ANL-6667 Engineering and Equipment (TID-4500, 19th Ed.) AEC Research and Development Report

ARGONNE NATIONAL LABORATORY 9700 South Cass Avenue

Argonne, Illinois

A STUDY OF THE FLOW OF SATURATED FREO„N:.JU THROUGH APERTURES AND SHORT rUBES

by

Hans K. Fauske and Tony C. Min Univers i ty of Minnesota

Reactor Engineering Division, ANL and

Associated Midwest Univers i t ies

January 1963

This r epo r t is one of a s e r i e s that desc r ibes hea t - t r ans fe r and fluid-flow studies per formed at Argonne under a p rog ram sponsored jointly by the Associa ted Midwest Univers i t ies and the Argonne National Labora tory .

The one e a r l i e r r epor t in this s e r i e s is ANL-6625.

Operated by The Universi ty of Chicago under

Contract W-31-1 09-eng-38 with the

U. S. Atomic Energy Commission

DISCLAIMER

This report was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor any agency Thereof, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof.

DISCLAIMER Portions of this document may be illegible in electronic image products. Images are produced from the best available original document.

2

T A B L E O F C O N T E N T S

P a g e

N O M E N C L A T U R E 4

A B S T R A C T 5

I. INTRODUCTION 5

II. E X P E R I M E N T A L E Q U I P M E N T 6

III. T E S T P R O C E D U R E 9

IV. ANALYSIS O F D A T A AND A P P L I C A T I O N 10

V. DISCUSSION 13

VI. CONCLUSIONS 17

A C K N O W L E D G E M E N T S 18

B I B L I O G R A P H Y 19

LIST O F F I G U R E S

No. T i t l e P a g e

1. D i a g r a m of the E x p e r i m e n t a l E q u i p m e n t 7

2. View of the E x p e r i m e n t a l E q u i p m e n t 7

3. View of T e s t A p e r t u r e s 8

4. View of T e s t T u b e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

5. D a t a f r o m S h o r t T u b e s 10

6. C o r r e l a t i o n N u m b e r D e t e r m i n i n g the O c c u r r e n c e of S i n g l e -

and T w o - p h a s e F l o w R e g i m e s 11

7. C o r r e l a t i o n of F l o w Ra te and L e n g t h - t o - d i a m e t e r R?.tio of S h o r t T u b e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

8. E u l e r N u m b e r V a r i a t i o n for V a r i o u s A p e r t u r e s 12

9. P h o t o g r a p h Showing the D i s c h a r g e d F l u i d f r o m a C i r c u l a r A p e r t u r e . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

10. P h o t o g r a p h Showing the D i s c h a r g e d F l u i d f r o m an E y e -s h a p e d A p e r t u r e . 14

11. P h o t o g r a p h Showing the D i s c h a r g e d F l u i d f r o m a Tube with L / D ~3 and Ca ' ~8 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

12. P h o t o g r a p h Showing the D i s c h a r g e d F l u i d f r o m a Sho r t Tube wi th a Modif ied Cav i t a t i on N u m b e r b e t w e e n 10 and 14 . . . . . . 16

13. P h o t o g r a p h Showing the D i s c h a r g e d F l u i d f r o m a Shor t Tube When C r i t i c a l F l o w O c c u r s 17

4

NOMENCLATURE

^2 A c r o s s - s e c t i o n a l a r e a of t h e o p e n i n g of t h e v e s s e l , ft

2g A P I / s C a ' = — ^^7 ( L / D ) m o d i f i e d c a v i t a t i o n n u m b e r , d i m e n s i o n l e s s

D d i a n a e t e r o r e q u i v a l e n t d i a m e t e r , ft

Q

A V 2 ^ E u = -—zz. Euler number, dimensionless

g accelerat ion of gravity, ft/sec^

g^ conversion factor, 32.2 (lbi-nft)/(lb£ sec )

h head of fluid, ft

L length of tube, ft

P local p r e s s u r e , Ibf/ft^

Pg exit p r e s s u r e , lb£/ft^

P]3 back p r e s s u r e , Ibf/ft^

P^ initial p r e s su re of fluid inside the vesse l at the level

of the exit, Ibf/ft^

Q discharge rate of fluid, ft^/sec

U = Q / A average velocity of the fluid in the vesse l flowing out, f t / sec

AP p re s su re difference, P^-Pg for two-phase flow,

P i - P b for single-phase flow, Ibf/ft^

p density of the fluid, Vo^i'v'

Pi initial density of the saturated or subcooled fluid in the vessel , Ibm/ft^

A STUDY OF THE FLOW OF SATURATED FREON-11 THROUGH APERTURES AND SHORT TUBES

by

Hans K. Fauske and Tony C. Min

A B S T R A C T

An e x p e r i m e n t a l s tudy on the d i s c h a r g e r a t e s of s a t u ­r a t e d and s u b c o o l e d F r e o n - 1 1 t h r o u g h a p e r t u r e s and s h o r t t u b e s i s r e p o r t e d . The e x p e r i m e n t c o v e r e d a r a n g e of m o d i -fied c a v i t a t i o n n u m b e r s b e t w e e n 0 and 500, l e n g t h - t o - d i a m e t e r r a t i o s of s m a l l d i a m e t e r t u b e s b e t w e e n 2 and 55 , and s h a r p -edge a p e r t u r e s of n ine d i f f e r en t g e o m e t r i c c o n f i g u r a t i o n s .

