36
is not smooth, it c o n s i s t s of many small a m pl i t u d e waves. The head of the slug is c h a r a c t e r i z e d by a step in the a i r - w a t e r interface, not as the smooth i nterface given in Figure 2.1 . The w a t e r enters the jump at point A in Figure 5.6 as a v i o l e n t jet of fluid, p e n e t r a t i n g
i n t o the slug. W i t h i n th i s j e t of f l u i d are m a n y s m a l l
bubbles. The air in the b u b b l e s in muc h less dense than water. This d e n s i t y d i f f e r e n c e results in some of the b u b b l e s c u r v i n g u p w a r d t o ward the top of the pipe before p e n e t r a t i n g deep into the slug. As the jet p e n e t r a t e s d e e p e r into the slug, its i n t e n s i t y di mi n is he s . T h r o u g h o u t their j o u r ne y into the slug, the b u b b l e s may curve u p wa r d or flow d o w nstream. As they flow farther into the slug, they b e g i n to grow in size due to the c o a l e s c e n c e of s m a l le r bubbles. The b u b b l e s r e a c h i n g point B in Figu re 5.6 f o l lo w one of three p o s s i b l e d i r e ct i o n s . T hey can flow d o w n s t r e a m and e v e n t u a l l y be p a s s e d out the tail. They can also flow u p w ar d and reach po i n t C in Figure 5.6 This point is c a l l e d the s t a g n a t i o n point. Here the b u b b l e s r e m a i n s t a t i o n a r y for an e x t e n d e d p e r i o d of time. The third choice for the b u b b l e flow is b a c k toward the head of the slug. This flow is c o u n t e r c u r r e n t to the b ulk flow and is very i n t e r e s t i n g to note why this flow occurs.
This c o u n t e r c u r r e n t flow results from the v i o l e n t jet of f l ui d at the h e a d of the slug. As the jet flows
37
p ast the f l u id above it, it e x erts a d ra g force on that fluid, and p u l l s the fl u i d al o n g the je t ' s path. The fl u i d above the jet is d i s placed, and the s u r r o u n d i n g fluid must flow o p p o s i t e to the m e a n flow to fill the space o c c u p i e d by the d i s p l a c e d fluid. A c o m p l i c a t e d c i r c u l a t i n g flow r e g io n r esults from this c o u n t e r c u r r e n t flow. This r e g io n Is b o u n d e d by the h ea d of the slug u p s t r e a m and by the s t a g n a t i o n point d o w n s t r e a m . W it h in this large c i r c u l a t i n g region, man y s m a l l e r swirls exist. As s t a t e d above, m any b u b b le s curve u p w a r d before r e a c h i n g p o i nt E in Figu re 5.6 The limit of their u p w a r d m o v e m e n t is the top of the pipe. Man y b u b b l e s are p u l l e d b a c k t o wa r d the front b e f or e r e a c h i n g the top of the pipe. T h e s e b u b b l e s can then be p u l l e d d o w n by the jet, and the many c i r c u l a t i n g flow p a t t e r n s formed. Since most of the b u b b l e s in the s l u g are r e c i r c u l a t e d from the head, to the s t a g n a t i o n point, and b a c k to the h e a d , onl y a small p o r t i o n of the bubbl s are p as s ed do o n s t r e a m .
A n o t h e r i n t e r e s t i n g p h e n o m e n o n o c c u r r i n g w i t h i n the h e a d of the slug I n v o lv e s the b u b b le size. The b u b b le s g r o w in size as they travel into the slug. A f t e r b e in g r e c i r c u l a t e d and p u l l e d in by the jet, the b u b b l e s are b r o k e n up into m an y s mall bubbles. T h e r e f o r e , a typical p a t t e r n of b u b b l e size w o u l d show l a r g e r b u b b l e s near the top of the pipe a n d also d o w ns t r e a m . The smal le r
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b u b b l e s w o u l d be near the front of the slug and a lo n g the jet.
Not all of the r e c i r c u l a t i n g b u b b l e s stay in the l i qu id phase. Some of the b u b b l e s reach the a i r - w a t e r i n t e r f ac e at the front of the slug and travel d own this interface. These b u b b l e s can either be p u l l e d d ow n bv the jet or can b u r s t and release the air w i t h i n them back to the gas p hase in front of the slug.
