Experimental Results for Eppler 387 Airfoil

8/8/2019 Experimental Results for Eppler 387 Airfoil

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ContentsAbstract

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Introduction................................. 1

Symbols ................................... 1

Model, Apparatus, and Procedure ........................ 2Instrumentation ...............................Tests and Methods

..............................

Presentation of Results............................

Discussion of Results.............................

Concluding Remarks .............................Tables

....................................

Figures ................................... 12Appendix A Uncertainty Analysis ....................... 86Appendix B Section Characteristics ...................... 90Appendix C---Spanwise Drag Coefficients ................... 106Appendix D--Chordwise Pressure Coefficients ................. 113Appendix E--Spanwise Pressure Coefficients .................. 204References ................................. 228

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AbstractExperimental results have been obtained for an

Eppler 387 airfoil in the Langley Low-TurbulencePressure Tunnel (LTPT). The tests were conductedover a Mach number range from 0.03 to 0.13 and achord Reynolds number range from 60 000 to 460 000.Lift and pitching-moment data were obtained fromairfoil surface pressure measurements, and drag datawere obtained from wake surveys. Oil flow visualiza-tion was used to determine laminar-separation andturbulent-reattachment locations. Comparisons ofthese results with data on the Eppler 387 airfoil fromtwo other facilities, as well as with predictions fromthe Eppler airfoil code, are included.

IntroductionRecent interest in low Reynolds number aerody-

namics has increased for both military and civil ap-plications with emphasis on providing better vehi-cle performance (ref. 1). Reynolds numbers below500 000 are usually identified as being in this classifi-cation. Applications are varied and include remotelypiloted vehicles, ultralight human-powered vehicles,wind turbines, and propellers.

Although the design and evaluation techniques forairfoils at Reynolds numbers above 500 000 are welldeveloped, serious problems related to boundary-layer separation and transition have been encoun-tered at lower Reynolds numbers. Presently avail-able design and analysis methods generally do notadequately model flow phenomena such as laminarseparation bubbles. Experimental results obtainedon an Eppler 387 airfoil at low Reynolds numbersin the Model Wind Tunnel at Stuttgart (ref. 2) andthe Low-Turbulence Tunnel at Delft (ref. 3) haveshown large differences in airfoil performance. Thisis not surprising because of the sensitivity of theairfoil boundary layer to free-stream disturbances,model contour accuracy, and model surface rough-ness. Also, the model forces and pressure differencesare small and difficult to measure accurately.

NASA Langley Research Center has initiateda research program to develop test techniques todetermine performance characteristics of airfoilsat low Reynolds numbers (R _< 500000) (ref. 4).This experimental program uses the Langley Low-Turbulence Pressure Tunnel and consists of perfor-mance evaluation of both force and pressure modelsof an Eppler 387 airfoil. Oil flow visualization andsurface-mounted thin-film gages were used to deter-mine laminar-separation and turbulent-reattachmentlocations. Also, test-section turbulence and acousticmeasurements were obtained.

This report presents only the pressure model re-sults obtained from this research program. Testson a pressure model of the Eppler 387 airfoil havebeen conducted over a Mach number range from 0.03to 0.13 and a chord Reynolds number range from60000 to 460000. Lift and pitching-moment datawere obtained from airfoil surface pressure measure-ments, and drag data were obtained from wake sur-veys. Oil flow visualization was used to determinelaminar-separation and turbulent-reattachment loca-tions. Comparisons of these results with data on theEppler 387 airfoil from two other facilities, as wellas with predictions from the Eppler airfoil code, areincluded. A discussion of the most pertinent resultsfrom this test is reported in reference 5. The dataare presented herein in both tabulated and plottedformats.Symbols

The symbols in parentheses are those used incomputer-generated tables in the appendixes.

b (B)Cpc (C)Cc

d

Cl

Cm

c12

h

MPptqR

(CD)

(CL)(CM)

(PT)

airfoil span, in.pressure coefficient, qooairfoil chord, 6 in.section chord-force coefficient,f cpsection profile-drag coefficient,fwake Ctdd(h/c)point-drag coefficient (seeappendix A)section lift coefficient,c ncOsO_- CcsinOl

section pitching-momentcoefficient about quarter-chord point, - f Cp(x/c -0.25) d(x/c) + f Cp z/c d(z/c)section normal-force coeffi-cient, -f Cp d(x/c)vertical distance in wakeprofile, in.free-stream Mach numberstatic pressure, psitotal pressure, psidynamic pressure, psiReynolds number based onfree-stream conditions andairfoil chord of 6 in.


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R/ft

x (x)y (Y)Z

(ALPHA)Subscripts:desdiffmaxmeascc (INF)Abbreviations:LS

LTPT

NT

rms

sep.TR

unit Reynolds numberratio of fluctuating velocity tomean velocity in streamwisedirectionairfoil abscissa, in.spanwise distance along modelfrom centerline, in.airfoil ordinate, in.angle of attack, deg

designdifferencemaximummeasuredfree-stream conditions

laminar separation from flowvisualizationLow-Turbulence PressureTunnelnatural transition from flowvisualizationroot mean square

separationturbulent reattachment fromflow visualization

Model, Apparatus, and ProcedureModelThe airfoil model was machined from stainless

steel. To provide structural integrity and room forpressure tubing, the trailing edge of the model wasthickened from 0 to 0.01 in. The additional thick-ness was blended into the Eppler 387 coordinates atx/c = 0.95. (See table I.) The basic camber distri-bution of the Eppler 387 airfoil was retained. Themodel had a chord length of 6 in. and a span of 36 in.A drawing of the Eppler 387 section shape is shownin figure 1. A photograph of the model mounted inthe LTPT is shown in figure 2. The model designcontour accuracy was within +0.001 in. The differ-ences between the design and measured coordinatesare shown in figure 3 as a function of both chord-wise and spanwise locations. In general, the specified2

fabrication tolerance was maintained except on themodel upper surface between chordwise locations ofx/c = 0.60 and z/c = 0.80. A surface finish of 64 #in.(rms) was specified.

Grooves were machined in the surface of the steelmodel and pressure tubing was routed through thegrooves for orifice locations. The grooves were filledwith epoxy resin. Orifices were drilled through themetal surface into the tubing with their axes per-pendicular to the local surface. Each orifice had adiameter of 0.020 in. except at x/c = 0.95 where adiameter of 0.010 in. was used. The locations of bothupper and lower surface orifices are indicated in ta-ble II. The orifices were staggered to alleviate mu-tual interference, as illustrated by the photograph offigure 4.

Wind TunnelThe test was conducted in the LTPT. This fa-

cility is described in detail in reference 6, and dy-namic flow quality measurements are reported in ref-erence 7. The LTPT is a pressurized, closed-circuit,continuous-flow wind tunnel with an operating pres-sure from approximately 0.10 to 10 atm. The testsection was designed for two-dimensional testing ofairfoil sections and is 7.5 ft high, 7.5 ft long, and3 ft wide. The contraction ratio is 17.6:1, and 9 anti-turbulence screens are installed in the settlingchamber.

This facility was selected to develop test tech-niques for low Reynolds number aerodynamics be-cause of its good flow quality, precision pressure in-strumentation, and variable pressure capability. Thetunnel operating envelope for a 6-in-chord airfoilmodel is shown in figure 5; test conditions for theEppler 387 model are also indicated. In order to en-chance the resolution of model forces and pressuredifferences, it is desirable to operate at the higherend of the dynamic pressure envelope.

To supplement the turbulence measurements forthe LTPT (see ref. 7) in the low Reynolds numberrange, additional test-section turbulence was mea-sured with a hot-wire anemometer by Gregory S.Jones of the Langley Research Center. These prelim-inary results, shown in figure 6, indicate that free-stream turbulence is increased for a constant unitReynolds number as the tunnel total pressure is de-creased. For example, at a unit Reynolds numberof 200000 per foot, the test-section turbulence level(frequency bandpass from 1 to 50000 Hz) increasesfrom about 0.06 percent to 0.18 percent as the to-tal pressure is reduced from 15 psi to 3 psi. It iswell known (ref. 1) that boundary-layer receptivityis strongly affected by the frequency content of the


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disturbanceenvironmentaswellasbythemagnitudeof both velocityandpressurefluctuations.Wake Survey RakeThe wake survey rake (fig. 7) was mounted on

the tunnel survey apparatus and located 1.50 chordsbehind the trailing edge of the airfoil. The rake con-tained seven total-pressure tubes, each 0.063 in. indiameter, which were flattened to 0.020 in. (inter-nal height) over a length of 0.25 in. from the tip ofthe tube. The rake is equipped with both standardand disc-type static-pressure probes. The standardprobes were used to measure the static pressure inthe wake for the present test. The static probeswere 0.125 in. in diameter with eight flush orifices(0.018 in. diameter) drilled 45 apart and located8 tube diameters from the tip of the probe. The rakealso contained two claw-type flow-angularity probes,which consisted of two open-ended probes inclined90 with respect to each other. These probes wereused to obtain the mean flow direction of the wake.

Survey ApparatusThe wake rake was positioned at various spanwise

stations behind the model by means of the remote-controlled survey apparatus (fig. 8). The apparatusbasically consists of an articulating arm mounted onan arc strut. Movement of the arm enables the wakesurveys to be made for various angles of attack.

