Film and Trasition Boiling Correlations for Quenching of Hot Surface With Water Sprays

8/3/2019 Film and Trasition Boiling Correlations for Quenching of Hot Surface With Water Sprays

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J . H e a t T r e a t i n g ( 1 99 2 ) 9 : 9 1 - 1 0 3 9 1 9 9 2 S p r i n g e r - V e r l a g N e w Y o r k I n c .

F i l m a n d T r a n s i t i o n B o i l i n g C o r r e l a t i o n s

f o r Q u e n c h i n g o f H o t S u r f a c es w i th

W a t e r S p r a y s

W . P . K l in z i n g , J . C . R o z z i , a n d I. M u d a w a r

Abstract. U s i n g a m i n i a t u r e g o l d p l a t e d c o p p e r d i s k a s t a r g e t , q u e n c h i n g e x p e r -

i m e n t s w e r e p e r f o r m e d w i t h w a t e r s p r a y s t o c o r r e l a t e h e a t f l u x q " t o s u r f a c e - t o -

f l ui d t e m p e r a t u r e d i f f e r e n c e A T , a n d t h e l o c a l v a l u e s f o r th e s p r a y h y d r o d y n a m i c

p a r a m e t e r s o f v o l u m e t r i c f lu x Q ", m e a n d r o p v e l o c i t y Um a n d S a u t e r m e a n d r o p

d i a m e t e r d32 o v e r a w i d e r a n g e o f o p e r a t i n g c o n d i t i o n s ( Q " = 0 . 5 8 • 1 0 - 3 - 9 . 9 6

• 1 0 - 3 m 3 s e c - a / m 2 , U m = 1 0 . 1 - 2 9 . 9 m / s e c , d32 = 0 . 1 3 7 - 1 . 3 5 0 m m ) , a n d s u r f a c e

t e m p e r a t u r e s u p t o 5 2 0 ~C . D r o p d i a m e t e r w a s f o u n d to h a v e a w e a k e f f e c t o n h e a t

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

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

u m e t r i c f l u x , l o w f lu x s p r a y s f o r Q " < 3 . 5 • 1 0 - 3 m 3 s e c - 1 / m 2 , a n d h i g h f l u x

s p r a y s f o r Q " > 3 . 5 • 1 0 - 3 m 3 s e c - 1 / m z . W h i l e Q " h a d a s i g n if i c a n t i n f l u e n c e o n

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

s p r a y s. A s p r a y q u e n c h i n g t e s t b e d w a s a l so c o n s t r u c t e d t o s i m u l a t e , u n d e r c o n -

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

m e n t . T h e t e s t b e d w a s u se d t o g e n e r a t e t e m p e r a t u r e - t i m e r e c o rd s f o r a r e c ta n g u l a r

a l u m i n u m p l a t e d u ri n g s p r a y q u e n c h i n g . U s i n g t h e s o f t w a r e p a c k a g e A N S Y S , t h e

m e a s u r e d t e m p e r a t u r e r e s p o n s e w a s s u c c e s sf u ll y s i m u l a t e d b y u t il iz i ng t h e n e w l y

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

s u r f a c e a f t e r a c c o u n t i n g f o r sp a t ia l v a r i a t io n s i n t h e h y d r o d y n a m i c p a r a m e t e r s

w i t h in t h e s p r a y f i e l d. T h e e f f e c t i v e n e s s o f t hi s n u m e r i c a l t e c h n i q u e f o r t h e t e s t e d

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

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

t io n s o f t h e h y d r o d y n a m i c p a r a m e t e r s a r e w e ll m a p p e d o r p r e d e t e r m i n e d .

No men c l a tu re

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C = e m p i r i c a l c o n s t a n t

cp = s p e c i f i c h e a t , J / k g . K

d32 = S a u t e r m e a n d i a m e t e r ( S M D ) , m

h = c o n v e c t i o n c o e f f i c i e n t, W / m e . K

ht g = l a t e n t h e a t o f v a p o r i z a t i o n , J /k g

k = t h e r m a l c o n d u c t i v i t y , W / m . K

n l , n 2 , n 3 , n 4 = e m p i r i c a l e x p o n e n t s

T h e a u t h o r s a r e w i t h t h e B o i l in g a n d T w o - P h a s e F l o w L a b -

o r a t o r y , S c h o o l o f M e c h a n i c a l E n g i n e e r i n g , P u r d u e U n i v e r s i t y ,

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h e a t f l u x, W / m 2

c r i ti c a l h e a t f l u x , W / m e

v o l u m e t r i c f l ux , m 3 s e c - l / m 2

R e y n o l d s n u m b e r b a s e d o n

v o l u m e t r i c f lu x a n d S a u t e r m e a n

d i a m e t e r , Q" d32/v f

t i m e , s e c

t e m p e r a t u r e , ~

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

c r i t i c a l h e a t f l u x , ~

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

d e p a r t u r e f r o m f i l m b o il i ng , ~



W . P . K l in z i n g e t a l . 9 S p r a y Q u e n c h i n g F a c t o r s

T M I N = t e m p e r a t u r e c o r r e s p o n d i n g t o

m i n i m u m h e a t f l u x , ~

U m = m e a n d r o p v e l o c i ty , m / s e c

w = cop pe r d isk t h i ckness , m

Greek SymbolsA T =

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sur face t ens ion , N/m;

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List o f Subscriptsc = cop pe r d i sk

CH F = c r i ti c a l hea t f l ux

D F B = d e p a r t u r e f r o m f i lm b o i li n g

f = l iquid

g = v a p o r

M I N = m i n i m u m h e a t f lu x

s = su r face

sa t = sa tu ra t i on

s u b = s u b c o o l e d

= a m b i e n t

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

Process ing o f al l oys by ex t rus ion , fo rg ing , o r c a s t i ng

wi th any degree o f con t ro l ove r t he me ta l lu rg i ca l and

mechan ica l p rope r t i e s dem ands ca re fu l con t ro l o f hea t

r e m o v a l f r o m t h e p r o d u c t . T h e r a t e o f h e a t r e m o v a l

dur ing t he coo l ing t ha t fo l l ows the fo rmin g p roces s

has a s ign i f ican t i n f l uence on ha rdne ss , s t r eng th , and

the occu r rence o f r e s idua l s t r e sse s , o f t en r e su l t i ng i n

st ress concent ra t ion o r cracking. In man y of the meta l

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

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

r e f e r r e d t o a s p r e s s q u e n c h i n g . I t i s c o m m o n p r a c t i c e

fo r t he ope ra to r t o conf igure t he sp rays ( i . e . , se t t he

n o z z le p o s i t io n a n d f l o w r a te ) b a s e d u p o n p r i o r e x -

pe r i ence , and l a t e r pe r tu rb t he sp rays by tr i a l and

error unt i l a configura t ion i s found which most c lose lya p p r o a c h e s m e e t i n g t h e d e s i r e d p r o d u c t s p e c i f i c a -

t i ons . Af t e r t he p re ss qu ench ing , a cos t l y pos t t r ea t -

men t , cons i s t i ng o f add i t i ona l hea t t r ea t i ng and co ld

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

t i ons . Th i s pos t t r ea tm en t i s o f t en t he r e su l t o f po or

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

i n a l a rge cos t pena l ty fo r t he me ta l fo rming ope r -

a t i o n a n d c o n s u m e r .

