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~ Pergamon0017-9310(95)00136--0

I n t . J . H e a t M a s s T r a n s f e r . Vol . 39, No. 2 , pp. 275-288, 1996Cop yright 1995 Elsevier Science LtdPr inted in G reat Br i ta in . Al l r ights reserved0017-9310/96 $9.50+0.00

F ilm b o i li n g f r o m a d o w n w a r d - f a c i n g c u r v e ds u r f a c e i n s a t u r a t e d a n d s u b c o o l e d w a t e rMOHA MED S. EL-GENK and ALEXANDER G. GLEBOV

Chemical and Nuclear Engineering Dept./Institute for Space and Nuclear Power Studies,University of New Mexico, Albuquerque, NM 87131, U.S.A.( R e c e i v e d 20 D e c e m b e r 1994a n d i n f i n a l f o r m 1 3 M a r c h 1995)

Abstract- -Film boiling from a downward-facing curved surface in saturated and 5 K, 10 K, and 14 Ksubcooled water was investigated experimentally. Local and surface average Nusselt number correlationsdeveloped for both saturation and subcooled conditions were within + 10% of data. Surface rewetting insaturation boiling was hydrodynamically driven, but thermally driven in subcooled boiling. Consequently,surface rewetting in the former occurred earlier at higher qmin the critical film thickness prior to rewetting,however, was higher than that a t 10 K and 14 K subcooling, but lower than at 5 K subcooling. Surfacerewetting occurred first at lowermost position, 0 = 0, then sequentially at higher inclinations. For satu-ration boiling, the critical film thickness was ~ 85 #m and 180 pm at 0 = 0 and 8.26, respectively. Forsubcooled boiling at 0 = 0, the critical film thickness (~ 50 #m) was smaller ; it increased, however, withincreased inclination and decreased subcooling, reaching ~ 175 #m at 0 = 8.26 and 5 K subcooling.

I N T RODUCT I O NFilm boiling heat transfer from inclined, downward-facing flat surfaces [1-8] and on the inside or outsideof curved surfaces is of interest in many fields. Forexample, film boiling on the inside of curved surfacesis important in thermal management of cryogenicliquids in ground storage tanks and for handling ofstorage tanks o f hazardous and liquid chemicals dur-ing a fire. In these applications, it is desirable toachieve film boiling at low wall heat flux in order toavoid pressurization and explosive rupture of thetanks. Other applications include cooling of electriccables by pool boiling of liquid helium in supercon-ductivity research and the telecomm unication industryand passive cooling of the lower head of an ad-vanced light water reactor pressure vessel by boiling inan unde rlying water pool following a core meltdownaccident [9-11]. In these applications, knowledge ofthe maxi mum heat flux and the m inim um film boilingsurface heat flux ( q m i n ) , and cor respondin g wall super-heats as well as of film boiling heat transfer is impor-tant for design purposes and for establishing oper-ation an d safety margins.Film boiling from curved surfaces has not receivedmuch a ttent ion ; only little work has been reported forinclined and downward-fa cing flat surfaces. Ishigai e ta L [1] pioneered the work on film boiling from flatdownward-facing fiat circular copper plates, 25 and50 mm in diameter, in saturated water. Jung e t a l .[2] and Seki e t a l . [3] investigated film boiling fromupward-facing and downward-facing flat surfaces insaturated R-11 ; Seki e t a l . [3] for saturated R-11 at 2bar. Seki e t a l . [3] reported that qmin or the dow nward-facing position was much lower than that for the

upward-facing position, The film boiling heat fluxvalues for R-11, however, were consistently lower tha nthose for water, which Jung e t a l . attributed to thedifference in physical properties of the two liquids.Neither Ishigai e t a l . nor Jung e t a l , reported valuesfor qmin or corr espo ndin g wall superheats, ( m T s a t ) m i n ;only one value each was reported by Jung e t a l . [2]showed film boiling heat flux to increase withincreased inclin ation angle from 0 = 0 (downwa rd-facing) to 0 = 180 (upward-facing). The vapor filmfor downward-facing surfaces was much more stablethan for inclined and upward-facing surfaces, delayingrewetting and resulting in much lower film boilingheat flux [2, 4, 5]. These investi gation s of film boilingfrom dow nward-fac ing and inclined flat surfaces [1-3]used steady-state heating and were only for satura tioncondition; few data is available for fiat and inclinedsurfaces in subcooled water [4, 5].

Guo and EI-Genk [4, 5] and EI-Genk and Guo [6]performed quenching experiments using a flat inclinedsurface, 50.8 mm in diameter and 12.8 mm thick, insaturated and subcooled water (5, 10, 15 and 20 Ksubcoo ling) at 0 of 0, 5, 10, 15, 30, 45 and 90 (ver-tical). The film boiling results agreed qualitatively withthose in refs. [1-3]. The values of qmin an d ( A T ~ a t ) m i nincreased as liquid subcooling increased. These resultsas well as those of other i nvestiga tors [1-3] are,however, not applicable to pool boiling from down-ward-facing curved surfaces, for which, to the best ofthe auth ors knowledge, there is very little experimentaldata available [7, 8].

Recently, E1-Genk e t a l . [7] and E1-Genk and Gle-bov [8] performed quenching experiments, whichemployed three copper sections of the same diameter(50.8 mm) and surface radius (148 mm), but of differ-

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276 M.S . EL-GE NK and A. G. GLEBOV

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w a t e r s u b c o o l i n g ( T s a - T p ) [K ]e m i s s i v i t yl o c a l i n c l i n a t i o n [~ ]k i n e m a t i c v i s c o s i t y [ m 2 s 1]d e n s i t y [ k g m - 3]S t e f a n - B o l tz m a n n c o n s t an t[5 .669 x 10 8 W m -Z K 4]d i m e n s i o n l e s s t i m e , ( t- to) /( trew-- tO).

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s u r f a c ec r i t i c a le v a p o r a t i o n a t l i q u i ~ v a p o r i n t e rf a c ef i l m b o i l i n g , l i q u i dl i q u i dm i n i m u m f i lm b o i l i n gn a t u r a l c o n v e c t i o ni n i t i a l o r a t t h e b e g i n n i n g o f q u e n c h i n gw a t e r p o o lr e w e t t i n gr a d i a t i o nc u r v e d s u r f a c es a t u r a t i o ns u b c o o l e dv a p o rb o i l i n g s u r f a c e , w a l l .

S u p e r s c r i p t ss u r f a c e a v e r a g e .

e n t t h i c k n e s s e s ( 1 2 .8 , 2 0 a n d 3 0 m m ) . L o c a l a n d a v e r -a g e p o o l b o i l i n g c u rv e s w e r e o b t a i n e d f o r s a t u r a t i o na n d 5 , 1 0 a n d 1 4 K w a t e r s u b c o o l i n g . T h e m a x i m u ma n d m i n i m u m f i l m b o i l i n g h e a t f lu x e s , w h i c h i n c r e a s e dw i t h i n c r e a s e d s u b c o o l i n g, w e r e i n d e p e n d e n t o f w a l lt h i c k n es s > 1 9 m m a n d B i o t n u m b e r > 0 . 8 a n d 0 . 00 8 ,r e s p e c t i v e l y , i n d i c a t i n g t h a t b o i l i n g c u r v e s f o r t h e 2 0a n d 3 0 m m t h i c k s e c t i o n s w e r e r e p r e s e n t a t i v e o f q u a s is t e a d y - s t a t e , b u t n o t t h o s e f o r t h e 1 2 . 8 m m t h i c ksec t ion .

