NASA NACA-TM-737-1934 Conversion of energy in cross-sectional divergences under different conditions of inflow《在流入量不同条件下代表性分歧的能量转换》.pdf

1、.3,complete conversion requires a discharge length which de-peilds upon the included angleand the velocity distribu-tion in tile entrance section For that reasou the effi-tie:.lcy(ratio of rise of pressure energy to difference ofkinetic energy of mean veloci,ty) was determined, once forthe diffuser

2、alone, then with the discharge le;lgth neces-sary for complete conversion. These efficiencies are, inpart, widely at variauce, and it was found that the veloc-ity distrilmtion in tile entrance section affects the pres-sure conversion very profoucdly in the diffuser, alone,*but only very little in th

3、e diffuser with exit length,.-_A comparison with Gibson!s experiments at a greater open-ing ratio, concedes the efficiency to be dependent on thisratio, especially for large included angles. Completeelucidation of”thins interdependence awaits further inves-tigations as comparative quantities ,The co

4、nversion losses proportionate to tlje losses by sudden divergence (Caraotloss) are preferable to the efficiency.fiorder .to compare diffusers with different ,energyIdistributions, we assume as efficiency of the. diffuserwith entrance length,ithe ratio of actual rise of energy. . . a,.,k. , INTiOtiUC

5、TIOti,.;.: ,- , ,: , . . .”. . .,., ,.,.: .,. ,. ,. Y-, ,., . Te” results of previ,ous ex,8,rirnent.s”ol,clrcular ,”con-.:;.”;,.“.”.,.i.cal,”,divergent channels,. assume a particu,lai “signifi-“ca.n”c”,ti.i,tinthe scope” of the pr.esen,paper. Figure 1 isa“i,a.tep,tto illustrate the re:u:l,tso,fAndra

6、s. (referencel-,of “Pranciti(reference 2), 3anninger (reference 3), andIiiffart.“(”reference 4) in form of an efticieilcy, qo versus,1.f“tli.eincluded angle 8:. . ,. : P+Pr .2qo=p- .-. -:- .,.,.#12 2) ,:. .” . . ,- *2.,. : , ., ,.,wher.e.in.:,p,”=.s”taticpressure, if= mean velocjty ,in crossSe:dtXOn

7、”:,V“ = d:erisity, subscripts 1 and 2 ther.espective-:1”n#rTo”w;, , .,.,: .,. L. ,.“B,j., .Bu-t his, results. are uncer-tai.nsin”cehe failed to,givd. any exa:ct”definition of the, I.spiral flow or of “the recor,d!dpress ue” . : ,.,.:.The present experirents were made wit,h pies of circu-lar section

8、with straight” conical divergences in air for. . : ,i .Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-.:,:. .,“+ , ,- ,) ! , , ,.;C:o.q,sta.n,:y”dlu,de:“of:.“fl”o”i+.:f“,h”inelud.e.d:angl e 20 with-c:o,:n:sjja,:.cioss-se“ct-ind”tiat”io F/JF2” was .v

9、ari.edbetw.een8 +:26“%ulct”=go .,:., ,.,., ,.:,:. .,. . -.,.,., “I: :,!The spiral flow was prodii.c”ds:by:a guide apparatus.(fan) (fig. .5) mounted between the entrance length and tne.transit ion,pie”cefrom:h”edfi:sta+ta:fi:til%a.i:+elocityas with,”a rigidbody% The flow-id%re+t”ion”ik”ilia”.with tan

10、 .ialcotiponek:t;and w = axial. co:np,o./.nent of veoez.t”y. “Thr“$-.-:;:“*mm X .03937 = incProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-iKA.C.,.,.Tecllriic9T”cxman.dun No. 737 5. . . ,.:. ., . . agd, the $ng.e.vtial doxapone.n,t,.u becomes?f,velo

11、city c,. . . .:. .,.,., -. -herefn” r“y: krbitra-,rrradius, R= pip”eradi,u”s; uR = “t:inJ”v,.elocity;.at “yall,” a:nd k“,= tingie o!:1Qw di-re-.c.til-oiiat, tb wall” .The.8pira,l.momentufi,“ , .,;- !.:., . .must equal the moment of the lift of the blades,P” ,r d A“= - W2Can z t: r I,dP”. ” .y,c .q2i