T h e o b j e c t i v e o f th e s p r a y q u e n c h i n g r e s e a rc h

p r o g r a m a t t h e P u r d u e U n i v e r s i t y B o i l i n g a n d T w o -

P h a s e F l o w L a b o r a t o r y s i n c e 1 9 8 5 h a s b e e n t o p r o -

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

conf igura t i on o f sp rays to v i r t ua ll y e l im ina t e t he nee d

f o r p o s t t r e a t m e n t . T h i s h a s b e e n p r o p o s e d b y g e n -

e ra t i ng ex t ens ive hea t t r ans fe r and ma te r i a l s da t a

base s , and i n t eg ra t i ng t he se da t a ba se s us ing a ge -n e r ic C A D m e t h o d o l o g y w h i c h c a n e a s il y b e a p p l i e d

to d i f f e ren t t ypes o f sp ray nozz l e s and a mul t i t ude

of ma te r i a l s . In implemen t ing t h i s sem iexpe r t t e ch -

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

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

p r o p e r t i e s , a n d t h e C A D s y s t e m w o u l d th e n c o n s u l t

a n d i n t e g r a t e i ts d a t a b a s e s an d o u t p u t a n u m b e r o f

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

s t r i ngen t p roduc t spec i f i ca t i ons may necess i t a t e au -

toma t ing t he pos i t i on ing o f t he nozz l e s and t he t h ro t -

t l i ng o f sp ray f l ow ra t e us ing sensor s and moto r i zed

t rans l a t i on p l a t fo rms , bo th o f wh ich can a l so be d i -

r e c tl y i n t e rf a c e d w i t h , a n d c o n t r o l l e d b y t h e C A D

s y s t e m .

A k e y g u i d e t o u n d e r s t a n d i n g t h e c o o l i n g p e r -

f o r m a n c e o f s p r a y s is th e r e l a t i o n s h ip b e t w e e n h e a t

f lu x f r o m t h e q u e n c h e d s u r f a c e a n d s u r f a c e t e m p e r -

a t u r e - - t h e b o i li n g c u r v e . A t a n y g iv e n su r f a ce t e m -

pe ra tu re , a l a rge r hea t f l ux amoun t s t o a f a s t e r r a t e

o f c o o l in g f o r t h e s u r f a c e . T h e r e l a ti o n s h i p b e t w e e n

h e a t f l u x a n d s u r f a ce t e m p e r a t u r e u n d e r g o e s d r a s ti c

c h a n g e s d u r i n g t h e q u e n c h , t r i g g e re d b y c h a n g e s in

t h e m e c h a n i s m o f w a t e r c o n t a c t w i t h t h e s u r f ac e b e -

twee n the va r iou s r eg ions o f t he bo i l i ng cu rve . F igure

1 show s a bo i li ng cu rve a ssoc i a t ed wi th quench ing o fa me ta l li c p rodu c t i n a s t agnan t ba th o f li qu id . For

m o s t q u e n c h i n g o p e r a t i o n s t h e p r o d u c t s u r f a c e i s

coo l ed f rom an i n i t i a l h igh t empera tu re usua l l y we l l

i n e x c e s s o f t h e p o i n t o f d e p a r t u r e f r o m f i l m b o il in g

(DFB; po in t E i n F ig . 1 ) . Dur ing t he i n i t i a l moment s

o f t h e q u e n c h t h e s u r f a c e e x p e r i e n c e s w h a t is k n o w n

as f i lm bo i l i ng , whe re a con t in uous v apo r l aye r (b lan -

k e t ) f o r m s o n t h e s u r f a c e p r e v e n t i n g t h e w a t e r f ro m

making d i r ec t con t ac t wi th t he su r face . A s l i gh t co l -

l a p s e i n t h e v a p o r b l a n k e t a t p o i n t E c a u s e s s o m e

e n h a n c e m e n t i n h e a t f l u x . T h i s w e a k e n h a n c e m e n t

p e r s is t s d o w n t o t h e m i n i m u m h e a t f l u x p o i n t ( M I N ;

po in t D in F ig . 1 ) , whe re co l l apse o f t he vapor l aye rp r o m o t e s a p p r e c i a b l e w e t t in g o f t h e s u r f ac e , a t r a n -

s i t i on marked by a s i gn i f i can t i nc rea se i n t he hea t

f l ux caus ing a r ap id dec rea se i n su r face t empe ra tu re .

The reg ion be tween po in t s D and C i s c a l l ed t r an -

s i t ion bo i l i ng , whe re pa r t s o f t he su r face unde rg o

wet t ing (and vigorous boi ling) wi th l iquid, whi le others

remain in f i lm boi l ing. Point C is the cr i t ica l heat

f lu x p o i n t b e l o w w h i c h ( d o w n t o p o i n t A ) t h e e n t i r e

9 2 ~ J . H e a t T r e a t i n g , V o l . 9 , N o . 2 , 1 9 9 2



W . P . K l i n z i n g e t a l . 9 Sp ray Quenching Factors

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O O_ ~ Vapor Blanket,

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Isolated _ J L _ Jets andBubbles -- Columns

C = , .e a t F l u x . <. ,

Departure ro

1 " I # \ I F i l m B o = i l in g ,

W a l l S u p e r h e a t l o g ATse~

F i g . 1 . B o i l i n g c u r v e f o r a h o t s u r f a c e i n a s t a g n a n t p o o l

of liquid at its saturation temperature.

su r face becomes ava i l ab l e fo r nuc l ea t e bo i l i ng . Be -

low po in t A bo i l i ng comple t e ly subs ides and d i r ec t

hea t t r ans fe r t o t he l i qu id fo l l ows wi tho u t evap ora -

t ion.S p r a y q u e n c h i n g i n v o lv e s t ra n s i ti o n b e t w e e n t h e

va r ious bo i l i ng r eg ions i nd i ca t ed i n F igure 1 , occur -r i ng wi th in d rops a s t hey impac t t he su r face i nd i -

v i d u a ll y o r c o a l e s c e w i t h o t h e r d r o p s o r b o t h . C o m -

p l i ca t i ons i ncur red i n de t e rmin ing t he exac t hea t

f l u x - s u r f a c e t e m p e r a t u r e r e l a ti o n s h i p i n c lu d e e f f e c ts

s u c h a s t h o s e o f s u r f a c e r o u g h n e s s a n d t h e h y d r o -

d y n a m i c s t r u ct u r e o f t h e s p r a y . C o m b i n e d , t h e s e e f -

f e c t s c a n c a u s e t h e t e m p e r a t u r e c o r r e s p o n d i n g t o

min imum hea t f l ux t o va ry f rom 300 to a s h igh a s

900~ [1] . In a lmos t a ll o f t he l i te ra tu re r ev i e we d by

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

n e c e s s a r y t o c h a r a c t e r i z e s p r a y h e a t t r a n s f e r w e r e

vo lum e t r i c fl ux ( i .e . , w a t e r f l ow ra te pe r un i t su r face

a r e a ) [ 2 - 7 ] , d r o p v e l o c i t y [ 3 , 5 - 8 ] a n d d r o p d i a m e t e r[ 6 - 8 ] .