T h e o b j e c t i v e o f t h i s w o r k w a s t o i n v e s t i g a t e f i l mb o i l i n g h e a t t r a n s f e r i n t h e e x p e r i m e n t s o f E 1 - G e n ka n d G l e b o v [ 8] , u s i n g t h e d a t a o f t h e 20 m m t h i c ks e c ti o n . E x p e r i m e n t a l d a t a a n d v i d e o i m a g e s o f b o i l-i n g s u rf a c e w e r e a n a l y z e d t o d e t e r m i n e : ( a ) t h eq u e n c h i n g m e c h a n i s m o f f il m b o i l in g i n s a t u r a t i o na n d s u b c o o l e d b o i l i n g , ( b ) t h e e f f ec t o f w a t e r s u b -c o o l i n g o n l o c a l f i l m b o i l i n g h e a t f l u x , v a p o r f i l mt h i c k n e s s , a n d r e w e t t i n g t i m e , a n d ( c ) q m i , , (mTsat)mina n d t h e c r i t i c a l f i l m t h i c k n e s s , p r i o r t o s u r f a c e r e w e t -t i n g , a s f u n c t i o n s o f l o c a l i n c l i n a t i o n o n t h e s u r f a c ea n d w a t e r s u b c o o l i n g . T h e l o c a l a n d s u r f a c e a v e r a g eN u s s e l t n u m b e r s w e r e a l so c o r r e l a t e d in t e r m s o f R a y -l e ig h a n d J a c o b n u m b e r s , f o r b o t h s a t u r a t i o n a n ds u b c o o l i n g c o n d i t i o n s .

E X P E R I M E N T A L S E T U P A N D P R O C E D U R E ST h e e x p e r i m e n t a l s e t u p a n d p r o c e d u r e s d e t a i l e d in

[ 7, 8] , a r e o n l y s u m m a r i z e d h e r e i n . T h e c o p p e r s e c t i o n[ F i g. l ( a ) ] h a d e i g h t , K - t y p e t h e r m o c o u p l e s ( T C 1 -T C S ) p l a c e d ~ 0 . 5 m m f r o m t h e b o il i n g s u r f ac e , top r o v i d e t e m p e r a t u r e d a t a f o r s u b s e q u e n t d e t e r -m i n a t i o n o f t h e l o c a l a n d a v e r a g e p o o l b o i l i n g h e a tf l u x e s a n d s u r f a c e t e m p e r a t u r e s i n t h e v a r i o u s b o i l i n gr e g im e s , a n d t h r e e t h e r m o c o u p l e s p l a c e d ~ 5 m mf r o m t h e t o p s u r f a c e ( T C 9 - T C 1 1) . T h e c o p p e r s e c t i o nm o u n t e d i n a w a t e r s e a l e d M a r i n i t e C i n s u l a t io n m o l dw a s h o u s e d i n a c y l i n d r i c a l B a k e l i t e s k u l l f o ra d d i t i o n a l i n s u l a t i o n a n d h a n d l i n g . T h e M a r i n i t em o l d a n d t h e B a k e l i te s k ul l w e re m a c h i n e d a t t h es u r f a c e t o t h e s a m e c u r v a t u r e a s t h e b o i l i n g s u r f a c e i no r d e r t o a v o i d e d g e e f f e c t s i n f l u e n c i n g t h e r e l e a s e o fv a p o r [ F i g . 1 a ) ] .

T h e q u e n c h i n g t a n k h a d l a r g e gl a s s w i n d o w s o nf o u r s i d e s f o r v i s u a l o b s e r v a t i o n . T o o b s e r v e t h e e n t i r eb o i l i n g s u r f a c e d u r i n g q u e n c h i n g , a w a t e r s e a l e d m i r -r o r w a s m o u n t e d a t a 4 5 a n g l e a t t h e b o t t o m o f t h et a n k . P r i o r t o e a c h t e s t , d i s t i l l e d w a t e r i n t h e t a n k w a sm i x e d t h o r o u g h l y a n d d e g a s s e d b y b o i li n g f o r a b o u t1 5 m i n . A l s o , t h e s u r f a c e o f t h e c o p p e r s e c t i o n w a s

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( a )Film boiling from a downward-facing curved surface

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3 8 0- 1 .0 - 0 . 8 - 0 . 8 - 0 . 4 - 0 . 2 0 0 . 2 0 . 4 0 . 8 0 . 8 1 .0R a d i a l L o c a t io n { r /R )

Fig. l . (a) Cross-sectional view of instrumented test section. (b) Mea sured tempe rature distr ibution nearthe bo iling surface during quenching.

p o l i s h e d u s in g N o . 1 20 0 S i l ic o n C a r b i d e s a n d p a p e rt h e n c l e a n e d w i t h a c e t o n e . T o a v o i d s u r f a c e o x i -d i z a t i o n b e f o r e q u e n c h i n g , t h e s u r f a ce w a s w r a p p e di n a l u m i n u m f o i l w h i l e b e i n g h e a t e d o n a h o t p l a t e t oa b o u t 5 1 0 K . T h e t e s t s e c t io n w a s t h e n s u b m e r g e di n t o t h e w a t e r p o o l , ~ 4 0 m m b e l o w t h e s u r fa c e . W h e nt h e d e p t h o f w a t e r v a r i e d b e l o w 4 0 m m , t h e e f f e ct w a sn e g l i g i b l e ; l a r g e r d e p t h s w e r e n o t c o n s i d e r e d ,h o w e v e r , b e c a u s e o f t h e s m a l l t a n k s i ze .

D u r i n g q u e n c h i n g , a l l th e r m o c o u p l e s w e r e s c a n n e ds e q u e n t i a l ly o n c e e v e r y 1 0 0 m s a n d t h e i r r e c o r d i n gt i m e a d j u s t e d f o r t h e i n t e r v a l ( ~ 9 m s ) b e t w e e n r e a d -i n g s t o o b t a i n s i m u l t a n e o u s t e m p e r a t u r e m e a s u r e -m e n t s . T h e r a w t e m p e r a t u r e m e a s u r e m e n t s h a d h i g hf r e q u e n c y , r a n d o m o s c i l l a t i o n s , d u e t o e l e c t r i c e q u i p -m e n t . I n o r d e r t o r e m o v e t h e s e o s c i l l a ti o n s w i t h o u tu n d u l y d e g r a d i n g t h e u n d e r l y i n g i n f o r m a t i o n ,n u m e r i c a l f i l te r i n g (o r s m o o t h i n g ) o f t h e r a w t e m -p e r a t u r e d a t a w a s p e r f o r m e d [ 8] u s i n g a m e t h o d s i m i -l a r t o t h a t d e s c r i b e d i n [ 12 ]. A f t e r n u m e r i c a l f i l t e ri n g ,t h e m e a s u r e d t e m p e r a t u r e s n e a r t h e b o i l i n g s ur f a c e

w e r e u s e d , i n c o n j u n c t i o n w i t h a t w o - d i m e n s i o n a l( r , z ) t r a n s i e n t s o l u t i o n o f h e a t c o n d u c t i o n i n t h e c o p -p e r s e c t i o n d u r i n g q u e n c h i n g , t o d e t e r m i n e t h e l o c a la n d a v e r a g e p o o l b o i l i n g h e a t f l u xe s a n d s u r f a c e t e m -pera tu res [7 , 8 ] .Determination of pool boiling heat lux

