Calhoun: The NPS Institutional Archive

Theses and Dissertations Thesis Collection

1955

Interference effects during buring in air for two

stationary n-heptane droplets.

Rex, James Foster

California Institute of Technology

http://hdl.handle.net/10945/14277

library

U. S. Naval Postgraduate School

Montei'ey, California

Tt;.'

INTLEFLIi.NCK EFFECTS DURI>;G BJR?li:i.3 I^. AIR

FOE Tr-Q SX.';TIONiu'J n-HitPTANi: DROPLETS

Thesis by

James Foster BexII

Lieutenant, United States iJavy

In Partial Fuimiinait of the I>equires2ents

for the Dei;ree of

Aeronautical En.'jir.eer

California Institute of Teciinolo^'

Pasadena, Cciliforriia

f) T'<,«1<!

R?^6

The author wishes to exprosa iiis appreciation to Br. S. G,

?enner for GUfc-^estin^-; this inveati-^tion and for his valuable

assistance during; tiie reduction of data. The author is indebted

also to Mr, D. «eber for iielp with the experinierital work, and

to Mr. D. East for perronaing many of the fiL^a measure^aeiits.

^<kQ f^ /

ii

ABS'VmCT

In order to gain soroe understanding of droplet interferenceduring buminc, ©xperinienta have been conducted for the deterr.iin-

ation of the eva;x)ratioii constant aijd flame i^li^pQH of two clocelyspaced n-heptaiie droplets buminrj in air. Droplete of ap')roxii2atel3'

tho Gaae a;.d of different diaraeters v<ere used at Vi^riouo distancesbetween the droplet centers,

Eoiperiinental reo\iLtQ on flaae j^haves and evaporation conetantsfor closely' spaced droplets shov soaev/hat surprlalnc behavior. Th^is

the appare.^t fla.je si ave shan.^ea very little dirinc the bumiiir ofthe droplet. The square of the droplet diameter decreases lii^early

with tine for fixed apacin;^ bet-.veen droplet centers, at least wit.'iin

the experinentcl liinits of accurac'/. Since r;eonetrically differentconditions are produced contiAuoasIy daring bumirii;^ the obaorvodLndependerico of the slor)e of plots for the sqaai'e of droplet diaoaterV8 tiiae is not obviously expected, t^therr.iore, for droplets 2^ ^^ 9different avera,^e L^.itial dianeters Ir, the frequency, K" = K»/(S^) »

where "S* is the usual evaporation constant, is well represented as a

universal function of the initial e-xiclng between droplet centers(C 4- D ) or od^ scent droplet surfaces (C ).

The evaporation conctuit "^» for constant u, and the frequencyIc" for artiitrary values of if, inciease at firet as C*^ is reducedand then decr-eaae a^^ain. For lar^^e values of C , K' approaches thenumerical value meaaured in stsidies on the bixming of sin^JLe droplets.Triio behavior ci^n be ondorstood in terms of a coupetition between lieat

loGSos to tho outside from the flane front surrounding a single di'O]^-

let, which decrease as the droplets are brou{jht together, and ojtj'.<7eri-

deficient at^osplieres, vthich are raore li}<ely to occur for very aiaall

values of C*^,

Althaitjh an acceptable empirical correlation of erpcrioental/aeaaurenients Juis i.ocn obtained, the processes vhicl: determine inter-ference during droplet burning are as yet not understood. In view ofthe possible practical iniportanoe of i: j lisiference during burning in

e.'rays, cdiitioral laboratory studies <»i the burning of simple ;jeo-

i.-etric arrays, other t .ar. c.?o dioplcts, ap. oar to be indicated.

Ui

TABLS OF COIJTILNTS

PAHT PAC&

Aclariowledfienent 1Abstract iiTable of Contents iiiList of FigureB ivNooenclatur© vi

I IViTWDUC^lCM 1

II EXPLEU-JK^TAL STUDIL3 OK THE BUfS;iKQ OF T^/O J*

STATiav'AEI n-KLPTANE DROPLhJTS

A • Apparatus hB, £xj>eriinent«il pjBffults fuelating to Flani* 6

Shape and Burnin,- Rat«

III EVAPORATION Ca\r.TANTS Aim EVAPOR^^TICN FEE- 6

'^UENCiEr. FOR Tivo sT.;Tia^'Ai3r a-:ii:PTAr:E drop-lets BUKa:;a im cloc-;], pfiOxiiiiTr

A, Evaporation CoriStanta 8

B« Evaporation Frequencies 10

IV FUilE HAPES 11

A, Flanre Jhapes for oincl® ^tationany Fael 11Droplets Biimint^ in Air

B. Flame v.hapes for Two n-Keptane Droplets IhBurning in Close ProxL'aity

V co:'CLu.:.:cN3 15

fAferences l6Figures 17

Iv

LI'iT OP FiaUKK^.