S o m e i n v e s t i g a t o r s [ 5 - 7 ] , b e c a u s e o f d i f f e r e n c e s

i n th e r e l a t iv e i m p o r t a n c e o f p a r a m e t e r s g o v e r n i n g

spray hea t t r an s fe r i n f i lm bo il i ng , found i t necessa ry

to c l ass i fy wa te r sp rays i n to two reg im es , t ha t o f

d i l u t e ( l ow vo lume t r i c f l ux ) sp rays and dense (h igh

vo lume t r i c f l ux ) sp rays . Whi l e vo lume t r i c f l ux was

f o u n d t o b e t h e t r e n c h a n t p a r a m e t e r f o r b o t h r e -

g i m e s , o t h e r p a r a m e t e r s s u c h a s d r o p d i a m e t e r , d r o p

v e l o c it y , a n d W e b e r n u m b e r w e r e f o u n d t o in f l u e n ce

hea t t r ans fe r i n t he ca se o f d i l u t e sp rays .

D u r i n g t h e q u e n c h i n g p r o c e s s , a n a b r u p t i n c r e a s e

in t he hea t f l ux occurs fo l l owing the depa r tu re f rom

f i lm to t r ans i t i on bo i l i ng . The t empera tu re a t wh ich

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

a s t h e L e i d e n f r o s t t e m p e r a t u r e ( t h e r e i s s o m e c o n -f u s i o n i n t h e l i t e r a t u r e o n w h e t h e r t h e L e i d e n f r o s t

t e m p e r a t u r e c o i n c i d e s w i t h p o i n t s E o r D i n F i g u r e

1 ). D u e t o t h e s p a r s e n a t u r e o f w o r k r e l a te d t o t h e

L e i d e n f r o s t t e m p e r a t u r e f o r w a t e r s p r a y s , i t i s d i f -

f i cu l t t o d raw any de f in i t i ve conc lus ions conce rn ing

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

p h e n o m e n o n . H o w e v e r , f r o m t h e l im i t e d i n f o rm a -

t i on ava i l ab l e , i t appea r s t ha t vo lume t r i c f l ux is aga in

the mos t i n f l uen t i a l pa rame te r a f fec t i ng t he Le iden-

f r o s t t e m p e r a t u r e [ 1 ,9 ] . A l s o , e x p e r i m e n t s p e r -

fo rm ed wi th s i ng l e d rop l e t s seem to be o f li t tl e o r

no va lue i n cha rac t e r i z ing t he Le idenf ros t t empera -

tu re fo r sp rays [1 ] .

Whi l e hea t t r ans fe r co r re l a t i ons fo r t he f i lm bo i l -

i n g r e g i o n a n d t h e m i n i m u m h e a t f l u x p o i n t a r e o f

g r e a t i m p o r t a n c e i n m o s t m e t a l f o r m i n g p r o c e s s e s ,

quenching o f a luminum par ts can be sensi tive to lowe r

t em pera tu re r eg ions o f t he bo i l i ng cu rve a s we l l ( i. e . ,

t r ans i t i on and nuc l ea t e bo i l i ng ) . Recen t ly , Mudawar

and Va len t ine [10] deve loped hea t t r ans fe r co r re l a -

t i ons fo r t he t r ans i t i on , nuc l ea t e , and s ing l e -phase

reg ions us ing an e l ec t r i c a l l y hea t ed ca lo r ime te r ba r

e x p o s e d a t o n e e n d t o t h e s p r a y . T h e i r c o r r e l a t i o n s

w e r e p r e s e n t e d a s fu n c t i o n s o f th e l o ca l h y d r o d y -

n a m i c p a r a m e t e r s o f t h e s p r a y ( v o l u m e t r ic f lu x , d r o p

d i a m e t e r a n d d r o p v e l o c i t y ) . U n f o r t u n a t e l y , t e m -

p e r a t u r e l im i t a ti o n s i m p o s e d b y t h e i r c a l o r i m e t e r b a r

des ign p rec luded t e s t i ng i n t he f i lm bo i l i ng r eg ion

and made i t d i f f i cu l t t o ob t a in measuremen t i n t he

t ransi tion boi l ing region, ex cept for a few d i lute sprays.

De i t e r s and Mudawar [11] i nves t i ga t ed t he spa t i a l

d i s t ri b u t io n s o f t h e s p r a y h y d r o d y n a m i c p a r a m e t e r s

and t he e f fec t o f t he se d i s t r i bu t i ons on coo l ing r a t e .

U s i n g m e a s u r e d a s w e ll a s m a t h e m a t i c a ll y f i tt e d h y -

d rodynamic d i s t r i bu t i ons , t hey demons t ra t ed t ha t t he

c o r r e l at i o n s d e v e l o p e d b y M u d a w a r a n d V a l e n t in e

we re spa t i a ll y i ndep end en t and app l i cab l e to a ll t ypes

o f s p r a y s ( e . g . , f u ll c o n e , h o l l o w c o n e , f l at ) e m p l o y e din ma te r i a l s p rocess ing .

Th i s pape r p re sen t s new co r re l a t i ons fo r f ilm bo il -

i ng , po in t o f depa r tu re f rom f i lm bo i l i ng , po in t o f

min imum hea t f l ux and t r ans i t i on bo i l i ng , p rov id ing

k n o w l e d g e w h i c h c o m p l i m e n t s t h e s t u d y b y M u d a -

war and Va len t ine i n cha rac t e r i z ing t he va r ious r e -

g ions o f t he b o i l ing cu rve fo r wa te r sp rays . Al so p re -

sen t ed i s t he de sc r ip t i on o f a sp ray quench ing t e s t

J . H ea t T r ea t in g , V o l . 9 , N o . 2 , 1 9 92 9 9 3



W . P . K l i n z i n g e t a l . 9 S p r a y Q u e n c h i n g F a c t o r s

bed which was constructed for simulating, under con-

trolled labora tory conditions, spray quenching of al-

loys in an industrial environment. Validity of the

correlations developed for each regime is examined

by comparing numerical predictions with ANSYS to

the temperature response of an aluminum plate

measured during quenching in the test bed.

E x p e r i m e n t a l M e t h o d s

In order to develop and then assess the validity of

the spray quenching correlations, two experimental

facilities were utilized. First an extensive data base

was collected using a single spray quench facility, the

details of which can be found elsewhere [10]. From

this data base the correlations were developed. These

correlations were then examined for the case of a

series 1100-0 aluminum plate using the newly con-

structed spray quenching test bed. M easurements ob-

tained in the test bed served as test cases for nu-merical modeling using the software package ANSYS.

The description of the two facilities follows.

Single Spray Quench Chamber

The film and trans ition boiling correlations were de-

veloped from quench data measured at the geometric

Fig. 2. Cross-sectional view of spray chamber in the singlespray facility.

Flame~

H e a t i n g Dish

HollowCylindrical

U ~ "~J Enclosure

IGold - P l a t e dC o p p e r D i s k

T h e r m o c o u p l eL e a d ~

I ~ avaRock n s u l a t i o n

,

I

I Ii I

I ! II d , i ~ g a r a c k e t

~ f " " " " T h e r m o c o u p l e e a d

Fig. 3. Schematic of copper disk assembly.

center of the spray inside the spray chamber illus-

trated in Figure 2. This is the same chamber utilized

by Mudawar and Valentine in their earlier spray work.

