90° apart, 8 tube diameters frcm the tip of the tube in the measurementplane of the kotal-pressure tubes.

8

INSTRUMENTATION

Measurements of the static pressures on the model surfaces and of thewake-rake pressures were made by an automatic pressure-scanning system utilizingvariable-capacitanceprecision transducers. Basic tunnel pressures were mea-sured with precision quartz manometers. Geometric angle of attack was measuredby a calibrated digital shaft encoder driven by a pinion gear and a rack attachedto the circular plates. Data were obtained by a high-speed data-acquisition sys-

+ tem and were recorded on magnetic tape.

. TESTS AND METHODS.

The model was tested at Reynolds numbers based on airfoil chord fran approx-imately 2 X 106 to 9 X 106. The Mach number was varied frcm about 0.1 to 0.3.The model was tested both smooth (transitionfree) and with transition fixed byroughness at 0.05c on both surfaces. The roughnessnumber by the method of reference 17. The granulartributed along the 3-mm (0.1-in.)wide strips whichwith lacquer.

For several test runs, the model upper surface

was sized for each Reynoldsroughness was sparsely dis-were applied to the model

was coated with oil to deter-mine the location as well as the nature of the boundary-layer transition fromlaminar to turbulent flow (ref. 18).

The statiepressure measurements at the model surface were reduced to stan-dard pressure coefficients and numerically integrated to obtain section normal-force and chord-force coefficients and section pitching-moment coefficientsabout the quarter-chord point. Section profile-drag coefficients were mmputedfrcanthe wake-rake total and static pressures by the method of reference 11.

Standard low-speed wind-tunnel boundary corrections (ref. 19)t a maximum ofapproximately 3 percent of the measured section characteristics and 0.20angle of attackl have been applied to the data. The wake-rake total-pressure-tube displacement correction (ref. 11), a maximum increase of approximately

2 percent of the measured profile-drag coefficients, has not been taken intoaccount in order that the data be directly comparable to previously publishedairfoil data.

‘

.

DISCUSSI~ OF RESULTS

EXPERIMENTAL RESULTS

Pressure Distributions.

The pressure distributions for various angles of attack with a flap deflec-tion df of 0° at a Reynolds number of 6.0 x 106 and a Mach number of 0.10 aresbwn in figure 6. At a = -13.08°, -12.08°, and -11.08° (figs. 6(a) to 6(c))?the entire lower surface is separated. As the angle of attack is increased from-10.15° (fig. 6(d)), which corresponds to cz,minl the lower-surface, leading-edge pressure peak decreases in magnitude until it has disappeared at a = O.O1°

9

(fig. 6(n)). At this angle of attack, the profile-drag coefficient is minimum,and favorable pressure gradients exist along the upper surface to about 0.40cand along the lower surface to about 0.60c. As the angle of attack is increasedfurther, the pressure gradient along the upper surface becomes less favorableuntil, at a = 3.06°, it is essentially flat (fig. 6(q)). As the angle ofattack is increased even further, the position of minimum pressure on the uppersurface roves slowly forward while the magnitude of the minimum pressureincreases (figs. 6(r) to 6(y)). This feature was one of the design goals discus-sed in “Philosophy” and represents an improvement over the sudden forward jumpof Cp,minl typical of the NACA 6-series airfoils. At a= 12.20° (fig. 6(z)), ‘the mmimum pressure on the upper surface occurs at x/c = 0.0, thus forming aleading-edge peak. At a = 13.21° (fig. 6(aa)), the lift inefficient is maxi- .mum, and turbulent trailing-edge separation has occurred on the upper surface “ “at about 0.85c. The leading-edge peak continues to increase in magnitude, evenbeyond cz,max, indicating that leading-edge separation does not occur(figs. 6(bb) to6(dd)).

.

The pressure distributions for various angles of attack with a flap deflec-tion of -10° at a Reynolds number of 6.0 x 106 and a Mach number of 0.10 areshown in figure 7. At a = -11.090, -10.10o, and -9.070 (figs. 7(a) to 7(C)),the entire lower surface is separated. As the angle of attack is increased from-8.17° (fig. 7(d)), which corresponds to cz,minf the lower-surface, leading-edge pressure peak decreases in magnitude. It should be noted that the kink(depression)in the upper-surface pressure distribution which occurs at approxi-mately 0.75c is the result of the corner formed in the upper surface by thenegative flap deflection. (See fig. 4(b).) Further negative flap deflectionincreases the magnitude of this depression and, correspondingly, the possibilityof separation in the corner. Thus, the negative flap deflection is limited bythe requirement of lW drag. The minimum profile-drag coefficient occurs ata= 1.52° despite the persistence of the lower-surface, leading-edge peak whichthe laminar flow apparently survives (fig. 7(p)). At a = 2.51° (fig. 7(r)),the peak has disappeared and favorable pressure gradients exist along the uppersurface to about 0.35c and along the lower surface to about 0.60c. As the angleof attack is increased further, the pressure gradient along the upper surfacebecomes less favorable until, at a = 4.05°, it is essentially flat (fig. 7(t)).As the angle of attack is increased even further, the position of minimum pres-sure on the upper surface moves slowly forward until, at a = 14.20°

(fig. 7(dd)), a leading-edge peak is formed. The maximum lift coefficient occursat a= 15.25° (fig. 7(ee)). The leading-edge peak continues to increase inmagnitude, even beyond cZ,maxF indicating that leading-edge separation does notoccur (figs. 7(ff) to 7(hh)). .

The pressure distributions for various angles of attack with a flap deflec- .

tion of 10° at a Reynolds number of 6.0 x 106 and a Mach number of 0.10 are .

shown in figure 8. The kink (spike) in the upper-surface pressure distributionat a~roximately 0.75c is caused by the radius formed in the upper surface by

.

the positive flap deflection. (See fig. 4(c).) At a =-11.180 (fig. 8(a)), asharp peak is evident in the lower-surface pressure distribution. As the angleof attack is increased, this peak decreases in magnitude until it has disap-peared at a = -3.04° (fig. 8(i)). At this angle of attack, the profile-dragcoefficient is minimum and a favorable pressure gradient exists along the uppersurface to about 0.45c. As the angle of attack is increased further, the

10

pressure gradient along the upper surface becomes less favorable until, ata= 1.05°, it is essentially flat (fig. 8(m)). As the angle of attackis increased even further, turbulent trailing-edge separation occurs on theupper surface (figs. 8(o) to 8(aa)). The maximum lift coefficient occurs ata= 12.20° with the flow over the entire flap separated (fig. 8(x)). Theleading-edge peak continues to increase in magnitude, even beyond c~,max,indicating that leading-edge separation does not occur (figs. 8(y) to 8(aa)).

,

Transition Location

b. For a flap deflection of 0° and a Reynolds number of 3.0 x 106, the mech-

anism of the boundary-layer transition from laminar to turbulent flow on theupper surface, at an angle of attack of O.OO, was a laminar separation bubblewhich extends from laminar separation to turbulent reattachment as shown infigure 9(a). This bubble occurred at about 0.5c and was caused by the slightadverse pressure gradient inunediatelydownstream of the minimum pressure onthe upper surface. (See fig. 6(n).) This gradient was a design goal asdiscussed in “Philosophy.” At a = 2.0° (fig. 9(b)), the laminar separationbubble has decreased in length and moved forward. At a = 4.0° (fig. 9(c)),the laminar separation bubble has disappeared and transition has moved furtherforward.

Section Characteristics

Reynolds number effects.- The section characteristics with a flap deflec-tion of 0° at a Mach number of 0.10 are shown in figure 10. The effects ofReynolds number on the section characteristics with this flap deflection aresummarized in figure 11. The angle of attack for zero lift coefficient, approx-imately -5.8°, was unaffected by Reynolds number. The lift-curve slope andpitching-mcment coefficients were relatively insensitive to Reynolds numbervariation. The maximum lift inefficient increased substantially with increasingReynolds number, whereas the minimum drag coefficient and the width of the lowdrag range decreased significantly.

The section characteristics with a flap deflection of -10° at a Mach numberof 0.10 are shown in figure 12. The effects of Reynolds number on the sectioncharacteristics with this flap deflection are sununarizedin figure 13. Theangle of attack for zero lift aefficient, approximately -0.2°, was unaffectedby Reynolds number. The lift-curve slope and pitching-moment coefficients werealso unaffected by Reynolds number. The maxi,mum lift coefficient increased.moderately with increasing Reynolds number, whereas the minimum drag coefficientand the width of the low-drag range decreased significantly.

●

The section characteristics with a flap deflection of 10° at a Mach numberof 0.10 are shown in figure 14. The effects of Reynolds number on the sectioncharacteristics with this flap deflection are summarized in figure 15. Theabrupt change in lift-curve slope at a lift inefficient of about 1.4 was causedby a forward jump of the transition location on the upper surface. This jumpwas caused by a disturbance generated by the chordwise orifices (fig. 16). Thepremature transition led to premature, turbulent trailing-edge separation and,

11

thus, a reduction in lift-curve slope. Premature transition also occurred witha flap deflection of 0°~ although it did not result in such a sudden trailing-edge separation (fig. 17). This phenanenon does, however, explain the changein lift-curve slope evident in figure 10(a).

Mach number effects.- The effects of Mach number on the section character-istics with a flap deflection of 0° for a Reynolds number of 6.0 x 106 aresummarized in figure 18. The angle of attack for zero lift mefficien~was unaffected by Mach number. The lift-curve slope increased moderately withincreasingMach number, whereas the pitching-mcxnentcoefficients decreased. h

The maximum lift coefficient decreased slightly with increasing Mach number(fig. 19), whereas the minimum drag coefficient was unaffected (fig. 20). ..

