structure and breakup properties of sprays

8/11/2019 Structure and Breakup Properties of Sprays

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~ ergamon

Int. J. Multiphase Flow

Vol. 21, Suppl. pp. 99-127, 1995

Copyright I995 Elsevier Science Ltd

03 01 -9 32 2(9 5)0 00 59 -3 Pr in ted in Great Br i ta in . All r ights reserved

0301-9322/95 29.00 + 0.00

S T R U C T U R E A N D B R E A K U P P R O P E R T I E S O F S P R A Y S

G. M. FAE TH, L . -P . HSIAN G and P .-K . WU

Department of Aerospace Engineering, 3000 FXB B uilding, The University of Michigan, Ann A rbor,

MI 48109-2118, U.S.A .

Received 25 Ju ly 1995)

A b s t r a e t - - M u l t i p h a s e f l o w p h e n o m e n a r e l e v a n t t o s p r a y c o m b u s t i o n a r e r e v i e w e d , e m p h a s i z i n g t h e

s t r u c tu r e o f t h e n ea r - in j ec to r d en s e - s p r ay r eg io n an d th e p r o p e r t i e s o f s eco n d ar y an d p r imar y b r eak u p .

Ex i s t in g meas u r em en t s o f d en s e - s p r ay s t r u c tu r e a r e l imi t ed to r o u n d p r es s u r e - a to mized s p r ay s in s t i ll g ases

an d s h o w t h a t t h e d i s p e r s ed f lo w r eg io n i s s u r p r i s in g ly d ilu t e , t h a t s ep a r a t ed f lo w ef fec ts a r e s ig n i f i can t

b ecau s e th e f lo w i s d i lu t e an d d ev e lo p in g , an d th a t a to miza t io n in v o lv es p r imar y b r eak u p a t t h e l i q u id

s u r f ace f o l lo w ed b y s eco n d a r y b r eak u p , w h i l e e f fec ts o f co l l i s io n s a r e s ma l l . A v a i l ab le in f o r ma t io n ab o u t

s eco n d ar y b r eak u p emp h as izes b r eak u p d u e to s h o ck w av e d i s tu r b an ces a t l a r g e l i q u id /g as d en s i ty r a t io s

an d s h o w s th a t s eco n d ar y b r eak u p i s a d o m in an t f ea tu r e o f d en s e s p r ay s th a t mu s t b e r e s o lv ed a s a

f u n c t io n o f t ime s o th a t s eco n d ar y b r eak u p can b e p r o p e r ly t r ea t ed a s a r a t e p r o ces s . F in a i ly , av a i l ab le

in f o r m a t io n ab o u t p r im ar y b r e ak u p h as b een d o m in a ted b y e ff ec t s o f d i s tu r b an ces in th e in j ec to r p as s ag e ;

t h e r ef o r e , w h il e s o m e u n d e r s t a n d i n g o f t u r b u l e n t p r i m a r y b r e a k u p h a s b e e n a c h i e v e d, m o r e i n f o r m a t i o n

ab o u t ae r o d y n amic p r imar y b r eak u p i s n eed ed to ad d r es s p r ac t i ca l s p r ay co mb u s t io n p r o ces s es .

Key words:

a to miza t io n , d i s p e r s ed f lo w , in j ec t io n , p r imar y b r eak u p , s eco n d ar y b r eak u p , s p r ay s

1 . I N T R O D U C T I O N

T h e r e h a v e b e e n n u m e r o u s s t ud i e s o f n o n - c o m b u s t i n g a n d c o m b u s t i n g s p r ay s , e m p h a s iz i n g t h e

d i l u t e r eg i on f a r f rom t he i n j ec t o r ex i t , where observa t i ons and model i ng a re r e l a t i ve l y t r ac t ab l e

due t o sm al l li qu i d vo l ume f r ac t i ons . As a r esu l t , man y f ea t u res o f d il u t e sp rays a r e unde r s t ood

reaso nab l y well , see t he r ev i ews due t o Gi f f en Mu raszew (1953), Lev i ch (1962) , Har r j e Re ardo n

(1972), Clift

e t a l

(1978) , Le febrv e (1980, 1983 , 1989), Law (1982) , Si r ignano (1983) , Wie rzba

Ta kay am a (1988), Anna ma l a i Ry an (1992) , Fae t h (1977 , 1983 , 1987 , 1990) and r e ferences c i t ed

t here in . Thus , a t t en t i on now i s be i ng d i r ec t ed t o t he l ess access ib l e dense- sp ray r eg i on near t he

i n j ec t o r ex i t , i n o rder t o de t e rmi ne how i n j ec t o r des i gn p roper t i es and t he sp ray env i ronmen t

i n f luence f l ow p roper t i es e n t e r i ng t he d i l u t e - sp ray r eg i on . T hus , t he ob j ec t i ve o f t h is pa per i s t o

b r i e f l y r ev i ew t hese e f fo r t s and t o i den t i fy a r eas where add i t i ona l r esearch i s needed .

Three aspec t s o f mu l t i phase f l ow re l evan t t o sp ray combus t i on a re r ev i ewed as fo l l ows : (1 ) t he

s t ruc t u re o f t he near - i n j ec t o r dense - sp ray r eg i on , in o rder t o he l p def ine t he env i ronme n t o f var i ous

dense sp ra y p rocesses ; (2 ) the p rope r t i es o f seconda ry b reaku p , w h i ch o f t en i s t he r a t e con t ro l l ing

p rocess o f dense sp rays i n much t he same w ay t ha t d rop vapor i za t i on o f t en is the r a t e con t ro l l ing

p rocess o f d i l u te sp rays ; and (3) t he p roper t i es o f p r i mary b reaku p , w h i ch def ine i ni t ia l cond i t i ons

fo r dense sp rays and mos t d i r ec t l y connec t i n j ec t o r des i gn p roper t i es (hardware) and sp ray

proper t i es . Due t o space l i mi t a t i ons , however , p r esen t cons i dera t i ons wi l l be l i mi t ed t o p rocesses

d i r ec t l y r e l evan t t o non-evapora t i ng round p ressu re-a t omi zed sp rays i n s t i l l gases . Ignor i ng

eva pora t i on i s r eason ab l e be cause t he dense- sp ray r eg i on o f com bus t i ng sp ray s genera ll y invo l ves

coo l po r t i ons o f t he f low where r a t es o f hea t and mass t r ans fer a r e modes t . A dd i t i ona l l y j e t f lows

i n s t il l gases a r e a s i mp l e c l ass i ca l f l ow conf i gu ra t i on t ha t exh i b i t mos t f ea t u res o f dense- sp rays

whi l e on l y r equ i r i ng a f ew def i n i ng paramet er s . In fo rmat i on abou t o t her sp ray p rocesses and

inject ion conf igurat ions can be found in the review ar t icles ci ted ear l ier , and references ci ted therein .

In t he fo l l owi ng , dense- sp ray s t ruc t u re , secondary b reakup and p r i mary b reakup wi l l be

cons i dered i n t u rn . T he descr i p t i on o f each t op i c i s su f fi c ien t ly com pl e t e so t ha t i t can be r ead

i ndepende n t l y , i f des ir ed .

IJMF 21 7~ 99


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1 G M FAETH

et a

2. D E N S E S P R A Y S T R U C T U R E

2 1

I n t r o d u c t i o n

Ro un d p ressu re-a t om i zed sp rays i n a s ti ll gas a r e a c l assi ca l sp ray con f i gu ra t i on t ha t wi l l be u sed

t o i l lu s t r a t e t he env i ronm en t o f dense sp rays , based on r esu l ts descr i bed by C l i ft

e t a l .

(1978) , Faeth

(1987, 1990), Ruf f & Fa eth (1995), R uf f

e t a l .

(1989, 1991, 1992), Tseng

e t a l .

(1992a, b , 1995) and

W u

et al .

(1995b) . Ear l y s t ud i es o f t h is sp ray c on f i gu ra t i on em phas i zed sp ray b re akup r eg imes ,

i n c lu d i ng c o n d i t i o n s r e q u i re d f o r th e i m p o r t a n t a t o m i z a t i o n b r e a k u p r e g im e w h e r e d r o p f o r m a t i o n

begins r ight at the jet exi t, see Rei tz & B racc o (1982), M iesse (1955), R an z (1958) and P hinne y

(1973). S ubseq uen t wo rk conc en t r a t ed on v i sua l i za t ion o f the near - i n j ec t o r r eg i on o f t he f l ow and

def i n i ti on o f the p rop er t i es o f the l i qu i d co re , wh i ch i s s i mi l ar t o t he po t en t i a l c o re o f a s i ng l e-phase

j e t , see Ph i nney (1973) , Hoy t & Tay l o r (1977a , b ) , H i royasu

e t a l .

(1982) and Chehroud i

e t a l .

(1985) . M ore r ecen t l y , W u

e t a l .

(1983, 1984) have s t ud i ed t he p rop er t i es o f t he d i l u te sp ray r eg i on

near t he ou t er edge o f t he sp ray . Em phas i s i n t he fo l l owi ng , howe ver , w il l be on t he dense sp ray

r e g io n , b a s e d o n t h e m e a s u r e m e n t s o f R u f f

e t a l .

(1989, 1991, 1992) and Tseng

e t a l .

(1992a, b) .

Fo r t hese con d i t i ons , f l ow reg i mes and f l ow s truc t u re wi l l be cons i dered , i n t u rn .

2.2.

F l o w r e g i m e s

T h e a t o m i z a t i o n b r e a k u p r e g im e o f r o u n d p r e s s u r e - a t o m i z e d s p r a y s is m o s t i m p o r t a n t b e c a u s e

i t p rov i des t he f i ne a t om i za t i on neede d fo r r ap i d m i x i ng o f l i qu id and gas phases du r i ng p rac t i ca l

com bus t i on p rocesses . A ske t ch o f t he fl ow wi t h i n t he near - i n j ec t o r r eg i on fo r th i s b reak up r eg i me

i s i l lu s t r a t ed i n f i gu re 1 . There a r e t wo m ai n m ul t i phase f l ow reg i ons wi th i n dense sp rays ; nam el y ,

t he l i qu i d co re and t he d i sper sed f l ow reg ion be yon d t he su r f ace o f t he l i qu i d co re . As no t ed ear l i e r ,

t he l i qu i d co re i s s i mi l a r t o t he po t en t i a l co re o f a s i ng l e phase j e t , a l t hough i t i s genera l l y much

l o n g e r . F o r e x a m p l e , C h e h r o u d i

e t a l .

(1985) f ind the fo l lowing expression for the length , Lo, of

the l iquid core:

Lc /d = Cc pL : /pG) t/2

[1]

wh ere d is the in jector d iam eter , PL and Pc are the l iquid an d gas densi t ies , respect ively , and Cc

i s an em pi r i ca l cons t an t i n t he r ange 7 -16 . T h i s i mp l ies

L c / d

i n t he r ange 200-500 fo r t yp i ca l sp rays

a t a t mospher i c p ressu re , w i t h t h i s r a t i o genera l l y be i ng i nver se l y p ropor t i ona l t o t he square roo t

o f p ressu re . Thus , l i qu i d co res a r e a very p rom i nen t f ea t u re o f roun d p ressu re-a t omi zed sp rays .