Embedde d in an insulating casing at the spray center

was the quent:h target, a 7.94 mm diameter oxygen-

free copper disk with a thickness of 3.56 mm. Tem-perature was measured by a Chromel-Alumel ther-

mocouple m ade from 0.127 mm wire, which was spot

welded to the disk underside. The disk was gold plated

to enhance resistance to oxidation at the high tem-

peratures associated with film boiling. Previous stud-

ies have shown traces of oxidation on copper during

prolonged quenching even at temperatures within

the t ransition boiling region [10].

The gold plat ed copper disk was designed to main-

tain a ratio of thermal resistance due to conduction

within the disk to the resistance due to convection

at the quench surface-- the Biot number (Bi)--wel l

below 0.1. This allowed the hea t transfer coefficientto be determined experimentally by solving the in-

verse heat diffusion equation assuming lumped ca-

pacitance in the disk.

As shown in Figure 3, the copper disk was pre-

heated to an initial temperature of approximately

530~ using an oxyacetylene torch. The flame was

directed against a heat shield which prevented the

gold plate on the disk surface from melting. The

94 ~ J. H ea t T rea t i ng , Vol. 9, No. 2, 1992



W . P . K l i n z i n g e t a l . ~ S p r a y Q u e n c h i n g F a c t o r s

pump was then engaged and the spray, which was

prevented from contacting the target by a diversion

device, was allowed to reach hydrodynamic equilib-

rium (purging of air from the water supply line caused

occasional pulsation of flow during start-up). The

torch and the diversion device were then quickly re-

moved permitting commencement of the quench.

Temperature was recorded every 20 msec during the

quench and wri tten to a data file for later processing.

Spray Quenching Test Bed

The test bed consisted of a preheating furnace , trans-

lation platform for the testpiece, spray chamber, water

reservoir, and external plumbing as shown in Figure

4. These componen ts (excluding the plumbing) were

supported by a carbon steel frame which measured

1.35 • 1.35 • 2.69 m high. Including the furnace ,

the overall height of the system measured 3.91 m.

The entire frame rested on a single welded platform

to the bottom of which lifter pads were welded to

ensure an even distribution of the system weight.

The testpiece was heated to a uniform tempera-

ture in a vertically orien ted tube fu rnace having three

independently controlled heating zones which en-

sured uniform heating over 70 cm of the furnace

length. A Maulite process tube was installed coaxi-

ally inside the furnace to shield the testpiece against

contact with the furnace heating elements as shown

in Figure 5. To avoid exerting any load on the fragile

refractory brick inside the furnace, the process tube

was supported by three posts which were affixed to

a plate bolted to the sturdy steel frame external to

~ F u r . , ~

Steam/Hood

SPray/Chamber

Quench/Tank

Fig. 4. Cutaway view of spray quenching test bed.

j Process ub e

. J

ProcessTubeSuppo~

Fixed Bracket

~ Workplece

I S 'BottomPlug

Fig. 5. Schematic of testpiece and process tube support

assembly.

the furnace. A three-zone programmable controller

was used to monitor and manipulate furnace heat up

rates.

The testpiece was transported from the furnace to

the spray chamber on a translation platform with the

aid of a counterweight. The translation platform rode

on two stainless steel shafts which were held in po-

sition by shaft mounts placed at the bottom of the

quench tank and on the process tube support plate

located directly beneath the furnace. These mounts

also allowed for thermal expansion of the shafts to

prevent buckling during workpiece descent. Mounts

on one of the shafts were equipped with aluminum

sliding mechanisms which made adjustable the dis-tance between the shafts and minimized shaft skew.

Water stored in the tank at the bottom of the test

bed passed through a strainer before entering a cen-

trifugal pump rated to deliver 25.2 • 10 -3 m3/sec

(40 gal/min) at 689 kPa (100 psi) and temperatures

up to 82~ Due to the large capacity of the pump,

most of the flow was bypassed to the tank via a

regulating globe valve. The spray water continued

J . H e a t T r e a t i n g , Vo l . 9 , No . 2 , 1992 95



W . P . K l in z i n g e t a l . 9 S p r a y Q u e n c h i n g F a c t o r s

ThermocouplePlane \ o.9~

%SprayedSurface

,,

,1~3

7.94 [ ? 0 . ~ ../.15.1

- 1 1 1

; I

,I128.6

~ ~ . ~ 1 Note:All Dimensions re n M i l l i m e t e r s

7.94ThermocouplePlane Fig. 6. Construction of the aluminum testpiece.

through a 5 p,m filter followed by a heat exchanger

before being directed into eight supply lines, each

fitted with a globe valve followed by a pressure gage

and a heavy duty rubber hose leading to the spray

nozzle. Following impingement onto the testpiece,

liquid supplied through each spray nozzle was col-

lected in the reservoir for recirculation. The frame

of the spray chamb er itself was fitted within the large

frame supporting the test bed hardware. One alu-

minum plate was located along the center of each of

the four sides of the spray chamber providing support

for the nozzle plumbing, with all the remaining sur-

faces of the spray chamber covered with transparent

polycarbonate plastic. Nozzle mounts connected to

the aluminum plates featured flexibility in the posi-

tioning of the nozzles at any desired location relativeto the testpiece.

Figure 6 shows details of the instrumented work-

piece used to assess the validity of the newly devel-

oped correlations for large surfaces. It consisted of

a series 1100-0, 2.52 cm thick aluminum plate having

a quench area of 24.13 • 6.03 cm which was blasted

with silica particles to ensure uniform surface finish

having a characteristic cavity size of 10 ~m. The plate

was instrumented with 11 thermocouples positioned

in a plane 0.508 mm away from the quench surface.

The thermocouples were cons tructed from 0.127 mm

Chromel-Alumel (type K) wire set in a 0.813 mm

Inconel sheath and insulated with magnesium oxide.Boron nitride powder filled the gap between the ther-

mocouple bead and the aluminum, enhancing ther-

mal contact and thermocouple temperature re-

sponse.

The aluminum bar was raised into the furnace by

pulling the counterweight of the translation platform,

and then heated well into the film boiling region.

Once the desired sta rting temperature (550 to 555 ~C)

was reached, the pump was engaged and the sprays

allowed to come to hydrodynamic equilibrium. T he

testpiece was then quickly lowered into the spray

chamber and the temperature response of selected

thermocouples recorded with a maximum sampling

rate of 50 msec.

D e v e l o p m e n t o f t h e C o r r e l a t i o n s

As indicated in the Introduction, most investigators

have correlated film boiling heat transfer data for

sprays with respect to surface-to-fluid temperature

diffe rence A T ( = T - Tr), and volumetri c flux Q".

Although some have reported secondary effects dueto drop velocity and drop diameter, conclusions con-

cerning these effects are often highly uncertain and

this uncertainty is primarily the result of limitations

on the ranges of drop velocity and drop diameter

attainab le from commercial sprays. It is for this rea-

son that efforts were made in the present study to

select nozzles which provided fairly extensive ranges

for each of the hydrodynamic parameters, allowing

in several cases for variation in one parameter while

holding the other two constant.

One flat spray nozzle and four different full-cone

nozzles were used in 26 tests to provide the following

ranges of hydrodynamic param eters : Q" -- 0.58 x10-3-9.96 • 10 -3 m 3 sec-1/m2, U m = 10.1-29.9 m/

sec and d32 = 0.137-1.350 mm. Var iation in the

hydrodynam ic parameter s for the same nozzle was

achieved by changing nozzle-to-surface distance and/

or supply pressure. For each of the tests, the tem-

perature-time history was recorded and later pro-

cessed to determine the relationship between heat

flux, q", and wall temperature difference, AT.