Effect of roughness.- The effect of roughness on the section characteris-tics with a flap deflection of 0° for various Reynolds numbers is shown in fig- -ure 21. The angle of attack for zero lift coefficient as well as thepitching-moment coefficients increased with transition fixed, whereas the lift-curve slope decreased. All these results are a consequence of the boundary-layer displacement effect which decambers the airfoil slightly; the displacementthickness is greater for the transition-fixed condition than for the transition-free condition. Increasing Reynolds number decreases the displacement thicknessand? therefore~ the displacement effect.

Of more importance, however, is the effect of roughness on the maximum liftcoefficient and on the drag coefficients. The addition of roughness had essen-tially no effect on Cl,max for any of the Reynolds numbers. Thus, one of themost important design requirements has been achieved.Constraints.“)

(See “Objectives andThe drag coefficients were, of course, adversely affected by the

roughness.

The effect of roughness on the section characteristics with flap deflectionsof -10° and 10° for various Reynolds numbers is shown in figures 22 and 23?respectively. All the previously mentioned effects are again apparent.

Effect of flap deflection.- The effect of flap deflection on the sectioncharacteristics for various Reynolds numbers with transition free is shown infigure 24. The effects of flap deflection and roughness on maximum lift coef-ficient and minimum drag coefficient are summarized in figures 25 and 26,respectively.

COMPARISON OF THEORETICAL AND EXPERIMENTAL RESULTS

Pressure Distributions

The comparison of theoretical and experimental pressure distributions isshown in figure 27. The pressure distributions predicted by the method of refer-ence 8 are inviscid (potential-flow)and incompressible. The experimental pres-sure distributions were obtained for a Reynolds number of 6.0 x 106 and a Machnumber of 0.10 and, thus, contain the same data presented in figures 6(n)~ 7(p)~and 8(l). With a flap deflection of 0° at an angle of attack of O.O1°(fig. 27(a)), the theoretical predictions and the experimental data are in close

●

✎

12

agreement. Although the values of the pressure coefficients do not matchexactly, the pressure gradients agree well. With a flap deflection of -10° atan angle of attack of 1.52° (fig. 27(b)), the agreement between theory andexperiment is very good. With a flap deflection of 10° at an angle of attackof 0.05° (fig. 27(c)), the decambering vismus effects have become more apparentand the disparities include small differences in the pressure gradients as wellas larger differences in the values of the pressure coefficients.

,

Section Characteristics

b. The theoretical section characteristics were computed by the method of

reference 8. A boundary layer is calculated using the potential-flow pressuredistribution. Hwever, no iteration between the boundary-layer displacement

. thickness and the pressure distribution is performed. The lift and pitching-moment mefficients are determined from the potential flow and then some simpleviscous corrections are applied including a correction for boundary-layer sepa-ration. The profile-drag coefficients are obtained by applying a modifiedSquire-Young formula to the boundary-layer characteristics at the trailing edge.

The mmparison of theoretical and experimental section characteristics witha flap deflection of 0° and transition free is shown in figure 28. The magni-tudes of both the angle of attack for zero lift coefficient and the pitching-manent coefficients are overpredicted by the method of reference 8 (fig. 28(c)).These results are obtained because the theoretical method does not contain aboundary-layer displacement iteration. The agreement between theoretical andexperimental lift-curve slopes is good. The maximum lift coefficients are over-predicted by the method of reference 8 although the agreement improves slightlywith increasing Reynolds number. Past experience indicates that this overpre-diction is not typical of the method of reference 8. (For example, seeref. 9.) The calculated drag coefficients agree well with the experimental dataand beccaneincreasingly conservative (high) with increasing Reynolds number.

The mmparison of theoretical and experimental section characteristics witha flap deflection of -10° and transition free is shown in figure 29. Becausethe displacement effect with this flap deflection is small, the agreement betweentheoretical and experimental angles of zero lift coefficient, lift-curve slopes,and pitching-mcment coefficients is very good. At the higher angles of attack,the theoretical method predicts separation in the corner formed in the uppersurface by the negative flap deflection; therefore, a realistic estimate of the

.maximum lift coefficient is not possible. The calculated drag coefficients

; agree well with the experimental data and again become increasingly conservative(high) with increasing Reynolds number.. The disparity in the lower limit of thelow-drag range is attributed to the increased turbulence in the wind tunnel at

. the higher Reynolds numbers. (See ref. 10.)

The mmparison of theoretical and experimental section characteristics witha flap deflection of 10° and transition free is shown in figure 30. The magni-tudes of both the lift and pitching-moment coefficients are overpredicted by themethod of reference 8. The agreement between theoretical and experimental lift-curve slopes is good up to the angle of attack at which separation occurs onthe upper suface of the flap. The maximum lift coefficients are overpredicted

13

by the method of reference 8. The calculated drag coefficients agree well withthe experimental data over the range of lift coefficients for which little sepa-ration occurs. The predicted drag mefficients become increasingly conserva-tive (high) with increasing Reynolds number. At the lower angles of attack, thetheoretical method predicts separation in the corner formed in the liner surfaceby the positive flap deflection; therefore, the calculated results are not real-istic and, accordingly, have not been included. No comparison for R = 2.o x 106has been made because the theoretical method predicts separation in the cornerat all angles of attack for this Reynolds number. ,

The comparisons of theoretical and experimental section characteristics withtransition fixed and flap deflections of 0°, -10°, and 10o are shown in fig- . ●

ures 31, 32, and 33, respectively. The results are the same as for thetransition-free condition except that the small differences between the theoret-ical.and experimental drag coefficients do not increase with increasing Reynolds .number.

CONCLUDING REMARKS

A flapped natural-laminar-fkw airfoil for general aviation applications,the NLF(l)-0215F, has been designed and analyzed theoretically and verifiedexperimentally in the Langley Low-Turbulence Pressure Tunnel. The basic objec-tive of ccxnbiningthe high maximum lift of the NASA low-speed airfoils with thelow cruise drag of the NACA 6-series airfoils has been achieved. The safetyrequirement that the maximum lift coefficient not be significantly affected withtransition fixed near the leading edge has also been met. Comparisons of thetheoretical and experimental results show generally good agreement.

The most important result is that the new natural-laminar-fkw airfoilachieves maximum lift coefficients similar to those of the NASA low-speed air-foils even with transition fixed near the leading edge. At the same time, thenew airfoil with transition fixed exhibits no higher cruise drag then canparableturbulent-flm airfoils. Thus, if the new airfoil is employed in an aircraftdesign and laminar flow is not achieved, nothing is lost relative to the NASAlow-speed airfoils. If laminar flow is achieved, a very substantial profile-drag reduction results.

Finally, this airfoil demonstrates the unique and powerful capabilities ofthe theoretical method to design and analyze multipoint designs, including thosewhich incorporate simple flaps. .

.

Langley Research Center.

National Aeronautics and Space AdministrationHampton, VA 23665

,

April 13, 1981

14

REFERENCES

1. Mcf3hee,Robert J.; Beasley, William D.; and Whitcomb, Richard T.: NASALow- and Medium-Speed Airfoil Development. NASA TW78709, 1979.

2. Jacobs, Eastman N.: Preliminary Report on Laminar-Flow Airfoils and NewMethods Adopted for Airfoil and Boundary-Layer Investigations.NACA WR L-345, 1939 (formerly,NACA ACR).

.3. Abbott, Ira H.; Von Doenhoff, Albert E.; and Stiversl Louis S.? Jr.: Sum-

mary of Airfoil Data. NACA Rep. 824, 1945. (SupersedesNACA WR L-560.)._.:;.,

. l,,,... !~4,;~:payne,Henry E.: Laminar Flow Rethink-Using Canposite Structure.

“u’I’:>, [Preprint] 760473, Sot. Autcanot.Eng., Apr. 1976.

.~, .

,5:);Alther,G. A.: A Significant Role for Canposites in Energy-Efficient Air--.<.. craft. Technical Sessions of the Thirty-Sixth Annual Conference -

Reinforced Plastics/Canposites Institute, Sot. Plast. Ind.~ Inc.1Feb. 1981, Sess. 12-D, pg. 1 - Sess. 12-D, pg. 4.

6. Eppler, R. (FrancescaNeff en, transl.):2

Laminar Airfoils for Reynolds Num-bers Greater Than 4 x 10 . B-819-35, Apr. 1969. (Available from NTIS asN69-28178.)

7. Eppler, Richard: Sane New Airfoils. Science and Technology of Low Speedand Motorless Flight, NASA CP-2085, Part I! 1979, pp. 131-153.

8. Eppler, Richard; and Saners, Dan M.: A Computer Program for the Design andAnalysis of Low-Speed Airfoils. NASA TM-8021O, 1980.

9. Saners? Dan M.: Design and Experimental Results for a Natural-Laminar-FlowAirfoil for General Aviation Applications. NASA TP-1861, 1981.

10. Von Doenhoff, Albert E.; and Abbott, Frank T., Jr.: The Langley Two-Dimensional Low-Turbulence Pressure Tunnel. NACA TN 1283, 1947.

11. Pankhurst, R. C.; and Holder~ D. W.: Wind-Tunnel Technique. Sir IsaacPitman & Sons, Ltd. (London), 1965.

120 Pfenninger, Werner: Investigations on Reductions of Friction on Wings, inParticular by Means of Boundary Layer Suction.a NACA TM 1181, 1947.

. 13. Wortmann, F. X.: Experimental Investigations on New Laminar Profiles fOK< Gliders and Helicopters. TIL/T.4906, British Minist. Aviat.1 Mar. 1960.

. 14. Stratford, B. S.: The Prediction of Separation of the Turbulent BoundaryLayer. J. Fluid Mech., vol. 5, pt. 1~ Jan. 19591 pp. 1-16.

>=.(tl=5‘:,,,.Eppler, Richard; and Scrners,Dan M.: Low Speed Airfoil Design and Analysis.

Advanced Technology Airfoil Research - Volume I, NASA CP-2045, Part 1,1979, pp. 73-99.

