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m i l it il i m mi;'-I H 1 t í ÍS» o> BIBLIOTHEEK TU Delft p 1662 5255ISBN 90 6231 088 5 soft-bound edition ISBN 90 6231 089 3 hard-bound edition
WATER AERATION WITH
PLUNGING JETS
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ter verkrijging van de graad van doctor
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T e c h n i s c h e H o g e s c h o o l Delft, op gezag
van de rector magnificus prof. ir. B.P.Th.
V e l t m a n , voor een c o m m i s s i e a a n g e w e z e n
door het college van d e k a n e n te verdedigen
op w o e n s d a g 10 juni 1 981 te 1 6.00 uur
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1 9 8 1Dit proefschrift is goedgekeurd
door de promotor:
PROF. J . M . S M I T H , M . S C , C. E N G .
R A P P O R T / R e p o r t
Vakgroep Transportverschijnselen
A f d e l i n g der T e c h n i s c h e N a t u u r k u n d e / D e p a r t m e n t of Physics
T e c h n i s c h e Hogeschool Delft/Delft University of Technology
Dit proefschrift kwam tot stand dank zij de medewerking van vele •personen.
Op de eerste plaats denk ik daarbij aan alle studenten, die hun afstudeerwerk,
kandidaatswerk en praktika in het kader van het onderzoek hebben gedaan. Zij
wisten mij met name te overtuigen van de juistheid van hun uitgebreide
meet-resultaten, die in dit onderzoek naar voren komen.
Mijn begeleider, prof. J.M. Smith en mijn kollega-onderzoekers, zijn altijd
bereid geweest om mijn werk met de nodige kritiese kanttekeningen te
onder-steunen. Hierbij denk ik ook aan alle mensen, die vanuit andere instellingen
en bedrijven hun belangstelling toonden en adviezen gaven.
Mijn kollega's op het Laboratorium voor Fysische Technologie: technici,
teke-naars, elektronici, sekretaresses, stokers en conciërges, hebben ieder met hun
eigen vaardigheden mijn werk ondersteund.
Tenslotte wil ik speciaal die mensen bedanken, die de laatste maanden zeer
nauw betrokken waren bij het tot stand komen van het proefschrift zelf.
Aan allen dank.
Jan,
C O N T E N T S
SYMBOLS 8 SUMMARY 13 SAMENVATTING 15 CHAPTER 1 AIM AND SCOPE 19
1.1 I n t r o d u c t i o n 19 1.2 A e r a t i o n 20 1.3 The p l u n g i n g j e t a e r a t o r 24
1.4 S t r u c t u r e o f t h e t h e s i s 26 CHAPTER 2 AIR ENTRAPMENT 29
2.1 I n t r o d u c t i o n 29 2.2 L i t e r a t u r e r e v i e w 30 2 . 2 . 1 t h e minimum e n t r a i n m e n t v e l o c i t y 30 2 . 2 . 2 t h e mechanism o f a i r e n t r a i n m e n t by a t u r b u l e n t j e t 31 2 . 2 . 3 t h e i n f l u e n c e o f n o z z l e d e s i g n on t h e e n t r a i n m e n t r a t i o 33 2 . 2 . 4 e x p e r i m e n t a l r e s u l t s 37 2 . 3 E x p e r i m e n t s 43 2 . 3 . 1 a p p a r a t u s and m e a s u r i n g method 44 2 . 3 . 2 r e s u l t s 47 2 . 3 . 2 . 1 n o z z l e d e s i g n and a i r e n t r a i n m e n t 47 2 . 3 . 2 . 2 e n t r a i n m e n t by l a r g e c o n i c a l j e t s 49 2.4 C o n c l u s i o n s 53
CHAPTER 3 HYDRODYNAMICS 55 3.1 I n t r o d u c t i o n 55 3.2 T h e o r y 56 3 . 2 . 1 g e n e r a l c o n c e p t and c o n s i d e r a t i o n s 56 3 . 2 . 2 t h e momentum b a l a n c e 59 3 . 2 . 3 w a t e r e n t r a i n m e n t 61 3 . 2 . 4 t h e gas b a l a n c e 62 3 . 2 . 5 i n i t i a l c o n d i t i o n s 65 3 . 2 . 6 method o f s o l u t i o n 68 3 . 2 . 7 n u m e r i c a l c a l c u l a t i o n s 68 3.3 E x p e r i m e n t s 71 3 . 3 . 1 e x p e r i m e n t a l programme 71 3 . 3 . 2 e x p e r i m e n t a l method and a p p a r a t u s 72 3 . 3 . 2 . 1 a p p a r a t u s 72 3 . 3 . 2 . 2 t h e gas f r a c t i o n d e t e r m i n a t i o n 73 3 . 3 . 2 . 3 t h e method o f m e a s u r i n g v e l o c i t y 77 3 . 3 . 3 r e s u l t s 79 3 . 3 . 3 . 1 b u b b l e v e l o c i t i e s i n t h e cone 79 3 . 3 . 3 . 2 v e l o c i t i e s o f r i s i n g b u b b l e s 81 3 . 3 . 3 . 3 t h e gas f r a c t i o n i n t h e cone _ 82 3 . 3 . 3 . 4 t h e gas f r a c t i o n o f t h e r i s i n g b u b b l e s 85 3 . 3 . 4 e s t i m a t i o n o f t h e model p a r a m e t e r s 87 3.4 C o n c l u s i o n s 93 CHAPTER 4 OXYGEN TRANSFER 95
4.1 I n t r o d u c t i o n 95 4 . 2 T h e o r e t i c a l c o n s i d e r a t i o n s 97 4 . 2 . 1 t h e mass t r a n s f e r c o e f f i c i e n t 97 4 . 2 . 2 t h e i n t e r f a c i a l a r e a 100 4 . 2 . 3 oxygen t r a n s f e r f r o m d e s c e n d i n g and r i s i n g b u b b l e s 103 4 . 3 E x p e r i m e n t s 106 4 . 3 . 1 i n t r o d u c t i o n 106 4 . 3 . 2 e x p e r i m e n t a l p r o c e d u r e 110
4 . 3 . 2 . 1 dynamic m e a s u r i n g method and a p p a r a t u s 110 4 . 3 . 2 . 2 s t e a d y s t a t e m e a s u r i n g method and a p p a r a t u s 114
4 . 3 . 3 r e s u l t s 116 4 . 3 . 3 . 1 s m a l l n o z z l e d i a m e t e r s 116
4 . 3 . 3 . 2 l a r g e n o z z l e d i a m e t e r s 122
4 . 3 . 4 t h e o x y g e n a t i o n e f f i c i e n c y 4 . 4 C o n c l u s i o n s 124 130 CHAPTER 5 CONTAMINANTS 131 5.1 I n t r o d u c t i o n 131 5.2 T h e o r e t i c a l c o n s i d e r a t i o n s 132 5 . 2 . 1 c o n t a m i n a n t s and mass t r a n s f e r 132 5 . 2 . 2 c o n t a m i n a n t s and c o a l e s c e n c e 133 5 . 2 . 3 c o n t a m i n a n t s and t h e mass t r a n s f e r c o e f f i c i e n t 134 5 . 2 . 4 s y s t e m i n f l u e n c e s 136 5.3 E x p e r i m e n t s 138 5 . 3 . 1 i n t r o d u c t i o n 138 5 . 3 . 2 e x p e r i m e n t a l r e s u l t s 138 5.4 C o n c l u s i o n s 147 CHAPTER 6 FULL SCALE DESIGN AND OPERATION 149
6.1 The p l u n g i n g j e t a e r a t o r i n a w a s t e w a t e r t r e a t m e n t p l a n t 149
6 . 2 J e t a e r a t i o n a p p l i e d i n a f e r m e n t o r 153
REFERENCES 157 APPENDICES 162
S Y M B O L S
