1、3 1176 00508 95mAERONAUTICSRF_ORT 1048:- :r BODIESProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-%*g r REPORT 1048A STUDY OF EFFECTS OF VISCOSITY ON FLOWOVER SLENDER INCLINED BODIESOF REVOLUTIONBy H. JULIAN ALLEN and EDWARD W. PERKINSAmes Aeronautic
2、al LaboratoryMoffett Field, Calif.Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-National Advisory Committee for AeronauticsHeadquarters, 1724 F Street NW., Washington 25, D. C.Created by act of Congress approved March 3, 1915, for the supervision a
3、nd direction of the scientific studyof the problems of flight (U. S. Code, title 50, sec. 151). Its membership was increased from 12 to 15 by actapproved March 2, 1929, and to 17 by act approved May 25, 1948. The members are appointed by the President,and serve as such without compensation.JEROME C.
4、 HUNSAKER, SC. D., Massachusetts Institute of Technology, ChairmanALEXANDER WETMORE, So. D., Secretary, Smithsonian Institution, Vic ChairmanDETLEV W. BRONK, PH.D., President, Johns Hopkins Univer-sity.JOHN H. CAss_oY, Vice Admiral, United States Navy, DeputyChief of Naval Operations.EDWARD U. CONDO
5、N, Pm D., Director, National Bureau ofStandards.HoN. THOMAS W. S. DAVIS, Assistant Secretary of Commerce.JAMES H. DOOL1TTLE, SC. D., Vice President, Shell Oil Co.R. M. HAZEN, B. S., Director of Engineering, Allison Division,General Motors Corp.WILLIAM LITTLEWOOO, M. E., Vice President, Engineering,A
6、merican Airlines, Inc.THEOnORE C. LONNQUEST, Rear Admiral, United States Navy,Deputy and Assistant Chief of the Bureau of Aeronautics.HON. DONALD W. NYROP, Chairman, Civil Aeronautics Board.DONALD L. PUTT, Major General, United States Air ForceActing Deputy Chief of Staff (Development).ARTHUR E. RAY
7、MOND. SC. D., Vice President, Engineering,Douglas Aircraft Co., Inc.FRANCIS W. RECHELDERFER, SC. D., Chief, United StatesWeather Bureau.GoRaor P. SAVILLE, Major General, United States Air Force,Deputy Chief of Staff (Development).HON. WALTER G. WmTMA_, Chairman, Research and Develop-ment Board, Depa
8、rtment of Defense.THEODORE P. WalCnT, So. I), Vice President for Research,Cornell Univers;ty.HuGs L. DRYDEN, Pm D., DirectorJOHN W. CROWLEY, JR., B. S., Associate Director for ResearchJOHN F. VICTORY, LL.D., Executive SecretaryE. H. CHAMBERLIN, Executive O_cerHENRY J. E. REID, D. Eng., Director, Lan
9、gley Aeronautical Laboratory, Langley Field, Vs.SMITH J. DEFHANCE, B. S., Director Ames Aeronautical Laboratory, Moffett Field, Calif.EDWARt) R. SHARP, SC. D., Director, Lewis Flight Propulsion Laboratory, Cleveland Airport, Cleveland, OhioTECHNICAL COMMITTEESAERODYNAMICS OPERATING PROBLEMSPOWER PLA
10、NTS FOR _kIRCRAFT INDUSTRY CONSULTINGAIRCRAFT CONSTRUCTIONCoordination of Research Needs of Military and Civil AviationPreparation of Research ProgramsAllocation of ProblemsPrevention of DuplicationConsideration of InventionsLANGLEY AERONAUTICAL LABORATORY, AMES AERONAUTICAL LABORATORY, LEWIS FLIGHT
11、 PROPULSION LABORATORY,Langley Field, Vs. Moffett Field. Calif. Cleveland Airport, Cleveland, OhioConduct, under _tnified control, for all agencies, of scientific research on the fundamental problems of flightOFFICE OF AERONAUTICAL INTELLIGENCE,Washington, D. C.Collection, classification, compilatio
12、n, and dissemination of scientific and technical information on aeronauticsProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-REPORT 1048A STUDY OF EFFECTS OF VISCOSITY ON FLOW OVERSLENDER INCLINED BODIES OF REVOLUTIONI33“ . JULIAN ALLEN AND EDWARD _V.
