1、cdj?“iNATIONALADVISORYCOMMITTEEFOR AERONAUTICSTECHNICAL NOTE 3346PREDICTION OF DOWNVifASH BEHIND SWEPT-WING AIRPLANESAT SUBSONIC SPEEDBy John DeYoung and Walter H. Barling Jr.Ames Aeronautical Laboratory,MoffettField, Calif.WashinonJanuary 1955AFM2CHPW.L LXHWLMI 2811Provided by IHSNot for ResaleNo r
2、eproduction or networking permitted without license from IHS-,-,-TECH LIBRARY KAFB, NMlUNATIONAL ADVISORY cowm FOR AEiONAI( Illllllllllllllllllllllillllllll-tiObbU77 TECHNICAL NOTE 3346PREDICTION OF DOWNWASH BEHIND SWEPT-WING AIRPLANESAT SUBSONIC SPEEDHy John DeYoung and Walter H.SUMMARYBarling, Jr.
3、A rapid method for estimating the downwash behind swept-wing air-planes is presented. The basic assumption is that of a flat horizontalsheet of vortices trailing behind the wing. The integrations for thedownwash are handled in a manner similar to both MulthoppCs andWeissingersapproximate integration
4、s in their span-loading calculations.The principal effects of rolling-up of the wake are treated as correc-tions to the flat-sheet wake. A simple approximate correction for the“d effect of the fuselage is applied. The agreement with available experi-mental data taken behind airplane models is good.
5、Computing forms areincluded together with charts of pertinent“d simple direct application.INTRODUCTIONfunctions, so as to enable The downwash induced by a lifting wing has, in the past, been pre-dictedby considering the wing as a lifting line with a vortex sheettrailing aft of the wing in a horizont
6、al plane. It was assumed thatspanwise distribution of vorticity did not change with downstream posi-tion and that the sheet did not roll up behind the wing. With theseassumptions, a procedure for determining downwash is given in refer-ences 1 and 2. In references 1 and 2, the wing span loading is ap
7、proxi-mated by several horseshoe vortices. The total dowuwash is the sum ofthe downwashes of the horseshoe vortices. It is apparent that such aprocedure can be extended to swept wings by using swept horseshoe vor-.-tices. The arithmetic of this procedure is, however, rather tediousand laborious. In
8、reference 3, a more rapid method in the form of aninfluence-coefficientapproach is presented for the downwasl at thecenter of the wake. References 1 and 2 also investigated the limitationsof representing the 13fting surface by a lifting line, and of the effectsof the rolling-up of the trailing sheet
9、. It was concluded that botheffects were negligible for the then conventional airplane configurations. * At the present time, the use of low-aspect-ratio plan forms andoccasionally of further rearward pasitions of the tail has made neces-? sary a re-examination of the assumption that the trailing vo
10、rtex sheetProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-2 NACA TN 3346can be considered nonrolling-up. An analysis of the rolling-up processis given in reference 4 which reveals that the trailing sheet becomesrolled-up at shorter distsnces behind t
11、he wing as (1) aspect ratiodecreases, (2) lift coefficient Increases, and (3) span loading increasesoutboard and decreases inboard. It is apparent that the downwash fieldsdetermined on the assumption of the flat trailing vortex sheet or a com-pletely rolled-up sheet (the simplified cases) omit wings
12、 of aspectratio of about two to four at moderate or high CLtS.The purposes of this report are, (1) to make available an influence-coefficient type of method of computing the downwash behind swept wingshaving arbitrary spanwise loading, a procedure that will be quicker andsimpler to use than methods
13、summing up the downwash due to elementalhorseshoe vortices, (2) to estimate the principal changes in the down-wash field due to the rolling-up process, and (3) to suggest a simplefirst approximation to the downwash at the tail due to a fuselage. Theeffect upon the downwash field due to substituting
14、a lifting line forsurface loading will also be investigated and an approximatemethod fortaking this effect into account will be presented for wings of low aspectratio.AasnaTnbcCavEclPRINCIPAL NOTATIONC dlocal lift coefficient, local liftqcProvided by IHSNot for ResaleNo reproduction or networking pe
15、rmitted without license from IHS-,-,-NACA TN 3346 32 b% b%E.c longitudinal position at which sheet is essentially rolled-upinto wing tip vorticesTc Yclateral position of center of wing-tip vortex, bcT dimensionless longitudinal coordinate,measured from the liftingline ( - T tanA)T trigonometric span
16、wise coordinate (cos-l q), radiansQ height above trailing sheet, - 6n= height above wing tip vortices, - ccSubscriptsS.vcfn,vsTEaveragetip vorticesfuselageintegers correspondingto span stations givenby q = Cos =J8or = cos (For n or v = 1, 2, 3, or 4; qv or qn = 6.9239,0.7071, 0.3827, or o.)pertainin