The arm is composed of three movable compo-nents: a main boom, an offset boom, and a forwardpivoting head. Each component has a position con-trol device. The main boom is mounted on the strutwith a pivot point allowing rotation in the verticalplane. Its motion is controlled by the linear actuator.The offset boom can be rotated about the main boomby the roll actuator. This allows survey positions tobe made at distances up to 12 in. from the tunnelcenterline. The forward pivoting head is mounted atthe end of the offset boom and may be rotated inthe vertical plane by the (internally mounted) pitchadjustment mechanism. Figure 8 shows the surveyapparatus with the wake rake mounted on the for-ward pivoting head assembly. In addition, the en-tire apparatus can be positioned vertically in thewind tunnel by using the movable strut that moveswithin the confines of fixed leading- and trailing-edgefairings. Positioning and rate of movement of therake are controlled by a microprocessor controller.In general, wake surveys using this apparatus pro-vided good drag results with a survey rate of about0.10 in/sec or less.

Instrumentation

Measurements of pressure on the model sur-faces, wake-rake pressures, and basic tunnel pressureswere made with variable-capacitance precision trans-ducers. These transducers have an accuracy of-t-0.25 percent of reading. An automatic pressure-scanning system was used to record the modelpressures. The following full-scale ranges of pres-sure transducers were used: Pt, 1000 mm Hg; q,10 mm Hg; wake rake, 10 mm Hg; model uppersurface, 50 and 10 mm Hg; model lower surface,10 mm Hg.

Model angle of attack was measured by a cali-brated digital shaft encoder driven by a pinion gearand rack attached to the pitch mechanism. Datawere obtained by a high-speed data acquisition sys-tem and recorded on magnetic tape. Real-time datadisplays on cathode-ray tubes were available for tun-nel parameters, model pressures, and wake profiles.Tests and Methods

The pressure model was tested at Reynolds num-bers based on airfoil chord from approximately 60 000to 460000 and Mach numbers from 0.03 to 0.13. Themodel was generally tested in a smooth condition ex-cept for a strip of turbulator tape used at a Reynoldsnumber of 100 000. This tape was 0.008 in. thick and0.08 in. wide. The leading edge of the tape formeda zig zag pattern and was located at 0.22c on themodel upper surface.

Laminar-separation and turbulent-reattachmentlocations were determined using the oil flow tech-nique reported in reference 8. These results areshown in table III and a typical result for a Reynoldsnumber of 300 000 is illustrated in the photograph offigure 9.

The static-pressure measurements at the modelsurface were reduced to standard pressure coeffi-cients and numerically integrated to obtain sectionnormal-force and chord-force coefficients and sec-tion pitching-moment coefficients about the quarter-chord point. Section profile-drag coefficients werecomputed from the wake-rake total and static pres-sures by the method of reference 9.

Standard low-speed wind-tunnel boundary cor-rections (ref. 9) have been applied to the section data.Corrections were applied to the free-stream dynamicpressure because of solid and wake blockage and ap-plied to lift, pitching moment, and angle of attack be-cause of the effects of floor and ceiling constraints onstreamline curvature. No blockage corrections havebeen applied to the pressure coefficient data. The


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magnitudeof these corrections for the Eppler 387airfoil are

a corrected = a + 0.0083(c/+ 4Cm)ct corrected = c/(0.9988 - 0.0333Cd)Cm corrected = Cm(0.9997 - 0.0333Cd) + 0.0002ctCd corrected = Cd(0.9995 -- 0.0333Cd)It is important when measuring performance

characteristics of airfoils to provide some indicationof the data accuracy. There are several areas in two-dimensional airfoil testing at low Reynolds numbersthat contribute to the overall uncertainty of the re-suits: tunnel flow quality, experimental apparatus,and instrumentation accuracy.

The major errors introduced by the apparatus areconfinement effects of the wind-tunnel walls, sidewallboundary-layer interaction, and large-scale vorticesin the wake if wake-rake surveys are used to deter-mine drag. For the present tests, the confinement ef-fect of the wind-tunnel walls was minimized by test-ing a model with a chord-to-tunnel-height ratio ofabout 0.07. The sidewall boundary-layer interactioneffect was reduced by using a pressure model withorifices near the center of the model and a modelspan-to-chord ratio of 6. To survey the spanwiseflow structure in the wake, the wake rake was tra-versed in the spanwise direction. However, the wake-rake technique of determining drag is still subject toerrors related to the changing flow direction in theunsteady wake. Figure 10 illustrates typical wakeprofiles where two different total-pressure probestraversed through the complete wake. Note the un-steady wakes for R < 100000. (See ref. 1.) Thedegree of uncertainty associated with the instrumen-tation accuracy was minimized by using precisionpressure transducers.

An estimate of the uncertainties in the sectiondata for a = 4 , using the technique of reference 10,is shown in appendix A.Presentation of Results

The results of this investigation have been re-duced to coefficient form and tabulated in appen-dixes B through E. Selected results are presented inthe following figures: FigureEffect of tunnel environment on sectiondata; R = 60000 and 100000 ...... 11

Spanwise drag data; R = 100 000to 300 000 ............... 12

Effect of tunnel environment on chordwisepressure distributions forR = 100 000 .............. 13

Effect of tunnel environment onchordwise pressure distributionsfor R = 60 000 ............. 14

Spanwise pressure data for c_ = 5;R = 60000 and 100000 ......... 15

Effect of Reynolds number onsection data .............. 16

Effect of angle of attack on chordwisepressure distributions;R = 60 000 to 460 000 .......... 17

Effect of Reynolds number onchordwise pressure distributions;R = 60 000 to 460 000 .......... 18

Variation of drag coefficient withReynolds numbers ........... 19

Variation of maximum lift coefficientwith Reynolds number ......... 20

Separation and reattachmentlocations from oil flow data;R -- 100 000 to 300 000 ......... 21

Comparison of pressure data withoil flow results illustratinglaminar-separation and turbulent-reattachment locations;R = 100 000 to 300 000 ......... 22

Hysteresis effects on section data;R = 60 000 to 300 000 ......... 23

Hysteresis effects on chordwise pressuredistributions for R -- 60 000 ....... 24

Hysteresis effects on chordwise pressuredistributions for R = 100 000 ...... 25

Effect of turbulator tape on sectiondata; R = 100000 ........... 26

Effect of turbulator tape on chordwisepressure distributions; R = 100 000 .... 27

Data from LTPT and other facilities;R = 60 000 to 200 000 .......... 28

Experimental data and predictions fromEppler airfoil code; R -- 60 000 to460 000 ................ 29

Discussion of ResultsExperimental ResultsEffect of tunnel environment. Figures 11 through

15 illustrate the effect of tunnel environment. It iswell known (ref. 1) that boundary-layer phenomena,


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suchaslaminar-separationbubbles,canbe affectedby the tunnelenvironment.The effectsof severalfree-streamconditionson the airfoil sectiondataat R = 100000 are shown in figure ll(b). Themeasured turbulence levels (fig. 6) vary from about0.06 percent at Pt = 15 psi and M = 0.03 toabout 0.16 percent at Pt = 5 psi and M = 0.08.Increasing the tunnel turbulence level at constantReynolds number showed no effect on the lift andpitching-moment data. However, some effect onthe drag data did occur as illustrated by the dragpolar of figure l l(b). Increasing the turbulencelevel of the tunnel would be expected to have abeneficial effect on the bubble characteristics, similarto that observed for surface roughness (ref. 1), andhence, cause a reduction in drag. However, thisresult is not clearly indicated. Significant spanwisevariations in cd are shown (fig. 12(a)) at R = 100000for these free-stream conditions. The lowest valuesof c d were measured at span station 3 in., whichis where the model surface pressure orifices werelocated. Large improvements in spanwise variationsof cd are shown (fig. 12(b)) at Reynolds numbers of200000 and 300000. The pressure data of figure 13illustrate the effect of the tunnel environment on thebubble characteristics for several angles of attack.The main effect of different free-stream conditionsis the location of flow reattachment on the uppersurface of the airfoil. These results illustrate thesensitivity of the bubble phenomena to the free-stream environment.

Figure ll(a) illustrates the effects of two free-stream conditions on the section data at R = 60 000.The tunnel turbulence levels were about 0.16 per-cent for pt = 5 psi and M = 0.05, and 0.20 per-cent for Pt = 3 psi and M = 0.09. For the datataken at Pt = 5 psi and M = 0.05, two differ-ent flow phenomena (laminar separation with andwithout turbulent reattachment) were observed atthe same angle of attack. This unsteady flow oc-curred for angles of attack between about 3 and7 . The pressure data of figure 14 illustrate the twoflow regimes for several angles of attack, and span-wise pressure data are shown in figure 15 for a = 5.It should be noted that the pressure data were ob-tained using an automatic pressure scanning system;thus each pressure was measured at a different time.The data at Pt = 3 psi and M = 0.09 for the angle-of-attack range where the two flow regimes were ob-served always resulted in laminar separation withoutflow reattachment. Consistent flow reattachment oc-curred at a = 7.5 (fig. ll(a)) for both tunnel con-ditions. Large increases in drag are shown in theangle-of-attack range where flow reattachment didnot occur. These results illustrate the extreme sensi-

tivity of the airfoil boundary-layer characteristics atR = 60 000.

Reynolds number effects. Figures 16 through 25illustrate Reynolds number effects. The effects of in-creasing Reynolds number from 60 000 to 460 000 onthe airfoil section data are shown in figure 16. Thedata presented are for the free-stream environmentwhere the lowest disturbance levels were measured(fig. 6). Increasing the Reynolds number results inlarge improvements in airfoil performance because ofthe decrease in size of the laminar-separation bub-ble. The pressure data of figure 18 illustrate thisfavorable Reynolds number effect. For example, for-- 4 (fig. 18(d)), a decrease in the extent of the

upper surface laminar-separation bubble from morethan 0.50c to about 0.10c is indicated for an increasein Reynolds number from 60 000 to 460 000. A cor-responding decrease in c d of 0.0310 is indicated. Asdiscussed earlier, two flow regimes (laminar separa-tion with and without turbulent reattachment) oc-curred at R ----60 000 for several angles of attack. ForReynolds numbers greater than 60 000, when laminarseparation occurred, turbulent reattachment alwaysresulted. The pressure data (fig. 18) also indicatethe changes in airfoil loading because of increases inReynolds number (R = 60000 to 200000) and theresulting decrease in the magnitude of the pitching-moment coefficients. Figures 19 and 20 summarizethe effects of Reynolds number on drag coefficientand maximum lift coefficient.