The d i sper sed f l ow reg i on beyond t he l i qu i d su r f ace i nvo l ves a deve l op i ng mul t i phase mi x i ng

l ayer i n t he r eg i on where t he l i qu id co re i s p resen t , f o l l owed by a m u l t i phase j e t t ha t ev o l ves i n t o

a d i l u t e round sp ray f l ow. The mul t i phase mi x i ng l ayer beg i ns c l o se t o t he j e t ex i t w i t h i n t he

a t o m i z a t i o n b r e a k u p r e gi m e . P r im a r y b r e a k u p o c c u r s d u e to t h e f o r m a t i o n o f l ig a m e n t s a n d o t h e r

i r r egu l ar l iqu i d e l emen t s a l ong t he su r f ace o f the l i qu id co re . Thus , r a t es o f p r i mary b rea kup t end

t o con t ro l t he l eng t h o f t he l i qu i d co re . The dense sp ray r eg i on genera l l y i s assoc i a t ed wi t h t he

+ DILUTE

DENSE SPRAY SPR AY

MULTIPHASE_ _ ~ _ _ _ - -- ~

. ~ MIXING LAYER . o

LIQUIFLoW

_ o : o

-- ~k ~---~'-,~'~ ~ o . v 2 .. o

/ ,NI LIQUID CORE r

~

INJECTOR DISPERSEDFLOW

Figure 1. Sketch of the near-injector region of a pressure-atomized spra y in the atomization breakup

regime.


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4/29

1 2

G M. FAETH

e t a l

and t he l i qu i d a r e no t very s ign i f ican t when t he f l ow i s mai n l y l i qu i d . F i na l l y , a l t hough t he var i a t i on

o f l iqu i d vo l um e f r ac t i on sugges t s a r e l a t i ve l y sho r t l i qu i d co re , t h i s is no t t he case wh en v i ew ed

i n t e rms o f mi x t u re f r ac t i on . Resu l t s t o be cons i dered nex t wi ll show t ha t Fa v re-ave raged m i x t u re

f r ac t i ons a r e near un i t y fo r a l l t he cond i t i ons i l l u s t r a t ed i n f i gu re 2 , so t ha t even l ow l eve l s o f

f l app i ng o f t he l i qu i d co re can exp l a i n t he l i qu i d vo l ume f r ac t i on r educ t i ons .

R i co u Spal d i ng (1961) have shown t ha t p roper t i es a long t he ax i s o f s i ng l e-phase var i ab l e -den -

s i ty j e t s shou l d sca l e in t e rms o f a no rm al i zed d ens i t y -wei gh t ed s t r eamw i se d i s tance , p G / p L ) l / 2 x / d ,

w h i l e C h e h r o u d i

e t a l

(1985) r eco mm end s i mi la r sca l ing based on t he i r me asu rem en t s o f l i qu id

co re l eng t hs as d i scussed i n conn ec t i on wi t h [1 ] . Thus , p red i c t ed and m easu red Fav re -average d

mi x t u re f r ac t i ons a l ong t he ax i s , r e , where t he subsc r i p t c deno t es a p rope r t y a l ong t he ax i s (mi x t u re

f r ac t i on s i mp l y co r r espo nds t o t he mass f r ac t i on o f wa t er fo r t hese cond i t i ons ) a r e p l o t t ed as a

func t i on o f t h i s var i ab l e i n f i gu re 3 , fo r t he same cond i t i ons as f i gu re 2 . When p l o t t ed i n t h i s

ma nner , bo t h mea su rem en t s a nd p red i c t i ons exh i b i t l it tl e ef f ec t o f am bi en t p ressu re and a l so show

t ha t l i qu i d vo l ume f r ac t i ons genera l l y a r e near un i t y i n t h i s r eg i on , as no t ed ear l i e r . Never t he l ess ,

t h e L H F p r e d i c ti o n s v a s t l y o v e r e s ti m a t e t h e s u b s e q u e n t r a t e o f r e d u c t i o n o f m a s s f r a c ti o n s w i t h

i ncreas ing s t r eamw i se d is t ance , and t hus t he mi x i ng r a tes . The co r r espond i ng s l ower r a t es o f mi x i ng

a l ong t he ax i s t han L H F p red i c t i ons sugges t s ign i fi can t e ff ec t s o f separa t ed f l ow j us t dow ns t r ea m

of t he end o f the l i qu i d co re . Th i s beha v i o r i s p l aus i b le , beca use b rea kup o f t he end o f t he li qu i d

co re y i e l d s l a rge d rops t ha t ma i n t a i n s i gn if i can t r e l a t i ve ve loc i t ies due t o t he i r l a rge i ner ti a . T hus ,

separa t ed f l ow ef f ec ts a r e an i mp or t an t f ea t u re o f dense sp rays . An o t her r esu l t il l u s tr a t ed i n f igu re

3 is t he e f f ec t o f j e t ex i t f low cond i t i ons on s p ray m i x i ng r a t es as ev i dence d by t he s l ower r a t e o f

deve l opm en t o f the non - t u rbu l en t s l ug f low in com par i son t o t he fu l ly -deve l oped t u rbu l en t p i pe

f l ow a t t he j e t ex i t (mos t ev i den t a t t he f a r t hes t downs t r eam pos i t i on ) .

Pred i c t ed and m easu re d r ad i a l p ro fi les o f me an l i qu id vo l ume f r ac t i ons a t a t mo spher i c p ressu re

are p l o t t ed as a func t i on o f r ad ia l d i s t ance , r , in f i gu re 4 , fo r t he same c ond i t i ons a s f igu res 2 and

3 . T h e i n d e p e n d e n t m e a s u r e m e n t s o f R u f f

e t a l

(1989) and Tseng

e t a L

(1992a) ag ree wi t h i n

exper i me n t a l uncer t a in t i es , excep t fo r

x / d

= 100 where t he g rea t e r c on f i nemen t o f t he f l ow s tud i ed

b y T s e n g

e t a l

(1992a) mi gh t be a f ac t o r . The m easu rem en t s show a p rog ress i ve i ncrease o f f l ow

w i d t h w i t h i n c re a s in g d i s t a n c e f r o m t h e j e t e x it . T h e c o m p a r i s o n b e t w e e n L H F p r e d i c ti o n s a n d

1.0

0.8

0.6

0.4

1.0

0.8

0.6

0.4

FULLY -D EVE LO PED F L O W ~

1

P R . E N T

2 PRESENT

V 4 PRESENT

0 8 PRESENT

I RUFF tol

THEORY

I-8 PRESENT

0.2

o.o

I I I I

0 2 4 6 I0 12

I 2

P e P t . ) x l c l

Figur e 3 . Favre-averag ed mix ture frac t ions a long the ax is o f round pressure-a tomized w ater sprays in s ti l l

a i r a t variou s pressures for a tom izat ion bre akup wi th fu l ly -developed turbulen t p ipe f low a t the je t ex i t.

F r o m T s e n g et al. 1992a).


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STRUCTURE AND BREAKUP PROPERTIES OF SPRAYS 103

m e a s u r e m e n t s i s r e a s o n a b l y g o o d , e x c e p t a t l a r g e r v a l u e s o f

x / d :

R u f f

e t a l .

(1989) show tha t th i s

d i f f ic u l t y i s d u e t o e f f ec t s o f s e p a r a t e d f l o w a s t h e f l o w b e c o m e s m o r e d i l u te .

T s e n g

e t a l .

( 1 99 2 b ) d i r e c t l y a s se s s e f fe c ts o f s e p a r a t e d f l o w in t h e d e n s e s p r a y r e g i o n o f r o u n d

p r e s s u r e - a t o m i z e d s p r a y s u s i n g d o u b l e - p u l s e d h o l o g r a p h y t o m e a s u r e d r o p s i z e a n d v e l o c i t y

d i s t r i b u t i o n s , i n t h e m i x i n g l a y e r , a s w e ll a s t h e p o s i t i o n o f t h e s u r f a c e o f t h e l i q u i d c o r e . T h e s e

r e s u l ts a l l o w e d t h e d e t e r m i n a t i o n o f F a v r e - a v e r a g e d f l o w v e l o ci ti e s, f o r d i r e c t c o m p a r i s o n w i t h

L H F p r e d i c t i o n s , a s s u m i n g t h a t t h e v e l o c it i es o f 5 [ t m d i a m e t e r d r o p s w e r e r e p r e s e n ta t i v e o f g a s

v e l o ci t ie s . T h e r e s u l t i n g m e a s u r e d a n d p r e d i c t e d s t r e a m w i s e m e a n p h a s e v e l o c i ti e s ( F a v r e - a v e r a g e d

a n d g a s p h a s e v e l o c i t i e s ) a t a t y p i c a l s t r e a m w i s e l o c a t i o n

x / d

= 25) a re p lo t t ed in f igure 5 fo r

a m b i e n t p r e s s u r e s o f 1 , 2 a n d 4 a t m . T h e v e l o ci t ie s o n t h i s p l o t a r e n o r m a l i z e d b y t h e i n j e c t o r ex i t

v e l o c i t y , U o. T h e r a n g e o f m e a s u r e d p o s i t i o n s o f t h e l i q u i d s u r f a c e ar e a l s o s h o w n o n t h e p l o t s f o r

r e f e r e n c e p u r p o s e s . I n g e n e r a l, t h e m e a s u r e d F a v r e - a v e r a g e d v e l o c i t y i s s i g n i fi c a n t ly g r e a t e r t h a n

t h e g a s v e l o c i t y , a l t h o u g h t h e d i f f e r e n c e s b e t w e e n t h e t w o d e c r e a s e a s t h e a m b i e n t p r e s s u r e

i n c r ea s e s. I n a d d i t i o n , t h e L H F p r e d i c t i o n s a r e n o t v e r y s a t i s f a c t o r y , w h i c h i s e x p e c t e d d u e t o t h e

p r e s e n c e o f s i g n i f i c a n t e f fe c ts o f s e p a r a t e d f l ow .

A d d i t i o n a l i n s i g h t c o n c e r n i n g s e p a r a t e d - f l o w e f f ec t s i n d e n s e s p r a y s c a n b e o b t a i n e d f r o m t h e

s t ruc tu re p ro pe r t i e s p lo t t e d in f igure 6 . The re su l t s in th i s f igure inc lude the e l l ip t i c ity o f the d ro ps ,

e p, t h e S a u t e r m e a n d i a m e t e r o f t h e s p r a y , S M D , a n d d r o p v e l o ci t ie s , Up f o r v a r i o u s d r o p d i a m e t e r s ,

d p. T h e s e r e s u lt s a r e f o r t h e s a m e c o n d i t i o n s a s f i g u re 5 , w i t h b o t h d a t a a n d p r e d i c t i o n s o b t a i n e d

f r o m R u f f

e t a l .

( 19 92 ), b u t t h e y a r e t y p i c a l o f f i n d in g s a t o t h e r c o n d i t i o n s w i t h i n t h e d e n s e s p r a y

reg ion . The reg ion nea r the l iqu id sur face cons i s t s o f l a rge , i r regu la r , l igam ent - l ike e lem ents ( l a rge

e v a n d S M D ) , e v e n t h o u g h t h i s s p r a y h a d g o o d a t o m i z a t i o n p r o p e r ti e s , w h i l e t h e d i l u t e s p r a y r e g i o n

n e a r t h e e d g e o f t h e f l o w i n v o l v e s s m a l le r r o u n d d r o p s . T h i s p r o v i d e s d i r e c t e v i d en c e o f s i g n i fi c a n t

l e v e l s o f s e c o n d a r y b r e a k u p i n t h e d e n s e s p r a y r e g i o n n e a r t h e l i q u i d s u r f a c e . I n a d d i t i o n , t h e

d i s p e r s e d f l o w r e g i o n , e x t e r io r t o t h e l i q u i d c o r e , w a s s u r p r i s in g l y d i l u t e ( w i th m e a n l i q u i d v o l u m e

f r a c t i o n s l es s t h a n 0 . 1 ) , se e R u f f

e t a l .

(1992) and Tseng

e t a l .