FIGRJFii PACE

1 Sciioaatic arraiii,«nient of flaiae Interferenceexperinent with tvfo droplets burning In closeproximity

17

2 Riototjmph of two n-heptane droplets burning in air 18

3 Sches^tic diagram of droplet ii^nition 19

1-26 Experimental resultsburning in still air

for t^7o n-heptane droplets 20^

(li)^l

ts .15li en. °2 e .166 Ota, 0° r: .020 (r<i 20

(5) ^lB .181 cm. =2 e • 17li ClOy c° JE .lilt ca 21

(6)'I

ts .166 era,^l

r; .1% cm. c° tr .133 CBt 22

(7)'I

S .192 en.°l

ZZ .176 cm. c» tr .230 ca 23

(G)^l

r: •16> GSlf'I

s .11a2 cm. 0° = .261i ani 7h

(9) 'I=r .102 cn,

'I=: .173 cm. 0° s- .752 cm 25

°l= .132 cm,

^ls .102 CEl, c° iS .392 CJl

(10)^l

= .173 ca.^l

=: .173 cm. 0° e 1.125 CO 26

^l= .182 era. °2 s .156 CSl, c° s 1.1*7 osi

(11)^l

B .130 CIB,^l

=: .127 ca. c° s .222 ca 27

'Ie= .13ti cm. ^\ = .13ii CHi, c° = .2oa cm

(12) 'I= •135 cm. ^\ rr .117 cm. c" •= .313 cn 26

-Is= .12li aii, ^\ 3r .12li ca. c"* s; .235 CIQ

(13) ^1 s .133 cm.^l

= .122 crn. c° = .5U0 cia 29

^lr: .126 cm. -\ e .126 Ctif c° s .1*0 CCl

(11)'I

=; .136 cm, -% s; .120 cm, c' c .1x96 cm 30

^lss .121 cm. ^2

•= .lis 0% c° s: .33Ji cm

(15)^l

s: .lii3 CIQ)'I

s= .lii2 cm, c" e: .533 era 31

(16) r>° t: .llil cm. < s .135 cm c" =: .536 cm 32

«v-

FIGUIE PA>X

(16) K rs .155 cm. °2 cr .lh2 en. c° =r .196 en 33

(17)-t

s .156 cm.°a

s: .lli7 en. c° =r .833 ca Hi

^° sz .156 cm.^a

= • llil cm. c° s .823 cm

K er .156 cci.°a

cr .156 cm. c" = 1.10 cm

(10)'I

cr • 208 CiB,''a

s: .155 ca. c" =: .126 cm 35

(19)°x

= .209 ca,=a

s .170 cm, 0° =: .352 Cin 36

(20) °1 r: .193 cm.'a

=r .liiO cm. c" sr .375 cw. 37

(21) 'It= .167 cm,

°°a=: .115 era, c° s: .520 cja 38

(22)^l

=: •160 cm,^a

B .131 CX;1, o" = .532 Cia 39

(23) ^lsr .192 cia,

''ae .11*3 CiT^ c' = .026 cm 1*0

{2h) K s • 205 CO,'a

s .I6i. cn. 0° s .150 en a(25) ^l

s .191 cm.>a

sr .170 oa. c' =r .21*6 CiU 1*2

(26)'I

s .192 ca,-'a

e .100 a-a. c" =: .355 cm 1»3

(27) >? :e .202 cia.^a

s .179 c^^ c° cr .362 cm 111*

(2G)^l

!= .200 cm,^°a

s: .156 cm. c° t= •1*66 em h$

29 Variation of the averac* evaporation constant If*

with C^ for droplet pairs with different initialaverage diameters d

hS

30 Dopei^.vience of the evaporation frequency f'" on C° 1*7

31 OfiPendeace of th«1 evaporation fre;,luency ^'^ on iiB

32 Dependence of the evaporation frequency ?** on 1*9

33 ijcheraatic diagram of burning fuel droplet 50

^ Plot of exDeriiner.tal and calcula^^d value8_ I'or 5lC vs tUe, where C^, = C® + ^[l -

J K' t.

'J

vi

nc/MrcSui'.wm.

a

C^

D

K»

X"

subscript 1

subscript 2

If

U

?'

I"

!Ti

n

w

vertical distance from center of droplet to lowerflame sari'ace

horisontal distance from ceriter of droplet tooutside flaa?e surface

initial ndnlmua distance betv?een adjacent dropletsurfaces

miniioum distance between adjacent droplet svirfaces

at tiise t

initial droplet diaaeter

droplet diameter at time t

evaporation constant

©va'XJration frequency

identifies U\e larger of two droplets

identUiea tlie sualler of two droplets

aritimetic average valae of D° for droplecs 1 and 2

aritiinetic average value of D for droplets 1 and 2

arit'iLaetic avera-e value of K» for droplets 3 aid 2

arithmetic averaj^e value of K" for droplets 1 and 2

vise constant ir; Ftosin-HaaBuler diatribiition law

distribution constant in Rosin-Raiamler distribution law

wei^.;at fraction of the spray coaposed of oroijlets "siith

diajieter lar>:er thai:i D

-1-

I. li^TrODUCTION

A conGitioruble nuob^r of tiieoreticol and eiTieriinor.tcl pr^-pera

"Mavc boon publishod or. the bimlrif, of siri';le drop?LetE o£ Tiul (3-5)

•

ijxperirjer.tai studies htivc bv.c»i pfirion^d on ij^'i.lt* dix;plete saspen-

dexi rro:2 f^jae quartz i'ibers arid bjirijir*^* i;i an oxidiai/:.^ atfiOiSj-uiere (5)*

A rcasoiiabl© tneoreticai psxdiction of aaas buniiiig rate for 3ii:r;le

droplets can be obtaixied oii tl'ifc as«u:i>j)tior» ti'iat raaos traau^xirt be/" dn!"

fasiori to thi© flan© surface arxl hoat coudMCtiojfi to Uve b.imiri{; droplet

control the burning rate (!<)•

Keccritl;" an attoa:fit ^35 bcoij .^jcde by Gi'avei* and Oeratein at the

MACA to utiliste the rei3..ilts obtai.;ed i;: aii^-ie droplot ;>tudie3 for

the description of biimini_i ratea in !3;)rais (6}» Tljese r.uthoi^i start-

ed v;ith the results of cui iaportant theoretical sta4/ carrifed out

soiiio years ago by Probcrt (?)• tl'obert tiade the foliowiri,: asciumptions i

(a) The eproy i^article sice follows ti-iC tosin-Raiaa-

ler diatribution lar/.

-^s-^'^/'')". Hi•J

irifiere w equals the voluxsc fraction orweight friiCt^oji of! t!je Ci:;ra^ co::ipo3ed ofdrops Tft'ith diaoctera f-^reator tJian D, 15' io

called tho siae coasixint, and : ia u£jual>-'

referred to as the distrioution canstant.

(b) The rate of l7irni;-.i.: of the droplets is tr-ken

to be prtjportionai to the first povrer of tlie

droplet diai.iGter» In thie caee it ia eaallyalKwn tliat

irhere P is the droplet diaiaeter at an;;,'

tiiaef D*^ is the initial diaacteri and K'

-2-

vrhich h.'ag th« dinenaions of area perUTilt tiBW;)is knorm as the eva:^i^tioXiconstant*

Probajrt has sboiTn hen: to compate the pei*centa£ie of onbuiTied

fiel as a f-mctlon of V K»t / u» for values of r. between 2 and

h, '.vliore t is the residence tLiie of the biirninf droplets.

TiBcesAly correlations similar to tl-»se of Probert have beeii woilced

out for arc "let distribution laws other than the r>o8ii>-Raian5lQr dis-

tributlor. law (3).

Equation [2], vrhic'i i-iBlates droplet diameter to the bamiiic

tiae, is kno'm to correlate all of the observed results for the

s;,eadj' burning of sinrle fael droplets in an oxidiaing atiaosphere

(ii). Therefore, it is of obvious interest to detemlne -.whether or

rot the value of the evarjoratlon aoris^^ant, K', for sin[:le droplet

tJieoi^/ or e::peri:rsent has aj\ir illation to the value of K» ap';ro-

priate for apra^ coiribusticn. Graves ar^d Gcrotein attca^ted to

answer this question by weasarir.^' the coaibustion ef^icienal^' £s a

function of oxi%';ffi\ concentration for a nir.r^le tubolar coabastor

us in;; iso-octane as fael sxmi countercurrent injection, TlnBy con-

pared observed combustion efficiencies ^ith calculated coiabustion

efficiencies using Probert' s theoretical analysis in conjunction

with val ios of K* aieasarcd for the burning- of sin;--le droplets. Tlois

corapmrison showed that all of the observed res ilts could not be ex-

plaineu. unless spray corabustion involves effects, at least for 03(;/i;;en

concentrations below 2h percent, wiiich can be i^priored in the buminc

of 3inc'.le droplets. In connection with the use of sin-le droplet

data for studies on spra?; co^nbastion, it is therefore, of obvious

-3-

.Importarice to carry out laboratorj- studies on interference beti/©en

droplets durin„ burning,

Althoui^h, as a ;;«neral rile, statistical arrave are aore ©asilj^

interpreted ti^an snail niuobers of droplets, such as 2, I, etc., sk-

peri:^ierUil st<idies on saall numbers of droplets jtaj provide a clue

for the iuiport«'int pl^'sioo-chenical processes operative in droplet

interference (iurintj buminj^. For t'nia reason exporiin^nts have been

carried out on the variation of K* irith droplet size and droplet

spacing for t»»'o closely sf^aced droplets.

-!i.-

II. iLX^xJUki^Ni^ I. -yumv-: CN thl muixo of two ^tatiomj^fy

A, Appor£ttus

In order to record the flane shape and the decrease in droplet

di£iiaeter VKith. tiiae, the droplets were snap&nded on thin quartz fibers

which ".ijere secured by raears of a Sduere.Lser cement to a iriCbal rod.

