1、/“/NATIONALAERONAUTICS LIBRARY “CaliforniaInstitu ADVISORY COMMITTEE FOR AERONAUTICSIIrlIRTIMI: RI: P()RTAlmil 19_ asAdvance Cc_fldential Re :t L6C13FIELD aF FL0W AI_Y0TA JET ARD EFFEC_ OF JETS 011ST_ OF /ET-PROPELLED AIRPLARES_y _rbart S. RiCherLangley M_ial Aeronautical La_atar7Langley Fie.BILITY
2、CF JE.T-P.“,OPELLED AI_PL.%_-S_y Herbert S. !/LProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-I! ,:.,CA ._C? “To. L_CI3 CONFIDENTIALincrement of jet temperature over stream tempera-ture at pclnt (x,r), degreest m Incremer.t of _et temperature over s
3、trea_, tempera-ture _t pclnt x cn jet ax_sjet-te_._erature cceffi?tent _u-_!_X _xial distance from print at which _o* in accord-ance with law of spreading _h_t holds at sub-stanttal distances from orifice, w_uld havezer3 cross sectionradial distance from jet axisradius of jet boundary at secti:_n xl
4、“_i= R V F =R/12:xV : xv_C pt._astcoefficient (_;_2S.).wing areail, 12 ccnstants cf velocity “:rc.fii-_;_eflned in text: , T _ I_ _.,_ s_ frrth-i “I -_ “ rune tlJns ._f T sndeel:ned in textU/V;o*-spre_alng car_.eter (_Pen as 0.2g6)_et-spre,llnS _3ar_qeter (t_ken ac _._ccnstar.t (taken as _ _) sire _
5、 funr tion“.Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-f-:j_eAbtdzr,Cit5e_FT_CONFIDEITIAL ITACA ACR He. i%013jet-induced inclination of flow toward Jet ax!a“aith subscript w, wing do_n_wazh averagedbetween Jet orifice and horizontal tallmean Jet
6、-induced downwash _ _v1_ : “ “ _ “ “ “ “local inclination of jet _xis to general flowangle cf attack _f thrust axisang!c cf aftack of thrust axis.relative, to averageflow between .let and t_,il _a- _w_/area cf Jet orificescan of h.-riz_ntal tail“et a_ic iro_., center _e k_ri-lateral dizt_.uce af _ ,
7、_zont al ,_aldist_.ce zf t,nrust axis below center of g._“av_j+.- cL._-.,.,_entcoefficient/_ n_.menth1wing chorddistance of nacelle inlet ahead of ce:.ter rt“_ravity; _o_ r_ured parallel to thr,_zt _xi_airpl_.ne lift coefficient -/Lift “_; p.ewer cnunless z1_b_cripteq k_l_-_S JIncidence .f horlz_nta
8、i ta_l, degreenelevator _._ coeff!ci,)nt._ _O_IF-cV-x E!_v._tor s_an x (Elevator :hera) 2CCNP!DF:iTI .!n. acs_.:l:tic:_z au:tablc ?of aet_.inin_ t:e 6.0,.-_i,$d st. Zhe :,.,l_.o_:_-_tail _-_9_v:i:_.g-:-u,.:bedjet z:cbc:s-C“S._ _:“ _- :“ C_I_C9 , “_;_ _“2_ :“:“ -_ _ C. -Velocity com,cheats parallel t
9、o t:,e jeb m-.:.s iniuce(;.b_ the :-t :._ the e“t_! 2io; are o-_:J-_.-_,in the. _s , _efl_._d-_._,_I. SLr.i,.!:-a_,al-s . This o_;iszic.neff/.c_s a _ _“ “,-_“:. ,. “ “ficatizn in ti:at it ._c:_.icsreTce,;e:-.tation of the f_?_Jof _.o;: out:. ,_ P,hc ._z bY a oln_ in a :_r_:._ is u,o_nted ou_ in refe
10、z_enee :, “ -“_ “ t:e “ “ “rjboundary“ of the “*.-_:_ io_ but J.s :_to ._“_ Gi. .i .3._rg_ d.stznce_ _ “ the _ot -:is. T:c ac6uai fl_v,_ o=_-, -,a-d,_Ar,s c!os-_i “- equiv,lent toZi.“te the _eh ca: ._,_ ,. ,.that “ . a ,. ,-_,_,-_._-7 a “,-.e:,:of =in:z a-:n_-t:_.c j2_ ;_. ,_.“_-*_ j,_t t:.c -._:._u
11、_:-tior._,. . _:7 ,c,-:“:-ssib-!_t:-.ms ab_:dcned ;“co ._.-.,_ the .pt b_._ _ ._e_ ,._ _ _ :“ “ 7 “ “ “: f .3_._!o:v ,SU_S_QO t: e ,.:Z. :;_.e nelfcc_-._-_ .-_., is -0“,:-:._9:,. :- ,_-_te1:i“c:-:-t._leal_v-_t.on at zp._“_o_-t i_: the j_:t_sstu:_ed to b_ .ro-crti%;_i 5t:._.;_.-,-_u.u=,_o :e_,cen _le
