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Mu(JTfpound(JrtTJ ciVQAVOI

Bu(nl tiiC napafio x1c tl1t ocpatplKfit OUIJ~Etpio~ 8lti l xroJJev lJ(av )Juvov IJEtCtP)llTi)v -tirol TtlV an6oTQOI V ll1t6 t oO KivTPOO Ifie otQyovolt Ex0IlEV t~ 6))00 9EwplioEl ltrilotT1)Jo 4 amptpCa)v

aoatQtlKOOV lilOl KUU0 1IJOU (F) o~f 1 5wtlK llO (Xl npo16v t Ol V 1C00(IOI(J (P) Kai aopuvwv (U) Qc be lOltOU d KltiOE aEOlV laxuE~ npocpavG)c 11 ox~a l C

Y-+ Yx + Yp + Yn = 1

6nou YK n 1(QlQ popoe 6va)oyiQ ro) aoalanKoD K

Of f)u9jloi ~El ocpo pfu tKaorou QUOtot1KOO e(wu

_ (dYp ) m = dmp ldl = Ap uY - OF ----u- =M(I-Z ) (t)

m = dmx dt = Ap (uYx - Ox _~x ) = i ~IZ (2)

(dYp) m = dm Idl = Ap uYp - Of - d-t - = ( -)MZ (3)

(4)

h F = C (I -1) hp = Cp (I -1)

hx = (1 - P) ql i ( 6)Cx

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~~ = ~I[ C(T-T) - 1Z + L]IAA (7)

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dY F )1---= [Yr- + Z -I) (8)

dr Ap[)F

Tt~ tK nl eIOll)(gtpoundCIllt (2) )a~ p6vo~Ev tl)v lCotavojltlv tfiC OV)ICEVTPOXtOO TOt 6Eamplool1llCoD

dY x ril --= [Y + iZ] (9)

d r AplJ x

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d7 B Y Yx lt p ( -FIRT)

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dT M (jf = AAA [CA (1-1) + L] (10)

dY F ~I ( II)dr- pOA [YF -I]

El TI)V rcEPIOXlV B( r c ~ r S r0) Elva I Z = I lCat 01 ~~(wshy0pound1 (7) Kat (9) Slooov

683 NOtf1PPIO~ 1970

dT ~[ = -- [Cn IT -PI + L-q) ( 12)

A)H

dYx 61 -- ~---(Y + i) (-t 3 ) d ApD 1l X

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t~ ~AOY

(14)

q - L [q - L JI [ YxoJT ~ --- - _ - + T - 1 1 + ~- ( 15)C t c ) I

rr [ 1 q)X0- ~ (T-Tol] In(1+ Y o)-= [n shyr L

( 16)

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Y Opoe -~ (1 + to) ovaptpEWl poundie trv EnlopooIV TOtl po-

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1[ = 1aO D

ETti011 e il = drn dl = d( Dpcr ) Id l

IT MEV dlmiddot trae = 2 pDd D

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r( I r = ~- [1 + ( 1 + i - oTa9 pVrtllllJ

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rllK = K CF ex

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nlNA2

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0099

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610 a lt oop 6 puOjl6~ tjc ~etaltpEpoIliVle OEPIlOT11lOlt dVOl apKETtl JllKP6c amplOTE va elvQt 686VOTOlt Tj O1lvtx1OLe lf e KOUmiddot OEWe

684 NotJ-l~pOr 1970

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E l~ I ~ rsin0 (18)

Nnlt a4- il ( t) 0 a ( ) T Tr a0 rsin0 - GtEJ Dr rsm0 sInEgt =

= Etrsin0 (19)

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NOtIJPPLO~ 1970 68S

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01 ap l9110v Reyn olds 100 Kat oui OICllpOPOUe TlJl6 e ptgt9~ol)XOUV illtavo lx9f1 S00 onai de TOe 6noia~ EX OUV npouap)lou9f1 livo A[1ftOt OW)~llviaKO I (II ) 810 tampv aWATlv[aKWV TOUtWV KCLl polle Tfie IJolne poundK -rfie aTay6vot Ttl ~Olleeuroiq O-ClltJiUe(ilv UUl) ~VWV 6011l OU)leuroflo pound( TO ICEKAIIIeuroVOV )lClVO)ltTpov To olacppa)l a (10) Kat TO )lav6JJEtpOV XP IlCJl shy H uuaTpoCP~ ooe 6E1KVUttal d~ TO Oxll)lQ 7 poundIJcpavilEI Tflv IIEshyJlCUOUV SUl TT]V )lETPllcrtV tfle napox fie fOCat poe 0 UWAIlV (9) yiOTllv HJlilv Tn de nJv ncptoxilv tGJv 400 COOt ROo 1tOA lK ~~ yurshyauvOEETCll ~lta4l IC WV lKf) l(uraulCpoundu ~ e (17) e~ pound)cia)lIltOC IJ ea viae To IJeuro YlaTov -roC-ro t10pTUTal Kat poundK -ro) pu9)l01) pofle aVpoundJltotfjpoe (12) 8Ul TOC oVpoundP IltJ1f1 poe tOOTOU EJtlTlrxci vOIJ ev -rfie Jl61 nt poundIC tf)e uTay6volt TO pound7tLOUIITlTOV PEU)lCl ciE poe npOC ICCl UTEpnv ltpO)TOyPCtltplat V fI UtClywv TOU Kouul)lOU cpwTiCETClI TIj PonGeiq AuXv[a~ nupashy Eie TOV n[vaKa oi6eTClI 1) omaetAKouoa OUVQ)lle olli 01acp6middot )(tWOE~ 750V (14) H cpWtOpacp IOI C nuv OtaOOXI Kampvamo[wv pOue apl(J)lOve Reynolds Kat OloSICtcp6po~ Tl)lae puiJloO poflc Tile l(a0aew~ poundm tUiXUVpoundClL TO DOl9euroiq ICI VllIJCl-rOypacp llCfle TOO KaVallJOU poundK -rfi~ aTayovo~ npoe tei ilsw Ete T6v au-rov nishy~Inxavlie Faslax (I )) epyalolltvnt)Ie TOxu-rllta400 cpcu-r0ipamiddot V(lI(CJ OiSpoundTClI eniOlIe 11 6vCtA1Xne Tf)C 6ma9euroAKOlKH 1e Eie Tflv ltPII~)V avO 6wTfp6Aeuro 1tTOV TU1ttlCo napaoElY~Q 6iltie1ClI elt Tilv 01tlU9tAKo~aav )oYltP TplaaV KClt 111V orrtafltAlCouaav )6Y19 eiK6va 2 h9a e1lCo iovtUl ouo CJmola 0 JlEta~ 6 -rampv 6rwiwv axlllJCtTO H )lEtaJ30AT] TOO pu6IJoC pof)e tf)e )lCtllle EK -rfe xpovoe EKTljJOTClI de 030 UTClyovOe QUICEi OflJJQVTlKT]V enili pam v tIti -rlle 6TnaeefICOu~le

686 NotI-PPlOt 1970

~

H~ bull bull 00

o Alit bull bull 0

6 6 bull bull 02

H~bullbullbull 00

6 bull 0

1IY1 bull bull OZ

EX middot 7 bullH xorOIJOPYJ dVrfYJlEwJr (1v(JT(orpiir 1ff(11 rp ~CIoJdtIP

OTaydva

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fTINA32

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10

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00 01

I CD

21 67 2137

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1080 1079

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3247 32 16

02 2107 1078 3 185 05 2019 1075 3094 I D 1880 1070 2950 20 1629 1062 269 1

100 594 1040 1634

400 00 1130 075 7 1887 01 0818 0830 1648 02 0673 0796 1469

1000 00 0 1

0601 0332 I

0520 062 1

1121 0953

I 02 0224 I 0567 I 0791

NNe A(j8fo~ Reynolds

ltP EraOted UV8)H)v Q() j c nj Wl~

CDF poundVIJTtMOT1r ti1lK10poundb~v(J1c M( reIPTjr

CDp EVlTrJffJtT fh tllrOt J)(IlI)(f1]C wif) C1(]p OTOr

CD middotO)tlti (TIJlICde(Tnj illltf8c)t(otJl1TC

i f~Y t)uy f~ ontoGtJltoooq k6YI ol~~afo H tAQrnl)OIt ti)C 6nla8EAlCoucrnC J[potPXETO ~ uno TnV orutQvTtmiddot ICV tAU TTWOW ti) btlfPUvt taK~ oOOt POqli)t )~6Yf) (tUl1iCiOOt toO po6)100 poilc TtiC ~u~l) C ilC T f~ a ruy6 voc

Til ilvtJltSpro Cu~nEpoC)IOTO 9u Ouvouo080uv lCutwdpw ~i Tilv lCaOOLV Tl)V (JWYOV10(u)V npoe 510tOnwOlv l Glv lholtp6pov tmshyop6CJewv lGlV XOPOlCt l1PIG1 IICGlV tilc po ~C tni laO qlOtVO~ltvOO OU100

n H Gt06Epcl KOUGampOl e

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n-pO C TOV iPOVOv 7tOPCL)ItVSI Oto6cp6C

(ltD 11)It OTo6epo = 1ltshy

ft Dl = OtQ8spci = K

We lOtiTO OAAWCJTC npOEICUyenC lCoi onO TtlV 6sWPl1T1 1CV elvashyAUOtV_ Til OO)I1tEp6cr~alo tpqgtOivOvtOl Eic 10 Oxi])IutO 10 lCoi 11 ~v6u KOTOf4)oivE10l1l i~(1)tl1OlC If)C 0106epd Ct t~ UPXIshy1Cij r 51 0)lttpOu lCollampV o uv8lICOOV TOU 1tEpd~aAAoVTOr 1-1 r pushyIp IlC1l napaOTOOLe lfle olo6EPU K OOvaptJ)OCI Tf) r 6PXllCtlr OIO)1EtpOU OHl cnoOl)lOV 1tSpt6oAAOV 5i5ETOI d r TO oxilJlO 12

611i tfl v Ott~ PEGvl1 OIV tilr poundm5paoEwe Tftr 0 XET IICft C ToXllt lltOC toO Qtpor np6c tTiv OTO)Ova btVl1)10tOYPolPi]6n 11 XOU(Ue CTta shyyOvwv apXJKampv 5la)1ETpwv 15 lCal 20 m nl 6Tav to pCU )IO t oO Ittpoc elxpound oxttllCilv toXOtlto ror npOr til v 0(1(611004 [II sec To unotEHo)lato E)1cpavi oVtOl Ei r t() Oxf))IO 1 Quro~6 pua 8)1or lCallOCWe dVQI Jll1cpOnpor dr tTlv 1ttpi1ttw(Jw orcou l shyXO)lsv OXETIICi]V tOXtJtfllO ItCp0r Ole npOe tTlV cnoyova Tout o 5uvoTo i va ~~l1Yn~ POOEI fl )Ipoundtwpopd 8tp)l6tlllOl Ii 61toiu Hpound(Xt l tOv po6~ov ICOUOEWr tOOv CJtayovlo iwv

0 It~p ICOtU Tll V OttAEOO (V too 1tep l ~ tf)e ICQIO)1EVT]C CJtarOshyVOl 8EP)lDI VE10I Olll ~EtUQOpUlt 6Ep~611ltOe tIC til e ~wVllC 0Vt1shy

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c1l e anotEAECJ)IO ITtV AAottWO IV t otgt poB)1ofi )IEtOcentlO~d~ tf)lt )1 6 shy~11lt tIC Tfl r otoy6vor np6r to e~(a) 511Aooi] UoTtWOlV l OU pushy8)100 ~ooOtwlt bull~ cU)ou il KoOale t~ r crtoy6voC tvtOC toO Qtploo PEOpClfOr tGlv O4111 s(C ~VEIPltvlte 11)V )IOPcentlflv laquofJ~IOmiddot 1toCJPt06Eicrllr centlAoyor)) )I t AofFO~vOV OIlAOOi] to )Itttll1tOV tilr ltPAOYO ToOto ~XEl tillt a1tOt~AEO)lQ 6 po6)1oe 1(UOOCtoc va dVDl nAOttrop~Voc Oiitw 5ul tQ( (JOv6flCac to(nEI ~6)IQtOC ltpoi vnQ I On 1) OXEt11CTl tuxotTl~ tugtv 04 m5ec d vo t Jl eyo~OTeuroshypo Ti)r )I EYi CJtl1t poundltllpE1tlllr 5ul 1tAi]pll (pACryU 1tEpt lflv 1(010shyPtvll v atay6vo

N II_ bullbull 00

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H nlEGtt etc ttlv trwPclVEIUV tflt otaY6vo~ bEV rtapOuoui~EI ti1v GUlliv fllJll V1(09 6)11 tliv iiKtucnv tflc bwpaVElut Etc (0 np6cr81Ov )IEpO Il nitolt dvOt )lquAuttpa )lIHotrrCllI5i ooo

auavt i) noAIKlj-ywvia ToltO npOKUAEi l1lXll)ltvoUC pu9J1out KUOOEWlt dC to 1tp609lov ptpo (11lt a Tcryovoc EvavH lWV AOI shynrov 9toEWV 0 IJ EY IO lOC pu8J1oC JCuuot wc pound1l(PClVi~EtCll Ei 16

otacn~ov orUlEiov 00((1) t~l1 )dlClI blud JlUpOUOt(I~Etal 1([1(0shy

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Kala Tflv KUOOW t(i)v crtayov loiwv T~lt Pcv~[ vn tVToe ptOjlClrOt aepolt nOpElTlPliOTl em Soov OUlCtvEI 1] lOXUtT)t lOu PEU)lClrO~ T6crov fl q)AO~ nA IlOl6~El nEPloo6rEPOV npot TitV oToy6va To JtIJPIVOV nEpij3AT1)lCl TO 6noiov nEplI( AE iEl lIlV oCCliova KOO (shyOlUlCll AEJtT01EPOV ToOto oUVUtu1 va tlTlY TlOn ~lt P60lV t6 Eril)lQ 8 Ono pound1lq)ovi~OVlCJl al OtaOljl Ol pOIKoi )PCl)l)lQ( orshyrIVEt KCl90piCoov Co lt6xo~ 100 1Wp(VOU JtCPlpAllJlOTO~