T h e t w o - d i m e n s i o n a l , t r a n s i e n t h e a t c o n d u c t i o ne q u a t i o n i n t h e c o p p e r s e c t i o n w a s s o l v e d n u m e r i c a l l yu s i n g , a s a b o u n d a r y c o n d i t i o n , t h e r e c o r d e d t e m -p e r a t u r e s n e a r t h e b o i l i n g s u r f a ce ( T C I - T C 8 ) d u r i n gq u e n c h i n g [ F i g . 1 b ) ] , t o d e r i v e t h e l o c a l s u r f a c e h e a tf l u x e s a n d s u r f a c e t e m p e r a t u r e s [ 7, 8] . T h e t i m e s l i s t e di n F i g . l ( b ) a r e m e a s u r e d f r o m t h e b e g i n n i n g o fq u e n c h i n g i n t h e s a t u r a t i o n b o i l i n g ex p e r i m e n t s , s t a r t -i n g a t a w a l l s u p e r h e a t o f 1 3 5 K . T h e n u m e r i c a l s o l u -t i o n e m p l o y e d a f u l ly i m p l i c i t a l t e r n a t i n g d i r e c t i o n ,f i n i t e c o n t r o l v o l u m e ( C V ) m e t h o d , ( 2 0 x 2 0 ) c a l -c u l a t i o n g r i d , a n d a c o n v e r g e n c e c o e f f i c i e n t o f 10 -6.W h e n a ( 3 0 x 30 ) g r i d a n d / o r a s m a l l e r c o n v e r g e n c ec o e f f i c ie n t w e r e u s e d , c o m p u t a t i o n t i m e i n c r e a s e d s i g -

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278 M.S. EL-GENK and A. G. GLEBOVnificantly with negligible changes in the calculatedvalues of the pool boiling heat flux and surface tem-perature.

The temperatures within the copper section werecalculated at the center and the heat flux at the boun-daries of the control volumes. The local heat flowat the boiling surface was determined from the heatbalance in the control volumes (CVs) bounde d by theboiling surface. The local pool boilin g heat flux wasthen determined by dividing the calculated heat flowby the corresponding surface area of the controlvolume. The local surface temperatures were deter-mined from the parabolic extrapolation of the cal-culated temperatures at centers of CVs in the threerows near the boiling surface. The surface averagepool boiling heat flux was determined by dividing thecalculated total heat flow from the boiling surface bythe total surface area. The average wall temperaturewas determined from the integral of the local walltemperatures over the entire boiling surface. The err orin numerical calculations, determined from the overallenergy balance after each time interval, was less than1.0%, and the difference between calculated and mea-sured temperatures by TC9 -TC I 1 was about -t-0.5 K.The overall uncertainties in the local and average filmboiling heat flux, determined using the method out-lined in [13], were _+ 9% and _+ 4%, respective ly. Moredetails on the numerical solution are given in [14].

R E S U L T S A N D D I S C U S S IO NExperimental results presented in this section show

the effects of water subcooling on both local and sur-face average film boiling curves and the critical filmthicknesses prior to surface rewetting. The local filmboiling curves presented are the average of two sep-arate tests performed at the same conditions to con-firm the reproducibi lity of experimenta l results [7, 8] ;results were rep roducib le to within _+ 5%.Visual obser~ations

Visual observat ions and video images of film boilingrevealed that the surface was covered initially by astable vapor film [Figs. 2(a), 3(a) and 4(a)]. T he desta-bilization and collapse of film boiling, resulting insurface rewetting, were hydrodynamica lly driven insaturation boiling [Figs. 2(b), 4(c) and 4(d)], but ther-mally driven in subcooled boi ling [Fig. 3(b)]. In satu-ration boiling, all the heat released from the surfacewas consumed in vapor generation. The vapor flowunder the effect of tangential gravity componentcaused the film to be thinnest at the lowermost posi-tion and thickest near the edge [Fig. 4(a)]. At highwall superheat , int ermi tten t releases of vapor fro m theperiphery of the swelled film caused the vapor-liquidinterface to oscillate repetitively [Figs. 2(b), 4(b) and4(c)], then fully stabilize as excess vap or in the filmwas released [Figs. 2(a) and 4(a)]. The average volu meof released vapor increased, but the release frequencydecreased as the surface temperature decreased with

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Fig. 2. Photographs showing the destabilization and collapseof saturation film boiling.

time in film boiling. Even tually , film oscillations, fol-lowing the release of vapor, destabilized film boiling,forcing surface rewetting [Figs. 2(c) and 4(d)].

In subcooled boiling, however~ only a fraction of

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Film boiling from a downw ard-facing curved surface 279

i li i i i i ; ; i i ! i !Fig. 3 . Photogra phs showing the destabilization and collapseof subcooled film boiling.

t h e h e a t r e l e a s e d f r o m t h e s u r f a c e w a s c o n s u m e d i nv a p o r g e n e r a t i o n ; t h e l a r g e s t f r a c ti o n w a s c o n d u c t e dt h r o u g h t h e v a p o r f i l m t o t h e u n d e r l y i n g w a t e r p o o lt o b e r e m o v e d b y n a t u r a l c o n v e c t i o n . V a p o r g e n e r a t e da t t h e l o w e r p o s i t i o n s o n t h e s u r f a c e a c c u m u l a t e d a t

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Surface -x Os ci l la t ingR e w e t t i n g V a p o r F il m( d ) S u r f a c e R e w e t t i n g

Fig. 4 . I l lustration of saturation fi lm boiling on a downward-facing curved surface.

h i g h e r l o c a t i o n s , i n c r e a s i n g t h e f il m t h i c k n e s s . A t 1 0a n d 1 4 K w a t e r s u b c o o l i n g , n o v a p o r w a s s e e n re l e a s e df r o m t h e p e r i p h e r y o f t h e v a p o r f i l m . A t 5 K s u b c o o l -i n g , h o w e v e r , v a p o r r e l e a s e f r o m t h e e d g e o f v a p o rf i l m o n l y o c c u r r e d a t h i g h w a l l s u p e r h e a t [ F i g s . 3 ( a )a n d 4 ( a ) ] . A s t h e s u r f a c e t e m p e r a t u r e d r o p p e d , l e s sv a p o r w a s g e n e r a t e d a n d t h e f i lm t h i ck n e s s c o n t i n u e dt o d e c r e a s e d u e t o c o n d e n s a t i o n . E v e n t u a l l y , t h ev a p o r f i lm i n t h e i n n e r p o r t i o n o f t h e s u r f a ce , w h e r ei t i s t h i n n e s t , c o l l a p s e d l o c a l l y [ F i g . 3 ( b ) ] , t h e n s u r f a c er e w e t t i n g p r o p a g a t e d r a d i a l l y o u t w a r d .