It w a s found tha t b e l o w the modi f i ed cav i t a t i on numb'=»r of 10 the fluid exh ib i t s c o m p l e t e l y m e t a s t a b l e s i n g l e - p h a s e flow. When the mod i f i ed c a v i t a t i o n n u m b e r e x c e e d s 14, t w o -p h a s e c r i t i c a l f low m a y e x i s t . In the r a n g e of modi f i ed c a v i ­t a t i on n u m b e r s b e t w e e n 10 and 14, u n s t a b l e t r a n s i t i o n a l flow o c c u r s ( a l t e r n a t i n g s i n g l e - and t w o - p h a s e flow).

E u l e r n u m b e r s for the a p e r t u r e s of v a r i o u s c o n f i g u r a ­t i o n s , i nc lud ing s q u a r e , r e c t a n g u l a r , and e y e - s h a p e d , w e r e found to be in the s a m e o r d e r of m a g n i t u d e a s t hose for c i r c u ­l a r s h a p e s . The t r i a n g u l a r o r i f i c e s w e r e found to p o s s e s s h i g h e r E u l e r n u m b e r s and the W - s h a p e d o r i f i c e s l o w e r than the c i r c u l a r o n e s .

I. INTRODUCTION

An u p s u r g e of i n t e r e s t h a s r e c e n t l y t aken p l a c e in o r d e r to c l a r i f y the m a n y p r o b l e m s a s s o c i a t e d wi th v a r i o u s c o n t a i n m e n t s y s t e m s for n u ­c l e a r r e a c t o r s . One of the m o s t v a l u a b l e too l s t ha t a c o n t a i n m e n t d e s i g n e r c a n p o s s e s s i s a m e t h o d for p r e d i c t i n g a c c u r a t e l y the r a t e of r e l e a s e of coo l an t u n d e r a v a r i e t y of p r o t o t y p e c o n d i t i o n s . To obta in such a tool would invo lve b a s i c s t u d i e s of flow of s a t u r a t e d f lu ids t h r o u g h v a r i o u s s i z e s of p i p e s , d u c t s , a p e r t u r e s , e t c . , going f r o m h i g h - to l o w - p r e s s u r e s y s t e m s , and i n c l u d i n g s t e a d y - s t a t e a s we l l a s h igh ly t r a n s i e n t f l ows . Th i s p r o b l e m b e c o m e s n a t u r a l l y t i ed to a p h e n o m e n o n c a l l e d c r i t i c a l flow.

Much e x p e r i m e n t a l w o r k r e g a r d i n g the c r i t i c a l p h e n o m e n o n in c i r ­c u l a r flow p a s s a g e s of c o n s i d e r a b l e l e n g t h s (>10 in . ) h a s a p p e a r e d in the p a s t t en y e a r s . ^ ^ " ' / E x p e r i m e n t a l d a t a of b a s i c va lue e x i s t , h o w e v e r , only up to about 400 p s i a ( c r i t i c a l p r e s s u r e ) .

A t h e o r e t i c a l m o d e l h a s b e e n p r e s e n t e d tha t shows s u b s t a n t i a l a g r e e -m e n t wi th t h e s e da t a . ( ^ ) As to the flow of s a t u r a t e d fluid t h r o u g h an a p e r t u r e and s h o r t t u b e , s o m e r e l a t e d e x p e r i m e n t a l i n v e s t i g a t i o n s a r e a v a i l a b l e , ^ " ' " ; bu t the r e s u l t s a r e no t suf f ic ien t to d e v e l o p the n e c e s s a r y c r i t e r i a for d e t e r ­m i n i n g s i n g l e - p h a s e and t w o - p h a s e flow r e g i m e s . S impson and Si lverv^^/ r e c e n t l y p r o p o s e d a h o m o g e n e o u s n o n e q u i l i b r i u m flow m o d e l to d e s c r i b e the s a t u r a t e d o r s u p e r s a t u r a t e d fluid t h r o u g h d u c t s . Ano the r t h e o r e t i c a l p a p e r by Isb in and G a v a l a s l ^ l ) p r o p o s e s a t w o - p h a s e m e t a s t a b l e o r a t w o - p h a s e g r o w i n g - b u b b l e h o m o g e n e o u s m o d e l for d e s c r i b i n g flow th rough an a p e r t u r e .