0 0 2 m m

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Oo middot l~ m m

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130

120

110

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15 2 25

I v XpovOt u(JnpilaEOOI

H hUUOlt li)~ OTClYOVO~ otv poundI VQI uKoplulo 6U1 n) v lvopllV TI)~ KOUoE~ 6namiTOl va )lEOOAOOrOll XPOVLKOV H 01CtOTlljlU IKClVO V npoe np09tp)lOVOIV tit~ oto)6vo~ Koi tOtJlIOlV noooshytTlrOC tIVO~ npot Evopltv ti)t KUOOcWe OunucElvcH q)UOlICOV va 6VUjlEVl] TIC Oll 6 roovDlt OOtEP110EOX aufuvpoundtaL 1-1pound niv aulT)Olv ti)~ 6PXtlCfl~ OtUIlEtPOU ti) e OlClYOVDlt

0 Il E tPTl9Ei~ XPovOt UO[Epi)OEWC Ol)VOPtflOEI tfl~ 6PXlKflc j)aCl-U-rpOU b(OElOI EIlt -rov ni VOKO 3

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0 5 2 0 25

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688 Not~Ppo~ 1970

Y K = KOtll Supae av(tAo((a tO u ltruOtQllKOi) K P = nipoundOllt

gt o(t1lt

mK =- ~l acatoDCL)atatIKo K A = brUpaVClQ

P 1tUKV~

D auvtdEOtll~ 15laxooEw~ toO mlatouKoC K t - Xp6vo~

M pl)a)l6~ ~(nmiddot)IiltJEOX Kaoa-iIlO)

ftoODarov ttpo1Jor01tOlicrewc tiC avnoptlcrtwr

atOIXEtO)lEtPll((~C )6yoC 6V (U)p6CI~Wlt

dStKt) ~vaaAJtia tOU auaTOtLKoi) K

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d on1 9e PIl6111C E evt pYpoundICl lvepyOltOlll mwC V d811(6C O(ICOt

He =- apl ell~ HlIynolds tV POiKT) OllVaptllCJtC

crucrtPOltPti

L Aov96votlltJQ 9EP)l6tqC trOrjllcrEWlt

Xp61o KauoECiH

OPX1KT) ollijlfrpo tfJc OtOy6vOC

I a vacptp EtCU de t l)v Ermpa VElov r i~ crtay6voC C aVOltp t PCTOI tic nlv wv rw dvn5p6(Jt~

o = aVQlPtPErCll d o ue(aAllv on6crtaaiV U1t6 t1)v CtQy6vQ A avaqgtpoundpECQI de ncp tOxliv A B ilVUqlEpEtal ELC 1tEPIOXilv B

BlpAloypa+ia I VD lAI U Dru ple~ Corn J1 lIs lio n An 1~ ~perlllllfJl ~ 1 tilm[loJtISOo

o r t wo Ib tO ri middot~ CII middotln ] ng Sci 11 jJi - iOl (l 9ti middot2)

1 M Hmiddot t1nfj C4 1Odun 1311rnlnO a f 1I tLUld Droplet AtI~a ll (~ In ClI~m Srcit ~ ~ u 1 111 31)

a P l JIflt On 11 1l IIUmllrful t nll erlYllI1 DCllllc l trJon~ Bul l(J n a mI COIIl i)mmiddottiull lU~ )r lCt_ (ombliMllnn 1IIr Flnrn r )1middot 2 ltS (I J I

II M lolnlQlw I i ~I(lrll llilll 11 11 1 T nnu~nc ( or I nl middot tl lil lJllIlIL l h1 till lli t CDlIl lu tgt lIn n uf Sln g lfl lito III vI L lu ld Fl1 Ih ld I ~ 1 lJ (I I~ ~)

5 E MOEditl middot T lw (HflbU Umiddotm I f Druplcl3 0 1 LIq ui d J- Il OI

G r d1ia mJ I ClilIU Lb SlllI JJ (I) 111- 14 (Iu)

D )puldlrJJ I ~)m JIO5[ Ulll Gr Cu m [lue llon r til ~ ( t 9 fl-n

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9 H HI G H Ilh ll H UI arid 1 ~lmJlS~HI b- S ~U[lQlt IlIlII1Jll COIII~ bUtillo ll 11 I t] l-I 2~ RclulJohl N Y I ~ DrJ owllu Q )(1Il II r ]Jutl n ttlll lmiddot l9

10 G M r ~= i SYlIl poSl u m un ttHll bul t1on p 732 (I [IH)

II J U)~I1 fl o ju Id U Carr J Chem P hYl lcs 26 p 327 ( 19ramp

t 2_ f Cr Pdtm i1r On lI ~e fill tll ln o r Sllq le DrtJ TI ~ ur Fuel llllJI OR x ydill11 jl A Utlo) lillCf fl It Pro pu lsio n ~f- p t 7~- l j lS (1 IlIl)

I S bullS K IiTnoCll 1 Id H Ii()(I - J lJId I 12 (1 1i5 fl )

It n yOO UUl aw l D W ood J e L Plo(Julslo lJ 28 I 18 (1 9flS)

fI na(lovu(l t[1Yoaia In JXt Tll~ olxolowdjq gt7001 rV~EW1 n iC AVld lVIOV E)tJlI Yrt _Erol(Jw IIngeAalwv TE XACO (hk ro 61loiav eufQdCOflpoundI ra eV)(l(IIltMitlC flor To lCIealWTI)(cW fll(O eHt)tafhl el TO Igyaanio~ov middot CfP1(JO (JfI~V11 EJFepmiddotlJdv-shyvowtij roO J(fJ R ( Ll1JoxQrroraquo TTi~ bAArVtij( eIfIQlmtt middot lrOIH)(j lJIttyeiO IQ(k T~ 1I ttfolav eXPI~OpIl htrTrJl t trlugIQTW TiA-n F11(JwTo 6j~ n il x A poundtV~fJJ lOi (h)shy(JrxQv 1 Q1) K fl E ((JrU()CUD I) oui n~ to Oe((l l TOtI r nil )(uraaXeWV tal UlWO(J1 tiAOrratv rij lTCI(OJUTIt ryr avax e-ur

The effect of sIze and velocity on the burning

conditions of fuel droplets By H Koumouhol - G Stephanopoulos

Silmmary

The wide nso of ~ pray injPot Uun for the burning or a li quid fuel in a combustion ch a mber IHS lead to the ntluU fol an oxLcus ive analys is of th n processes which govern lhe cumbustion of liquid aerosols

Thi Jllp cr p rescnt~ lheorutical (l nd experimenlal aspects involvuci i n the burnin of a sin gll fu el drople t I ti s nl5sumshymiddotd tha t Ihe singhgt dropl cL li llllling i ts(tlf r l rn ai ns a probl~m or fund amen tal irliporlanclJ in combus tion re~ middotmiddotarc h In Ihtl pItsen t tl ll ll lys is uf 1 s teady Slate llderogc neo lls combushys lion as encounlIlHl in lh t burni ng of a liqu id drop let f a spherically 6ym Hlol ric model is asSUIIWC[ wi th a fin ito cold bound rt ry bulll a nam l holner the latter corre6pondiug to the llquid - val lu r ill tGImiddotrace

lo 56t up the matlw lfHllic il l model of thu ph enomenon in cunsidero Li on a numuur of s imple assullli-tions is ne(essary

Th us II wns- IlSsumcd th al 51(o1(ly s tal l cO mbu g l ion OCC UJS undt1 r i s o bari ~ cotlditiuns that the hea t ril ltlused as a result of th ) the mical n-lc lion is removNJ by conduction and Jnass tranl fet th ~lt quantili Oi s uch as thermal conductivi ty dCrlAi ty etc 3 r(gt considei d to be illdepend ll nt of temperashyture tl lld cDrnpositioH and so on

In case of ze ro 8cti vHtion en ergy a (lame toni r)[ inHnit lsshysimal thickness resul ts a t which the weight fr ac tions of both ruel and ox icii zer become zero TIll wllole nli lQ is there shyby middotjlJ para tad intI two lfgions rn th i fi rS the cllerll or dlttmiddot mica l readion ie Zlro In tlto scond the reaction goes to comple tion r h ll an alysis then knds t o ll fysk lO v f i1 rst ord el dil1( ren ti a l o qll a tion~ from hich x plid t ~olu lio ns can bt t ~kc n Amung ot hc-Js lhe fu el muss low rfllL t he ( ombution s urface IflT1 p cra t rm~ and lhlgt fuel frac tion a t Uk liqu id s urface art Cl vtainod

TtL l Nov iclmiddotS lo kes equ ation tor viscous axisy mruetrico fl ow was solvtJ d by u6ing a digital computer Thwl he pressure and vorti city pruOls around the burnin~ droshyplet along with the drng coeffici en t ( 01 various Reynolds num be rgt using the air velocity as a parameter werO ob fa inlHl

Exporun onlal m eaSUrf JJl ents have lead to values or burning cUllStan Ls for va riou air-now velodties and in itial d op lc t ~ i l)s Ultimat ely a condition is Icached whon du e Lo d(t shyc(0Rsed temp era ture the weight rraction or rt lle lanls preshysen t in the Nnc tion lo ne can no longl1 r be t unsumf)u Then unburued or paJti ally burn ed ma k middotl ilJ pas~e~ lll ro ugh Ut e lone FU I lhnr d O( I~asc in torllpcra lUlu li3su lls in a 1Illumiddot clion of the reaction rale and SV on unlillinalJy the 111 11 11 van ishes

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Mu(JTfpound(JrtTJ ciVQAVOI

Bu(nl tiiC napafio x1c tl1t ocpatplKfit OUIJ~Etpio~ 8lti l xroJJev lJ(av )Juvov IJEtCtP)llTi)v -tirol TtlV an6oTQOI V ll1t6 t oO KivTPOO Ifie otQyovolt Ex0IlEV t~ 6))00 9EwplioEl ltrilotT1)Jo 4 amptpCa)v

aoatQtlKOOV lilOl KUU0 1IJOU (F) o~f 1 5wtlK llO (Xl npo16v t Ol V 1C00(IOI(J (P) Kai aopuvwv (U) Qc be lOltOU d KltiOE aEOlV laxuE~ npocpavG)c 11 ox~a l C

Y-+ Yx + Yp + Yn = 1

6nou YK n 1(QlQ popoe 6va)oyiQ ro) aoalanKoD K

Of f)u9jloi ~El ocpo pfu tKaorou QUOtot1KOO e(wu

_ (dYp ) m = dmp ldl = Ap uY - OF ----u- =M(I-Z ) (t)

m = dmx dt = Ap (uYx - Ox _~x ) = i ~IZ (2)

(dYp) m = dm Idl = Ap uYp - Of - d-t - = ( -)MZ (3)

(4)

h F = C (I -1) hp = Cp (I -1)

hx = (1 - P) ql i ( 6)Cx

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~~ = ~I[ C(T-T) - 1Z + L]IAA (7)

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dY F )1---= [Yr- + Z -I) (8)

dr Ap[)F

Tt~ tK nl eIOll)(gtpoundCIllt (2) )a~ p6vo~Ev tl)v lCotavojltlv tfiC OV)ICEVTPOXtOO TOt 6Eamplool1llCoD

dY x ril --= [Y + iZ] (9)

d r AplJ x

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d7 B Y Yx lt p ( -FIRT)

npoc 7t~ poIT ipro anho11oillolV toO 11f)OPA11)Jol~ 9EWPOiJjJpoundv 6-u 11 toXl TllC QvtISpaapoundcu~ Elval lircElPO jlE 6rco tf)pounda~o t o nalCl~ fie CWVI1e t lle dvtl6p6oc~ v6 lCuOiatota l 115poundv6v O UtfO 96 olOKphCojlpoundv 5uo nEP1OXa tT1 V A Koi B EI Ttl V 11 EPloX11 V A (r ~ r= rc) CVUI Z 001 5t t~I(j(taEH (7) Cal (8) filoouv

dT M (jf = AAA [CA (1-1) + L] (10)

dY F ~I ( II)dr- pOA [YF -I]

El TI)V rcEPIOXlV B( r c ~ r S r0) Elva I Z = I lCat 01 ~~(wshy0pound1 (7) Kat (9) Slooov

683 NOtf1PPIO~ 1970

dT ~[ = -- [Cn IT -PI + L-q) ( 12)

A)H

dYx 61 -- ~---(Y + i) (-t 3 ) d ApD 1l X

At t~lcrooOW (0) ( II ) (12) ml ([3) 5Boov ta~ KO taVop6~ T ri~ OtWIlOKpacriuc tOU KallcrlllO)) Kul toO 6euroIOO)t tKOCi pound~ t6~ ouo ntptOX6~ A Koi B AI t~IOWOt U auto euroIvOI YPOIlIlIKeti 1lpoomiddot tTlC topoundliIt ouvoll poundVOl vo t1tlAo900v poundUKO)~ TO cmotpoundAto~oshyto tGw OAOKA11PWOeWv 5pound00uy to~ KCHWOI tKltPpaow 010 tOV puapov Ilpoundto(popd~ tf1 Pat l1~ TO) KOUO [1l0U t J1V Opound PIJOK pooiov Tc els tl1v tWV l1v oVTlopomw~ Koi T11 v aKtTvo rc TO) IJEtoonou

t~ ~AOY

(14)

q - L [q - L JI [ YxoJT ~ --- - _ - + T - 1 1 + ~- ( 15)C t c ) I

rr [ 1 q)X0- ~ (T-Tol] In(1+ Y o)-= [n shyr L

( 16)

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Y Opoe -~ (1 + to) ovaptpEWl poundie trv EnlopooIV TOtl po-

O~oO IlEta(flO poo )l tlt l1 6 SE eurotEpOe o opoe ~ (T - TU) de

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1[ = 1aO D

ETti011 e il = drn dl = d( Dpcr ) Id l

IT MEV dlmiddot trae = 2 pDd D

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r( I r = ~- [1 + ( 1 + i - oTa9 pVrtllllJ

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pWV tXEI 61Tooux8ij 6n 0 pu8jl0e OVtl 8pocrEWe Tfe KauapoundWlt 015Etoi ono t ije axecrpoundox

rllK = K CF ex

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Al(i crOVOIlUOjl o) tooV (14) Kol ( 16) npO KU1T1el 011 o 16yoe rel rt poundIvetl avoloyolt np6e 10V pua~IOV KOOOEWlt To)To crTll10iVEI on tAanOUI1euroVOO l OU poOpo Koooewlt tAOttOUlOL KCli 6 10yoe re r jl t cruvenElUv 1l tWV I1 aVTt8poopoundux va n1110Iolt npolt 11)v otayova ToOTo K010qlOLVEtOI Kol et~ TOY nLVOI(O 1

nlNA2

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o o 04 27

50 25

0099

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a

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610 a lt oop 6 puOjl6~ tjc ~etaltpEpoIliVle OEPIlOT11lOlt dVOl apKETtl JllKP6c amplOTE va elvQt 686VOTOlt Tj O1lvtx1OLe lf e KOUmiddot OEWe