12、e efficiency is the ratio:,of the actual rise in pressureeneray to-tne difference in.kirietic energies-,1;zp2.w2:d -:L . . :pll:d .-,;,.,m H n- - - -_ . - - .-.- =total,:;:”;C12 22 “$C,22;2; ,;”:,., ,m d,l?- , . /). -Provided by IHSNot for ResaleNo reproduction or networking permitted without licens

13、e from IHS-,-,-/N.A. C.A, .Tecnnicql Memorandum No. 737 7,.,., ,”.”“.”,., :-. . . . .The representative trend of the pressure at the wall,“:illu.strated “iifigurb”7;“”:rov”esthat the pressur”e conver- _sior. is not conpleted in “tfieexit s“.ect.io”nof the diffuser,that there is rather ,afuri?er rise

14、 of pressure in theds.cliarge cllafnbl, As” af%u”lt”; two efficiencies ”can bededuced.nam?ely:. , .7:.:,.! , ,. .-.,. ,.VI fo.r”;.the.22B w2 ; ,rp;: ( 4a).-/ , ,. /- , 27 1.- :.: /?! , ,:The definit ioilof the efficiency solely on the basis of “”illeanvelocity E?, jields an efficiency in accord with

15、equatioa (1) WLOS6 connection with Ttotal is given in, .,.For nearl re”ctanguiar velocity distributions, i.ea,.w=i, A becOmes = 3 W 1 aild tilerof”oret m = ntotalOutside of the rccta;gul?.r“di”stibution of velocity the de- aveloped turbuleat distribution produced with sufficiently).Provided by IHSNo

16、t for ResaleNo reproduction or networking permitted without license from IHS-,-,-.By lt.;,AfiC,.A, Techil.ical,ioandug $To,. 37 -1.ww: e.nt?acelength, is mo:re rea.di-“amenabl.,eto calcula- t.ip.u.;andl:zst.h,ereforegiveq.ibre- ,:. , ,-., . ., ,. . . , ,-. . . . . . . . . .PrW$l *s”.hegrem (.r.efere

17、nc”e 6)”, accri”ing to.whichtfi.e;.poi%tiiesat-a .Reynolds Number o.f .?;,;:.,2,.x 105 areproportionate to the 1/7power of the wall,i,s,tance,dis-closes for the turbulent velocity distribution./ J“!: .:!.:,? , :,. , ,., ,., ,.!- Wj” 1/7.” : “ “ -: ( r-. = l-.$.“.-Wmax :R :,.:.: %.”.:“:.”, .,. .“, ,

18、Wnax being the velocity in the axis of the pipe Then.tlie:“mean velocity. is .,.:.-“ ,., ,.,., ., .-ii.- = om816.,:.wmax.rithe “relation of”the actual flow of kinetic k.seenunco- Lditionally cogent, the final result ,Pu = : (fil”z- w2) tan 8 with divrgent angles up to f)”.dep,icts the .,.3 .:,: . i=

19、 .,.resul.t;sfor snooth pipes very WO1l. :.:”,!. . . ., :. .,.,. “, ., .,. . . . . ., .1A 1Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-N*A. C.A. Technical !ier.ora)dumNo.737 97aAs regards the velocity distribution in the disch-argechallne_land co

20、nsequently .of B, no summary predictionscan be mad?,. Ihit otie result of the present investiga-.tion.i is that the velocity dis”tributfon in the eection ofmaximum pressure of the discharge channel is somewhat morecomplete than the developed turtmlent velocity distribu-tion and practically independe

21、nt of the angle of divergenceand,ofthe,distribution in inflow section.: . . The.evaluationgave ., -”-Figuring with a meaz”-B = 1.03 for turbulent velocitydistribution in the inflow section, and,wi.th, iw=.,.=”.,.lufll:nd =0. +2croSs -sec:onratioje .,o-btain”rT “:,. . = 1.05.TtotalThe pressure losses

22、 “pv, computable from equations(3) and (5) as . 2.A - 71“:p B .,l?2/“-.-.-.-.-= -._ _2, 2; (WI - W2 ) 1- (gL)2 “U72 )can be divided in”towall friction losses pr and conver-sion losses PU”* The former can be.defined like the .,”;losses in a straight pipe as i) v.: J“ .P P “.-,:4,.J”-”:.-.:.,;j 2 -2;,