a s p e c i f i c a r e a m a j e t s e p a r a t i o n d i s t a n c e m 2 A i n t e r f a c i a l a r e a m 2 A " " i n b i p h a s i c cone m c 2 A " " o f r i s i n g b u b b l e s m r A " " f o r c o n t a m i n a t e d s y s t e m s n f z 2 AQ " " f o r u n c o n t a m i n a t e d s y s t e m s m b w i d t h o f submerged j e t m c oxygen c o n c e n t r a t i o n kgm 3-3
c " " i n gas phase kgm9 .3
C-, " " i n l i q u i d phase kg m -3 c " " i n a i r kg m 9 . T _3 c " e q u i l i b r i u m c o n c e n t r a t i o n kgm e-3
c£ " s a t u r a t i o n c o n c e n t r a t i o n kgm Gjj| s a l t c o n c e n t r a t i o n mol 1 c c o n c e n t r a t i o n o f c o n t a m i n a n t ppm •1 z cQ i n i t i a l c o n c e n t r a t i o n kgm C c o n s t a n t -3 d w i d t h o f b i p h a s i c cone m dc mean w i d t h o f b i p h a s i c cone m dn n o z z l e d i a m e t e r m d j j e t d i a m e t e r a t i m p a c t p o i n t m dg w i d e n i n g o f t h e j e t by a i r e n t r a i n m e n t m d^ b u b b l e d i a m e t e r m d p a r t i c l e d i a m e t e r m 8U • n ng D r i n g d i a m e t e r d i f f u s i o n c o e f f i c i e n t m 2 -1 m s f F ( t ) F r g » gz H , HC I k k K' kl klA1 0 ° C Ln gas f r a c t i o n o f r e c i r c u l a t i n g b u b b l e s c r o s s c o r r e l a t i o n f u n c t i o n F r o u d e number: v ^ / g dn g r a v i t y c o n s t a n t b i p h a s i c cone d e p t h i o n i c s t r e n g t h oxygen p r o b e c o n s t a n t model p a r a m e t e r ( e q u a t i o n 3.5) model p a r a m e t e r ( e q u a t i o n 3 . 1 3 ) mass t r a n s f e r c o e f f i c i e n t a e r a t i o n f a c t o r a e r a t i o n f a c t o r a t 10°C b r e a k up l e n g t h j e t l e n g t h n o z z l e l e n g t h
m V
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1 m m mc O.E. P P. in APgem AP A P f r e q u i l i b r i u m c o n s t a n t r e l a t i v e i n c r e a s e o f k-j A i n c o n t a m i n a t e d systems l i q u i d f l o w r a t e i n t h e b i p h a s i c cone o x y g e n a t i o n e f f i c i e n c y power o f t h e pump power o f t h e p l u n g i n g j e t measured p r e s s u r e d r o p o v e r t h e n o z z l e p r e s s u r e d r o p o v e r t h e n o z z l e p r e s s u r e d r o p due t o f r i c t i o n l o s s e s kg s •1 kg02/kWh 2 -3 kg m s u 2 -3 kg m s • -1 -2 kg m s kg m "1 s"2 kg m "1 s"2 r r R Re s s Se t t u r a d i a l c o o r d i n a t e c o r r e l a t i o n c o e f f i c i e n t e n t r a i n m e n t r a t i o : (j>a/<t>w R e y n o l d s number: ov dn/n. d i s t a n c e s u r f a c e r e n e w a l f r e q u e n c y S c h m i d t number: n / p D — t i m e s l i q u i d r e s i d e n c e t i m e i n t h e r e c i r c u l a t i n g s y s t e m s-1
t s u r f a c e renewal t i m e T m e a s u r i n g t i m e u r a d i a l v e l o c i t y
UQ gas f r a c t i o n probe v o l t a g e
TJ0 mean gas f r a c t i o n probe v o l t a g e
gas f r a c t i o n probe v o l t a g e i n w a t e r oxygen p r o b e v o l t a g e i n i t i a l oxygen p r o b e v o l t a g e oxygen p r o b e v o l t a g e i n s a t u r a t e d w a t e r AU s t e p i n oxygen probe v o l t a g e max c0 s s ms V V V V V V V v v e l o c i t y ms vb b u b b l e v e l o c i t y ms vg gas v e l o c i t y ms Vj j e t v e l o c i t y a t t h e i m p a c t p o i n t ms vn j e t v e l o c i t y a t t h e n o z z l e ms vr e l r e l a t i v e v e l o c i t y ms vo model p a r a m e t e r ( e q u a t i o n 3.4) ms vg volume o f e n t r a i n e d gas m3 vi volume o f l i q u i d m 3 vt volume o f l i q u i d i n t h e t a n k m 3 VP volume o f l i q u i d i n t h e r e c i r c u l a t i n g s y s t e m m3 w v e r t i c a l l i q u i d v e l o c i t y i n t h e cone ms m v e r t i c a l l i q u i d v e l o c i t y a t t h e j e t a x i s m s We Weber number: p V p dn/ a
-x ( t ) v e l o c i t y p r o b e s i g n a l V y ( t ) s h i f t e d v e l o c i t y p r o b e s i g n a l V z v e r t i c a l c o o r d i n a t e m a gas f r a c t i o n i n t h e cone_
am gas f r a c t i o n a t t h e j e t a x i s -as gas f r a c t i o n a t t h e o r i g i n a l j e t s u r f a c e -6 a i r b o u n d a r y l a y e r t h i c k n e s s m 6 0 j e t d i s t u r b a n c e a t n o z z l e e x i t m e power d i s s i p a t i o n p r o u n i t mass 2 m a i r f l o w r a t e 3 m gas f l o w r a t e m3 1 0<t>-| l i q u i d f l o w r a t e d> w a t e r f l o w r a t e Tw * gas f l o w r a t e t h r o u g h t h e cone <f>n oxygen f l o w r a t e ri v i s c o s i t y kg m 1 s" n r a t i o between v and w — o m p d e n s i t y kg m" p d e n s i t y o f a i r kg m o P d e n s i t y o f w a t e r kgm a s u r f a c e t e n s i o n kg s o mean s t a n d a r d d e v i a t i o n — Tq s h i f t e d t i m e o f v e l o c i t y p r o b e s i g n a l s s xb mean r e s i d e n c e t i m e o f t h e b u b b l e s s xk mean r e s i d e n c e t i m e o f t h e b u b b l e s i n t h e cone s m s . 3 s "1
• V
1 kg s"S U M M A R Y
A p p l i c a t i o n o f p l u n g i n g w a t e r j e t s t o l a r g e s c a l e a e r a t i o n p r o c e s s e s i s r e l a t i v e l y r e c e n t and h i t h e r t o s c i e n t i f i c i n t e r e s t has been l i m i t e d . T h i s r e s e a r c h d e a l s w i t h r e l e v a n t p h y s i c a l a s p e c t s o f t h e p l u n g i n g j e t . C h a p t e r 2 c o n s i d e r s t h e mechanism o f t h e a i r e n t r a i n m e n t by t h e p l u n g i n g j e t . S t u d i e s r e p o r t e d i n t h e l i t e r a t u r e c o n c e r n i n g s m a l l d i a m e t e r j e t s (d < 1 cm) show l a r g e d i f f e r e n c e s i n t h e measured a i r e n t r a i n m e n t volume r a t e s , even f o r s i m i l a r j e t d i a m e t e r s and j e t v e l o c i t i e s . T h i s has been e x p l a i n e d by g e o m e t r i c a l d i f f e r e n c e s between t h e v a r i o u s n o z z l e s u s e d , w h i c h have an i m p o r t a n t i n f l u e n c e on t h e d e v e l o p m e n t o f t h e j e t s u r f a c e r o u g h n e s s and t h e a c c o m p a n y i n g e n t r a i n e d a i r volume r a t e .