684 NotJ-l~pOr 1970

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[Iy)(tv pOt~ -shyr e l(~UO I I-i O U

I lJ yx h t pwaq Yo o fuyOvou

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middot OAoV t6 1t pol1oy6lJEVOV ICQuatjlOv Kat TO 6luy6vov KQTQvashyli (J1COVt(II Jl t WrOtt)IOUIl Ot)ftl KOUOlllOV v6 OlonEp) Til (00 Ill ltVtlOPUCJ(W (jIll DEVtlCO D mxxoX) np6lt TO euro1w oCn r6 otJy6 vo y toO ((1 tow

9 c p)IOKpoolo

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T

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rso~VlIOtW(77 feAh 1J

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(1 )

dnou

H ~1iawOllt ((7) ovvotOt va Olooltocr9tl Eilt ouo tootoxp6vO)lt OXUOI)Out t~IOWalSllt

E l~ I ~ rsin0 (18)

Nnlt a4- il ( t) 0 a ( ) T Tr a0 rsin0 - GtEJ Dr rsm0 sInEgt =

= Etrsin0 (19)

6la eli v tniAUOlv tOO aV(JIiEpfl) B(P110l1101toll18 lllJt90ooe t(i)v 1tftPUOIl~VWV OlQqgtOpOOV Ii 5t opl9jJllt1Kn A00l~ poundnEtEvx81l ~i tnV Pon9E10VllAeuroKtPOVLIC OO lgtnOAo1lOlOC OUl f) 1t POE)~iCJV al KOtOVOl1al tlie nleOEWlt Kal -rne crumporpfle ntptl tT1lt Olo~ y6voC KaL ot 1ljJOt tilc 61nCJ6pound)K000lI~ oui 8 10qgt6 po~ tljJalt TOO 6p16Jlou Reynolds 00 Kat a [ bt l~ p6cret btl toO p06jJoC Ko601S WC tEPI Tne KOIOJlEV11e ota16volt

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--

NOtIJPPLO~ 1970 68S

---([a--shy~ 2

fogt 12

~------~~~________J~==~

~I~ 9 ~

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01 ap l9110v Reyn olds 100 Kat oui OICllpOPOUe TlJl6 e ptgt9~ol)XOUV illtavo lx9f1 S00 onai de TOe 6noia~ EX OUV npouap)lou9f1 livo A[1ftOt OW)~llviaKO I (II ) 810 tampv aWATlv[aKWV TOUtWV KCLl polle Tfie IJolne poundK -rfie aTay6vot Ttl ~Olleeuroiq O-ClltJiUe(ilv UUl) ~VWV 6011l OU)leuroflo pound( TO ICEKAIIIeuroVOV )lClVO)ltTpov To olacppa)l a (10) Kat TO )lav6JJEtpOV XP IlCJl shy H uuaTpoCP~ ooe 6E1KVUttal d~ TO Oxll)lQ 7 poundIJcpavilEI Tflv IIEshyJlCUOUV SUl TT]V )lETPllcrtV tfle napox fie fOCat poe 0 UWAIlV (9) yiOTllv HJlilv Tn de nJv ncptoxilv tGJv 400 COOt ROo 1tOA lK ~~ yurshyauvOEETCll ~lta4l IC WV lKf) l(uraulCpoundu ~ e (17) e~ pound)cia)lIltOC IJ ea viae To IJeuro YlaTov -roC-ro t10pTUTal Kat poundK -ro) pu9)l01) pofle aVpoundJltotfjpoe (12) 8Ul TOC oVpoundP IltJ1f1 poe tOOTOU EJtlTlrxci vOIJ ev -rfie Jl61 nt poundIC tf)e uTay6volt TO pound7tLOUIITlTOV PEU)lCl ciE poe npOC ICCl UTEpnv ltpO)TOyPCtltplat V fI UtClywv TOU Kouul)lOU cpwTiCETClI TIj PonGeiq AuXv[a~ nupashy Eie TOV n[vaKa oi6eTClI 1) omaetAKouoa OUVQ)lle olli 01acp6middot )(tWOE~ 750V (14) H cpWtOpacp IOI C nuv OtaOOXI Kampvamo[wv pOue apl(J)lOve Reynolds Kat OloSICtcp6po~ Tl)lae puiJloO poflc Tile l(a0aew~ poundm tUiXUVpoundClL TO DOl9euroiq ICI VllIJCl-rOypacp llCfle TOO KaVallJOU poundK -rfi~ aTayovo~ npoe tei ilsw Ete T6v au-rov nishy~Inxavlie Faslax (I )) epyalolltvnt)Ie TOxu-rllta400 cpcu-r0ipamiddot V(lI(CJ OiSpoundTClI eniOlIe 11 6vCtA1Xne Tf)C 6ma9euroAKOlKH 1e Eie Tflv ltPII~)V avO 6wTfp6Aeuro 1tTOV TU1ttlCo napaoElY~Q 6iltie1ClI elt Tilv 01tlU9tAKo~aav )oYltP TplaaV KClt 111V orrtafltAlCouaav )6Y19 eiK6va 2 h9a e1lCo iovtUl ouo CJmola 0 JlEta~ 6 -rampv 6rwiwv axlllJCtTO H )lEtaJ30AT] TOO pu6IJoC pof)e tf)e )lCtllle EK -rfe xpovoe EKTljJOTClI de 030 UTClyovOe QUICEi OflJJQVTlKT]V enili pam v tIti -rlle 6TnaeefICOu~le

686 NotI-PPlOt 1970

~

H~ bull bull 00

o Alit bull bull 0

6 6 bull bull 02

H~bullbullbull 00

6 bull 0

1IY1 bull bull OZ

EX middot 7 bullH xorOIJOPYJ dVrfYJlEwJr (1v(JT(orpiir 1ff(11 rp ~CIoJdtIP

OTaydva

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fTINA32

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10

I I

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00 01

I CD

21 67 2137

I I

CDp

1080 1079

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3247 32 16

02 2107 1078 3 185 05 2019 1075 3094 I D 1880 1070 2950 20 1629 1062 269 1

100 594 1040 1634

400 00 1130 075 7 1887 01 0818 0830 1648 02 0673 0796 1469

1000 00 0 1

0601 0332 I

0520 062 1

1121 0953

I 02 0224 I 0567 I 0791

NNe A(j8fo~ Reynolds

ltP EraOted UV8)H)v Q() j c nj Wl~

CDF poundVIJTtMOT1r ti1lK10poundb~v(J1c M( reIPTjr

CDp EVlTrJffJtT fh tllrOt J)(IlI)(f1]C wif) C1(]p OTOr

CD middotO)tlti (TIJlICde(Tnj illltf8c)t(otJl1TC

i f~Y t)uy f~ ontoGtJltoooq k6YI ol~~afo H tAQrnl)OIt ti)C 6nla8EAlCoucrnC J[potPXETO ~ uno TnV orutQvTtmiddot ICV tAU TTWOW ti) btlfPUvt taK~ oOOt POqli)t )~6Yf) (tUl1iCiOOt toO po6)100 poilc TtiC ~u~l) C ilC T f~ a ruy6 voc

Til ilvtJltSpro Cu~nEpoC)IOTO 9u Ouvouo080uv lCutwdpw ~i Tilv lCaOOLV Tl)V (JWYOV10(u)V npoe 510tOnwOlv l Glv lholtp6pov tmshyop6CJewv lGlV XOPOlCt l1PIG1 IICGlV tilc po ~C tni laO qlOtVO~ltvOO OU100

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(ltD 11)It OTo6epo = 1ltshy

ft Dl = OtQ8spci = K

We lOtiTO OAAWCJTC npOEICUyenC lCoi onO TtlV 6sWPl1T1 1CV elvashyAUOtV_ Til OO)I1tEp6cr~alo tpqgtOivOvtOl Eic 10 Oxi])IutO 10 lCoi 11 ~v6u KOTOf4)oivE10l1l i~(1)tl1OlC If)C 0106epd Ct t~ UPXIshy1Cij r 51 0)lttpOu lCollampV o uv8lICOOV TOU 1tEpd~aAAoVTOr 1-1 r pushyIp IlC1l napaOTOOLe lfle olo6EPU K OOvaptJ)OCI Tf) r 6PXllCtlr OIO)1EtpOU OHl cnoOl)lOV 1tSpt6oAAOV 5i5ETOI d r TO oxilJlO 12

611i tfl v Ott~ PEGvl1 OIV tilr poundm5paoEwe Tftr 0 XET IICft C ToXllt lltOC toO Qtpor np6c tTiv OTO)Ova btVl1)10tOYPolPi]6n 11 XOU(Ue CTta shyyOvwv apXJKampv 5la)1ETpwv 15 lCal 20 m nl 6Tav to pCU )IO t oO Ittpoc elxpound oxttllCilv toXOtlto ror npOr til v 0(1(611004 [II sec To unotEHo)lato E)1cpavi oVtOl Ei r t() Oxf))IO 1 Quro~6 pua 8)1or lCallOCWe dVQI Jll1cpOnpor dr tTlv 1ttpi1ttw(Jw orcou l shyXO)lsv OXETIICi]V tOXtJtfllO ItCp0r Ole npOe tTlV cnoyova Tout o 5uvoTo i va ~~l1Yn~ POOEI fl )Ipoundtwpopd 8tp)l6tlllOl Ii 61toiu Hpound(Xt l tOv po6~ov ICOUOEWr tOOv CJtayovlo iwv

0 It~p ICOtU Tll V OttAEOO (V too 1tep l ~ tf)e ICQIO)1EVT]C CJtarOshyVOl 8EP)lDI VE10I Olll ~EtUQOpUlt 6Ep~611ltOe tIC til e ~wVllC 0Vt1shy

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c1l e anotEAECJ)IO ITtV AAottWO IV t otgt poB)1ofi )IEtOcentlO~d~ tf)lt )1 6 shy~11lt tIC Tfl r otoy6vor np6r to e~(a) 511Aooi] UoTtWOlV l OU pushy8)100 ~ooOtwlt bull~ cU)ou il KoOale t~ r crtoy6voC tvtOC toO Qtploo PEOpClfOr tGlv O4111 s(C ~VEIPltvlte 11)V )IOPcentlflv laquofJ~IOmiddot 1toCJPt06Eicrllr centlAoyor)) )I t AofFO~vOV OIlAOOi] to )Itttll1tOV tilr ltPAOYO ToOto ~XEl tillt a1tOt~AEO)lQ 6 po6)1oe 1(UOOCtoc va dVDl nAOttrop~Voc Oiitw 5ul tQ( (JOv6flCac to(nEI ~6)IQtOC ltpoi vnQ I On 1) OXEt11CTl tuxotTl~ tugtv 04 m5ec d vo t Jl eyo~OTeuroshypo Ti)r )I EYi CJtl1t poundltllpE1tlllr 5ul 1tAi]pll (pACryU 1tEpt lflv 1(010shyPtvll v atay6vo

N II_ bullbull 00

_ hooo p~ 1

I oCl lol 110

I n~h OY otOO I~~ middotga4lmv nO~LILOY

g trv II ~IUlo~

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H nlEGtt etc ttlv trwPclVEIUV tflt otaY6vo~ bEV rtapOuoui~EI ti1v GUlliv fllJll V1(09 6)11 tliv iiKtucnv tflc bwpaVElut Etc (0 np6cr81Ov )IEpO Il nitolt dvOt )lquAuttpa )lIHotrrCllI5i ooo

auavt i) noAIKlj-ywvia ToltO npOKUAEi l1lXll)ltvoUC pu9J1out KUOOEWlt dC to 1tp609lov ptpo (11lt a Tcryovoc EvavH lWV AOI shynrov 9toEWV 0 IJ EY IO lOC pu8J1oC JCuuot wc pound1l(PClVi~EtCll Ei 16

otacn~ov orUlEiov 00((1) t~l1 )dlClI blud JlUpOUOt(I~Etal 1([1(0shy

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Kala Tflv KUOOW t(i)v crtayov loiwv T~lt Pcv~[ vn tVToe ptOjlClrOt aepolt nOpElTlPliOTl em Soov OUlCtvEI 1] lOXUtT)t lOu PEU)lClrO~ T6crov fl q)AO~ nA IlOl6~El nEPloo6rEPOV npot TitV oToy6va To JtIJPIVOV nEpij3AT1)lCl TO 6noiov nEplI( AE iEl lIlV oCCliova KOO (shyOlUlCll AEJtT01EPOV ToOto oUVUtu1 va tlTlY TlOn ~lt P60lV t6 Eril)lQ 8 Ono pound1lq)ovi~OVlCJl al OtaOljl Ol pOIKoi )PCl)l)lQ( orshyrIVEt KCl90piCoov Co lt6xo~ 100 1Wp(VOU JtCPlpAllJlOTO~

0 0 2 m m

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o t(~ec ) 3

Oo middot l~ m m

K 0 0 09

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K

130

120

110

DO(mm) 100L---~---~--~---_

15 2 25

I v XpovOt u(JnpilaEOOI

H hUUOlt li)~ OTClYOVO~ otv poundI VQI uKoplulo 6U1 n) v lvopllV TI)~ KOUoE~ 6namiTOl va )lEOOAOOrOll XPOVLKOV H 01CtOTlljlU IKClVO V npoe np09tp)lOVOIV tit~ oto)6vo~ Koi tOtJlIOlV noooshytTlrOC tIVO~ npot Evopltv ti)t KUOOcWe OunucElvcH q)UOlICOV va 6VUjlEVl] TIC Oll 6 roovDlt OOtEP110EOX aufuvpoundtaL 1-1pound niv aulT)Olv ti)~ 6PXtlCfl~ OtUIlEtPOU ti) e OlClYOVDlt

0 Il E tPTl9Ei~ XPovOt UO[Epi)OEWC Ol)VOPtflOEI tfl~ 6PXlKflc j)aCl-U-rpOU b(OElOI EIlt -rov ni VOKO 3

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Xp6voe uonproE Wt sec

0 5 2 0 25

005 010 018

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688 Not~Ppo~ 1970

Y K = KOtll Supae av(tAo((a tO u ltruOtQllKOi) K P = nipoundOllt

gt o(t1lt

mK =- ~l acatoDCL)atatIKo K A = brUpaVClQ

P 1tUKV~

D auvtdEOtll~ 15laxooEw~ toO mlatouKoC K t - Xp6vo~

M pl)a)l6~ ~(nmiddot)IiltJEOX Kaoa-iIlO)

ftoODarov ttpo1Jor01tOlicrewc tiC avnoptlcrtwr

atOIXEtO)lEtPll((~C )6yoC 6V (U)p6CI~Wlt

dStKt) ~vaaAJtia tOU auaTOtLKoi) K

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d on1 9e PIl6111C E evt pYpoundICl lvepyOltOlll mwC V d811(6C O(ICOt