12、local jet ve!oc,t V :.n.ir.:ezt_c_._origin the .,_t_s_ueads_ as the one-third power of the axial distance x. Sone further com-mcrts on the screa_.“ of a jet are made in appen_ B.For the velocity prcf_,!e (fig. 2), experimentallyfound for a jet 7_n a still fluid, I1 = 0.0991 and12 = 0.0b_O95. For gre
13、ater generality k will be leftundetermined for the present. :_ith these values of I1and I_, equation (_) has been used to prepare figure 5,“ . o -, -vILich sho.:s the v_ria /_oT_-j_cI vzithEquation (_) has also been used with equation (2i topi-ovide the variation of U/V “_“ / _V_-T_c,_n kx shown inf
14、igure jThe point ori_sin cf the idsa!ized jet of the presenttreatment, -:hich is the origin of the coordinat_ x, islocatad a distance xj upstr(_ of the or-_fice of theactual jet. (See fi Z. I.) The value of xj varies. _, m t “ ,_ value is 2.3 crif_ce dx_ncters,un *c ou_ a, ave._oeHere precise values
15、 can be obtained from figure 3 v:ith R_nter,w,oted as the orifice radius ,qj.Flow inclinat!on.- The condition of continuity maybe exnressed by formin_ the str_.: functionC0_ ID IENT IALProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-n/,.-_:=-_R Uo. L
16、6C15 COhq_I DENTI AL iiJ_r|= I (u + V)r drCutside the Jet this expression is approximately_, = UR2II + Vr2T (5)if the small values of u induced by t_m jet in theexternal flow are ignored. The _igle at “:hich theexternal flow inclines toward the jet _xis is then, fcrsmall _ngles,rV Ax. _ T + _ JThe u
17、se of _ and _ in place of R and x,respectivel_; (with ratios of the f_rm x/_ permitted,however) serves te eliminate the tl_rust as a separateparameter. “_hen this change is made in equ_tl-n (6)if x,/_ is written for its equ_l R/_. Then by the usecf equations (2) to (h) there results finallykIl2 x 0
18、, 11 is very small, and equa-tions (7) s_ud (7a) become ao.oroximately(7b)where the assumption that ( is small is dropped. Suchconditions may occur with rockets at tal_e-_ff and at l-wspeeds. For rockets the mass flew from the nnzz!e isnot taRen from the stream and, az has been stated, thecoefficien
19、t Tc must be multiplied by one minus theratio ef the s_re_ veloclt_T to the Jet exit velocityfor use in the fo_nulas. Rocket jets are ordlnar!ysu_ersonlc near the nozzle and the equatins are notstrictly applicsb!e.Hot Jet Parallel to StreamVelcct- in jet.- The !ccai air density in the hotJet will be
20、 some w_rlable fracti._n _ of the density inthe free stre_-._. For the present purpnse the temperatureelevation at any point in the Jet will be assumed to b_proportional to the _ifference b,-tween the Incal jetvelocity _nd the ztream, vel_city (see section of presentpaper ent_.t!_d “_ssu_mptions“);
21、that is,t TUT VCONFIDE_TI ALPProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-7.,.-_._- .wCONFIDENTIAL .,_.:. ,-,_ ,.-,._, iTr. L_CL3where T is e con:tent. (See fig. l(b) for nctaticn.)By the perfect-gas IEw then1tI + -T= 1 (3)uU! _T-“JV“,ith tze inc,
22、.-p-,rat._cn ._f tna density inctor c,_e_ “:;-.Iibe mcdlf.ed t_ zsol;the equations for _?.e ceid j .t_ the i,ea%e.l jet. Tz,-_r,;cm_ntum e iuat_cn .:Ill take thef “:ZL_where;,T. 2 + lI U _ = o (9)C;/ !2 V 2_-_12,R211_ u r dr = I“ U R RJ u UO0 i + T- -UVi_ := 7: F.- UO_ ? TE -U VS_-_pe_i-n _-f II _r.