E n t r a i n m e n t measurements made w i t h v a r i o u s n o z z l e t y p e s w i t h d i a m e t e r s up t o 10 cm, w h i c h can be r e g a r d e d o f i n t e r e s t f o r p r a c t i c a l p u r p o s e s , a r e r e p o r t e d . The a i r e n t r a i n m e n t volume r a t e i s e x p r e s s e d i n terms o f t h e j e t p a r a m e t e r s by a s i m p l e e m p i r i c a l c o r r e l a t i o n f o r n o z z l e s w i t h a c o n i c a l e n t r y . C h a p t e r 3 d e a l s w i t h a h y d r o d y n a m i c model i n w h i c h t h e p l u n g i n g j e t ' i s c o n t i -nued below t h e w a t e r s u r f a c e i n a c o n i c a l f o r m . The e n t r a i n e d a i r i n t h i s b i p h a s i c cone i s b r o k e n up i n t o f i n e b u b b l e s . L a r g e r b u b b l e s a r e formed by c o a l e s c e n c e i n t h e l o w e r p a r t o f t h e c o n e . In t h i s r e g i o n t h e buoyancy f o r c e s overcome t h e momentum o f t h e j e t and b u b b l e s e s c a p e s i d e w a y s f r o m t h e cone and r i s e t o t h e w a t e r s u r f a c e .
T h i s model c o n t a i n s f o u r p a r a m e t e r s w h i c h d e s c r i b e : (1) t h e w a t e r e n t r a i n m e n t by t h e j e t , (2) t h e gas f r a c t i o n o f t h e r e c i r c u l a t i n g f l u i d , (3) t h e l i q u i d v e l o c i t y a t w h i c h b u b b l e s e s c a p e f r o m t h e cone and (4) t h e r a t i o between t h e w i d t h o f t h e d o w n f l o w i n g l i q u i d v e l o c i t y and gas f r a c t i o n p r o f i l e s .
The m a g n i t u d e o f t h e p a r a m e t e r s e s t i m a t e d f r o m measurements o f t h e p e n e t r a t i o n depth o f t h e b u b b l e s , b u b b l e v e l o c i t y and gas f r a c t i o n p r o f i l e s , a g r e e w i t h such v a l u e s as a r e f o u n d i n t h e l i t e r a t u r e .
The model p r e s e n t e d h e r e i s more r e s t r i c t e d as a means o f p r e d i c t i o n f o r t h e r i s e and r e s i d e n c e t i m e o f t h e b u b b l e s i n t h e c o n e . P o s s i b l e i n t e r a c t i o n between t h e r i s i n g b u b b l e s and t h e cone i s n o t c o n s i d e r e d i n t h e model and a b e t t e r d e s c r i p t i o n o f t h e e s c a p e o f b u b b l e s from t h e cone i s a l s o n e c e s s a r y . The u n c e r t a i n t y o f t h e r i g h t m a g n i t u d e o f t h e e n t r a i n e d volume a i r r a t e ( C h a p t e r 2 ) , w h i c h i s an i m p o r t a n t i n i t i a l c o n d i t i o n i n t h e m o d e l , r e s t r i c t s a l s o t h e u t i l i t y o f t h e h y d r o d y n a m i c m o d e l . C h a p t e r 4 d e a l s w i t h t h e oxygen t r a n s f e r from t h e a i r b u b b l e s i n t o t h e w a t e r o f t h e p l u n g i n g j e t a e r a t o r . E x p e r i m e n t s show t h a t t h e c o n t r i b u t i o n s t o t h e o v e r a l l mass t r a n s f e r o f d e -s c e n d i n g b u b b l e -s and o f t h e r i -s i n g b u b b l e -s a r e o f t h e -same o r d e r o f m a g n i t u d e . A l a r g e number o f measurements a r e made w h i c h d e t e r m i n e t h e i n f l u e n c e o f v e l -o c i t y , d i a m e t e r and l e n g t h -o f t h e j e t , t h e n -o z z l e g e -o m e t r y , t h e a n g l e -o f i m p a c t and t h e e f f e c t o f m u l t i p l e j e t s on t h e a e r a t i o n f a c t o r , k , A .
The a e r a t i o n f a c t o r can be e x p r e s s e d i n terms o f t h e e n t r a i n e d volume a i r r a t e , b u b b l e s i z e and p e n e t r a t i o n d e p t h o f t h e b u b b l e s . T h i s e x p l a i n s why l a r g e r k-jA v a l u e s and d i f f e r e n t k-jA c o r r e l a t i o n s w i t h r e s p e c t t o j e t p a r a m e t e r s a p p l y t o d i s t u r b e d j e t s .
The e f f i c i e n c y o f t h e a e r a t i o n p r o c e s s d e c r e a s e s w i t h i n c r e a s i n g j e t v e l o c i t y and d i a m e t e r b u t i s n o t v e r y s e n s i t i v e t o t h e n o z z l e geometry and t h e j e t l e n g t h : t h e e x t r a power needed t o d i s t u r b t h e j e t s u r f a c e o r t o r e a c h a g r e a t e r d i s c h a r g e head i s compensated by an i n c r e a s e i n t h e mass t r a n s f e r r a t e . F o r p r a c t i c a l a e r a t i o n p u r p o s e s d i s t u r b e d j e t s a r e t o be recommended.