He =- apl ell~ HlIynolds tV POiKT) OllVaptllCJtC

crucrtPOltPti

L Aov96votlltJQ 9EP)l6tqC trOrjllcrEWlt

Xp61o KauoECiH

OPX1KT) ollijlfrpo tfJc OtOy6vOC

I a vacptp EtCU de t l)v Ermpa VElov r i~ crtay6voC C aVOltp t PCTOI tic nlv wv rw dvn5p6(Jt~

o = aVQlPtPErCll d o ue(aAllv on6crtaaiV U1t6 t1)v CtQy6vQ A avaqgtpoundpECQI de ncp tOxliv A B ilVUqlEpEtal ELC 1tEPIOXilv B

BlpAloypa+ia I VD lAI U Dru ple~ Corn J1 lIs lio n An 1~ ~perlllllfJl ~ 1 tilm[loJtISOo

o r t wo Ib tO ri middot~ CII middotln ] ng Sci 11 jJi - iOl (l 9ti middot2)

1 M Hmiddot t1nfj C4 1Odun 1311rnlnO a f 1I tLUld Droplet AtI~a ll (~ In ClI~m Srcit ~ ~ u 1 111 31)

a P l JIflt On 11 1l IIUmllrful t nll erlYllI1 DCllllc l trJon~ Bul l(J n a mI COIIl i)mmiddottiull lU~ )r lCt_ (ombliMllnn 1IIr Flnrn r )1middot 2 ltS (I J I

II M lolnlQlw I i ~I(lrll llilll 11 11 1 T nnu~nc ( or I nl middot tl lil lJllIlIL l h1 till lli t CDlIl lu tgt lIn n uf Sln g lfl lito III vI L lu ld Fl1 Ih ld I ~ 1 lJ (I I~ ~)

5 E MOEditl middot T lw (HflbU Umiddotm I f Druplcl3 0 1 LIq ui d J- Il OI

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9 H HI G H Ilh ll H UI arid 1 ~lmJlS~HI b- S ~U[lQlt IlIlII1Jll COIII~ bUtillo ll 11 I t] l-I 2~ RclulJohl N Y I ~ DrJ owllu Q )(1Il II r ]Jutl n ttlll lmiddot l9

10 G M r ~= i SYlIl poSl u m un ttHll bul t1on p 732 (I [IH)

II J U)~I1 fl o ju Id U Carr J Chem P hYl lcs 26 p 327 ( 19ramp

t 2_ f Cr Pdtm i1r On lI ~e fill tll ln o r Sllq le DrtJ TI ~ ur Fuel llllJI OR x ydill11 jl A Utlo) lillCf fl It Pro pu lsio n ~f- p t 7~- l j lS (1 IlIl)

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fI na(lovu(l t[1Yoaia In JXt Tll~ olxolowdjq gt7001 rV~EW1 n iC AVld lVIOV E)tJlI Yrt _Erol(Jw IIngeAalwv TE XACO (hk ro 61loiav eufQdCOflpoundI ra eV)(l(IIltMitlC flor To lCIealWTI)(cW fll(O eHt)tafhl el TO Igyaanio~ov middot CfP1(JO (JfI~V11 EJFepmiddotlJdv-shyvowtij roO J(fJ R ( Ll1JoxQrroraquo TTi~ bAArVtij( eIfIQlmtt middot lrOIH)(j lJIttyeiO IQ(k T~ 1I ttfolav eXPI~OpIl htrTrJl t trlugIQTW TiA-n F11(JwTo 6j~ n il x A poundtV~fJJ lOi (h)shy(JrxQv 1 Q1) K fl E ((JrU()CUD I) oui n~ to Oe((l l TOtI r nil )(uraaXeWV tal UlWO(J1 tiAOrratv rij lTCI(OJUTIt ryr avax e-ur

The effect of sIze and velocity on the burning

conditions of fuel droplets By H Koumouhol - G Stephanopoulos

Silmmary

The wide nso of ~ pray injPot Uun for the burning or a li quid fuel in a combustion ch a mber IHS lead to the ntluU fol an oxLcus ive analys is of th n processes which govern lhe cumbustion of liquid aerosols

Thi Jllp cr p rescnt~ lheorutical (l nd experimenlal aspects involvuci i n the burnin of a sin gll fu el drople t I ti s nl5sumshymiddotd tha t Ihe singhgt dropl cL li llllling i ts(tlf r l rn ai ns a probl~m or fund amen tal irliporlanclJ in combus tion re~ middotmiddotarc h In Ihtl pItsen t tl ll ll lys is uf 1 s teady Slate llderogc neo lls combushys lion as encounlIlHl in lh t burni ng of a liqu id drop let f a spherically 6ym Hlol ric model is asSUIIWC[ wi th a fin ito cold bound rt ry bulll a nam l holner the latter corre6pondiug to the llquid - val lu r ill tGImiddotrace

lo 56t up the matlw lfHllic il l model of thu ph enomenon in cunsidero Li on a numuur of s imple assullli-tions is ne(essary

Th us II wns- IlSsumcd th al 51(o1(ly s tal l cO mbu g l ion OCC UJS undt1 r i s o bari ~ cotlditiuns that the hea t ril ltlused as a result of th ) the mical n-lc lion is removNJ by conduction and Jnass tranl fet th ~lt quantili Oi s uch as thermal conductivi ty dCrlAi ty etc 3 r(gt considei d to be illdepend ll nt of temperashyture tl lld cDrnpositioH and so on

In case of ze ro 8cti vHtion en ergy a (lame toni r)[ inHnit lsshysimal thickness resul ts a t which the weight fr ac tions of both ruel and ox icii zer become zero TIll wllole nli lQ is there shyby middotjlJ para tad intI two lfgions rn th i fi rS the cllerll or dlttmiddot mica l readion ie Zlro In tlto scond the reaction goes to comple tion r h ll an alysis then knds t o ll fysk lO v f i1 rst ord el dil1( ren ti a l o qll a tion~ from hich x plid t ~olu lio ns can bt t ~kc n Amung ot hc-Js lhe fu el muss low rfllL t he ( ombution s urface IflT1 p cra t rm~ and lhlgt fuel frac tion a t Uk liqu id s urface art Cl vtainod

TtL l Nov iclmiddotS lo kes equ ation tor viscous axisy mruetrico fl ow was solvtJ d by u6ing a digital computer Thwl he pressure and vorti city pruOls around the burnin~ droshyplet along with the drng coeffici en t ( 01 various Reynolds num be rgt using the air velocity as a parameter werO ob fa inlHl

Exporun onlal m eaSUrf JJl ents have lead to values or burning cUllStan Ls for va riou air-now velodties and in itial d op lc t ~ i l)s Ultimat ely a condition is Icached whon du e Lo d(t shyc(0Rsed temp era ture the weight rraction or rt lle lanls preshysen t in the Nnc tion lo ne can no longl1 r be t unsumf)u Then unburued or paJti ally burn ed ma k middotl ilJ pas~e~ lll ro ugh Ut e lone FU I lhnr d O( I~asc in torllpcra lUlu li3su lls in a 1Illumiddot clion of the reaction rale and SV on unlillinalJy the 111 11 11 van ishes

Page 3: 0 poAoC; TijC; TaXUTr'ITOC; Kal TOU JjEyt8ouc; Kara TI1V ...library.tee.gr/digital/techr/1970/techr_1970_11_533_681.pdf · 1970 ~[ = --+ + (0), ~ --+ + ~-- ~ o) ( '0 -~ + ~ 'Av =

683 NOtf1PPIO~ 1970

dT ~[ = -- [Cn IT -PI + L-q) ( 12)

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1[ = 1aO D

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686 NotI-PPlOt 1970

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The effect of sIze and velocity on the burning

conditions of fuel droplets By H Koumouhol - G Stephanopoulos

Silmmary

The wide nso of ~ pray injPot Uun for the burning or a li quid fuel in a combustion ch a mber IHS lead to the ntluU fol an oxLcus ive analys is of th n processes which govern lhe cumbustion of liquid aerosols

Thi Jllp cr p rescnt~ lheorutical (l nd experimenlal aspects involvuci i n the burnin of a sin gll fu el drople t I ti s nl5sumshymiddotd tha t Ihe singhgt dropl cL li llllling i ts(tlf r l rn ai ns a probl~m or fund amen tal irliporlanclJ in combus tion re~ middotmiddotarc h In Ihtl pItsen t tl ll ll lys is uf 1 s teady Slate llderogc neo lls combushys lion as encounlIlHl in lh t burni ng of a liqu id drop let f a spherically 6ym Hlol ric model is asSUIIWC[ wi th a fin ito cold bound rt ry bulll a nam l holner the latter corre6pondiug to the llquid - val lu r ill tGImiddotrace

lo 56t up the matlw lfHllic il l model of thu ph enomenon in cunsidero Li on a numuur of s imple assullli-tions is ne(essary

Th us II wns- IlSsumcd th al 51(o1(ly s tal l cO mbu g l ion OCC UJS undt1 r i s o bari ~ cotlditiuns that the hea t ril ltlused as a result of th ) the mical n-lc lion is removNJ by conduction and Jnass tranl fet th ~lt quantili Oi s uch as thermal conductivi ty dCrlAi ty etc 3 r(gt considei d to be illdepend ll nt of temperashyture tl lld cDrnpositioH and so on

In case of ze ro 8cti vHtion en ergy a (lame toni r)[ inHnit lsshysimal thickness resul ts a t which the weight fr ac tions of both ruel and ox icii zer become zero TIll wllole nli lQ is there shyby middotjlJ para tad intI two lfgions rn th i fi rS the cllerll or dlttmiddot mica l readion ie Zlro In tlto scond the reaction goes to comple tion r h ll an alysis then knds t o ll fysk lO v f i1 rst ord el dil1( ren ti a l o qll a tion~ from hich x plid t ~olu lio ns can bt t ~kc n Amung ot hc-Js lhe fu el muss low rfllL t he ( ombution s urface IflT1 p cra t rm~ and lhlgt fuel frac tion a t Uk liqu id s urface art Cl vtainod

TtL l Nov iclmiddotS lo kes equ ation tor viscous axisy mruetrico fl ow was solvtJ d by u6ing a digital computer Thwl he pressure and vorti city pruOls around the burnin~ droshyplet along with the drng coeffici en t ( 01 various Reynolds num be rgt using the air velocity as a parameter werO ob fa inlHl

Exporun onlal m eaSUrf JJl ents have lead to values or burning cUllStan Ls for va riou air-now velodties and in itial d op lc t ~ i l)s Ultimat ely a condition is Icached whon du e Lo d(t shyc(0Rsed temp era ture the weight rraction or rt lle lanls preshysen t in the Nnc tion lo ne can no longl1 r be t unsumf)u Then unburued or paJti ally burn ed ma k middotl ilJ pas~e~ lll ro ugh Ut e lone FU I lhnr d O( I~asc in torllpcra lUlu li3su lls in a 1Illumiddot clion of the reaction rale and SV on unlillinalJy the 111 11 11 van ishes

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01 ap l9110v Reyn olds 100 Kat oui OICllpOPOUe TlJl6 e ptgt9~ol)XOUV illtavo lx9f1 S00 onai de TOe 6noia~ EX OUV npouap)lou9f1 livo A[1ftOt OW)~llviaKO I (II ) 810 tampv aWATlv[aKWV TOUtWV KCLl polle Tfie IJolne poundK -rfie aTay6vot Ttl ~Olleeuroiq O-ClltJiUe(ilv UUl) ~VWV 6011l OU)leuroflo pound( TO ICEKAIIIeuroVOV )lClVO)ltTpov To olacppa)l a (10) Kat TO )lav6JJEtpOV XP IlCJl shy H uuaTpoCP~ ooe 6E1KVUttal d~ TO Oxll)lQ 7 poundIJcpavilEI Tflv IIEshyJlCUOUV SUl TT]V )lETPllcrtV tfle napox fie fOCat poe 0 UWAIlV (9) yiOTllv HJlilv Tn de nJv ncptoxilv tGJv 400 COOt ROo 1tOA lK ~~ yurshyauvOEETCll ~lta4l IC WV lKf) l(uraulCpoundu ~ e (17) e~ pound)cia)lIltOC IJ ea viae To IJeuro YlaTov -roC-ro t10pTUTal Kat poundK -ro) pu9)l01) pofle aVpoundJltotfjpoe (12) 8Ul TOC oVpoundP IltJ1f1 poe tOOTOU EJtlTlrxci vOIJ ev -rfie Jl61 nt poundIC tf)e uTay6volt TO pound7tLOUIITlTOV PEU)lCl ciE poe npOC ICCl UTEpnv ltpO)TOyPCtltplat V fI UtClywv TOU Kouul)lOU cpwTiCETClI TIj PonGeiq AuXv[a~ nupashy Eie TOV n[vaKa oi6eTClI 1) omaetAKouoa OUVQ)lle olli 01acp6middot )(tWOE~ 750V (14) H cpWtOpacp IOI C nuv OtaOOXI Kampvamo[wv pOue apl(J)lOve Reynolds Kat OloSICtcp6po~ Tl)lae puiJloO poflc Tile l(a0aew~ poundm tUiXUVpoundClL TO DOl9euroiq ICI VllIJCl-rOypacp llCfle TOO KaVallJOU poundK -rfi~ aTayovo~ npoe tei ilsw Ete T6v au-rov nishy~Inxavlie Faslax (I )) epyalolltvnt)Ie TOxu-rllta400 cpcu-r0ipamiddot V(lI(CJ OiSpoundTClI eniOlIe 11 6vCtA1Xne Tf)C 6ma9euroAKOlKH 1e Eie Tflv ltPII~)V avO 6wTfp6Aeuro 1tTOV TU1ttlCo napaoElY~Q 6iltie1ClI elt Tilv 01tlU9tAKo~aav )oYltP TplaaV KClt 111V orrtafltAlCouaav )6Y19 eiK6va 2 h9a e1lCo iovtUl ouo CJmola 0 JlEta~ 6 -rampv 6rwiwv axlllJCtTO H )lEtaJ30AT] TOO pu6IJoC pof)e tf)e )lCtllle EK -rfe xpovoe EKTljJOTClI de 030 UTClyovOe QUICEi OflJJQVTlKT]V enili pam v tIti -rlle 6TnaeefICOu~le

