1、.REPORT 1295AN ANALYSIS OF ONCE-PER-REVOLUTION OSCILLATING AERODYNAMIC THRUST LOkDSON SINGLE-ROTATION PROPELLERS ON TRACTOR AIRPLANES AT ZERO YAW By VEENONL. ROQALLO,PAUL F. YAQGY, and JOHN L. MCCLOUD IIISUMMARYA timplijied procedure b shown jor calculating the once-per-revoluiwn oscillati aerodynam
2、ic thrust load-s on pro-pellers oj tractor airplunm at zero yaw. The mdy j?ow ji%iiiinformation required Jor the appliwztion of the procedure ti aknowledge qf the upj%w angles at the horizon$ul center bine ofihe propelle? disk. Methods are pre+wnted whereby tieangle8 may be computed without reeour8e
3、 to apa+imental 8ur-cqy oj the.llm.The loads computed by the 8impliJed procedure arc mm-pared with those computed by a more rigorom method and t-h-eprocedure h apgiiea? I% 8ever airphw con$guration$ whichare believed typ”cul oj current d-eiw. The redts are gerwr-ally 8alictmy.INTRODUCIIONAn importan
4、t consideration in the structural design ofpropellers is that which deals with vibratory stressesresult-ing from the blade bending flhvise 1 cyole per propellerrevolution (hereafter referred to as 1-P stresses). Thisflntwise bending of the propeller blade is due primarily toaerodynamic thrust 10MIso
5、scillating 1 cycle per propellerrevolution (hereafter referred to as 1-P thrustloads) whichme imposed on the blade as a result of propeller thrust-axisinclination and/or asymmetries of the flow fields in whichthe propellers operate.Methods have been developed whereby these 1-P stresseshavo been comp
6、uted satisfactorily for isolated propellers(e, g., refs. 1 and 2). These methods assumed a uniformflow field at the propeller disk, that is, the flow of air intothe propeller disk was assumed to beat a uniform speed andstream angle at all points on the disk. However, for camsof propellers operating
7、in nonuniform flow fields of wing-nacelle-fuselage combinations, the validity of these assump-tions ww in question and it was not known to what degreethe values thus computed would agree with those mewured.In considering where errors might possibly arise incomputing the 1.P stresses when the flow fi
8、eld is nonuni-form, it should be pointed out that prediction of the 1Pstresses requires a knowledge of the 1.P thrust loads andthe structural properties of the propeller. In turn, methodsof computing the 1.P thrustloads require a knowledge ofthe flow-field characteristics, the blade physical propert
9、ies(airfoil section, plan form, etc.) and the blade aerodynamicproperties (two-dimensional). Finally, methods of com-puting tho flow-field characteristic require taking properaccount of the influence of the various airplane componentsand their interference effects Orieach other.It was reoo.tied that
10、 the blade structural, geometric,and aerodynamic characteristics did not depend upon theuniformity of the flow field; however, sources of error mightpossibly lie in the answers to one or more of the followingquestions.(1) If the 1.P aerodynamic thrust load is known, can the1.P stressesbe computed?(2
11、) If (1) oan be accomplished, can the 1.P thrust loadsbe computed if the flow-field characteristics are known?(3) If numbers (1) and (2) cm be accomplished, can theflow field characteristics be computed for any given airplaneconflratio9?To answer the above questions, an analysis of the methodsemploy
12、ed to obtain 1.P blade stresses, 1.P thrust loads, andflow-field parameters was undertaken. An investigationof a propeller operating in the nonuniform flow field of awing-nacelle-fuselage combination was made in the Ames40- by 80-foot wind tunnel. The data obtained from thisinvestigation were report
13、ed in referene.es 3 and 4. The-sedata consisted of surveys of the flow field in the absence ofthe propeller, measurements of stresses on the propellerblades operating in this flow field, and surveys of the wakepressures behind the operating propeller. During tbeanalysis of these data, a simpli.fleat
14、ionwas devised wherebythe 1.P thrust loads could be computed by a method re-qti#.16a02 ,:mz .-eCJmz/go .1 (2 3 .4 5 .6 .7 .8 .9 10. Fmctkm of tip rodius,xFmmm 3.MeaEnredradial variation of the masimum 1-P inmementalthrust coefficient; V.= 165 mph, = 1250 rpm, “u=80, pM5=200,four-blade propeller.I.P