C h a p t e r 5 d e a l s w i t h t h e i n f l u e n c e o f c o n t a m i n a n t s on t h e a e r a t i o n c o n s t a n t . The i n f l u e n c e o f s a l t s , a l c o h o l s , soap and o i l on t h e k-jA v a l u e i s d e t e r m i n e d by e x p e r i m e n t . The r e s u l t s c o n f i r m t h a t c o n t a m i n a n t s n o t a f f e c t t h e k-jA v a l u e a d v e r s e l y .
C h a p t e r 6 d e a l s w i t h two examples o f p r a c t i c a l a p p l i c a t i o n o f t h e p l u n g i n g w a t e r j e t s : an a e r a t i o n b a s i n f o r t h e t r e a t m e n t o f w a s t e w a t e r and a f e r m e n t o r f o r t h e p r o d u c t i o n o f y e a s t .
These examples c o n f i r m t h a t p l u n g i n g j e t a e r a t o r s can a c h i e v e mass t r a n s f e r e f f i c i e n c i e s up t o 2 kg02/kWh u s i n g a i r i n c o m m e r c i a l s c a l e a p p l i c a t i o n s .
SAMENVATTING
De t o e p a s s i n g van p l o n z e n d e w a t e r s t r a l e n i n b e l u c h t i n g s p r o c e s s e n v i n d t pas s i n d s e n k e l e j a r e n op een g r o t e r e s c h a a l p l a a t s . e n de w e t e n s c h a p p e l i j k e b e -l a n g s t e -l -l i n g v o o r deze b e -l u c h t i n g s m e t h o d e i s t o t nu t o e dan ook b e t r e k k e -l i j k k l e i n g e w e e s t .
D i t o n d e r z o e k b e h a n d e l t e n i g e b e l a n g r i j k e f y s i s c h e a s p e k t e n van de p l o n z e n d e w a t e r s t r a a l .
H o o f d s t u k 2 b e h a n d e l t h e t mechanisme van de luchtmeename d o o r de p l o n z e n d e s t r a a l . U i t de l i t e r a t u u r b l i j k t , d a t v o o r k l e i n e d i a m e t e r s t r a l e n (d < 1 c m ) , g r o t e v e r s c h i l l e n gemeten z i j n i n de m e e g e s l e u r d e l u c h t d e b i e t e n , hoewel d e z e l f -de s t r a a l d i a m e t e r s en s t r a a l s n e l he-den wer-den g e b r u i k t . D i t i s v e r k l a a r d d o o r v e r s c h i l l e n i n de g e b r u i k t e s p u i t s t u k g e o m e t r i e , d i e een b e l a n g r i j k e i n v l o e d h e e f t op de o n t w i k k e l i n g van de o p p e r v l a k t e r u w h e i d van de s t r a a l en daarmee op h e t meegenomen l u c h t d e b i e t .
De m e e g e s l e u r d e l u c h t d e b i e t e n z i j n gemeten v o o r d i v e r s e t y p e s s p u i t s t u k k e n met d i a m e t e r s t o t 10 c m , d i e van b e l a n g g e a c h t worden v o o r p r a k t i s c h e t o e p a s s i n g e n . V o o r s p u i t s t u k k e n met een c o n i s c h e i n l o o p i s h e t m e e g e s l e u r d e l u c h t d e b i e t u i t -g e d r u k t i n de s t r a a l p a r a m e t e r s d . m . v . een e e n v o u d i -g e e m p i r i s c h e k o r r e l a t i e . H o o f d s t u k 3 b e h a n d e l t een model van de h y d r o d y n a m i c a van de p l o n z e n d e s t r a a l , z o a l s d i e z i c h k o n u s v o r m i g o n d e r w a t e r v o o r t z e t . In d e z e konus i s de meege-s l e u r d e l u c h t o p g e b r o k e n i n k l e i n e b e l l e n , d i e c o a l e meege-s c e r e n i n h e t o n d e r meege-s t e d e e l van de k o n u s . Waar de o p w a a r t s e k r a c h t van de b e l l e n de i m p u l s van de s t r a a l o v e r w i n t , o n t s n a p p e n b e l l e n z i j w a a r t s u i t de konus en s t i j g e n weer op n a a r h e t w a t e r o p p e r v l a k .
d o o r de s t r a a l , (2) de g a s f r a k t i e van de r e c i r o u l e r e n d e v l o e i s t o f , (3) de v l o e i s t o f s n e l h e i d , w a a r b i j b e l l e n u i t de konus o n t s t a p p e n en (4) de v e r h o u d i n g t u s s e n de b r e e d t e van de w a t e r s n e l h e i d s p r o f i e l e n en de g a s f r a k t i e p r o f i e l e n . U i t m e t i n g e n van de i n d r i n g d i e p t e van de b e l l e n , b e l s n e l h e i d en g a s f r a k t i e p r o f i e l e n i s de g r o o t t e van de m o d e l p a r a m e t e r s g e s c h a t . Deze z i j n i n o v e r e e n s t e m -ming met s o o r t g e l i j k e g r o o t h e d e n u i t de l i t e r a t u u r . In de h i e r g e p r e s e n t e e r d e vorm i s h e t model s l e c h t s b e p e r k t b r u i k b a a r v o o r een a d e q u a t e v o o r s p e l l i n g van de v e r b l i j f t i j d en de g r o o t t e van de b e l l e n i n de k o n u s : de m o g e l i j k e i n t e r a k t i e van de o p s t i j g e n d e b e l l e n k o l o m en de konus i s n i e t i n het model opgenomen en ook een b e t e r e b e s c h r i j v i n g van h e t o n t s n a p -p i n g s m e c h a n i s m e van b e l l e n u i t de konus b l i j k t n o o d z a k e l i j k t e z i j n .
Het m e e g e s l e u r d e l u c h t d e b i e t i s een b e l a n g r i j k e r a n d v o o r w a a r d e i n h e t m o d e l . De o n z e k e r h e i d o v e r de j u i s t e g r o o t t e van h e t l u c h t d e b i e t , z o a l s i n h o o f d s t u k 2 b e s p r o k e n , vormt ook een b e l a n g r i j k e b e p e r k i n g v o o r de b r u i k b a a r h e i d van h e t h y d r o d y n a m i s c h e m o d e l .
H o o f d s t u k 4 b e h a n d e l t de z u u r s t o f o v e r d r a c h t van de l u c h t b e l l e n n a a r h e t w a t e r i n de p l o n z e n d e w a t e r s t r a a l b e l u c h t e r .