A more detailed effect of Reynolds number andangle of attack on the upper surface bubble charac-teristics from the oil flow results is shown in figure 21for Reynolds numbers from 100 000 to 300 000. Thepressure data and oil flow results are shown in com-parison in figure 22. A decrease in bubble length isshown for either an increase in angle of attack at aconstant Reynolds number or an increase in Reynoldsnumber at a constant angle of attack. Increas-ing the Reynolds number resulted in only a smalleffect on the location of laminar separation com-pared with turbulent reattachment. For example, fora = 4 , increasing the Reynolds number from 100 000to 300000 produced only about 0.05c movement inthe laminar-separation point compared with about0.15c movement in the turbulent-reattachment loca-tion. At Reynolds numbers of 200 000 and 300 000and angles of attack between 7 and 8 , the flowremained attached and natural transition occurred.This condition generally resulted in the best lift-to-drag ratio for the airfoil.

The importance of hysteresis phenomena for air-foils at low Reynolds numbers is pointed out in ref-erence 1. The presence and extent of these phe-nomena are generally determined by the location of


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separationand/ortransitionin theboundarylayer.Hysteresisdatawereobtainedat Reynoldsnumbersfrom60000to 300000by increasingthe angleof at-tackfrom-3 to stallandthendecreasingtheangleof attack fromstall to about 0. Figure23 illus-tratesthe hysteresiseffecton the sectiondataandfigures24and25showtheeffectson the chordwisepressuredata. Generally,no hysteresisloopswereobserved;however,aspreviouslydiscussed,twoflowregimeswerepresentforasmallangle-of-attackrangeforR = 60 000.Effect of turbulator. Figures 26 and 27 illustrate

the effect of the turbulator. Performance character-istics of airfoils at low Reynolds numbers are domi-nated by laminar-separation bubbles. One approachto provide improvements is the introduction of suit-able disturbances in the boundary layer such thattransition occurs ahead of where laminar separationwould normally occur. Thus, a boundary-layer dis-turbance or turbulator was employed. A spanwisestrip of tape was placed at 0.22c on the model up-per surface, and the results for R = 100000 are il-lustrated in figures 26 and 27. The turbulator waseffective in reducing drag up to a lift coefficient ofabout 1.0, as shown by the drag polar of figure 26.The pressure data for _ = 4 (fig. 27(h)) show typ-ical effects on the laminar-separation bubble due tothe turbulator. The turbulator tape did not elim-inate the bubble; however, turbulent reattachmentoccurred further forward on the airfoil upper surface,as indicated by the forward movement of the aft pres-sure recovery. A reduction in cd of about 17 percentresulted. For a = 7 (fig. 27(k)), transition occurredahead of the turbulator tape (because of the adversepressure gradient near the leading edge) and as ex-pected, no reduction in c d resulted.

Comparison With Results From OtherFacilitiesThe results of the present experiment are com-

pared with data obtained on an Eppler 387 air-foil model in the Model Wind Tunnel at Stuttgartand the Low-Turbulence Tunnel at Delft, where thefree-stream turbulence levels are 0.08 percent and0.03 percent, respectively. Data shown for the LTPTare for the environment where the lowest turbulencelevels were measured (0.06 percent for R = 100000and R = 200 000, and 0.16 percent for R = 60000).The lift data for the LTPT tests were obtained fromsurface pressure measurements while the data fromthe other facilities were obtained from force-balancemeasurements. Drag data for all three facilitieswere obtained from pressure measurements by us-ing a wake survey rake. For Reynolds numbers of6

100000 and 200000 (figs. 28(b) and 28(c)), generallygood agreement between the LTPT and Delft datais shown; the major discrepancy is in the lift data inthe high-angle-of-attack range where the LTPT datashow higher values of lift coefficients. This differencemay be attributed to the flow interference effects be-tween the tunnel sidewall and model end plates, sincea balance was used for the Delft tests. However, largedifferences are shown between the Stuttgart data anddata from the LTPT or Delft. The Stuttgart lift dataare generally lower, particularly at the higher anglesof attack, and large differences in drag data are indi-cated. The Stuttgart drag data, compared with theother tunnels, indicate lower values of cd at lift coef-ficients where the bubble has a large influence on Cd,and generally higher values of cd in the low lift co-efficient range. (See fig. 28(b), R = 100000.) Thesedifferences in drag data may be attributed to tunnelflow quality, or perhaps model contour accuracy andsurface roughness effects.

The data from the three facilities at R = 60 000 isshown in comparison in figure 28(a). As previouslydiscussed, the LTPT data displayed two flow regimesat several angles of attack and showed extreme sensi-tivity to the tunnel environment at R -- 60 000. TheLTPT and Delft data both indicate that laminar stallnear c l ,_ 0.6 occurred with large increases in Cd, andflow reattachment occurred near c I = 1.0. However,the Stuttgart data do not display these phenomena.

Comparison of Results With Eppler AirfoilCodeThe Eppler airfoil code (ref. 11) has been oneof the most useful codes for the design and analy-

sis of low-speed airfoils. The most important anddifficult part of the boundary-layer calculations forlow Reynolds numbers is to account for the laminar-separation bubble. This code contains a bubble ana-logue that is evaluated from conventional computa-tional methods based on the integral momentum andenergy equations.

Lift and pitching-moment coefficients are deter-mined from the potential flow. Viscous correctionsare applied, including a correction for boundary-layer separation. Drag coefficients are obtained byapplying a modified Squire-Young formula to theboundary-layer characteristics at the trailing edge.The prediction of separation is determined by theshape factor based on energy and momentum thick-nesses. The prediction of transition is based on anempirical criterion that contains the Reynolds num-ber (based on local conditions and momentum thick-ness) and the shape factor. The code predicts the ex-istence of significant laminar-separation bubbles andprovides a warning to indicate that the predicted


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dragcoefficientis probablytoo low. However,thecodedoesnot accountquantitativelyfor the influ-enceof thebubbleondrag.TheLTPTdataandpredictionsfromtheEpplercodeare shownin comparisonin figure 29 forReynoldsnumbersfrom 60000 to 460000. ForReynoldsnumbersof 200000or larger,agreementbetweentheoryandexperimentis consideredgood.Bubblewarningsoccurredonlyat theextremitiesofthe dragpolar. ForR = 100000 (fig. 29(b)), goodagreement between theory and experiment is indi-cated for the lift and pitching-moment data. How-ever, the experimental drag data are higher than pre-dicted except near a lift coefficient of about 1.06.Bubble warnings appear for all lift coefficients exceptcl = 1.06. For R = 60000 (fig. 29(a)), bubble warn-ings appear at all conditions. The code does predictlaminar stall for a lift coefficient of about 0.6 withflow reattachment occurring at a higher Cl, as is alsoindicated by the experimental results. Thus, eventhough the code cannot account for the influence ofbubbles on the drag, the boundary-layer phenomenathat occur at low Reynolds numbers are predictedwell. The code prediction of laminar-separation loca-tions and the oil flow data are shown in comparison infigure 21 for different angles of attack and Reynoldsnumbers. Generally good agreement between theoryand experiment is indicated.

Concluding RemarksWind-tunnel tests have been conducted in the

Langley Low-Turbulence Pressure Tunnel to deter-mine the performance characteristics of theEppler 387 airfoil at Reynolds numbers from 60 000to 460000. These tests are part of a research effort

to develop test techniques for low Reynolds numberaerodynamics. The tests were conducted in a man-ner as to minimize both experimental apparatus andinstrumentation uncertainties. The following resultswere determined from this investigation:

1. The performance of the Eppler 387 airfoil isdominated by laminar-separation bubbles atReynolds numbers below 200 000.

2. The wind-tunnel test-section environment hada measurable influence on the size of thelaminar-separation bubble and, thus, on air-foil performance.

3. Two flow phenomena, laminar separation withand without turbulent reattachment, were ob-served at the same angle of attack for aReynolds number of 60 000.

4. A boundary-layer turbulator was effective indecreasing bubble size and, hence, drag at aReynolds number of 100 000.5. The comparison of results from the LangleyLow-Turbulence Pressure Tunnel with datafrom the Delft tunnel generally showed goodagreement; however, the comparison withdata from the Stuttgart tunnel showed largedifferences.

6. Comparison of the present results with pre-dictions from the Eppler airfoil code gener-ally showed good agreement for the lift andpitching-moment data. However, large differ-ences between predicted and measured dragoccurred at Reynolds numbers below 200 000.