686 NotI-PPlOt 1970

~

H~ bull bull 00

o Alit bull bull 0

6 6 bull bull 02

H~bullbullbull 00

6 bull 0

1IY1 bull bull OZ

EX middot 7 bullH xorOIJOPYJ dVrfYJlEwJr (1v(JT(orpiir 1ff(11 rp ~CIoJdtIP

OTaydva

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fTINA32

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10

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00 01

I CD

21 67 2137

I I

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1080 1079

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3247 32 16

02 2107 1078 3 185 05 2019 1075 3094 I D 1880 1070 2950 20 1629 1062 269 1

100 594 1040 1634

400 00 1130 075 7 1887 01 0818 0830 1648 02 0673 0796 1469

1000 00 0 1

0601 0332 I

0520 062 1

1121 0953

I 02 0224 I 0567 I 0791

NNe A(j8fo~ Reynolds

ltP EraOted UV8)H)v Q() j c nj Wl~

CDF poundVIJTtMOT1r ti1lK10poundb~v(J1c M( reIPTjr

CDp EVlTrJffJtT fh tllrOt J)(IlI)(f1]C wif) C1(]p OTOr

CD middotO)tlti (TIJlICde(Tnj illltf8c)t(otJl1TC

i f~Y t)uy f~ ontoGtJltoooq k6YI ol~~afo H tAQrnl)OIt ti)C 6nla8EAlCoucrnC J[potPXETO ~ uno TnV orutQvTtmiddot ICV tAU TTWOW ti) btlfPUvt taK~ oOOt POqli)t )~6Yf) (tUl1iCiOOt toO po6)100 poilc TtiC ~u~l) C ilC T f~ a ruy6 voc

Til ilvtJltSpro Cu~nEpoC)IOTO 9u Ouvouo080uv lCutwdpw ~i Tilv lCaOOLV Tl)V (JWYOV10(u)V npoe 510tOnwOlv l Glv lholtp6pov tmshyop6CJewv lGlV XOPOlCt l1PIG1 IICGlV tilc po ~C tni laO qlOtVO~ltvOO OU100

n H Gt06Epcl KOUGampOl e

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(ltD 11)It OTo6epo = 1ltshy

ft Dl = OtQ8spci = K

We lOtiTO OAAWCJTC npOEICUyenC lCoi onO TtlV 6sWPl1T1 1CV elvashyAUOtV_ Til OO)I1tEp6cr~alo tpqgtOivOvtOl Eic 10 Oxi])IutO 10 lCoi 11 ~v6u KOTOf4)oivE10l1l i~(1)tl1OlC If)C 0106epd Ct t~ UPXIshy1Cij r 51 0)lttpOu lCollampV o uv8lICOOV TOU 1tEpd~aAAoVTOr 1-1 r pushyIp IlC1l napaOTOOLe lfle olo6EPU K OOvaptJ)OCI Tf) r 6PXllCtlr OIO)1EtpOU OHl cnoOl)lOV 1tSpt6oAAOV 5i5ETOI d r TO oxilJlO 12

611i tfl v Ott~ PEGvl1 OIV tilr poundm5paoEwe Tftr 0 XET IICft C ToXllt lltOC toO Qtpor np6c tTiv OTO)Ova btVl1)10tOYPolPi]6n 11 XOU(Ue CTta shyyOvwv apXJKampv 5la)1ETpwv 15 lCal 20 m nl 6Tav to pCU )IO t oO Ittpoc elxpound oxttllCilv toXOtlto ror npOr til v 0(1(611004 [II sec To unotEHo)lato E)1cpavi oVtOl Ei r t() Oxf))IO 1 Quro~6 pua 8)1or lCallOCWe dVQI Jll1cpOnpor dr tTlv 1ttpi1ttw(Jw orcou l shyXO)lsv OXETIICi]V tOXtJtfllO ItCp0r Ole npOe tTlV cnoyova Tout o 5uvoTo i va ~~l1Yn~ POOEI fl )Ipoundtwpopd 8tp)l6tlllOl Ii 61toiu Hpound(Xt l tOv po6~ov ICOUOEWr tOOv CJtayovlo iwv

0 It~p ICOtU Tll V OttAEOO (V too 1tep l ~ tf)e ICQIO)1EVT]C CJtarOshyVOl 8EP)lDI VE10I Olll ~EtUQOpUlt 6Ep~611ltOe tIC til e ~wVllC 0Vt1shy

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c1l e anotEAECJ)IO ITtV AAottWO IV t otgt poB)1ofi )IEtOcentlO~d~ tf)lt )1 6 shy~11lt tIC Tfl r otoy6vor np6r to e~(a) 511Aooi] UoTtWOlV l OU pushy8)100 ~ooOtwlt bull~ cU)ou il KoOale t~ r crtoy6voC tvtOC toO Qtploo PEOpClfOr tGlv O4111 s(C ~VEIPltvlte 11)V )IOPcentlflv laquofJ~IOmiddot 1toCJPt06Eicrllr centlAoyor)) )I t AofFO~vOV OIlAOOi] to )Itttll1tOV tilr ltPAOYO ToOto ~XEl tillt a1tOt~AEO)lQ 6 po6)1oe 1(UOOCtoc va dVDl nAOttrop~Voc Oiitw 5ul tQ( (JOv6flCac to(nEI ~6)IQtOC ltpoi vnQ I On 1) OXEt11CTl tuxotTl~ tugtv 04 m5ec d vo t Jl eyo~OTeuroshypo Ti)r )I EYi CJtl1t poundltllpE1tlllr 5ul 1tAi]pll (pACryU 1tEpt lflv 1(010shyPtvll v atay6vo

N II_ bullbull 00

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H nlEGtt etc ttlv trwPclVEIUV tflt otaY6vo~ bEV rtapOuoui~EI ti1v GUlliv fllJll V1(09 6)11 tliv iiKtucnv tflc bwpaVElut Etc (0 np6cr81Ov )IEpO Il nitolt dvOt )lquAuttpa )lIHotrrCllI5i ooo

auavt i) noAIKlj-ywvia ToltO npOKUAEi l1lXll)ltvoUC pu9J1out KUOOEWlt dC to 1tp609lov ptpo (11lt a Tcryovoc EvavH lWV AOI shynrov 9toEWV 0 IJ EY IO lOC pu8J1oC JCuuot wc pound1l(PClVi~EtCll Ei 16

otacn~ov orUlEiov 00((1) t~l1 )dlClI blud JlUpOUOt(I~Etal 1([1(0shy

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0 0 2 m m

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o t(~ec ) 3

Oo middot l~ m m

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130

120

110

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I v XpovOt u(JnpilaEOOI

H hUUOlt li)~ OTClYOVO~ otv poundI VQI uKoplulo 6U1 n) v lvopllV TI)~ KOUoE~ 6namiTOl va )lEOOAOOrOll XPOVLKOV H 01CtOTlljlU IKClVO V npoe np09tp)lOVOIV tit~ oto)6vo~ Koi tOtJlIOlV noooshytTlrOC tIVO~ npot Evopltv ti)t KUOOcWe OunucElvcH q)UOlICOV va 6VUjlEVl] TIC Oll 6 roovDlt OOtEP110EOX aufuvpoundtaL 1-1pound niv aulT)Olv ti)~ 6PXtlCfl~ OtUIlEtPOU ti) e OlClYOVDlt

0 Il E tPTl9Ei~ XPovOt UO[Epi)OEWC Ol)VOPtflOEI tfl~ 6PXlKflc j)aCl-U-rpOU b(OElOI EIlt -rov ni VOKO 3

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Xp6voe uonproE Wt sec

0 5 2 0 25

005 010 018

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688 Not~Ppo~ 1970

Y K = KOtll Supae av(tAo((a tO u ltruOtQllKOi) K P = nipoundOllt

gt o(t1lt

mK =- ~l acatoDCL)atatIKo K A = brUpaVClQ

P 1tUKV~

D auvtdEOtll~ 15laxooEw~ toO mlatouKoC K t - Xp6vo~

M pl)a)l6~ ~(nmiddot)IiltJEOX Kaoa-iIlO)

ftoODarov ttpo1Jor01tOlicrewc tiC avnoptlcrtwr

atOIXEtO)lEtPll((~C )6yoC 6V (U)p6CI~Wlt

dStKt) ~vaaAJtia tOU auaTOtLKoi) K

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d on1 9e PIl6111C E evt pYpoundICl lvepyOltOlll mwC V d811(6C O(ICOt

He =- apl ell~ HlIynolds tV POiKT) OllVaptllCJtC

crucrtPOltPti

L Aov96votlltJQ 9EP)l6tqC trOrjllcrEWlt

Xp61o KauoECiH

OPX1KT) ollijlfrpo tfJc OtOy6vOC

I a vacptp EtCU de t l)v Ermpa VElov r i~ crtay6voC C aVOltp t PCTOI tic nlv wv rw dvn5p6(Jt~

o = aVQlPtPErCll d o ue(aAllv on6crtaaiV U1t6 t1)v CtQy6vQ A avaqgtpoundpECQI de ncp tOxliv A B ilVUqlEpEtal ELC 1tEPIOXilv B

BlpAloypa+ia I VD lAI U Dru ple~ Corn J1 lIs lio n An 1~ ~perlllllfJl ~ 1 tilm[loJtISOo

o r t wo Ib tO ri middot~ CII middotln ] ng Sci 11 jJi - iOl (l 9ti middot2)

1 M Hmiddot t1nfj C4 1Odun 1311rnlnO a f 1I tLUld Droplet AtI~a ll (~ In ClI~m Srcit ~ ~ u 1 111 31)

a P l JIflt On 11 1l IIUmllrful t nll erlYllI1 DCllllc l trJon~ Bul l(J n a mI COIIl i)mmiddottiull lU~ )r lCt_ (ombliMllnn 1IIr Flnrn r )1middot 2 ltS (I J I

II M lolnlQlw I i ~I(lrll llilll 11 11 1 T nnu~nc ( or I nl middot tl lil lJllIlIL l h1 till lli t CDlIl lu tgt lIn n uf Sln g lfl lito III vI L lu ld Fl1 Ih ld I ~ 1 lJ (I I~ ~)

5 E MOEditl middot T lw (HflbU Umiddotm I f Druplcl3 0 1 LIq ui d J- Il OI

G r d1ia mJ I ClilIU Lb SlllI JJ (I) 111- 14 (Iu)

D )puldlrJJ I ~)m JIO5[ Ulll Gr Cu m [lue llon r til ~ ( t 9 fl-n

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9 H HI G H Ilh ll H UI arid 1 ~lmJlS~HI b- S ~U[lQlt IlIlII1Jll COIII~ bUtillo ll 11 I t] l-I 2~ RclulJohl N Y I ~ DrJ owllu Q )(1Il II r ]Jutl n ttlll lmiddot l9

10 G M r ~= i SYlIl poSl u m un ttHll bul t1on p 732 (I [IH)

II J U)~I1 fl o ju Id U Carr J Chem P hYl lcs 26 p 327 ( 19ramp

t 2_ f Cr Pdtm i1r On lI ~e fill tll ln o r Sllq le DrtJ TI ~ ur Fuel llllJI OR x ydill11 jl A Utlo) lillCf fl It Pro pu lsio n ~f- p t 7~- l j lS (1 IlIl)

I S bullS K IiTnoCll 1 Id H Ii()(I - J lJId I 12 (1 1i5 fl )

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fI na(lovu(l t[1Yoaia In JXt Tll~ olxolowdjq gt7001 rV~EW1 n iC AVld lVIOV E)tJlI Yrt _Erol(Jw IIngeAalwv TE XACO (hk ro 61loiav eufQdCOflpoundI ra eV)(l(IIltMitlC flor To lCIealWTI)(cW fll(O eHt)tafhl el TO Igyaanio~ov middot CfP1(JO (JfI~V11 EJFepmiddotlJdv-shyvowtij roO J(fJ R ( Ll1JoxQrroraquo TTi~ bAArVtij( eIfIQlmtt middot lrOIH)(j lJIttyeiO IQ(k T~ 1I ttfolav eXPI~OpIl htrTrJl t trlugIQTW TiA-n F11(JwTo 6j~ n il x A poundtV~fJJ lOi (h)shy(JrxQv 1 Q1) K fl E ((JrU()CUD I) oui n~ to Oe((l l TOtI r nil )(uraaXeWV tal UlWO(J1 tiAOrratv rij lTCI(OJUTIt ryr avax e-ur

The effect of sIze and velocity on the burning

conditions of fuel droplets By H Koumouhol - G Stephanopoulos

Silmmary

The wide nso of ~ pray injPot Uun for the burning or a li quid fuel in a combustion ch a mber IHS lead to the ntluU fol an oxLcus ive analys is of th n processes which govern lhe cumbustion of liquid aerosols

Thi Jllp cr p rescnt~ lheorutical (l nd experimenlal aspects involvuci i n the burnin of a sin gll fu el drople t I ti s nl5sumshymiddotd tha t Ihe singhgt dropl cL li llllling i ts(tlf r l rn ai ns a probl~m or fund amen tal irliporlanclJ in combus tion re~ middotmiddotarc h In Ihtl pItsen t tl ll ll lys is uf 1 s teady Slate llderogc neo lls combushys lion as encounlIlHl in lh t burni ng of a liqu id drop let f a spherically 6ym Hlol ric model is asSUIIWC[ wi th a fin ito cold bound rt ry bulll a nam l holner the latter corre6pondiug to the llquid - val lu r ill tGImiddotrace

lo 56t up the matlw lfHllic il l model of thu ph enomenon in cunsidero Li on a numuur of s imple assullli-tions is ne(essary

Th us II wns- IlSsumcd th al 51(o1(ly s tal l cO mbu g l ion OCC UJS undt1 r i s o bari ~ cotlditiuns that the hea t ril ltlused as a result of th ) the mical n-lc lion is removNJ by conduction and Jnass tranl fet th ~lt quantili Oi s uch as thermal conductivi ty dCrlAi ty etc 3 r(gt considei d to be illdepend ll nt of temperashyture tl lld cDrnpositioH and so on

In case of ze ro 8cti vHtion en ergy a (lame toni r)[ inHnit lsshysimal thickness resul ts a t which the weight fr ac tions of both ruel and ox icii zer become zero TIll wllole nli lQ is there shyby middotjlJ para tad intI two lfgions rn th i fi rS the cllerll or dlttmiddot mica l readion ie Zlro In tlto scond the reaction goes to comple tion r h ll an alysis then knds t o ll fysk lO v f i1 rst ord el dil1( ren ti a l o qll a tion~ from hich x plid t ~olu lio ns can bt t ~kc n Amung ot hc-Js lhe fu el muss low rfllL t he ( ombution s urface IflT1 p cra t rm~ and lhlgt fuel frac tion a t Uk liqu id s urface art Cl vtainod