75

16. Eppler, Richard: The Effect of Disturbances on a Wing. Science and Tech-nology of Low Speed and Motorless FlightF NASA CP-2085, Part 1, 1979,pp. 81-91.

17. Braslow, Albert L.; and Knox, Eugene C.: Simplified Method for Determina-tion of Critical Height of Distributed Roughness Particles for Boundary-Layer Transition at Mach Numbers frcm O to 5. NACA TN 4363, 1958.

18. Loving, Donald L.; and Katzoff, S.: The Fluorescent-Oil Film Methodand Other Techniques for Boundary-Layer Flow Visualization.

.NASA

MEkll3-17-59L, 1959..

19. Allen, H. Julian; and Vincenti, Walter G.: Wall Interference in a Twe .

Dimensional-FluwWind Tunnel, With Consideration of the Effect of Canpres-sibility. NACA Rep. 782, 1944. (SupersedesNACA WR A-63.) .

.

.

.

16

.

..

.

●

✌

☛

TABLE I.- NLF(l)-0215F AIRFOIL COORDINATES (df = oo)

[c = 60.960 cm (24.000 in.)]

UPPER SURFACE LOWER SURFACEx/c

,00240.00909.02004,03527.05469.07816.10546.13635.17050.20758.247?0.28894.332?37.37702.42253.46864.51524.56247●61010.65752,70408,74914.792C6,83222.86902.90193,93044,95409,97285.98710.99658

1.00000

Zlc.00917.01947.03027.04120,05201.06250,07247,08175.09019.09761.10389.10887.11240.11428.11427.11219.10784.10147.09373.08513,07603.06673.05746.04844.03983.03175.02428.01737.01082.00507.00126●00000

x/c.00000.00245.01099.02592.04653.07242.10324.13!354,17788.22073.26654.31473.36468,41576.46731.51867.56920.61825.66662,71614.76645.81565,86198.90359.93862,96588.98504.99630

1000000

z/c-000006-.00704-.01211-.01656-.02052-.02399-.02699-.02954-.03166-003334-.03456-.03531-.03554-.03519-.03415-.03225-.02925-.02441-.01663-000705.00167●00804●01155.01198●00990.00655,00323.00086.00000

?7

TABLE II.- kIIDELORIFICE LOCATIONS

[c = 60.960 cm (24.000 in.)]

.

..

UPPER SURFACEx/c z/c

●COO146 ,000625.005713 ,015346.010538 .021233.015313 .026138.020421 .030596,025425 .0344?9.030733 .038267,040425 .044354.050333 .049806.060283 ,054721,075242 .061313.100425 ● 070779.150950 .085604.200571 .096329,250650 .104325.300717 .109963,350792 ,113358.400571 .114463,450671 .113167.500904 .109354c550633 ,103158,600850 .095242,650742 ●0815363.700500 .076742.746638 .067304.802404 ,055258.851800 .044013,901758 ,031804.950917 .018442●974675 .010325

LOWER SURFACEx/c

,000146.004379,009975,014979.019983,024892.030021.040096,050096.059950,074850.099883,149996.200117,250071.299896,350188.400063.449963,499933●550167.600188,649913.699396,745754,800988.851267.899833,94f?883,974208

Zlc,000625

-.008742-.011800-.013642-.01’5133--016396-.017546-,019488-,021129-s022500-.024288-.026733-s030225-,032592-.034142-.035092-.035454-.035317-.034513-,033013-.030417-.026417-,019392-.010138-.001542.006450,011025,012079,008863●005071

.

.

.

m

.

-1.6

[

‘P

.

.

-1.2 -Uppersurface

-.8 -

-.4 -

0

~.4 “

Lower surface

.8

I1.2~’.i’.,~,~’.~’,5 1 I 1 ! I

,6 .7 .8 ,9 1,0

x/c

-1.6

-1,2

-.8

-.4

‘P ~

.4

,8

(a) c1 = 0.7; ~f = 0°=

Upper surface

,,~“ O .1 .2 .3 ,4 .5 06 .7 ,8 .9 1,0

x/c

(b) Cl = 0.2; df = -100.

Figure l.- Inviscid pressure distributions.

,

..

-1,6

-1.2

-,8

-.4

CPo

.4

.8

~Upper surface

\

/

\ Lower surface

1.2A ‘ .; , 1 I 1 , 1 t 1 I.2 .S .4 .5 .6 .7 ,8 .9 1.(I

x/c

(c) c1 = 1.0; df = 100.

Figure 1.- Concluded.

.

.

. .

.

. .

.2-

.1-

z/c

-.1; t 1 1 I , 1 1 [ 1 I

.1 .2 .!3 .4 .5 .6 .7 .8 .9 Lo

x/c

(a) df = OO.

Figure 2.- NLF(I)-0215F airfoil shape.

N

.2-

.1-

z/c

o

, 1 1 1 I t 1 1 I-. l! !

.1 ,2 .3 .4 .5 .6 .7 .8 .9 Lo

x/c

(b) df = -1Oo.

Figure 2.- Continued.

*

.

#

.

, 1

..

. .

A

. .

.

.2-

.1-

z/c

o

-.1A 1 t 1 I 1 1

.1 .21 !

.31

.4 .5 .6I

.7 .8 .9 Lo

x/c

(c) 6f = 100.


l+-Accessto pressuretubes

Diem =1.67c/

Ik HA’s W//////////////////////k~

Circular plete

v ~ ~ f&@z/////////////////

Tunnel center he 7

II

I1

I1

I—-L-. — -

I1

I1

II

I

I

Top view

1,

1A

~Mde’ ‘tachmen’p’ateI #l

L-— Zero angle of atlack reference

----- ------ --

4- Cll 4

End view, section A-A

Figure 3.- T~ical airfoil model mounted interms of model chord, c =

wind tunnel. All dimensions are in61.0 cm (24.0 in.).

*

..

.

.

.

●

24

J

,

z/c

.

z/c

.

*

.1

0

I I 1 I 1 I !—. II

.6 .7 .8 .9 I.0

x/c

(a) df = OO.

.1

0

I I I I 1 I 1 J

-. 1’

.6 .7 .8 .9 I.0

x/c

(b) df =-lOO.

Figure 4.- Flap brackets.

25

,

,

z/c

.1

0

.

I I I I 1 I I

-. II I.6 .7 .8 .9 I.0

x/c

(c) df = 100.


.

.

.

●

26

.

Static-pressure

,

,

.

~-–~<==-> -.125c

probe

L

Rod ,=0,021c) ——

.042c+ P ,,,~.250c+

‘3--L

T.02 [c

(typ.)

static- pressure probes

——

Airflow ~

Tunnel ~ — –

3 (typ.)

Total- pressure probes

(tubes flottened) 4

=1

+-T

L .188C(typ.)

1

.042c

—

1.16c

-——

Y

Figure 5.- Wake rake. All dimensions are in terms of model chord,c = 61.0 cm (24.0 in.).

27

-8.4

.8.0

.7,6

-7.2

-6.8

.6.4

.6.0

-6.6

.6.2

-4.8

.4.4

-4.0

12p -9.6

.s.2

4.8

-2.4

:2.0

.1.6

-1.2

-.8

..4

0

.4

.6

1:20 ,1 ,2 .3 .4 .5 .6 .7 ~ .g lo

x/c

(a) a = -1s.08”:c1 = -0.28E;cd = 0.1781:cm = 0.001,

AA — —,—. -— .—-..“. .

-8.0

-7.6

-7.2

.6.6

-6.4

-6.0

-6.6

-6.2

-4.8

-4.4

-4.0

Cp -9.6

.8.2

-2.8

-2.4

-2.0

-1.6

-1.2

-.8

-A

B

.4

.8

120 .1 ~ .3 ,4 ,5 ,6 .7 ,8 .g lo

x/c

(b) a - -12.08e; Cl = -0.299: Cd = 0.1758; cm = 0,001.

.

,.

.

.

.

.

Figure 6.- Pressure distributions with df = 0° for R = 6.0 x T06 andM= 0.10.

28

.

.

.

.

-2.4

-3.0

-7,6

-7.2

.6.8

.6.4

.6.0

.5.6

-5,2

.4.8

.4.4

.4.0

Cp -3,6

-9.2

-2.8

-2A

-2.0

-1.6

-1.2

-.8

-.4

0

.4

.8

1,20 .1 .2 .3 .4 .5 .6 ,7 ,8 ,9 lo

Xlc

(c) a = -11.08°; Cl m -0.287; Cd = 0.1544; cm = -0,022,

-6.4

-8.0

-7,6

-7.2

-6.8

-6.4

-6.0

-5.6

.5.2

-4.8

-4.4

-4.0

Cp -9.6

.3.2

-2.8

-2.4

-2.0

-M

-1.2

-.6

-.4

,

0

.4

.3

1.20 .1 ,2 ,3 ,4 ~ ,6 .7 .8 .91.0

x/c

(d) a = -10.15°; Cl = -0.482; Cd = 0.0121: Cm” = -0.125.


29

-6.4

-6.0

-7.6

.7.2

.6.8

-6.4

.6.0

-5.6

.5.2

-4.8

-4.4

-4.0

Cp -S.6

-9.2

-2.8

-2.4

-2.0

-1.6

-1.2

-.6

-.4

0

.4

.6

1.2

1

0 .1 .2 .6 .4 .5 .6 .7 .8 .9 1.0

Xjc

(e) a = -917’: c~= -0s75; cd = 0.0105; cm = -0.128.

-6.4

-8.0

-7.6

-7.2

.6.6

.6.4

.6.0

-6.6

-5.2

-4.6

-4.4

-4.0

Cp -2.6

-3.2

-2.6

4.4

-2.0

-1.6

-1.2

-.6

-.4

0

.4

.6

1.2

I

o J .2 .3 .4 .5 .6 .7 .6 ,9 1.0

Xlc

(f) u = -8.15”; Cl- -0.264; Cd = 00090; cm = -0130

.

..

.

.

.

Figure 6.-

30

Continued.