Tne rod was bent at ai. ai:;ie of 50 de-rees at one end to insure a

lar,j-e suppcrtin^;. surface. The rod v^ad supported on -c st&nd by neans

of a clarap. Hods of vari.o-js diariieters yjere used .'or different tiiinimuci

spacinjs betcoer, the a:i,is,cent sirfaces of the droplets, C (see Fi^;. 1).

The fibers were enclosed iiii a circular olastlc tube of several i.chos

diameter in order to elL~inat€ a;abient air cirrer.ta. 3in :le droplets

of fuel ivsre auspendtd froin the fibers by forcing]; fuel through a

hyoo.ierr;'.Lc nee.i3.e onto tn.e TLber. Tlie droplet diameters varied froai

.117 to •2j9 o\.j3, Tiie droplets were reasonably 3Di::erical as shovYr* in

the p:;oto,rapri of Fi-.. 2.

The drops xvere ic-ited by u.sin;: ^n autoriobile i^utLon si'steir.

connected to electroaes which stradaled the ttvo quartz fibers throu^;h

holes iii the tube (see Fij. 3). Ihis ^aethod of ignition "'.vas found to

be usefiil for values of G less than or equal to 0.3 cas. For runs

of C ,-reater than O.-J ens, a inP.tch w-.s used in order to i,^nite the

droplets.

An electrically driven Arriflex 3^'i'»^ ;novie caniera wao used Tor

photo <-,raphin- the burriinij droplets. In order to photo-rraph the fla^e

front, a 100 watt bulb ivas olaoed behind and off to one side of the

burning; drops. Tnis h.etiod silhouetted the drops and also left the

flarae fnjnt visible as shewn in Fl;,. 2. A ten Irich adapter tube and

telephoto leria were eniplo"©d 1ji order to obtain as lars^e an iroatje

as possible on each i'rame ol' fiLi, Kodak Pl';n X stnd Kodak Saper XZ

fili^is '«ei-9 used ^'ith apertures of f6 and f9, rt-^spectively.

A stix)boacope served as tiri.in;-; standaj\i, A ten liich circular

aluainum plate, with tliree holes placed 120 dej^^ees apart, was

secured to a 75 fJ^ ooastant speed .TiOtor £lvin,;: 3*75 flaa'^es per

second. The stroboscope A'as plsctd directly beliirjd the birainj^

drops. The caa-.era speed v.as adjusted to almost 25 frfinies ner second,

as deterinined frora observations o£ the stroboscope,

A 3/3^ inch ball bearing wao photo.-raphed at the be:..innin<.;^ of

each 100 foot roll oi film used. The iaa^je served for calibration

and was obtained UHvier the sm-ia fociislnr: cord it: Oi;? as for the bamini;;

droplets.

The filjn was n^easired by iieinr; a mlcroriln recorder and a

steel scale j-^-ad latcd in rrdllr^etera. Tf>o iTxeasareiaents .mre liade

on each dro:> per frujiOf ne..:.aly, the two pcrpendic ilar diameters

inclined h^ degrees to the inajor ond ndnor axes in Ihe plane of

observation. Tlie mean valje ox' tUeae tv.o reaain^s was recorded as

the "effective diameter" 01 the droplet. lo is easily shovm that

if the liiajoi- and i^iinor axt^s do not differ f;r^.-iatly, as ':/as the c:vse

in our experiaents, then the volu.ae of a spr:ere with the measared

effective diaraeter is not £,reetl,/ different frora that of the prolate

spheroid, ;vru.ch actiall^^ corresijor/is to the 'shape of oar droplets.

In iLOst cases measureitients viere taken frora i^j.ition to bum out aiid

recorded approximately every fifth or sixth frf-.^r.e. The flame shape

parameters a , a , b , and b- (see Tvj,* l), k.ere also aeasurea.

-A.

^* ^^erliiental r.caultg :'.elat.l:ijj to ria-ae>'^f'-^'>^

^J^ IVaniin;; Rate

KKperineritGl atu-iic^ v.-ero carried oafc for tvTc etationar:^/ n-he^^tano

2droplets in sir and s"riov/ed that the square of tlie droplet dia-rseter, D ,

was a linear f-inction of "Mio tiTiC, t, for each of the bur!iii->r dropleto,

at least withiii the li:r.Lt£ of exporiniontal accr.imcy. The flcu:3C shape

oarameters ?rer© fonnd to v^rj renarirGbl:* little as the droplcto bumod.

In Fico# U to 2C tutid lii ..able X "*'e auiiuarizod all of the observed ex-

periraental results. IIjq riarrie eitape ]»araaeters are plotted cs functions

of time for tliose sets of data lor w.iicn Uie^r were aieaajred. 'Clss squares

2 2of the droplet diameters, D and D-, ai^e plotted as a function of the

tic« for all of the laeasurejoente^ ^Jeet" straii^ht lines liave been

drsnTO throu£;h the experiLiSi-:tally doterc±:icd points c:ccept for those

cases iii which the dfita were not adequately roproserited vj Linear cor-

relatiorxa. In soute caseti the i:jea»ar©a duta su;;,;est puriodic variations

2of observed ;'araiuotex« i&ee, p*rticuiariv, tl;;s. 23 to 26;. Data of D

ae a function of i, wrdch could not be oorrelatea b^ straif^ht linec,

have been ifcnored In sabae^uent attetiots at finding i^.iversal correlations,

In several Instances, where droplets of ^x-eatlj' diffcrei^t cizes

were used, observations irare possible on the larjjcr reiriaisiing droplet

after ttie SLjaller droplet had ained out. In nost of tl^es© cai;es the

2slope of the C vs t c jt/o c^i^.;;^! rat/?«r abruptly and yielded

data in fair fc^roGr;ent irith t:xj 'ccrm si:-i'le drcnlot riit-.Qts (K*^ 0.008

cm /sec) after tlie s..uller c'.iv'^eit 'i^.d bii-.-al co>„;.lete!i>" (see PMjs. 13

to 2-.')t For droplets of nearly; O'-^jal dieneters {Dl - D^j tiie evapor-

ation constants Z* ai>d Kl are nearly e<jaal (see 11 a. h to 17)

•

TABLE I

FIGUr-R

10

10

11

11

12

12

13

13

Ih

lli

rj

16

16

17

17

17

Ij

i;

a:)

21

22

23

2]^

2:^

26

27

26

-7-

EXPEKIMEBaru^'I?•;G

D^, cm

0.19li"

i!;TAL EK;.ULToEJ oTILJ. I' IK

v^, era

0.166"

FOR no n-

^ , crtj

0.020 0,0091;- 2..