TtL l Nov iclmiddotS lo kes equ ation tor viscous axisy mruetrico fl ow was solvtJ d by u6ing a digital computer Thwl he pressure and vorti city pruOls around the burnin~ droshyplet along with the drng coeffici en t ( 01 various Reynolds num be rgt using the air velocity as a parameter werO ob fa inlHl

Exporun onlal m eaSUrf JJl ents have lead to values or burning cUllStan Ls for va riou air-now velodties and in itial d op lc t ~ i l)s Ultimat ely a condition is Icached whon du e Lo d(t shyc(0Rsed temp era ture the weight rraction or rt lle lanls preshysen t in the Nnc tion lo ne can no longl1 r be t unsumf)u Then unburued or paJti ally burn ed ma k middotl ilJ pas~e~ lll ro ugh Ut e lone FU I lhnr d O( I~asc in torllpcra lUlu li3su lls in a 1Illumiddot clion of the reaction rale and SV on unlillinalJy the 111 11 11 van ishes

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01 ap l9110v Reyn olds 100 Kat oui OICllpOPOUe TlJl6 e ptgt9~ol)XOUV illtavo lx9f1 S00 onai de TOe 6noia~ EX OUV npouap)lou9f1 livo A[1ftOt OW)~llviaKO I (II ) 810 tampv aWATlv[aKWV TOUtWV KCLl polle Tfie IJolne poundK -rfie aTay6vot Ttl ~Olleeuroiq O-ClltJiUe(ilv UUl) ~VWV 6011l OU)leuroflo pound( TO ICEKAIIIeuroVOV )lClVO)ltTpov To olacppa)l a (10) Kat TO )lav6JJEtpOV XP IlCJl shy H uuaTpoCP~ ooe 6E1KVUttal d~ TO Oxll)lQ 7 poundIJcpavilEI Tflv IIEshyJlCUOUV SUl TT]V )lETPllcrtV tfle napox fie fOCat poe 0 UWAIlV (9) yiOTllv HJlilv Tn de nJv ncptoxilv tGJv 400 COOt ROo 1tOA lK ~~ yurshyauvOEETCll ~lta4l IC WV lKf) l(uraulCpoundu ~ e (17) e~ pound)cia)lIltOC IJ ea viae To IJeuro YlaTov -roC-ro t10pTUTal Kat poundK -ro) pu9)l01) pofle aVpoundJltotfjpoe (12) 8Ul TOC oVpoundP IltJ1f1 poe tOOTOU EJtlTlrxci vOIJ ev -rfie Jl61 nt poundIC tf)e uTay6volt TO pound7tLOUIITlTOV PEU)lCl ciE poe npOC ICCl UTEpnv ltpO)TOyPCtltplat V fI UtClywv TOU Kouul)lOU cpwTiCETClI TIj PonGeiq AuXv[a~ nupashy Eie TOV n[vaKa oi6eTClI 1) omaetAKouoa OUVQ)lle olli 01acp6middot )(tWOE~ 750V (14) H cpWtOpacp IOI C nuv OtaOOXI Kampvamo[wv pOue apl(J)lOve Reynolds Kat OloSICtcp6po~ Tl)lae puiJloO poflc Tile l(a0aew~ poundm tUiXUVpoundClL TO DOl9euroiq ICI VllIJCl-rOypacp llCfle TOO KaVallJOU poundK -rfi~ aTayovo~ npoe tei ilsw Ete T6v au-rov nishy~Inxavlie Faslax (I )) epyalolltvnt)Ie TOxu-rllta400 cpcu-r0ipamiddot V(lI(CJ OiSpoundTClI eniOlIe 11 6vCtA1Xne Tf)C 6ma9euroAKOlKH 1e Eie Tflv ltPII~)V avO 6wTfp6Aeuro 1tTOV TU1ttlCo napaoElY~Q 6iltie1ClI elt Tilv 01tlU9tAKo~aav )oYltP TplaaV KClt 111V orrtafltAlCouaav )6Y19 eiK6va 2 h9a e1lCo iovtUl ouo CJmola 0 JlEta~ 6 -rampv 6rwiwv axlllJCtTO H )lEtaJ30AT] TOO pu6IJoC pof)e tf)e )lCtllle EK -rfe xpovoe EKTljJOTClI de 030 UTClyovOe QUICEi OflJJQVTlKT]V enili pam v tIti -rlle 6TnaeefICOu~le

686 NotI-PPlOt 1970

~

H~ bull bull 00

o Alit bull bull 0

6 6 bull bull 02

H~bullbullbull 00

6 bull 0

1IY1 bull bull OZ

EX middot 7 bullH xorOIJOPYJ dVrfYJlEwJr (1v(JT(orpiir 1ff(11 rp ~CIoJdtIP

OTaydva

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fTINA32

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10

I I

ltIgt

00 01

I CD

21 67 2137

I I

CDp

1080 1079

I I

CD

3247 32 16

02 2107 1078 3 185 05 2019 1075 3094 I D 1880 1070 2950 20 1629 1062 269 1

100 594 1040 1634

400 00 1130 075 7 1887 01 0818 0830 1648 02 0673 0796 1469

1000 00 0 1

0601 0332 I

0520 062 1

1121 0953

I 02 0224 I 0567 I 0791

NNe A(j8fo~ Reynolds

ltP EraOted UV8)H)v Q() j c nj Wl~

CDF poundVIJTtMOT1r ti1lK10poundb~v(J1c M( reIPTjr

CDp EVlTrJffJtT fh tllrOt J)(IlI)(f1]C wif) C1(]p OTOr

CD middotO)tlti (TIJlICde(Tnj illltf8c)t(otJl1TC

i f~Y t)uy f~ ontoGtJltoooq k6YI ol~~afo H tAQrnl)OIt ti)C 6nla8EAlCoucrnC J[potPXETO ~ uno TnV orutQvTtmiddot ICV tAU TTWOW ti) btlfPUvt taK~ oOOt POqli)t )~6Yf) (tUl1iCiOOt toO po6)100 poilc TtiC ~u~l) C ilC T f~ a ruy6 voc

Til ilvtJltSpro Cu~nEpoC)IOTO 9u Ouvouo080uv lCutwdpw ~i Tilv lCaOOLV Tl)V (JWYOV10(u)V npoe 510tOnwOlv l Glv lholtp6pov tmshyop6CJewv lGlV XOPOlCt l1PIG1 IICGlV tilc po ~C tni laO qlOtVO~ltvOO OU100

n H Gt06Epcl KOUGampOl e

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n-pO C TOV iPOVOv 7tOPCL)ItVSI Oto6cp6C

(ltD 11)It OTo6epo = 1ltshy

ft Dl = OtQ8spci = K

We lOtiTO OAAWCJTC npOEICUyenC lCoi onO TtlV 6sWPl1T1 1CV elvashyAUOtV_ Til OO)I1tEp6cr~alo tpqgtOivOvtOl Eic 10 Oxi])IutO 10 lCoi 11 ~v6u KOTOf4)oivE10l1l i~(1)tl1OlC If)C 0106epd Ct t~ UPXIshy1Cij r 51 0)lttpOu lCollampV o uv8lICOOV TOU 1tEpd~aAAoVTOr 1-1 r pushyIp IlC1l napaOTOOLe lfle olo6EPU K OOvaptJ)OCI Tf) r 6PXllCtlr OIO)1EtpOU OHl cnoOl)lOV 1tSpt6oAAOV 5i5ETOI d r TO oxilJlO 12

611i tfl v Ott~ PEGvl1 OIV tilr poundm5paoEwe Tftr 0 XET IICft C ToXllt lltOC toO Qtpor np6c tTiv OTO)Ova btVl1)10tOYPolPi]6n 11 XOU(Ue CTta shyyOvwv apXJKampv 5la)1ETpwv 15 lCal 20 m nl 6Tav to pCU )IO t oO Ittpoc elxpound oxttllCilv toXOtlto ror npOr til v 0(1(611004 [II sec To unotEHo)lato E)1cpavi oVtOl Ei r t() Oxf))IO 1 Quro~6 pua 8)1or lCallOCWe dVQI Jll1cpOnpor dr tTlv 1ttpi1ttw(Jw orcou l shyXO)lsv OXETIICi]V tOXtJtfllO ItCp0r Ole npOe tTlV cnoyova Tout o 5uvoTo i va ~~l1Yn~ POOEI fl )Ipoundtwpopd 8tp)l6tlllOl Ii 61toiu Hpound(Xt l tOv po6~ov ICOUOEWr tOOv CJtayovlo iwv

0 It~p ICOtU Tll V OttAEOO (V too 1tep l ~ tf)e ICQIO)1EVT]C CJtarOshyVOl 8EP)lDI VE10I Olll ~EtUQOpUlt 6Ep~611ltOe tIC til e ~wVllC 0Vt1shy

OpacrEror Totlto poundxEl ooe U7tOttMOJlO to 11oa6v T~C 6Ep~6T1lt0e TO 6notov avO Jlov6c50 xpovoo ~Etoltpeppoundtol1tp6C tTl v OtCly6vo va e(VOi ~llCp6t~pov Elr tl~V 6EWpOO)ltvllv 7tEp[1t[WOW ft ti TllV 1tEplntwOIv ttlC ~auatroc tv Otaac H AAOttWOllt uih ll tO u pu8)100 ~CtolPOpalt lflr 6EP)l6111t0e np6e t-nv aloyoVD h EI

c1l e anotEAECJ)IO ITtV AAottWO IV t otgt poB)1ofi )IEtOcentlO~d~ tf)lt )1 6 shy~11lt tIC Tfl r otoy6vor np6r to e~(a) 511Aooi] UoTtWOlV l OU pushy8)100 ~ooOtwlt bull~ cU)ou il KoOale t~ r crtoy6voC tvtOC toO Qtploo PEOpClfOr tGlv O4111 s(C ~VEIPltvlte 11)V )IOPcentlflv laquofJ~IOmiddot 1toCJPt06Eicrllr centlAoyor)) )I t AofFO~vOV OIlAOOi] to )Itttll1tOV tilr ltPAOYO ToOto ~XEl tillt a1tOt~AEO)lQ 6 po6)1oe 1(UOOCtoc va dVDl nAOttrop~Voc Oiitw 5ul tQ( (JOv6flCac to(nEI ~6)IQtOC ltpoi vnQ I On 1) OXEt11CTl tuxotTl~ tugtv 04 m5ec d vo t Jl eyo~OTeuroshypo Ti)r )I EYi CJtl1t poundltllpE1tlllr 5ul 1tAi]pll (pACryU 1tEpt lflv 1(010shyPtvll v atay6vo

N II_ bullbull 00

_ hooo p~ 1

I oCl lol 110

I n~h OY otOO I~~ middotga4lmv nO~LILOY

g trv II ~IUlo~

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0(mm2 )

omiddot

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pound 10 H ar-a(hen )(avapoundw~ oW orocupov nEflflciMov

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H nlEGtt etc ttlv trwPclVEIUV tflt otaY6vo~ bEV rtapOuoui~EI ti1v GUlliv fllJll V1(09 6)11 tliv iiKtucnv tflc bwpaVElut Etc (0 np6cr81Ov )IEpO Il nitolt dvOt )lquAuttpa )lIHotrrCllI5i ooo

auavt i) noAIKlj-ywvia ToltO npOKUAEi l1lXll)ltvoUC pu9J1out KUOOEWlt dC to 1tp609lov ptpo (11lt a Tcryovoc EvavH lWV AOI shynrov 9toEWV 0 IJ EY IO lOC pu8J1oC JCuuot wc pound1l(PClVi~EtCll Ei 16

otacn~ov orUlEiov 00((1) t~l1 )dlClI blud JlUpOUOt(I~Etal 1([1(0shy

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Kala Tflv KUOOW t(i)v crtayov loiwv T~lt Pcv~[ vn tVToe ptOjlClrOt aepolt nOpElTlPliOTl em Soov OUlCtvEI 1] lOXUtT)t lOu PEU)lClrO~ T6crov fl q)AO~ nA IlOl6~El nEPloo6rEPOV npot TitV oToy6va To JtIJPIVOV nEpij3AT1)lCl TO 6noiov nEplI( AE iEl lIlV oCCliova KOO (shyOlUlCll AEJtT01EPOV ToOto oUVUtu1 va tlTlY TlOn ~lt P60lV t6 Eril)lQ 8 Ono pound1lq)ovi~OVlCJl al OtaOljl Ol pOIKoi )PCl)l)lQ( orshyrIVEt KCl90piCoov Co lt6xo~ 100 1Wp(VOU JtCPlpAllJlOTO~

0 0 2 m m

Ilt 00079

PciJl-IU O 4ml~

o t(~ec ) 3

Oo middot l~ m m

K 0 0 09

PEti~u 0 4 mls

o

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K

130

120

110

DO(mm) 100L---~---~--~---_

15 2 25

I v XpovOt u(JnpilaEOOI

H hUUOlt li)~ OTClYOVO~ otv poundI VQI uKoplulo 6U1 n) v lvopllV TI)~ KOUoE~ 6namiTOl va )lEOOAOOrOll XPOVLKOV H 01CtOTlljlU IKClVO V npoe np09tp)lOVOIV tit~ oto)6vo~ Koi tOtJlIOlV noooshytTlrOC tIVO~ npot Evopltv ti)t KUOOcWe OunucElvcH q)UOlICOV va 6VUjlEVl] TIC Oll 6 roovDlt OOtEP110EOX aufuvpoundtaL 1-1pound niv aulT)Olv ti)~ 6PXtlCfl~ OtUIlEtPOU ti) e OlClYOVDlt

0 Il E tPTl9Ei~ XPovOt UO[Epi)OEWC Ol)VOPtflOEI tfl~ 6PXlKflc j)aCl-U-rpOU b(OElOI EIlt -rov ni VOKO 3

nINA 3

Xp6voe uonproE Wt sec

0 5 2 0 25

005 010 018

Ovo~aToAoyia

R pu9)loc X T1)llKi)t avnopaoEwl

T = 9poundPlOKpaolu

688 Not~Ppo~ 1970

Y K = KOtll Supae av(tAo((a tO u ltruOtQllKOi) K P = nipoundOllt

gt o(t1lt

mK =- ~l acatoDCL)atatIKo K A = brUpaVClQ

P 1tUKV~

D auvtdEOtll~ 15laxooEw~ toO mlatouKoC K t - Xp6vo~

M pl)a)l6~ ~(nmiddot)IiltJEOX Kaoa-iIlO)

ftoODarov ttpo1Jor01tOlicrewc tiC avnoptlcrtwr

atOIXEtO)lEtPll((~C )6yoC 6V (U)p6CI~Wlt

dStKt) ~vaaAJtia tOU auaTOtLKoi) K

OUVt euroA EOTnc eEp)JI I(~ 1 ufwf t)l6-rr]TOC

d on1 9e PIl6111C E evt pYpoundICl lvepyOltOlll mwC V d811(6C O(ICOt

He =- apl ell~ HlIynolds tV POiKT) OllVaptllCJtC

crucrtPOltPti

L Aov96votlltJQ 9EP)l6tqC trOrjllcrEWlt

Xp61o KauoECiH

OPX1KT) ollijlfrpo tfJc OtOy6vOC

I a vacptp EtCU de t l)v Ermpa VElov r i~ crtay6voC C aVOltp t PCTOI tic nlv wv rw dvn5p6(Jt~

o = aVQlPtPErCll d o ue(aAllv on6crtaaiV U1t6 t1)v CtQy6vQ A avaqgtpoundpECQI de ncp tOxliv A B ilVUqlEpEtal ELC 1tEPIOXilv B