4

.

●

.

.

-8.4

.8.0

.7.6

-7,2

-6.8

-6.4

.6.0

.6.6

-5.2

-4.8

-4.4

-4.0

Cp -8.6

-8.2

-2.8

-2.4

-2.0

-1.6

-1.2

-.8

-.4

0

.4

.81 1

‘,!’.;’.;’.;’;’.&’ ,; ’,/: ’10. .

-8.4

-8.0

-7.6

-7.2

.6.8

.6.4

.6.0

-5,6

-5.2

-4.8

-4.4

.4.0

Cp .S.6

-8.2

-2.8

-2.4

-2.0

-1.6

-1.2

-.8

-.4

0

.4

,8

1.20 .1 .2 ,3 .4 .5 .6 .7 .8 ,9 lo

x/c

(s) a - -7.11°; et = -0,149; cd = 0.0078; cm = -0,132. (h) a = -6.08”; CJ = -0.034; cd = 0.0075; cm = -0.134.


37

CP

Xjc

(i) a = -5.09”: c, = 0,081; cd = 0.0074: Cm = -01S6.

CP

(1) a - -4.05”:.1- fJ.19E3 Cd = 00071: cm - -0.13s

.

..

.

.

.

.“


32

.

.

*

.

-8.4

-&o

-7.6

-7.2

.6.8

-6.4

-6,0

-6.6

.6.2

-4.8

-4.4

.4.0

Cp -3.6

-!3.2

-2.8

-2.4

-2.0

-1.6

-1.2

-.8

-,4

0

.4

.8

1,20 ,1 ,2 .3 .4 ,5 ,6 .7 .8 ,9 lo

x f c

(k) a = -3.05°: cl = 0.312: Cd = o.oo~e: Cm = ‘o.141.

Figure 6.-

CP

,

Xfc

(1) a = -2.04”; .l= 0.428: cd = 0.0062; cm = -0.144.

Continued.

33

-8.4

-8fJ

-7.6

-7.2

-8.6

.6.4

-8.0

-5.6

.5,2

-4.8

-4.4

-4.0

Cp -8.6

-8.2

4.6

-2.4

-2.0

-1.6

-1.2

..8

-.4

c

.4

.6

1.2

1

0 .1 .2 .9 .4 .6 .6 .7 .8 .9 1.0

x~c

(m)a = -10 Zc:. t=0.55Wcd = 0.004*cm = -0.147.

-8.4

-6.0

-T.6

-7.2

.6.8

4.4

-6.0

-6.6

-6.2

-4.8

-4.4

.4.0

Cp -S.6

-9.2

4.6

-2.4

-2.0

-1.6

-1.2

-.8

..4

(

.4

.8

1.2“o .1 .2 .s .4 .6 .6 .7 .6 ,9 1.0

qc

(n) m = O.O1°: c1 = 0.657: cd = 0.0045; cm = -o:14&

.

.

.

.

.

.

Figure 6,- Continued.

34

.

.

.

●

‘

.

.8.4

-&o

-7.6

-7.2

-8,8

.6.4

-6.0

.5.6

-6.2

-4.8

.4.4

“4.0

Cp -3.6

-8.2

-2.8

-2.4

.2.0

.L6

-1.2

-.8

..4

0

.4

.8

1.20 .1 ,2 .3 ,4 ~,6 .7 .8 .9 1.0

x/c

(o) a = 1.02°; .1 = 0,767; cd = 0.0046: cm = -0.149.

CP

x/c

(P) a = Z.030: c1 - 0.876: cd = 0.0052: cm = -0.150.


35

●

CP

x/c

(4a = 3.06’; c1 - 0.981: cd = 0.0057: cm = -o.l~z. (r) a = 4.07”; c1.= 1.075:cd = 0.0072; Cm - -o.15~.

.

..

“

.

●

.

Figure 6.- Continued-

36

.

..

.

.

.

k

-8.4

.8.0

-7,6

-7,2

-6.8

-6.4

-6.0

.5.6

-5,2

-4.8

.4A

-4,0

Cp -3.6

.%2

-2.8

-2.4

-2.0

-1.6

.1.2

-,8

-.4

0

.4

.8

1.20 .1 ,2 ,3 .4 .5 .6 .7 ,8 ,9 lo

(s) a = 5.09°: c1 - 1.171; cd = 0.0085; cm = _o. ~49,

-8.4

-8.0

-7,6

-7.2

.6.8

-6.4

-8.0

-5.6

-5,2

-4.8

.4.4

-4.0

Cp -S.6

+3.2

-2.8

-2.4

-2.0

-1.6

-1.2

-.8

-.4

0

.4

.6

1.20 .1 ,2 .~ ,4 ,5 ,6 ,7 .8 ,9 lo

Xlc

(t) a = .5.100; Cl= 1..263; Cd = 0.0092: Cm = -o.147.


37

-8.4

-8.0

-7.6

-7.2

.6.8

.6.4

-6.0

-5.6

.5.2

.4.8

.4.4

-4.0

Cp -8.6

-s,2

-2.8

.2.4

-2,0

-1.6

-1.2

-.8

-.4

0

.4

.8

1.20 .1 .2 .~ ,4.5 .6 .7 .8 .9 1.0

Xjc

(u) a = 7.136: c1 = 1.313* cd = 0.0107; cm = -0.143.

-2.4

-8.0

-7.6

-7.2

-6.6

-6.4

-6.0

.5.6

-6.2

-4.8

-4.4

-4.0

Cp -2.6

-3.2

-2.8

-2.4

-2.0

-1.6

-1.2

-.8

-.4

0

.4

.8

120 .1 ~ ~ .4 .6.6 .7 .8 .9 1.0

(v) u. - .3.14”; CL= 1.443: cd - 0,0124; Cm = -0.142.

.

..

.

..

*

.


38

.

*

.

.

-8.4

.8.0

-7.6

-7.2

.6.8

.6.4

-6.0

.5.6

-5,2

-4.8

-4.4

-4.0

Cp -8.6

-3.2

-2.8

-2,4

-2.0

-1,6

-1.2

-.8

-.4

0

.4

.8

1,20 .1 .2 .8 .4 .5 ,6 .7 .8 .9 lo

x/c

(w) a = 9.16”; c1 = 1.527; cd = 0.0140: cm - -0.138.

-8.4

-8.0

-7.6

-7.2

-6.8

.6.4

-6.0

-5.6, \I r , , , , , , ! , ! ! ! !

, , 1-6.2

-4.8II, , 1 I , I 1 , , 1 I , 1 , ( -1

-4.4

I!llll

-4.0 I II I I I I I I I J I I I I I I I I i

Cp .S.6

-9.2

-2.8

-2.4

-2.0

-1,6

-1.2

-.8

-.4

0

.4

.8

1.20 ,1 ,2 ,3 .4.6 .6 .7 .8 ,9 1,0

x~c

(x) a = 10.17°; .l= 1.601; cd = 0.0159; cm = -0,134.


39

-8.4

-8.0

-7,6

-7.2

6.8

-6.4

-6,0

-5.6

.5.2

-4.8

-4.4

-4,0

Cp -2.6

-9.2

-2.8

-2,4

-2.0

-1.6

-1.2

-.0

-.4

0

.4

.8

1.20 .1 .2 .3 ,4 .5 .6 .7 .8 # lo

X}c

(Y) u = ~1.lg”’;C!= 1.667: cd = o.ola~: cm = -o.l~g.

Figure 6.-

-6.4

-0.0

-7.6

-7.2

.6.8

.8.4

-6.0

-5,6

-5.2

48

-4.4

-4.0

Cp -3.6

-8.2

-2.8

-2.4

-2.0

-1.6

-1.2

-.8

%4

o

.4

.6

1.20 ,1 ,2 .3 .4 .5 .6 .7 .8 ,9 lo

●

✎

●

.

●

1,

x jc.

(z) a = 12. S30°; cl= 1719; cd - 00211; cm = -0.123.

Continued.

40

.

.*

*

.

*

.

-8.4

-8.0

-7.6

-7,2

-6.8

-8.4

-8,0

-5.6

-5.2

-4.8

-4.4

-4.0

Cp -3.6

-3.2

-2.8

-2.4

-2.0

-1.6

-1.2

-.8

-.4

0

.4

.8

1.20 .1 .2 ~ .4 .5 .6 .7 .8 ,8 lo

x/c

(aa) a = 13.21°: CL= 1.738; cd = 0.0272; cm = -0.112.

-8.4

-8.0

-7.6

-7.2

.6,8

.6.4

.6.0

-6,6

-6.2

4.8

-4.4

4.0

Cp 43.6

-3.2

-2.8

-2.4

-2.0

-1.6

-1.2

-.8

-.4

0

.4

.8

1,20 .1 ,2 ~ .4.6 .6 .7 .8 .9 1.0

x/c

(bb) a = 14.20°; Cl = 1,601; Cd = 0.0826; Cm = -0.101.


47

-6.4

-8.0

-7.6

-7.2

-6.6

-6.4

.6.0

-6.6

-5.2

.4.8

.4.4

-4.0

Cp -9.6

-.3.2

.2.8

-2.4

-2.0

-1.6

-1.2

-.8

-.4

0

.4

.8

1.2

I

o .1 .2.8.4.5.6.7 .8.PI.O

x/c

(CC) a - 15.21”:c1= 1.566:cd = 0.1059: Cm = ‘0.093.

Figure 6.-

-..0 Upper surface

@ Lower surface.8.0

:. -

-7.6 1 1 1 1 1

-7.2

4.8

.6.4

-6.0

-5.2

-4.8

-4.4

-6.6

I ,

-— .-

1 I1

-4.0

Cp -9.6

-s.2

-2.8

-2.4

-2.0

-1.6

-1.2

-.8

-.4

.4

I

I I I I TI I I I 1 I I I1 I I i 1-1-1

.61 I I h~ I I I I I I I I I I I I

9“ i

-t I I I I I 1 I I I I I-t-tRTH.=

o .1 .2.2.4.5.6.7 .8 .91.0

Xfc

(old) a = 16.21°; CI = 1.559: cd = 0.1241; cm m -o,ofl!,

Concluded.