U i t e x p e r i m e n t e n b l i j k t , d a t de b i j d r a g e n t o t de t o t a l e s t o f o v e r d r a c h t van de d a l e n d e b e l l e n i n de konus en van de s t i j g e n d e b e l l e n van g e l i j k e o r d e van g r o o t t e z i j n . Een g r o o t a a n t a l s t o f o v e r d r a c h t s m e t i n g e n werd gedaan om de i n v l o e d van de s n e l h e i d , d i a m e t e r en l e n g t e van de s t r a a l , de s p u i t s t u k g e o m e t r i e , de i n s p u i t h o e k en het e f f e k t b i j meerdere s t r a l e n op de b e l u c h t i n g s -k o n s t a n t e , -k-|A, t e b e p a l e n . De b e l u c h t i n g s -k o n s t a n t e -kan u i t g e d r u -k t worden i n termen van het m e e g e s l e u r d e l u c h t d e b i e t , de b e l g r o o t t e en de i n d r i n g d i e p t e van de b e l l e n . De gemeten g r o t e r e k-|A waarden b i j g e b r u i k van v e r s t o o r d e s t r a l e w o r d t hiermee v e r k l a a r d en t e v e n s de v e r s c h i l l e n i n de k-jA a f h a n k e l i j k h e i d van de s t r a a l p a r a m e t e r s b i j g e b r u i k van v e r s c h i l l e n d e s p u i t s t u k geometrieën. De e f f i c i ë n t i e van h e t b e l u c h t i n g s p r o c e s d a a l t met toenemende s t r a a l s n e l h e i d en d i a m e t e r , maar i s n i e t e r g g e v o e l i g v o o r de s p u i t s t u k g e o m e t r i e en de s t r a a l l e n g t e : h e t e x t r a v e r m o g e n , n o d i g v o o r v e r s t o r i n g van de s t r a a l o f een g r o t e r e o p v o e r h o o g t e w o r d t gekompenseerd d o o r een toename i n de s t o f o v e r d r a c h t -s n e l h e i d . Voor p r a k t i -s c h e b e l u c h t i n g -s d o e l e i n d e n v e r d i e n t h e t a a n b e v e l i n g met v e r s t o o r d e s t r a l e n t e b e l u c h t e n . H o o f d s t u k 5 b e h a n d e l t de i n v l o e d van v e r o n t r e i n i g i n g e n op de b e l u c h t i n g s -k o n s t a n t e . E x p e r i m e n t e e l i s de i n v l o e d van z o u t e n , a l c o h o l e n , z e e p en o l i e op de k,A waarde b e p a a l d e . De r e s u l t a t e n b e v e s t i g e n , d a t v o o r de p l o n z e n d e w a t e r -1 6
s t r a a l b e l u c h t e r v e r o n t r e i n i g i n g e n geen n e g a t i e v e i n v l o e d hebben op de b e l u c h -t i n g s k o n s -t a n -t e .
H o o f d s t u k 6 t e n s l o t t e b e h a n d e l t de p r a k t i s c h e t o e p a s s i n g van de p l o n z e n d e w a t e r s t r a a l aan de hand van twee v o o r b e e l d e n : een b e l u c h t i n g s b a s s i n v o o r a f v a l w a t e r en een f e r m e n t o r v o o r g i s t p r o d u k t e . Z i j b e v e s t i g e n , d a t h e t g e b r u i k van v e r s t o o r d e s t r a l e n t o t een b e t e r e z u u r s t o f o v e r d r a c h t s n e l h e i d l e i d t . Een e f f i c i ë n t i e van rond de 2 kg02/kWh b r u t o e n e r g i e kan b e r e i k t w o r d e n .
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1 . 1 . INTRODUCTION
In r e c e n t y e a r s t h e r e has been an i n c r e a s i n g i n t e r e s t i n p r a c t i c a l a p p l i c a t i o n s o f p l u n g i n g w a t e r j e t s as a e r a t i o n d e v i c e s .
The most a p p o s i t e example i s p e r h a p s t h e w a t e r j e t a e r a t i o n s y s t e m , a p p l i e d i n t h e e f f l u e n t t r e a t m e n t p l a n t o f D . S . M . (The N e t h e r l a n d s ) w i t h a p u r i f i c a t i o n c a p a c i t y e q u i v a l e n t t o t h a t needed by a p o p u l a t i o n o f 1 m i l l i o n . Such l a r g e s c a l e a p p l i c a t i o n s r e q u i r e d e t a i l e d knowlegde o f t h e p r o c e s s f o r good d e s i g n r u l e s and r e l i a b l e p r o c e s s c o n t r o l . S y s t e m a t i c r e s e a r c h i n t o t h e v a r i o u s a s p e c t s o f t h e w o r k i n g o f w a t e r j e t a e r a t o r s was d e s i r e d i n o r d e r t o s u p p o r t t h e s e a p p l i -c a t i o n s .
T h e r e has been an i n t e r e s t i n t h e mechanism o f a i r e n t r a i n m e n t by p l u n g i n g j e t s , b u t more u s u a l l y i n a r e v e r s e d s e n s e . In some i n d u s t r i a l p r o c e s s e s i n w h i c h l i q u i d j e t s p l u n g e i n t o a r e c e i v i n g l i q u i d b a t h , a i r e n t r a i n m e n t by t h e j e t i s u n d e s i r e d and has t o be p r e v e n t e d . F o r example i n t h e f i l l i n g o f b o t t l e s , p a r -t i c u l a r l y w i -t h v i s c o u s l i q u i d s , o r i n -t h e p o u r i n g o f m o l -t e n s -t e e l , when -t h e c a p t u r e o f a i r i n t h e b u l k f l u i d l e a d s t o t r o u b l e s o m e i n c l u s i o n s i n t h e c a s t p r o d u c t . In t h e l i t e r a t u r e a b o u t p l u n g i n g j e t s we see t h a t t h e e a r l y a u t h o r s r e s t r i c t e d t h e i r r e s e a r c h t o t h e p r o c e s s o f a i r e n t r a i n m e n t and t h e way i n w h i c h t h e j e t p a r a m e t e r s i n f l u e n c e t h i s . In l a t e r p u b l i c a t i o n s , a p p l i c a t i o n as an a e r a t i o n d e v i c e comes more t o t h e f o r e and as a r e s u l t t h e r e i s more i n t e r e s t i n t h e a s p e c t s o f mass t r a n s f e r and m i x i n g i n t h e r e c e i v i n g l i q u i d b a t h . In t h i s t h e s i s t h e s e l a t t e r a s p e c t s w i l l be e m p h a s i z e d ; t h e a i r e n t r a i n m e n t i s p a r t o f t h e r e s e a r c h i n so f a r as i s r e l
-e v a n t t o t h -e mass t r a n s f -e r .
B e f o r e g i v i n g t h e s c o p e o f t h e t h e s i s i n more d e t a i l i n s e c t i o n 1 . 4 . a r e v i e w o f v a r i o u s a e r a t i o n s y s t e m s used i n w a t e r p u r i f i c a t i o n p l a n t s w i l l f i r s t be p r e s e n t e d .