15、stresses in a propeller operating in a nonuniform flowfield can be computed if the 1.P thrust load is known.COMPUTAON OF THE VP AERODYNAMIC THRUSP LOAD FROM KNOWNFLOW-FIRLD CHARAOTERfSCSA method utilizing strip analysis to compute the thrustload variation horn known flow-field characteristics has be
16、endeveloped and is presented in Appendis A. An evaluationof the method was undertaken for propellers in nonuniformflow fields by attempting to compute the 1.P thrust loadsmeasured during the tests of the wing-nacelle-fuselagecombination shown in figure 2.The flow-field characteristics required for t
17、his wing-nacelle-fuselage combination were obtained by survengthe flow field at the plane of the propeller in the absence ofthe propeller. A rake of eight directional pitot-static tubes(described in ref. 3) was employed for the survey. Theflow field was defined by three parameters; the rotationalflo
18、w angle, +, the outtlow angle, 0, and the velocity ratio,VT”., all of which are defined in the Notation and shownin figure 1. Typical variations of these parametem withProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-976 REPORT 1295NATIONAL ADV180RY C
19、OMMFITEE FOR AERONAUTIC%. - - _*12000 Io Measured-ComputedImoo /“ 1t Q/ , l it resulted primarily from rotation of theslipstream before it reached the thrust rake.:-So -20(c) .9I I 10 90 180 270 360Angulor position, Q, degI I I I II I I I I(l.,P)TJo -.10I I Io 90 180 270 360(c) Model C inboard nacel
20、le.l?mmm 8.The flow-field parameters and their effects on the 1-P variation of incremental seotion thrust coetlicient for an isolatednacelle and mveral wdng-fusekge-nacee combinations.Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-980 REPORT 129 o -
21、 - _z. - 0 (l. P)*-O “? $. =-20 -0 .9 g 0I 1 In G0 3L 220 -0-Jo t -1I I . I I1 I I.10 (I”:)r-20,(e) .9I I Io 90 180 270 360-.10t -1II I I Io 90 180 270 3WAngular position, Q, deg(e) iModel D.FIGURE8.Concluded.load was periodic, (2) the components were rdl integer func-tions of one propeller revoluti
22、on, and (3) no odd-order com-ponents above the fundamental were prewnt. For example,at the specitic angular positions !2=0, 90, 180, and 270,expressions for determining the phase and amplitude of the1.P component are1 (%)wO”-(c).m”=wl cos w (la)1 (%)o-o”- (%)Q.,W=% sin% (lb)where pa is the phase ang
23、le between the position at whichthe maximum magnitude of the 1. component occurs andthe Q=900 position. As noted previously, for tlm casesinvestigated, values of pa were found to be quite small,Hence, it is believed plausible to make the approximationthatz=O.7, V.=165 mph, w=125fl rpm,/lo,70=2.7.The
24、 introduction of this simplified procedure reduces theflow field information required to the values of the param-eters at the $2=90 and 270 positions (the horizontal centerline of the propeller disk). This fact and certain character-istic of the flow-field parameters preclude the need forexperimenta
25、l surveys of the flow field. It can be seen infigure 8 that, generally speaking, at the Q=90 and 270positions Ortnd VVm are near the free-stream values of 0and 1.0, respectively, as noted previously, while # is atnearly its mtium and minimum values. Hence, O andVJVa can be approximated by the free-s
26、tream values.Values of+ on the horizontal center line of the propeller diskmay be computed by the methods which are presented andevalurttedin Appendixes B, C, and D. Thus, the need forexTerimentoJsurveys of the flow field has been obviated.To indiente the accuracy and general applicability of thepro
27、cedure, 1.P thrust loads on a propeller computed by theprocedure are compared in figure 9 with those presentedm figure 8 which were computed by 16-point computationsbrtsedon all measured flow parametem. As noted above, thevfdues of 0 d 1.0 were assumed for o and VJVO hmnpplying the simplified proced
28、ure. Compariwms in figure9 nre at the 0.7-radial station of the propeller blade for allthe test configurations. Comparisons of radial variationsfor two of the models me shown in figure 10 and, as furtherevctluntiort,the 1.P blade stressescomputed using these loadvariations nre compared in figure 11.