.

*

.

.

.

42

.

.

.

.

*

i

;

.8.4

-8.0

-7.6

-7.2

-6.8

-6s

-6.0

-5.6

-5.2

.4.8

-4.4

-4.0

Cp -8.6

-s.2

.2,6

.2.4

-2.0

-1.6

-1,2

-.8

-s

o

.4

.8

1,20 ,1 ,2 .8 .4 .5 .6 .7 .8 .9 lo

x f c

(a) a = -11.09°; Cl= -0,497; Cd = 0.2129; Cm = 0.072.

Figure 7.- Pressure distributions wi.th

-2.4

.8.0

-7.6

-7.2

.6.8

-6.4

-8.0

.5.6

-5,2

-4.8

-4.4

-4.0

Cp -S.6

-8.2

-2.6

4.4

-2.0

-1.6

-1.2

-.8

-.4

0

.4

.8

1.2

I

o .1 .2 .3 .4 .5 .6 .7 .8 .9 1,0

x/c

,

(b) a = -lO.lOO; Cl = -0.522: Cd = 0.2036: cm = 0.068.

df = -10° for R = 6.0 x 106 andM= 0.10.

43

-8.4

-6.0

-7.6

-7.2

.6.8

45.4

.6.0

-5.6

.5.2

-4.2

.4.4

-4.0

Cp -S.6

-s.2

-2.8

-2.4

-2.0

-1.6

-1.2

-.8

-.4

0

.4

,8

1.20 ,1 .2 .3 .4 ,5 ~ .7 ,8 ,9 lo

qc

(C) m = -9.07C; Cz= -0.542; C*= 0.18213 cm = 0.050.

-8.4

.6.0

.7.6

-7.2

-6.8

-6.4

.6.0

-5.6

-5.2

-4.8

-4.4

-4,0

Gp -2.6

-%2

-2.2

4.4

-2.0

-1.6

-1.2

-.2

-,4

G

.4

.8

1.2

t

o .1 .2 .S .4 .5 .6 .7 .6 .9 LO

Xjc

(d) a = -8.17’; cL= -0.849; cd - O.OM& cm - -0.035.

.

.●

.

●


44

.

.

.

.

.8.4

-8.0

-7.6

-7.2

.6.8

-6.4

.6.0

-6.6

.6.2

.4.8

-4.4

-4.0

Cp -3.6

-s.2

.2.8

-2.4

-2.0

-1.6

-1.2

-.8

-.4

0

.4

.8

1.2

I

o .1 .2 .S .4 .6 .6 .7 .6 .9 1.0

x f c

(e) a = -7.13”; cl= -0.749: cd = 0.0131: cm = -0.035.

-8.4

-8.0

~7.6

-7.2

-6.8

.6.4

-6.0

-6.6

-6.2

-4.8

-4.4

-4.0

Cp -8.6

-3.2

-2.8

-2.4

-2.0

-1.6

-1.2

-.6

-.4

c

.4

.8

1.2

I

o .1 .2 .S .4 .6 .6 .7 .8 .9 1.0

x f c

(f) a- -6.12°: Cl = -0.647; Cd = 0.J118; Cm = -0.035.


45

.8.4

-6.0

-7.6

-7.2

ea

.6.4

.6.0

-5.6

-6.2

da

-4.4

-4.0

Gp .S.6

-9.2

.za

.2.4

-2.0

-1.6

-1.2

-.6

-.4

0

.4

a

1.20 .1 .2 ,3 .4 ~ .6 .7 a .9 lo

Xjc

k) a = -5.11’: Cl= -o.541; cd = 0.0104 cm = -o.038

-6.4

-6.0

-7.6

-7.2

-6.8

-6.4

.6.0

~a

-s.2

-4.8

-4.4

-4.0

Cp -%6

-3.2

-2a

-2.4

HiM—-.-.=..—.=

-2.0 +j I I 1 1 1 1 I I 1 1t

‘ WJ?J

..— —. ----

,.-

.=-.

-1.2 Ie I I 1 I I 1 I I 1 I I

q

Wk&H

-.”

MW-HHI!-—____JFl=Rwl-..

Iiil”

..—:..

-.4

L+!’---?’ r!% I ]

—

111.IWT

.x/c

(h) a = -4,10”; .1 = -0.431: cd = 0.0091: cm --0.037,

.#


46

.

.

-8.4

-8.0

-7.8

-7.2

.6.8

-6.4

-8.0

.5,6

-6.2

-4.8

-4.4

-4.0

Cp -8.6

-9.2

-2.8

-2.4

-2.0

-1.6

-1.2

-.6

..4

0

.4

.8

1.2

I

I 1 1 1 1 1 1 I 1 1 1 I I 1 1 ! [ 1 I I Io .1 .2 .S .4 .5 .6 .7 .8 .9 1.0

x/c

(i)a = -3.06°; cl= -0.3172 cd = 0.0080: cm = -0.038.

-8.4

-8.0

-7.6

-7.2

-8,8

-6.4

-6.0

-5.6

.5.2

-4.8

-4.4

-4.0

Cp -3,6

-3.2

-2.8

-2.4

-2.0

-1.6

-1.2

-.3

-.4

0

.4

.6

1.2

I

o .1 .2 .8 .4 .5 ,6 .7 .8 .9 1,0

x/c

(j)a = -2.05 ”;ct= -o.205; cd.- o.oo72; cm = -0.039.


47

.8.4

.8.0

-7.6

-7.2

-6.8

-6.4

.6.0

.5.6

.6.2

-4.0

-4.4

.4.0

Cp -9.6

-2.2

-2.8

.2,4

-2.0

-1.6

-1.2

..8

-.4

0

,4

.8

1.2

Xjc

(k)a= -1.04”; cl= -0.090 :cd=o.oo70:cm = ‘o.041.

.8.4

-6.0

-7.6

-7.2

-6.8

-6.4

.6.0

-5.6

-6.2

-4.0

-4.4

-4.0

Cp -8.6

-8.2

-2.8

-2A

-2.0

-1,6

-1.2

-.8

-.4

0

.4

.2

1.20 .1 ~ .3 .4 .5 .6 .7 ,8 ,* lo

X/c

(II a = -0.54”; ct= -o.032: cd= 0.00w Cm - -0.042.

.

B

r


48

●

✎

i,

.8.4

-8.0

-7.6

-7,2

-6.8

-5,4

.6,0

-5.6

-5.2

-4.8

-4.4

-4,0

Cp -3.6

-9.2

-2.8

-2.4

-2.0

-1.6

-1.2

-.8

-.4

0

.4

.8

1,20 ,1 ,2 .3 .4 ,5 .6 ,7 .8 .9 lo

x fc

(m) a = -0.02”: cl = o.027: Cd - 0,0069; cm = -o,04~,

-8.4

.8.0

-7.6

-7.2

-6.8

-5.4

-6.0

-5,6

-5.2

--4.8

-4.4

-4.0

Cp -S.6

-3.2

-2.8

-2.4

-2.0

-1.6

-1.2

-.8

4-..

0

.4

.8

1.20 .1 .2 ,3 .4 #5 .6 .7 ,8 ,9 lo

(n) u = 0.48°; ci= 0.082; cd = 0.0068: cm = -0.044.


49

-8.4

-8.0

-?.6

-7.2

-6.8

-6A

-6.0

-5,6 1111

I I I I I I I I I t I 1 I I I I

.5,2

-4.8

-4.4

-4.0

~ -S.6

-s,2

-2,8

-2.4

.2.0

-1.6

-1.2

..8

> I I I I I I–.=

o

.4

.8

1.20 ,1 ,2 ,3 ,4 .5 .6 .7 ,8 Q lo

x f c

(0) u = Loo”; ci= o.142:c~ = 0.0064 cm= -0.045.

4.4

-8.0

-7.6

-7.2

-6.8

-8.4

-6.0

-5.6

=6,2

-4.6

-4.4

-4.0

Cp .S.6

-2.2

4?.6

-2.4

4?.0

-1.6

-1.2

-.8

-,4

0

.4

.6

120 .1 ~ ~ .4 ,5 ,6 ,7 ,8 .9 ~a

x/c

(P) = = 1.520;%= o.197:c~ - o. fJo43: cm --0.047.

.

,

●


50

.-

-8.4

-8.0

.7.6

-7,2

-6.8

-6.4

+,0

-6.6

-5.2

-4.8

-4.4

-4.0

Gp .S.6

-6.2

-2.8

-2.4

.2.0

-1.6

-1.2

-.8

-.4

c

.4

.8

1.2

I

o .1 .2 .3 .4 ,5 ,6 .7 .8 .9 1.0

x/c

(q) cl= Z.ol”; ct= 0.282; cd = 0.0044: cm = -0.049

-8.4

9.0

-7.6

-7.2

.6.8

.6.4

-6.0

-5.6

-6.2

-4.8

-4.4

-4.0

Cp -3.6

-s.2

-2.8

-2.4

-2.0

-1.6

-1.2

-.8

-,4

0

.4

-w. J-4-+-A II I I

x/c

(r) a = 2.51°; c1 = 0.311: cd = 0.004s; cm = -0.049.


51

.8.-4

-3.0

-7.6

-7.2

-6.8 uluuuu—-6.4

.6,0

-5.6

-5,2

-4.3

-4.4

“4.0

Cp -S.6

-3.2

-2.8

-2.4

4.0

-1.6

-1.2

-.3

-.4

0

.4

.3

1.20 .1 .2 .$ .4 .5 ,6 .7 ~ ,9 lo

! f f 1 1 1 I

x/c

(s) a = 3.03°:c1= O.fma; cd= 0.0043; cm = -0.050.