(1992b) ; the re fore , the l a rge m ean

l i q u i d v o l u m e f r a c t i o n s o b s e r v e d i n s o m e p o r t i o n s o f th e d e n s e s p r a y r e g i o n a r e m a i n l y d u e t o t h e

.J

I o

Lo 9 c ~

o 5

L

x . o ~

~

\ O o

_

x / d = ~ o o f

, o . _ -1

1.0 12.5

o.5~ ~ X

| L ~ L O P E D

0 .5 ~ - , I m T H E O R Y

o 2

2r d

Figure 4. Ra dial profiles of time-averaged liquid volume

fractions along the axis of round pressure-atomized water

sprays in still air at atmospheric pressure for atomization

breakup w ith fully-developed urbulent pipe flow at the jet

exit. From Tseng

et al.

(1992a).

1 . 0

0 . 5

0 . 0

1 . 0 '

~ . = l l i : : i l l F U L L Y -O E V E L O P E D -I i : i i i :~ FLOW

~]

o ~AVRE V~RA~ ~

I:::~:~ . A G A S * P H A S E ( 5 .u m )

/ i i l \ = ,

?}?.{ ; i I ~ E 4 a r m

i i i l l

Q U I O S U R F A C E

x . . o o 2 o * m

0 . 0

1 . 0 ; i ~

0 . 5

0.0

0.00 O 0

r / x

c

~ J o t m

J I

0 . 2 0

Figure 5. Rad ial profiles of m ean phase velocities or rou nd

pressure-atomized wa ter spray s in still air at variou s press-

ures for atomizationbreakup with fully-developed urbulent

pipe flow at the jet exit. From Tseng

et al.

(1992b).


6/29

104 G.M. FAETH

e t a l

Q

1 5 0 0

E I 0 0 0 -

.j

: i

o3

5 0 0 -

0

/

6 0

= 4 0 :

2 0

0

0

) I

0 0

0

0

0

0

I

FULL Y- DEVELOPED

FLOW

x / d 2 5

0 0

I I

SURFACE TYP)

o

o

U p d p p m ) -

_ 0 I 0

3 0

i O 0

e __ 3

- T H E O R Y

-

- ~ -

o

I 1 , , . I

0 . 1 0 0 . 2 0

r l x

Figure 6. Radial profiles of dispersed-phase properties for round pressure-atomizedwater sprays n still

air at atmospheric pressure for atomizationbreakup with fully-developed urbulent pipe flow at the jet

exit. Data from Ruff t al (1992).

presence of the liquid core. The low liquid volume fract ions within the dispersed flow region imply

tha t collisions between liquid elements are improbable, see Faeth (1977, 1983, 1987). Thus, these

findings support the conventional picture of atomizat ion within dense sprays, as discussed by Giffen

Muraszew (1953), which involves primary breakup into ligaments and large drops at the liquid

surface followed by secondary breakup into smaller round drops, with negligible effects of

collisions.

A useful experimental finding of the studies of Ruff e t a l (1992) and Tseng e t a L (1992b) was

that drop size distributions throughout the dense spray region are well correlated by the universal

root-normal distribution with MMD /SMD = 1.2 due to Simmons (1977), where MMD is the mass

median drop diameter of the spray. See Belz (1973) for a discussion of the properties of this

distribution function. Then, since this distribution only has two parameters, the entire size

distribution can be represented by the SMD alone. Another observation was that the drop sizes

after primary breakup, as well as mixing rates throughout the flow which was noted earlier, were


7/29

S T R U C T U R E A N D B R E A K U P P R O P E R T I E S O F S P R A Y S 1 5

very depende n t up on f l ow cond i t i ons a t t he i n j ec t o r ex i t - - a f i nd ing t ha t para l l e l s t he well know n

i mp or t ance o f j e t ex i t cond i t i ons on t he de ve l opm en t r eg i on o f s i ng le-phase t u rbu l en t j e t s .

The d i s t r i bu t i ons o f d rop ve l oc it i es i l lu s t r a t ed i n f i gu re 6 show t ha t t hey vary cons i derab l y wi t h

d rop d i amet er a t each po i n t i n t he f l ow, p rov i d i ng d i r ec t ev i dence o f s i gn i f i can t separa t ed f l ow

ef fec ts i n dense sp rays . Ne ar t he l i qu id co re , t he l a rges t d rops have ve l oc it i es com para b l e t o m ean

l i qu i d i n j ec t i on ve l oc i t i es , however , ve l oc i t i es decrease wi t h bo t h decreas i ng d rop s i ze and

i ncreas ing r ad i a l d i s t ance . A su rp r i s ing f ea t u re o f these obs erva t i ons i s t ha t gas ve l oc i t ies (wh i ch

appro x i m at e t he ve l oc it i es o f t he smal l es t d rops ) a r e l ow and are near l y cons t an t across t he wi d t h

o f t he d i sper sed f l ow reg i on . Th i s i mp l i es r e l a t i ve l y i nef f ec t i ve momen t um exchange be t ween t he

p h a s e s b e c a u s e t h e l a rg e d r o p s c o n t a i n m o s t o f th e m o m e n t u m a n d t h e y r e sp o n d s l ow l y t o d r a g

fo rces due t o t he i r r e l a t ive l y la rge i ner ti a . F i na l ly , co ns i s t en t wi t h observa t i ons i n connec t i on w i t h

f i gures 2 -5 , t he L H F p red i c t i ons i l l u s t ra t ed i n fi gu re 6 a re p oor because se para t ed f l ow ef fec t s a r e

i mp or t an t wi t h i n mos t o f t he dense sp ray reg i on .

2 4 C onc l us i ons

Based on t he s t udy o f t he s t ruc t u re and m i x i ng p roper t i es o f dense sp rays found near t he i n j ec t o r

fo r round p ressu re-a t omi zed sp rays i n s t i l l gases , t he fo l l owi ng maj o r conc l us i ons a r e ob t a i ned :

(1 ) The l a rge l i qu i d vo l ume f r ac t i ons observed i n dense sp rays genera l l y a r e due t o t he

p resence o f t he l i qui d co re ; i n con t r as t , l i qui d vo l um e f r ac t i ons i n t he d i sper sed f l ow reg i on

bey ond t he l i qu i d su r f ace a r e smal l , l es s than 0 .1 , so t ha t t he f l ow i n t h is r eg i on

cor resp onds t o a d i lu t e sp ray b u t wi t h added com pl i ca t i ons due t o t he p resence o f i r r egu lar

l i qu i d e l emen t s and secondary b reakup .

(2) M easu re me n t s genera l l y suppor t t he t r ad i ti ona l v i ew o f a t om i za t i on exp ressed by Gi ff en

& M urasz ew (1953) ; namel y , p r i ma ry b rea kup a t t he l iqu i d su r f ace is fo l l owed by

secon dary b re aku p i n a d i l u t e sp ray env i ronm en t w here e f fec t s o f d rop co l l i si ons a r e

negl ig ible (except for sp ray co ndi t ion s th at s t r ive for s igni f icant ef fects of col l i s ions to

enhance b reakup r a t es , such as i mp i ng i ng i n j ec t o r s ) .

(3) Ra t es o f mi x ing , d r op p roper t i es and f l ow s t ruc t u re wi t h i n dense sp rays a r e s t rong l y

depe nden t on t he deg ree o f fl ow devel op me n t and t u rbu l ence l eve ls a t t he j e t ex it , and o n

t he l i qu i d /gas d ens i t y r a t io , s om ew hat ana l og ous t o t he e f fec t o f t hese p roper t i es on t he

s t ruc t u re o f t he f l ow devel opmen t r eg i on o f s i ng l e-phase j e t s .

(4 ) Ef fec t s o f separa t ed f l ow are i mpor t an t wi t h i n dense sp rays , w i t h s i gn i f i can t d i f f e r ences

be t wee n t he ve l oc it i es o f l a rge d rops a nd t he gas due t o t he poor r esponse p roper t i es o f

l a rge d rops . T hus , L H F p red i c t i ons o f t he s t ruc t u re o f dense sp rays a r e n o t very e ff ec ti ve ,

excep t a t t he h i ghes t l i qu id vo l um e f rac t i ons where t he mo m en t u m o f the gas and sm al l

drops i s negl ig ible in any event .

(5 ) Drop s i ze d i s t r i bu t i ons a f t e r p r i mary b reakup , as wel l as a f t e r secondary b reakup and on

approach t o t he d i l u t e sp ray r eg i on , a l l sa t i s f i ed t he un i ver sa l roo t -no rmal d rop s i ze

d i s t r i bu t i on wi t h MM D / S M D = 1 .2 due t o S i mmo ns (1977) a t each po i n t in dense sp rays ;

t herefo re , t he en t i r e d rop - s i ze d i s t r i bu t i on can be charac t e r i zed by a s i ng l e momen t , e .g .

t h e S M D .

3. S E C O N D A R Y B R E A K U P

3 1 I n t roduc t i on

Based on t he p rev i ous cons i dera t i ons o f the s t ruc t u re o f t he dense sp ray r eg i on fo r roun d

pressu re-a t omi zed sp rays , seconda ry b reaku p c l ear ly i s an i mpo r t an t p rocess o f dense sp rays ,

t h rough i t s e f f ec t on d rop s ize d i s tr i bu t i ons as t he d i l u t e sp ray r eg i on i s app roa ched . In par t i cu l a r,

p r i m ary b reak up a t t he su r f ace o f t he l iqu i d co re y i el d s d rops t ha t a r e i n t ri n s ica l l y uns t ab l e t o

s e c o n d a r y b r e a k u p . I n a d d i t i o n , h i g h - p r e s s u r e c o m b u s t i o n f o r t y p i c a l p o w e r a n d p r o p u l s i o n

sys t ems i nvo l ves cond i t i ons where t he su r f ace t ens i on o f d rops be com es smal l, because t he l i qu i d

su r f ace app roaches t he t hermodynami c c r i t i ca l po i n t ; na t u ra l l y , such cond i t i ons sugges t po t en t i a l

fo r s i gni f ican t e ff ec t s o f d rop defo r ma t i on and secon dary b reakup . P ro mp t ed by t hese observa t i ons ,

cu r r en t under s t and i ng o f secondary b reakup wi l l be d i scussed i n t he fo l l owi ng .


8/29

106 G.M. FAETH

tal.

Gi f fen & Mura szew (1953) , Lev i ch (1962) , Har r j e & R eard on (1972), C l i f t

e t a l .

(1978) , Wierzba

& Taka ya m a (1988) , H i nze (1955) and K rzeczk owsk i (1980) have r ev iewed earl y wo rk on seco ndary

b reak up ; t herefo re , t he fo l l owi ng d i scuss i on wi l l emphas i ze m ore r ec en t s t ud ies . O f par ti cu l a r

i n t e r es t a r e t he s t ud i es o f Hs i an g & F ae t h (1992, 1993 , 1995) and H s i ang

e t a l .

(1995) which have

c o n s i d e r e d b r e a k u p r e gi m e s , b r e a k u p d y n a m i c s a n d t h e o u t c o m e s o f b r e a k u p . I n g e n e r al , p a s t w o r k

h a s b e e n l im i t e d t o t w o k i n d s o f w e ll d e f in e d d i s tu r b a n c e s t h a t c a u s e d e f o r m a t i o n a n d b r e a k u p

o f d r o p s : s h o c k w a v e d i s t u r b a n c e s t h a t p r o v i d e s t e p c h a n g e s in t h e a m b i e n t e n v i r o n m e n t o f a d r o p

t yp i ca l o f a d rop a t t he end o f p r i ma ry b rea kup ; and s t eady d i s t u rbances t yp i ca l o f f r ee ly - f a ll i ng

d rops i n r a i n s t o rms o r i n sp ray d ry i ng p rocesses . Ef f ec t s o f shock wave d i s t u rbances have r ece i ved

t h e m o s t a t t e n ti o n a n d a p p r o x i m a t e t h e s e c o n d a r y b r e a k u p e n v i r o n m e n t o f d en s e s p r a y s; t h e re f o r e ,

t hese d i s t u rbances wi l l be emphas i zed i n t he fo l l owi ng . Defo rmat i on and b reakup r eg i mes , b reakup

d y n a m i c s a n d b r e a k u p o u t c o m e s w i l l b e c o n s i d e r e d , i n t u r n .