A s i n d i c a t e d l a t e r , t h e r e w e t t in g t i m e ( o r d u r a t i o no f f i l m b o i l i n g ) o f ~ 27 3 s i n s a t u r a t i o n b o i l i n g w a sm u c h s h o r t e r t h a n i n s u b c o o l e d b o i l i n g (4 1 5 s - 6 7 8 s ).I n s u b c o o l e d b o i l i n g , t h e d e c r e a s e i n r e w e t t i n g t i m ew i t h i n c r e a s e d w a t e r s u b c o o l i n g , r e s u lt e d i n s m a l l e rf i lm t h i c k n e ss p r i o r t o r e w e t t in g , b u t h i g h e r m i n i m u mf i l m b o i l i n g h e a t f l u x . I n t r a n s i t i o n b o i l i n g , v a p o rn u c l e a t i o n i n t h e i n n e r p o r t i o n o f t h e s u r f a c e w a sm o r e c o a r s e [ F i g . 2( c ) ] t h a n i n s u b c o o l e d b o i l i n g [ F i g .3 ( c ) ] . A l s o , t r a n s i t i o n b o i l i n g w a s a c c o m p a n i e d b yf r e q u e n t v a p o r r e l e a s e f r o m t h e e d g e o f t h e c o p p e rs u r f a c e [ F i g . 2 ( c ) ] . I n s u b c o o l e d b o i l i n g n o v a p o rr e l e a s e w a s o b s e r v e d a t t h e b e g i n n i n g o f t r a n s i t i o nb o i l i n g a t h i g h w a l l s u p e r h e a t [ F i g . 3 (c ) ] .

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280 M.S. EL-GENK and A. G. GLEBOV0 . 0 2 5

~ 0 .020U"

u . o . o 1 50-r~ o.o~o0fl l

u _ 0 . 0 0 5

t-

2 0 , 0 t u r n t h i c k T S ( a }

. . . . ~ . - . . . ~ " t l ~ ' ~ . . . ~ t . - i . . . .. . . .. . . .. . . .. . . .. . . .. . . .. . . .. . . .. a tu r a te d ..........

ATsul== 10 K . . . . . . . . . . . . . . ~ t ZA T s , ~ - 5 K

s i = = = =0 2 4 6 8 10

E q u J v a l e n t S u r f a c e I n c l i n a ti o n . e (o )

vJF -

O "

0t-OQ .

03

1 2 0

9 0

6 0

3 0

i l i

S a t u r l t l o n ( b )V A T s u l o 5 K[ ] &T=u b - 10 K0 & T s u b . 14 KA v a ' ~ t g e V a l u e s

| | iI I ~ I ~ i - 1 ~ l l - i l l0 2 4 6 8

Equ ivalen t Su rface InoUnation. e (a)Fig. 5. Minimum film boiling heat flux and corresponding wall superheat.

1 0

M i n i m u m p o o l b o i li n 9Figu res 5(a) and (b) show tha t qm~n and (AT~a0m,,

both increased with increased subcooling; higherwater subcooling caused film boiling to qu ench earlier.The minimum film boiling heat flux also increasedwith decreased inclination, 0. The values (ATsat)mi,,,however, were ind ependen t of 0 because the high ther-mal conductivity of the copper stimulated lateral con-duction near the surface, resulting in a uni form surfacetemperature [Fig. 5(b)]. In saturation boiling, theminimum film boiling heat flux was significantlyhigher than that at 5 and 10 K subcooling, but onlyslightly lower than that at 14 K subcooling. As indi-cated earlier, because film boiling destabilization insatura tion boiling was hydrodynamica lly driven, sur-face rewetting occurred earlier, at both higher heatflux and wall superheat.

F i l m b o i l i n 9 c o r r e l a t i o n sThe local film boiling Nusselt number was cor-

related in terms of the Rayleigh number and Jacobnumbers as :

N u = C ( R a / J a ) ~ . ( 1 )This correlation is similar to that obtained for la minarfilm boiling on an isothermal sphere using integralbound ary layer analysis [15], except that thecoefficient " C" and the exponent "a" are functions of0 as follows :

C = exp (C] 0+ C2), (2)and,

a = a l O + a 2 . (3)For saturati on boiling, these coefficient are: C~ =

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Fi l m b o i l in g f ro m a d o w n w a rd - fa c i n g c u rv e d su r fa c e 2 81I O 0

1 0

0. 10

0 . 0 0 1

0 . 0 0 0 0 1 0 2 4 6 8 10

0 .8

0 .6

0 .4

0 .2

s a t u r a u o n ] ( b )I v A T u - S K I. I - I A T ~ b - - 1 0 Ka ~ 0 . 6 31 5 - 0 . 0 1 6 9 9 I - IK I. . . . . . . . . . ' . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ! . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

o o , , , " 0 . 5 , 3 - 0 . 0 4 3 2 o

0 2 4 6 8 1 0E q u i v a l e n t I n c R na t lo n . 0 ( * )

Fig . 6 . Nussel t n umb er corre la t ion coeffic ien ts for f i lm boi l ing .

0 . 80 6 , C 2 = - 2 . 8 8 2 , a l = - 0 . 0 3 6 6 a n d a 2 = 0 .3 6 6 .F o r w a t e r su b c o o l i n g , 5 K ~ < A Tsub ~< 1 4 K , t h e sec o e f f ic i e n ts w e r e c o r r e l a t e d a s f o l l o w s :

C ~ - -- 0 .9 8 4 - 1.0 2 x 1 0 -6 e x p (0 .9 5 4A Tsub ) (4 )C 2 = -8 .0 - 1 .7 4 1 0 -2 e x p (0 .3 1 A T~ u b) (5 )a l -- - 0 . 0 4 5 + 8 . 7 5 1 0 - 7 e x p ( 0. 74 A Ts ub ) ( 6 )a 2 = - 0 . 5 7 5 + 8 . 8 6 5 1 0 - 4 e x p ( 0. 30 A Ts ub ). ( 7 )

A s s h o w n i n F i g s. 6 ( a ) a n d ( b ) t h e c o ef f i c ie n t " C "[ e q u a t i o n ( 2 ) ] i n c r e a s e d w i t h i n c r e a s e d i n c l i n a t i o na n g l e , b u t d e c r e a s e d w i t h i n c r e a s e d s u b c o o l i n g [ F i g .6 ( a )] . C o n v e r s e l y , t h e e x p o n e n t " a " i n e q u a t i o n ( 1)d e c r e a s e d w i t h i n c r e a s e d i n c l i n a t i o n , b u t i n c r e a s e dw i t h i n c r e a s e d w a t e r s u b c o o l i n g [ F i g . 6 ( b ) ] . F i g u r e7 ( a ) s h o w s t h a t t h e c o r r e l a t i o n f o r t h e l o c a l N u s s e l tn u m b e r , e q u a t i o n ( 1 ), is w i t h i n + 1 0 % o f t h e d a ta .N o t e t h a t t h e v a l i d i ty o f e q u a t i o n ( 1) i s l i m i t e d to t h ep r e s e n t d a t a f o r w h i c h A T ~u b < 1 4 K .