Figure 7.-

-a.4

-6.0

-7.6

.7.2

6.8

.6.4

.6.0

-6.6

-5.2

-4.8

-4.4

“4.0

Cp -S.6

-8.2

-2.8

-2.4

-2.0

-M

-1.2

-.6

-#4

0

,4

.6

1,20 ,1 ,2 .~ .4 ,5 .6 ,7 .8 ,9 loTiiiiiiiiiiiil

x!=

(t) a = 4.05°: c’ - o.4a3: cd - 0.0045: cm - -0.052.

Continued.

t..*

,

52

●

*

ii9

.8.4

.8.0

-7.6

-7.2

.6.8

.6.4

-6.0

.5.6

-6.2

.4.8

-4.4

-4.0

Cp .9.6

-3.2

-2.8

-2.4

.2.0

-1.6

-1,2

-.8

-.4

0

.4

.8

L2o .1 .2 .3 .4 ,5 .6 .7 .8 .9 1.0

x/c

(u) a - 5.07°; c1 = 0.593; cd = 0.0048, cm = -0.054.

.8.4

-8.0

-7.6

-1.2

-6.8

-6.4

-6,0

-5.6

.5.2

.4.8

-4.4

-4.0

Cp .3.6

-3.2

-2.8

-2.4

-2.0

-1.6

-1.2

-.8

4-.

0

I I 1’4 I I I I I I I I

Xlc

(v) a = 6.08°; cl.= o.7’04; cd = 0.0055:0= = -0.05s.


53

-8.4

-8.0

-7,6

-72

-&8

.6.4

.8.0

-6.6

-5.2

-4.0

.4.4

-4.0

Cp -9,6

-9.2

.2.8

-2.4

+?.0

+.6

-1.2

-.8

..4

0

,4

.8

1.20 .1 .2 .8 .4 .5 .6 .7 .8 .9 1.0x fc

(Yr) a = 7,09°; Ci = 0.810: c~ = o.oo6& cm = -o.o~~.

-8.4

-8.0

-7.6

-7.2

-6.8

-6.4

-6.0

.5.6

-6.2

4.8

.4.4

-4.0

Cp -8.8

-8.2

-2.8

-2.4

-2.0

-1.6

-1.2

-.8

-.4

0

.4

.8

1.2

1

0 J .2 .8 .4 .5 .6 .7 .S .9 LO

Xlc

(X) a = 0.12”; cl= 0.918; cd - 0.0080; Cm = ‘0.059.

●

✎✎

F@Ure 7.- con~inued~

54

.8.4

-8.0

-7.6

-7.2.

.6.6

4 -6.4

●

.6.0

. -6.6

.6,2

.4.6

-4.4

-4.0

Cp -3.6

-3.2

-2.8

-2.4

-2.0

-1.6

-1.2

..8

-.4

0

.4

4

.8

31.20 .1 ,2 .~ .4 .5 .6 .7 .8 ,9 lo

-6.4

-8.0

-7.6

-7.2

.6.8

.6.4

-6.0

-6.6

-6.2

-4.8

-4.4

-4.0

Cp -S.6

-8.2

-2.8

-2.4

-2.0

-1.6

-1.2

-.6

-,4

0

.4

.6

120 .1 ,2 .3 .4 ~ ,6 ,7 ,8 ,9 lo

x/c

(z)a= 10.16°; .l= 1.127; cd = 0.0099; cm = -0.059


55

.s.4

-6.0

-7.6

-1.2

-6.8

-6.4

.6.0

-5.6

-5.2

-4.8

.4.4

-4.0

C+ -3.6

-9.2

-2.6

-2.4

4.0

-1.6

-1.2

-.8

-.4

0

.4

.8

1.20 .1 .2 # .4 ~ ,6 .7 .8 .9 lo

56

x/c

(an) a = 11.17”: CL= 1.229: Cd = 0.0106: Cm = ‘0.059.

Figure 7.-

-8.4

4.0

-7.6

-7.2

-6.8

.6.4

-6.0

-5.6

-5.2

-4.8

-4.4

-4.0

Cp -S.6

-9.2

-2.8

.2.4

-2.0

-1.6

-1.2

-.8

-.4

‘E#E13H.4

.8

,.20y+_14J+Xlc

(bb) a = 12.16°; C~= 1.325: cd = 0.0122:cm - -0.05S.

continued:

*

*

e

.8.4

.8,0

-7.6

-7.2

.6.8

-6.4

-6.0

.5,6

.5.2

-4.8

.4.4

.4.0

Cp -3.6

.9.2

-2.8

-2.4

-2.0

-1.6

-L2

-.8

-.4

0

.4

.8

1,20 ~ ,2 .8 ,4 .6 .6 .7 .8 ,9 lo,.

(cc) a = 13.18”; cl= 1.417; cd = 0.0139: cm = -0.059.

-3.4

-8.o

-7.6

-7.2

-0.8

-0.4

.6.0

.6.6

-5.2

-4.8

.4.4

-4.0

Cp -9.6

-9.2

-2.8

-2.4

-2.0

-1.6

.1.2

-.8

-.4

0

.4

.8

1.20 .1 ,2 .3 .4 ,6 ,6 .7 .8 ,9 lo

Xlc

(old) a = 14.20°; Cl= 1,506; C~= 0.0164:cm = -0.059.


!57

-6.4

.8,0

-7.6

-7.2

.6.8

-6.4

-6.0

.6,6

-6,2

-4.8

.4.4

-4.0

Cp -9.6

-s.2

-2.8

-2.4

-2.0

-1.6

-1.2

-.8

I

II

-.41 1 I 1 1 I 1 I 1 I 1 1 1s1

h I_, ,I I I ).rl

-—

x/c

(..) a = 15.25”: c1 = 1.568; cd = 0.0214 cm = -0.057.

-8.4

.6.0

-7.6

-7.2

.6.8

.6.4

.6.0

.6.6

-6.2

-4.8

-4.4

-4.0

Cp .s.6

-8.2

-2.8

-2.4

-2.0

.1.6

.1.2

-.8

-.4

0

.4

.8

lL?O .1 .2 # ,4 ~ .6 .7.6 .9 Lo

X,’c

(ff) a = le.zl”; C1 = 1.505; cd = 0.0684: cm = _o,@36.

*

?

L


58

.

.8.4

.8.0

-7.6

-7.2

.6.8

.6.4

.6.0

.5.6

.5,2

-4.8

.4.4

-4.0

Cp -S.6

-3,2

-2.8

-2.4

-2.0

.1.6

-1.2

-.8

..4

0

.4

.8

1,20 .1 .2 ,3 .4 ~ .6 .7 .8 ,9 lo

x/c

(gg) ~ s 17,22°; Cl - 1.429; cd = 0.1089: cm = -0.064.

-8.4

-6.0

-7,6

-7.2

.6.8

-6.4

-6.0

-5.6

-5,2

-4.8

-4.4

-4.0

Cp -S.6

.3.2

-2.8

4?.4

.2.0

-1.6

-L2

-.8

..4

0

.4

.8

L20 ,1 .2 ,3 .4 ~ ,6 .7 .8 ,9 lo

x/c

(hh) a - 18.21°; C~= 1.388; Cd = 0.1250: cm = -0.060.


59

CP

(da = -11.18’:CL= 0.059: cd = IJ.ooa~; Cm = -O=s,

CP

Xfc

?..

Figure 8.- Pressure distributions with &f = 10° for R = 6.0 x 106 and

M= 0.10.

60

‘?

-8.4

.8.0

-7.6

-7.2

-6.8

.6.4

-8.0

-5.6

-6.2

.4.8

-2.0 J

-1.6 :

-4.4

.4.0

Cp +?.6,

.3.2

-1.2 \l I I I I I 1.

I I I I I I I I I t I I I

o

“4LEkHttt.8 j

B

1.20 ,1 .2 ,3 ,4 ,5 ,6 .7 .6 .9 lo

x/c

(c) a = -9.11°; cl= 0,2B4; cd = o.oo77:cm = -0.233.

.8.4

.8.0

-7.6

-7.2

.6.8

.6.4

-6.0

-6.6

-6.2

-4.8

-4,4

.4.0

Cp -3,6

.3.2

.2.8

-2.4

-2.0

-1.6

-1.2

..8

-.4

0

.4

.8

1.20 .1 .2 .8 ,4 ,5 .6 .7 .8 ,9 lo

Xfc

(d) a = -8.11°; cl= 0.S87: cd = 0.0080: cm = -0.234.


61

-8.4

-8.0

-7,6

-7.2

-6.8

-6A

-6.0

.5,6

-6.2

.4.8

-4.4

-4.0

Cp -2.6

-9.2

-2.8

-2,4

-2.0

-1.6

-1.2

-.8

-.4

0

.4

.8

1.2.,1.23.43 ~.7a.910

x/c

(c)a= -T.08°; cl= 0.500; cd= 0.0075: cm= -0.2.37.

Figure 8.-

-6,4

-3.0

-7.6

-7.2

-6.8

.6.4

-6.0

-6.6

-5,2

-4.8

-4.4

-4.0

Cp -S.6

-9.2

-2.3

-2.4

-2.0

-1,6

-1.2

-.8

-.4

0

.4

.3

1.20 .1 ,2 .3 .4 ~ ,6 .7 ~ .9 lo

Xfc

(f) a- -6.06”; c1 = 0.60’J; cd = 0,0073: cm - ..o,~~~,

Continued.

62

)’

.4

CP

-8.4

-8.0

.7.6

.’7.2

-6.8

.6.4

.6.0

-5.6

-5.2

-4.8

-4.4

.4.0

-3.6

+3.2

-2.8

-2.4

.2.0

-1.6

-1.2

-.8

-.4

0

.4

.8

1.20 .1 ,2.3 .4 .5 .6 .7 .8 .9 1.0

Xlc

(g) a = -5.04°; .~= 0.721: cd = 0.0068: cm = -0.240.