H o w e v e r , the f u n d a m e n t a l s upon which t h e s e m o d e l s a r e f o r m e d m a y not s i m u l a t e the a c t u a l p h y s i c a l p r o c e s s . It is s t r o n g l y b e l i e v e d tha t c r i t i c a l f lows in s t r a i g h t t u b e s of c o n s i d e r a b l e l e n g t h s differ s ign i f i can t ly f r o m the flow f r o m a sudden b r e a k in the v e s s e l con ta in ing h igh ly p r e s s u r i z e d s a t u ­r a t e d f luid . Th i s l a s t e x a m p l e m a y be a m o r e r e a l i s t i c p i c t u r e of what m i g h t happen in a n u c l e a r r e a c t o r a s s e m b l y in the c a s e of an a c c i d e n t . The de­p e n d e n c e of c r i t i c a l flow r a t e s f r o m d i f fe ren t shaped flow p a s s a g e s i s at p r e s e n t not c l e a r . P e r h a p s the m o s t i m p o r t a n t ques t i on to c l a r i f y i s , "does one ob ta in c r i t i c a l flow when a sudden b r e a k in the cool ing s y s t e m of a r e ­a c t o r o c c u r s ? " If so , to what ex t en t ? Is the fluid l eav ing the b r e a k in p h y s ­i c a l e q u i l i b r i u m , or c o m p l e t e l y or p a r t i a l l y m e t a s t a b l e ? Th is i s v e r y i m p o r t a n t i n a s m u c h a s the flow r a t e i s v e r y s e n s i t i v e to the c o m p r e s s i b i l i t y of the fluid, which i s d e t e r m i n e d by the above p h e n o m e n o n .

In o r d e r to t h r o w s o m e l igh t on t h e s e v a r i o u s ex i s t i ng u n c e r t a i n t i e s , an e x t e n s i v e p r o g r a m h a s been i n i t i a t e d at A r g o n n e Nat iona l L a b o r a t o r y . In t h i s r e p o r t i s shown how a n s w e r s to s o m e of t h e s e q u e s t i o n s c a n be o b t a i n e d f r o m a b a s i c and s i m p l e l a b o r a t o r y e x p e r i m e n t .

II . E X P E R I M E N T A L E Q U I P M E N T

The t e s t a p p a r a t u s u s e d in t h e s e e x p e r i m e n t s c o n s i s t e d of a v e s s e l , t e s t s e c t i o n , v a c u u m p u m p , and a c o n d e n s e r ( see F i g s . 1 and 2) . A r e c t a n ­g u l a r v e s s e l , 8 X 12 X 33 in . , w a s m a d e of - | - - in . - th ick Luc i t e p l a t e s . At the top of the v e s s e l a p r e s s u r e gauge and a ven t , and a t the b o t t o m a d r a i n p ipe wi th a v a l v e , w e r e p r o v i d e d . The v e s s e l was c o n n e c t e d to the p u m p t h r o u g h a 2 - i n . - I D P y r e x tube a f t e r a 90° t u r n . The t e s t s e c t i o n w a s l o c a t e d b e t w e e n two Luc i t e f l a n g e s , one c o n n e c t e d to an open ing , 3 in . in d i a m e t e r , in a wa l l of the v e s s e l and the o t h e r to the P y r e x t u b e .

In the t e s t s of a p e r t u r e s , the t e s t s e c t i o n s w e r e L u c i t e d i s k s hav ing a p e r t u r e s of v a r i o u s r u p t u r e c o n f i g u r a t i o n s in the c e n t e r . S a m p l e s of t h e s e a r e shown in F i g . 3 . The s h o r t t u b e s shown in F i g . 4 w e r e m a d e of s t a i n l e s s s t e e l and w e r e t h r e a d e d to the c e n t e r of the Luc i t e d i s k s to r e ­p l a c e the a p e r t u r e in the c a s e of t e s t s of s h o r t t u b e s . The ou t l e t end of

7

DRY ICE

VESSEL

Fig. 1

Diagram of the Experimental Equipment

Fig. 2

View of the Experimental Equipment

F i g . 3. View of the T e s t A p e r t u r e s

ttl

m us HI ^^H^H B

^ j ^ ^ g

^^B^Hfe^K^

llMiii^artilll

^B^^^

K •

" ^

fc-^

IHG^ y »

•^

1 •1

'

1

^P s p g n * A'"

' . 4f

fc^" i | ' i . ^

• H M M B ' t

i^aJHw^B

j i

' j '

Mr »

1 w

^

i

m

%

m

1i '"^•i

i '<^w

J F i g . 4 . View of the T e s t Tubes

e a c h t e s t tube w a s c a r e f u l l y f i led to p r o v i d e a p l a n e , s h a r p c r o s s s e c t i o n . A p r e s s u r e t ap of ( - r r - in . d i a m e t e r ) w a s i n s t a l l e d a ha l f -p ipe d i a m e t e r f r o m the ou t l e t of e a c h t e s t s e c t i o n . In one of the Luc i t e f l anges c o n c e n t r i c t ub ings w e r e r u n t h r o u g h so t h a t ex i t p r e s s u r e cou ld be m e a s u r e d , by m e a n s of the p r e s s u r e t a p s i n s t a l l e d in the t e s t s e c t i o n and b a c k p r e s s u r e , by the c o n n e c t i o n to a m a n o m e t e r .

The v a c u u m p u m p w a s a v o l u m e t r i c d i s p l a c e m e n t type wi th s l id ing v a n e s and h a d a c a p a c i t y of about 29 in . Hg u n d e r n o r m a l o p e r a t i n g c o n d i t i o n s .