1 . 2 . AERATION
One o f t h e common methods o f w a s t e w a t e r p u r i f i c a t i o n i s t h e o x i d a t i o n d i t c h . The w a t e r i n t h e d i t c h c o n t a i n s m i c r o - o r g a n i s m s , t h e s o - c a l l e d a c t i v e s l u d g e , w h i c h p r o v i d e s t h e c l e a n i n g a c t i o n . F o r t h i s b i o c h e m i c a l p r o c e s s oxygen i s r e -q u i r e d w h i c h i s commonly s u p p l i e d by an a e r a t i o n d e v i c e . In g e n e r a l t h e f o l l o w i n g r e q u i r e m e n t s s h o u l d be met by t h e a e r a t i o n d e v i c e : 1. A h i g h o x y g e n a t i o n e f f i c i e n c y ( O . E . ) w h i c h means t h a t t h e o x y g e n , needed f o r t h e p u r i f i c a t i o n p r o c e s s , has t o be b r o u g h t i n t o t h e w a t e r w i t h t h e minimum p o s s i b l e e n e r g y c o n s u m p t i o n . 2. Good m i x i n g o f t h e w a s t e w a t e r , a c t i v e s l u d g e and a e r a t e d w a t e r , u s u a l l y c o u p l e d w i t h a need t o e s t a b l i s h some minimum c i r c u l a t i o n r a t e i n t h e a e r -a t i o n b -a s i n . 3. S i m p l e , r e l i a b l e and f l e x i b l e o p e r a t i o n . 4 . Low c a p i t a l c o s t s . 5. No d e l e t e r e o u s e f f e c t s on t h e l o c a l e n v i r o n m e n t , e s p e c i a l l y w i t h r e g a r d t o n o i s e , s p r a y , o d o u r , l a n d s u r f a c e use and w a s t e s l u d g e d i s p o s a l . Some o f t h e more u s u a l a e r a t i o n d e v i c e s w i l l be c o n s i d e r e d i n t e r m s o f t h e f i r s t 3 p o i n t s m e n t i o n e d a b o v e .
The o l d e s t and s t i l l most common s y s t e m s a r e t h e s o - c a l l e d b u b b l e a e r a t o r s . Compressed a i r i s blown d i r e c t l y i n t o t h e w a t e r t h r o u g h some d i s p e r s i o n o r s p a r g i n g s y s t e m .
In p r a c t i c e many d i f f e r e n t v e r s i o n s o f t h i s s y s t e m a r e used and new d e s i g n s a r e s t i l l b e i n g d e v e l o p e d .
The more t r a d i t i o n a l s y s t e m s , as shown i n f i g . 1.1 and 1.2 have t h e d i s a d v a n -t a g e o f a r e l a -t i v e low O.E. ( 0 . 7 - 1 . 5 k g 02/ k w h ) .
A t h i g h gas volume r a t e s t h e upward l i q u i d v e l o c i t y i n c r e a s e s , w h i c h s h o r t e n s t h e r e s i d e n c e t i m e o f t h e b u b b l e s r e m a r k a b l y ( P b ' p e l , 1 9 7 7 ) .
A s e c o n d d i s a d v a n t a g e i s , t h a t t h e m i x i n g between b u b b l e s and w a t e r i s n o t as i n t e n s e as i t i s i n m e c h a n i c a l l y a g i t a t e d s y s t e m s , w h i c h makes b u b b l e a e r a t i o n more l i a b l e t o a d e c r e a s e i n e f f i c i e n c y i f t h e s y s t e m i s c o n t a m i n a t e d .
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f i g . 1.1 s k e t c h o f b u b b l e a e r a t i o n w i t h low p r e s s u r e . f i g . 1.2 s k e t c h o f b u b b l e a e r a t i o n w i t h h i g h p r e s s u r e . F u r t h e r t h e e x t e n s i v e n e t w o r k o f b l o w e r o r c o m p r e s s o r , a i r f i l t e r s , a i r d i s t r i b u t i o n s y s t e m and d i f f u s e r e l e m e n t s r e q u i r e s c o n t i n u i n g m a i n t e n a n c e and c o n t r o l . In r e c e n t y e a r s new d e s i g n s have been d e v e l o p e d t o r e d u c e t h e s e d i s a d v a n -t a g e s . The mos-t i m p o r -t a n -t p r o b l e m was -t o p r o l o n g -t h e r e s i d e n c e -t i m e o f -t h e b u b b l e s i n t h e w a t e r i n o r d e r t o i n c r e a s e t h e O . E . One way t o a c h i e v e t h i s i s t o p r o d u c e a h o r i z o n t a l f l o w i n t h e a e r a t i o n b a s i n . T h i s c a n s i m p l y be done w i t h t h e a i d o f a p r o p e l l o r as i s shown i n f i g . 1.3 ( R o t o f l o w s y s t e m , Van de G r a a f , 1 9 7 6 ) . A n o t h e r d e s i g n i s shown i n f i g . 1 . 4 : a s l o w l y r o t a t i n g b r i d g e ( v e l o c i t y a b o u t 1 ms ) p r o v i d e s a h o r i z o n t a l f l o w i n t h e a e r a t i o n t a n k : d i f f u s e r s a r e mounted on t h e b o t t o m o f t h e t a n k and a l s o on t h e b r i d g e . An O . E . o f 3 - 3 . 5 kg02/kWh i n c l e a n w a t e r may be r e a c h e d ( B l o m , 1 9 7 8 ) ,c o m p r e s s e d
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f i g . 1.3 s k e t c h o f r o t o f l o w a e r a t o r . f i g . 1.4 s k e t c h o f c o u n t e r c u r r e n t b u b b l e a e r a t o r . A h o r i z o n t a l f l o w c a n a l s o be p r o d u c e d by a j e t f l o w i n w h i c h a i r i s d i s p e r s e d i n t o f i n e b u b b l e s ( s e e f i g . 1 . 5 ) . The j e t c r e a t e s an i n t e n s e m i x i n g between b u b b l e s and w a t e r , w h i c h makes t h e mass t r a n s f e r p r o c e s s l e s s s e n s i t i v e t o n e g a t i v e i n f l u e n c e s i n c o n t a m i n a t e d s y s t e m s . An O . E . o f 2 . 2 kg02/kWh i n c l e a nA r e c e n t d e v e l o p m e n t i n b u b b l e a e r a t i o n , aimed a t e x t e n d i n g t h e r e s i d e n c e t i m e o f t h e b u b b l e s , i s by d i s t r i b u t i n g t h e d i f f u s e r e l e m e n t s o v e r t h e w h o l e b o t t o m o f t h e b a s i n , i n o r d e r t o r e d u c e t h e upward l i q u i d v e l o c i t y . An improvement o f t h e O . E . t o 4 kg02/kWh has been measured i n c l e a n w a t e r (De K o r t e , 1 9 7 7 ) . I t
w i l l be c l e a r t h a t t h e m a i n t e n a n c e p r o b l e m s a s s o c i a t e d w i t h such an e x t e n d e d a i r d i v i d e r c a n be c o n s i d e r a b l e i n a b i o l o g i c a l s y s t e m . The most advanced method t o l e n g t h e n t h e r e s i d e n c e t i m e o f t h e b u b b l e s i s p r e s e n t e d i n t h e ICI deep s h a f t a e r a t o r ( f i g . 1 . 6 ) .