96 ~ J. H e a t T r e a t in g , Vol. 9, No. 2, 1992




U s i ng t h e l u m p e d c a p a c it a n c e m e t h o d , t e m p e r a -

t u r e t h r o u g h o u t t h e 3 . 5 6 m m t h i c k c o p p e r d i s k w a s

a s s u m e d t o b e u n i f o r m a t e v e r y in s t a n t d u r i n g t h e

q u e n c h . T h e r e f o r e , t h e s u r f a c e t e m p e r a t u r e a n d

t e m p e r a t u r e r e c o r d e d b y t h e t h e r m o c o u p l e s p o t

w e l d e d t o t h e d i s k u n d e r s i d e w e r e a s s u m e d e q u a l .

T o f u r t h e r r e d u c e e r r o r i n u s i n g t h e l u m p e d c a p a c -

i t a n c e m e t h o d , d a t a w a s o n l y u s e d w h ic h c o r r e -

s p o n d e d t o B i < 0 . 0 5 ( h < 5 1 4 9 W / m 2 K ) . D a t a c o r -

r e s p o n d i n g t o B i e x c e e d i n g t h i s v a l u e d u r i n g t h e l a t e r

s t a g e s o f t h e q u e n c h ( i . e . , p a r t o f t h e t r a n s i t i o n b o i l -

i n g r e g i o n a n d a l l o f t h e n u c l e a t e b o i l i n g a n d s i n g le -

p h a s e r e g i o n s ) w e r e d i s c a r d e d .

F r o m t h e m e a s u r e d t e m p e r a t u r e r e s p o n s e , a d e -

r i v at i v e f o r e a c h t i m e i n c r e m e n t w a s c o m p u t e d f r o m

a c e n t e r e d , s e c o n d o r d e r , 1 1 p o i n t l e a s t s q u a r e s f it

t o t h e d a t a ( i . e . , t h e d e r i v a t i v e w a s c a l c u l a t e d a t t h e

s i x t h p o i n t i n e a c h 1 1 p o i n t f i t ) , a n d f r o m t h e d e r i v -

a t iv e th e h e a t f l u x w a s d e t e r m i n e d f r o m t h e e q u a t i o n

d Tq " = - p c cp , c w - ~ - - (1 )

w h e r e P c , C p , c a n d w a r e t h e d e n s i t y , s p e c i f i c h e a t ,

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

7 s h ow s a n e x a m p l e o f t e m p e r a t u r e - t i m e p l ot s g en -

e r a t e d f o r t h e c o p p e r d i s k f o r in c r e a s in g v o l u m e t r i c

f l u x . T h e c o r r e s p o n d i n g q u e n c h c u r v e s d i s p l a y e d i n

F i g u r e 8 w e r e d e t e r m i n e d u s i n g t h e l u m p e d c a p a c i -

t a n c e m e t h o d .

F i g u r e 8 c le a r l y d e m o n s t r a t e s t h a t t h e s l o p e o f t h e

h e a t f l u x v e r s u s t e m p e r a t u r e d r o p c u r v e i s l o w e r f o r

s p r a y f lu x e s e x c e e d i n g a p p r o x i m a t e l y 3 . 5 • 1 0 - 3 m 3s e c - V m 2 t h a n f o r l o w e r s p r a y f l u x e s . T h e d a t a b a s e

w a s , t h e r e f o r e , d i v i d e d i n t o t w o r a n g e s : l o w s p r a y

f l u x f o r Q " < 3 . 5 • 1 0 - 3 m 3 s e c - 1 / m a a n d h i g h s p r a y

6 0 0 . . . . I . . . . I . . . . I . . . . I . . . . I . . . .

U = 1 6 . 8 - 1 9 . 4 m / s U m d 3 =

~ , : , \ = ~ " I d ~ - = O 4 9 7 . l " 2 0 8 m m I ( m / s ) ( m m )0O

\ ,~ , .~" " , - - 1 6 . 8 0 . 5 4 5

~ , ~ / Q " = 0 . 9 0 4 x 1 0 " 3 m a s l / m ~ - - 1 7 . 2 0 , 5 0 6

4 0 0 ~ e k . / ~ ' ~ " ~ L / Q " 1 0 4 x 1 0 . 3 m 3 s . ~ / m 2 - - - 1 9 . 4 0 . 4 9 7

~ . ~ . ~ . . ~ = " - ' " 1 8 . 7 0 . 5 4 4

e . ~ . - . , ) N . ; , . , - - 17.6 1 .123

3 0 0 . , . ~ . . . - - - , 6 . 6 1 . ~

, ,

" ~ ' \ / Q . = 0 .5 8 x 1 0 ~1 m 3s -l / m 2

t \ ' .~

Q ' = 8 . 1 5 x l O " m s / m / , ~ r " . - ' - - ' = - - - _ " ~ ' ~

O " = 9 . 9 6 x 1 0 - 3 m 3 s - t / m 2 /

0 . . . . I . . . . I . . . . I . . . . I . . . . I . . . .

5 1 0 1 5 2 0 2 5 3 0

Time ( s )

F i g . 7 . Var i a t i o n o f t emp era tu re r esp o n se o f t h e co p p er

d isk wi th increasing vo lum etr ic f lux .

2 . 0 x 1 0 e . . . . 9 . . . . I . . . . I . . . . I . . . . I . . . .

i I U ] d ~ U m = 1 6 A - 1 8 " 8 m / s

I d 3 2 = 1 " 1 6 0 " 1 " 2 0 8 m m

l . S x 1 0 61 ~ 1 ~ 6 - 6 I 1 , 1 ~ 0 I

i ~ 1 .o . o I i . ~ u o I O ~ / O ' = 8 . 1 5 x 1 0 3 n 1 3 sl l m 2

1 . 0 x 1 0 6 z ~ ~ [ ~ O < ~ o ~ O 0 0 0 0 0 0 0 0 0 0 0

0 . 6 x 1 0 6 ~ - 3 3 i / m 2

\ Q ' = 4 . 2 4 x 1 0 a m 3 s l / r n 2

. . . . I . . . . I . . . . I . . . . I . . . . I . , , ,0

1 5 0 2 0 0 2 5 0 3 0 0 3 5 0 4 0 0 4 5 0

T - T ( ~

Fig. 8. Variatio n of the co ppe r disk boiling curv e with

increasing vo lume tr ic f lux .

f l u x f o r Q " > 3 . 5 • 1 0 - 3 m 3 s e c - V m 2. A s s u m i n g

h e a t f l ux c o r r e l a t i o n s o f t h e f o r m

n I t t n 2 n 3 n 4q " = C A T Q Umd32 ( 2 )

t h e A T e x p o n e n t w a s d e t e r m i n e d b y a v e r a g i n g e x -

p o n e n t s f o r a l l t h e t e s t s i n e a c h v o l u m e t r i c f lu x r a n g e ,

w h i c h r e s u l t e d i n t h e v a l u e s 1 . 6 9 1 a n d 0 . 4 6 1 f o r t h e

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

t e r m i n i n g t h e e x p o n e n t s i n t h e h i g h fl u x r a n g e , e x -

p o n e n t s f o r t h e i n d i v i d u a l t e s t s w e r e w e i g h t e d t o

e n s u r e e q u a l r e p r e s e n t a t i o n o f d a t a o v e r t h e r a n g e

