NASA NACA-TR-586-1937 Airfoil section characteristics as affected by variations of the Reynolds number《受多种雷诺数影响的翼剖面特性》.pdf

1、q,_“i-_I, “FOR AERONAUTICs .- 1939_,oo._._ -: -_7.I,_/-ONA L TECHNICAL f! tLN“ I95 / 7,. .,8 _ _ ,_ %._-._ 1.4 “,-,oo , /, =.,22 - _b.05 - i_5/opeof_oo,_s_ I I i l ;.fq_b.,_“l-._ / .,.- _.04 - m,-ou_ end o6_ I I I _ I -Fq- “_-_._-_ _- -_ A 0._LX-I.I i I -.I ( I .4: .01. x- . .8 i-2 -.I l_ +-I.0 i-2

2、-.I l_ _ 0. S_e: 5“x30“ Vel (fZ/sec)69,_ 2t P,-es.tsf_ :-i:I:,-,m l:v_. _ Mi_. i- 338,000/ I i , , , I I,_ i i :I / I “IS _ A/rfo/I: _A.C.A. 430/2 w/tn splitflop Pres.(sYnc/. otmJ.“ liD 20Z : “:“x3_“: Tes_2d: LM.A.L., V_I2_6;1227, 1232 -.2-16 -12 -G -4 0 4_ 8 /2 IG 20 24 28Angle of ottock for inhn/e

3、 ospect r-or/o, _o (degrees)_I6u_,_: 2I.-N. A, 0. A. 4302 wltl_ split flap dettecced 75 .Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-AIRFOIL SECTION CIIARACTERISTICS AS AFFECTED BY VARIATIONS OF THE REYNOLI)S NUMBER 15flop deflected -3_Resu/Is co

4、rrecied to J)_fin/t_0 .2 .4 .6 .8 ZOLift coefficient, QFIGURZ 22.- N. A. C .A. 2,3012 with external-airfoil flap deflected-3 .Main wing section . N.A.C.A. 23012 Main wing chord, c_ _ _ 0.2 -8 -4/0 20 4O 60 8OPercenl of chord(i “u“, x,-I2,220/.8/.6/.4j,e_-l“-4.4.20-.4.ll,10.02.01. Ab-foH: _A.C.A. 830

5、12 withexternal-airfoil flop.Pres.(sPnd. otto.): ira 20Size: 5“x30“ Dole.7-35, 8-35Tested: L.M.A.L, V.D.T. /_780 4 8 /_ /G 20 _4deflected 30“_ Dote 7-35, 8-35_esulls corrected to z;_hhife aspect rohb :0 .2 .4 .6 .8 1.0 /.2 L4 L6 /.8LiH coefficient, C,Angle of attack or infinite aspect roho, _z_ (deg

6、rees)FI(IUR 23.-N. A. C. A. 23012 with external-airfoil flap deflected 30 .Main wing section N. A. C. A. Z3012Flap _ction . N. A. C. A. 7J012_ecf ratio :L2 1.4 1.6 1.8Datum chord, c-e:+et.Main wing chord, ct . 0.833cFlap chord, c_=0.2c_ 167eDatum chord, -c_+_.tI_4380 0-39-3Provided by IHSNot for Res

7、aleNo reproduction or networking permitted without license from IHS-,-,-16 REPORT NO. 586-NATIONAL ADVISORY COMMITTEE FOR AERONAUTICSA/PFoz7.“ C/ark Y with Handley-Poge slotfA/A CA. TR400)jDote: 6-3Z Test: _D. 7-. 848Results corrected/o _b_hNe aspect rohb , _0 .2 .4 .6 .8 1.0 L2 /.4 L6 L8 ZO 2.2L/ft

8、 coefficient, C=.o tl_4oo - l _ _8,00o,ooo./_“qTi _ “ “. _.q zao -_ /,ooo,ooo_Z40 . _20_O0 4 8 12 /G 20 Z4A/rfo/ th/ckne_s, f , per-cent cFIGU_ 2.5.-Airfoil speed-range indexes lot various Reynolds Numbers. N.A.C. A,2_0 series sections; c_.= taken lot airfoil with 0.20c split flap deflected 75; c_0

9、takenfor airfoil with flap retracted for a high-speed value of c= aad at 3.5 times the R forthe c_.most efficient for a larger airplane landing at a ReynoldsNumber of 8,000,000. An analysis such as that ofthe foregoing example or further analyses such as thoseAs an example of scale effects within th

10、e flight range,figure 25 has been prepared to show how the choice ofan airfoil section for maximum aerodynamic efficiencymay depend on the flight Reynolds Number at whichthe airfoil is to be employed. The efficiency is judgedby the speed-range index c_,JCdo. Values of c_,= weredetermined for the air

11、foil sections (N. A. C. A. 230series) with a deflected 20 percent chord split flapand at a Reynolds Number as indicated on each curvecorresponding to the landing condition. The cor-responding values of c,0 were taken as the actual profile-drag coefficients associated with a high-speed liftcoefficien