0.0062

O.lCl 0.1?ii O.llh 0.0096 o.o;;9i;

0.166 o.i5i! O.lc-3 0,0135 0.0130

0.192 0.176 0.230 C,G105 0.0096

0.165 o.i;42 0.26]i 0.0136 0.0122

0.1G2 0.173 0.752 0.0153 O.Olal

0.132 0.132 0.392 0.0.1 liO O.JII4O

0.173 0.173 1.125 0.0139 0.0133

0.1o2 0,15c 1.1*7 0.01 2li 0,0115

0,130 0.12? 0.222 o.ooeo 0.0072

0.13a 0.131; 0,20a 0.0063 0,0063

0,135 0.117 0.313 0.0035 0.0025

0.12^ U.124 0.235 0,0073 0.0070

0.133 0.122 0,510 0,^091 O.OOVO

0.126 0.126 O.liO 0.00G6 0,'00o6

0.136 0.120 0.1496 0.0091 0.0063

0.121 0,113 0.381: 0. 00714 0.0071

0.lli3 0.lLi2 ^>:^33 O.Ollo 0.0110

O.liil 0.135 0.53a 0.0097 0.0J93

0.155 0.lii2 0.1^96 0.0122 O.Cllii

0.156 0.1h7 0.313 0.0123 0.0113

0.156 O.li.1 o.::j 0.0110 0.0112

0.156 >J .l>o 3.10 0.0107 o.oioa

0.203 0.155 0.126 0.0307 O.OlOi;

0.2Uy 0.170 0.3:.

2

0.0123 0.0109

0.1-yo o.iU 0.375 0.0090 0.0089

0.167 0.115 0,520 0.0150 0.0090

O.16O 0.131 0.532 O.Oli.0 0.0150

0.1?2 O.lliC 0.026 - o.oa^'^s

0.200 0.i6i4 0.150 - 0.012li

0.191 0.17a 0,2li6 0.0157 .

0.112 0.1.J 0.355 - ~

0.202 0.179 0.362 - —

0.2O3 0.156 0,1466 0.0133 „

-0-

III. I'JAPQUf.'nOK COrii;?A\TL: ..CD 'LVAi CRATir^i ITa'AiULhCUu FCIl TV-O

•ST/TI0.N/.E5r n-FIEPTAIcL DKOjtLLTo BUK-ISG Hi CLC.'w^i. PROXIkliy

A , Ivaporation Constants

If the evaporation conotant, X', of a stationair;;/ fael droplet

snspenued from a quartz fiber is codified extensively bv the presence

of a second droy.let bumin:^ iii close proxiinit?', then one 'Jnould exoect

the value of K» to depend both on the Inst&nta^.eous vf^Vies of tJie

droplet dia-neters and on the distance between the droplets. In other

woris, one miKht expect K' to be a function of the tine, Contrf.iy

to this idea. It has been found that X' is co:iStarit, vdthin the

experinient&l li;idt3 of accuracy, for two droplets of r.-heptane

burni:.^ ir. close pixaiuity, I:, fact, cs will be shown in greater

detail presently', the observed valjes of K' seem to defend only

on bhe initial droplet dianeters and on '..he initial spacing betv;een

the droplets burning in &ir.

The observed valatu of K« ~ (l/2) (KJ + K') for droplets in

which D^ and D^ did act differ by more than 20.^i ere plotted as a

function of C in Fi^-, 2v, Eeference to Fi, . 2> shows that the ex-

perlmer:tal results fall rourlOLj- i:ito two catetf,ories depending on the

initial average droi-let dianoter ^ = (l/2) (D + D^). The n^j^abers in

Fig, 29 corresfjond to the naiabers of the f Icnrea in which the raw data

2 2of 2^ vs t a:;.! of D' vs t are shown (Fi^-s, h to 17;. Reference to

Fic> 29 arrows fiSt t!ie average ova oration constant increases vtiien

C is reduced from lar er \-alae8 with ne* lit;ible droplet interference,

pres-inably because heat losses from ..he flaine sarfaoe are reduced

by the prcxLaity of a second heat soiree for safficiently a;iall

values of C j K* reacaes a :jaxinura -^nd then decreases a.;;;ain

as C is made still sr.allcr, A decrease u: X' Tor '.ci^' small

val.'es of C could be prefaced throu.^h the crcatioii o: o:<:; ;:en-

deficient ataospherea re^iultlng froia incrt.-ic.si.Jl co:;ipotitlon Tor oho

oxy^ijr. supply runilshe.: b;; coavcction and dii'i^'-Slo'-, Or. the basis

of i.^e proposea pic cure th.e ;;:a7.i.r;aii ir; olots of K' -v?: C resalta

throu^i.: a balance bcti^eoa owo o^^)fp^JSl:.i^ facte x\-<, viz., Jtcren-jeJ heat

loss :ind decreasea o^^/ er. su.r^ly. The proposed inlfT'pretrtion, if

applicable to a.yx'ny coMdustlon, ...ay ba of cons La«:;i"aoie pri-ctioal

A nuir.ber of atteiii-^-u -Aere aade to relf.te X* .vith simple f;inctioris

oi' C , C / ^, C + L", (C + li*^) / V , etc., ii-. crdfai' to reduce

t'.ie scatter o.f exper bier.tal points Tor diX'ferent vcljes of It. Tr«e3e

efforts v?ere, hov;ever, ji).successful aiid su, ,est tr\at r-he e\u .citation

cor start, K', which is indepi^ndont c?' initial urop?wet dilamer.er ui

sin-.le djpoplet studies, loses its si/jiificance as a basic co:.*rel2tinj

parair.eter j'or Iho droplets ui!rnin«; i,; close pro:>; !..,iit, ' • ''.ether or

not this ccnciuslcn ap. 3 ley to spra; s carj-iot be said v.it:'iou'. further

ejrperL:iental work. In t:io ,::eartt.uae, noKt.ver, it a--ears tiiat, v Lthout

f-'.rthfcr proof, &/plicabliity of Cie droplet o,\rr,i'- relation D - (D ) -

K'bj'.ised ill Fix)bert*s analysis, i3 e abject to soao vxaestion, Th£5 fact

ti'.at K« varies with I)^ is sacwr. lEore directly by plotlin.:; "X» as

~oa f iTiction of D for a --rc/ip of e. porLT.e.'ital data >vlth nearly eqial

Vcilaea of C •

T«fo burainc droiileto iiet.t the re..>.ilrer.i€ints o^ jeonetrxc

sirailaritj imer. laey have tho same vnlias of C/ V a :d of iT, It

-10-

is easily' shoiflm from plois of c/ D v£ L thot (nearly) inter-

secting Curves; are chari^cterised by -reatl^^ dii-Tcre-it vclues of

K* if the valuttb of D are different. In ether -livoras, the value

of the ovciporatloR constant is dcter.iiinci prLii-.ril;. )yj the initial

conditions 5ind, if fit all, or^l^y to a lesser extont by jecneli-^ical

arran;x*uent. It ia pcssible that the initial convection cirrsnts,

rriich depend on the initial conditions, exert a profoiind ii-ifliiencc

on the humirii^ of two adjacent droplets throM;^'hout the droolct

life.