4 • 1 0 - 3 - 9 • 1 0 - 3 m 3 s e c - 1 / m 2 s i n c e m o r e t e s t s

w e r e c o n c e n t r a t e d t o w a r d 4 x 1 0 - 3 m 3 s e c - 1 /m 2 i n

t h e h i g h f lu x r a n g e . W i t h t h e e x p o n e n t o f A T k n o w n ,

c o r r e l a t i o n o f t h e f i l m b o i l i n g h e a t f l u x t o t h e h y -

d r o d y n a m i c p a r a m e t e r s w a s a c c o m p l i s h e d b y a l e a st

s q u a r e s f i t t o t h e d a t a , r e s u l t i n g i n t h e f o l l o w i n g fi l m

b o i l i n g c o r r e l a t i o n s :

L o w s p r a y f lu x (0 . 5 8 x 1 0 - 3 < Q " < 3 . 5 x 1 0 - 3

m 3 sec - 1 /m2 ):

Q" < 3.5 x 10 -3 m 3 sec-1/m2: q"

= 63.250 AT1-691Q"~176176 ( 3 )

Hi g h sp ray f l u x (9 .9 6 • 1 0 -3 > Q " > 3 .5 • 1 0 -3

m 3 s e c - l /m 2 ) :

Q " > 3.5 • 10 -3 m 3 sec-l/m 2: q"

= 141345 AT~176 639 (4 )

F i g u r e s 9 ( a ) a n d ( b ) s h o w t h e f i l m b o i l i n g c o r r e -

l a t i o n s p l o t t e d a g a i n s t t h e r e s p e c t i v e d a t a i n e a c h

r a n g e a n d t h e a s s o c i a t e d m e a n a b s o l u t e e r r o r a n d

m a x i m u m e r r o r . E q u a t i o n s ( 3 ) a n d ( 4 ) d e m o n s t r a t e

J . H e a t T r e a t in g , V o l . 9 , N o . 2 , 1992 9 97



W . P . K l i n z i n g e t a l . 9 S p r a y Q u e n c h i n g F a c to r s

2 x 1 0 6

1 x 1 0 6

i i

M a x i m u m e r r or : 1 3 . 5 %

M e a n a b s o u t e e r r o r : .4 % J

3 x 1 0 6

" 6 3 2 5 0 A T 1 " 6 91 ~ . . o .' z ~ 4 d - O . 0 6 4~ = 6 3 . 2 L J " 3 2 . .

9 B ' .-? i : . , : . "

,N0 " < 3 . 5 x t f f a m a s - 1 / m a

I I

2 0 0

T - T , ( ~

1 x 1 0 s

5 0 0 2 0 0

(a) (b )

I I

Maximum error; 184% I

M e a n a b s o l u t e e r r o r : 7 . 0 % I

9 . . . .

C # > 3 . 5 x l O ' 3 m 3 s 1 / m 2

J

5 O 0

T - T l ' C )

Fig. 9. Correlation of film boiling for (a) low volumetric spray flux and (b) high volumetric spray flux.

t h a t d r o p d i a m e t e r h a s a n e g l i g i b l e e f f e c t o n f i l m

bo i l ing hea t f lux fo r the co nd i t ions inves t iga ted . Whi le

v o l u m e t r i c f lu x is s h o w n t o h a v e a n i m p o r t a n t e f f e c t

o n h e a t f l ux in b o t h r a n g e s , m e a n d r o p v e l o c i ty se e m s

t o p l a y a p a r a m o u n t r o l e i n s p ra y h e a t t r a n s f e r i n

t h e h i g h s p r a y r a n g e a n d n o n e i n t h e l o w f l u x o n e .

T h e t e c h n i q u e d e s c r i b e d a b o v e w a s a l so e m p l o y e d

t o d e v e l o p c o r r e l a t i o n s fo r t h e p o i n t s o n t h e q u e n c h

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

a n d m i n i m u m h e a t f l u x

L o w f lu x :

q~,FR = 6.100 X 106 Q"~ (5)

A T D F B = 2. 80 8 x 102 ~tltt~ "32~ (6 )

q~,N = 3.324 x 106 Q"~ (7)

ttO.066 0 . 1 3 8 - - 0 . 0 3 5ATMIN -- 2.04 9 x 102 Q Um d32 (8)

H i g h f l u x :

" = Q Um (9)DF B 6 .5 3 6 • 106 "0.995 0.924

ATDFB = 3.0 79 X 104 ~f)tt--0"194r[l922r]l651Ijm3 2 ( 1 0 )

" = Q Um (11)~rN 6.069 • 106 ,,0.943 0.864

p t - 0 . 0 2 7 1 . 0 3 3 0 . 9 5 2ATMIN -- 7.990 x 103 O U ,, d32 (12)

E r r o r s a s s o c ia t e d w i t h e a c h o f t h e a b o v e c o r r e l a t io n s

a r e g i v e n in T a b l e 1 .

N u m e r i c a l S i m u l a t i o n

C o u p l e d w i t h h e a t t r a n s f e r c o r r e l a t io n s r e c e n t l y d e -

v e l o p e d a t P u r d u e ' s B o i l in g a n d T w o - P h a s e F l o w

L a b o r a t o r y f o r t h e o t h e r b o i l i n g r e g i m e s [ 1 0 ] , t h e

c o r r e l a t io n s o f t h e p r e s e n t s t u d y w e r e u t i li z e d a s

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

q u e n c h i n g o f t h e a l u m i n u m p l a t e s h o w n i n F i g u r e 6

u s i n g t h e s o f t w a r e p a c k a g e A N S Y S . T h e n u m e r i c a l

p r e d i c t io n s a r e c o m p a r e d t o q u e n c h c u r v e s f o r v a r -

i o u s p o i n t s i n t h e a l u m i n u m p l a t e m e a s u r e d e x p e r -

i m e n t a l l y in t h e t e s t b e d . A c o m p i l a t i o n o f a ll t h e

c o r r e l a t i o n s u t i l i z e d i n t h e n u m e r i c a l s i m u l a t i o n i s

p r e s e n t e d i n T a b l e 2 .