S i m i l a r ly , th e s u r f a c e a v e r a g e N u s s e l t n u m b e r f o rs a t u r a t i o n a n d s u b c o o l e d b o i l i n g ( A T su b < 1 4 K ) w a sc o r r e l a t e d a s

Nu = B(Ra/Ja) b (8 )w h e r e , B = 4 . 8 a n d b = 0 . 1 6 2 f o r s a t u r a t i o n f i l m b o i l -i n g . F o r s u b c o o l e d b o i l i n g , th e c o e f f i c i e n t B a n d t h ee x p o n e n t b a r e

B = 6 .5 3 x 1 0 -2 -3 .9 3 x 1 0 -3 e x p (0 .2 0 A Tsu b) (9 )b = 0 . 3 4 + 1 .6 6 x 1 0 - ' e x p (0 .5 0 6A Ts~ b) . (1 0 )

A s s h o w n i n F i g . 7 ( b ), t h e c o r r e l a t i o n o f th e a v e r a g ef i lm b o i l i n g N u s s e l t n u m b e r [ e q u a t i o n ( 8) ] i s i n a g r e e -m e n t w i t h e x p e r i m e n t a l d a t a t o w i t h i n + 5 % .Rewetting t ime

A s s h o w n i n F i g s . 5 a n d 8 , t h e r e i s a d i r e c t c o r -r e l a t i o n b e t w e e n t h e v a l u e s o f b o t h q mi, a n d ( A T s a t ) m i na n d t h e r e w e t t i n g ti m e . F i g u r e 5 ( a ) a n d t h e i ns e r t i n

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282 M.S. EL-GENK and A. G. GLEBOV1 0 0 0

8 0 0

6 0 0Z

4 O O

2 0 0

f Saturationv , T . . -0 ~ T -O ATmu b - 14 K

+ 1 o %l

( a )

0 2 0 0 4 0 0 6 0 0 8 0 0 1 0 0 0C(RaATa)=

6 0 0 . . . . , . . . . . . . . . . . . . . ! . . Q .

5 0 0

z 4 0 0G)

/. ~j ~r - IsNgal e t aL[3]) Z 3 0 0 / ~ 1 ~ J ~ " W a t e r. f l a t . ( i l L - 5 0 m rn/ . i ~ S~turm tlono~ ~ ~ V A T , , , , - 5 K~ " [] ATaub - 10 K> 2 0 0 0 &T=ub - 14 K

. . . . . . . . . . . i i I , i , , , i i i , i ,1 0 01 0 0 2 0 0 3 0 0 4 0 0 5 0 0 6 0 0B ( R s / ~ ' a ) b

Fig. 7. (a) Nusselt number correlation for local film boiling heat transfer. (b) Nusselt number correlationfor surface average film boiling heat transfer.

Fig. 8(a) show that in subcooled boiling lower qm,,and (AT~a0mm were always associated with long errewetting time. Unlike q,,~,,, the rewetting timeincreased as the local inclination on the boilingsurface, 0, increased or water s ubcoo ling decreased.The insert in Fig. 8(a) compares the rewetting timemeasure d for the lowermost position (0 = O) at satu-ration a nd at different water subcooling. The smallestrewetting time of 273 s was for sa tura tion film boiling,followed by that for 14 K subcooling (415 s), thenincreased to 506 s and 678 s at 10 K an d 5 K subcool-ing, respectively. These times were meas ured in exper-iments starting at a wall superheat of 135 K.

In order to examine the progression of rewetting onthe surface, the rewetting time is normalized to thatat the lowermost position and results plotted in Fig.8(a). The slowest progression of surface rewettingoccurred at saturation and the fastest at 14 K subcool-ing. For example, in saturation film boiling surface

rewetting at 0 = 8.26 occurred about 285 ms afterthe lowermost position (0 = 0"). At 14 K subcooling,however, surface rewetting at the same locationoccurred only about 115 ms after the lowermostposition.

Determination oJfi lm thickness and volume o[re leasedvaporDurin g film boiling, thermal energy is transferred

from the metal section surface to the liquid-vaporinterface by conduction and radiation; convection isnegligible due to the low vap or flow relative to thesurface. Because the initial surface temperature atquenching (~513 K) and the emissivity of copper(0. t) are relatively low, the rad iation co ntribu tion wassmall compared to that by conduction. Therefore, theaverage vapor film thickness in film boiling can beexpressed as [17]:

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Film boiling from a downward-facing curved surface 283

E0

fI -o_=on "

3 0 0

2 5 0

2 0 0

1 5 0

1 0 0

5 0

0

i ~ , . . - " ( )

......... [ .... ... . ~ : i ~ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . z c . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .i i I i f ! . ,. .- s i_ _

. . . . . . . . . . . . . . . . ~ ......................................... ... ... ... ... .. i . . . . . . . . . . . . . . . . . . . . . . . . . . , , 6 . . . . . . . . . . . . . . . . . . . . . . ~ - ~ - - - ~ . . . . . . . . . . . . . .

. .. .. .. .. .. .. .. .. .. .. W i r e r ~ g . ~ t T i , ~ ( K , , J ~"~ ~10~~ ~ ......~ , , " ~ ~: . . ~ _ ~ - . - < : r ~ I s a ~ = u o n I : l

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I V ~ V ~ " ~ K t l l ' ]- - , i , i , . . . . . . . . . . . . . . . . . . ; . . . ; . . . . . . . . . . . . . . . i . . . . . . . . =0 2 4 6 8

E q u i v a l e n t S u r f a o e I r ~ l l n a t l o r ~ O (= )

~ ' 3-1-oc0 r 2

U-0

o

11:

2. 5x 10 5 C b )

0 0 . 2 0 . 4 0 . 6 0 . 8 1 . 0D i m e n s i o n l e s s T i m e .

Fig. 8. (a) Rewetting time for saturation and subcooled film boiling. (b) Vapor release frequency andvolume in film boiling.

w h e r e ,

a n d ,

3 r e ( t ) = k v / [ h f a - O . 7 5 / ~ R ] (11)

h ra = ( . ~ u ' k v / D ) (12)--4 4/~R = e~r(Tw - T s a t ) / A ~ s a t (13)

e = { l / e + + l / e , - - 1 } - ' . ( 1 4)I n e q u a t i o n ( 1 4 ) , t h e w a t e r e m i s s i v i t y , eL, w a s t a k e ne q u a l t o 0 . 9 5. T h e l o c a l f i l m t h i c k n e s s c a n a l s o b ee x p r e s s e d in t e r m s o f t h e l o c a l h e a t t r a n s f e rcoef f ic ien ts a s

6 ra (O , t ) = k v / ( h r B - - O . 7 5 h R ) (15)w h e r e , h r , a n d h a a r e t h e l o c a l f i l m b o i l i n g a n d r a d i -a t i o n h e a t t r a n s f e r c o e f f i c i en t s , r e s p e c t i v e l y . E q u a t i o n( 1 5) a p p l i e s b e t w e e n r e l e a s e s o f v a p o r f r o m t h e e d g e

o f t h e b o i l i n g s u r fa c e . T h e a v e r a g e v o l u m e o f r e l e a s e dv a p o r , V B ( t ) , i s d e t e r m i n e d f r o m t h e m a s s b a l a n c e

V B f p v = ( q e v A / h ' f g ) + p v A ( d 6 m / d t ) . (16)S i n c e t h e a v e r a g e f i l m t h i c k n e s s c h a n g e s s l o w l y w i t ht i m e , th e s e c o n d t e r m o n t h e r i g h t h a n d s i d e o f e q u a -t i o n ( 1 6 ) i s n e g l ig i b l e c o m p a r e d t o t h e f i r s t t e r m , t h u s

VB(t) = [ ( g l e v A ) / ( f p v h ' f g ) ] (17)w h e r e ,

qo+ = ~ma L~ ,-h Nc a Lub. ( 1 8 )T h e n a t u r a l c o n v e c t i o n h e a t t r a n s f e r c o e f f i c i e n t f r o mt h e v a p o r - l i q u i d i n t e r f a c e to t h e u n d e r l y i n g s u b c o o l e dl i q u i d p o o l i s d e t e r m i n e d f r o m t h e f o l l o w i n g c o r -r e l a t i o n f o r a h e a t e d , d o w n w a r d - f a c i n g f i a t s u r f a c e[181