The c o n d e n s e r w a s a r i g h t c i r c u l a r c y l i n d r i c a l c o n t a i n e r of -g- in . -th i ck L u c i t e s h e e t . The in le t w a s c o n n e c t e d by f lexible p l a s t i c h o s e to the ou t l e t of the v a c u u m p u m p . D r y i c e , u s e d as a condens ing m e d i u m , w a s p l a c e d in a p e r f o r a t e d m e t a l t r a y hang ing o v e r the u p p e r p o r t i o n of the c o n d e n s e r . The c o n d e n s a t e Avas r e t u r n e d by g r a v i t y f r o m the b o t t o m of the c o n d e n s e r t h r o u g h a ^ - i n . - I D pipe to the v e s s e l .

III. T E S T P R O C E D U R E

F r e o n - 1 1 w a s s e l e c t e d as the w o r k i n g fluid for the fol lowing r e a s o n s :

1. R e f r i g e r a n t - 1 1 bo i l s at a t e m p e r a t u r e s l igh t ly above r o o m t e m ­p e r a t u r e at a t m o s p h e r i c p r e s s u r e . T h i s m e a n s tha t a s l igh t r e d u c t i o n in p r e s s u r e w i l l p r o d u c e a s a t u r a t e d o r s u p e r s a t u r a t e d fluid wi thout adding h e a t to the s y s t e m ,

2. As i t i s a r e c o g n i z e d h e a t t r a n s f e r m e d i u m in c o m m e r c i a l u s e , m a n y t h e r m o d y n a m i c p r o p e r t i e s a r e t a b u l a t e d .

3. It i s n o n t o x i c , n o n i n f l a m m a b l e , and o d o r l e s s .

4. It i s w a t e r wh i t e in c o l o r , f ac i l i t a t i ng p h o t o g r a p h i c s tud ies .

5. It i s e a s i l y a v a i l a b l e and no t too e x p e n s i v e .

The s a t u r a t e d o r n e a r l y s a t u r a t e d F r e o n - 1 1 w a s p o u r e d in to the v e s s e l to about t w o - t h i r d s full , and d r y i ce w a s f i l led into the top p a r t of the c o n d e n s e r . The v a c u u m punap vc^as s t a r t e d and, when s t eady s t a t e w a s r e a c h e d ( tha t i s , a c o n s t a n t d i s c h a r g e r a t e ) , the t e m p e r a t u r e of the l iqu id F r e o n - 1 1 in the v e s s e l , i n i t i a l p r e s s u r e , ex i t p r e s s u r e , b a c k p r e s s u r e , v o l u m e d i s p l a c e m e n t r a t e of F r e o n - 1 1 in the v e s s e l , and v i s u a l o b s e r v a ­t i ons of the f luid b e h a v i o r w e r e r e c o r d e d . The t e m p e r a t u r e of the l iqu id F r e o n - 1 1 w a s s e n s e d by a 3 0 - g a u g e i r o n - c o n s t a n t a n t h e r m o c o u p l e i m ­m e r s e d in the l iqu id a t the l e v e l of the t e s t s e c t i o n .

F o r m e a s u r e m e n t of flow r a t e , the u s e of o r i f i c e and r o t a m e t e r w e r e found to be i m p r a c t i c a l , s i nce c a l i b r a t i o n of t w o - p h a s e flow for the f o r m e r

IS difficult and boi l ing o c c u r s a r o u n d the f l oa t e r and wa l l of the l a t t e r . It w a s , t h e r e f o r e , dec ided to m e a s u r e the vo lume d i s p l a c e m e n t r a t e by t iming a d i s p l a c e m e n t of about 0.08 ft^ of l iquid, o r a d r o p in l iquid l eve l of about 2 in . , in m o s t of the t e s t s c a r r i e d out. Th i s c o r r e s p o n d s to a m a x i m u m change of 0.1 p s i in i n i t i a l u p s t r e a m p r e s s u r e du r ing a run . Since the v e s s e l w a s open to a t m o s p h e r e dur ing o p e r a t i o n , the u p s t r e a m p r e s s u r e can , for a l l p r a c t i c a l p u r p o s e s , be c o n s i d e r e d cons t an t . In a few t e s t s even s m a l l e r d i s p l a c e m e n t s w e r e t i m e d to check the s t e a d y - s t a t e r a t e . T h i s m e t h o d w a s found suff ic ient for the a c c u r a c y r e q u i r e d .

In o r d e r to c h e c k if c r i t i c a l flow o c c u r r e d in some of the tube t e s t s , the back p r e s s u r e w a s v a r i e d by p a r t i a l l y c los ing the in le t va lve of the v a c u u m p u m p to s ee if any c h a n g e s in ex i t p r e s s u r e and vo lume d i s p l a c e ­m e n t r a t e o c c u r r e d .

In the a p e r t u r e t e s t s , s e v e r a l r u n s wi th v a r i o u s b a c k p r e s s u r e s w e r e m a d e and c o r r e s p o n d i n g flow r a t e s and t e m p e r a t u r e s w e r e m e a s u r e d .