P r o b l e m s o l v in g u s i n g A N S Y S i s c o m p r i s e d o f

t h r e e d i s t i n c t p h a s e s : p r e p r o c e s s i n g , s o l u t i o n , a n d

p o s t p r o c e s s i n g . P r e p r o c e s s i n g i n v o l v e s t h e d e v e l-

o p m e n t o f a l l t h e i n f o r m a t i o n n e c e s s a r y f o r t h e s o -

l u t i o n p h a s e , s u c h a s g e n e r a t i n g t h e s o l id m o d e l a n d

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

d i t i o n s . T h e s o l u t i o n p h a s e i s e x e c u t e d i n t e r n a l t o

t h e s o f t w a r e a n d i s n o t a c c e s s i b l e t o t h e u s e r . T h e

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

E x p e r i m e n t a l l y , t w o f l a t s p r a y s , o n e p o s i t i o n e d

v e r t i c a l ly a b o v e t h e o t h e r , p r o v i d e d a f a i r l y c o m p l e t e

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

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

c o n d i t i o n . U s i n g t h e s p a t i a l d i s t r i b u t i o n s f o r t h e h y -

d r o d y n a m i c p a r a m e t e r s m e a s u r e d b y D e i t er s a n d

M u d a w a r [ 11 ] f o r th e s a m e s p r a y c o n d i t i o n s u s e d in

9 8 ~ J . H e a t T r e a t i n g , V o l . 9 , N o . 2 , 1 99 2



W . P . K l i n z i n g e t a l . 9 S p r a y Q u e n c h i n g F a c t or s

T a b l e 1 . E r r o r s A s s o c i a t e d w i t h t h e C o r r e l a t i o n o f H e a t F l u x a n d W a l l T e m p e r a t u r e D r o p f o r t h e P o i n t s o f D e p a r t u r e

F r o m F i l m B o i l i n g a n d M i n u m u m H e a t F l u x in e a c h S p r a y F lu x R a n g e

M a x im u m E r r o r M e a n A b s o l u t e E r r o r

q~vB A Tt , vB q~lr~ A TM,N q~FB A TDFB qMIN a TMIN

( W / m z ) ( ~ ( W / m 2 ) ( ~ ( W / m 2 ) ( ~ ( W / m z ) ( ~

H i g h Q " r a n g e 1 1 . 2% 0 . 9 % 1 2 . 0% 4 . 9 % 8 . 1 % 0 . 4 % 7 . 8 % 2 . 4 %L o w Q " r a n g e 1 7 . 3% 9 . 1 % 2 0 . 5 % 9 . 6 % 7 . 1 % 2 . 6 % 9 . 0 % 3 . 1 %

T a b l e 2 . S u m m a r y o f S p r a y H e a t T r a n s f e r C o r r e l a t i o n s

B o i l i n g ( Q u e n c h i n g ) R e g i o n C o r r e l a t i o n

F i l m b o i l in g Q " > 3 . 5 1 0 - 3 : q " = 1.413 105 AT~176176 .639

Q " < 3 .5 1 0 - 5 : q " = 6 3 . 2 5 0 AT1.691Q"O.264d320~

Q " > 3 .5 10 -3 : q~F B = 65 .361 105 Q t ' ~ 1 7 6

ATDvB = 30 79 3. 20 1 Q "- ~ U~l.922d321.651

q~,VB = 61.00 3 105 Q"~176

A TI~FB = 280. 762 Q" ~17 6UO,r

q " = N o + N ~ A T + N 2 A T 2

No = q~.l lN -- N1ATM IN - N2AT•,N

N1 = - 2 N2A TMIN

q~FB -- q~alNN 2=

(ATDvB -- ATMIN)2

q~ lN = 60 .694 105 Q"~

ATMIN = 7990 .273 Q" 0.027Um1330d32o.952

q~IN = 33 .244 I05 Q"~176

ATMIN = 204 .895 Q"~176176 ~176

q~HF - - q~ lNq "= q ~ n v - [ A T ~r e .v - 3 A T ~H F A T M , N

( A T c H F - A T M m ) 3

+ 6 A T c H v A T M I N A T - 3 ( A T c a F + AT~I , , )AT 2 + 2 A T 3 ]

q ~n v _ 1 2 2 . 4 1 1 + O . O l 1 8 ( 9 s ) ~pghrgQ" pg \ pghig I J

= 1 8 _ [ ( P g h r ' Q " ) ( ~ ) O " 198 1/5.55ATcHF

q " = 1 .87 10 5 (AT)555

0 2 2 0

A T = 1 3 . 4 3 Re~ -123 \d3 2/

P o i n t o f d e p a r t u r e f r o m f i l m b o i l i n g

F i l m w e t t i n g r e g i o n

M i n i m u m h e a t f l ux p o i n t

T r a n s i t i o n b o i l i n g

C r i t i c a l h e a t f l u x [ 1 0 ]

N u c l e a t e b o i l i n g [ 1 0 ]

I n c i p i e n t b o i l i n g [ 1 0 ]

S i n g l e p h a s e c o o l i n g [ 1 0 ]

Q " < 3 . 5 1 0 - 3 :

Q " > 3 .5 x 1 0 - 3 :

Q " < 3 . 5 x 1 0 - 3 :

Nu32 2.51 2 0 167 0 56= Re3~ Pr7

N O T E S : U n i t s o f t h e p a r a m e t e r s a r e : q " ( W / m 2 ) , A T ( ~ Q " ( m 3 s e c 1 /m 2 ), U r n ( m / se e ) , d 3 2 (m ) , p y ( kg / m 3 ), o g( k g /m 3 ) , cp.f(J/kg K ) ,h l g ( J / k g ) , o r ( N / m ) .

R a n g e s o f v a l i d it y o f t h e c o r r e l a t i o n s a r e : Q " = 0 . 6 - 9 . 9 6 1 0 - 3 m 3 s e c - I / m z , U ,, = 1 0 . 1 - 2 6 . 7 m / s e c a n d d 32 = 4 0 5 1 0 - 3 - 1 3 5 0 1 0 - 3 m , T = 2 3 ~

J . H e a t T r e a t i n g , V o l . 9 , N o . 2 , 1 9 9 2 9 9 9



W.P. Klinzing et ai . 9 Spray Quenching Factors

!

g

h equlvslen1,1".

NumericalSolution

Domain

- - % 7 = .

7 . 9 4 T e

25.3

h K~,vm~ T .

\

\

\

\

I---

f

f/ /

f

/

, - - /

/

/

/ /

/

Note: NI Dimensions meIn Millimeters

Fig. 10. Location of numerical solution domain and thermocouples TC1 and TC2 with respect to the aluminum plate.

the present study, local values for Q", d32, and Um

were calculated along the minor axis of the spray for

the numerical domain shown in Figure 10. The com-

puted values for the local hydrodynamic paramete rs,

Figure 11, were then used in the correlations given

in Table 2 to determine the heat transfer boundary

conditions for the sprayed surface.

Radiative and convective losses from the un-

sprayed surfaces were accounted for through an

equivalent heat transfer coefficient defined as:

hequivalent = h .. .. .. . ion -~- hradiation (13)

where

hradiatio n = Eo' (T s "1- T~ )(T ] + T 2) (1 4)

Losses due to natural convection were co mputed us-

ing an average heat transfer coefficient for a vertical

height equal to that of the plate computed from a

correlation by Churchill and Chu (see ref. [12]). Val-ues estimated for hequivalent (~28 W/m2K) were neg-

ligible compared to the heat transfer coefficient of

film boiling on the sprayed surface.

ANSYS was used to predict the temperature re-

sponse for points corresponding to thermocouples T1

and T2 located as shown in Figure 10, and a com-

parison of the predicted to the measured response is

shown in Figure 12(a) and (b). Thermocouple T1

was positioned along the geometric center of the spray

field, where all the spray heat transfer correlations

given in Table 2 were developed, and T2 was located

closer to the oute r edge of the spray field. Fair agree-

ment was achieved in both cases and with a similar

degree of accuracy, confirming a conclusion arrived

at earlier by Deiters and Mudawar [11] for a quench

initiated in transition boiling, that heat transfer cor-

relations developed for the center are valid for other

points in the spray field, provided these correlations

are based upon the local values of the hydrodynamic

parameters.

Several reasons exist for the discrepancies be-

tween the ANSYS predictions and experimental data.