17、g to downwash at the sheet or displacement of the sheetwing trailing edgeProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-NACA TN 334-6 *F3YSICAL PROBLEM AND BASIC ASSUMPTIONS5The physical picture is one of a lifting surface shedding a trail-ing sheet
18、 of vortices. As the trailing vortices are left farther behindthe wing, he sheet of vortices is displaced downward in varying amountsdepending upon the span station considered, that is, it assumes a curvedshape. While this displacement is going on, the vorticity in the sheetis continually shifting f
19、rom the sheet toward the tips or edges of thesheet. The lifting surface and the trailing vortex sheet sre inclinedwith respect to the free-stream direction.zSketch (a)% The first assumption for the analysis will be that all of the chord-wise lift is concentrated at the chordwise center of pressure w
20、hich will? be taken as the wing quarter-chord line. Second, it till be assumed thatthe flow on the ting is not separated. Third, it will be assumed that theProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-6 NACA TN 3346.downwash due to a symmetrical s
21、heet can be approximatedby a horizontal #flat sheet passing through the symmetrical sheet at the lateral stationwhere the downwash is to be computed. It should be noted that atIrvArbitrary shaped sheet Substitute flat sheet+Sketch (b)the horizontal flat sheet is.given asome allowance is made for the
22、 shapedifferentverticalof the sheet.each q station,location and thusFourth, it will be assumed that the vertical-longitudinalinclination ofthe systemhas no effect upon the downwash. Hence, the real system willbe approximatedby a horizontal flat system passing through the real tsystem at the downstre
23、am station,x, at which downwash is to be computed,as is shown below. The coordinatesot the real and substitute systems oSketch (c)are shown in figure 1. It should be noted that these four assumptionsare ideriticalwith those made by Silverstein and Katzoff in referencesand 2. The first two asswptions
24、 are comuon in aerodynamics and thelimitations are fairly well known for the higher aspect ratios. Thefirst assumptionwill nowbe further investigatedfor wings of fairlylow aspect ratio.1Two wings having taper ratios of O and 1.0, aspect ratio equal to2.o, and sweep angle of 56 were investigated. Eac
25、h wing was assignedboth cotangent-typechord loading and uniform chord loading. The spanwise loadings were obtained from reference 5. For each wing and chord- *wise loading, the downwash in the wake 66 was computed tith each ofthree alternative approximations;namely, the chordwise loading wasreplaced
26、, respectively,by a single lifting line, by three lifting lines dProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-NACA TN 3346 7L. and by five lifting lines. The strength and chordtise positions of thelifting lines were set by dividing the chord into
27、equal segments andfinding the lift and center of lift of each segment. Each lifting line-dwas treated as a flat, horizontal vortex system in the Q = O plane.The downwash angles of the lifting-line systems were added and the sumsare plotted in figure 2 for four spanwise stations.Figure 2 indicates th
28、at the single lifting line does not giveaccurate downwash predictions just aft of the trailing edge of the wing.The downwash fields for the wings of equal A are essentially the sameone mean chord (one semispan) aft of the wing trailing edge. This con-currence at one mean wing chord aft agrees with t
29、he two-dtiensionalexample of reference 1. For cotangent chord loading, the five-lifting-line method very nearly predicts /a equal to unity at the wing trail-ing edge. This can be considered as a check to the approximation sincethe flat-plate downwash must be equal to a at the trailing edge.Examinati
30、on of figure 2 shows that the curve of downwash obtained byusing one lifting line is translated forward a nearly constant longitu-dinal distance from the curve of downwash obtained by using five liftinglines. In figure 2(a), this distance is one eighth the mean wing chord.- In reference (1), contour
31、s of downwash angles due to a two-dimensional Clark Y airfoil section are compared to contours of down-4 wash angles computed for a ltiting line at the c/4 point. If the lift-ing line is shifted back to the(3/8)c point, the shifted field agreeswell with that of the airfoil section even very near the
32、 trailing edge.From this, it would appear that the downwash field due to surface loadingmight be well approximated for all wings by using a single lifting linewith all longitudinal distances reduced by (1/8)cav,or replacing T byT - (1/4)(cb)av= It should be noted that this correction is of signifi-c
33、ance only in vicinity of the trailing edge.The third assumption has been consideredby comparing the resultsobtained by using the assumption against results calculated for an ellip-tically shaped sheet whose ratio of minor to major sxes was 0.4. Atl-l= O, 0.383, and 0.707, the difference of the resul