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• A* f i g . 1.5 s k e t c h o f j e t d i f f u s e r a e r a t o r . f i g . 1.6 s k e t c h o f deep s h a f t a e r a t o r . The a e r a t e d volume i s c o n t a i n e d i n two l o n g c o a x i a l p i p e s , i n w h i c h t h e w a s t e wat i s c i r c u l a t e d . T h i s c i r c u l a t i o n i s p r o d u c e d by t h e d i f f e r e n c e i n mean d e n s i t y i n t h e two p i p e s , a r i s i n g f r o m t h e g r e a t e r t o t a l gas volume i n t h e o u t e r p i p e . Gas i s f i r s t c a r r i e d downwards b e f o r e b e g i n n i n g t h ^ g a s - l i f t a c t i o n i n t h e r i s e r , so a c h i e v i n g a r e s i d e n c e t i m e o f t h e o r d e r o f some m i n u t e s . The O . E . i s f o u n d t o be a b o u t 6 kg02/kWh i n c l e a n w a t e r (Hemming, 1 9 7 9 ) . A f u r t h e r i m -provement o f t h e deep s h a f t a e r a t o r , i n c o m p a r i s o n w i t h o t h e r b u b b l e a e r a t i o n d e v i c e s , i s t h a t t h e a i r d i s t r i b u t i o n d i f f u s e r s y s t e m s a r e l o c a t e d a t some s p e c i f i c p l a c e s and n o t s p r e a d t h r o u g h t h e w h o l e s y s t e m . T h i s s i m p l i f i e s m a i n t e n a n c e . A d e c r e a s e o f t h e oxygen t r a n s f e r as a r e s u l t o f t h e p r e s e n c e o f c e r -t a i n c o n -t a m i n a n -t s w o u l d r e m a i n a p r o b l e m i n mos-t b u b b l e a e r a -t i o n d e v i c e s as l o n g as no i n t e n s e g a s - l i q u i d m i x i n g zone i s p r e s e n t . R e d u c t i o n s t o 50% o f t h e measured O . E . i n c l e a n w a t e r , d e p e n d e n t o f t h e k i n d o f c o n t a m i n a n t s , a r e n o t u n u s u a l . In c o n t r a s t t o t h e s y s t e m s d e s c r i b e d a b o v e , w h i c h make use o f c o m p r e s s e d a i r , t h e r e i s a n o t h e r group o f a e r a t o r s w h i c h u t i l i s e t h e a m b i e n t a i r above t h e w a t e r s u r f a c e . T h e r e i s a l w a y s some n a t u r a l oxygen t r a n s f e r f r o m a m b i e n t a i r t h r o u g h t h e w a t e r s u r f a c e i n t o t h e w a t e r . In g e n e r a l t h i s c o n t r i b u t i o n i s 2 2s m a l l , b u t t h i s c a n be s t i m u l a t e d by a i d o f a m e c h a n i c a l s t i r r e r d e v i c e . We speak t h e n a b o u t a m e c h a n i c a l s u r f a c e a e r a t o r . In f i g . 1.7 and 1.8 s k e t c h e s a r e g i v e n o f two t y p e s , w h i c h a r e w i d e l y u s e d : t h e b r u s h a e r a t o r and t h e p o i n t a e r a t o r . B r u s h a e r a t o r s a r e r o t a t i n g c y l i n d r i c a l b r u s h e s mounted w i t h h o r i z o n t a l a x e s , w i t h t h e l o w e r p a r t o f t h e b r u s h u n d e r t h e w a t e r s u r f a c e , so a i r i s b e a t e n i n t o t h e w a t e r . P o i n t a e r a t o r s a r e c o n i c a l c o n s t r u c t i o n s , w h i c h r o t a t e a r o u n d a v e r t i c a l s h a f t . Water i s drawn f r o m below and i t i s r e l e a s e d a t t h e w a t e r s u r -f a c e , where i t i s a e r a t e d . Both t y p e s a r e used i n p r a c t i c e i n many d i -f -f e r e n t v e r s i o n s ( K a l b s k o p f , 1 9 7 8 ) . These s u r f a c e a e r a t o r s a r e u s u a l l y o f heavy c o n s t r u c -t i o n , and r e q u i r e b o -t h r o -t a -t i n g and v e r -t i c a l a d j u s -t m e n -t -t o c o n -t r o l -t h e oxygen i n p u t . T h i s c o m p l e x i t y l e a d s t o a g r e a t e r r i s k o f d e f e c t s and a need f o r c a r e f u l m a i n t e n a n c e . F o r some y e a r s t h e a c h i e v e d O . E . o f s u r f a c e a e r a t o r s ( a b o u t 2 k g 02/ kWh) was r e g a r d e d as s a t i s f a c t o r y t h o u g h t h e new d e v e l o p m e n t s i n b u b b l e a e r a t o r s a r e t e n d i n g t o l e a d t o t h i s b e i n g q u e s t i o n e d . One a d v a n t a g e , e s p e c i a l l y f o r t h e p o i n t a e r a t o r i s t h e i n t e n s e g a s - l i q u i d m i x i n g , w h i c h makes t h e s y s t e m l e s s l i a b l e t o a d e c r e a s e i n t h e O . E . i n c o n t a m i n a t e d s y s t e m s . A n o t h e r g r o u p o f a e r a t o r s a v o i d t h e use o f m e c h a n i c a l c o m p r e s s o r s f o r t h e a i r by u t i l i s i n g t h e e n e r g y i n f l o w i n g w a t e r . A good example o f such a d e v i c e i s s k e t c h e d i n f i g . 1 . 9 , t h e v e n t u r i a e r a t o r .
f i g . 1.7 s k e t c h o f b r u s h a e r a t o r . f i g . 1.8 s k e t c h o f p o i n t a e r a t o r .
m i x i n g
\ r e g i o n
T h i s u t i l i s e s t h e r e l a t i v e u n d e r p r e s s u r e i n t h e t h r o a t o f a v e n t u r i t o draw i n a m b i e n t a i r t h r o u g h s m a l l h o l e s . The g r a d u a l e x p a n s i o n o f t h e p i p e a f t e r t h e c o n t r a c t i o n i s n e c e s s a r y t o p r o v i d e a minimum e n e r g y l o s s . The O . E . i s c o m p a r -a b l e w i t h t h -a t -a c h i e v e d by o t h e r -a e r -a t i o n d e v i c e s -and t h e i n t e n s e m i x i n g zone i s an a d v a n t a g e . The v e n t u r i a e r a t o r i s an a t t r a c t i v e p o s s i b i l i t y when a pump i s a l r e a d y r e q u i r e d t o t r a n s p o r t t h e w a t e r , f o r example i n a e r a t i o n o f d r i n k i n g w a t e r pumped f r o m t h e g r o u n d ( S i m h o f f e r , 1 9 7 6 ) . The p l u n g i n g j e t a e r a t o r , w h i c h p r o v i d e s t h e main theme o f t h i s r e s e a r c h can be r e g a r d e d as a f o r m o f v e n t u r i a e r a t o r , i n t h a t t h e momentum o f f l o w i n g w a t e r i n d u c e s t h e a i r e n t r a i n m e n t t o g e t h e r w i t h t h e s u b s e q u e n t d i s p e r s i o n m i x i n g and mass t r a n s f e r . T h i s i s d e a l t w i t h i n t h e n e x t s e c t i o n .