IV. ANALYSIS O F DATA AND A P P L I C A T I O N

F i g u r e 5 shows flow r a t e v e r s u s p r e s s u r e d i f fe rence c u r v e s wi th the l e n g t h - t o - d i a m e t e r r a t i o as p a r a m e t e r for the da ta ob ta ined on s h o r t

18001 -—=^ 1

0 I 2 3 4 5 6 7 8 9 10 II PRESSURE DIFFERENCE P | - P b , l b f / i n ^

F i g . 5. D a t a f r o m Shor t Tubes

11

t u b e s . A l s o in F i g . 5 a r e p lo t t ed the flow r a t e s c a l c u l a t e d f r o m the o r i f i ce flow equa t i on wi th a d i s c h a r g e coef f ic ien t equa l to 0 .611 . It i s i n t e r e s t i n g to note f r o m F i g . 5 tha t for c e r t a i n c o m b i n a t i o n s be tween m a s s ve loc i ty , p r e s s u r e d i f f e r ence and l e n g t h - t o - d i a m e t e r r a t i o the fluid b e h a v e s l ike a s i n g l e - p h a s e i n c o n n p r e s s i b l e fluid, a l though the l oca l p r e s s u r e is we l l b e ­low the v a p o r p r e s s u r e . The in i t i a t ion of t w o - p h a s e flow and, if back p r e s ­s u r e is low enough, c r i t i c a l flow can be s e e n f r o m F i g . 5 to depend on G, AP and L / D . It s e e m s l ike ly t h a t to a f i r s t a p p r o x i m a t i o n , c o m b i n a t i o n s of G, AP and L / D would i n d i c a t e the t r a n s i t i o n f r o m s ingle to t w o - p h a s e flow. The fol lowing d i m e n s i o n l e s s g r o u p w a s chosen to c h a r a c t e r i z e th i s t r a n s i t i o n .

Ca- = ^ ^ ( L / D ) Pi u ^ (1)

T h i s g r o u p wi l l be t e r m e d the modi f ied cav i t a t i on n u m b e r . The d i m e n s i o n l e s s g r o u p e v a l u a t e d wi th i n i t i a l dens i ty p^ , i n i t i a l ve loc i ty u, p r e s s u r e d i f f e rence of i n i t i a l and ex i t p r e s s u r e , and l e n g t h - t o - d i a m e t e r r a t i o L / D a r e shown in F i g . 6. The s ign i f i cance of th is g r o u p i s tha t it e s t a b l i s h e s a c r i t e r i o n for d e t e r m i n i n g s i n g l e - p h a s e o r t w o - p h a s e flow r e g i m e s in s h o r t t u b e s . As i n d i c a t e d in F i g . 6, for modi f ied cav i t a t i on n u m b e r be low 10, the fluid exh ib i t s c o m p l e t e l y m e t a s t a b l e s i n g l e - p h a s e flow. When the mod i f i ed c a v i t a t i o n n u m b e r e x c e e d s 14, t w o - p h a s e flow e x i s t s . In the r a n g e of C a ' b e t w e e n 10 and 14, u n s t a b l e t r a n s i t i o n a l flow o c c u r s . T h e s e c o n c l u s i o n s f r o m the ob ta ined e x p e r i m e n t a l da ta w e r e v e r i ­f ied by v i s u a l o b s e r v a t i o n s .

-METASTABLE SINGLE-PHASE FLOW-

TRANSITIONAL UNSTABLE

FLOW -TWO- PHASE FLOW

2g AP Ca' = — (L/D)

p u2

F i g . 6. C o r r e l a t i o n N u m b e r D e t e r m i n i n g the O c c u r r e n c e of S i n g l e - and T w o - p h a s e Flow^ R e g i m e s

In F i g . 7 the c r i t i c a l flow r a t e i s p lo t ted v e r s u s l e n g t h - t o - d i a m e t e r r a t i o for i n i t i a l p r e s s u r e equa l to 15 p s i a . It can be s e e n tha t for the s a ine i n i t i a l cond i t i ons the c r i t i c a l flow r a t e i s i n c r e a s i n g s h a r p l y for d e c r e a s i n g l e n g t h - t o - d i a m e t e r r a t i o . In m o s t p r a c t i c a l s i t u a t i o n s , the i n i t i a l and b a c k p r e s s u r e and L / D r a t i o of the tube a r e known. T h e r e f o r e , if c u r v e s l ike the one in F i g . 7 w e r e a v a i l a b l e for a v a r i e t y of i n i t i a l c o n d i t i o n s , one could ob ta in a c o r r e l a t i o n for e s t i m a t i n g the m a x i m u m flow r a t e . An e x p e r i m e n t a l p r o g r a m is u n d e r way to ob ta in such c u r v e s for s t e a m - w a t e r for in i t i a l p r e s s u r e s up to 2000 p s i a , and wi l l a p p e a r in a l a t e r r e p o r t .