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284 M.S. EL-GENK and A. G. GLEBOVh N c = 0 . 2 7 ( k f / D ) [ ( [ l g A L u b D 3 ) / V r ~ r ] 2 5 . (19)

Equation (17) is rearranged to give the following gen-eral expression for VBV B ( t ) = B J a ( R a / J a ) b [ A ~ / ( D f ) ]

- [ h y c A A T ~ o b i '( ./ ~ o v h 'r g )] . ( 2 0 )In saturation boiling, the second term on the righthand side of equation (20) drops out, thus :

V B ~, ,( t) = B J a( R a / J a ) b[ A c ~ , . / ( D [ ' ) ] . (21)In equations (20) and (21), the vapor release fre-quency is determined from the video images of theboiling surface during quenching. The video recordingspeed was about 60 field s ~, thus the r eported fre-quencies in Fig. 8(b) are accurate to within 0.016 Hz.As indicated earlier and shown in Fig. 8(b), at 5 Ksubcooling, intermittent release of vapor from theedge of the vapor film was only observed at highwall superheat (AT~a, > 105 K). In sa tura tion boiling ,however, va por release contin ued until surface rewet-ting occurred. The insert in Fig. 8(b) presents esti-mates of vapor release volume for saturation and 5K subcooling. At 5 K subcooling, while the averagevolume of released vapor was larger, the release fre-quency was lower than at saturation. The vaporrelease frequency for 5 K subcooled boiling was sig-nificantly lower than that for sat uratio n film boiling.In sa turation film boiling, the vapor release frequencydecreased from ~ 2.9 Hz at the be ginn ing of film boil-ing (at wall superheat of 135 K) to ab out 0.8 Hz priorto rewetting at AT~,t ~ 80 K [Fig. 8(b)]. The va porrelease frequen cy at 5 K su bcooli ng decreased froman in itial value of ~ 1.2 Hz to zero at z = 0.4; adimensionless time, r, of unity corresponds to surfacerewetting.F i l m b o i l i n g c u r v e s

Figures 9(a)-(d) compare the experimental valuesof local (at three locations) and surface average filmboilin g curves for satu rati on and 5, 10 and 14 K sub-cooling. The min imum film boiling heat flux at 14K subcooling was higher than at saturation, while( A T s a t ) m i n for saturati on boiling was higher than at 14K sub cooling . For lower subcoo ling, the values of qm~,and (AT~,0mm as well as o f the f ilm boil ing heat fluxwere much lower and increased with increased watersubcoolin g. The values of qmi, also increased withdecreased i ncli nati on on the surface, (ATs,t)mi,,however, were independe nt of local inclinati on (Figs.5 and 9). The film boiling heat flux also increasedwith decreased inclinatio ndue to the reduction in filmthickness.V a p o r f i l m t h i c k n e s sFigures 10(a)-(d) show the dependence of filmthickness, calculated from equation (15), on wallsuperheat at four different locations on the surface, atsaturation and 5, 10 and 14 K subcooling. The film

thickness all along the surface decreased withincreased water subcooling, but increased withincreased inclination due to vapor accumulation. Forexample, at ATsa, = 100 K, the vap or film thicknessfor 14 K subc ooling increased from ~ 90 #m at 0 = 0to ~ 160/~m at 0 = 8.26". At lower subcool ing, therate of heat removal by natural convection from thevapor film decreased, causing the film thickness toinitiall y increase. At 5 an d 10 K subcool ing, the filmswelled significantly at higher locat ions due to theaccumulation of vapor generated at lower positions.The film thickness increased with decreased wallsuperheat, reaching a maxim um when the rate of heatrelease from the surface became equal to tha t removedby natura l convection from the vap or-li quid interface.Beyond this point, film thickness decreased, as thewall superheat decreased, due to condensation. Figures10(a)- (d) show tha t at 0 = 8.26 ~and 5 K subcooling,the maxim um film thickness of ~ 280/~m occurred ata wall superheat of 75 K. At higher subcooling of 10K, this film thickness decreased to ~2 40 ~tm andoccurred at a higher wall superheat of ~90 K [Fig.10(d)]. At 14 K subcooling, no swelling of the vaporfilm occurred because of the relatively higher rate ofheat removal from the film by natural convection inthe water pool. Eventually, surface rewetting occurredwhen the film thickness reached a cr itical value, whichwas dependent on water subcooling and local incli-nation on the boiling surface. Because of the inter-mittent vapor release in saturation film boiling, theswelling of the va por film was negligible compared tothat which occurred at 5 and 10 K subcooling [Figs.10(a)-(d)].

Figures l l(a) -(g) show the vapor film thicknessprofiles, calculated from equation (15) for 5, 10 and14 K subcooling, at wall superheats of 130, 115, 100,85, 70, 60 and 50 K and at the min imu m film boiling(or surface rewetting ), respectively. For all wall super-heats an d water subcoolings, the vapor film thicknesswas lowest at the lowermost position on the surfaceand increased in the direction of vapor flow towardthe edge of the copper surface. At ATsa, = 130 K,the film thickness for all values of water subcoolinginvestigated was almost the same at the lowermostposition, but increased with decreased subcooling athigher i ncli nati on on the surface. As ATsa, decreasedto 70 K, the difference in film thickness due to watersubco oling increased. Furt her decrease in A T~a,causedthe values of the vapo r film thickness for 5, 10 and 14K subcooling to decrease and become closer.C r i t i c a l v a p o r f i l m t h i c k n e s s

As indicated in Figs. 10(a)-(d), in saturationboiling at the lowermost position on the surface(0 = 0), the critical film thickness prior t o rewettin g,6c, is ~ 50+5 /~m , a nd almost indep endent of watersubcooling. This film thickness, however, increasedwith increased inclination on the surface, but withdecreased water subcooling. For instance, at0 = 8.26 , 6c increased t o ~ 104, t40 and 175 pm a t

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Fi lm b o i l i n g f r o m a d o w n wa r d - f a c in g c u r v e d su r f a c e 2 8 5c , ~ ) ri

VDO

!

O .O 25

t

| 0.O 150 0 1 0 .2 8

0 . 0 2 5

0 . 0 2 0

0 .015

30 ( SO 90 120 166 0" 0" 1026 30 66 gO 120 150

0 . 0 2 0

0 . 0 1 5

1~ 0 . 0 1 0

0 . 0 0 52 5 3 0

0 . 0 2 5

0 . 0 2 0

0 ,015

0 .010

i I! ] ] Ia] Avwq s

O.OO56 0 g O 1 2 0 1 6 6 2 0 3 O 6 6 g 0W a l l S ~ t . A T u t ( 1< ) W l ll l ~ 4 N d l e a t . A T N t 0 < )

Fig . 9 . Local and surface average fi lm boi l ing cu rves.

0 . 0 3 0

0 .15==

i 0.10

0 . 0 6

0 2 5

a _ ,Rn. Ax_.ff.- O K IO k F B . A T , . ~ . 1 4 K I . . . . .

= [=0 TO #1 (e . ,0 )L8 0 7 5 1 0 0 1 2 5 1 5 0

0.20

0.15

0 .10

0 . 0 5

0 L-2 5~ i x o , s ( e - = ~ , )

6 6 7 5 1 00 1 2 8 1 8 0

0 . 2 0 ,

0.15 I

0 .0 5 . . . . .