The re f or e, the b u bble m o v e m e n t in the h ea d of the slug is c h a r a c t e r i z e d by several c i r c u l a t i o n p a tt e r n s and s w i r l i n g motion. Figure 5.7 is a s e r ie s of pictures,
taken wich a camera, of a high sp e e d film w hich
i l l u s t r a t e the p h e n o m e n a d i s c u s s e d above. The Frcude n u m b e r (Fr^) of the a p p r o a c h i n g flow is 2.82, and the value of Q a / Q w is .0058 for a h/D of .3 79 The time in t e rv al b e t w e e n s u c c e s s i v e p i c tu r e s is a p p r o x i m a t e l y
.007 seconds.
No m e n t i o n of the a e r a t i o n m e c h a n i s m has b e en made until now b e c a u s e it is first i m p or t a n t to u n d e r s t a n d the b u b b l e m o v e m e n t and c i r c u l a t i o n p a t t e r n s in the head of the slug. The a e r a t i o n occurs at the h e a d of the slug. The m e c h a n i s m is be d e s c r i b e d as a t u m b l i n g of the interface, s i m i l a r to c r a s h i n g waves. This t u m b l i n g traps air p o ck e t s w i t h i n the slug, from w h e r e the air is b r o k e n up into m a n y small b u b b l e s as the liqu id above the air p o c k e t t um b l e s over the pocket. F i g ur e 5.8 shows
40
47
a s <e r i e s o f p i c t u r e s of the tumbl ing m e c h a n i s m descir i b e d . The Froude numb e r (Fri) of the a p p r o a c h i n g flow is 2. 84, and the
Qa/Qw
*s .0048 for a h/D of .41 . The time inte r v al b e t w e e n s u c c e s s i v e pic tures is about.002 s e c o n d s . T<o d i s t i n g u i s h b e t w e e n an air p o c k e t and w a t e r , 1. 6 erams of Fluorc>ac«ln dye (Aldrich) was d i s s o l v e d in 73 . 5 gal l o n s of w a t e r . The air p o c k e t in the p h o t o g r a p h s is the white r e g i o n that is s u r r o u n d e d by the d yed water.
This t u m b l i n g of the i n t e r f a c e can o c c u r at any p o s i t i o n a l o n g the interface, a l t h o u g h the t u m b l i n g occurs most o f t e n at the front of the slug. The t u m b l i n g can also occur s i m u l t a n e o u s l y at more than one place on the i n t e r f a c e . At the front of the slug the liquid In the i n t e r f a c e r o t a t e s c o u n t e r c l o c k w i s e and air is e n t r a i n e d b e t w e e n this r e g i o n and the jet b e l o w it. This e n t r a i n m e n t is not c o n s t a n t over time. The a m o u n t of air the slug e n t r a i n s v a r i e s about the a v e r a g e value. This r e s u l t was c o n f i r m e d d u r i n g the m e a s u r e m e n t of the a e r a t i o n rate. The r o t a m e t e r r e a d i n g f l u c t u a t e d about the mean. This r e s u l t was also c o n f i r m e d in the h i g h s p e e d films. The b u b b l e s that w e r e p a s s e d d o w n s t r e a m o c c u r r e d in b u n c h e s , n o t as a c o n s t a n t a m o u n t c o n t i n u a l l y over time. T h e r e f o r e , the p o s i t i o n on the i n t e r f a c e w h e r e the t u m b l i n g o c c u r s c h a n g e s w i t h time and the a m o u n t of air e ntrained.
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A series of p i c t u r e s of the tail r e g i o n of a slug are g i v e n in F i g u r e 5.9 w ith a time i n t erval of .014 seconds. The F r o u d e n u m b e r (Fr^) is 6.48 and
Qa/Qw *s
.0269 for a h/D of .242 Th e s e p i c t u r e s and the films show a d e f i n i t e p a t t e r n for the e s c a p e of air from the slug t h r o u g h the tail. A large m a j o r i t y of b u b b l e s that reach the tail r e g i o n are at the top of the pipe, where as more b u b b l e s c o a l e s c e a large air p o c k e t forms. At this time, the tail shape is the same as gi v e n in Figure 2.1 As the air pock e t grows and m o v e s closer to the I n t e rface, the I n t e r f a c e b e g i n s to deform. W h e n the air p o c k e t is s u f f i c i e n t l y close to the Interface, the i n t e r f a c e is broken, r e l e a s i n g the air in the pocket, and a new i n t e r f a c e is formed. This h i g h l y d i s t o r t e d
i n t e r f a c e has a m u c h more g r a d u a l sl o p e as s h o w n in F i g u r e 5.10 T h i s i n t e r f a c e exist o n l y t e m p o r a r i l y . S oon a f t e r its formation, it is r e p l a c e d by the p h y s i c a l m o d e l interface, a n d the p r o c e s s of air p o c k e t f o r m a t i o n and i n t e r f a c e b r e a k i n g is repeated.
A