The most obvious is that the two-dimensional nu-

merical solution does not properly account for heat

diffusion perpendicular to the solution domain. The

actual field o f each of the two sprays (which were

positioned one vertically above the other to quench

one surface of the aluminum plate) takes the form

of an ellipse with a large ratio of majo r to minor axis.This feature of the flat sprays promote d a rather two-

dimensional cooling pattern on the sprayed surface.

Nevertheless, the numerical solution domain coin-

cides with the quenched surface along the minor axis

of the upper spray, a region of slightly higher volu-

metric flux (i.e., higher heat transfer coefficient) than

the rest of the spray field; consequently, as heat was

being extracted by the spray from this region, some

100 " J . Heat Treating, V o i . 9 , N o . 2 , 1 9 9 2



W . P . K l i n z in g e t a l . 9 S p r a y Q u e n c h i n g F a ct o r s

4

3 1

-41 2 3

Q " x 1 0 a ( m a s - l / m 2 )

d= (pro)50 100 150 200 250

4

1

0 - - - -

-1

._~g -2

Q 0 - 3

5 10 15 20 25

u m r rvs)

Fig. l l . Two-dimensional curve fits to spatial distributionsof Q", U,. and d32 measured by Deiters and Mudawar alongthe minor axis of the flat spray.

heat was also being imported from regions in the

plate located above and below the numerical solution

domain where heat flux to the water spray was rel-

atively low. Since the numerical model is two di-

mensional it could not account for this heat addition

and therefore slightly overpredicted the cooling rate.Also contributing to error in the numerical pre-

dictions are the approximations in determining the

spatial distributions of the hydrodynamic paramete rs

themselves. The distributions for the two flat sprays

used in the present study were approximated by dis-

tribution functions of a similar spray nozzle measured

by Deiters and Mudawar. Machining tolerances are

known to alter the hydrodynamic characteristics for

nozzles of identical part number and this can cause

differences in cooling performance be tween the two

nozzles used in the present s tudy as well as between

each and the nozzle used by Deiters and Mudawar.

Small deviations in the single-phase region of theboiling curve evident from Figure 12(a) and (b) can

be the result of liquid run-off along the sprayed sur-

face due to the lack of vaporization of liquid upon

impacting the surface. Under the influence of grav-

ity, the vertical orientation of the plate may cause

water impacting the top portion to fall down the

plate, heat ing up as it traverses its length. This heated

liquid can impair the effectiveness of droplet impact

6 "o...

E

I -

(a )

6 0 0 , . .

5 0 0

4 0 0

3 0 0

2 0 0

1 0 0

' ' ' i ' ' i ' i ' , , i ' ' ' i

- - E x p e r i m e n t a l d a t a f o r, ~ . I t h e r m o c o u p l e C 1

% \ I o N u m e r i c a l p r e d i c t i o n

f o r T ~

, , i , , , i , , i , . . i . . . i , , ,

2 0 4 0 6 0 8 0 1 0 0 1 2 0

T i m e ( s )

6 00 " ~ =

6 "

E =

I -

(b )

5 00

40 0

3 00

20 0

10 0

- - E x pe r im e n ta l d a ta fo r

)kN t h e r m o c o u p l e T C 2

~ ~ o N u m e r i c a l predic tion

_ _ fo r T C 2

b u . . I . . . i . . i . . . i . . . i , . .

2 0 4 0 6 0 8 0 1 0 0 1 2 0

T i m e (s )

Fig. 12. ANSYS predicted temperature response for pointscorresponding to (a) thermocouple TC1 and (b) thermo-couple TC2.

with the sprayed surface, thereby influencing local

spray heat flux. It is very important to note, however,

that the numerical predictions are important to ma-

terials processing only in the film, transition, and

nucleate boiling regions, which are most responsible

for determining the metallurgical properties of the

alloy.

Figure 13 shows the numerically predicted tem-perature distributions for the solution domain for

times corresponding to the center of the sprayed

undergoing film boiling, transition boiling, nucleate

boiling, and single-phase cooling, respectively. These

distributions demonstrate the strong effect of volu-

metric flux on heat flux in the various regions of the

boiling curve. At the onset of the numerically sim-

ulated quench, the higher volumetric fluxes toward

J. Heat Trea ting, Vol . 9 , No. 2 , 1992 ~ 101




1=20.0 see =40.8 sec t=41 .4 sec t=80.O s e c

3~ 261 215 25.0

213 242

Is ,,, ( / / f ( , , ,i l m B o i l in g T r a n s i t io n a l B o i l i n g N u c l e a t e B o i l i n g S i n g l e - P h a s e C o o l i n

a t S p r a y C e n t e r a t S p r a y C e n t e r a t S p r a y C e n t e r a t S p r a y C e n t e r

F i g . 13. ANSYS predicted tempera-ture for selected times during the

quench.

the center of the spray promote faster cooling near

the center and a delayed response to the quench

toward the corners. As indicated earlier, the distri-

bution functions for the hydrodynamic parameters

used in determining the heat transfer bound ary con-

ditions for the sprayed surface were disto rted slightly

away from the geometrical center of the spray ac-

cording to the measurements of Deiters and Muda-

war, which were also adopted in the present numer-

ical simulation, due to minute imperfections in the

manufacturing of spray nozzles. The small displace-

ment of the point of maximum volumetric flux from

the geometrical center produced a similar displace-

ment of the coo lest surface point slightly away from

the center as shown in Figure 13 for t = 20 sec. It

is important to note that, despite their small mag-

nitude during film boiling, surface temperature dis-

tortions can lead to pronounced distortions in the

transition and nucleate boiling regions as shown in

Figure 13 for t = 40.8 and 41.4 sec. As ymm etr y in

surface temperature during film boiling seems to pro-

mote wetting on one side of the spray center earlier

than on the other side. The sudden drastic increase

in heat flux immediately following wetting renders

the wetting side very favorable for heat to be trans-

ferred from the aluminum plate, resulting in an even

greater asymmetry in the temperature distribution.The numerical findings of the present s tudy dem-

onstrate t he import ance of carefully mapping the spa-

tial distributions of the hydrodynamic parameters in

order to numerically simulate temperature response

with any reasonable accuracy. Conversely, the re-

suits point to a need for spray nozzles manufactured

with much closer tolerances if any predictability and/

or repeatability are to be realized in the quenching

process. As indicated earlier in this paper, the ulti-

mate goal in a controlled spray quenching environ-

ment is to optimize the spray configuration in order

to achieve temperature response within a narrow

window, prescribed by a min imum, corresponding to

the need to produce the desired material properties,

and a max imum, above which large temperature gra-

dients in the quenched part may lead to unacceptable

stress concentration causing warping or cracking of

the part. This goal becomes very challenging with

complex shapes as section thickness varies in differ-

ent regions of the quenched par t and/or varying ma-

terial properties are to be developed for different

regions. These challenges are fur ther evidence of the

need for spray nozzles with predictable and repeat-

able performance.

Acknowledgments. Financial support for this work by thePurdue University Engineering Research Center for In-telligent Manufacturing Systems is gratefully appreciated.The authors thank Messrs. Jerry Hagers and Rudolf Schickof Spraying Systems Co., and Gerry Dail of ALCOA for

their valuable technical assistance.

R e f e r e n c e s

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Documents

Film and Trasition Boiling Correlations for Quenching of Hot Surface With Water Sprays