34、ts was less than thedifferences found in the examination of the first assumption. Atl-l= 0.924, use of the shove third assumption did not compare well withthe results for the elliptically shaped sheet. However, at low anglesof attack, since the distortion of the sheet is small the downwash canstill
35、be computed at q = 0.924. The fourth assumption has been checkedby numerical computation for a o sweptback wing of aspect ratio equalto 3.5. It was found that provided that e of the noninclined systemis taken as w/V rather than tan-l(w/V), the differencebetween thedownwasheswas less than the differe
36、nces noted in examination of thefirst assumption. This appears to hold true up to about a = 20.Thus, throughout this report, e will be taken as w/V and the subjecta71 is thus treated as if only small angles were involved.Provided by IHSNot for ResaleNo reproduction or networking permitted without li
37、cense from IHS-,-,-NACA TN 3346It should also be noted that these four assumptions are commonlyused in th:=calculationof wing span loading. As a result, the fnon-rolling-up system can be treated in a manner analogous to Multhoppts(ref. 5) or Weissingers (given in ref. 6) approximate integrationsinth
38、eir calculationsof span loading. However, a principal problem notencountered in span-loadingwork is the downwash at arbitrary verticallocations.Generally, the amount of rolling-up present is so small that theforegoing assumptions are sufficientfor good answers. However, asCL/A increases, an increasi
39、ng smount of rolling-up appears and a cor-rection must be made for this effect. The principal features of atrailing-vortex systemwhere the rolling-up is conspicuous are, (1) thevorticity becomes vertically displaced and shifts outboard from theplane of symmetry, and (2) the wing tip vortices trail b
40、ack approximatelyin a horizontal plane which is parallel to the free stresm. The centerof the sheet,however,-is still displaced downward. As the vortex sheetis left farther behind the wing, the tips of the sheet rolJ up and formconcentratedtip vortices. An outward motion of the vorticity in thesheet
41、 between the tip vortices results in less vorticity in the mid-semispanregions. These two changes in vorticity configurationcan (inthe main) be taken into account by making a fifth assumption, (1) advertically displaced trailing flat sheet having a reduced amount ofvorticity, and (2) a pair of tip v
42、ortices which liein a horizontal plane uand whose strength is drawn from the sheet. With this arrangement,thesheet can be handled in much the same fashion as the flat sheet, thatis, by using the first four assumptions. The tip vortices can then behandled as a separate computation.Tip vortex-L Weaken
43、ed flat sheet 1Real vortex sheetSketch (d)At various distancesbehind the wing, the rolling-up is in variousstages of development. To obtain an accurate approximation,one shouldlNohrolling-up system assumes that the trailing vortex sheet has rthe same lateral distributionof vorticity at all distances
44、behind thewing as at the wing trailing edge. However, it need not be flat although .,for determining downwash it is assumed flat. tProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-NACA TN 3346 9consider the tratlhg syEtem in longitudinal segments, eac
45、h segmenthaving a different smount of rolling-up. The downwash would then be thesum of the downwashes of all the segnents. However, this involves anexorbitant smount of work and to obtain a practical solution, a sixthassumption will be made. It willbe assumed that the entire trailingsystem behind th
46、e wing is of one form, nsmely, the form which the realsystem has at the selected downstream location . The substituterolling-up system is then pictured as shown in sketch (e).This sixth assumption was examined by numerical computations for a 60sweptback wing of A = 3.5 using the segment approximatio
47、n. It was foundthat the results of the use of this assumption were within the accuracyof the theory for this case.While the foregoing assumptions aid in simplifying the physicalpicture, additional itiormation is necessary in order to calculate theeffect of the rolling-up process. The relative streng
48、ths of the vortexProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-10 NACA TN 3346sheet as well as the,tip vortex and also the poitio.nOf the tiP vortexfor various distancesbehind.the tiw Wst beobtained. From an anYsisof the downwash behind a series of swept-wing plan forms obtained fromlarge-scale wind-tunnel data, an empirical relationshipwas developedgiving the approximate lateral position of the tip vortex. From this, amethod is developed for obtaining the relative strengths of the tip vortexand flat sheet.As will be shown in the text