NASA Langley Research CenterHampton, VA 23665-5225August 4, 1988

7


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Table I. Design and Measured Airfoil Coordinates With Thickened Trailing Edge

=-014]

0.00000.00043.00518.01423.02748.04493.06643.09185.12093.15345.18907.22742.26813.31078.35505.40077.44767.49548.54393.59272.64137.68922.73567.78007.82183.86035.89510.92553.951281.00000

Upper surface Lower surface

Zd_ Zme_e c

0.00000 0.00000,00233 .00197.00932 .00920.01727 .01742.02562 .02555.03408 .03398.04238 .04233.05033 .05032.05775 .05772.06448 .06440.07037 .07025.07528 .07518.07908 .07903.08157 .08160.08247 .08260.08173 .08182.07937 .07935.07547 .07535.07020 .07005.06390 .06372.05697 .05675.04975 .04955.04248 .04227.03540 .03518.02867 .02845.02242 .02227.01678 .01673.01183 .01188.00763 .00787.00083 .00147

(z)di.0.00000- .00037-.0O012.00015

-.00007-.00010-.00005-.00002-.00003-.00008-.00012-.00010- .00005.00003.00013.00008

-.00002-.00012-.00015-.00018- .00022-.00020-.00022-.00022-.00022-.00015-.00005.00005.00023.00063

0.00000.00092.00717.01890.03597.05827.08568.11800.15490.19598.24083.28892.33968.39252.44678.50182.55693.61147.66472.71602.76475.81027.85202.88943.92205.949421.00000

ZdesC

0.00000-.00287-.00682-.01017-.01265-.01425-.01500-.01502-.01442-.01328-.01177-.00998-.00803-.00605-.00410-.00228-.00065.00073.00187.00268.00320.00342.00337.00307.00258.00197

-.00083

Zme_C

0.00000-.00288-.00678-.01017-.01278-.01430-.01498-.01497-.01433-.01318-.01165-.00987-.00793-.00597-.00402-.00220- - , 00 0_ 0.00077.00187.00265.00317.00333.00323.00317.00257.00182

-.00098

(Z) diff"

0.00000- .00002.00003.00000

-.00013- .OO005.00002.00005.00008.00010.00012.00012.00010.00008.00008.00008.00005.00003.00000

- .00003-.00003- .00008-.00013.00010

-,00002-.00015-.00015

8


15/238

Table I. Concluded

[A=0.56]

0.00000.00043.00518.01423.02748.04493.06643.09185.1209315345.18907.22742.26813.31078.35505.40077.44767.49548.54393.59272.64137.68922.73567.78007,82183.86035.89510.92553.951281.00000

Upper surface Lower surface

Zd_ Zm_c c

0.00000 0.00000,00233 .00220.00932 .00912.01727 .01715,02562 .02572,03408 .03407.04238 .04230.05033 ,05022.05775 .05772.06448 .06432.07037 .07018.07528 .07515.07908 .07900.08157 .08153.08247 .08247.08173 .08172.07937 .07930.07547 .07535.07020 .07008.06390 .06380.05697 .05688.04975 .04967.04248 ,04237.03540 .03535.02867 .02863,02242 .02243.01678 .01685.01183 .01197,00763 .00788.00083 .00083

(Z) diff

0.00000-.00013-.00020-.00012.00010

-.00002-.00008-.00012-,00003-.00017-.00018-,00013-.00008-,00003.00000

-.00002-.00007-.00012-.00012-.00010-.00008-.00008-.00012-.00005-.00003.00002.00007.00013.00025.00000

0.00000.00092.00717.01890.03597,05827.08568.11800.1549019598,24083.28892,33968.39252.44678.50182.55693.61147.66472.71602.76475,81027.85202,88943.92205.94942

1,00000

Zde_C

0.00000-.00287-.00682-.01017-.01265-.01425-.01500-.01502-.01442-.01328-.01177-.00998-.00803-.00605-.00410-.00228-.00065.00073.00187.00268.00320.00342.00337.00307.00258.00197

-.00083

Zme_C

0.00000- .00268-.00695-.01028-.01267-.01430-.01502-01498-.01435-.01320-.01167- .00987-.00793-.00597-.00402-.00220-.00062.00077.00187.00267.00317.00337.00330.00295.00243.00190

-.00090

(Z) diff

0,00000.00018

-.00013-.00012-.00002-.00005-,00002,00003.00007.00008.00010.00012.00010.00008,00008.00008.00003.00003.00000

-.00002- .00003- .00005-.00007-.00012-.00015-.00007-.00007

9


16/238

Table II. Model Orifice Locations, c = 6 in.

Upper surfaceOrifice Zc b_2 Zc

Chordwise1234567891011121314151617181920212223242526272829

0.0000.0047.0100.0150.0200.0250.0300.0400.0500.0600.0750.1000.1500.2000.2500.3001.3500.4000.4500.5000.5500.6000.6500.7000.7500.8000.8500.9000.9500

O. 1667.1722.1778.1556.1611.1667.1722.1778.1556.16121667.1722.17781556.1611.1667.1722.1778.1556.16111667.1722.1778.1556.1611.1667.1722.17781556

0.0000.0095.0138.0180.0215.0245.0272.0320.0363.0402.0453.0527.0640.0720.0775.0810.0823.0817.0792.0750.0695.0630.0557.0482.0402.0322.0238.0160.0080

Spanwise31323334353637383940414243444546

0.0500.0500.0501.0500.0500.0500.0500.0501.9000.9000.9000.9000.9000.9001.9001.9000

0.2223.3334.4445.55566667.7778.88909446.2222.3334.4445.5556.6667.7778.8889.9446

0.0363.0363.0363.036303630363.0363.0363.0160.0160.0160.0160.0160.0160.0160.0160

Lower surfaceOrifice z_C102103104105106107108109110111112113114115116117118119120121122123124125126127128129

C

00051 0.1055.0100 .1111.0150 .1167.0201 .1222.0251 .1000.0307 .1056.0402 .1111.0499 .1167.0600 .1222.0750 1000.1001 .1056.1500 .1111.2000 .1167.2500 .1222.3O00 .1000.3500 .1056.4000 .1111.4501 .1167.5049 .1224.5500 .1000.6000 .1056.6500 .1112.7001 .1167.7501 .1222.8000 .1001.8500 .1056.9000 .llll.9501 .1167

-0.0062-.0072-,0092-.0105-.0113-.0122-.0132-.0143-.0143-.0148-.0150-.0147-.0130-.0113-.0093-.0077-.0058-.0040-.0022-.0008.0005.0015.0025.0032.0035.0034.0030.0022

10


17/238

Table III. Upper Surface Chordwise Locations (x/c) of Separationand Reattachment From Oil Flow Visualization

R = 100 000 R = 200 000 R = 300 000a, deg LS TR a, deg LS TR a, deg LS TR

0.97 -2 0.53 0.80 -2-2.9-202456788.59

0.51.50.45.41.35.34.33.32.29.03.02

.90

.87

.79

.73

.67

.62

.56

.47

.11.02

02456788.5

.48 .74

.43 .67

.40 .62

.38 .59

.37 .55

.33 .48(NT at .32).03 .18

024566.577.588.5

0.53.48.45.40.39.38.38 i(NT at(NT at(NT at.04 I

0.74.69.62.58.55.50.44.40).3o).20).12

LS laminar separationTR turbulent reattachmentNT natural transition

11


18/238

z/o.1

0 _.

-.li I I0 .1

I.2

i I I I i I i I I I.3 .4 .5 .6 .7

x/cFigure 1. Section shape for Eppler 387 airfoil.

I.9

I1.0

12


19/238

ORI_L P;_GE ISOF FOOR QUALITY

I'-,.oO0'3

oO

O

'-oC

t_oO

""O,-::I

t:u0O

13


20/238

(J (JO O"E'E:3:3I,.,. I,-(I.)o.. 3O.O:D ...JOn

III

O,IJov

OOd

oOOo,oO_,oIOPbod_

O

[] []fJI- D-6 []= [] Oo:.= DO

I I,, C_l 0 ("40 0 00 0 0o d oI"Ul 'SaPz -- SDaUJz

E)LO

04.O

I I

',:1-OO(:3

o j lpoLJ_2B O O I= [] OIo= [] O IO gg,

, 2o_-04 0(:3 (:30 0o d

I

000I

"Ul 'saPz -- SDOUJz

0

cO0

E)0

(Jx

0

o40

0,,:t-oOOO

I

O

000

_00

0

("40

0,,_.000dI

ux

0J.q

o_ o

0 ""_,._ el

i. ,...,

14


21/238

o u"ET:L I,,=,

o._O.o:::)..JOD

IO] I

IU'- O Ol

O _ III .9 []U U

X a

I I0 n

0 00 00 0

I9>

I II [] OI

U

.,,in cpO c4 _, I I,- I I" P q

x o [] 01_- I

II I I041 OO OO OO O

_ O

UC-_ po *

c4 II .9o-O

x o>,,u_

- OI

O I

0 00 0o dI

"Ul 'SaPZ -- 8D8LUz

_ 0

_ LO0

C4_o_o J0vuO

- 0III o

c41oodI

(J U

X O

I0 [] I

I0 1

II

DIOn I,. i0

I 0 D II I IOOOd

0

00

DO0

i.

I IOOI I I IC4 00 00 00 0

"U! 'SaPz -- SOaUJz

_ 0

d

_0d .o

-oI

0

000I

_ 0

_ u_d

c__o.0 ..Qv

-0 I

jO00dI

,-d

.,,=_

15


22/238

OF FOG;__L_.k,LfTYgO

gO

Q;0

Q;

t_-O0

.e

_Jq::

16


23/238

F_

10 e

10 5

4100.00

P t' psi 16 .20 15,0psiq' .08

.03 .04 .0_,..__10.0.0 5.0

.005 3.0

-_ Eppler 387 Test

t I t I t I t0.04 0.08 0.12U

Figure 5. Low Reynolds number operating envelope for LTPT for c = 6 in.

I0.16

17


24/238

"U/U,I 0 -1

P t' psi M- O 3 .050 to .208

[] 5 .050 to .21510 .025 to .161A 15 .018 to .133

0 -2 i i i _ I , _ II I i i i i i _ I I10 4 10 5 10 'R/ft

Figure 6. Preliminary test-section turbulence levels for LTPT.

18


25/238

+ L _ -1_]-.....

2.0 in. _ \Flow-angularity probes

(Clawtype) _._Static-pressure probes \

(Standard typel ",,_ , .___

Total-pressure probes

(Tubes flattened} _Static-pressure probes ._ __

(Disctype)

Airflow 0.50 in.0.50i-_n. ( "__t

1.0 in.