12

Pi =15 0 psia

Pj, - 7 5 psia

!0 20 30 40 50 LENGTH-TO-OIAMETER RATIO L/D

Fig 7

Correla t ion of Flow Rate and Length-to-d iameter Ratio of Short Tubes

For the t e s t s of a p e r t u r e s , data a r e plotted in velocity against preS ' sure difference as in Fig . 8. It can be seen that the Euler numbers of

30

25

I I I I

20

15

10

USUAL RANGE FOR

CIRCULAR ORIFICE

•7 »

S

An

# AREA, f t

c 2 .3 X 1 0 - ^ , 30° SHARP EOGE -5

9 8.5 X 10

® 3.7 X lO"

A 4.1 X 10

D 1.2 X 10

• 1.5 X IQ-

7 1.1 X 10

A 1.4 X IQ-

c 8.5 X 10 '',

LJ I I I I

-5 S

-4

-4

30°

30°

30°

30°

30°

30°

30°

15°

4 5 6 7 8 9 10

AP, Ib^/ing

15

Fig. 8. Euler Number Variation for Various Aper tures

square , rec tangula r , and eye-shaped ape r tu re s exhibit the same c h a r a c t e r ­i s t i cs as those of c i r cu la r ones , but not the t r iangular and W-shaped ones . The fo rmer seems to be assoc ia ted with higher and the la t te r with lower Euler n u m b e r s .

Hence, Fig . 8 becomes a useful tool in determining the ra te of flow of sa tura ted or subcooled fluid through a known aper tu re configuration where u p s t r e a m p r e s s u r e and t empe ra tu r e and back p r e s s u r e a re specified.

V. DISCUSSION

A. Aper ture Tests

In the introduction, the following question was ra i sed : "does one ob­tain c r i t i ca l flow when a sudden break in a vesse l containing sa tura ted fluid occurs?" A p r e s s u r e drop is r equ i red for the fluid to go through the break or opening. Hence, close to the b reak (inside the vesse l ) the vapor p r e s s u r e becomes higher than the corresponding local p r e s s u r e , and one could s p e c ­ulate that flashing of the fluid will take place inside the break such that c o m ­press ib i l i ty i s achieved and, hence , cause cr i t ica l flow if the back p r e s s u r e is sufficiently low. However, this is not the case in this work. No bubble formation seems to take place, and the fluid leaves the break as a supe r ­heated or completely metas tab le s ingle-phase fluid and remains as a s ing le -phase jet up to 3 ft from the d ischarge hole . At this point the metas tabi l i ty of the s ingle-phase jet is d is turbed e i ther by hitting the before-ment ioned 90" elbow or , due to gravi ty, the bottom surface of the expansion tube where the fluid f lashes ins tantaneously. It should be mentioned he re that this p o r ­tion is very much cooled, due to the latent heat of vaporizat ion of F r e o n - 1 1 , whereas the portion of the expansion tube ups t r eam of this point r emains fair ly close to the room t e m p e r a t u r e . Maximum superheat of 40°F was achieved in these liquid j e t s . Higher superheats could not be achieved due to the capacity of the vacuum pump. A typical superheated liquid Freon-11 jet , formed from a c i r cu la r ape r tu re of - | - i n . - ID , is shown in Fig . 9.

In F ig . 10 a c lose-up view of the superheated liquid jet d ischarged from an eye-shaped ape r tu re is shown. Here "the vena con t rac ta" of the d ischarged fluid can be readi ly observed . In all of the ape r tu re configura­tions uti l ized in this work s imi la r s ingle-phase superheat je ts were obtained, as shown in F igs . 9 and 10. It i s , the re fore , concluded that a sa tura ted fluid discharging through an ape r tu re can be descr ibed with subcooled s ing le -phase fluid-flow theory . F u r t h e r m o r e , c r i t i ca l flow does not occur under these condit ions. The d ischarge flow r a t e s become, the re fore , natural ly much l a r g e r than one would have expected previous to this work.

In F ig . 8 it is noted that, for a fixed p r e s s u r e difference, the Euler number s for t r i angu la r , rec tangular , square , eye-shaped and W-shaped a p e r t u r e s depend on a r e a or equivalent d i a m e t e r s . The l a rge r the d iameter

14

F i g . 9. P h o t o g r a p h Showing the D i s c h a r g e d F l u i d f r o m a C i r c u l a r A p e r t u r e

F i g . 10. P h o t o g r a p h Showing the D i s c h a r g e d F lu id f r o m an E y e - s h a p e d A p e r t u r e

b e c o m e s , the s m a l l e r i s the E u l e r n u m b e r . Th i s h a s p r e v i o u s l y been found to be the c a s e for c i r c u l a r s h a r p - e d g e o r i f i c e s . ( 1 ^ / A s i m i l a r c o n c l u s i o n was m e n t i o n e d for r e c t a n g u l a r a p e r t u r e s .^^ •'•/

B S h o r t - t u b e T e s t s , C a ' < 14

F o r modi f i ed c a v i t a t i o n n u m b e r s be low 10, the d i s c h a r g e d fluid b e ­h a v e s l ike a s i n g l e - p h a s e j e t . A t y p i c a l e x a m p l e i s shown in F i g . 11 for a tube with L / D = 3 . In t h i s p a r t i c u l a r r u n the s y s t e m p o s s e s s e d a modi f ied c a v i t a t i o n n u m b e r of a p p r o x i m a t e l y 8. It i s p o s t u l a t e d tha t any modi f ied c a v i t a t i o n n u m b e r be low 10 wil l c a u s e the d i s c h a r g e fluid ( s u p e r h e a t e d ) to s p r i n g f r ee of the s i d e s of the t u b e . The tube wil l then function a s an o r i ­f i c e . (This i s r e l a t e d to the p h e n o m e n a c a l l e d "vena c o n t r a c t a . " )