23、J 12 _ w_n the c_rr_._ximcticnc :“,“?T_,“-“TIALProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-/_L.CA AIR N_. L6c_13 CONFIDXNTIAL_l= I_!12 12I2I2 - _rT2 U1 _,.- KT -J15(IO).,here _. is a constant t be !eterzfned b7 subst!_uting- - _ :.he eccnd ofvalu
24、es ccml;uted -_ the exsct e_:_t_n_ .n sequations ,!C) An average value cv_r th. range cfgr_stest ntere3t, 0 :,lon.)C?:_2:!LE_TI.QLProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-. =,_,_A ACR No. L6C13 CO_IDE_I)_L 21flow in the cold jet can be made eq
25、ual to that in the _:_ L63!5or-d+ d+_= 5t ani + tan-lr (20)Lifting-line theory suggests that an averageweighted accerding to the chord :.rould i_rcvLde the mostaccura_ v_lues of tall llft. an unwelghted averageover, say, 0.9 of the tail span would appear to approxi-mate t_is c_ndition. The curves of
26、 figure _, ac_ordLngly,have been prepared from equation (2C) with C.gb t sub-stituted for bt. The curves give the variatlcn efZ/c ,15th r/b t and 2d/b t where _“ is now the effec-tive ;:_an Jet-Lnduce_ downwash acrc_._ the ta_l plane,Is t._e fic;_ inclination at a radius r from the Jet,and r/b t and
27、 2d/b t Iccate th,_ jet axis relative tothe tail o!_ne, as sncv:n in flgire _. The curves applyt_ a single 2at, _nd the dovn-.wash !s adcitive for severaljets.Pztchlng-:_:o_v.ent increme_.ts Due t_ Jet OperationGenera! c_nsiderati_ns.- Ac a glven anzle ef attack,_erstzc, n _f tha jet motors _iil, in
28、 zeneral, change bccnthe pitching moment :_nd the l:.ft coefficient. Confusionwill be avoided if tLe changes _.n ;tching zcment andilft ceeffi,:ien_ are nltiai!y obtal_lcd as func_ns _fthe ?o,:er-off (zero thrust) lift coefficient CLc, whichIs a knc,-:nfunction ._f angle of _ttac, The severalpltc!_n
29、_-lor.ent ncre:-ents due to jet operation are dis-cussad in the foi!owin_ paras_tachs. Each lncrament istc b_ re_:-rded a_ a function of C,LC., The increments aregiven for a single Jet and are to be _ultipiled by then:Tbcr of .iets.Pit_,-_,.,gmot.ant crntrlhuted b_- direct t?.rust.- ifthe thrust aki
30、s ff t_e Jet pass=s a d_stance z belo;-.the eel.tar cf _r:_vitv the tkr_st ,_,ill contribute anincr_:ment_l itching mcm_-nc, ,v._ich is in ceefflcIentfc r_l,C _“ T _-_ k_ _“ A,Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-ACmT = Zc ToThe thrust c(e
31、fflcient Tc, ordinarily will be known asa function of the power-on llft coefficient CL. Inorder tc obtain Tc, as a function of the power-offllft ccefflclent C50 , use can be made of the knownrelation between CLo _nd a together with the relationCL - CLo = aTc ,where CL and CLO are measured at the sam
32、e angle ofattack a and a is taken in radlan measure. A “cut-and-try“ crocedure _a_r be used and a curve of C,against _- can be obtained at the sa_,e time.Pitching moment contributed by jet-lnduced downwasb.-It has been sLown that a jet induces outside itself anaxlall_ sy_:letrlc flow field. The incl
33、ination _ (meas-ured in degrees) relative to the _hrust axis at thepoint (x,r) (see finis. 1 and _) for a given t_hrustcoefficient Tc, , can be deter:nined from figure 5- Asmall deflection Ar experienced by the jet _hen Inclinedto the genelal stream c:_n be deter_,_ined from equation (19)and figure
34、7 and used t_ correct r and then . Theratio of the value _f average down.rash over the horizontaltail %- to the value of is given in figure 8 as afunction of the geometry of the j_t-tail co_2igur,tion.The pltc2, ing-moment coefficient contributed oer jetby the Jet-inuced _ownwash is then, _“ _o_ the
35、 st!el: fixed,_ dCm _ACm(flxe d di t (1 (21)if t_ st“ _ is. _c,_ free and if the jet units mountedunder the wing so that the horizontal tall is well awayfrc_ the orifice, expression (23.) becomesC_ ,_“ ID_ TI?LProvided by IHSNot for ResaleNo reproduction or networking permitted without license from