BlpAloypa+ia I VD lAI U Dru ple~ Corn J1 lIs lio n An 1~ ~perlllllfJl ~ 1 tilm[loJtISOo

o r t wo Ib tO ri middot~ CII middotln ] ng Sci 11 jJi - iOl (l 9ti middot2)

1 M Hmiddot t1nfj C4 1Odun 1311rnlnO a f 1I tLUld Droplet AtI~a ll (~ In ClI~m Srcit ~ ~ u 1 111 31)

a P l JIflt On 11 1l IIUmllrful t nll erlYllI1 DCllllc l trJon~ Bul l(J n a mI COIIl i)mmiddottiull lU~ )r lCt_ (ombliMllnn 1IIr Flnrn r )1middot 2 ltS (I J I

II M lolnlQlw I i ~I(lrll llilll 11 11 1 T nnu~nc ( or I nl middot tl lil lJllIlIL l h1 till lli t CDlIl lu tgt lIn n uf Sln g lfl lito III vI L lu ld Fl1 Ih ld I ~ 1 lJ (I I~ ~)

5 E MOEditl middot T lw (HflbU Umiddotm I f Druplcl3 0 1 LIq ui d J- Il OI

G r d1ia mJ I ClilIU Lb SlllI JJ (I) 111- 14 (Iu)

D )puldlrJJ I ~)m JIO5[ Ulll Gr Cu m [lue llon r til ~ ( t 9 fl-n

~ G GQflta1)6 IL hJ [I IHS-Durn lns cU Furl Or Il INS

9 H HI G H Ilh ll H UI arid 1 ~lmJlS~HI b- S ~U[lQlt IlIlII1Jll COIII~ bUtillo ll 11 I t] l-I 2~ RclulJohl N Y I ~ DrJ owllu Q )(1Il II r ]Jutl n ttlll lmiddot l9

10 G M r ~= i SYlIl poSl u m un ttHll bul t1on p 732 (I [IH)

II J U)~I1 fl o ju Id U Carr J Chem P hYl lcs 26 p 327 ( 19ramp

t 2_ f Cr Pdtm i1r On lI ~e fill tll ln o r Sllq le DrtJ TI ~ ur Fuel llllJI OR x ydill11 jl A Utlo) lillCf fl It Pro pu lsio n ~f- p t 7~- l j lS (1 IlIl)

I S bullS K IiTnoCll 1 Id H Ii()(I - J lJId I 12 (1 1i5 fl )

It n yOO UUl aw l D W ood J e L Plo(Julslo lJ 28 I 18 (1 9flS)

fI na(lovu(l t[1Yoaia In JXt Tll~ olxolowdjq gt7001 rV~EW1 n iC AVld lVIOV E)tJlI Yrt _Erol(Jw IIngeAalwv TE XACO (hk ro 61loiav eufQdCOflpoundI ra eV)(l(IIltMitlC flor To lCIealWTI)(cW fll(O eHt)tafhl el TO Igyaanio~ov middot CfP1(JO (JfI~V11 EJFepmiddotlJdv-shyvowtij roO J(fJ R ( Ll1JoxQrroraquo TTi~ bAArVtij( eIfIQlmtt middot lrOIH)(j lJIttyeiO IQ(k T~ 1I ttfolav eXPI~OpIl htrTrJl t trlugIQTW TiA-n F11(JwTo 6j~ n il x A poundtV~fJJ lOi (h)shy(JrxQv 1 Q1) K fl E ((JrU()CUD I) oui n~ to Oe((l l TOtI r nil )(uraaXeWV tal UlWO(J1 tiAOrratv rij lTCI(OJUTIt ryr avax e-ur

The effect of sIze and velocity on the burning

conditions of fuel droplets By H Koumouhol - G Stephanopoulos

Silmmary

The wide nso of ~ pray injPot Uun for the burning or a li quid fuel in a combustion ch a mber IHS lead to the ntluU fol an oxLcus ive analys is of th n processes which govern lhe cumbustion of liquid aerosols

Thi Jllp cr p rescnt~ lheorutical (l nd experimenlal aspects involvuci i n the burnin of a sin gll fu el drople t I ti s nl5sumshymiddotd tha t Ihe singhgt dropl cL li llllling i ts(tlf r l rn ai ns a probl~m or fund amen tal irliporlanclJ in combus tion re~ middotmiddotarc h In Ihtl pItsen t tl ll ll lys is uf 1 s teady Slate llderogc neo lls combushys lion as encounlIlHl in lh t burni ng of a liqu id drop let f a spherically 6ym Hlol ric model is asSUIIWC[ wi th a fin ito cold bound rt ry bulll a nam l holner the latter corre6pondiug to the llquid - val lu r ill tGImiddotrace

lo 56t up the matlw lfHllic il l model of thu ph enomenon in cunsidero Li on a numuur of s imple assullli-tions is ne(essary

Th us II wns- IlSsumcd th al 51(o1(ly s tal l cO mbu g l ion OCC UJS undt1 r i s o bari ~ cotlditiuns that the hea t ril ltlused as a result of th ) the mical n-lc lion is removNJ by conduction and Jnass tranl fet th ~lt quantili Oi s uch as thermal conductivi ty dCrlAi ty etc 3 r(gt considei d to be illdepend ll nt of temperashyture tl lld cDrnpositioH and so on

In case of ze ro 8cti vHtion en ergy a (lame toni r)[ inHnit lsshysimal thickness resul ts a t which the weight fr ac tions of both ruel and ox icii zer become zero TIll wllole nli lQ is there shyby middotjlJ para tad intI two lfgions rn th i fi rS the cllerll or dlttmiddot mica l readion ie Zlro In tlto scond the reaction goes to comple tion r h ll an alysis then knds t o ll fysk lO v f i1 rst ord el dil1( ren ti a l o qll a tion~ from hich x plid t ~olu lio ns can bt t ~kc n Amung ot hc-Js lhe fu el muss low rfllL t he ( ombution s urface IflT1 p cra t rm~ and lhlgt fuel frac tion a t Uk liqu id s urface art Cl vtainod

TtL l Nov iclmiddotS lo kes equ ation tor viscous axisy mruetrico fl ow was solvtJ d by u6ing a digital computer Thwl he pressure and vorti city pruOls around the burnin~ droshyplet along with the drng coeffici en t ( 01 various Reynolds num be rgt using the air velocity as a parameter werO ob fa inlHl

Exporun onlal m eaSUrf JJl ents have lead to values or burning cUllStan Ls for va riou air-now velodties and in itial d op lc t ~ i l)s Ultimat ely a condition is Icached whon du e Lo d(t shyc(0Rsed temp era ture the weight rraction or rt lle lanls preshysen t in the Nnc tion lo ne can no longl1 r be t unsumf)u Then unburued or paJti ally burn ed ma k middotl ilJ pas~e~ lll ro ugh Ut e lone FU I lhnr d O( I~asc in torllpcra lUlu li3su lls in a 1Illumiddot clion of the reaction rale and SV on unlillinalJy the 111 11 11 van ishes

Page 6: 0 poAoC; TijC; TaXUTr'ITOC; Kal TOU JjEyt8ouc; Kara TI1V ...library.tee.gr/digital/techr/1970/techr_1970_11_533_681.pdf · 1970 ~[ = --+ + (0), ~ --+ + ~-- ~ o) ( '0 -~ + ~ 'Av =

686 NotI-PPlOt 1970

~

H~ bull bull 00

o Alit bull bull 0

6 6 bull bull 02

H~bullbullbull 00

6 bull 0

1IY1 bull bull OZ

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The effect of sIze and velocity on the burning

conditions of fuel droplets By H Koumouhol - G Stephanopoulos

Silmmary

The wide nso of ~ pray injPot Uun for the burning or a li quid fuel in a combustion ch a mber IHS lead to the ntluU fol an oxLcus ive analys is of th n processes which govern lhe cumbustion of liquid aerosols

Thi Jllp cr p rescnt~ lheorutical (l nd experimenlal aspects involvuci i n the burnin of a sin gll fu el drople t I ti s nl5sumshymiddotd tha t Ihe singhgt dropl cL li llllling i ts(tlf r l rn ai ns a probl~m or fund amen tal irliporlanclJ in combus tion re~ middotmiddotarc h In Ihtl pItsen t tl ll ll lys is uf 1 s teady Slate llderogc neo lls combushys lion as encounlIlHl in lh t burni ng of a liqu id drop let f a spherically 6ym Hlol ric model is asSUIIWC[ wi th a fin ito cold bound rt ry bulll a nam l holner the latter corre6pondiug to the llquid - val lu r ill tGImiddotrace

lo 56t up the matlw lfHllic il l model of thu ph enomenon in cunsidero Li on a numuur of s imple assullli-tions is ne(essary

Th us II wns- IlSsumcd th al 51(o1(ly s tal l cO mbu g l ion OCC UJS undt1 r i s o bari ~ cotlditiuns that the hea t ril ltlused as a result of th ) the mical n-lc lion is removNJ by conduction and Jnass tranl fet th ~lt quantili Oi s uch as thermal conductivi ty dCrlAi ty etc 3 r(gt considei d to be illdepend ll nt of temperashyture tl lld cDrnpositioH and so on

In case of ze ro 8cti vHtion en ergy a (lame toni r)[ inHnit lsshysimal thickness resul ts a t which the weight fr ac tions of both ruel and ox icii zer become zero TIll wllole nli lQ is there shyby middotjlJ para tad intI two lfgions rn th i fi rS the cllerll or dlttmiddot mica l readion ie Zlro In tlto scond the reaction goes to comple tion r h ll an alysis then knds t o ll fysk lO v f i1 rst ord el dil1( ren ti a l o qll a tion~ from hich x plid t ~olu lio ns can bt t ~kc n Amung ot hc-Js lhe fu el muss low rfllL t he ( ombution s urface IflT1 p cra t rm~ and lhlgt fuel frac tion a t Uk liqu id s urface art Cl vtainod

TtL l Nov iclmiddotS lo kes equ ation tor viscous axisy mruetrico fl ow was solvtJ d by u6ing a digital computer Thwl he pressure and vorti city pruOls around the burnin~ droshyplet along with the drng coeffici en t ( 01 various Reynolds num be rgt using the air velocity as a parameter werO ob fa inlHl

Exporun onlal m eaSUrf JJl ents have lead to values or burning cUllStan Ls for va riou air-now velodties and in itial d op lc t ~ i l)s Ultimat ely a condition is Icached whon du e Lo d(t shyc(0Rsed temp era ture the weight rraction or rt lle lanls preshysen t in the Nnc tion lo ne can no longl1 r be t unsumf)u Then unburued or paJti ally burn ed ma k middotl ilJ pas~e~ lll ro ugh Ut e lone FU I lhnr d O( I~asc in torllpcra lUlu li3su lls in a 1Illumiddot clion of the reaction rale and SV on unlillinalJy the 111 11 11 van ishes

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T = 9poundPlOKpaolu

688 Not~Ppo~ 1970

Y K = KOtll Supae av(tAo((a tO u ltruOtQllKOi) K P = nipoundOllt

gt o(t1lt

mK =- ~l acatoDCL)atatIKo K A = brUpaVClQ

P 1tUKV~

D auvtdEOtll~ 15laxooEw~ toO mlatouKoC K t - Xp6vo~

M pl)a)l6~ ~(nmiddot)IiltJEOX Kaoa-iIlO)

ftoODarov ttpo1Jor01tOlicrewc tiC avnoptlcrtwr

atOIXEtO)lEtPll((~C )6yoC 6V (U)p6CI~Wlt

dStKt) ~vaaAJtia tOU auaTOtLKoi) K

OUVt euroA EOTnc eEp)JI I(~ 1 ufwf t)l6-rr]TOC

d on1 9e PIl6111C E evt pYpoundICl lvepyOltOlll mwC V d811(6C O(ICOt

He =- apl ell~ HlIynolds tV POiKT) OllVaptllCJtC

crucrtPOltPti

L Aov96votlltJQ 9EP)l6tqC trOrjllcrEWlt

Xp61o KauoECiH

OPX1KT) ollijlfrpo tfJc OtOy6vOC

I a vacptp EtCU de t l)v Ermpa VElov r i~ crtay6voC C aVOltp t PCTOI tic nlv wv rw dvn5p6(Jt~

o = aVQlPtPErCll d o ue(aAllv on6crtaaiV U1t6 t1)v CtQy6vQ A avaqgtpoundpECQI de ncp tOxliv A B ilVUqlEpEtal ELC 1tEPIOXilv B

BlpAloypa+ia I VD lAI U Dru ple~ Corn J1 lIs lio n An 1~ ~perlllllfJl ~ 1 tilm[loJtISOo

o r t wo Ib tO ri middot~ CII middotln ] ng Sci 11 jJi - iOl (l 9ti middot2)

1 M Hmiddot t1nfj C4 1Odun 1311rnlnO a f 1I tLUld Droplet AtI~a ll (~ In ClI~m Srcit ~ ~ u 1 111 31)

a P l JIflt On 11 1l IIUmllrful t nll erlYllI1 DCllllc l trJon~ Bul l(J n a mI COIIl i)mmiddottiull lU~ )r lCt_ (ombliMllnn 1IIr Flnrn r )1middot 2 ltS (I J I

II M lolnlQlw I i ~I(lrll llilll 11 11 1 T nnu~nc ( or I nl middot tl lil lJllIlIL l h1 till lli t CDlIl lu tgt lIn n uf Sln g lfl lito III vI L lu ld Fl1 Ih ld I ~ 1 lJ (I I~ ~)