Figure 8.-

-6.8

.8.4

.8.6

-7.6

-7’.2

-0.4

-0.0

.5.6

-5,2

-4.8

-4.4

-4.0

Cp -8.6

-3,2

-2.8

-2.4 1 I I I / I I I t I I I I I I I I I I

-2.0

-1.6

-1.2

-.8

-.4

0

.4

.8

1.20 ,1 ~ ,3.4 .5 .6 .7 .8 ,9 1.0

x/c

(h) m = -4,08”; .1- 0.830; Cd = 0.0063; cm - -0.243.

Continued.

63

-6.4

-8.0

-7.6

-7.2

-6.8

-6.4

.6.0

-5.6

-5.2

.4.8

.4.4

.4.0

Cp -S.6

-s.2

-2.8

-2.4

-2.0

-1.6

-1.2

..8

-.4

0

.4

.8

1.20 .1 .2 .3 .4 ,5 .6 .7 ~ ,9 lo

x~c

(i) a = -3.04’; c1 = 0.926; cd = 0.0057: cm = -0.241.

Figure 8.-

CP

Cent

-0.4

-6.0

-7.6

-7.2

.6.0

-6.4

-6.0

-5.6

-6.2

-4.8

-4.4

-4,0

-S.6

-3.2

-2.8

-2.4

-2.0

-1.6

-1.2

-.8

-.4

0

.4

.6

1.20 ,1 .2 ~ .4 .5 .6 .7 .8 .9 lo

x/c

(j) a - -2.009; c1 = 1.030: cd = o.oo5e; cm - -o,~40

,inued.

1

4 ““

1

64

-8.4

-8.0

-7.6

-7.2

.6.8

-6.4

.6.0

-5,6

-5,2

-4.8

-4.4

-4.0

Cp -3.6

-9.2

-2.8

-2.4

-2.0

-1.6

-1.2

-.8

-.4

0

.4

.8..

1.2

I

o .1 .2 .8 .4 .5 .6 .7 .8 .9 1.0

Xlc

(k) a = -0.98°; .[ = 1.129; cd = 0.0059; cm = -0.242.

-2.4

-8.0

-7.6

-7,2

-6.8

-6.4

-6.0

-5.6

-5.2

.4.8

-4.4

.4.0

Cp -8.6

-3.2

-2.8

-2.4

-2.0

-1.6

-1.2

-.8

-.4

0

.4

.8

1,2

I

o .1 .2 .8 .4 .5 .6 .7 .6 .9 LO

x/c

(1) a = 0.05°; et = 1.223: Cd = 0.0061: cm - -..240.


65

-8.4

-8.0

.7.6

4.2

-6.8

-6.4

.6.0

.5.6

-5.2

-4.6

-4.4

-4.0

Cp -8.6

-s.2

-2.3

-2,4

-2.0

-1.6

-1.2

-.8

-.4

0

.4

.s

120 .1 .2 .~ .4 .5 .6 .7 ~ .9 lo

x/c

(m) a = 1.05”: c1 - 1.30S: cd = 0.0064: cm = -0.236.

Figure 8.-

-8.4

-3.0

-7.6

-7.2

-6.8

.6.4

.6.0

.s.6

-4.6 I II I I I I I

i I I I I I I I t

.--— —

-4.4-WI-L :-””EH

-4.0

Cp -8.6

-8.2

-2.8

-2.4

-2.0

-1.6

-1.2

-.8

..4

.4

.611 /ttltF-llli’7

I I I I I I I

Xjc

(n) a - 2.08°: c1 = 1.356: cd - 0.0084; cm - - 0.22tl.

Continued.

66

-8.4

.8.0

-7.6

-7.2

.6.8

-6.4

.6.0

-5.6

-5.2

-4.8

.4.4

-4.0

Cp .3.6

-3.2

.2.8

-2.4

-2.0

-1.8

-1.2

-.8

-.4

0

.4

.8

1.20 .1 ,2 ,3 .4 ~ .6 .7.8 .9 1.0

Xlc

(o) a - 3.09”; c1 = 1.395; Cd = 0.0114; Cm = -0.215.

-8.4

-0.0

-’/.6

-7.2

.6.8

.6.4

-6.0

.5.6

-5.2

.4.8

-4.4

.4.0

Gp .9.6

-3.2

-2.8

-2.4

-2.0

-1.6

-1.2

-.8

-.4

0

.4

.8

1.20 ,1 .2 .3 ,4 .5 .6 .7 .8 .9 lo

x/c

(p) a - 4.08”; C1= 1.443; cd = 0.0145; cm - -0.207.


67

-8.4

-6.0

-7.6

.7.2

-6.8

-2.4

.6.0

-5.6

-5.2

-4,8

-4.4

-4,0

Cp -3.6

-3.2

-2.8

.2.4

-2.0

-1.6

-1.2

%9

..4

0

.4

a

1.20 ,1 .2 ~ .4 .5 .6 .7 ~ # lo

(q) R = 5.lo”; c[= 1.469: cd = o.0239: cm = -!.19S.

-6.4

-6.0

I

-7.6

-7.2

-6.8

-5.4

-&o

-5.6

-5.2

-4.2

-4.4

-4.0

Cp -3.6

-3.2

-2.8

-2.4

-2.0

-1.6

-1.2

-.6

-.4

0

.4

.8,

12. .12$.43.6 ,7,8,910

(r) u = 6.11°; cl- 1.551; cd E 0.0309: cm - ‘0. JB5:


68

.8.4

-8.0

.7.6

-7.2

-6.8

-5.4

.6,0

-6.6

-5.2

-4.8

-4.4

-4.0

Cp -9.6

-8.2

-2.8

-2.4

-2.0

-1.6

.1,2

-.8

-.4

0

.4

,6

1,20 .1 .2 ,5 ,4 .5 .6 ,7 .8 .9 lo

x/c

(S).7 = 7.13°:ct= 1.61 Z?:cd= 0,0336; cm E -0.189,

,. -8.4

.8.0

.7.6

-7.2

-6.8

.6.4

-6.0

.5.6

-5.2

-4.8

4.4

.4.0

Cp -3.6

-%2

+4.8

+2.4

-2.0

-1.6

-1.2

-.8

-.4

0

.4

.8

1.20 .1 ,2 ,8 .4 .5 .6 .7 ,8 .9 lo

Xjc

(t) a = 6.14”; cl- 1.6’/4; Cd = 0.0358; cm = -0.164.

Figure 8.- continued.

69

-8.4

.8.0

.7.6

.7.2

.6.8

-5.4

-&o

.5.6

-5.2

.4.8

-4.4

-4.0

Cp -3.6

-9.2

-2.8

-2.4

-2.0

-1.6

-1.2

-.6

-.4

.4

.8

1.2

I I I I I I I I I I

)

o .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0

x/c

(u) a = 9.16°; C( = 1,736: Cd = 0.0418; Cm = -o.I~&

. ..

-6.0

-7.6

-7.2

-5.8

.6.4

.6.0

-5.6

-5.2

-4.8

-4.4

-4.0

Cp .3.6

-2.2

-2.8

-2.4

-2.0

-1.6

-1.2

x~c

(v) a = 10.17°: c1 - 1.7s6; cd - 0.0429; cm D -0,173


70

.8.4

.8.0

-7.6

-7.2

-6,8

-6.4

-6.0

-6.6

-5.2

-4.8

-4.4

.4.0

Cp -9.6

-9.2

2.8

-2.4

-2,0

-1.6

-1.2

-.0

-.4

0

.4

.8

1.20 .1 ,2 .8 .4 .5 .6.7 .8 ,9 1,0

x~c

(W) a = 11,19”: Cl = 1.852; cd = 0.0425; cm = -0.170.

-8.4

-8.0

-7.6

-7.2

.6.8

-6.4

-6.0

.5.6

-5.2

.4,8

.4.4

-4,0

Cp -S.6

-9.2

-2.6

-2,4

-2.0

-1.6

-1.2

-.8

..4

0

.4

.8

1.20 .1 .2 .8 .4 .5 ,6 ,7,8 .9 1.0

z/c

(x) a = 12.2.0°; Ct = 1.892; cd = 0.0481; Cm = -o, ~60,

Figure 8.- COntinUed.

71

‘JP

x/c

(y) a = 13.20’: cc - 1.78’% ‘=~ = 0.10s9; cm = -0,14!3.

GP

Xjc

(z) u = 14.21’: CL= 1.745; Cd = o.1312:cm = -o.1~~,

F~gIre 8.- cmtinued~

72

-2.4

.8,0

-7.6

-7,2

-6,8

-6.4

$.0

-5,6

.5.2

-4.8

4.4

.4.0

Cp -3.6

-9.2

-2.8

-2.4

-2.0

-1.6

-1.2

-.8

-.4

0

.4

.8

1.2

,.

I

o .1 .2 .S .4 .5 .6 .7 .8 .9 1.0

14=t

x/c

(aa) R - 15.21°; Ct = 1.726: C,j = 0.1529; cm = _o.~~o,


73

Twbulentreattachment

L-81-118(a) a = 0.00; c1 = 0.7.

Figure 9.- Oil-fla photographs of upper surface with 6f = 0° forR= 3.0 x 106 and M = 0.21.

74

L-81-119

(k)) a = 2.00; cl = 0.9.


75


L-81-120

76

a,deg

Figure 10.- Section

(a) R = 3.()x 106.

characteristicswith tif= 0° at M = 0.”10.

-1al

..—:20 -16 -12 -8 -4 0 4 8 12 16 20 0 ,004 .008 .0[2 .016 .020 .024 .028 -.3 -.2 –.1 o .1

a,deg cd %

(b) R = 6.0 x 106.


(c) R = 9.o x 106.


2!

a,deg cd cm

Figure 11.- Effects of Reynolds number on section characteristics with 6f = 00

at M = 0.10.

a ,deg Cd cm

(a) R = fjoo”x 106.