29、 From these figures,it is seen that” the simplified procedure yielded generallysatisfactory results for these configurations.4Aconvordentdesign footor,now in mmmon W, forfndfcatlng the relative strm Ievofsonpropclforsfor vorfow sltgbt condltiom k the 1-P lmd erdtfng peramek Ag (rofs. I rmd2).By dcfl
30、nlt!on, A Is Identlcnl to tho absolute vfduss of # at tho horfxontal contarRne of theMOpOkIdisk.16I I ITT.08 /(8cI,)#J.04(d)3 .4 .5 .6 .7 .8 .9 10Fmction of tip mdiu x(a) Model B port propeller.(b) Model B etarboard propeller.(a) Model C port inboard propeller.(d) Model C port outboard propeller.Fmu
31、RE 10.Comparison of the radial variation of the 1-P thrustloadcomputed by the procedure of thfareport with that computed usingthe entire measured flow field; V.= 165 mph, = 1250 rpm,hence y is quite small as is the angle of attack of the bladesection which is equal to the quantity (I?=p). It can bes
32、een that if these tm are neglected in the above expres-sion, the term in the bracket becomes unity which is tanta-mount to saying that the drag force on a blade element con-tributes little to the blade element normal force. It iscautioned that such approximation may not be valid forrdl possible oper
33、ating conditions. For simplicity, t that is, the adjacmtbodies influenced the wing tital angle of attack so slightlythat the resultant change in e- was negligible.This conclusion is veri.6ed in figure 13 where cw, com-puted by the method presented in Appendix C from measuredspan loading on a wing af
34、fected by a nacelle is comparedto that computed for the isolated wg. The differencesare seen to be negligible.In the case of determining the correct total angle of attackfor a body, it was found that the effect of upwash from thewing and from other bodies generally could not be ignored.The wing upwa
35、sh contribution to the angle of attack of abody wn be computed by considering only the wing geo-metric angle of attack, since bodies have been shown tohave little effect on the W induced upwash. For a wing-body combination (i. e., a fuselage or single-engine airplane)the body effective angle of atta
36、ck is taken as the arithmeticsum of the geometric angle of attack of the body and the1.4i+ -w4.2 u e +. /c M= O.18, CL= O.32.Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-ONCE-P13R-REVOLUTION OSCILLATING AERODYNAMIC UST LOADSONSINLE-ROTATIONPEOPELR
37、8 985value of wing upw.sh in the propeller plane at the.axis of thebody%q= %cwlatrlo+ %mJ (B2)I?or tho cam of n confration having more than one body(i, o, multiengine-type airplanes where the propulsiveunits me housed in nacelles outboard of a fuselage) the totalangle of attack of a second body, for
38、 illustration assumedto be n nacelle, is espressed as%= %metrio+ %+ %jacent My (333)where the value of Etiwis the magnitude of wing upwa.shin the propeller plane at the nacelle axis. The value ofdjbo at the nacelle axis is computed for the adjacentbody at the effective angle of attack determined fro
39、m equa-tion (332). This ignores the fact that the adjacent bodyis under the influence of the nacelle; this semndarder effectis believed to be negligible.While wing upwash is always important, the importanceof considering upwash from adjacent bodies w-henobtaininga body total angle of attack varies w
40、idely depending on bodyproximity, relative size, and longitudinal position. Forexample, in the case of a multiengined airplane, the effectof one nacdle on the total angle of attack of the other canbo slIown to be small if the first nacelle lies behind thepropeller plane of the second. Thus wing swee
41、p would varythe importance of upwash from adjacent nacelles in biingthe total, angle of attack of a given nacelle. On the otherhand, if the adjacent body -werelarge compared to a nacelle,for example, a fuselage where the fuselage nose was down-stream of the propeller plane, its effect on the nacelle
42、 totalangle of attack would be important. GeneraXy speaking,any body which extends ahead of the propeller plane atwhich 4 is being computed will have a significant effect onthe total angle of attack of the body containing the thrustaxis corresponding to that propeller plane; for example,usually fuse
43、lages and inboard nacelles both must be takeninto account in finding the total angle of attack of the out-bomd nacelle in four-engined swept-wing con.iiguratiom,whereas only the fuselage signihmtly affects the inboardnacelle.To evaluate the use of equation (B1) and the methodswhich have been describ
44、ed, the variations of the upwashangle due to the various components and the curve repre-senting the summation of these and the geometic angle ofattack of the thrust axis are shown in figure 14“for severalwing-nacelle-fuselage combinations at a Mach number of0,22. Also shown is a comparison of these
45、results with themeasured values which indicates good agreement. Similarcomparisons are made in figure 15 for the wing-nacelle-fuselage combination dwcribed in reference 9 for a Machnumber range from 0.25 to 0.92. In computing the upwashfor this combination, account was taken of compressibilitytiects
46、, except for the effects on the body-induced upwash,whose mechanics were not clearly understood. Good agree-ment between computed and measured upwash angles isindicated up to a Mach number of about 0.8. Compressi-bility effects are discussed more fully in Appendixes C and D.“7c+iModel B26 . 0:22u3-
47、00 098 OWL / zz%14a!m (0)z0 J .2 .3 .4 .5 .6Sponwme statian, T, fmction of semispan(a) Mode3 B.FI 14.Mweured and predioted upflow anglee and predictedupwash components at the horizontal center line of the propellerdisks of several wing-fueelage-nacelle combination; q= 10.M= O.22.436875-6744Provided
48、by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-.REPORT 129lnbod ,nocdk I ./ o._. 1Nate lle- - Inhoord noeelleo 1 1 .a71Lo I - .8t-tI IM= 0.60 M=(2YZ! 9 1 I If 1I )/ I I Q Iry. Ii oc. L-4 x/ -0.6 .7 .8 .1 .2 .3 .4 .5- .6 .7 .,Sponwise stolion, q, fraction of
49、semispan Sponwlse stahan, q, froclian of semispanI 1 t ,0J .2 .3 -4 .5 IFICtUItE15.The effects of Maoh number on the upwaah at the horizontal center line of the propeller dieke of a wing-fuselage-nacelle combinationutilizing a awept wing.APPENDIX cA METHODFOR COMPUTINGTHE WING-INDUCEDUPJV.4SHANGLES AT THE HORIZONTAL CENT