3 .2 . D e f o r m a t i o n a n d b r e a k u p r e g i m e s

Nu m ero us s t ud i es have cons i dered t he def i n i ti ons and cond i t i ons fo r t he onse t o f var i ous

d e f o r m a t i o n a n d b r e a k u p r e g im e s o f d r o p s s u b j e c t e d to s h o c k w a v e d i st u r ba n c e s . W h e n e f fe c ts o f

l i qu id v i scos i t y a r e smal l , the b re aku p r eg i me obse rved a t t he onse t o f b rea kup has been t e rm ed

bag b re akup : i t invo l ves defl ec t i on o f t he d rop i n t o a t h i n d i sk no rm al t o t he f l ow d ir ec t ion ,

fo l l owed by defo rm at i on o f the cen t er o f t he d i sk in t o a t h i n , ba l l oon- l ike s t ruc t u re , bo t h o f wh i ch

subseq uen t l y d i v ide in t o d rops , see W i erzba & Tak ay am a (1988), H i nze (1955), Krze czkow sk i

(1980) , Hanson

e t a l .

(1963) , Gel ' fand

e t a l .

(1974) , Ranger & Ni cho l l s (1969) and Rei necke &

M c K a y ( 1 96 9) a n d R e i n e c k e & W a l d m a n ( 19 70 ) f o r p h o t o g r a p h s o f al l t h e b r e a k u p r e g im e s

d i scussed here . The shear b reakup r eg i me i s observed a t h i gher r e l a t i ve ve l oc i t i es : i t i nvo l ves

def l ec t ion o f the per i phe ry o f t he d i sk i n t he dow ns t r eam d i r ec t ion , r a t her t han def l ec t ion o f the

cen t er o f t he d isk , and t he s t r ipp i ng o f d rop s f rom t he per i phery o f t he d isk . The t r ans i t i on be t ween

t he bag an d shear b re aku p r eg i mes i s a comp l ex mi x t u re o f t he t wo bound i n g r eg i mes wh i ch wi ll

b e d e n o t e d t h e m u l t i m o d e b r e a k u p r e g i m e i n t h e f o l l o w i n g . A c o m p l e x b r e a k u p m e c h a n i s m a l s o

has been observed a t very l a rge r e l a t i ve ve l oc i t i es , wh i ch has been ca l l ed ca t as t roph i c b reakup by

Rei necke & McKay (1969) and Rei necke & Wal dman (1970) , never t he l ess , t h i s r eg i me i s no t seen

i n t yp i ca l dense sp rays and wi l l no t be cons i dered here .

Ex i s t i ng observa t i ons o f secondary b reakup have genera l l y i nvo l ved

P L / P ~

> 500 and R e > 100,

w h e r e R e =

p o d u / a

and Po is t he mo l ecu l ar v i scos i t y o f t he gas . F o r t hese cond i t i ons , H i nze (1955)

s h o w s t h a t b r e a k u p r e g im e t r a n s i ti o n s a r e f u n c t io n s o f t h e i ni ti a l W e b e r n u m b e r o f a d r o p ,

W e

= P c d o u 2 / a ,

where o - i s t he d ro p su r f ace t ens i on and t he subsc r i p t o deno t es an i n i ti a l cond i t i on ,

a n d t h e O h n e s o r g e n u m b e r o f a d r o p , O h I , L / p L d o f f ) 1 /2 , where L i s t he mo l ecu l ar v i scos i ty o f

t he l i qu i d , wh i ch a re measu res o f t he r a t i o s o f d rag and l i qu i d v i scous fo rces t o su r f ace t ens i on

fo rces , r espec t i ve l y . The r esu l t i ng defo rmat i on and b reakup r eg i me map based on ava i l ab l e r esu l t s

f rom Hin ze (1955), Krzec zko ws ki (1980) , Hs iang & Fa eth (1992,1993,1995), H an so n (1963) , La ne

(1951) an d Lo pare v (1975) i s i l l u s tr a t ed i n f i gu re 7 . The va r i ous b rea kup r eg imes i den t i fi ed by Hi nze

(1955) , Krzeczkowsk i (1980) and Hs i ang & Fae t h (1992 , 1995) a r e i n exce l l en t ag reemen t i n t he

reg i ons where t hey over l ap ; i n v iew o f the sub j ec t i ve na t u re o f i den ti fy i ng b reakup r eg i me

t r ans i ti ons , t h i s deg ree o f ag reem en t i s qu i t e sa t is fy ing . The t r ans i t i ons t o t he defo rm at i on r eg i mes

are i mpor t an t because t hey def i ne cond i t i ons where d rop d rag depar t s s i gn i f i can t l y f rom t ha t o f

a so l id sphere ; t hese r eg i mes a re def i ned by t he r a t i o o f t he max i m um (cross s t r eam) d i m ens i on

t o t he o r i g ina l d ro p d i am et er . The osc i l l a t o ry defo rm at i on r eg i me i s def i ned by cond i t i ons whe re

t he d rop osc i ll a t es wi t h a weak l y dam ped a mpl i t ude , see Hs i a ng & Fae t h (1992) fo r d iscuss i on o f

t h i s behav i o r .

Al l r eg i me t r ans i t i ons i l l u s tr a t ed i n f i gu re 7 a r e r e l a t i ve ly i ndepend en t o f l iqu i d v i scous fo rces

(o r Oh) fo r O h < 0 .01. Th e o rd er o f t he t r ans i t ions wi t h i ncreas ing W e i n th i s r eg i on f rom H s i ang

& F ae t h (1995) i s as fo ll ows : 5% defo rm at i on , W e = 0 .6 ; 10% defo rm at i on , W e = 1 .0 ; 20%

d e f o r m a t i o n , W e - - 2 . 1 ; o s c i ll a to r y d e fo r m a t i o n , W e - - 3 . 0 ; b a g b r e a k u p , W e = 1 3; m u l t i m o d e

break up , W e = 35 ; and shear b reak up , W e = 80 . As no t ed ear li e r , the W e a t b re aku p r eg i me

t r ans i t ions due t o H i nze (1955) an d K rzeczk owsk i (1980) a r e s i mi l a r t o t hese r esu lt s . These f i nd ings

sugges t qu i te p l aus i b l y t ha t s i gn i fi can t l eve ls o f defo rma t i on and b re aku p occ u r when dyn am i c


9/29

STRUCTURE AND BREAKUPPROPERTIES OF SPRAYS

1 7

t - -

o

1 0 4

1 0 3

1 0 2

101

1 0 0

L i q u i d L i q u i d S o u r c e

o n - H e p t a n e G l y c e r o l 9 2 % (5 H a n s o n etal ( 1 9 6 3 )

o W a t e r * G l y c e r o l 9 7 % & H i n z e ( 1 9 5 5 )

A G l y c e r o l 2 1 % G l y c e r o l 9 9 . 5 % ~ > L a n e ( 1 9 5 1 )

v G l y c e r o l 6 3 % ~ M e r c u r y < 1 L o p a r e v ( 1 9 7 5 )

0 G l y c e r o l 7 5 % D. 2 0 0 f lu i d - - - K r z e c z k o w s k i ( 1 9 8 0 )

G l y c e r o l 8 4 % ~ P r e s e n t

< 1

I I I I I

1 0 4 1 0 3

p L /P G = 5 8 0 - 1 2 0 0 /

S h e a r b r e a k u p . , ~ 2 / ~ Y

v 0 o . ~ .. .. - -Q ~ - , , ~ / D e f o r m a t i o n

_ _ . . . . . ~ _ / . / ~ Z > 2 0 / ~'/ ;'~//,Z

Multimode breakup ~...~ /~ ~

B a g b r e a k u p . ~ . . - ~

O s c i l l a t o r y

d e f o r m a t i o n f

,0 o 1. In addition oscillatory deformation disappears at Oh ~ 0.3 and bag breakup

disappears a t Oh ~ 4. Hinze (1955) and Levich (1962) observed this tendency for the limited ranges

of Oh where data were available at the time, and conjectured that breakup might not be observed

for Oh > 1 to 2. However, the large Oh behavior observed in figure 7 does not suggest such a

limitation; rather, there is an almost linear increase of We at the deformation and breakup

transitions with increasing Oh.

Clearly, it is crucial to establish whether large values of Oh imply no deformation or breakup

as suggested by Hinze (1955) and Levich (1962), or simply rather large values of We at the

transitions, as suggested by the measurements illustrated in figure 7; therefore, Hsiang Faeth

(1995) undertook phenomenological analysis in an attempt to explain the effect of Oh on

deformation and breakup regime transitions. Their approach was based on the observation that

the main effect of liquid viscosity for shock wave disturbances was to reduce the rate of deformation

of the drop. This behavior allows more time for drop velocities to relax toward the local ambient

velocity at large Oh, tending to reduce the relative velocity, and thus the driving potential for drop

deformation, at each stage of the deformation process. The motion of the drop was analyzed for

these circumstances, assuming Oh >> 1 so th at maximum deformation occurred at a multiple o f the

characteristic viscous time, ~, of Hinze (1948), defined as follows:

= ~ / ( p o u ~ o ) [ 2 ]


10/29

108 G.M. FAETH

e t a l

Thi s ana lys i s y i e lded t he fo l l owing r e l a t i onsh ip be tween We and Oh fo r par t i cu l a r defo rmat ion o r

b reakup t r ans i t i ons a t l a rge Oh :

W e = (W ecr/4) (1 + 4

K W e g ] / 2 ( p G / P L f / E O h )

[3]

I n [ 3 ], W e c r is t h e l o c a l W e b e r n u m b e r a t t h e m a x i m u m d e f o r m a t i o n c o n d i t io n r e q u i r e d f o r t h e

t r ans i t i on o f in t e res t t o occu r , wh i l e K ' i s an empi r i ca l f ac to r . Values o f Wecr and K ' were f i tt ed

to [3] to y ield the best f i t predicted t ransi t ions at large Oh i l lust rated in f igure 7 : in v iew of the

s imp l i fi ca t ions o f t he t heo ry , t he ag reeme n t be twe en t he p red i c t ed and m easu red r eg ime t r ans it i ons

i s seen to be r ea sonab ly good . N o tab ly , [3] sugges t s t ha t t r ans i t i on W e ~ O h a t l a rge Oh ra the r

t han an u l t imat e l imi t fo r par t i cu l a r t r ans i t ions as sugges t ed by Hinze (1955) and Lev i ch (1962) .

Th i s i s a very impo r t an t d i f f e rence in beha v io r t ha t has s i gn if i can t r e l evance fo r p rocesses o f

h i g h -p r e s su r e c o m b u s t i o n , w h e r e O h b e c o m e s la r g e a s d r o p s a p p r o a c h t h e ir t h e r m o d y n a m i c c r it ic a l

po in t (because t he i r su r f ace t ens ion app roac hes ze ro wh i le t he i r v iscos i t y r emains f in it e) . A no the r

i s sue concern ing [3 ] i s the e f f ec t o f l i qu id /gas dens i t y r a t i o , wh ich sugges ts fu r t her i ncreases i n W e

at a g iven t ransi t ion a s

PG PL

ncreases , a parameter var i a t i on t ha t has no t been exp lo red t hus f a r .

Thus , t he l a rge Oh reg ime t r ans i t ion c r i t e ri a o f [3] c l ear l y mer i t ad d i t i ona l s t udy , em phas i z ing t he

l a r g e O h a n d

PG PL

cond i t i ons r e l evan t t o h igh -p ressu re sp ray combus t i on p rocesses .