B, Eva: oration Frequencies

La view of the apparent deoendence of F' o;i ^, ctte^pts

»?ere made to fLnd a cimple fjnction of K« and S^ which would

depeiid only on C or or. a IciottTi i"unci Ion of c' aivl D • In

obvious choice ia the ratio K" = 7j/ {u) to ^^ihicn we sli«ll refer

as the evaporatLon fr-eqaoncy«

In Fi.vS. 30 to 32 vv© ruive plotted ?" as a f'lriCtlon of C ,

G -4- D , P:xA C / D , Inspect ivelj--. fieference to Fir a. 3-' to 32

shows that a fair correlation of all of the exp-erl-nental daita has

beer: obtained, the scatter bein^ perhaps sr.ialler in the plots usini;;

C and C + D as abscissa than in the plot us in.-; the diiLonsionless

quantity (f^/ D • In the absence of an adequate theor;^' concer.iini^

droplet interfer'erice, tho ai::r-ifica;ice of tne ohservud "correlations"

is obscurfc, ag is also any e^.trai^olatior: to sprang. For this reason

WG nra3t content ourselvc-s vvitli ine observation th^it, for tvjo ii-hepUrie

2droplets .irninr! in close proxi.'::ity, !.hc obsejn'od val.es of "^'/ (^)

-31-

ore fairly werul represented fcs a i'liriction of elirier C or cf C + D •

Ccnstancy of the evaporaiion fre.iaency, e:^:cept for rarj.utions in c"^,

j-'eans that tiiG fundanien t^.! b-imir.;; rate law for fixed Voluss of C

}i£.3 the To I'm

(D)^ = {Iff - K* (D^)^ t

Tiie fla.iib sl';«tpeG for t^.u ciropletG, an for single drofletb, are

doteriuined liir^ely bv convection cjrrerxts* A qualitativti description

of flatic shapes O'm bt riven on the basis of G.vaileble ext eri:.iCAtal

nieasureiaen ta

.

A. Fla;:ve : napes for i- iri; le Stationar;;,- I-\tel Droplets Burniag iri i-ir

According to an elaboration* of obsci-vatlons bj' Kimiajai and Kixrtura

(9), a realistic description can be obtained Tor the ilaTie sliape uur-

rounding a burntnc siiij^le, stationary, droplet of fuel in air by

ailowin^: Cor rlie influence of free convGction*

ix bumin- fuel droplet i:"; air must produce free convection

currents. I;; Vxi, 33 w« anow a acharaatic aia-ran: of the flaasG

3hai>e ."or a 6i!\:lfc droplet* 'Vo s^iall assane that tlie convection velocity

corresponds to a unifonn flow with velocity U at aoiae distance upstroan

from the initial \indistarbed fianic front. The combination of ::iniing

droplet and convective flov then acts as a source in a u.nifonn flow

field and, at steady burning,, establishes the flow f>attern corresnond-

irij to a half bodj as lower boandai^.-. The streaia surface tVax»jJi the

Tiie present discussion is based on ideas for::;alated by L. Lees a-^

3, :•• Penner.

-12-

lovTSr stat,riatiox\ j^oint rjE;- be tlioUjjht of as dividi:-.,- initially the

3tre3ni lliiea orifjiiiaoini, JTrosi the syurce (fuel droplet) and the stream-

liner; establishfed b;;' con vective Hw-w. This 8itu£tion is, however,

unstable mid difiusJ.ve traa.suort or oxidizer and I'uel across the stream

surface aust be- established, llie tango:..tiel Ilov^ velocitiea at the

stream, surface of fuel vapor azA air are iititially cquol. :'rt sdjrjfiblj'

concentration and teiuperatare gradients are establicliel durinr; steadj'

burii^jig in such a Tvay that difrusiv^e trar^sport of fael and ox^r.^-on

brings a stoichiometric mixture rou,:r)ly to the stream surface, thereby-

makinc the lower stream surface a flacae surface.

Most of the Tuel varor is deflecLed around the stream srarface

and ultiinatcly foovcn verLically u.-marxi through e cylinUfcr or diameter

b« iin air flow if establiaiicd ];.arallGl to the fuel How, iaoving v;ith

the same uniform, velocity U as t-he approach strcan and the fuel

vapor. He/xe ccnUilicjji; arc established for Uie i'oriu.tion of an

over/entilated diffusion rie;ue «na cho florae height h can presum-

ably be calculuttd, in first a/iroxinifation, rr-oz the classJ.cal trent-

liient of Bj-rke ar^d J;Chur::c;.i. ior diffusion flar.es.

The precedLnt, ren^arl-i /lay be suiisnarized by notin;; ihe^t the effect

of freu convection i^, i . lirsb afnro>.LT.ation, a distortion oi the

sphericril fltine front to a fLame surface whose lower bouri.ary is the

stream surface corresponc-ir-' to a source of strenr-th n^ j>~, ('^y =

ma23 rate of burr.int,- of f.iel droplet, /^, = density of fuel vapor)

-1>

in a iinii'ona flow of velocity U5 the upper flfiine durface may be

described as the ilaae fronc i'or a cylindrical diilualon flcurte with

the iiiside cylinder ol' dianeter b and the ilov< velocities of i'uel

and air eqaai to U.

Th€» postialated description of the flarne surface leaaa to resiilts

v/iiica are In accord with tlic observat ons of Ko-iia-ai and Kii'aura. Thus

2b = V'sy/j, T, U ,'

[k]

and

2b/a =: 2 \| 2. [5]

Piirbharrr.ore, since U siii 6 (i.e., Ihe ta.i,:\3."itir'J. :1ow velocity'

of air at the stre&n surface) imst be eqicT.l to the ta::jtjntial i^.ovv

velocity of :?acl va;^or, o.-;e .voold expect t'li&t U and 'A-, are pro-

portional to each othGr#

Tliusj-ij [6]

since n^ is ki'iown to be projrortional to the diaiaeter oi Uit burriing

fuel droplet, ..Isc b saouli be a constant for a ivei'i luel drop-

let and oxidizi/:(j medi-rr.; Kaniarjai and Kir. - (9) ^v/^u^id b to re;.Tain

unchanged, for e^iaranle, foi" cctanc oil ay tne droplet dia..cter was

increased from about 0,0? to 0,12 ca.

The functional foni of tlic relc-tion bec-eari b, ll,, and li,

aD jjiveri in Evj^ation \k\ , ia in accoi'd both uith ttie picture of a

lower fliicie s-irface corresponding; to the jtrei-;i surfo-Co ^"d also «ith

the foliovi'inti conaidertttio/.s, L'osx. of trie energy trails orx, co the fuel

droplet occurs frojii t;*e uppti' flai^io suritcfc, T':d ai<.a or tiiic surface

(for h5:b) is rougirjlj' proportional to bh, :But for a cylindrical

2 3diffusLon ilaae h ~b U# hence Jne fiauo siirface varies aa b J.

Tlie enerjjiy trarisport to trie fiiel droplet is pi^op-ortionai to zt\e pro(iict

of ilaue surfcuct and tciii:>oi'«iLure ^radiait at liie fla'ue ii^rface* The

lacter qvmntity woald be oipected to vc^ry roag:iiy as l/b, i'^inallv,

trie total enerj-y transport to the fuel di'olet :.ia5t be :)rcr>ortlonal

Lo iip' y?r^, T'nerefore,

b^U ~ V/^F

or"1

Although the picture of the foiii.ation of a hetero^er.eoua diffasion

fla.7je tiiven above seems qjalitativel.^- correct, it is apparent that a

complete solution of the nrobler. under consideration ca.jiot be ob-

tained without a quar.titative ai;al;>si8 of erers;- transr.>ort to the

droplet from the fla:ne boundaries, Ho^evtr, the qualiUitlve consider-

ations baaed on tne vior^. of Kunva.ai and Kicura and sketciied above

suu.:,:'est that the following in-'ort-ant resilte ivlll be obtair.eci: (a)

iUjj, weakly deT>endent on flaiiie shape; (b) \] and h propoxi/ional to

L| (c) h proi^ortional to b j (d) b ;Ln iependent of D,

B. Fla_.e ::hace8 for Two n-Heotane D-oivlets Burn I j; ir; Clioe Proxiiui^

For two n-heptar.e droplets burnlr.j; in close r^roxl..dty it Vias

-ir-

al,rf>od:.- bcGT /.o-'.od ^avt^. a , b , a , r.;:d b cbi^ncro vert' ?JLttIe diirlnc12 2 c

droplet birnino Parth-enrzope, reference to Fir:3» U to 0, Pic* 1-^ ^^^

Fills, 1') to 26 ahowJt'vit t.he rctio oi" b to a is not oesisibl^r

di i'foi'ont rzxHa iirilt;/ £nd doec not sgcjj:. to depcrid strong:;!:/ o;. C •

Iri sa-.\e c^^icoc, the dititGiicea of tJie flc-ae s.irfacee frc-ia the drop-

let surfaces reri^ilned constant d;:riiij bumliij (see i^o 2).