12、t suitable to an actual speed range of 3.5,but corrected by the methods of this report to the high-speed Reynolds Number (indicated landing ReynoldsNumber R times 3.5). Four curves were thus derivedindicating the variation of speed-range index withsection thickness for four values of the landing Rey

13、noldsNumber: 1, 2, 4, and 8 million, the extremes correspond-ing to a small airplane and to a conventional transportairplane. The tfighest value shown, 414, of the speed-range index may appear surprisingly high, but it shouldbe remembered that the corrections to section character-istics and for Reyn

14、olds Number, as well as the use offlaps, are all favorable to high values. The importantpoint brought out by figure 25 is that the section thick-ness corresponding to the maximum aerodynamicefficiency is dependent on the Reynolds Number.The most efficient airfoil for a landing ReynoldsNumber of 1,00

15、0,000, for example, is definitely not theProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-AIRFOIL SECTION CttARACTERISTICS AS AFFECTED BY VARIATIONS OF THE REYNOI, DS NUMBER 17discussed in reference 8 concerning the determinationof the characteristics

16、 of wings evidently require aknowledge of the variation of airfoil section character-istics with profile shape over the practical range offlight Reynohts Numbers.I)ETERM|NAT|ON OF SECTION CHARACTERISTICS APPI.ICABLE TOFLIGHTThe present analysis is intended primarily to supplya means of arriving at a

17、irfoil section characteristics thatare applicable to flight at Reynolds Numbers withinthe practical flight range. This object is best ac-cmnplished by applying corrections to the standardairfoil test results from the variable-density tunnel.The standard airfoil characteristics at large ReynoldsNumbe

18、rs are customarily defined in terms of a fewparameters or important airfoil section characteristicsthat may be tabulated for each airfoil section. Theseimportant characteristics are:c_,_, the section nmxinmm lift coefficient.ao, tim section lift-curve slope._0, the angle of zero lift.%),., the nfini

19、mum protile-drag coefficient. the optimum lift coefficient, or section lift co-(lopt,efficient corresponding to cao=_.c,., the pitching-nmment coefficient about the sec-tion aerodynamic center.a. c., the aerodynanfic center, or point with respect tothe airfoil section about which the pitching-moment

20、 coeffictcnt tends to remain constantover the range of lift coefficients between zerolift and maximum lift.Essentially, the general analysis therefore reduces to ananalysis of the variation of each of these importantsection characteristics with Reynolds Number. Beforethis analysis is begun, however,

21、 it will be necessary toconsider how values of these section characteristicsapplicable to flight are deduced from the wind-tunneltests of fnite-aspect-ratio airfoils in the comparativelyturbulent air stream of the tunnel. The variation of theimportant section characteristics with Reynolds Numberwill

22、 then be considered. Finally, consideration will begiven to methods of arriving at complete airfoil charac-teristics after the important section characteristics havebeen predicted for flight at the desired value of theReynolds Number.Correctionto infiniteaspectratio,-Thederivationof thesectioncharac

23、teristicsfrom the testresultsun-correctedfor turbulencewillbe discussedfirst;theturbulenceeffectswillbeconsideredlater.The reduc-tiontosr“on characteristicsisactuallymade inthreesuc-cv, _pproximations.First,themeasuredcharac-teristicsfortherectangularairfoilofaspectratio6 arecorrectedforthe usual do

24、wnflow and induced drag,usingappropriatefactorsthatallowat the same timefor tunnel-wall interference. These induction factorsare based on the usual wing theory as applied to rec-tangular airfoils. The methods of calculation arepresented in reference 1. (Second-order influences havealso been investig

25、ated; that is, refinement of the tunnel-wall correction to take into account such factors as theload grading and the influence of the tunnel interferenceon the load grading. (See reference 6.) For the con-ditions of the standard tunnel test such refinements werefound to be unnecessary.) The results

26、thus yield thefirst approximation characteristics, e. g., the profile-dragcoefficient C.0 that has been considered a sectioncharacteristic in previous reports (reference 2).These first-approximation section characteristics areunsatisfactory, first, because the airfoil theory does notrepresent with s

27、ufficient accuracy the flow about thetip portions of rectangular airfoils and, second, becausethe measured coefficients represent average values forall the sections along the span whereas each sectionactually operates at a section lift coefficient that may(lifter markedly from the wing lift coeffici

28、ent. Thesecond approximation attempts to correct for theshortconfings of the wing theory as applied to rec-tangular airfoils.It is well known that pressure-distribution measure-ments on wings having rectangular tips show humps intim load-distribution curve near the wing tips. Thesedistortions of the

29、 load-distribution curve ave not rep-resented by tim usual wing theory. The failure of thetheory is undoubtedly associated with the assumption ofplane or two-dimensional flow over the airfoil sectionswhereas the actual flow near the tips is definitely three-dimensional, there being a marked inflow f

30、rom the tipson the upper sorface and outflow toward the tips on thelower surface. This influence not only affects theinduction factors and hence the over-all characteristicsof the rectangular wing but also produces local dis-turbances near the tips that may be expected to affectthe average values of