0.50 in.0.50 in.

Y _t

0.375 in.t

Dia. - 0.437 in._ -1"0 in.--_---"

Dia. - 0.018 i_ view

7.5 in.

I

X\\/_- Pivot assembly

fT

1.5 in. --_ /- Support webo / Outside dia. - 0.040 in.

_45" //f Inside di_- 0.024 in., /' _ ._" I IM"( 0.20 in.

___ d'__-----L^ Side viewoA+o/I_ 0.70 in.--------_

I- 0,094 in. Outside din. - O.063 in. Claw probe detailI Inside dia. - 0.043 in .

Top view _- & ......... \ ._ ^^ _'_0.07 in. Front view Outside dla. - 0.063 in,Red. 0.047 in. Disc probe detail u.uL tn_ nsde din. 0.043 in.

Dia- 0.018 in.I

Front view

Outside dia. O. 125Inside dia. I 01061_ad. - 0263 in. _0.04 in . - ]

_--1.0 in.-_-_'.O in. _V-_Side view

Static-pressure probe detail

_---0.25 in. ^ It------- I.0 in._r_---"lTotal -pressure probe detail

Side view

Figure 7. Wake survey rake.

19


26/238

oO

O

-Z

O

h0

GomD

O

O

or)06

2O


27/238

t_"_" r,, lp_.' F';

21


28/238

ID0l-

ID

ID

O0O0O_t-o-O_00II 11

0O0OrOoq_-'0II II

0OrO0 _-o o.O4O11II

I

dI a,,.- oo o

0

It

o_u

c_

22


29/238

_ ---.-_ r v/ _n

o

I

o_I

Ec_

rY _

c5

(3_0 []

CJ

I/

E

f9

0

_-_ _oc- ..[3

000

oo_ _

0

0

0 II

_0-0

0

II

23


30/238

O

k'NI

Eo

O

O OOd_

o_o_

c_c _

_- e_ O cO

J_

c.o O

O

o oO ,_

._

00

O

Ik'N

24


31/238

c d

0.040

0.035

0.030

0.025

0.020

0.015

P t' psi M0 5 .09[] 10 .04

0 15 .030 o

____o__o %_ ooo_- ooodeg

5

0

0.010

0.005

0.000 -15 -5 0Span, in.

(a) R = IO0000.Figure 12. Spanwise drag data.

5 10 15

25


32/238

a, deg

0.020 -

O 0D 5

0.015

Cd 0.010

0.005

0.000

C) D D D D D rlrID Fl D D DID CIDD DD I-ID D D D DOoOoOOOOOOOO OoOoOOoOOO OOO

R = 300,000 M = .08I I I I ] I I I I I I I I I I I I I I ] I ' K I I I ' I I I

5 -10 -5 0 5 10 15Span, in.

0.020 -

0.015

Cd 0.010

0.005

0.000

DD D D D D D D DID D 0 DD _ I-ID _ DID D DI_oooooooooo oooooo8oOoooo

R = 200,000 M = .06I I I I l I I I I I , I ' I I _ I I l I I I I [ I , I , _ l-10 -5 0 5 10 15

Span, in.(b) R = 200 000 and 300 000.

Figure 12. Concluded.

26


33/238

-1.4

-1.

kmm_,--,8 -.._[-.6 I-.4

Cp -.2

P.2 {z.4 y}

PV psi M cz cd cm0 5.47 .08 ,111 .0203 -.1012[3 9.62 .04 .101 .0201 -.1005

14.79 .03 .102 .0217 -,1040

" k P-IILJ,-i r"_

.6

0 .1

Cp

.6

.81

.2 .3 .4 :5 .6 .7 .8 ,9 1.0 0 .1 .2 ,3 .4 .5 .6x/c x/c

(a) a ,_ -3 . (b) a = -2 .

C t Cd Cm

.7 .8 .9 1.0

Cp

-1.2 -1.2Pt, psi M ct cd Cm-1. p_ psi M cI cd Cm0 5.43 .08 .287 ,0143 -.og5_ -1.0 0 5.08 .08 .391 .0156 -.0965rq 9.66 .04 .289 .0155 -.0955-.; _ 14.79 ,03 .294 .0159 -,0978 [] 9.66 .04 .392 ,0173 -,0971-.8 _ 14.78 .03 390 .0173 -.097S

5 _., _> Cp "__.,. \_,

,49.6[ [

1.00 .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0 0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0

X/C X/C

(c) _ = -1 o. (d) ,_ = oo.Figure 13. Effect of tunnel environment on chordwise pressure distributions for R = 100 000. Centered symboldesignates lower surface.

27


34/238

Cp

-I .2,

-I .0

--,8

--.6

--.2

0

.4

16

.81

,@[_--r"(2

_,...r ""

o[](>

"'-(>,.j

Pr psi M c l cd cm5,26 08 .492 .0183 -.09639.68 .04 ,491 .0189 -.0972

14.80 .03 .487 ,0188 -.0967

'_II_IIN L, ......

.2 .3 .4 .5 .6 .7x/c

i}.4 _-; _4 |

.8 .9

(e) _ ----- 1 .

Cp

1.0

-1.2 tt Pt" psi M c! cd cm-1.0 0 5,10 .08 .591 .0221 -.1003

r-I 9,69 .04 .589 .0216 -.0983-.8 _ 14.80 .03 .587 D211 -,0981

-.6 _ }-, t-45 _t

r

.8I

0 .I .2 .3 .4 .5 .6 .7 .8x/c

.9 1.

(f) _ = 2 .

Cp

-I .4-I .2

-I .0

--.8

0,,_ h,.4

.2 .,d r

.4 Re

.6' }

J=1 I

0 .1

pr psi0 5.29[] 9.700 14.80

.2 3 .4 .5x/c

(g) c_= 3.

M C l C d Cm.08 .692 .0236 -.0994.04 686 .0238 - .09831.03 .694 .0227 -.0988

\ \.

_IHH_ _e4 _)

L.6 .7 .8 .g 1.0

-1.4

-1.2

-1.0

-.4

Cp -.20

.2_r.4 ||

.8l1 0 .1 .2 .3

Figure 13. Continued.

PV psi M c I c a cm0 5.31 08 .787 0250 -.0970[] 9.71 .04 .786 .0241 -.0943

14.80 .03 .778 .0230 -.0920

1 \

k_J

_4

.4 .5 .6 .7/c

.8 .9

(h) c_ = 4 .

28


35/238

Cp

C p

-1.8

-1.6

-1.4

-1.

-1

-.8

-.6

L

-.4

-.2

-3.2

-2.8

0!

.4 J.6 _K.8_

)

1.2 0

-2.C

-1.6

-1

-,8

-.4

0

.4.8 jV1 0

tm_k

r

.1

Jlwr:

.1 .2

.2

k

p_ psi M c l cd cm0 5.13 .08 .881 .0248 -.090[] 9,72 .04 .880 .0234 -.0879

14.80 .03 .873 ,0240 -,0889

,-(

-1.8

-1 .z

-1 ._

-1.0

--.8

--,6

Cpt-.4

0

.2

.4t

.8 |r

.3 .4 .5x/c

(i) _ = 5 .

.6 .7 .8 .9 1.0 1.2 0

p? psi M c t cd cm0 5.17 .08 1.083 .0213 -.0799[] 9.76 .04 1.077 .0212 -.0786

14.80 .03 1.072 .0206 -.0777

-3.2[

-2.4 _1_-2.( _

-1 .(

.3 .4 .5x/c

q,,_

"- r-( L( )_; )

.6 .7 .8 ,9 1.0

Cp-1

.4

F1.2 0

(k) e = 7.Figure 13. Concluded.

|

,%

_rr

.1 .2

y-

p_ psi M ct c d c m0 5.35 .08 984 .0236 -.0846[] 9,73 .04 .978 .0230 -.0835

14.80 .03 .974 .0224 -.0829

)\\\

}.

._ .4 .5x/c

O) e = 6

.6 .7 .8 .9 1.0

p_ p=i M c! ca c m0 5.20 .08 1,186 .0215 -.0767[] 9,76 .04 1.179 .0212 -.0752

14.81 .03 1,172 .0210 -.0752

% ),,,

H " HHH

.2 .3 .4 .5x/c

(l) _, = 8 .

.6 .7 .8 .9 1.0

29


36/238

Cp

-1.4

-1.2

-1 .o

-.8

-.6

-.Z

co_

L.I..L.2_.4 _,L.6

1.C0 .1 .2

-1.4Pt" psi M c t c d cm Pt' psi M c i c d c m

0 2.79 09 .351 .0263 -.1117 -1.2 0 2.81 .09 .582 .0316 -,1248[] 4,81 .0.5 ,343 .0237 -.1104 [] 5.19 .05 .559 0322 -.1171

-1 0

-.8

i--.[l=ll:t]l=i i-.6 _ ,-, lh c

i_, 1- _1.,>,_, ,_, >._, ,.1 i,I; =li=]l! :.l.... cp -.2 _ "_t ..... O_J

"-Irl-tl" )-tB'ID-I t-fl'l'l'l)'iT'=_-lt'l'_ ir - - ,.-_-, r-i;l-l_.lp.i 1._t-l-i_,1 l.fl-.2 r

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

X/C X/C

(a) o_ ---- 0 0

1.0

(b) ol = 2.