Tlie vIrorxLe3t spacin:; jjcraiiictcr C is, 0'2 coi-irse, detorr.iined

tiuX/fJi^li til© £eix.xitrlc iii-ranrer^ient, Tlx:q

C =: C^ ^ (1/2) (D^ - D^) + (1/2;(D^ - Dg)

or

c .= c^(i/2;d^j

1-J

^jt/ (dJj^' V(i/2)d^ \ 1 . ' k^~(e|)^ I 17]

ISeedlesB to say, t'jo Ih^e dei^ondonce of C is v;ell repreoailod "by

ikfiation [?] , ae a'-iovsn ii'i Pi;:. ^*

V. ca;cu-£io!iG

Tie .LriVeatijatioiie of droplet interi'erei\oe dur.sj:j j<ani*ng

described in tiiis ru^x^rt liave sixj^ftin a vdirioar of ii..exp»«5t©*.i i^o-olto

which aa:, r/oll be of iiaportojnce for a fuiidaxjental ondorataiidi^i.: o»

spray ca.Tbustion. Iii particular, the fact tiiat tl:je evaporation

conatiint is no lon^jer independej;t of dirsplet diajaeter for fixed

spacing; roquii^es further stud;/* Aii obvious extension of tli© preaer.t

experjj.jental proi^rara leads to bumin,; rate 8t:-wiie8 on ai..rple ^eo^-^etric

ax*ra^s, saoi'i as five droplets. It ia also app-arwit tiiat soiae funda-

LTter/KfOl tliOGi^tical studies on iiitez'rorence djriiio' biix^il'i,'; are re-

qiiii^ed.

-16-

bntion and He^at Tranorer in •^^^e-Fli-.-nc Be.^JLor.," by -;, A, /.• 3odcave,

National C-as Tiirtjine t'Stablis>inent (Fncl^nd) Iiepor-t Mo. K« 66, l^/i^O,

2. "Tt^ iini:Lnc of 5in:;le Drops of Pads Part 11, l^terLmriUJi

iieffviitii, " b;,^ G» A, •.• uo:lsave, i-,atioi;cl :;tts 'Airblno iie'UiiJiia.V

3» "An ^jcporJjrj©::':^! C^iUQ^j- oi* tiio ;rjrr*i.-*ij of ^iri^e lirci^B oi? F\iel

ii". Air at Pr'^^i^Mca .r. to ;%.€«?V .'.t.*oap.»«r«o, " by /i, !•.• iiall a; id

J# Di6J.eric?"?SQn, •^.-i-^h drtexiiftlcna?.) ,'-'.':apo;; iu.,: an Goribr^cilona

'. illiasiw aiid vvilkiris Coft;<!>£w)y, lJcJ.ti iJie, l/:^3» PP« o3?-oi4(.'»

2i. "Or^ t^ie liumiiit. of iln-le- uro'-s of Tiel L* a-i i:icidi2iirij i\t-

...-c-rjjlusre, •* b^ ^. Joidsiiitii aid w-. o, P«j-::.er, Jet ?ropJLwlo.':,

;ol« 2h,> ii>5'ii, y?« 2li:?-25l« ""cfe also ^£HAH.'iHi?iiJ-lJi!^

Sti.'iy oC Ctiatalcal re^i^tionj in .'-lav/ _ -jiterjc;, by S, 3, ye,r~,Gr,

£k»ti.orj?.>irS;lio Publicistioas, Lt-d«, lA/::don VJl'St Ohapt>ej. h«

i?« "]jQ-;erii3onts on Um Ikimln^, of iiln->Le Drops of JUel in Qx/rf,en-

Xnero 3to ;i1xt.*rGSp " l^r ;<, CQlas-:dt'i and C, K« Perici:-.2, Tecbiiical

Koj-ort Mo# ti, Co::.vruct -^a» iIA-;il,>-0*i-UiC, Ccllforua I.-atlUite

of TBc'Ticlo::/, bva^j" 19514.

6, "ro-iO i'spects of the (>>fib-iat.io'\ o.^ T..;'.q :id M:elc," Ir. C. C. :i'av©o

and jj. '.erstein In Co:.j?.)ustiori i'iesea.i'cr.cs ajiiu. I^evieivs, !>;:•:>,

bwlter^'Oi't .& Pablic&tiona, Ltu., lAHiaoa l>'5i'.

?. "T;:c I.'.na&.-xe oi' r-'A.- i'art..3le ..lie ar.u L-lstrlbut Ion iii Uie

Oai^: -tic:-: o; Oi:i rroolets,'» !y -. -^. Proboi^, .^'sUojo :>Lcal' ' ...... I .1. f .1

;^a_£3lne. Vol. 3'', ior:3^ pp oi;«iO''.

-]. "Oi f.he CorfviEt^-o-r'. \iRtQ of a C-ro;ip of Fuel ?a;*t.iclcs Injcctod

TiiSMJi^n a :A?irl i.ozale, " b;.- f. iaoasfatja. Vfac'i ;olo.^, i.u /or"u"i of

'^^oltok'.^ ''ii.\ve:;c;Lv::, , Vol. IvO, i;/>.^, ,;p. l^;.'"2w ,, ...eiidai, Jaj-^u:.

>. "Coi.'.avii» iaon of Fuel Dropi^ti;, " by :j. ;:'ir:c,ai and I. Kii.v.:rs,

->aier.cc o:: .jachirie^ Vol. 3, T'^l* 1}P» It31"4i3li«

-17-

/Quartz fibers

Liquid droplets

Flome surface

FIGURE I. SCHEMATIC ARRANGEMENT OF FLAMEINTERFERENCE EXPERIMENT WITH TWO DROPLETSBURNING IN CLOSE PROXIMITY

-18-

IGNITION

T = 0.53 SEC. T=l.70 SEC.

T= 0.75 SEC.

FjiT=0.92 SEC.

T = l.90 SEC

T=2.I5 SEC

T=l.28 SEC. T=2.40SEG.

FIGURE 2. PHOTOGRAPH OF TWO n -HEPTANE

DROPLETS BURNING IN AIR (D? =

0.181cm, D?=0. 174cm, C*=O.II4cm)

-19-

2U

0)

Q>n«^ I.