23、. . . .:-:, ml - 2.,.;!,.,.!-. . 7 . .f j : 2-r.!;,.J:.,-, ,. 3, -“23% .,.,.:! ,.,. .,Taking cognizance of these frictional losses, it yields-.,.:”h . (3?2,=P1)! ATO .-_ = I+4tan,. - r?l 1,.- (1. ,.,-. 2 . ;).2 - .“,:,8;.,:,.,.,.for the”diffuser alone, and, .,. . :.”,. A+ _ _+ .,._7L,._l%4 tan (-y-

24、- “RF “,:. ,for the dif fnser mitll:.discharge chain-e”. . For spiral flow”, .equat.ion (3) gives.: .,2?2 y.-.“. .,: P2 w2 d - .,flpl 1 dl? .,totl = -_.-.+- _L0;.ti1P 12 ”Pc12W-dF-/c22 w2dF,rC2.= + AL,i,verein and P-= Pr=)+. l P 2 r. ,?:.Tor the special case of rigid spiral”U”= constantald w = W = c

25、onstant, and efficiezlcy can be deduced wilosefactors lend. t“nemselves nore readily to measurement. Tkeeilergy is computedas .F .2+p#JwdFE=J P(r=o) + p2 r . ,.:= P(r=o) .-2 “ o 2 R 31= “R”“ g 2 ;. .-L,.-.,.L. L 1Provided by IHSNot for ResaleNo reproduction or networking permitted without license fr

26、om IHS-,-,-.N.A.C.A T.achnical Memorandum. No.,737 11so-+liatthe energy.oequat ion. (2) can-be”.written, :., .,.-, P P -2, . .,., .PR1 -ti12 - R2 “Z”W2 - V “0. .,.,.,:, ,., .,;,and,f,ina,l.1-y,.t,e“.if,ci,ency , ., . . ,.:., : ,. ,. , .”=. R2-pRl- .-.P “_”2 - 2 “ (Wl - W2 ),.,:,. - .;(8).,. . .,. .“

27、O,bvio.usly“the thus-de”fnei,e,fficiebcy .“isvalid only forthi,s,;a.ssumed.s“p.iral”dis.trih.utiop and inappl”ic.able to otherdist.ri.:b,ut.io.ns. . ,.:., .,. ; . .,.,. ,., ., . El ;“.,2,.;,;s“4i%ut ion.(. .Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS

28、-,-,-12 N.A. CA.Te:h-nijcalMexnorandumNo. 737.,separately for differentand of the !spiral, flow,:w.er:;madeentrance lengths,Figure 8;slio.,y”Sthe:.”elocit.ydist ib.utions -.*:X = f(;:).,recorded. in pure. axial flow without diffuser. The profilewas symmetrical to the axis ofltfie:uppe;-:The istru”rn

29、e“:cr“epa-ncya-s”n”obtained :“”It”ijkghtbeliie to erroneous”measurement of the static pressure through th” wall “ori-fic es,* or it might have been caused b erroneous u,easure-melt of the tOt:ai fires”sur adjacent“-to”tie,tiall. Anothersource of error is the inevitable velocity fluctuation,since the

30、 pitot tube records the mean value of WZ withLr:espeetto”tirne”“fidis“coriseq-dentl:altiaysgreater than!: .:“(neanjz .“ , .From the velocity distribution we deduced the value.A, which compares thti”:flow “o.f:linetiicenergy per secoildwith the product of flow volume GL l? and tlekineticP (._L;:)2 “:

31、 .,.“energy of”mean veloe”ity,. =,0.0083,-Wl.2 .-.-.-_.-.-_._suhungen ,aq.W.l.ln:iod.el,len,!l3el in, 191.2.,:tilem,e.asu,r.g-=ilts .wer,ejmade w$,tz,a,i”OS9 gird.o.r,:i$ice,di,a.met8T,and, gav,e,static press tiresaproximately 0.8 percent too low.h.-Provided by IHSNot for ResaleNo reproduction or ne

32、tworking permitted without license from IHS-,-,-.-.xiii-. c ;AT6e.hnical Memdra.iwlum.Eo:.73?. 13!:This fi,gure .agr,ee.s.,mi.ththat o. ., ,- . ., , . . . . . .: ”.”. :. ,.for the individual sec”ions. The lack of symmetry with t“hepipe axis is du to inccuraci-q,s im .w,o,i.,s:tep“.int,egration . . ,