36、IHS-,-,-26_ (dCm dCm Cha_ _. (99.,_.-_-_r._. _ _oa_ force actin._ uD%sfd, atthe inlet. The .+orce, “;hlcr-is negllglb!e compared _,;!ththe v,ln_ i_ft, equals the m_a_s flc_w-,_er Jeccnd throughthe nacelle _.ultip!led by the srres:,velcclty and thesl,a_ cf the Icca! angle ef attack. _ne contribution
37、tothe a_rpl_n_ pitching-moment ccefiicient isAC_iC =(_as_,Isec) _ sin (a - ) (;_,_)CC_.FIDE_TIALProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-_7where _ is the lever _r-n from tLe inlet og“ the nacellet_ the center of _ravty of the _:._aneand - _s t
38、heupwash induced Ivo_the _Ing _t the n_ce!ie inlet. Theupwash - can be estimated fro_,_.Sigure 5 of reference 5.This upwash is large only when _/c in equation (2_) issr,la!l, _nd its neglect therefore introduces small err:_rin the moment.Pitching moment contributed by boundar-la_erremoval,- The suct
39、ion and other effects of the Jet maytend to remove soze of the boundary la-er on adjacentsurfaces. The pressure distribut,_on .ould be somewhataltered. In some instances fio?_ separation may be ir2_b-!ted, which w,_uld result in rather large changes inpressure distribution. In ease fi_ separatlon on
40、 thewang is suporessed, an increased acwnwash will occur atthe ta:l with a consequent positive pitching-mo,ner:tincrement. The determination of the n,oment changes dueto these several effects must be left to ex_“eriment._%y change in the fuselage p_.tcAing mo:.:ent due toboundary-layer removal with
41、t_zl on may pcsslbly be dif-feren_ from such a change with tail o_f because of teeinterference between the ho_izental tall and the fuse-lage. For this reason the cozpsrls_.n of tests of modelswith tail on and with tall off may not necessarily yieldthe part of the power-on pitch_nl-ccment ch-.nge tha
42、t canbe attrlbuted to the Jet-i_.duced do._n:as-:.Neutral-Point “ _i._n_ts Erie to PowerThe power-on cur_es of Cm against CL for variouselevator _ett_n_s should be -_“_ar .- _ike the power-offcurves. The shift in neutral point due to power ist-_erefcrein units of the wing chord. The derivatlves are
43、evalu-ated at any convenient elevator setting for the stic_-fixed condition and at any convenient elevator tabsetting for the stlck-free condition,CCXFIDENTIALProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-28 C_N_IDE_;TIAL “ i_? . i._ ._. . . From t
44、he earlier di_cu_ion-it i_L/o,S that-_es “J “slons ef the fc._mdAC.n.np- dCr._opAnp =d IL-are not qul_e co-rect, where aC_n is the sur._of theseveral in_.remental moment coefficients of ti%e .ore_edlnparagraphs :itipli_d by t:-_ n_nber of jet units, CL_is the p_wer-cff lilt coefficient, a:.d CL -. t
45、hepoller-on i_./t coefrl._kent. Since CL - Cio is small,howev-.r, e,.t_er of the two equations .s a geca flr._ap_rcxlmaticn. The exact ncutral-pelnt shift is slijhtlydo_ende_,t cn the position of the power-off n_utral po_.n_.,.tue_ _xan:_,le :nd D.scus_ien3Fccif._-cations for a hypet!.et:.csl air“.l
46、ane Dr_eiedbV t_;Inv,in:-reun_d j,_* r.,_rs _re _ven in table I.Deta/._ co:_.ut_.tion_ cf the effect o the Jets _nlongitadinzl zt_biity and t:l.v.a._.eZiv_n “n tables and l!i. ._,_-ymoment rest: tl,._fret boun_ry-l:,.vorremoval th_ msy he caused by j_ action is :or acns!d-.r_d.ih3 conput9 of ilft c_
47、ef;:i:e:_ts andboth ccid .-nd ho_ je_s. Th= mere ir.-:_ort_nt factors csi-culated are tLe toe-in Jet-ind,_cd d_vn,ash anile _vr t?:c._or!znntal tall; the c_._nzes in the pltrhng :_._ment wit-:the stick fzxed _ne with t-c stl: fr_e Cue tm t:_ _o.vn-wash, to the dlrect thrust uo.:ent, and to the nscetlenormsl force; and ti_e co:.respencn_ _.ifts in the stlcx -fixed _._ s_!ck-free neutr_i O3ints.Table ii is s sugce_ted _hcrc _.:;_t:.ccof c_mput_t_.-.,The r_etAod is apgroxl:n_te In that the elf_ct of j:.tdeflection que te _nglc cf attqck is :e_!ected,