13、PERKINSSUMMARYThe ob,_er_ed flow field about slender inclined bodies ofrevolution is eot_ff_ared with tee calculated characteristics basedupon potential theory. The comparison is instructive inindicatil_g the mo_,ner it_ wb_ct_ the effects of viscosity areBased on this and other studies, a method is
14、 developed toallow.for viscous effects on the.force and moment ckaracteristicsof bodies. The calculated .force and moment characteristics oJtwo bodies oj high .fineness ratio are shown to be in good agree-ment, .for most engineering purposes, with experiment.INTRODUCTIONThe problem of the longitudin
15、al distribution of cross forceon inclined bodies of revolution in inviscid, incompressibleflow, which was primarily of interest to airship designers inthe past, was treated simply and effectively by Max Munk(reference 1). Munk showed that the cross force per unitlength on any body of revolution havi
16、ng high fineness ratiocan be obtained by considering the flow in planes perpendicu-lar to the axis of revolution to be approximately two-dimen-sional. By treating the problem inshowed thatdS.f = qo _- sin 2 awhere.fqodS/dxthis manner, Munk(1)cross force per unit lengthstream dynamic pressurerate of
17、change in body cross-sectional area withlongitudinal distance along the bodyangle of inclinationTsien (reference 2) investigated the cross force on slender bodies of revolution at moderate supersonic speeds-a prob-lem of more interest at the present to missile and supersonicaircraft designers-and sh
18、owed that, to the order of thefirst power of the angle of inclination, the reduced Munkformulao dS.f=“ q -d-i _ (2)was still applicable. This is not surprising when it is realizedthat the cross component of the flow field corresponds to across velocityV,0= V0 sin ai Supersedes NACA TN 2044, “Pressur
19、e Distribution and Some Effects of Viscosity onSlender Inclined Bodies of Revolution“ by H. Julian Allen, 1950.where 1o is the steam velocity. Thus tile cross componentof velocity, and hence, the cross .Maeh number will, forsmall angles of inclination, have a small subsonic value sothat the cross fl
20、ow will be essentially incompressible incharacter.Using equation (1) for the cross-force distribution, then,the total forces and moments experienced by a body in aninviscid fluid stream can be calculated. Comparison of thecalculated and experimental charaeteristies of bodies hasshown that the lift e
21、xperienced exceeds the ealeulated liftin absolute value by an amount which is greater the greaterthe angle of attack; the center of pressure is farther aft thanthe calculations indicate, the discrepancy increasing withangle of attack; while the absolute magnitude of the momentabout the center of vol
22、ume is less than that calculated. Ithas long been known that these observed discrepancies aredue pTimarily to the failure to eonsider the effects of viscosityin the flow.Experience has demonstrated, notably in the developmentof airfoils, that the behavior of the boundary layer on abody is intimately
23、 associated with the nature of the pressuredistribution that would exist on the body in inviscid flow.In particular, bounda_-layer separation is associated withthe gradient, of pressure recovery on a body. The severityof the effect of sueh separation can be correlated, in part,with the magnitude of
24、the total required pressure recover5-indicated by inviseid theor3,. It is therefore t.o be expectedthat it will be of value to compare the actual pressure dis-tribution on inclined bodies of revolution with that calculatedon the assumption that the fluid is inviseid. For the purposeof this study, a
25、simple method is developed for detelznining,for an inviscid fluid, the incremental pressure distributionresulting from inclined flow on a slender body of revolution?The experimental incremental pressure distributions about.an airship hull are compared with the corresl)onding dis-tributions calculate
26、d by this method. The comparisons areinstructive in indicating the manner in which the viscosityof the fluid influences tim flow. In the light of this and otherstudies, a method for allowing for viscous effects on the forceand moment characteristics of slander bodies is developedand the results comp
27、ared with experiment.: The problem of dctermining the pressure distribution on inclined bodies ha_ been treatedby other authors, but for several n_asons the_ methods are not satisfactory for the presentpurposes. For example, Kaplan (reference 3) treated, in a thorou_h manner, the flow aboutslender i
28、nclined bodies, but the solution, which is expressed in Le!zendre polynomials, isunfortunately tedious to evaluate. On the other hand. Lailone Ireferent_, 4L by linearizingthe equations of motion, obtained a solution for the pressure distribution on slender inclinedbodies of revolution, hut, as will
29、 be seen later, the solution is inadequate in the _enerai easedue io the linearization.1Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-REPORT1048-NATIONALADVISORYCOMMITTEEFORAERONAUTICSACaCff_ .900C(,dot. 90 Co F( _DF let - 0CLC._tDIfLM0Pp0pat_0PPtt
30、=D_PQrRReI?_Re pSSYMBOLSreference area for body force and pitching-moment coefficient evaluationplan-form area (2 L Rdx)circular-cylinder section drag coefficient basedon cylinder diameterlocal cross-flow drag coefficient at any z stationbased on body diameterconstant of integration (r: )2ca, -900 R
31、d xcross-flow drag coefficient . 0 ,4p(foredrag_body foredrag coefficient q-0A- body foredrag coefficient at zero angle ofinclinationincremental foredrag coefficient due toinclination(lift _body lift coefficient q-0 A/body pitching-moment coefficient about station(pitching moment_mean body ,liameter