Figure 12.- Section characteristicswith 6f = -10° at M = 0.10.

co

,

%-Ia,deg cd

(b) R = 9.0 x 106.

Figure 12.- Concluded=.

a,deg Cd cm

FiCJUre 13.- Effects of Reynolds number on section characteristics with 6f = -10°at M = 0.10.

2.4

2.0

1.6

I .2

.8

.4

0

-.4

-. 8

-1.2-20 -16–12-8-4048 1216200 .0I .02 .03 .04 .05 .06 .07 -,3 -.2 -.I o .1

a,deg cd %

(a) R = 2.0 x 106.

Figure 14.- Section characteristics with 6f = 10° at M = 0.10.

a,deg %cm

(b) R = 3.0 x 106.

Figure 14.- Continued=

cmu,deg Cd

(C) R= 6.OX 106.


a,deg Cd cm

Figure 15.- Effects of Reynolds number on section.characteristics with ~f = 10°at M = 0.10.

L-81-121Figure 16.- Oil-flow photograph of upper surface with df = 10° for

R= 3.0 x 106, M = 0.22, a = 4.0°, and c1 = 1.5.

88

Figure 17.-L-81-122

Oil-flm photograph of upper surface with dfR= 3.()X 106, M = 0.2,, ~ = 0° for

= 5.Oo, and c1 = 1.2.

89

wo

2.4

2.0

1.6

1.2

.8

.4

0

-.4

-.8

-1.2

a,deg

Figure 18.- Effects

cd %1

of Mach number on section characteristies with &f = (=jO

for R = 6.0 X 106.

1,

Cl,max

1.8

1.6

1.40 .1 .2 .3 .4

M

FiCJUre 19.- Variation of maxim~,,lift ~effi.cient with Mach,number with 6f = 0° forR= 6.(IX 106.

.006

Cd,min.004

nn9

Figure 20.- Variation of minimum dragR

.2 .3 .4

Mcoefficient with Mach number with 6f = 0° for= 6.0 X 106.

I

2.4

2.0

1.6

I .2

.8

.4

0

-.4

—.8

-1.2–20 –16 -12 -8 -4 0 4 8 12 16 20 0 .004 .008 .012 .016 .020 .024 .028 -.3 -.2 -.1 0 .1

a,deg Cd cm

(a) R = 3.o x 106.

Figure 21.- Effect of roughness on section characteristics with ‘f = 0° for variousReynolds nurnhersat M = 0.10.

cd cm

(b) R = 6.o X 106.


I

2.4

2.0

1.6

1.2

.8

.4

0

-. 4

-. 8

-1.2–20 -16 -12 -8 -4 0 4 8 12 16 20 0 .004 .008 .012 .016 .020 .024 .028 -.3 -.2 -. I O I

a,deg cd Cm

“(c) R = 9.0 x 106.


w(n

a,deg cd cm

(a) R= 6.0 x 106.

Figure 22.- Effect of roughness on section characteristicswith &f = -10° for variousReynolds numbers at M = 0.10.

(b) R = 9.0 x 106:


-2o –16 -12 -8. -4 0 4 8 12 16 20 0 .0I .02 .03 .04 .05 .06 .07 -.3 -.2 -.1 0 .1

a,deg Cd %

(a) R = 2.(Ix 106.

Figure 23.- Effect of roughness on section characteristicswith ~f = 10° for variousReynolds numbers at M = 0.10.

c1

A

o0

-20 -16 -12 -8 -4 0 4 8 12 16 20 0 .01 .02 .03 .04 .05 .06 .07 -,3 -.2 -.1 0 ,1

a,deg Cd Cm

(c) R = 6.0 X 106.

Figure 23.- Concluded=

a,deg

(a) R = 3.0 x 106.

Figure 24.- Effect of flap deflection on section characteristics for various Reynoldsnumbers at M = 0.10.

-20 -16 -12 -8 -4 0 4 8 12 16 20 0 .004 .008 .012 .016 .020 .024 .028 -,3 -.2 -.1 0 ,1

a,deg cd %

(b) R = 6.0 x 106.


..-–20 -16 -12 -8 -4 0 4 8 12 16 20 0 .004 .008 .012 .016 .020 .024 .028 -.3 -.2 –.1 O“ .1

a,deg cd cm

(c) R = 9.0 x 106.

Figure 24. - Concluded.

2.0

1.8

1.6

I .4

I .,: !,-, !:.,, , ., ..., d

J—,–.:.--+---~—.r-+-+---+.&-. -i:= ..+ .+-t Llj,l.,!,: ‘W-+ ~ ,.-:- +..+ ,. ;- .,.... . . .. . .. . . I . . . . .. . I........ .,..........-

“1 2 3 45 10

R

X106

Figure 25.- Variation of maximum lift coefficient with Reynolds number for various flapdeflections at M = 0.10. open symbols represent data with transition free; solidsymbols, data with transition fixed.

6 f, deg

000 -lo

Cd,mk

.020

.010

.008

.006

.004

.002

.001

I I I 1 i I 1 [ { [ 1, 1 1 I 1 1 I 1 { I 144

,,~L-—l-~--kPlPl--l-tH

-hHw+-H-l-’+-i+m-kw

,1.1.{1,11,1,1 ! ! !’”! !’!”! .~.+.{ .!+’{.’~l

I

. 1111.1,1.1.1,1 ,. .,,,, . . . ,. .1..1-1 i... .. . . . . . I . .-,. , ,.. . . . . . . . . . . . . . I . .,, ... .,, ., ,.. i. ..{.... I ... ,, . . . . . . . . .

-II “ _!”” ~~1“” ““ ““ ‘“”““”””““” ““““””““”““-,,. Illlllfl . ~ . . . . . . . . . . . . ,,, ,,. ... ,., ..

1 I., .,.... ..... . ..., ,.. ,.. ., ,.. . . ,, ,. . .,

I . . . . . . . . . . ,,, ..,,, . . . . .,, ,,, .,. .. 1.. . -1

[ ,. .

1 ,, 1 1 1 1 1 t

,. .,.. . . . . . .

,!. . .

1 1

I 2 3

R

45 Ioxlo’

Figure 26.- Variation of minimum drag coefficient with Reynolds number forvarious flap deflections at M = 0.10. Open symbols represent data withtransition free; solid symbols, data with transition fixed.

105

— Theory

~ Experiment

CP

-2.00 Upper surface

@ Lower surface-1.6

-1.2

-.8 A s

-.4

0

.4

.8

c>

1.20 ●1 .2 .8 ,4 .5 ●6 .7 .8 .9 lo*

x/c

(a) df = OO; a= O.O1°.

Figure 27.- Comparison of theoretical and experimental pressure distributions.

106

— Theory

~ Experiment-2.0

-1.6

-1.2

-.8

CP ‘“4

o

.4

.8

1.2

0 Upper surface

@ Lower surface

4# - ~ ~ ~ — —

— ~

()

o .1 .2 .3 .4 .5 .6 .7 .8 .9 1.Ox/c

(b) cSf= -lOO; ct = 1.52°.


—

“2.0

-1.6

-1.2

-.8

CP ‘*4

— Theory

-0- Exper~me~t

O Upper surface

@ Lower surface

o

.4

.8

A.& o .1 .2 .3 .4 .5 .6 .7 .8 .9 LOx/c

(c) 6f = 100; a = 0905°.


108

a,deg cd cm

(a) R = 3.0 x 106. ‘

Figure 28.- Comparison of theoretical and experimental section characteristics withdf = 0° and transition free.

d

ow

2.4

2.0

1.6

I.2

.8

.4

0

-.4

-. 8

-1.2–:

(b) R= 6.0 X 106.


a,deg cd C*

(c) R = 9.o x 106.


4

d

d

a,deg Q

(a) R = 6.0 X 106.

Figure 29.- Canparison of theoretical and experimental sectionfif= -1oo and transition free.

%

characteristicswith

2.4

2.0

1.6

I .2

.8

.4

0

-. 4

—.8

-1.2..—–20 –16 -12 –8 -4 0 4 8 12 16 20 0 .004 .008 .012 .016 .020 .024 .028 -.3 -.2 -.1 0 .1

a,deg Cd cm

(b) R = 9.0 x 106.


.4

(d

a,deg Cd %

(a) R = 3.0 x 106.

Figure 30.- Canparison of theoretical and experimental section characteristics with6f = 10o and transition free.

a,deg cd Cm

(b) R = 6.0 X 106.


:20 -16 -12 -8 -4 0 4

Figure 31.-

a,deg

Comparison

8 12 16 20 0 .004 .008 .012 .016 .020 .024 .028 -,3 -.2 -.1 0 .I

cd Cnl

(a) R = 3.0 x 106.

of theoretical and experimental section characteristicswith6f = 0° and transition fixed.

a,deg Cd cm

Figure 31:- Continued.

..— ——-20 –16 –12 -8 -4 0 4 8 12 16 20 0 .004 .008 .012..016 .020 .024 .028 ‘.5 -.2 -.I u .1

cd C*a,deg

(a) R“= 6.0 X 106.

Figure 32.- Comparison oftheoretical and experimental section characteristics with6f = -10° and transition fixed.

d

.

m

–20 -16-12-8-4048 1216200 .004 .008 .012 .016 .020 .024 .028 -.3 -.2 –.1 o ,1

a,deg ‘% cm

(b) R = 9.() x 106.


2.4

2.0

1.6

I .2

.8

.4

0

-.4

-.8

-1.2-:

Figure 33.-

a,deg

Canparison

‘4

cd

(a) R= 3.0” X 106.

of theoretical and experimental sectionaf = 100 and transition fixed.

cm

characteristics with

a$eg

(b) R = 6.(IX 106.


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NASA Technical Paper - N91CZ · NASA Technical Paper 1865 4. ... twoof which are discussedin this report. First, ifa highmaximum lift inefficient Cl,max can be realized,the wing area