0 .3

i

( ,~ ~ o . , ( , . , . , . )7 8 1 0 0

W tll ~ t . & T it (K )

0 .2

0.1

0 ~ ~ 02 5 8 0 1 3 5 1 5 0 2 5

(= ~ re , 0 (o . [8 0 7 5 1 0 0 1 2 5 1 6 6

w d ~ t . 6 T M t 0

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286 M.S. EL-GENK and A. G. GLEBOV0.300 2 50.2O0.15lo 0.100.05

0

0.300.250.200.150.10

O.05

( a ). .. .. ~ T , = t - K

. . . . . . . . . . . [ & T s u b " 5 K [i ~ " T s u b ' l K I&T = ub - 14 K I0 2.5 5.0 7.5 ~.0

0.300 . 2 5 & T ' t " 7 0 K !0 . 2 0 . . . . . . . . . ;

. . . . . . ~ J0.15 ~ . 90.10 -0.05 ,

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0 . 2 5 & T s a t

0.050 0 2.5 5.0 7.5 ~.0

~o

0.300.250 2 00.150.100.05

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THe" ~! S (0 )

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0.300.250.200.150.10

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o 2.5 5.0 7.5e (o )

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At Ml r i'm, m F i lm ~ , (h)~ T s u b - 5 K ( A T s m t - 3 5 K )g ~ Ts u b- lO K ( & T s l t - 4 1 K )AT sub- 14 K (ZkTsmt-42 K) ~ v

0 2.5 5.o 7.5 lo.oe (o)

Fig. I I. Angular distribution of vapor film thickness in saturation boiling.

For saturation and subcooled boiling, 6c increasedwith increased inclination on the surface. F or ex-ample, 6c for sat ura tion boi ling increased from ~ 85/ma at 0 = 0" to as mu ch as 180 pm at 0 = 8.26' .At 0 = 8.26', 6c for 14, 10 and 5 K subco oling was

104, 140 and 175 pm, respectively. Figure 12 alsoshows th at the difference between c5~ values at variou sincli natio ns on the surface decreased with increasedsubcooling. The present results confirm the criticalvapo r film thickness concep t [16, 19, 20] for rewettingin pool boiling from downward-facing surfaces. Fig-ure 12 shows th at the values of 6c for 0 < 4.94 atsatu rati on to 0 < 6.6 at 14 K sub cooling, lie betweenthe predictions of the wave theory of Chang [20]

and the hydrody namic instability theory of Berenson[18] for film boiling on a flat plate facing upward.At higher surface inclinations, the present values of6~ are higher than that predicted by the hydro-dynamic theory [19]. The lower the incl ination angle,however, the closer are the present values of thecritical film thickness to the predictions based onthe wave theory [20].

S U M M A R Y A N D C O N C LU S I O N SFilm boiling heat transfer from a downward -facing

curved surface in saturated and 5, 10 and 14 K sub-cooled water was investigated. The local and surface

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Fi l m b o i l in g f ro m a d o w n w a rd - fa c i n g c u rv e d su r fa ce 2 8 7

E

0 . 2 0

0.15

0.10

0 . 0 5

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AT 5 K i O TO #1 tO - 0=) [ !=ub- [ ] TC #2 (e - 1 .66"} A~. / v TC, ate -~g 'l l Ii " ~ T C # 4 ( e - 4 . 9 4 ~ }i / \ TC #15 {e . 6 6" )V \ I , , r c , s c e - a ~ l q[ " # 1 0 K 1LV B e r e n s o n ' s M o d e l t 1 8 ] ! "~

" . .. . ' ' " ! . .. .. . o . , . o o . ,...... ...... ., i , i , t , i , i ,

4 0 5 0 6 0 7 0 8 0 g 0W a ll S u p e r h e a t . L I T N t ( K }

Fig . 12 . Cri t ica l vapo r f i lm th ickness for surface rewet ting .

a v e r a g e N u s s e l t n u m b e r s w e r e c o r r e l a t e d in t e r m s o ft h e R a y l e i g h a n d J a c o b n u m b e r s , f o r b o t h s a t u r a t i o na n d s u b c o o l i n g c o n d i t i o n s ; t h e c o r r e l a t i o n s w e r e ing o o d a g r e e m e n t w i t h t h e d a t a t o w i t h i n _ 1 0 % a n d_ 5 % , r e s p e c t i v e l y .

I n s a t u r a t i o n f i l m b o i l i n g , t h e r e w e t t i n g t i m e ( ~ 2 7 3s ) w a s m u c h s h o r t e r t h a n i n s u b c o o l e d b o i l i n g ( 4 15 s -6 7 8 s ). T h e d e c r e a s e i n r e w e t t i n g t i m e w i t h i n c r e a s e dw a t e r s u b c o o l i n g , r e s u l t e d i n a s m a l l e r c r i t i c a l f i l mt h i c k n e s s a n d , h e n c e , h i g h e r m i n i m u m f i lm b o i l i n gh e a t f l ux a n d c o r r e s p o n d i n g w a l l s u p e r h e a t . R e s u l t sd e m o n s t r a t e d a d i r e c t c o r r e l a t i o n b e t w e e n t h e v a l u e so f b o t h q m in a n d ( A T s a t ) m i n a n d r e w e t t i n g t im e . L o w e rqm m a n d ( A T sa t)m i w e r e a l w a y s a s s o c i a t e d w i t h l o n g e rr e w e t t i n g t i m e a n d l a r g e r 6c . T h e r e w e t t i n g t i m e a n d 6 ci n c r e a s e d a s e i t h e r t h e l o c a l i n c l i n a t i o n o n t h e b o i l i n gs u r f a c e , 0 , i n c r e a s e d o r w a t e r s u b c o o l i n g d e c r e a s e d .T h e v a l u e s o f q m in a n d ( A T s a t ) m i n b o t h i n c r e a s e d w i t hi n c r e a s e d s u b c o o l i n g . T h e f i lm b o i l i n g h e a t f l u x al s oi n c r e a s e d w i t h d e c r e a s e d i n c l i n a t i o n , w h i l e ( A T s a t ) m i nw a s i n d e p e n d e n t o f s u r f a c e in c l i n a t io n .

T h e s h o r t e s t f i lm b o i l i n g d u r a t i o n i n s a t u r a t i o nb o i l i n g w a s c a u s e d b y e a r l y c o l l a p s e o f v a p o r f i l m a n dr e w e t t i n g o f t h e s u r f a c e, t r i g g e r e d b y t h e o s c i l l a ti o n s( o r h y d r o d y n a m i c i n s t ab i l it y ) i n d u c e d b y v a p o rr e l e a se f r o m t h e e d g e o f t h e f i l m . I n s u b c o o l e d b o i l in g ,h o w e v e r , t h e c o l l a p s e o f t h e v a p o r f i l m a n d r e w e t t i n go f t h e s u r f a c e w e r e t h e r m a l l y d r i v e n . S u r f a c e r e w e t t i n go c c u r r e d f i r s t a t t h e l o w e r m o s t p o s i t i o n , 0 = 0 , t h e ns e q u e n t i a l ly a t h i g h e r i n c l i n a t i o n p o s i t i o n s . F o r s a t u -r a t i o n b o i l i n g , 6 c w a s 8 5 # m a t 0 = 0 , i n c r e a s i n g t o1 8 0 p m a t 0 = 8 . 2 6 . F o r s u b c o o l e d b o i l i n g a t 0 = 0 ,t h e c r it i c a l f i lm t h i c k n e s s ( ~ 5 0 p m ) w a s s m a l l e r a n dw e a k l y d e p e n d e n t o n s u b c o o l i n g ; i t in c r e a s e d ,h o w e v e r , w i t h i n c r e a s e d i n c l i n a t i o n a n d d e c r e a s e ds u b c o o l i n g , r e a c h i n g ~ 1 7 5 / ~ m a t 0 = 8 . 2 6 a n d 5 Ks u b c o o l i n g .