5 E MOEditl middot T lw (HflbU Umiddotm I f Druplcl3 0 1 LIq ui d J- Il OI

G r d1ia mJ I ClilIU Lb SlllI JJ (I) 111- 14 (Iu)

D )puldlrJJ I ~)m JIO5[ Ulll Gr Cu m [lue llon r til ~ ( t 9 fl-n

~ G GQflta1)6 IL hJ [I IHS-Durn lns cU Furl Or Il INS

9 H HI G H Ilh ll H UI arid 1 ~lmJlS~HI b- S ~U[lQlt IlIlII1Jll COIII~ bUtillo ll 11 I t] l-I 2~ RclulJohl N Y I ~ DrJ owllu Q )(1Il II r ]Jutl n ttlll lmiddot l9

10 G M r ~= i SYlIl poSl u m un ttHll bul t1on p 732 (I [IH)

II J U)~I1 fl o ju Id U Carr J Chem P hYl lcs 26 p 327 ( 19ramp

t 2_ f Cr Pdtm i1r On lI ~e fill tll ln o r Sllq le DrtJ TI ~ ur Fuel llllJI OR x ydill11 jl A Utlo) lillCf fl It Pro pu lsio n ~f- p t 7~- l j lS (1 IlIl)

I S bullS K IiTnoCll 1 Id H Ii()(I - J lJId I 12 (1 1i5 fl )

It n yOO UUl aw l D W ood J e L Plo(Julslo lJ 28 I 18 (1 9flS)

fI na(lovu(l t[1Yoaia In JXt Tll~ olxolowdjq gt7001 rV~EW1 n iC AVld lVIOV E)tJlI Yrt _Erol(Jw IIngeAalwv TE XACO (hk ro 61loiav eufQdCOflpoundI ra eV)(l(IIltMitlC flor To lCIealWTI)(cW fll(O eHt)tafhl el TO Igyaanio~ov middot CfP1(JO (JfI~V11 EJFepmiddotlJdv-shyvowtij roO J(fJ R ( Ll1JoxQrroraquo TTi~ bAArVtij( eIfIQlmtt middot lrOIH)(j lJIttyeiO IQ(k T~ 1I ttfolav eXPI~OpIl htrTrJl t trlugIQTW TiA-n F11(JwTo 6j~ n il x A poundtV~fJJ lOi (h)shy(JrxQv 1 Q1) K fl E ((JrU()CUD I) oui n~ to Oe((l l TOtI r nil )(uraaXeWV tal UlWO(J1 tiAOrratv rij lTCI(OJUTIt ryr avax e-ur

The effect of sIze and velocity on the burning

conditions of fuel droplets By H Koumouhol - G Stephanopoulos

Silmmary

The wide nso of ~ pray injPot Uun for the burning or a li quid fuel in a combustion ch a mber IHS lead to the ntluU fol an oxLcus ive analys is of th n processes which govern lhe cumbustion of liquid aerosols

Thi Jllp cr p rescnt~ lheorutical (l nd experimenlal aspects involvuci i n the burnin of a sin gll fu el drople t I ti s nl5sumshymiddotd tha t Ihe singhgt dropl cL li llllling i ts(tlf r l rn ai ns a probl~m or fund amen tal irliporlanclJ in combus tion re~ middotmiddotarc h In Ihtl pItsen t tl ll ll lys is uf 1 s teady Slate llderogc neo lls combushys lion as encounlIlHl in lh t burni ng of a liqu id drop let f a spherically 6ym Hlol ric model is asSUIIWC[ wi th a fin ito cold bound rt ry bulll a nam l holner the latter corre6pondiug to the llquid - val lu r ill tGImiddotrace

lo 56t up the matlw lfHllic il l model of thu ph enomenon in cunsidero Li on a numuur of s imple assullli-tions is ne(essary

Th us II wns- IlSsumcd th al 51(o1(ly s tal l cO mbu g l ion OCC UJS undt1 r i s o bari ~ cotlditiuns that the hea t ril ltlused as a result of th ) the mical n-lc lion is removNJ by conduction and Jnass tranl fet th ~lt quantili Oi s uch as thermal conductivi ty dCrlAi ty etc 3 r(gt considei d to be illdepend ll nt of temperashyture tl lld cDrnpositioH and so on

In case of ze ro 8cti vHtion en ergy a (lame toni r)[ inHnit lsshysimal thickness resul ts a t which the weight fr ac tions of both ruel and ox icii zer become zero TIll wllole nli lQ is there shyby middotjlJ para tad intI two lfgions rn th i fi rS the cllerll or dlttmiddot mica l readion ie Zlro In tlto scond the reaction goes to comple tion r h ll an alysis then knds t o ll fysk lO v f i1 rst ord el dil1( ren ti a l o qll a tion~ from hich x plid t ~olu lio ns can bt t ~kc n Amung ot hc-Js lhe fu el muss low rfllL t he ( ombution s urface IflT1 p cra t rm~ and lhlgt fuel frac tion a t Uk liqu id s urface art Cl vtainod

TtL l Nov iclmiddotS lo kes equ ation tor viscous axisy mruetrico fl ow was solvtJ d by u6ing a digital computer Thwl he pressure and vorti city pruOls around the burnin~ droshyplet along with the drng coeffici en t ( 01 various Reynolds num be rgt using the air velocity as a parameter werO ob fa inlHl

Exporun onlal m eaSUrf JJl ents have lead to values or burning cUllStan Ls for va riou air-now velodties and in itial d op lc t ~ i l)s Ultimat ely a condition is Icached whon du e Lo d(t shyc(0Rsed temp era ture the weight rraction or rt lle lanls preshysen t in the Nnc tion lo ne can no longl1 r be t unsumf)u Then unburued or paJti ally burn ed ma k middotl ilJ pas~e~ lll ro ugh Ut e lone FU I lhnr d O( I~asc in torllpcra lUlu li3su lls in a 1Illumiddot clion of the reaction rale and SV on unlillinalJy the 111 11 11 van ishes

Page 8: 0 poAoC; TijC; TaXUTr'ITOC; Kal TOU JjEyt8ouc; Kara TI1V ...library.tee.gr/digital/techr/1970/techr_1970_11_533_681.pdf · 1970 ~[ = --+ + (0), ~ --+ + ~-- ~ o) ( '0 -~ + ~ 'Av =

688 Not~Ppo~ 1970

Y K = KOtll Supae av(tAo((a tO u ltruOtQllKOi) K P = nipoundOllt

gt o(t1lt

mK =- ~l acatoDCL)atatIKo K A = brUpaVClQ

P 1tUKV~

D auvtdEOtll~ 15laxooEw~ toO mlatouKoC K t - Xp6vo~

M pl)a)l6~ ~(nmiddot)IiltJEOX Kaoa-iIlO)

ftoODarov ttpo1Jor01tOlicrewc tiC avnoptlcrtwr

atOIXEtO)lEtPll((~C )6yoC 6V (U)p6CI~Wlt

dStKt) ~vaaAJtia tOU auaTOtLKoi) K

OUVt euroA EOTnc eEp)JI I(~ 1 ufwf t)l6-rr]TOC

d on1 9e PIl6111C E evt pYpoundICl lvepyOltOlll mwC V d811(6C O(ICOt

He =- apl ell~ HlIynolds tV POiKT) OllVaptllCJtC

crucrtPOltPti

L Aov96votlltJQ 9EP)l6tqC trOrjllcrEWlt

Xp61o KauoECiH

OPX1KT) ollijlfrpo tfJc OtOy6vOC

I a vacptp EtCU de t l)v Ermpa VElov r i~ crtay6voC C aVOltp t PCTOI tic nlv wv rw dvn5p6(Jt~

o = aVQlPtPErCll d o ue(aAllv on6crtaaiV U1t6 t1)v CtQy6vQ A avaqgtpoundpECQI de ncp tOxliv A B ilVUqlEpEtal ELC 1tEPIOXilv B

BlpAloypa+ia I VD lAI U Dru ple~ Corn J1 lIs lio n An 1~ ~perlllllfJl ~ 1 tilm[loJtISOo

o r t wo Ib tO ri middot~ CII middotln ] ng Sci 11 jJi - iOl (l 9ti middot2)

1 M Hmiddot t1nfj C4 1Odun 1311rnlnO a f 1I tLUld Droplet AtI~a ll (~ In ClI~m Srcit ~ ~ u 1 111 31)

a P l JIflt On 11 1l IIUmllrful t nll erlYllI1 DCllllc l trJon~ Bul l(J n a mI COIIl i)mmiddottiull lU~ )r lCt_ (ombliMllnn 1IIr Flnrn r )1middot 2 ltS (I J I

II M lolnlQlw I i ~I(lrll llilll 11 11 1 T nnu~nc ( or I nl middot tl lil lJllIlIL l h1 till lli t CDlIl lu tgt lIn n uf Sln g lfl lito III vI L lu ld Fl1 Ih ld I ~ 1 lJ (I I~ ~)

5 E MOEditl middot T lw (HflbU Umiddotm I f Druplcl3 0 1 LIq ui d J- Il OI

G r d1ia mJ I ClilIU Lb SlllI JJ (I) 111- 14 (Iu)

D )puldlrJJ I ~)m JIO5[ Ulll Gr Cu m [lue llon r til ~ ( t 9 fl-n

~ G GQflta1)6 IL hJ [I IHS-Durn lns cU Furl Or Il INS

9 H HI G H Ilh ll H UI arid 1 ~lmJlS~HI b- S ~U[lQlt IlIlII1Jll COIII~ bUtillo ll 11 I t] l-I 2~ RclulJohl N Y I ~ DrJ owllu Q )(1Il II r ]Jutl n ttlll lmiddot l9

10 G M r ~= i SYlIl poSl u m un ttHll bul t1on p 732 (I [IH)

II J U)~I1 fl o ju Id U Carr J Chem P hYl lcs 26 p 327 ( 19ramp

t 2_ f Cr Pdtm i1r On lI ~e fill tll ln o r Sllq le DrtJ TI ~ ur Fuel llllJI OR x ydill11 jl A Utlo) lillCf fl It Pro pu lsio n ~f- p t 7~- l j lS (1 IlIl)

I S bullS K IiTnoCll 1 Id H Ii()(I - J lJId I 12 (1 1i5 fl )

It n yOO UUl aw l D W ood J e L Plo(Julslo lJ 28 I 18 (1 9flS)

fI na(lovu(l t[1Yoaia In JXt Tll~ olxolowdjq gt7001 rV~EW1 n iC AVld lVIOV E)tJlI Yrt _Erol(Jw IIngeAalwv TE XACO (hk ro 61loiav eufQdCOflpoundI ra eV)(l(IIltMitlC flor To lCIealWTI)(cW fll(O eHt)tafhl el TO Igyaanio~ov middot CfP1(JO (JfI~V11 EJFepmiddotlJdv-shyvowtij roO J(fJ R ( Ll1JoxQrroraquo TTi~ bAArVtij( eIfIQlmtt middot lrOIH)(j lJIttyeiO IQ(k T~ 1I ttfolav eXPI~OpIl htrTrJl t trlugIQTW TiA-n F11(JwTo 6j~ n il x A poundtV~fJJ lOi (h)shy(JrxQv 1 Q1) K fl E ((JrU()CUD I) oui n~ to Oe((l l TOtI r nil )(uraaXeWV tal UlWO(J1 tiAOrratv rij lTCI(OJUTIt ryr avax e-ur

The effect of sIze and velocity on the burning

conditions of fuel droplets By H Koumouhol - G Stephanopoulos

Silmmary

The wide nso of ~ pray injPot Uun for the burning or a li quid fuel in a combustion ch a mber IHS lead to the ntluU fol an oxLcus ive analys is of th n processes which govern lhe cumbustion of liquid aerosols

Thi Jllp cr p rescnt~ lheorutical (l nd experimenlal aspects involvuci i n the burnin of a sin gll fu el drople t I ti s nl5sumshymiddotd tha t Ihe singhgt dropl cL li llllling i ts(tlf r l rn ai ns a probl~m or fund amen tal irliporlanclJ in combus tion re~ middotmiddotarc h In Ihtl pItsen t tl ll ll lys is uf 1 s teady Slate llderogc neo lls combushys lion as encounlIlHl in lh t burni ng of a liqu id drop let f a spherically 6ym Hlol ric model is asSUIIWC[ wi th a fin ito cold bound rt ry bulll a nam l holner the latter corre6pondiug to the llquid - val lu r ill tGImiddotrace

lo 56t up the matlw lfHllic il l model of thu ph enomenon in cunsidero Li on a numuur of s imple assullli-tions is ne(essary

Th us II wns- IlSsumcd th al 51(o1(ly s tal l cO mbu g l ion OCC UJS undt1 r i s o bari ~ cotlditiuns that the hea t ril ltlused as a result of th ) the mical n-lc lion is removNJ by conduction and Jnass tranl fet th ~lt quantili Oi s uch as thermal conductivi ty dCrlAi ty etc 3 r(gt considei d to be illdepend ll nt of temperashyture tl lld cDrnpositioH and so on

In case of ze ro 8cti vHtion en ergy a (lame toni r)[ inHnit lsshysimal thickness resul ts a t which the weight fr ac tions of both ruel and ox icii zer become zero TIll wllole nli lQ is there shyby middotjlJ para tad intI two lfgions rn th i fi rS the cllerll or dlttmiddot mica l readion ie Zlro In tlto scond the reaction goes to comple tion r h ll an alysis then knds t o ll fysk lO v f i1 rst ord el dil1( ren ti a l o qll a tion~ from hich x plid t ~olu lio ns can bt t ~kc n Amung ot hc-Js lhe fu el muss low rfllL t he ( ombution s urface IflT1 p cra t rm~ and lhlgt fuel frac tion a t Uk liqu id s urface art Cl vtainod

TtL l Nov iclmiddotS lo kes equ ation tor viscous axisy mruetrico fl ow was solvtJ d by u6ing a digital computer Thwl he pressure and vorti city pruOls around the burnin~ droshyplet along with the drng coeffici en t ( 01 various Reynolds num be rgt using the air velocity as a parameter werO ob fa inlHl

Exporun onlal m eaSUrf JJl ents have lead to values or burning cUllStan Ls for va riou air-now velodties and in itial d op lc t ~ i l)s Ultimat ely a condition is Icached whon du e Lo d(t shyc(0Rsed temp era ture the weight rraction or rt lle lanls preshysen t in the Nnc tion lo ne can no longl1 r be t unsumf)u Then unburued or paJti ally burn ed ma k middotl ilJ pas~e~ lll ro ugh Ut e lone FU I lhnr d O( I~asc in torllpcra lUlu li3su lls in a 1Illumiddot clion of the reaction rale and SV on unlillinalJy the 111 11 11 van ishes