Cp

-1.4

-1.2

-1.0

-.6

-.4

-.2

-1.4Pt' psi M c,L c d cm ] Pt" psi M c l cd cm

0 2.83 .09 628 0368 -.1205 0 2.87 ,09 608 .0477 -.1132[] 4.84 .05 .634 .0368 -.1199 [] 5.04 .05 643 D431 -.1180

-1 ,[ _ 4.87 ,05 .721 .04-00 -.1125

_t_,--,...... -


37/238

Cp

-1.4

-1.2

-1.0

-.6

-.4

)C

.2 A

.6"_B

7

5)

#,

%[ 1"[

,_(

,.6>-()-(;" r41-EH

0 .1 .2

Pt" psi M c i cd cmO 2.91 .09 .623 .0547 -.1099[] 5.06 .05 .638 .0439 -.1139

%[ ]_

_4 L \)-()-( _-()-()-()-i w() "()2

3-1 I-I:]-t_-I _ _

_-c i.C)_.\

_


38/238

Cp

-3.2

-2.4

-2,0

-1 2

-.8

_z

%

w1.2 0 .1

Pt* psi M cz c d cm0 3.00 .09 1.158 .0287 -.0783[] 5 19 .05 1,142 .0280 -.0756

,-q p. }-{)-(1

\"- I.{ )_f 'l

-I J- i.{ ].r _

}-( ,-! r-_

.2 .3 .4 .5 6 .7 .8 .9x/c

(i) a = 8 .

1.0

Cp

-3.23-2._

-2.' Ii1_-2.0 _1

-1.6 \-1.2 [l-z_l

-.4

0

4

m-1.20 .1

Pt' psi M c?, cd cm0 278 ,og 1.217 .04.72 -.0614E] 5 28 .05 1.208 .0471 -.0596

.l_-q

}=1_.,t, I,,,

-t 1-1;

I-CL-{

.2 .3 .4 .5 .6x/c

(j)_ = 10Figure 14. Concluded.

.7 .8 ,9 1 0

32


39/238

-1.8

-_ .2

-.8Cp

--.4

.4

0 x/c = 0.05[] x/c -- 0.90

0 0 0 0 00DD [] [] [] D

o Oo

[][]

l I I I0 .2 .4 .6 .8

y/(b/2)I

l.O

(a) Pt = 3 psi; M = 0.09; R = 60000.

-I .6

-_ .2

-.8Cp

--,4

.4

0 x/c = 0.05[] xYc = 0.90

0 0 0 0 0 0 0 0 0

D D D [] [] D []

I I I l I.2 .4 .6 .8 J..O

y/ (b/2)(b) Pt = 5 psi; M = 0.05; R = 60000.

Cp

-1.6 0 x/c = 0.05[] x/c = 0.90

-i .2 0 0 0 0 0 0 0 0 0

-.8

-.4

D D [] D [] D D D

.4 I I I I0 .2 .4 .6 .8y/(b/2]

(c) Pt = 5 psi; M = 0.08; R = 100000.

!

1.0

Cp

-_ .6

-1.2

-.8

-.4

.4

o x/c = 0.05[] x/c = 0.90

0 0 0 0 0 0 0 O0

DO O O [] D [] O

I I I I I

.2 .4 .6 .8 I 0y/(b/2)(d) pt = 15 psi; M = 0.03; R = 100 000.

Figure 15. Spanwise pressure data for _ = 5.

33


40/238

_v

0

I

c,lI

E0

_ oO _-D _c- 04 .,-.-- "--r.." _" o

0,1 ,--. "-

0 0 00 0 O0 0 0r',.- ddd',.0 0 0_.- o,1omo

,- /q/ /U

/ // o"> ," "Q-O.___O01)_ rlyO / )OC

I. ___7 O. c /< ml_ -_ cs-cs--s-- q _--o_s

,v i_D

_" C_ O

O

COO

COO

OdO

O

CO

(N

0(3

O

IOdI

O

d

d

.oo

,..o

o

34


41/238

O

n_ I

oqI

EO

w]09 ,- L6]

n- _-. rOc_O O OO O oO O O0_ dcSo"O O cOc,J w] _-

080

o

\

i--] j

y_v%

.0

/LJ

Oq O o3T-- _-- T--

m. 0


42/238

Cp

-1.4

-1.2-1.0

a,deg c z cd cm' O -2.94 -.056 .0336 -.0757

D L2.00 .114 .0236 -.0941.00 .348 .0243 -.1102

_ 2.01 .559 .0322 -.1171

.4

.6

JT"_>-,J !_I1-I

?_'Oi

r

'_ )_'--L l-- J--[]--L |--C]--It

>--"_H _'-' -' I-Jl:l_-t'-_l--i i.--__. ,l--i i-- t,--t _--I i -lt-I --i i--t t--i --it----

0 .1 .2 .5 .4 .5 .6 .7 .8 .9 1.0X/C

(a) R = 60 000.Figure 17. Effect of angle of attack on chordwise pressure distributions. Centered symbol designates lower

surface.

36


43/238

-321-2.8 I-2.41-2. )_

161 , ,

a.deg0 4.0013 4.990 6.01z_ 7.01

ct cd Cm721 .0400 -.1125

838 .0439 -.1139661 .0639 -.1080

1.040 .0337 -.0876

L j-1.2 _"" '

Cp \z_..,

-.l ",_ N;\ ""/

4_,'-ILt'

1.2r"0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0

(a) R = 60 000. Continued.Figure 17. Continued.

37


44/238

Cp

_3.2

-2.-2.0-1.6-1.2

--.8

--.4

%_J) CL

J o,

0

.4

t_llr1.2 0

-,< _. ',-,


45/238

CP

-1.4ot,deg-1.2 t 0 -2.98

[] -1.99-1.0 D 0 .ooZ& 1.99

ct c d cm102 .0217 -.104.0.210 .0162 -.1069.390 .0167 -.0978.587 .0211 -.0981

r

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

x/c1.0

(b) R = 100 000.Figure 17. Continued.

39


46/238

-3.6

-2.8-2.4

[I a,deg l c d C m0 4.00 .778 .0230 -.0920[] 6.00 .974 .0224 -.08290 8.00 1.172 .0210 -.0752

10.06 1.200 .0413 -.0599

3m,0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0

(b) R = 100000. Continued.Figure 17. Continued.

4O


47/238

Cp

-3.6

-3.' _

-2.4-2.0 I_[-1.6 I-1.2 I 1_ 1

N

R

0

.4 I I , ,--,,-'-"-'

.81.2 _-----

0 .1 .2 .3 .4

a,deg c/. cd cmO 11.00 1.201 .0525 -.0550[] 12.01 1.189 **** -.0517O 13.01 1.160 **** -.0541A 14.00 .84.2 **** -.1378

__ L--,"-" "_ _i-&-t_ _,.._ ,-t_

It-4_-4 -' '-"

.5x/c

.6 .7 .8 .9 1.0

(b) R = 100 000. Concluded.Figure 17. Continued.

41


48/238

Cp

-1 .o

a.deg c t cd cm

.4

O -2.84 .066 .0163O -1.99 .156 .0133O .01 .352 .0105A 2.04 .574 .0118

-.0813-.0814-.0782-.0794

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

(c) R = 200 000.Figure 17. Continued.

42


49/238

Cp

-4.0,

--,.3. L_

,k-2.8, ,_

- o-2.0 i_:_],,

-1.2 ].,.,..[_r _;'--- )--..-(

-.8)

-.4

i J - .. .. .. _)'( _-.-.-)_ _ _,_c]...

a,deg c/, Cd Cm0 3.99 .785 .0133 -.0803[] 6.04 .999 .014-4. -.07900 8.03 1.182 .0174 -.0751Z_ 10.02 1.231 .0357 -.0643

0.4

.8

'"-__'1_ _

1.2 0 .1 .2 .3 .4 .5 .6 .7 .8 .9x/c

(c) R = 200000. Continued.Figure 17. Continued.

1.0

43


50/238

-4.4

-3.6Is

a,deg ct cd cmO 11.04 1.214- .0570 -.0606El 12.09 1.174. **** -.0593O 14,01 1.155 **** -.0727A 16.09 .851 **** -.1 463

-3.2=t-2.8 ,

Cp

-2.4

-2-1.6-1.2

"5.,"I k,,"_&,\'t--,,_,,,,.J_[ "l_._.

--I.'--r_ ,'%,.__r_(_, J"-L

8"--. ,,/

-.1-) -_h

1. 90 .1 .2 .3 .4. .5 .6 .7 .8 .9 1.0

X/C(d) R = 300000. Continued.


46


53/238

Cp

_,_IITI__IJ.I

a,deg c/, cd c m0 11.02 1.24.1 .0621 -.067013 12.01 1.215 **** -.0690

14.01 1.179 **** -.0751A 16.00 .999 **** -.1693

-1

11_, "4 ,1211

0 .1 .2 .3 .4. .5 .6 .7 .8 .9x/c

1.0

(d) R = 300000. Concluded.Figure 17. Continued.

47


54/238

Cp

El

0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0X/C

(e) R = 460 000.Figure 17. Continued.

48


55/238

Cp

-4.4-4.-3.6

ka,deg ct

O 4.01 .803ID 6.03 1.022O 8.01 1.179A 10.00 1.275

c d cm.OO9O -.0801.0101 -.0807.0161 -.0759.0276 -.0671

-3.i,

-2.8 _-2. _:_

-2.0' __


56/238

-6

-4

e_,deg c% cd c mO 11.00 1.284 .0603 -.06850 12.02 1.264 **** -.07660 13.00 1.240 **** -.0813

Cp

-3

-1A A

0

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

x/c(e) R--460000. Concluded.Figure 17. Concluded.

1.0

5O


57/238

Cp

-1.6 [I

-1.2[iFI-i III_l-.a_IIl_Ii--61

-.2 V_1 tgr_

.8VII0 .1

_A

.2

_4._,

i,a

.5

t-4

R cI cd cm0 60,000 .113 .0233 -.0941[] 100,000 .210 .0162 -.1069

200,000 .156 .0153 -.0814

'" qb,-,"-I I - b f -- _ _'1

-I .'