32、 (_)local cross force (normal to body ax-is) at anystation x on bodybody lengthfree-stream Mach numbercross-flow Mach number (-Y/0 sin a)local surface pressurefree-stream static pressurelocal surface pressure at zero angle of inclinationlocal surface-pressure coefficient ( p-p_local surface-pressure
33、 coefficient at zero angle of(P.-o-Pqinclination ,. qo /incremental surface-pressure coefficient due toangle of inclination q0 /free-stream dynamic pressurebody volumepolar radius about axis of revolutionlocal bodv radius at any station xfree-stream Reynohls nun:ber based on maxi-mum body diametercr
34、oss-flow Reynol(Is number (I?o sin a)cross-flow Reynolds number based on _lianleterDbody cross-sectional area at station xSbt:oV_oX_tttXYZ_XV0body base area (at x=L)timefree-stream velocitylocal axial velocity at body surface at anystation xaxial component of the stream velocity ( Io cos a)cross-flo
35、w component of the stream velocity(t_o sin a)axial distance from bow of body to any bodystationaxial distance from bow of body to pitching-moment centeraxial distance from bow of body to center ofviscous cross forcereference lengtt) for moment coefficientevaluationordinate in plane or inclination no
36、rmal to axis ofrevolutionordinate normal to plane of inclination and toaxis of revolutionangle of body-axis inclination relative to free-stream-flow directiontan_ t oo,P -+ P oC = po+ V_o:o 2illi(i iicll( (t“ “_ i_,i lil(! t)rt_ure ,it the surface of thel,Iv i,.,.,i_,)(._ r,)., 1l(ySJ“-=2 _, I-_0 ta
37、n _ cos 0+ (11-4 sin 2 0i tl 0)Pand writinglu,+= V0 sin a1“%= Ir, COS athe siirfii(.(, l)rcssm( in ,I_ ;ti:,t I,_,ikr)t_ lr,h,r,nce 7/ancy, particularly at values of 0 near 180 , is evident whichincreases with increasing distance from the bow. Down-stream of the maximum diameter section (figs. 2() a
38、nd 2(d)the discrepancy increases very rapidly.The disagreement that exists at the afterbody stationsresults from effects of viscosity not considered in the theory.as will be seen from the following: R. T. Jones, in reference8, showed that, for laminar flow on an infinitely long yawedcylinder of arbi
39、trary cross section, the behavior of the com-ponent flow of a viscous fluid in planes normal to the cylinderaxis was independent of the component flow parallel to theaxis? For an inclincd circular cylinder, then, viewed alongthe cylinder axis the viscous flow about the cylinder wouhlappear identical
40、 to the flow about a circular cylinder sectionin a stream moving at the velocity Vo sin a. Hence separa-tion of the flow would occur in the yz plane as a result ofthe adverse pressure gradients that exist across the cylinder.Jones demonstrated that this behavior explained the crossforces on inclined
41、 right circular cylinders that were experi-mentally observed in reference 10. That such separationeffects also occur on the inclined hull model of the “Akron“is also evident from the pressure distributions in figures2(c) and 2(d).While the treatment of reference 8 explains qualitativelythe observed
42、behavior of the flow field about the hull modelconsidered, it cannot be used quantitatively for a low fine-ness ratio body such as the “Akron“ for at least two reasons.First, the influence of the term2 tan fl cos 0 sin 20of equation (12) is to distort the typical circular-cylinderpressure distributi
43、on, given by the term(1-4 sin _ 0) sin a 0so as to move the calculated position of minimum pressureaway from the 0 = 90 point and to change the magnitude ofthe pressure to be recovered on the lee side of the body. Overthe forward stations of the body, where tan fl is positive, theposition of minimum
44、 pressure lies between 9t) and 180 andthe theoretical pressure recovery is small and even zero at themost forward stations. For the rearward station where tan flis negative, the minimum press,re lies l,etv,er_ 0e nn,l !*(_.and the theoretical pressure recovery is large and incceasesproceeding toward
45、 the stern. Fro“ the hull of the “AkrmVmodel, the theoretical line of minim,l,n pr,-f attack of O_. I2:,itllll 1NO. +i ime Selmrali,m lllll (,lll ,)qll“ iI 111 :1,1:,-_ The lq,(iTlt ,_)lk of . P. Y,)tlII_2 311| I. ta; hliJIfl e, b rq Ilc, !_ i.t,13 :r,.q ia : :trllC h)r the, tUl+_lll_tll Ill)w cll4c
46、 Lls well.5 It is of illtori,-;t _o lll ill this _i_llrt. thltr ,_,.ll t_! .IILai :l.2_ _ ,_1 !, :_,vJ .: : . _.;,. ,_rrllHiHlllltn pressure )t,lOllleS ,oriented dose ill th,. ,iilt.(liOll _ll ri, :_.!: _, _v,. ,;:a t,.ri. :; _:4 ,!zero inclination it IllUSt. Of course, b_, lI(WIII:%I Io this axis.P
47、rovided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-i I“_ _ “should contain . )_lit of s3ntnmtri(mlly ,li,q.,s,_! v,_ i,e- mthe lee side (of. reference 12). These vortices should in(,reasein strength as the plane moves rearward nnd eventu_ll,v, if _hebody
48、 is long enough, shouhl discharge to form a KumSnvortex street as viewed in the moving moss plane. h,wed illCOMMITTEE FOR AERONAUTICSthis moving plane tile vortices wouhl appear to be shed andslip rearward in the wake, but viewed with respect to thestationary body tile shed vortices would appear fix
49、ed. Thisprocess of tile growth and eventual discharge of tile lee-sidevortices shouhl occur over a shorter length of body the higherthe angle of attack since the movement of the cylindricaltrace in tile cross plane at any given station is greater thegreater the angle of attack. For a low fineness ratio body,however, t