3 . 3 . Breakup dynamics

The d i scuss ion o f defo rm at ion and b reak up r eg ime t r ans it i ons h igh li gh ts t he impor t ance o f

b reakup t imes and a l r eady has i n t roduced t he charac t e r i s t i c b reakup t ime, z , when l i qu id v i scous

fo rces a re l a rge i n comp ar i son t o su r face t ens ion fo rces a t l a rge Oh , see [2 ]. Avai l ab l e me asu rem en t s

o f d rop b reak up t imes f rom Engel (1958) , S impk ins Bal es (1972) , Ran ger Nicho l l s (1969)

R e i n e c k e W a l d m a n ( 19 70 ) a n d H s i a n g F a e t h (1 99 2) a r e p l o t te d a s a f u n c t io n o f W e a n d O h

in f igure 8 . In th is p lot , the breakup t imes, t b , are no rmal i zed by t he charac t e r i s t i c b reakup t ime

fo r shear b reak up a t l ow Oh , t * , def i ned by Ran ger Nicho l l s (1969) as fo l lows :

t * = do (pL/PG

) 1 / 2 / / / o [4]

Excep t fo r t he r esu l ts o f Hs i a ng Fae th (1992), wh ich a re g roup ed acco rd ing t o Oh , t he

measu remen t s a re fo r Oh < 0 .1 ; t herefo re , t he defo rmat ion and b reakup r eg imes def i ned ear l i e r fo r

t hese cond i t i ons a re marked on t he p lo t fo r r e fe rence pu rposes .

102

101

1 0 0 - -

1 0 1

100

S o u r c e S o u r c e C o r r e l a t i o n

o R a n g e r N i c h o l l s ( 1 9 6 9 )

[ ] S i m p k i n s B a l e s ( 1 9 7 2 )

z~ Enge l (1958)

v R e i n e c k e W a l d m a n ( 1 9 7 0 )

R e i n e c k e M c K a y ( 1 9 6 9 )

P r e s e n t (O h < 0 .1 )

P r e s e n t ( 1 .0 < O h < 2 .8 )

P r e s e n t ( 3 .5 < O h )

- - O h : 3 . 5

- - ' - - O h : 2 . 0

~ O h : 0 . 0

A - - - - - -

u - - n - - n ~

. .A . . . . . . .

A A O 0

r-,

z

V

N o n - o s c . B a g S h e a r

O s c . d e f . M u l t i m o d e

101 102 103 104 105

e

F i g u r e 8 . D r o p b r e a k u p t i m e s a s a f u n c t i o n o f t h e W e b e r a n d O h n e s o r g e n u m b e r s f o r s h o c k - w a v e

d i s tu r b a n c e s w i th li q u id /g a s d e n s i t y r a t i o s g r e a t e r t h a n 5 0 0 . F r o m Hs i a n g Fa e th (1 9 92 ).

10 6


11/29

S T R U C T U R E A N D B R E A K U P P R O P E R T I E S O F S P R AY S 1 0 9

A re ma rkab l e f ea t u re o f t he b re aku p t i me r esu l ts i l lu s t r a t ed i n f igu re 8 fo r Oh < 0 .1 is t ha t t b / t

var i es very l i t t l e even t hough We var i es wi de l y and severa l b reakup r eg i mes a re i nvo l ved . In f ac t ,

t he co r r e l a t i on deve l oped fo r shear b rea kup by Ran ger Ni cho l l s (1969) :

t b / t = 5.0 [5]

p rov i des a go od r ep res en t a t i on o f a ll t he measu rem en t s i l l u s t r a ted i n f i gure 8 fo r Oh < 0 .1 . A t l a rger

O h , h o w e v e r , t b / t i ncreases due t o e f f ec ts o f l iqu i d v i scos i t y r e t a rd i ng t he r a t e o f defo rm at i on as

d i scussed ear li e r . I n t h is r eg ion , an empi r ica l co r r e l a ti on is def i ned by Hs i ang Fae t h (1992) bu t

t h i s exp ress i on i s on l y app rop r i a t e fo r Oh < 3 .5 . Su rp r i s i ng l y , no a t t empt has been made t o app l y

t he charac t e r i s t i c v i scous t i me, ~ , t o co r r e l a t e b reakup t i mes a t l a rge Oh : t h i s shou l d be done i n

o rder t o bo t h check t he deve l opm en t o f t he l a rge Oh r eg i me t r ans i t ion c r i t e ri a o f [3 ] and t o ga i n

a b e t t e r u n d e r s ta n d i n g o f d e f o r m a t i o n a n d b r e a k u p b e h a v i o r a t la r g e O h .

Dr op s unde rgo s i gn i f ican t defo rma t i on i n t he per i od p r i o r t o t he onse t o f b reakup . A s d i scussed

ear li e r , d rops a r e i n i ti a ll y d raw n i n t o f l a t t ened (ob l a t e sphero i d ) shapes due t o t he r e l a t ive mo t i on

of t he gas phase , wh i ch a f f ec ts t he i r m o t i on by in f l uenc i ng d rag fo rces . Hs i an g Fae t h (1992) have

s u m m a r i z e d a r e l at iv e l y la r g e d a t a b a s e o f m a x i m u m d r o p d e f o r m a t i o n s f o r s t e a d y d i s t u rb a n c e s ,

cons i der i ng bo t h d rop -gas and d rop - i mmi sc i b l e l i qu i d env i ronmen t s . Phenomeno l og i ca l ana l yses

l e a d t o a r e a s o n a b l y g o o d c o r r e la t i o n o f th e s e r es u lt s i n te r m s o f t he m a x i m u m c r o s s - st r e a m d r o p

diam eter , dmax, and the m inim um st ream wise d iame ter , drain , as fo l lows:

dmax/dmin

= (1 + 0.07W el/2) 3, W e < 20 [6]

d m i n d m a x d o .

The co r r e l a t i on

here t he second r e l a t i onsh i p needed t o f i nd a l m ax a n d d m i n i s g iven by 2 _ 3

o f [6 ] was i nde pend en t o f Oh wi t h i n exper i men t a l u ncer t a i n ti es , w h i ch is r easonab l e because l i qu i d

v i scous fo rces mai n l y ac t t o i nh i b i t the r a t e o f defo rm at i on fo r uns t ea dy cond i t i ons a f t e r shock

wav e d i s t u rbances . T he l i mi t a t i on o f W e i n [6 ] fo l l ows because d rops sha t t e r a t W e ~ 20 fo r s t eady

d i s t u rbances . F i na l ly , d rop de fo rm at i ons fo r shock wave d i s t u rbances a r e app rec i ab l y l a rger t han

es t i mat ed b y [6 ] due t o i nert i a l e f f ect s , see Hs i ang Fae t h (1992) fo r i n it ia l a t t empt s t o quan t i fy

t h i s behav i o r .

Defo rmat i on causes t he d rag fo rce on a d rop t o i ncrease due t o bo t h t he i ncreas i ng c ross -

sec t i ona l a r ea o f t he d rop an d an increase o f t he d rag coef fi c ien t , Co . Hs i ang Fae t h (1992) have

r e p o r t e d m e a s u r e m e n t s o f t h e e f f ec t o f d e f o r m a t i o n o n t h e d r a g c o e ff ic i en ts f o r s h o c k w a v e

d i s t u rbances a t Oh < 0 .1 and Re i n t he r ange 1000-2500 where e f fec t s o f Re on t he d ra g coef f ic i en t

o f d rops i s expec t ed t o be smal l , see Fae t h (1987) . I t was found t ha t Co l a rge l y was a func t i on

o f d e f o r m a t i o n s a t t h e s e c o n d i t io n s a n d c o u l d b e c o r r e l a te d i n t e r m s o f de~do as i l lust rated in f igure

9 , where dc i s t he c ross - s t r eam d rop d i amet er . Me asu rem en t s o f CD fo r so l i d spheres and t h i n d i sks ,

ob t a i n ed f rom W hi t e (1974) fo r t he same r ange o f Re , a lso a r e i l lu s t r a t ed on t he p l o t . I n genera l,

CD appro x i ma t es r esu l ts fo r so l i d spheres when dc/do i s near un i t y , and t hen i ncreases t o app roach

resul t s for th in d isks at

d~/do

~ 2 (wh i ch i s r ep resen t a t i ve o f ma x i mu m defo rm at i ons a t t he po i n t

w h e r e d r o p b r e a k u p b eg i ns ) . L a t e r w o r k b y H s i a n g F a e t h (1 99 5) s h o w e d t h a t CD/CDsp , w h e r e

CDsp i s t he d ra g coef f ic i en t o f a so l i d sphere a t t he same Rey no l ds nu mb er , were r e l a t i ve l y

i ndepen den t o f the t ype o f d i s t u rbance ( shock wave o r s t eady) , t he d rop / su r round i ngs dens i t y ra t i o ,

W e, Oh an d R e , and co u l d be co r r e l a t ed i n t e rms o f defo rma t i on a l one a l ong t he l ines o f f i gu re

9 . The i ncrease o f

C o

and cross - sec t i ona l a r ea , due t o d i s t o r t i on , causes d rag fo rces t o i ncrease by

f a c t o r s o f r o u g h l y 4 a n d 1 3 a t d e f o r m a t i o n c o n d i t i o n s t y p ic a l o f th e o n s e t o f b r e a k u p f o r s t e a d y

a n d s h o c k w a v e d i s t u r b a n c e s , w h i c h c l e a r l y h a s a n i m p o r t a n t i m p a c t o n b r e a k u p d y n a m i c s , s e e

Hs i an g Fae t h (1995) .

3 . 4 . B r e a k u p o u t c o m e s

Under t he assumpt i on t ha t b reakup t i mes and d i s t ances a r e smal l i n compar i son t o charac t e r i s t i c

dense sp ray r es i dence ti mes and d i s t ances , secon dary b reak up can be t r ea t ed us i ng j um p cond i t i ons .

Fo r t h is app ro ach t o be worka b l e , i n fo rmat i on abo u t d rop s i ze and ve l oc i t y d i s t r i bu t ions a f t e r

s e c o n d a r y b r e a k u p i s n ee d e d . E a r l y m e a s u r e m e n t s a l o n g t h e s e li ne s w e r e r e p o r t e d b y G e l ' f a n d et a l .

(1963) fo r t he bag b reak up r eg i me, bu t t h is i n fo rmat i on was t oo l i mi t ed t o p rov i de genera l gu i dance

a b o u t th e d r o p s iz es p r o d u c e d b y s e c o n d a r y b re a k u p . L a t e r w o r k b y H s i a n g F a e t h ( 19 92 , 1 99 3,

1 99 5) u s in g p u l s e d h o l o g r a p h y a c h i e ve d a m o r e c o m p l e t e d e s c r ip t io n o f t h e o u t c o m e s o f s e c o n d a r y


12/29

110 G.M. FAETH e t a l

D

2 . 4

1.6

0.8

0.001 < Oh < 0.1

1000 < Re < 2500

Disk o

/ i

.Sphere

o

0 I I I I I

.0 1.2 1.4 1.6 1.8 2.0

dc/d o

Fig u r e 9 . Dr o p d r a g c o e f f i c ie n t p r i o r t o b r e a k u p a s a f u n c t i o n o f d e f o r m a t io n f o r sh o c k - wa v e d i s tu r b a n c e s

wi th l i q u id /g a s d e n s i t y r a t i o s g r e a t e r t h a n 5 0 0 . F r o m Hs i a n g Fa e th (1 9 92 ) .

b re a k u p fo r s h o c k wa v e d i s t u rb a n c es

a t PL/PG

> 500 and O h < 0 .1 . Some o f the ma in f ind ings o f

this work wil l be discussed in the fol lowing.