-1.

-I .0

-,8

_zCp

.4 .5 .6 .7 .8 .9 1.0x/c

(a) o_ = --2 .

_L

j'( ...

.8_

10 .1

R C_ Cd Cm0 200,000 .156 D133 -0814[] 300,000 .146 0118 -.0788

460,000 .153 .0103 -0774

L) },,.( T" r-_tN

2 .3 .4 .5 .6 .7 .8 .9/c

1.0

Cp

-I.2

-1.0

-.6

-.4

R ct c d c m0 60,000 .345 .0237 -.1104[] 100,000 .390 .0167 -.0978

200,000 .352 .0105 -.0782

,,,_Y_!=_,',-t!'It-,)-_,- _ i-_:_'-I .,.,;( \


58/238

C P

-1.4

-1 2

-1 .l

-.1

-,6

-,4-

0

.4

.6

.81.C

R cz % cm0 60,000 .559 0322 -.1171I -I 100,000 .587 .0211 -.0981

200,000 .574. .0118 -.0794

.}

\ C

,1 .2 .3 .4 .5 .6 .7 .8x/c

.9

Cp

1.o

(C) c_ ---- 2 .

-1.4

-1.2

-1.0

-.8

-.6

-.4-

.2

z:,,t

2

?illt

p


59/238

-2,4-2.1-1-1.2

0.4

I.8

1.20

I R c 2 Cd Cm0 60,000 .661 .0639 -.1080I_ [] 100.000 974 .0224 -0829_ 0 200.000 1.004 0141 -,0609

>.

r-(), )_()__ _-(_-()-( }.().()_q )-()-,_

r

H_-4

.1 .2 .3 .4 .5

_- .)-{

)

)-{.)-! !-_)-_)-I') -I )-, _,

/c

Cp

1.o

(e) e = 6.

-2.4

-2.q-1.6

-1.2

0

.4

1.20

iL

J=4_j _P-II

.1 .2 .3

P_P_

R cz Cd Cm0 200,000 1.004 .0141 -0809[] 300.000 1.009 .0117 -.0799

460.000 1.022 .0101 ~.0807

&

.4 .5 .6 .7 .8

/c

k

I.9 1.0

-3.1

-3.:

-2._

-2_

-2.1

-1 .t

Cp -1.2

--.8

--.4

0

.4

1.20

!

_tt""l hko

.2 .3

R c t cd cm0 60.000 1.142 .0280 -.0756

100.000 1,172 .0210 -.0752200,000 1.180 .0175 -.0763

I rkF_d

-3.6

-3.:

-2._

-2.0

-1.6

Cp -1,2

--.8

--.4

0

.4

.4 .5x/c

"tt

1.2.6 .7 .8 .9 1.0 0 .1 .2

(f) _' = 8.Figure 18. Continued.

,J _.4

.3

L

.4

R c! cd Cm0 200,000 1.180 .0175 -.0763[] 300.000 1.180 .0168 -.0756

460.000 1.179 .0161 -.0759

H._ _ ,,_ r,,

.5 .6 .7 .8 .9 1.0x/c

53


60/238

Cp

-51

q-2

-1

0

20 ,1

_ L_ l

.2 .3

R c t Cd CmO 60,000 1.208 .0471 -.0596[] 100.000 1.200 .0413 -.0599

200,000 1,231 .0357 -.0643

Ib_.v-

_HH-:H P4HHP4 P4H_L ,.4 .5 .6 .7 .8 .9

x/c

-5

-2Cp

-1

O_

1! F.,,

2.0 0

(g) o_---- 10 .

t

1 ,2 .3

R c I c d c mO 200.000 1,231 .0357 -,06430 300,000 1.251 .0316 -,0661

460,000 1.275 .0276 -.0671

p(p4 _4

.4 .5x/c

_HP4 p4HP4

.6 .7 .8 .9 1.0

-6I-5

,f_ Jill3- I

qi,4Cp -2-1

0 i.2 0

Xt_-.;.\

_ _ZL _JI_ ,.4:t'-' ' v

#,,

,1 .2 .3 .4

R c l c d c m0 60.000 1.193 .0797 -.0528[] 100,000 1.189 **** -.0517

200,000 1.174 **** -.0593

.... _ _HH_ r_HH_

.5 .6 .7 .8 .9x/c

.0

-6

0 .1

(h) a = 12 .Figure 18. Concluded.

R Cl Cd CmO 200.000 1.174 **** -,0593[] 300.000 1.215 **** -,0690

460.000 1,264 **** -.0766

I 1

m

.2 ,3 .4 .5 ,6 ,7 .8 .9x/c

54


61/238

10 -1 186

4

2

C d 10 -2 186

4

2

lO-S 11

10 4

0 O_ = 0 [] O_ = 4

[-4 \

(}.\ \

_3,,,

() [].._.(,-,)

2 4 6 8 1 2 410 5R

Figure 19. Variation of drag coefficient with Reynolds number.

6 8 110 6

55


62/238

1.4

1.3

C?,,max 1.2

1.1

1.0 110 4

2 4 6 8

--(

210 5R

)J..0

4 6 8

Figure 20. Variation of maximum lift coefficient with Reynolds number.

110 6

56


63/238

o

o.oii)

o-- d

II 0i'-I0 n,.

o

ooo

o 0x

o

o,Io

1 "-/ n_

z L i I l l I 00 0 0 0 0 0 0 0 0

I I

oo

oo o

o C) u

0 L_

0o

_ur_ooo _

_.D b.o

X0

O40

57


64/238

-.8

.4Cp

0

.4

.8 _ o_ = -2 ,].2 I I I I I I0 .2 .4 .6 .B 1.0

x/c

-.8

-.4Cp

0

.4

.8

1.2

LS

\

O( =0

____ 1 1 I I I0 ,2 .4 .6 .8 1.0

x/c

-1.6 -'I ,6

-'I .2

-.8

-.4Cp

0

.4

.8

LS

0000_M., M/

-1.2

-.B

-.4Cp

0

.4

o= 2 .8 0(_--4

_.2 1 I I I --J 1.2 _--- 1 I I ]0 .2 .4 .6 .8 1.0 0 .2 .4 .6 .8 _.0x/c x/c(a) R = i00 000.

Figure 22. Comparison of pressure data with oil flow results illustrating laminar-separation and turbulent-reattachment locations. Centered symbol designates lower surface.

58


65/238

-4 0

-:3.0

-2.0P-1.0

1.0

0(=5

TR0000%

0 .2 .4 .6 .B 1.0x/c

-4.0

-3.0

-2.0CD

-i .0

1.O

t O( ----6 I .... _ - J .2-.... J

0 .2 .4 .6 .8 '1.0x/c

-4.0 -4.0

-3.0

-2,0Cp

-1.0

1.0

a='r -3.0

i

TR

J0 .2 .4 .6 .B 1.0

x/c

-2.0P-I .0

1.O

(a) R = 100 000. Concluded.Figure 22. Continued.

__ G =8

0 .2 .4 .6 .8 1.Ox/c

59


66/238

-:1.6 F

-I .2 i-.B

LS TR

Cp-'4 __0

.4

.B O_ = -2

1.2 [..... L.... L.... L _ _t....0 .2 .4 .6 .8

x/c

l1.0

-I 6

-1.2

Cp

-.8

-.4

LS

4!.8 _ = 0I1.2 L---- .... ___0 .2 .4

x/c

J_____ J .... 1.6 .8 1.0

-_..6

-1.2

-.8

- 4Cp

0

I 2

LS

0(=2

.... J. I L I0 .2 .4 .6 .8

x/cI 1

1.0

-1.6 mI-12L

- 8

- 4Cp

0

G(: 4

.... ] .... _J_ ___ . __ I_ _d0 .2 .4 .6 .8

x/c(b) R=200000.


1.0

60


67/238

-4.0

-3.0

-2 0CD

-1 0

0 0

_ ___ 5

-- L .... 1 ..... I _ __ ..... j.2 .4 .6 .8 1 .0

X/C

-4.0

-3.0

-2.0CD

-1.0

1.0

0(----6

LSTR

-- -- iI _i t 1 J

.2 .4 .6 .8 1.0x/c

-4.0

-3.0

-2.0P-J..0

1.O

a=/

-4.0

-3.0

.2 .4 .6 .B 1.0x/c

-2.0Cp-i .0

1 0

(b) R = 200 000. Concluded.Figure 22. Continued.

I _=8o

---L t I ..... _J.__ __j0 .2 .4 .6 .8 1.0X/C

61


68/238

-1.6 i-1 2

Cp0

.4

.8

1.2 ___l_--0 .2

O( ---- -- 2

L - - [....... L .... .I.4 .6 .8 I .0

X/C

-1.6 FI1

Cp

62

-1.6

-1 2

.2 L-__r__0

LS

0(---- 2

_ [ . _J_ J J.2 .4 .6 .8

x/c

-1

Cp

[ LSB _TR4 Xo s.%%

0_:4

J1.0

i_..2 L..... J_- _[ ____L ..... _L___ . J0 .2 .4 .6 .8 IX/C

(c) R = 300000.Figure 22. Continued.


69/238

-4.0

-3.0

-2.0Cp

-I[ .0

1.0

O( ----6

...... _L_ .... _L ...... i J.2 .4 .6 .8 _ .0

x/c

-4.0

-3.0

-2.0Cp

-1.0

1 0

I a = 6.5 )

_ _ _ _ .......

0 .2 .4 .6 .8 1.0x/c

-4.0

-3.0

-2.0P-i ,0

1.0

i _=7 ----L ..... .... ______ JL ...... _I

.2 .4 .6 .8 I .0X/C

-4.0

-3.0 ._ a = 8

-2.0CD-1.0

0

1.0 .... J _ ____L ___.6 .8 1.00 .2 .4 x/c

(c) R = 300000. Concluded.Figure 22. Concluded.