T h e c r i t i c a l f i l m t h i c k n e s s f o r 0 < 4 . 9 4 a t s a t u -r a t i o n t o 0 < 6 . 6 a t 1 4 K s u b c o o l i n g , f e l l b e t w e e n

t h e p r e d ic t i o n s o f th e w a v e a n d t h e h y d r o d y n a m i ci n s t a b i l i t y t h e o r i e s f o r f i l m b o i l i n g o n a f l a t p l a t e f a c -i n g u p w a r d . T h e c r i t i c a l f i l m t h i c k n e s s a t h i g h e r s u r -f a c e i n c l i n a t i o n s w e r e l a r g e r t h a n p r e d i c t e d b y t h eh y d r o d y n a m i c t h e o r y . A t l o w e r in c l i n a t io n , h o w e v e r ,t h e c r i t i c a l f i l m th i c k n e s s w e r e c l o s e r t o t h e p r e d i c t i o n so f t h e w a v e t h e o r y .A c k n o w l e d g e m e n t s - - R e s e a r c h sponsored by the Inst i tu te forSp a c e a n d N u c l e a r Po w e r S t ud ie s , U n i v e rs i t y o f N e wM e x i c o , A l b u q u e rq u e , N M .

R E F E R E N C E S1. S. Ish igai , K. Inoue, Z. Kiwa ki and T. Ina i , Boi l ing heatt r a n s fe r f ro m a f i a t su r fac e fa c i n g d o w n w a rd , Proc . In t .H e a t T r a n s . C o n f , Paper No. 26 (1961).2 . D. S. Jung , J . E. S. Venart an d A. C. M . Sousa , Effec tsof enhanced surfaces and surface orien ta t ion on nuclea teand f i lm boi l ing heat t ransfer in R-I 1 , I n t . J. H e a t M a s sT r a n s f e r 30(12), 2627 2639 (1987).3 . N. Seki , S. Fukushako and K. Torikosh i , Experimenta ls tudy on the effec t o f o rien ta t ion of heat ing c i rcu lar p la teon f i lm boi l ing heat t ransfer fo r f luorocarbon refr igeran tR-11, J . H e a t T r a n s f e r 100, 624-628 (1978).4 . Z . G u o a n d M . S . E l -G e n k , A n e x p e r i me n t a l s t u d y o fsa t u ra t e d p o o l b o i l i n g f ro m d o w n w a rd fa c i n g a n dinclined surfaces, I n t . J. H e a t M a s s T r a n s f e r 35(9), 2109-2117 (1992).5 . Z. Guo and M . S. EI-Genk, Effects o f l iqu id subcool ingo n t h e q u e n c h i n g o f i n c l in e d a n d d o w n w a rd - fa c i n g f i a tsurfaces in water, A . I . C h . E . S y m p . S e r . 288(88), 241-248 (1992).6 . M . S . E l -G e n k a n d Z . G u o , T ra n s i e n t b o i l i n g f ro mincl ined and downward-fac ing surfaces in a sa tura tedpool , I n t . J . R e f r i g . 16(6), 414-422 (1993).7 . M. S. E1-Genk, A. G. Gle bov and Z. Guo, Po ol bo i l ingf ro m d o w n w a rd - fa c i n g c u rv e d su r fa c e i n sa t u ra t e dwater , P r o c . l O t h I n t . H e a t T r a n s . C o n f . , Brighton , Vol .5, pp. 45 50 (1994).8 . M. S. E1-Genk and A. G. Glebov , Transien t pool bo i l ingfrom downward-fac ing curved surfaces , I n t . J . H e a tM a s s T r a n s f e r 38, 2209-2224 (19951.9 . J . E . O ' B r i e n a n d G . L . H a w k e s , Th e rm a l a n a ly s i s o f areactor lower head wi th core re locat ion and ex ternal

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2 88 M . S . E L - G E N K a n d A . G . G L E B O Vb o i l i n g h e a t t r a n s f e r , A I C h E S y m p . S e r . 283(87) , 159-168 (1991).1 0. H . Pa r k a n d V . K . Dh i r , S t e a d y - s t a t e t h e r m a l a n a ly s i s o fe x t e r n a l c o o l in g o f a PW R v e sse l l o we r h e a d , A . L C h . E .S y mp . S e r . 283(87) , 1 -7 (1991) .1 1. R . E . He n r y , J . P . B u r e lb a c h , R . J . Ha m m e r s l e y , C . E .He n r y a n d G . T . K lo p p , C o o l in g o f c o r e d e b r i s w i th inth e r e a c to r v e sse l l o we r h e a d , J. Nucl. Technol. 101 ,385- -399 (1993).1 2. A . S a v i t z k y a n d M . J . E . Go la y , Sm o o th in g a n d d i f f e r-e n t i a t i o n o f d a t a b y s im p l i f i ed l e a s t sq u a r e p r o c e d u r e s ,Anal . Chem. 36 , 162 7-1639 (1964) .1 3 . M. K l in e a n d F . A . M c C l in to c k , D e sc r ib in g u n c e r -t a in t i e s i n s i n g l e - sa m p le e x p e r im e n t s , M e c h . E n y n g ( 3 - 8Ja n u a r y 1 9 5 3 ) .1 4. M. S . E 1 - Ge n k a n d A . G . G le b o v , Nu m e r i c a l so lu t i o n o ft r a n s i e n t h e a t c o n d u c t io n i n a c y l i n d r i c a l se c t i o n d u r in g

q u e n c h in g , J . Numer. Heat Transfer , Part-B: Appl i -cations ( i n p r e ss ) .15. V. P. Carey, Liq u id - V a p o r P h a se - C h a n g e P h e n o me n a ,C h a p . 7 , p p . 2 7 5 - 2 7 8 He m isp h e r e W a sh in g to n , DC(1992).1 6 . A . Ab d u l - R a z z a k , M. Sh o u k r i a n d A . M. C . C h a n ,R e w e t t i n g o f h o t h o r i z o n t a l t u b e s, N u c l . E n g n g De s i y n138, 375-388 (1992).17 . J . A. Brom ley , Hea t t ransfe r in s tab le f i lm bo i l ing , Chem.E n g n # P ro g . 46(5) , 221-227 (1950) .1 8 . W . H . Mc Ad a m s , Heat Transmission , Chap. 7 , p . 180 .Mc Gr a w- Hi l l , Ne w Yo r k ( 1 9 5 4 ) .1 9. P . J . B e r e n so n , F i lm - b o i l i n g h e a t t r a n s f e r f r o m ah o r i z o n t a l su r f a c e , J . He a t Tra n s f e r 83 , 351-358(1961).2 0 . Y . P . C h a n g , W a v e t h e o r y o f h e a t t r a n s f e r in f i lm b o i li n g ,J . He a t Tra n s f e r 1-12 (1959).