0)

^ o.^ oo L.3 "OO \ ^ ^

\

—

o

1

o

O <D

^?IfO

I-LiJ

_ia.occQ

o

<or

iQO<UJXo

o

z:

00 S2

ro

UJor3O

-20- .3t

.2-

\:

Bo

••

(Ai.0)

0)

£SoQ.

a>Q.o(0

0>

EoLL

• 1 >^ t •7Sg

.3

— -A .2

.1

02Ea

D?K!=.0094

Kf.0082

.03+

.02

.01

o

.2 .4 B 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4

trme, sec

FIGURE 4, EXPERIMENTAL RESULTS FOR TWO n-

HEPTANE DROPLETS BURNING IN STILL AIR (D?=QI94

cm, Df=O.I66cm, C°=0.020cm)

A

-21- •3-H

A.̂- .2 -

Eo

a;

•1--V' ' E

3 -

A '^^-—^

''\ .2

E.._o

Ll_

I-

-\[ h

02

-» « \-

oQ.

(UCLOxzto

.3"

--0

K=.0094

.2 .4 6 .8 1.0 1.2 1.4 1.6 1,8 2.0 2.2 2.4time, sec

FIGURE 5. EXPERIMENTAL RESULTS FOR TWO n -

HEPTANE DROPLETS BURNING IN STILL AIR (D?=O.I8lcm,

D?=O.I74cm, C°=O.II4cm)

-22-

.0 .2 .6 .8 1.0 1.2 14 1.6 1.8 2.0 2,2 2.4time, sec

FIGURE 6. EXPERIMENTAL RESULTS FOR TWO n-

HEPTANE DROPLETS BURNING IN STILL AIR (D?-0.I66

cm, D?= 0.154cm, C°= 0.183cm)

-23-

.̂y

.3

.2

£o

u.<b

6ooQ.

a>Q.o

a>

Eou.

• t-

-* r- -* *- -Ji'^

^r

.3

.a

.1 +

.3

.2

.1

Eo

-J-O

K=.0096

.2 .4 .6 .8 1.0 (.2 1.4 1.6 1.8 2.0 2.2 2.4time, sec

FIGURE 7 EXPERIMENTAL RESULTS FOR TWO n-

HEPTANE DROPLETS BURNING IN STILL AIR (D?=0.I92

cm, D^O.I76cm, C°=0.230cm)

-24-

^-^-'^a-

A

.3t

.2-

.Ifff

Eo

bi

--X__u

H 1- H f-

.3-

oQ.

Q.o

.2-1-1^

E

.35-

.30-

.25-ao

O

^' K^ .0136

Kf.OI22

.034-

.02

.01.

™Eo

Q

2 .4 .6 .8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2-4

time, sec

FIGURE 8. EXPERIMENTAL RESULTS FOR TWO n -

HEPTANE DROPLETS BURNING IN STILL AIR (D{^-QI65

cm, DS= 0.142cm, C^=0.264cm)

25-

A A

2 X

k;=K=.0I40

.04

.03

.02

01

o

.8 10 l.a 1.4 1.6

time, sec

(D?=O.I82cm, D?=0. 182cm, C°=Q892cm)

1.8 2.0 2.2 2.4

^

.04

.03

.02 4-

.01

—i1 1 1 1 1 1 1 1

\1

—

.2 A g a 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4time, sec

(D°=O.I82cm, D?=O.I73cm, C°=0.752cm

)

FIGURE 9. PLOTS OF D^vs time FOR TWO n -HEPTANEDROPLETS BURNING IN STILL AIR FOR VARIOUS C

-26-

.2 .4 .6 .8 1.0 12 1.4 1.6 18 20time, sec

^2 2,4

(D*'=O.I82cm , D^=O.I56cm, C^= 1.47cm )

A

K2=X)I33

.03 -

,02

.01

•6

a-jHQ

D 2 A ,6 JB 10 1.2 W 1.6 1.8 20 22 2v4»

time, sec

(D?=O.I73cm, D?=O.I73cm, C^=l. 125cm)

FIGURE 10. PLOTS OF Cfvs time FOR TWO n -HEPTANEDROPLETS BURNING IN STILL AIR FOR VARIOUS G^

-27

.4 .6 .8 1.0 1.2

time, sec

1.4 1.6 1.8 2.0 2.2 ^4

(D?=0. 138cm, D^O.I34cm, C°=0.208cm)

.2 -6 .8 1.0 12 1.4

time, sec

1.6 IJB 2.0 22 2,4

(D^O.I30cm, D;=0.127cm, C°=0.222cm)

FIGURE II. PLOTS OF D^vs time and Cvs time FOR TWOn -HEPTANE DROPLETS BURNING IN STILL AIR FORVARIOUS C°

'28-

.2 .4 6 .8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4

time, sec

(D?=ai24cm, D?=O.I24cm, C^=0.235cm)

1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4

time, sec

tD?=O.I35cnv D?= O.II'Jm,C°=Q3l3cm)

FIGURE 12. PLOTS OF D%s time and C vs time FOR TWOn-HEPTANE DROPLETS BURNING INSTILL AIR FORVARIOUS C

6 .8 1.0 1.2 1.4 1.6 1.8 20 2.2 2.4

time, sec

(C?=J33 cm, D^J22cm, C=.540cm)

.2 .6 .8 2.0 2.2 Z4».0 1.2 U 1.6 L8

time, sec

(D?=. 126cm, DP=. 126cm , (7=0.40cm)

FfGURE 13. PLOTS OF D\s time and C vs time FORTWOn-HEPTANE DROPLETS BURNING IN STILL AIR

FOR VARIOUS C^

-30-

ih.

.5--

.4-

'^dKrKf.0074

.oaf

-I 1 ( ^-

Eo

O

"o-

1.2 1.4 1.6 1.8 2.0 2.a 2.4time, sec

2 .4 .6 .8

{D?=0.l2lcm,Df=O.II8cm,C°=0.384cm)

2 1.4 1.6 1.8 2.0 2.2 2.4time, sec ,

(D?«O.I36crnp?=0.120cm C°=0.496cm)FIGURE 14. PLOTS OF D'vs time and Cvs time FOR TWOn-HEPTANE DROPLETS BURNING IN STILL AIR FOR

VARIOUS C°

-31-

^ 2 X.

-—^

.3

.2

Eo

a>

a>

Eooo.

a>

o

Eo

H 1\

1 1 H

.3

.2

.54-

.53-

Eo

O

^^

K=0II8

Kf.OIIO

4-

03+

.02

.014-

o

.2 .4 .6 .8 I.O 1.2 1.4 1.6 1.8 2.0 2.2 2.4

time, sec

FIGURE 15. EXPERIMENTAL RESULTS FOR TWO n -

HEPTANE DROPLETS BURNING IN STILL AIR (D?=0.I43 cm,

D^O.I42cm,C°=0.533cm)

-3a-

(D?=0J55crT^ DS=O.I42cm, C°=0.496cm)

.2 .4 6 1.8 2.0 2.2 2.48 1.0 1.2 1.4

time,sec

(D?=O.I4lcm , DJ=O.I35cm , C°=0.538cm )

FIGURE 16. PLOTS OF D%s time ond vslime FOR TWOn-

HEPTANE DROPLETS BURNING IN STILL AIR FORVARIOUS C**

-33-

D^

__k;=.oio7

' Kf.0108

P3

.02-

.01

-f

-- d£

.2 .4 .6 .8 1.0 1.2 1.4 L6

time,, sec

(D?=ai56cm,D?=O.I56crn CMIOcm)

8 2.0 22 2.4

.03"

-- CM

Eo

.8 1.0 1.2

time, sec

2.0 2.2 2.4

(D?= 0. 15 6cm, D?=ai4lcm , C^=0.883crTi

C4

Eo

1.0 1.2 1.4 16 1.8 2.0 2.2 2.4time, sec

(D?=0.l56tm, D?=0.147cm, C"'=0.8l3crti)

FIGURE 17. PLOTS OF D'vs time FOR TWOn- HEPTANEDROPLETS BURNING IN STILL AIR FOR VARIOUS C"

-34-

A-

-b,

-1—1.-^

4 h -I 1 1-

.3t

.2

H \2

BEouOQ.