31、 the section profile-drag coefficients.Theoretical load distributions for wings with well-rounded (elliptical) tips agree much more closely withexperiment than do the distributions for rectangular-tip wings. Local disturbances near the tips should alsobe much less pronounced. Test results for rounde

32、d-tipwings were therefore employed to evaluate the rectangu-lar-tip effects and hence to arrive at the second approx-imations. Four wings, having N. A. C. A. 0009, 0012,0018, and 4412 sections, were employed for the purpose.The normal-wing airfoil sections were employedthroughout the rounded-tip por

33、tion of the wing but theplan area was reduced elliptically toward each tipbeginning at a distance of one chord length from thetip. Section characteristics were derived from testsof these wings in the usual way but using theoreticalinduction factors appropriate to the modified planform. These section

34、 characteristics when comparedProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-18 REPORT NO. 586-NATIONAL ADVISORY COMMITTEE FOR AERONAUTICSwith the first approximation ones from tests of wingswith rectangular tips served to determine the secondapprox

35、imations. These values indicated by doubleprimes were given from this analysis in terms of thefirst approximation values indicated by single primesas follows:CLma_“- 1.03CL,/ao“: 0.96aoao“= ao+ 0.39C,/(degrees)CDo“ Cvo-_O.OO16CL2-3(t-6)O.OOO2(t _6)where t is the maximum section thickness in percentc

36、hord, in some recent reports on airfoil characteris-tics (references 3, 5, and 7) these values have beenpresented as section characteristics except that a smallcorrection has in some cases been applied to the aero-dynamic-center positions. This correction is no longerconsidered justifiable.These cor

37、rections are, of course, entirely empirical.They must be considered as only approximately correctand as being independent of the Reynolds Number.The corrections themselves, however, are small so thatthey need not be accurately known. All things con-sidered, it is believed that through their use the

38、reliabil-ity of the section data is definitely improved, at leastwithin the lower part of the range of lift coefficients.For lift coefficients much greater than 1, however, theprofile-drag coefficients from the rounded tip and rec-tangular airfoil tests show discrepancies that increaseprogressively

39、with lift coefficient and, of course, becomevery large near the maximum lift coefficient owing tothe different maximum-lift values. This differencebrings up the necessity for the third approximation.The second approximation values may, however, beconsidered sufficiently accurate to determine the sec

40、tionprofile-drag coefficient c_o over the lower lift range andalso the following important section parameters thatare determined largely from the characteristics in thelow lift range:Oil0a0C loptCdo rot.Cma.c“a.c.In this range of the lift coefficient the deviations fromthe mean of the ct values alon

41、g the span have beenadequately taken into account. The mean values of ctand cd0 represent true values as long as the deviationsalong the span are within a limited range over whichthe quantities may be considered to vary lineally. Nearthe maximum lift, however, the deviations becomelarger and the rat

42、es of deviation increase so that theprofile drag of the rounded-tip airfoil, for example, ispredominantly influenced by the high c_0 values of thecentral sections which, according to the theory, areoperating at c_ values as much as 9 percent higher thanthe mean value indicated by the wing lift coeff

43、icient CL.Moreover, the actual lift coefficient corresponding tothe section stall (in this case the center section) mightthus, in accordance with tim theory, be taken as 9 per-cent higher than the measured wing lift coefficientcorresponding to the stall.Several considerations, however, indicate that

44、 this9 percent increase indicated by the simple theory is toolarge. The simple theory assumes a uniform sectionlift-curve slope in arriving at the span loading andhence the distribution of the section lift coefficientsalong the span. Actually on approaching the maximumlift the more heavily loaded se

45、ctions do not gain lift asfast as the more lightly loaded ones owing to the bend-ing over of the section lift curves near the stall. Thiseffect has also been investigated approximately. Theresults showed that for commonly used airfoil sectionsthe center lift drops from 9 percent to 5 or 6 percenthig

46、her than the mean at the stall of rectangular airfoilswith rounded tips. For some unusual sections thathave very gradually rounding lift-curve peaks and withlittle loss of lift beyond the stall, this correction maypractically disappear either because the lift virtuallyequalizes along the span before

47、 the stall or because themaximum lift is not reached until most of the sectionsare actually stalled. Omitting from consideration thesesections to which no correction will be applied, thequestion as to whether or not such a correction shouldbe applied t9 usual sections was decided by consideringhow i

48、t would affect predictions based on the c_values.Maximum-lift measurements had been made for anumber of tapered airfoils of various taper ratios andaspect ratios. The same airfoil section data presentedin this report were applied (taking into account the re-duced Reynolds Number of the sections near

49、 the tipsof highly tapered wings) by the method indicated inreference 8 to predict the maximum lift coefficients ofthe tapered wings. These predictions appeared some-what better when the section data were obtained onthe assumption that the center-section lift coefficientat the stall of the rectangular airfoil with rounded tipsis 4 percent higher than the wing lift coefficient. Hencethe