33、., . . , :r“ .,. r.“p”.=.pR”+ j P.U2 ii + .2sinz d.(.p,- P,) “., R R:,. .“,-.,.“.,.,.“ll;igu”res11-16 ive velocit components, u”/*l and *i/iversu”s rl/Rl. :The vales “ “the ,r”ings“totheother “half of the test diameter. , . ., .,.The i.nstrumen.%al a:ccuracy; again chec”ked”by coniparingthe. integra

34、tion result with that from the .standardnozzle,ranged within -1 percent and i-2percent. ,.The flow of energy- per second throug. ,.eachsectionwith spiral flow, was” determined as for axial flow andequated to the flow” energy per second of the mea-n velocity.These equations are:.I: “(:-); d,”,for the

35、 kinetic ”energy,. . a. . . ,.,.- .,.,-,.+ jF/yf al?,(Wlj ii. for the” spiral energy, , ,.,., : . . .,., ,. . . ”Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-14 N.A,G.A. Te.chni,calMemorandum No. 7371 ;p% :-, ,r-_ii; for the pressure energy,-1 - d

36、F, for the total energy.FI-2 WI WI.They are given in figure 17 versus entrance length t/D1 .PRThe plot also shows the pressure - at the pipe wallg2 .,r.o ,2W1 .and the pressure in the”pipe axis. b The actual diffuser tests.- They revealed the pres-.-_.-sure long the test section through holes in the

37、 walls, acase iiipoint being shown in figure 18. Trom these dia-grams the pressure pl in the entrance section is obtainedby extrapolation of the pressure carve in the entrancelength, the pressure p2I in the exit section by “extrapo-lation of the pressure curve in the discharge channel up to the disc

38、harge section of the-diffuser and pressurep2iI as maximum pressure in the discharge channel. (Com-pare fig. 17.) :.We start with an analysis of the investigation forpure axial flow. To define ie efficiency accordig to(4a)22 -Pitotal = ._._L9P -A. #)2-2- W12 1.F2/ F2 - - fF1(;: d conforma”oly to A as

39、 func-1.tion of the entrance length (fig. S). The value B =1F2F2(; d , lilcorrespoilds to the flow of kinetic,)energy per second in section F2 ,ust be defined from., I1.Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-.,I: N.A,:,C.A., Technical Memora

40、ndum No. 73”7 15j ,:,.,.:.,; -:.:,.,.:, ,.IL- the y,l.ocitydistrilmtion survey in section Pa ,., which,Ihmwqve is very difficult unless the flow is orderly.AS,:.,:”!,., . . . . ,. ,.“ f, ., . iP2 - P1)II =1 71.!.”. qtotal = - .-.-.- ._ .-.- 7,wlU?-j2 ,., j .:W23 dFfor irrotational flow with 2Dl entr

41、ance leilgth. Theseefficiencies are valid only for the diffuser” fitted withentran ce length. “The determination of other efficiencies,say-, according to equation (8), wherei only tfieall”:.“pressure and F2/F1 are evaluated, was omitted, becausethe coalitions LO = constant and v?=c could in no caseb

42、e exactly complied witil. The efficiency for the diffuseraione was also omitted because the ueasureme:t of the,ve-Jocity distribution and of the flow direction directl”y inthe exit section involves great obstacles aild even the. ex-trapolation of the wall pre,ssure”up to tile exit sectionengenders g

43、reater inaccuracy as a result of the marked”pressure gradient, especially with larce -$. ,.!.Tbe distance ta/D2 of the section of maximum”pres-sure from the discharge section of the diffuser is shown”iProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-.

44、,+. -,Y. A.C. A. Technical lemoraridun loa71 737 19in figure 29 plotted against $8 for the three exploredSpiral f,low$q .Translation by J. Vanier,National Advisory Committeefor Aeronautics.RET?ERENOES1. Andres, K.: Versuche ber die Umsetzung on lfasserge-schwindigkeit in Druck. Mitteilungen uber For

45、sch-ungsarbeiten. V.D. Io (1909), p: 76-2. I?rancis: Lowell Eydr. Exper: 1883.3. Bnninger: 2S f.d. ges. Turbinenwesen 3 (1306), p. 12.4. Iiiffart, A.: ,lberVersuche mit Verdichtungsd:sen. Mit-teilungen uber Forschungsarbeiten* V.D,Ia (1922),pa 257.5. Gibson, A. H.: Proc. of Roy. Sot., London A 83 (1910),P“ 366.6. Karman, Th. v.: Zs f* ailg. Math. u. Hech. 1 (1921),p. 233*Hikuradse, J.: fiber turbulence asserstrmtmgen ingerad