0)Q.O

.2-

Eo

10

ioLL

.24-

.15

.1

£

-- O

k;=.oio7 OT-

.02

.01

L- N£o

1d^

:^J—

+

4 1 1 1 1 1 1 1 1 1

O'' .6 .8 1.0 1.2 1.4 \£ 1.8 2.0 2.2 2.4 2.6 28time, sec

FIGURE' 18. EXPERIMENTAL RESULTS FOR TWO n-HEPTANE DROPLETS BURNING IN STILL AIR (D?=0.208cm, D1=0. 155cm, C^=O.I26cm)

-35-

CL-^Vv:

.3+

•2+Eoto

a>

%Eo1-oo.

.3-1- Q>o.o(0

.2-

EJOLl

Eo

.2 .4 .6 .8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4

tim6 S6C.

FIGURE 19. EXPERIMENTAL RESULTS FOR TWO n-

HEPTANE DROPLETS BURNING IN STILL AIR (D?=Q209

cm, Dt=O.I70cm,G°=0.352cm )

-36-

b,--

•—

•

• • • f f^—^ * ^

~oA A_

br

\.

H h H h

.3t

.2+ Eotol_0)

0)

Eooaa.

o

Io

.45

.40t

.35

Eo

K?.0090

K=.0089

6

.03-

k;=:.oo8';^2Eo

Q

4- + +.8 1.0 1.8 2.0 2.2 2.4 2.6 2.81.2 14 1.6

time, sec.

FIGURE 20. EXPERIMENTAL RESULTS FOR TWO n-HEPTANE DROPLETS BURNING IN STILL AIR (D?=0.I98

cm, D?=O.I40cm , C^=0.375cm )

-37-

Eo

I-

Eok_oQ.

0)Q.O

a>

Eo

Eo

- O

Eo

"a

1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4

time sec.

FIGURE 21. EXPERMENTAL RESULTS FOR TWO n-

HEPTANE DROPLETS BURNING IN STILL AIR (D'?=

0.167cm, D?=0.II5 cm, 0"= 0.520 cm)

1.0 L2 1.4

time sec.

FIGURE 22. EXPERIMENTAL RESULTS FOR TWOHEPTANE DROPLETS BURNING IN STILL AIR (D?

cm, DS=O.I3lcm, C°=0.532cm)

n -

0.160

-39-

^

-^~^r^,

.3t

2- E

L.Q)

0)

Eo

.3"

.2--

.064-

.04

02

K =0068

.034

.02

.01 +

HI + H 1-

oQ.

a>Q.o

Eo

Eo•s

O

t*.

Eo

.8 1.0 1.2 1.4 1.6 1.8 Z.0 2.2 2.4 2.6 2.8 3.0

time sec.

FIGURE 23. EXPERIMENTAL RESULTS FOR TWO n-

HEPTANE DROPLETS BURNING IN STILL AIR (D?=0.I92

cm, D?=O.I48crn. G°=0.026cm)

-40-

FIGURE 24. EXPERIMENTAL RESULTS FOR TWO n-

HEPTANE DROPLETS BURNING IN STILL AIR (Df=0.208• cm, Df=O.I64cm, C°=O.I50cm)

-t h

.0 1.2 1.4 1.6 1.8 2.0 2.2 2Atime, sec

FIGURE 25. EXPERIMENTAL RESULTS FOR TWO n-

HEPTANE DROPLETS BURNING IN STILL AIR (D? =

QI9lcrrv Df=Q178cni, G°=0246cm)

A

-42-

^A *^

^T"^—«—^—

*

Eo

+-

Eo

^ ) 1 1 1 1 1 1 1 1 f-

.2 A .6 .8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4

time, sec

FIGURE 26. EXPERIMENTAL RESULTS FOR TWO n-

HEPTANE DROPLETS BURNING INSTILL AIR (Df=

QI92cm, D?=QI80cm, G^=0355cm)

-43- 3t

J fc_ t—-*-* ^.2-

.1"

Eo

«EooQ.<DO.O(O

0>

Eo

51..

.3 -

.2-

\-Ql-^1

.45-

^^

Dl

d:

•x

i^

.03 -

.02-- -

.01

Eo

3 .2 .4 .6 .8 1.0 1.2 1.4 1.6 1.8 20 2.2 2.4

tim^, sec

FIGURE 27. EXPERIMENTAL RESULTS FOR TWO n-

HEPTANE DROPLETS BURNING IN STILL AIR (D?=0.202

cm, DS=0.I79 cm, C°=0362crr)

h

-44-

b,-

"E"I f

'1\

^

,3t

.24Eo

-Eok.oa<DQ.o

.3-

.2-

E

,55-

.50 -

.45

(0

Eo

Kr.OI33

.03

.02.-

.01-Eo

.2 A .6 .8 l£) 1.2 1.4 1.6 1.8 2.0 2.2 2.4

time, sec

FIGURE 28. EXPERIMENTAL RESULTS FOR TWO n-

HEPTANE DROPLETS BURNING IN STILL AIR (D?=

0.200 cm, D?=O.I56 cm, G°= 0.466cm)

-45-

UJ«> 1^

.^

enI-UJ

/

.«vi

-00

-^

sOQ

jCVJ

^^o^

o —

< c,

£s

o-h- CO

ogo tiP -»

> IQcr

m P ^S ^ ^UJ ^ h-tr -r UJ=^ s ^o l: <LL 5 Q

ooQ '^j cm sec

-46-

K" secI

-47-

,-lD

.-^

00

.-Q

-^IQ

.-vp

CD

OO

•-'^.

oO+oOzo

UJ3O

o

q:o

%UJ

u

oLiJOzLlI

OzUJa.UJQ

••<\j

^ in ro-• O u.

CVJ

K". sec

-48-

i-CO

-K

O

>-o2:UJ

-.<o

--«o

- "*

-fO

"(VJ

UJCC

O

CCoa.

LU

o LlJ

oOLi.

OLUozLJQUJa.UJQ

ro

LU

3 IQS2 ^

49-

FIGUFE 33. SCHEMATIC DIAGRAM OF BURNINGFUEL DROPLET. STREAMLINES IDENTIFIED

BY ARROWS.

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'o0>(0

t . ^

8 if)

•o 00lO

11

s CVJ

l>d d•k -II

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1

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Gj ,cm

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CM*

(b

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^. E

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.-co

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-CM

COLU

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QUJ

3

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UJ 3.= IQcr +LU oa. oUJ ou.O LiJ

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Interference effects^ring burning in air fortwo stationary n-heptanedroplets

,

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Interference effects duringburning in air for two stationaryn-heptane droplets.