S imi la r to observa t ions d i scussed ear l i e r fo r the dense sp ray reg ion , H s iang & Fae th (1992, 1993 ,

1995) foun d tha t d rop s ize d i st r ibu t ions a f te r secondary b reaku p cou ld be rep resen ted by the

un iversa l roo t - norm al d i s t ribu t ion wi th M M D /S M D = 1 .2 , due to S im mons (1977), see Belz (1973)

fo r a d i scuss ion o f the p roper t i es o f the roo t -normal d i s t r ibu t ion func t ion . Th is behav io r was

o b s e rv e d fo r t h e b a g , m u l t i m o d e a n d s h e a r b r e a k u p r e g i m e s, b u t o n l y i f t h e c o re o r p a re n t d ro p

was removed f rom the d i s t r ibu t ion fo r the shear b reakup reg ime. Th is behav io r i s i l lu s t ra ted in

f igu re 10 fo r shear b r eaku p invo lv ing a var ie ty o f d rop l iqu ids . Thus , g iven the un iversa l roo t

nor ma l d rop s ize d is t r ibu t ion , d rop s izes a re fu l ly p rescr ibed by the SM D alone , excep t fo r shear

b rea kup whe re the p roper t i es o f the co re d rop m us t be p rescr ibed independen t ly as well .

A c o r r e l at i n g e x pre s si o n fo r t h e S M D a f t e r s e c o n d a ry b re a k u p w a s d e v e l o p e d co n s i d e ri n g t h e

shear b rea kup reg ime. The ana lys i s focuses on the s t r ipp ing o f l iqu id f ro m the co re d ro p as

i l lu s t ra ted in f igu re 11 . I t was assumed tha t the re la t ive ve loc i ty a t the t ime o f b reakup can be

rep resen ted by the in i t ia l re la t ive ve loc i ty , tha t the d rop s izes a f te r b reak up ar e com parab le to the

t h ic k n e s s o f t h e l a m i n a r b o u n d a ry l a y e r t h a t f o rm s i n t h e l i q u id a l o n g t h e f ro n t s u r f a c e o f t h e d ro p

due to i t s mot ion , tha t the charac te r i s t i c l iqu id phase ve loc i t i es a re on the o rder o f

pr/pL)~/~Uo,

as sugges ted by Ranger & NichoUs (1969) fo r shear b reakup , and tha t the SMD is dominated by

the la rges t d rop s izes in the d i s t r ibu t ion so tha t the l eng th o f the l iqu id phase boundary layer i s

p ropor t iona l to the in i t i a l d rop d iameter , do . Based on these ideas , the fo l lowing express ion was

ob ta ined as the bes t f it o f the ava i lab le SM D mea sureme n ts , see Hs iang & Fae th (1992) :

p~ SM D u ~/~r = 6.2(pL/PG)I/4[ L/( Pr do uo)] /2We

[ 7

Surface tens ion has been in t roduced in to [7 ] in o rder to s impl i fy d i scuss ion o f the po ten t ia l fo r

subsequen t b reakup . Cons i s ten t wi th i t s der iva t ion , however , su r face tens ion ac tua l ly does no t

in f luence the f ina l SMD . Ins tead , the m ain phy s ica l p roper t i es con t ro l l ing the SM D are /~r , PL

a n d p r .

The ava i lab le mea surem en ts o f SMD af te r second ary b reaku p , a long w i th the co rre la t ion o f [71,

a re i l lu s t ra ted in figu re 12. Rem arkab ly , a s ingle co rre la t ion deve lope d fo r the shear b rea kup reg ime

expresses the SMD af te r bag , mul t imode and shear b reakup . Th is behav io r s t i l l needs to be

exp la ined , a l though o ther p rope r t i es l ike b reaku p t ime are a l so re la t ive ly indepe nden t o f the


13/29

STRUCT URE ND BRE K UP PROPERTIES OF SPR YS

1 1

4 0 - -

a

3 . 0

2 . 0

1.0

0.5

0.1

We 125 250 375

W a t e r

-

G ly c e ro l 42% o - - M M D / SM D

Gly c e ro l 63% - -

1.5

_ n - H e p t a n e []

E t hy l -a l c oho l V A /

1.2

. . . . o ~ 1.1

v o ~ ' , ~ ~ -

_ / ~ ~ S he ar b re a k u p

0 I I I I J J [ I

0.1 1 10 30 50 70 90 99

C u m u l a t i v e v o l u m e p e r c e n t a g e

F igu re 10 . D rop d iam e t e r d i s t r i bu t i on a f t e r s hea r b reak up (ex c lud ing t he pa ren t d rops ) f o r s hoc k -w av e

d i s t u rbanc es w i t h l i qu id / gas dens i t y ra t ios g rea t e r t han 500 . F rom H s iang & F ae t h (1993 ) .

u

~ d

Figure 1 . Sketch of the shear breakupprocessfor shock-wavedisturbances. From Hsiang Fae th (1992).


14/29

112 G.M . FAETH

etal

bre aku p r eg i me, as no t ed ear l i e r. Th e r esu l t s il l u s tr a t ed i n fi gu re 12 a re i n te rms o f a W eber nu mb er

based on t he SMD af t e r b reakup and t he i n i t i a l r e l a t i ve ve l oc i t y . Super f i c i a l l y , i t i s ev i den t t ha t

t h i s Weber number exceeds c r i t e r i a fo r secondary b reakup a t l ow Oh , as i nd i ca t ed on t he p l o t ,

wh i ch i mp l i es t ha t a l a rge f r ac t i on o f t he d rops fo rm ed by b re aku p sho u l d s t il l be uns t ab l e fo r

s u b s e q u e n t b r e a k u p ( in p a r t ic u l a r, m o r e t h a n h a l f th e m a s s o f t h e s p r a y f o r m e d b y b r e a k u p h a s

d r o p d i a m e t e r s g r e a te r t h a n t h e S M D s in c e M M D / S M D = 1 .2 ). N e v e r th e l e s s, t h e re w a s n o

e v i de n c e o f s u b s e q u e n t b r e a k u p o f la r g e d r o p s . T h e r e a s o n f o r t h is b e h a v i o r w a s e x p l o r e d b y

s t udy i ng t he p ro per t i es o f the pa ren t d rop i t se lf as d i scussed nex t.

T h e v e l o c it y a n d s iz e o f th e p a r e n t d r o p a t t h e e n d o f s h e a r b r e a k u p m u s t b e k n o w n i n o r d e r

t o t r ea t i t separa t e l y f rom t he r es t o f the d rop popu l a t i on . T hese cons i dera t i ons a r e descr i bed by

Hs i a ng & F ae t h (1995), w here a s i mp l i fi ed ana l ys i s was deve l oped t o es t i mat e pare n t d rop ve l oc i ti es

a t t he end o f b reakup . The m ai n assu mpt i ons o f th i s ana l ys is were t ha t gas ve l oc it i es, d rop mass

a n d t h e d r a g c o e ff ic i e nt w e r e c o n s t a n t o v e r t h e p e r i o d o f b r e a k u p , w h i le t h e t i m e o f b r e a k u p w a s

t a k e n t o b e tb It = 5.0. In spi te of the s impl i f icat ions, the resul t ing correla t ion p rov ed to be ef fect ive

fo r es t imat i ng paren t d rop ve l oc it i es a t t he end o f b reakup . Pa ren t d ro p ve l oc i t y -measu reme n t s

s h o w e d t h a t t h e r e la t iv e v el o ci ti e s o f th e p a r e n t d r o p a t t h e e n d o f b r e a k u p w e r e 3 0 - 4 0 l o w e r

t han t he i n it i a l re l a t ive ve l oc i ty . Th i s s t il l imp l i ed t ha t t he l oca l W ebe r num ber s o f the paren t d rop

a t t h e e n d o f b r e a k u p g e n e r al ly w e r e g r e a te r t h a n t h e c r it ic a l W e b e r n u m b e r f o r s h o c k w a v e

d i s t u rbances (We = 13 ) . Thus , t he c r i t e ri on fo r t he end o f paren t d rop s t r i pp ing i s mo re r e l a t ed

t o c o n d i t i o n s f o r b r e a k u p d u e t o m o r e g r a d u a l d r o p m o t i o n s , w h i c h i s p l a u s ib l e b e c a u s e th e p a r e n t

d r o p h a s a p p r e c i a b le t i m e t o a d j u s t to t h e f l ow o v e r t h e b r e a k u p p e r io d . D e f o r m a t i o n a n d b r e a k u p

t r ans i t ions fo r g radual d i s t u rbanc es genera l l y a r e co r r e l a t ed i n t e rms o f the E6 t v6s nu mb er , E o ,

wh i ch i s def i ned as fo l l ows :

E o = a p L d 2 / a [8]

r,q

Q.

102

1 0 1 - -

L i q u i d B a g M u l t i S h e a r

W a t e r o

G l y c e r o l 4 2 % r a e a

S h e a r b r e a k u p G l y c e r o l 6 3 % A ~ x

n-Heptane V V

. . . . . . . E t h y l - a l c o h o l O ~

M u l t i m o d e b r e a k u p j

v / -

Bag b r e a k u p o / / / / ~

D e fo rm a ti on ~ / rmA

y

lOo J

10-1 10 0 101

(pG/pL)-1/4 [I.tL/(PLdUo)]1/2 (PGdU2o)/t~.

F i g u re 1 2 . C o r re l a t i o n o f SM D a f t e r s e c o n d a ry b re a k u p fo r sh o c k -w a v e d i s t u rb a n c e s w i t h l i q u i d / g a s

d e n s i ty ra t i o s g re a t e r t h a n 5 0 0 . F ro m H s i a n g Fa e t h (19 9 2) .


15/29

STRUC TURE ND BRE K UP PROPERTIES OF SPR YS ~,13

2o

100

Liquid Sym.*

Water O

Glycero l 42 []

Glycerol 63

x

n-Heptane

V

Ethyl-a lcohol @

*darkened sym. denote

core drops.

o O v i v

Correlation

1 0 1 I r r I ] I I I I I

10 2 10-1 100

(pG/PL)1/2 do/d

F ig u r e 1 3 . C o r r e l a t i o n o f d r o p v e lo c i t i e s a f t e r se c o n d a r y b r e a k u p f o r sh o c k - wa v e d i s tu r b a n c e s w i th

l i q u id /g a s d e n s i t y r a t i o s g r e a t e r t h a n 5 0 0 . F r o m Hs i a n g & Fa e th ( 1 9 9 3 ) .

f o r c o n d i t i o n s w h e r e P L / P c >> 1 , where a i s t he l oca l acce l e ra t ion o f the d rop . I t was fou nd t ha t d rop

s t r i pp ing fo r shear b r eak up ended w hen E o = 16 fo r t he paren t d rop . F i na l l y , th i s exp ress ion y i e ld s

t h e p a r e n t d r o p d i a m e t e r a t t h e e n d o f b r e a k u p b a s e d o n e s t i m a te s o f p a r e n t d r o p a c c e l e r a t io n f r o m

t he s i mp l if i ed ana l ys is fo r paren t d rop ve l oc it ies , see Hs i an g Fae t h (1993) fo r the de t a i ls o f t h is

co r r e l a t i on . Wi t h d rop d i amet er d i s t r i bu t i ons def i ned a f t e r secondary b reakup , and paren t d rop

d i amet er s and ve l oc i t i es def i ned a f t e r shear b reakup , t he f i na l p rob l em i s t o ob t a i n t he co r r e l a t i on

bet ween d rop s i zes and ve l oc i t i es (o t her t han fo r t he paren t d rop ) a f t e r b reakup . Th i s was done

us i ng t he sam e ap proa ch as t he ana l ys i s t o f i nd paren t d rop ve l oc it ies , f i nal ly y i e ld i ng t he fo l lowi ng

drop s ize and ve l oc i t y co r r e l a t i on due t o Hs i ang Fae t h (1993):

U o / U b - - 1 = 2 . 7 ( ( p c / p L ) l Z d o / d ) z /3

[91

where u b i s the ve l oc i t y o f d rops hav i ng d i amet er d a t t he end o f t he b re aku p per i od . T he

drop-size/veloci ty correlat ion based on [9] i s i l lust rated in f igure 13. The exper imental resul t s

i nvo l ve a var i e t y o f d rop l i qu ids over t he bag , mu l t i mode and shear b reak up r eg imes . The

m e a s u r e m e n t s c l e a r ly a r e i n d e p e n d e n t o f t h e b r e a k u p r e g im e a n d a r e c o r r e la t e d r e a s o n a b l y w e l l

by [9 ] . Resu l t s fo r t he paren t d rops a l so a r e i l l u s t r a ted i n f igu re 13 , and exh i b i t a f a i r co r r e l a t i on

wi t h [9] ; never t he l ess , t he spec if ic p aren t d rop ve l oc i t y exp ress i on i s r ecom me nded i n s t ead be cause

i t p rov i des a m uch be t t e r es t i mat e o f paren t d rop ve l oc it ies .