63


70/238

0

tOe-O-E_r" J --tD

c_I

(n 00 c'_c c,_ M')n r--"e" c.a _

oa"_ _3Ou- 00

_D0_g

co._go0 []

U

CA

J

Cj_

/Yo_/ _/

_-C __'_0_

1[ []I

_


71/238

o

o_I

o

E_E ,--

0o_o_- oo_ QJ

o

o []

D

K_ J

))

I._.0

O4 0 CO

s...

,q.-

(/

r_o

o

o

TI

c'q

oO

o

II

_ o

,._I _D_

65


72/238

0

t_a

_-- E_ Q-- 0 -0- -0-0I

cqI

E(J

bO09 _--c- C{rY '---o_

c)

cJ4- 0o

c_c oo

C -121

N c_ []

I

g0(5

.i

C'4 0

:N'"9"'"0"" "{_""O_- -0"

5

}....i....I.,F_ "0..

"0...."000 _0 _- (N O

O

O

O

gO

O

(N

00

O

Ic_I

-OO

o

O7-O

66


73/238

0

I.---{ )---I 0---{9---0-(;00- -0- -

O4I

0

01 U'3c _ 00Z3

0o oo

N-.-"- 00

- oo

._cm"_0__c c_ []

1,,(

C j_JC

0

O4

_L O,

0

a...

i".-. bO_

"s..."0.(

00 cO _ c,4

0

.

..0 cxl

I

t,q0

0

0

o4

o3

0

I

_

67


74/238

Cp

ilR_4P

-1.4

-1

-1.0

-.8 I_

-.6 _

-.4, _r

2.2 ./

.6 ,_nT

.8"_

0 .1 .2

-1.4Angle of attack c z cd c m Angle of attack cl c d c m

0 Increasing -.056 .0336 -.0757 -1._, 0 Increasing .343 .0237 -.1104[] Decreasing -.045 .0310 -.0767 [] Decreasing .342 .0227 -.1098-1 ._

-.t

-.6i t'

_C -.4 _fc ,,tJ .... tJ, )"_'CJ-rL,_-I I-r L"'" '" _-,_ Cp _lli_"i I-_ D-q t-( }. B-i Lr .... 0 r '_'_ |-I a.,_

.2_!P

.6}"

.3 .4 .5 .6x/c

1..7 .8 .9 1.0 0

a-=j_=j_,j_j_._ -(

1 .2 .3 ,4 .5 .6 .7 .8 9 1.0x/e

(a) a_-3 . (b) a=O .

Cp

-1.2 -1 2Angle of attack c_ c d cm Angle of attack c 2 c= c m

-1.0 0 _ncreasing .559 .0322 -.1171 -1.0 0 increasing .643 .0431 -.1180[] Decreasing 557 .0307 -.1179 [] Increasing .721 .0400 -.1125

-.8 -.8___ -_ L_L'[:,_.) _-_]_- _ Decreasing .681 .0464-.1158

_ c _-.O,r, i_._1___ _........ o

.2 _ .... _-_,-_-_u-,_-_*-_H_-_-,,-_,-,"" 2 _--_=_=i_:-414_li=ll:_tr41_f_#t "__'_ _-"

.6

.81 1.0 .1 .2 .3 .4 .5 .6 .7 .8 ,9 1.0 0

x/c1 .2 .3 ,4 .5 ,6 .7 .8 ,9 1.0

x/c

(c) a:2 . (d) a=4 .Figure 24. Hysteresis effects on chordwise pressure distributions for R : 60 000. Centered symbol designates

lower surface.

68


75/238

Cp

-1.8

-1 .i

-1.,

-1.2

-1.0

-.6

-,4

_.2 [

0

.2

]

D0

_1 i-E] -_

T

.1 .2

'\().]. " ).(

;J..

Angle of attack

0 increasingD Decreasing

c z c d cm338 .0439 -.1139628 .0533 -.1086

'_ ]_[ w v \3 -1 I-[1-[1- [3-1 i -[ )~ [] -

3-II-r.l-L-_-j-,_'E-'-'

I-El- r\\ (

-i t-E

-[

1

.5 .4 .5 .6 .7 .8 .9x/c

(e) o_= 5 .

Cp

1.o

-_gLI-1 5_J 0

-1.4 I,_ 0[]I I'_>.- 1.2 i " ,>

I,ll

I_>".81_1_li, I

.1 .2 .3

Angle of attack c_ c d cmincreasing 685 .0684 -.1083Decreasing .672 .0677 -.1075Decreasing .985 .0375 -.0960

/

\\

. ,J _. -I l1 ""

.4 .5x/c

I.6 .7 .8 .9 1.0

(f) c_ = 6.5 .

CP

-3.2

-2.E

-2.4

-1 .e-1.2

--,8

.4,a

m,1.20

3

4k

Fr

" " '( L,,

.,_1_ |l| _-I

.2

Angle of attack cz c d cm0 Increasing 1.142 .0280 -.0756r3 Decreasing 1.146 .0283 -.0762

]-(]. "1 \ k,

_-_)-_B-_-e

.3 .4 .5 .6x/c

(g) _=8 .

I-{|-()-'L,

-3.2

-2.,

-2,,

-2.0

-1.6

-1.2Cp

-.4

.7 .8 .9 1.0


\\\{

0

.4

,_li _IF1.20 .1 .2

Angle of attack

0 increasing ,17 Decreaeing

)'[}- 3.,'7: )...

1P"ri.

_._ _.1+1-1 t-I_'[) -I )-I_

.3 .4 .5 .6x/c

(h) _ = 10 .

Cz c d Cm

1.208 .0471 -.059_1.206 .0472 -.059,

_'_'- )- i_d

.7 .8 .9 1.0

69


76/238

Cp

-2) = _j-2., In ___

\-2.0-1.6

-1.2

-.4

0

.4

m_1.2 0 .1

\-\ 'l "1

0[]

Angle of attackIncrea@ln9Decr easing t

C_ C d Cm1.193 .0797 -.05281.195 .0797 -.0530

L-_ "(

)_f' i_-{ 1 " 1"1

,_J k-I_)-I

k()_.'- 3- t-()-r__,2 m _"

_-I I-( -t

.2 .3 .4 .5 .6x/c

(i) a = 12.Figure 24. Concluded.

.7 .8 .9 .0

70


77/238

CP

-1.4

-1.2

-1.0

-8

-.6

-.4&

or_9LJ

.2:3

4' I.6 ).8

/,dr

"'E L(

0 .1 .2

0[]

Angle of attack c z cd CmIncreasing ,3go .0167 -.0978Decreasing .391 ,0169 -.0972

Angle of attack c I c d Cm0 Increasing .778 .0230 -.0920[] Decreasing .780 .0238 -.og30

.3 .4 .5 .6 .7 .8 .9 1.0 0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0x/c x/c

(a) _ = 0a. (b) c_= 4.-3.6

-2.1

-2.4 _1_-2.C "_

-1.6

Cp -1.2--,8

--,4

0

.4

_ il1.2 0

5."eL_

Angle of attack c t c d Cm0 Increasing 1.174 .0207 -.0755[_ Decreasing 1.175 .0207 -.0751

-3.6

-3.-2.

-2., b-2.o :_-1,6 _1

Cp -1.2

Angle of attack c= c d cm0 Increasing 1.200 .0413 -.05gg[] Decreasing 1.202 .0403 -.0607

,. ,_t _-! _-( I-E ]-t _-| _-I

Ill _1.2.1 .2 .3 .4 .5 .6 .7 .8 .9 1.0 0 .1

x/c(c) c_= ,S.

}.-[

"Ck,,--,8},

-.4" )" L. LI. )._ ,_" ]" }-I"'" }- :L, 0

, =_-i_-( I-l} "(}-( '}-I I-_I-=T'_( ,-I r'

.2 .3 .4 .5 .6x/c

.7 .8 .9 1.0

(d) a = 10 .Figure 25. Hysteresis effects on chordwise pressure distributions for R = 100000. Centered symbol designateslower surface.

71


78/238

Cp

-1Angle of attack c_ cd c m

-1.0 0 increasing .842 ,*** -.1378i

-.8 _ I-1 Decreasing .835 ***= -,1361

-.4

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0

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.6

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imlIrJE'li'

.1 .2 ,3

I't -t "'v

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.7 .8

(e) o_= 14.Figure 25. Concluded.

1.0

72


79/238

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80/238

-1.4

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l =1=]=1 'l_J k .

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(a) a_ -3 .

-1.4

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L

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0 .1 .2

Turbulator c l c d cm0 Off .210 .0162 -.1069[] On .167 .0152 -.0895

..l_li:{I-II.,_ ['Cl-rl -k,.I

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-1,2 0 Off .294 .0156 -,0978 -1.2[] On .242 .0136 -0789

-1.0 -1.0

Cp

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81/238

Cp

-1.4

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-1 .o

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0

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.81

6/it!

Turbutator cl c d cm0 Off .487 .0188 -.0967[3 On .455 .0163 -.0819

'


82/238

Cp

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x/c

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(k) a = 7.Figure 27. Continued.

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83/238

-3.6-3.2

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(1) a = 8.

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r_._

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.8 .9 1.0

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Appendix ESpanwise Pressure Coefficients

This appendix contains a computer listing of the upper surface spanwise pressure coefficient data forvarious angles of attack for the Eppler 387 airfoil section as measured in the Langley Low-TurbulencePressure Tunnel. No wind-tunnel blockage corrections have been applied to the data.

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.

Documents

Experimental Results for Eppler 387 Airfoil