F i g . 1 1 . P h o t o g r a p h Showing the D i s c h a r g e d F lu id f r o m a Tube with L / D ~ 3 and C a ' ~ 8

F o r a modi f ied c a v i t a t i o n n u m b e r be tween 10 and 14, u n s t a b l e t r a n s i t i o n a l flow o c c u r s . In th i s r a n g e s i n g l e - and t w o - p h a s e flow o c c u r a l t e r n a t e l y . It i s p o s t u l a t e d h e r e tha t the tube flows full a t the ex i t and

t ha t the c o n t a c t t i m e b e t w e e n wal l and fluid m a y or m a y not be l a r g e enough to c a u s e f l ash ing and, h e n c e , p r o d u c e a t w o - p h a s e flow r e g i m e . It should be m e n t i o n e d h e r e tha t the b e h a v i o r of the fluid for th i s r a n g e of modi f ied c a v i t a t i o n n u m b e r s i s s t r o n g l y dependen t upon how i n v a r i a n t the u p s t r e a m cond i t i ons c a n be m a i n t a i n e d . F i g u r e 12 shows a t yp i ca l p i c t u r e of a run in a r a n g e of C a ' b e t w e e n 10 and 14. Vapor f o r m a t i o n in the l iquid j e t i s d i s ­c e r n i b l e at s o m e i n s t a n c e s .

F i g . 12. P h o t o g r a p h Showing the D i s c h a r g e d F lu id f r o m a Shor t Tube with a Modified C a v i t a ­t ion N u m b e r b e t w e e n 10 and 14

P a s q u a w ) showed in h i s da ta t ha t , for a given p r e s s u r e d i f f e r e n c e , the l a r g e r the L / D r a t i o , the s m a l l e r i s the coeff ic ient of c o n t r a c t i o n . A l s o , he i n d i c a t e d tha t the coef f ic ien t i s i n v e r s e l y p r o p o r t i o n a l to the p r e s s u r e d i f f e r e n c e . T h e s e s t a t e m e n t s w e r e c o n f i r m e d by our f ind ings , a s can be s e e n in F i g . 5.

C. Shor t T u b e s , C a ' > 14

F o r a modi f ied cav i t a t i on n u m b e r g r e a t e r than 14, c r i t i c a l t w o - p h a s e flow c a n be a c h i e v e d if the back p r e s s u r e i s suff ic ient ly low. F i g u r e 13 shows a t y p i c a l p i c t u r e of the d i s c h a r g e d fluid when c r i t i c a l flow o c c u r s . As m e n t i o n e d in the i n t r o d u c t i o n , c o n s i d e r a b l e a m o u n t of w o r k h a s been d e ­vo ted to s t u d i e s of c r i t i c a l flow. Mos t of t h e s e s t u d i e s have b e e n m a d e with L / D r a t i o s g r e a t e r t han 4 0 .

F i g . 13. P h o t o g r a p h Showing the D i s c h a r g e d F l u i d f r o m a Sho r t Tube when C r i t i c a l F low O c c u r s

In t h e s e e a r l i e r t e s t s , a c l o s e a p p r o a c h to t h e r m o d y n a m i c e q u i l i b r i u m w a s b e l i e v e d a c h i e v e d . The F a u s k e mode l , (^ ) b a s e d on e q u i l i b r i u m and i n ­c luding s l ip , p r e d i c t s t h e s e da ta r a t h e r we l l . Th i s m o d e l w a s , t h e r e f o r e , t e s t e d for the c r i t i c a l flow da ta ob ta ined in t h i s w o r k . The da ta p r e s e n t e d in F i g . 5 for L / D > 20 can be p r e d i c t e d with th i s m o d e l within ± 10 p e r ­c e n t . As the L / D r a t i o d e c r e a s e s be low 20, the dev ia t ion be tween th i s s e p a r a t e d flow m o d e l and the ob ta ined da ta b e c o m e s l a r g e r and l a r g e r , the p r e d i c t e d v a l u e s be ing l o w e r than t hose ob ta ined . One con t r ibu t ing r e a s o n to th i s i s tha t the con tac t t ime i s s h o r t e r for s m a l l e r L / D r a t i o so tha t the d e p a r t u r e f r o m p h y s i c a l e q u i l i b r i u m i s l a r g e r . Th i s m e a n s tha t the a c t u a l qua l i ty of the m e t a s t a b l e t w o - p h a s e flow is m u c h s m a l l e r than the qua l i ty c a l c u l a t e d by a s s u m i n g t h e r m o d y n a m i c e q u i l i b r i u m . Since d e p a r t u r e f r o m t h e r m o d y n a m i c e q u i l i b r i u m is v e r y difficult to inc lude in a m a t h e m a t i c a l m o d e l , the da t a w e r e c o r r e l a t e d in a r e s t r i c t i v e m a n n e r a s shown in F i g . 7. It c an , t h e r e f o r e , be conc luded t h a t , for L / D < 20, m e t a s t a b l e t w o - p h a s e c r i t i c a l flow def in i te ly o c c u r s .