F i na l l y , t he var i a t i on o f d rop ve l oc i ti es wi t h s ize imp l i es tha t secon dary b re akup p rocesses ex t end

over a cons i derab l e r eg i on o f space . Fo r exam pl e , paren t d rops m ove 30 -40 i n i ti a l d rop d i amet er s

du r i ng t he pe r i od o f b rea kup wh i l e the l a rges t and sma l l est d rops i n t he s ize d i s t r i bu t ion beco me

separa t ed by mo re t han 100 i n i ti a l d rop d i am et er s . In add i t i on , t i mes o f b rea kup e x t end fo r 5 .5 t* ,

a t l ow Ohneso rge number s , and p rog ress i ve l y i ncrease wi t h i ncreas i ng Ohneso rge number . Thus ,

i n some i n s t ances , secondary b reakup i s more p roper l y t r ea t ed as a r a t e p rocess , somewhat l i ke

d r o p v a p o r i z a ti o n , r a t h e r t h a n a s a n i n s ta n t a n e o u s p r o c e s s t h a t c a n b e c h a r a c te r i ze d b y j u m p

cond i t i ons . Such cond i t i ons a r e f r equen t l y encoun t ered a t h i gh p ressu res , where t he dense sp ray

reg i on be com es r e l a t ive l y sho r t as d i scussed in conn ec t i on w i t h [1 ] , see Ruf f e t a l . (1992) for a


16/29

114 G M FAETH e t a l

det a i l ed d i scuss i on o f th i s sca li ng . As a r esu l t , t he focus o f cu r r en t r esearch on t he ou t co me s o f

s e c o n d a r y b r e a k u p is s h if ti n g f r o m o u t c o m e s a s j u m p c o n d i t i o n s f o r a r a p i d b r e a k u p p r o c e s s, t o

o u t c o m e s a s a r a t e p r o c e s s, s e e H s i a n g

e t a l

(1995) for in i t ial work along these l ines l imi ted to

s h e a r b r e a k u p a t l o w O h n e s o r g e n u m b e r s .

3 5 C o n c l u s i o n s

S e c o n d a r y b r e a k u p o f d r o p s h a s b e e n c o n s i d e r e d , e m p h a s iz i n g s h o c k - w a v e d i s t u rb a n c e s f o r a

var i e t y o f l i qu ids i n a ir a t no rmal t emp era t u re and p ressu re . The m ai n conc l us i ons a r e as fo ll ows :

(1 ) D rop defo rma t i on an d b reak up beg i n a t We --~ 1 and 10 , r espec t ive l y , a t l ow Oh ; howeve r ,

t hese tr ans i t i ons bec om e p ropor t i ona l t o O h a t l a rge Oh , e .g . Oh > 10. Th i s i nh i b i ti on o f

d e f o r m a t i o n a n d b r e a k u p a t l a r ge O h i s i m p o r t a n t f o r h ig h p r e s s u re c o m b u s t i o n p r o c e s se s

where d rops r each l a rge Oh as t he i r su r f ace app roaches t he t hermodynami c c r i t i ca l po i n t .

(2) D rop- s i ze d i s t r i bu t i ons a f t e r seconda ry b reaku p sa t i s fy t he un i ver sa l roo t -no rma l d i s t r i-

b u t i o n w i t h M M D / S M D = 1 .2 d u e to S i m m o n s ( 19 77 ), s i m i la r t o o t h e r o b s e r v a t i o n s

wi t h i n dense sp rays ( excep t fo r t he paren t d rop fo r shear b reakup wh i ch mus t be t r ea t ed

separa t e l y ) . Thus , t he d rop - s i ze d i s t r ibu t i on a f t e r seconda ry b reak up i s compl e t e l y def i ned

b y t h e S M D a l o n e .

( 3) T h e S M D a f t e r s e c o n d a r y b r e a k u p c o u l d b e c o r r e l a te d r a t h e r s i m p ly i n te r m s o f a

charac t e r i s t ic l i qu i d bou nda ry l ayer t h i ckness fo r a l l t h r ee secon dary b rea kup r eg i mes , see

[7].

(4) The r e l a t ive s tr eamw i se ve l oc it i es o f d rop s a f t e r secon dary b reak up are r educed 30 -70 ,

depen d i ng on d rop s ize , f rom t he i n i ti a l r e l a ti ve ve l oc i ty . These e f f ec t s were co r r e l a t ed

reason ab l y w el l based on a s i mp l if i ed ana l ys i s o f d rop m ot i on , see [9 ].

(5) The s t r eam wi se ve l oc i ty and s i ze o f the paren t d rop a f t e r shear b reaku p cou l d be co r r e l a t ed

success fu l ly base d on s i mp l if i ed cons i dera t i ons o f d rop m ot i on d u r i ng b reak up , and t he

obse rva t i on t ha t Eo - - 16 fo r t he paren t d rop a t t he end o f d rop s t r i pp i ng , see Hs i a ng &

Faeth (1995) .

(6) Sec ondary b re aku p i n dense sp rays i s no t p rop er l y r ep resen t ed by j um p cond i t i ons a t the

h i g h p r e s s u re s o f m a n y p r a c ti c a l s p r a y c o m b u s t i o n d e v i c es . U n d e r s u c h c i rc u m s t a n c e s ,

s e c o n d a r y b r e a k u p s h o u l d b e t r e a t e d a s a r a t e p r o c e s s .

A s i d e f r o m t h e d e f o r m a t i o n a n d b r e a k u p r e g i m e m a p , e x i s t i n g i n f o r m a t i o n a b o u t s e c o n d a r y

b rea kup i s l i mi t ed t o O h < 0 .1 and

P L / P G

> 500 . C l ear ly , e f f ec ts o f bo t h Oh and

P L / P o

mer i t

a d d i t io n a l s t u d y i n o r d e r t o b e t t e r u n d e r s t a n d t h e s e c o n d a r y b r e a k u p p r o p e r t i e s o f p r a c ti c a l

c o m b u s t i n g s p r a y s. F i n a ll y , t h e ra t e a s p e c t s o f s e c o n d a r y b r e a k u p a r e u n k n o w n a n d m u s t b e

addresse d i n o rder t o t r ea t h i gh p ressu re sp ray s where charac t e r iz i ng t he e f fec t s o f seconda ry

b re aku p by j um p cond i t i ons is no t app ro p r i a t e ; i n i t ia l work a l ong t hese li nes fo r shear b reak up

a t l o w O h n e s o r g e n u m b e r s h a s b e e n r e p o r t e d b y H s i a n g

e t a l

(1995).

4. P R I M A R Y B R E A K U P

4 I I n t r o d u c t i o n

P r i m a r y b r e a k u p t o f o r m d r o p s n e a r l iq u i d s u r fa c e s is a m o s t i m p o r t a n t p r o c e s s o f sp r a y s

becaus e i t i n i ti a t es t he a t om i za t i on p rocess , con t ro l s t he ex t en t o f the l i qu i d co re and p rov i des t he

i n i ti a l cond i t i ons o f t he d i sper sed f low reg i on . Unfo r t un a t e l y , cu r r en t unde r s t and i ng o f p r i mary

b r e a k u p i s l im i t e d d u e t o p r o b l e m s o f o b s e rv i n g p r im a r y b r e a k u p i n d en s e s p r a y e n v i r o n m e n t s,

e f fe c ts o f s e c o n d a r y b r e a k u p a n d i n te r p h a s e t r a n s p o r t t h a t m o d i f y d r o p p r o p e r t i e s p r io r t o d r o p s

reach i ng con d i t i ons whe re t he i r p roper t i es ca n be me asu red r ead i ly , and e f f ec ts o f f low deve l opme n t

and l i qu id d i s t u rbance s ( t u rbu l ence) a t t he j e t ex i t t ha t have an u nusua l l y l a rge i mpact on p r i ma ry

b r e a k u p p r o p e rt ie s . R e c e n t l y , h o w e v e r , p u l s e d h o l o g r a p h y t e c h n i q u es h a v e p r o v i d e d a m e a n s o f

observ i ng t he p roper t i es o f dense sp rays so tha t so me p rog ress i s be i ng made t ow ard ga i n i ng a

b e t t e r u n d e r s t a n d in g o f p r i m a r y b r e a k u p p r o c e ss e s , s e e R u f f

e t a l

(1991, 1992), Tseng

e t a l

(1992b) ,

W u

e t a l

(1991, 1992, 1995) and W u & Fa eth (1993) . Thus, the f indings of these s tudies , which

are l imi t ed t o p r i ma ry b re aku p a l ong t he su r f ace o f t he li qu i d co re fo r p ressu re-a t omi zed sp rays


17/29

STRUCT URE ND BRE KUP PROPERTIES OF SPR YS

5

i n s t i l l gases , w i l l be emphas i zed i n t he fo l l owi ng . Fo r t hese cond i t i ons , t he onse t and ou t come o f

p r i mary b reakup wi l l be cons i dered , i n t u rn .

4 .2 . O n s e t o f b r e a k u p

Pas t s t ud i es o f p ressu re-a t omi ze d sp rays have es t ab l i shed t ha t a l l sp ray p roper t i es , i nc l ud i ng

cr i t e ri a fo r t he onse t o f b reaku p , a r e s t rong l y i n f luenced by t he deg ree o f f l ow devel op me n t and

t he p resence o f t u rbu l ence a t t he j e t ex it . F i r s t o f a ll , ea r ly s t ud i es o f p ressu re a t omi za t i on by

D e J u h a s z

et al .

(1932) and Lee Spencer (1933) show ed t ha t bo t h a t omi za t i on qua l i ty and mi x i ng

ra t es d i f fe r ed fo r l ami nar and t u rb u l en t f l ow a t t he j e t ex it . Nex t , Gra n t Mi d d l em an (1966),

Ph i nney (1973), H oy t Ta y l o r (1977a , b ) , H i ro yas u

et al .

(1982) an d M an sou r Chigier (1994)

concl ude t ha t t u rbu l ence genera t ed i n t he f low passage has a s i gn i f ican t e f fec t on je t b r e akup

proper t i es . T h i s beha v i o r i s hard l y su rp r i s i ng i n v iew o f t he wi de l y r ecogn i zed i m por t ance o f j e t

ex i t cond i t i ons on t he p roper t i es o f s ing l e-phase j e t s , see Lau fer (1950), Tennek es Lum l ey (1972),

Hinze (1975) and Schl icht ing (1979) , among others . Final ly , Arai

et al .

(1988) , H i royasu

e t a l .

( 1 9 9 1 ) a n d K a r a s a w a

e t a l .

(1992) showed t ha t b reakup cou l d be suppressed en t i r e l y fo r

supercav i t a t i ng f l ows , where t he l i qu i d j e t separa t es f rom t he passage wal l near t he end o f t he

con t r ac t i on sec t i on ( and does no t r ea t tach ) , wh i ch have very un i fo rm and non - t u rbu l en t ve l oc i t y

d i s t r i bu t i ons a t t he j e t ex i t. I n r e t ro spec t , t h i s beh av i o r i s no t su rp r i s i ng be cause j e t ex it cond i t i ons

o f t h is t yp e a re wi de l y used fo r l i qu i d j e t cu t t i ng sys t ems , where av o i d i ng b re aku p i s a maj o r des i gn

o b j e c ti v e , s e e Y o k o t a

e t a l .

(1988).

R e c e n t s t u d i e s u s i n g g a m m a - r a y a b s o r p t i o n a n d p u l s e d h o l o g r a p h y t e c h n i q u e s t o p e n e t r a t e t h e

dense sp ra y r eg i on a l so have he l ped t o qua n t i fy e f fec t s o f f l ow devel op me n t and t u rbu l ence a t t he

j e t ex i t on p r i m ary b rea kup p roper t i es , mi x i ng r a t es and t he s t ruc t u re o f t he d isper sed - f l ow reg i on ,

s e e R u f f e t

al.

(1991, 1992), Tscng

e t a l .

(1992a, b) , W u

e t a l .

(1991, 1992 , 1995) and W u Fae t h

(1993) . T hese s t ud i es i nvo l ved l i qu i d j e t s i n s t il l gases a t var i ous p ressu res wi t h b o t h fu l l y -deve l oped

t u rbu l en t f l ow and n on- t u rb u l en t quas i - s l ug fl ow (a non- t u rbu l en t f l ow wi t h a un i fo rm ve l oc i t y

d i s t r i bu t i on bu t wi t h wal l boundary l ayer s p resen t whose p roper t i es were no t wel l def i ned ) .

M e a s u r e m e n t s o f li q u id v o l u m e f r a c t io n d i s t r i b u ti o n s s h o w e d m u c h f a s t e r m i x in g r a t es , a n d m u c h

l arger d rop s i zes a f t e r p r i mary b reakup , fo r t u rbu l en t t han non- t u rbu l en t j e t ex i t cond i t i ons even

t houg h t he o t he r p rope r t i es o f these f l ows were near l y i den t ica l . I t was a l so es t ab l i shed t ha t

a e r o d y n a m i c e f f ec t s h a d n o i n f lu e n c e o n d r o p p r o p e r t ie s a f t e r p r i m a r y b r e a k u p f o r c o n d i ti o n s

t yp i ca l o f p ressu re-a t omi zed i n j ec t ion i n t o a i r a t no rma l t em pera t u re and p ressu re . In par t i cu l a r ,

no e f f ec t o f l i qu i d / gas dens i t y r a t i o on d ro p s i zes a f t e r p r i mary b reaku p , as an t i c i pa t ed f rom t he

c l ass ica l aerod yna mi c p r i ma ry b re aku p t heo r i es o f Tay l o r (1963) and L ev i ch (1962), was observe d

fo r l i qu i d / gas dens i t y r a t i o s g rea t e r t han 500 . In s t ead , p r i mary b reakup p roper t i es were con t ro l l ed

a l mos t en t i r e l y by l i qu i d phase f l ow p roper t i es a t t he ex i t o f t he i n j ec t o r passage .

Ot her s t ud i es a l so have found t ha t l i qu i d phase f l ow p roper t i es have dom i nat ed o} ~serva ti ons o f

p r i m a r y b r e a k u p i n p r e s s u r e - a to m i z e d s p r a y s a n d t h a t a e r o d y n a m i c e f fe c ts a r e n o t v e r y i m p o r t a n t

a t t he l i qu i d / gas dens i t y r a t i o s t yp i ca l o f observa t i ons o f p ressu re-a t om i zed i n j ec t i on a t no rmal

t e m p e r a t u r e a n d p r e s s u re . F o r e x a m p l e , H o y t T a y l o r (1 97 7a , b ) f o u n d t h a t b r e a k u p o f l iq u id

j e t s i n a ir a t a t mos pher i c p ressu re was assoc i a t ed wi t h t he p resence o f t u rbu l en t b oun dar y l ayer s

a l ong t he i n j ec t o r passage wal l s near t he ex i t . They a l so demons t r a t ed t ha t l a rge changes i n t he

aerod ynam i c env i ronm en t , i nc l ud i ng bo t h co f l ow i ng and c oun t er f l owi ng a i r, had l i t tl e e f f ec t on

b rea kup p rop er t i es . Unfo r t una t e l y , s i mi l a r to mo s t pas t s tud i es o f p ressu re a t omi za t i on , t he ac t ua l

p r o p e r t ie s o f t h e t u r b u l e n t b o u n d a r y l a y e rs a l o n g t h e p a s s a g e w a l ls w e r e n o t q u a n t if i e d b y H o y t

Ta y l o r (1977a , b ) fo r the i r exper i men t a l c ond i t i ons .

W u

e t a l .

(1995) r ecen t l y have r e po r t ed a s t udy w here t he deg ree o f f low devel opm en t a t t he je t

ex i t was con t ro l l ed , so t ha t i t s e f f ec t on p r i mary b reakup p roper t i es cou l d be exami ned . Th i s

e x p e r i m e n t i n v o l v e d p r e s s u r e - a to m i z e d j e t s p r o v i d e d b y a c o n v e r g in g p a s s a g e h a v i n g a l a rg e

con t r a c t i on r a t i o t o y i e l d a non- t u rbu l en t f l ow a t i ts exi t. Th e deg ree o f f low devel opm en t a t t he

i n j ec t o r ex it was t hen con t ro l l ed b y r emo v i ng t he bou nda ry l ayer fo rmed a l ong t he converg i ng

passage , and p rov i d i ng c ons t an t -d i am et er passag es o f var i ous l eng ths , L , (o r

L / d

a f t e r b o u n d a r y

l ayer remov al . Tes t cond i t i ons i nc l uded wat er , n -hep t a ne and va r i ous g l ycero l mi x t u res

i n j ec t ed in t o he l i um, a i r and Freo n 12 a t p ressu res o f 1 and 2 a t m, t o y i e ld

P c ~ P c

i n t he r ange

104-7240.


18/29

116

G M FAETH

etal

The experiments of Wu et al. (1995) showe d that the onse t of bre aku p along the surface o f the

l iquid core was affected by both the L i d rat io 'of the constant area sect ion of the injector passage

and the Reyno lds numb er of the flow through the injector passage. The effect of L i d is illustrated

by the pulsed photographs of the flow appearing in figure 14. Three conditions are shown:

boundary layer removal fol lowed by

L i d

= 4 and 10, and a round contract ion fol lowed by

L i d = 41. Passage Rey nolds n um bers for all three cond itions exc eed 105, which is sufficient to

obtain fully-developed turbulent pipe flow for sufficiently long L/ d , see Hinze (1975) and

Schlichting (1979). In facL measurements made by Ruff et al. (1991) for L i d = 41, at similar

condi t ions , showed that f low propert ies at the jet exi t approximated the propert ies of ful ly-devel-

oped tu rbulen t pipe flow repo rted b y Laufe r (1950). Thus, i t is not surprising th at the liquid surface

exhibi ts the format ion of l igaments and drops very near the jet exi t , corresponding to what has

been te rmed tu rbu len t p r imary b reakup by Wu et al. (1991, 1992, 1995) and W u Fa eth (1993),

for the large L i d condi t ion. In contrast , the f low remains smo oth near the jet exit and no br eakup

is observed for L i d = 4, yielding behavior similar to the findings for very short passage lengths

L / d = 0.15) suggesting the absence o f bre aku p in the absence o f liquid vorticity, i.e. for condition s

where the liquid velocity distribution is uniform and no turbulence is present. Increasing the length

of the constant area sect ion to L i d = 10, however, al lows the development of turbulent bo unda ry

layers along the walls and the corresponding developm ent of turbulent primary br eakup along the

liquid surface.

Addi t ional visualizat ion of the breakup of l iquid jets for various passage Rey nolds numb ers a nd

L i d can be found in Wu et aI. (1995); a breakup regime map summarizing all the test results as

a funct ion of L i d and ReLd is il lustrated in figure 15. Obse rvation s of turbulen t prim ary bre aku p

are denoted on the f igt~re by cross-hatched, half-darkened and d arkened symbols; open symb ols

denote laminar-l ike condi t ions where turbulent primary breakup was not observed al though large

scale wavy (sinuous) disturbances were seen in some instances. Results shown on the figure include

the observat ions of Ruff et al. (1991), Tseng et al. (1992b), Wu et al. (1991, 199 2, 1995), Wu

Fae th (1993) and Gr ant Mi ddlem an (1966). The results of Gra nt Mid dlem an (1966) were of

interest because they involved sharp-edged inlets which provided more dis turbed flows than the

other condi t ions .

C U T T E R ; L i d = 4 C U T T E R ; L i d = 1 0 F D F ; L i d = 4 1

d = 4 0 d = 4 0 d = 3 6

u o = 50 m/ s u o = 50 m/ s u o = 35 m/ s

L I Q U I D :

W T E R

Figure 14. Pulsed-pho tograp hs of round l iquid je t s injec ted into s ti l l a i r for various L / d F r o m W u et al

1991).


19/29

STR U C TU R E A N D B R EA K U P PR O PER TIES O F SPR A Y S l i 7

,d

1 0 2

1 0 1

1 0 0

t ~ t ~

m [ ]

0 0 0 0 0 0 ~ ) 0 ~

9 L / P G d ( m m ) T y p e L a in , s i n u

/ t u r b

W a t e r

6 2 3 0 c 6 . 2 , 3 . 6 F D F h i

8 6 7 ' c 9 . 5 , 6 . 4 , 6 , 2 F D F A

3 . 6

8 6 7 4 . 0 C u t t e r O

2 1 3 b ' c 9 . 5 , 6 . 2 , 3 . 6 F D F ~

1 0 4 b ' c 9 . 5 , 6 . 2 , 3 . 6 F D F ~ ~ '

8 6 7 a 0 . 6 2 - o o

G l y c e r o l 4 2 %

9 5 7 6 . 4 c , 6 . 2 F D F v v

4 . 0 C u t t e r ~ r

G 1 y c e r o I 6 3 %

7 2 4 0 6 . 2 F D F 71

1 0 0 7 6 . 4 , 6 . 2 F D F

]

4 . 0 C u t t e r t ~

2 4 7 6 , 2 F D F [ ] [ ]

1 2 0 6 . 2 F D F [ ] [ ]

n - H e p t a n e

5 9 4 c 6 . 4 F D F 0

t , , k

. ~

4 4 w

Q ~ 0 O 0

I

t

I

S i n u o u s j e t s ~ T u r b u l e n t j e t s

I

o .

0 0 0 0 0

a D a t a f r o m G r a n t & M i d d l e m a n

( 1 9 6 6 ) .

b D a t a i n c l u d e s r e s u l t s f r o m

R u f f et al ( 1 9 9 1 ) a n d T s e n g et al

( 1 9 9 2 ) ,

c D a t a i n c l u d e s r e s u l t s f r o m

W u et al ( 1 9 9 2 , 1 9 9 3 ) .

i i i i I f

1 0 3

L a m i n a r j e t s

0 0 0 0 0 0

0 0 0 0 0 0 0

l O I I I I [ I I I I ] I I I

1 0 2 1 0 4 1 0 5

R e L d

,__3

1 0 6

F i

structure and breakup properties of sprays

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