VI. CONCLUSIONS

The e x p e r i m e n t c o v e r e d a r a n g e of modi f ied cav i t a t i on n u m b e r s b e ­tween 0 and 500, and of l e n g t h - t o - d i a m e t e r r a t i o b e t w e e n 2 and 55 . Within the l i m i t s of e x p e r i m e n t a l p r e c i s i o n , the fol lowing c o n c l u s i o n s m a y be d r a w n :

1. Saturated or near ly sa tura ted Freon-11 discharged through various ape r tu r e s behaves like a s ingle-phase incompress ib le fluid.

2. Aper tu res with an i r r e g u l a r configuration produce essent ia l ly the same behavior as those of c i r cu la r shapes , except for the t r iangular and W-shaped ones . The t r iangular ape r tu re yields higher , whereas the W-shaped one yields lower , Euler n u m b e r s .

3. The modified cavitation number is a useful c r i t e r ion for de ­termining when s ingle- or two-phase flow reg imes occur in short tubes .

4. The "c r i t i ca l" modified cavitation number is about 14.

5. A simple method to predic t d ischarge ra t e s from short tubes is p resen ted in F igs . 7 and 8.

6. For L/D > 20, the Fauske model can be util ized to predict critical flow r a t e s .

7. For L/D < 20, the exper imenta l flow ra tes a r e g rea te r than predic ted by the Fauske model . The difference i nc rea se s for decreas ing L /D ra t io .

8. The main d iscrepancy between the predict ions of the Fauske model and the data for L /D < 20 is believed to be caused by existing non-equi l ibr ium conditions in the two-phase flow sys tem.

ACKNOWLEDGEMENTS

The authors a r e indebted to the following people:

Matthew P. Gats, who a s s i s t ed in most of the testing and prepared all the photographs;

Pe te r Zaleski and E l m e r Gunchin, who constructed most of the test equipment;

Branko Dokmonovic ' , for his a s s i s t ance in some of the computational and test ing work,

Michael Pe t r ick , for helpful suggestions during the course of this invest igat ion; and to

H. S. Isbin and P . A. Lot tes , for their encouragement and active i n t e r e s t .

BIBLIOGRAPHY

H. K. F a u s k e , C o n t r i b u t i o n to the T h e o r y of T w o - p h a s e , One-c o m p o n e n t C r i t i c a l F l o w , A N L - 6 6 3 3 (Oct 1962).

H. K. F a u s k e , C r i t i c a l T w o - p h a s e , S t e a m - W a t e r F l o w s , 1961 P r o c . H e a t T r a n s f e r and F l u i d M e c h . In s t . , S tanford U n i v e r s i t y P r e s s , S tanford , p. 79.

H. S. I sb in , J . E . Moy, and A. J . R. G r u z , T w o - p h a s e , S t e a m - W a t e r C r i t i c a l F l o w , A . I . C h . E . J o u r n a l , _3j 361-365 (1957).

H. S. I sb in , H. K. F a u s k e , T. G r a c e , and I. G a r c i a , T w o - p h a s e S t e a m -W a t e r P r e s s u r e D r o p s for C r i t i c a l F l o w s , S y m p o s i u m on T w o - p h a s e F l u i d F l o w , F e b r u a r y 7, 1962, In s t i t u t i on of M e c h . Eng . , London, E n g l a n d .

D. W. F a l e t t i , T w o - p h a s e C r i t i c a l F l o w of S t e a m - W a t e r M i x t u r e s , P h . D . T h e s i s , Univ. of W a s h i n g t o n (1959).

F . R. Z a l o u d e k , The Low P r e s s u r e C r i t i c a l D i s c h a r g e of S t e a m -W a t e r M i x t u r e s f r o m P i p e s , H W - 6 8 9 3 4 R E V ( M a r c h 1961).

R. J a m e s , S t e a m - W a t e r C r i t i c a l F l o w t h r o u g h P i p e s , P r e p r i n t of T h e r m o d y n a m i c s and F l u i d M e c h a n i c s Group , The Ins t , of M e c h . E n g . , J u n e , 1962.

J . F . B a i l e y , M e t a s t a b l e F l o w of S a t u r a t e d W a t e r , T r a n s . ASME, 73, 1109-1116 (Nov 1951).

P . F . P a s q u a , M e t a s t a b l e F l o w of F r e o n - 1 2 , R e f r i g e r a t i n g E n g i n e e r i n g , 6 1 , 1084A-1088 , 1131 (Oct 1953).

H. C. S i m p s o n and R. S. S i l v e r , The T h e o r y of O n e - d i m e n s i o n a l , T w o -p h a s e H o m o g e n e o u s N o n - e q u i l i b r i u m F low, S y m p o s i u m on T w o - p h a s e F l u i d F l o w , Ins t , of M e c h . E n g . , F e b . 7, 1962.

H. S. I sb in and G. R. G a v a l a s , T w o - p h a s e F l o w t h r o u g h an A p e r t u r e , P r o c e e d i n g s of the 1962 Hea t T r a n s f e r and F l u i d M e c h a n i c s I n s t i t u t e , pp. 126-139 .

R. L . D a u g h e r t y and A. C. I n g e r s o U , F l u i d M e c h a n i c s , F i f th Ed i t i on , M c G r a w - H i l l Book Co . , New Y o r k (1954), p. 125.