1 . 3 . THE PLUNGING JET AERATOR
A s k e t c h o f a p l u n g i n g j e t i s shown i n f i g . 1 . 1 0 . A l i q u i d j e t p l u n g e s f r o m a n o z z l e i n t o a p o o l . The a i r a r o u n d t h e f r e e j e t i s b r o u g h t i n t o a movement as a d e v e l o p i n g b o u n d a r y l a y e r . A t t h e pool l i q u i d s u r f a c e some o r a l l o f t h i s a i r i s c a r r i e d w i t h t h e j e t under t h e f r e e l i q u i d s u r f a c e . The c a p t u r e d a i r i s d i s p e r s e d i n t o f i n e b u b b l e s by t h e i n t e n s e s h e a r f o r c e s and t u r b u l e n c e t h a t a r e p r e s e n t . The f i n e b u b b l e s a r e c a r r i e d downwards by t h e momentum o f t h e p l u n g i n g j e t , w h i c h a l s o e n t r a i n s f u r t h e r w a t e r f r o m t h e s u r r o u n d i n g s , f o r m i n g an a p p r o x i m a t e l y c o n i c a l b i p h a s i c r e g i o n .
f i g . 1.10 s k e t c h o f t h e p l u n g i n g j e t .
The f o r c e s a r i s i n g f r o m t h e buoyancy o f t h e a i r and t h e a c c e l e r a t i o n o f t h e w a t e r e n t e r i n g t h i s b i p h a s i c r e g i o n r e d u c e t h e l i q u i d phase v e l o c i t y . In t h e l o w e r p a r t o f t h e b i p h a s i c r e g i o n t h e f i n e b u b b l e s c o a l e s c e t o f o r m b u b b l e s ( o f a b o u t 4 mm d i a m e t e r i n c l e a n w a t e r ) , w h i c h a r e l a r g e enough to be no l o n g e r c a r r i e d downwards by t h e r e d u c e d l i q u i d phase v e l o c i t y . These b u b b l e s e s c a p e s i d e w a y s f r o m t h e b o t t o m o f t h e p l u n g i n g cone and most r i s e t o t h e f r e e s u r f a c e o f t h e p o o l , though some may be r e c a p t u r e d by t h e r a d i a l f l o w o f w a t e r i n t o t h e b i p h a s i c p l u n g i n g - j e t r e g i o n . The m a j o r i t y o f t h e oxygen t r a n s f e r p r o c e s s t a k e s p l a c e by d i f f u s i o n from t h e a i r b u b b l e s i n t o t h e w a t e r , a l t h o u g h some oxygen i s t a k e n up b o t h i n t h e f r e e j e t above t h e l i q u i d pool s u r f a c e and a l s o t h r o u g h t h e pool s u r f a c e i t s e l f . In f i g . 1 . 1 1 . a p i c t u r e i s shown o f t h e p l u n g i n g j e t a e r a t o r s used i n t h e w a s t e w a t e r t r e a t m e n t p l a n t o f D . S . M . i n Ge-l e e n (The N e t h e r Ge-l a n d s ) .
f i g . 1.11 a e r a t i o n w i t h m u l t i p l e p l u n g i n g j e t s . Water i s pumped from t h e a e r a t i o n b a s i n i n t o a p i p e and t h e n p l u n g e s back t h r o u g h a row o f n o z z l e s . The j e t s have a v e l o c i t y o f a b o u t 5 ms ^ a t t h e p l u n g i n g p o i n t . The i n j e c t o r a n g l e w i t h t h e pool s u r f a c e i s 6 0 ° , w h i c h p r o -v i d e s a s u f f i c i e n t . h o r i z o n t a l f l o w i n t h e a e r a t i o n b a s i n (5 m d e e p , 25 m w i d e ) t o keep t h e a c t i v e s l u d g e i n s u s p e n s i o n . F u l l s c a l e e x p e r i m e n t s o f t h i s a e r -a t o r show t h -a t -an O.E. o f -a b o u t 2 kg02/kWh i s a c h i e v e d i n c l e a n , i n d u s t r i a l and d o m e s t i c w a s t e w a t e r ( J e n n e k e n s , 1 9 7 5 ; D i j k s t r a , 1 9 7 9 ) . I f we compare t h e p l u n g i n g j e t a e r a t o r w i t h o t h e r a e r a t i o n d e v i c e s i n terms o f t h e c r i t e r i a s e t i n p a r . 1 . 2 . t h e f o l l o w i n g c h a r a c t e r i s t i c s can be n o t i c e d , a . A l t h o u g h an O.E. o f a b o u t 2 kg02/kWh i s n o t bad compared w i t h o t h e r d e v i c e s
(deep s h a f t e t c . ) . The r e a s o n f o r t h i s i s t h a t t h e r e s i d e n c e t i m e o f t h e b u b b l e s i s r e l a t i v e l y s h o r t and i n t h i s s e n s e t h e p l u n g i n g j e t a e r a t o r can be r e g a r d e d as a s h o r t b u b b l e c o l u m n . F o r such s y s t e m s g e n e r a t i n g o f a h o r i z o n t a l f l o w i n c r e a s e s t h e O . E . and an improvement i n t h e e f f i c i e n c y o f p l u n g i n g j e t a e r a t o r can be s o u g h t i n t h i s d i r e c t i o n .
2. The p l u n g i n g j e t c r e a t e s an i n t e n s e l o c a l m i x i n g zone between a i r b u b b l e s and w a t e r j u s t l i k e a p o i n t a e r a t o r o r a j e t d i f f u s e r so t h a t t h e n e g a t i v e i n f l u e n c e o f some k i n d s o f c o n t a m i n a n t s on t h e oxygen t r a n s f e r p r o c e s s i n b u b b l e a e r a t i o n s y s t e m s i s h e r e l e s s s e r i o u s .
3. The p l u n g i n g j e t a e r a t o r makes use o f t h e a m b i e n t a i r , but has a m o r e . f l e x -i b l e l a y o u t t h a n m e c h a n -i c a l s u r f a c e a e r a t o r s , w h -i l e t h e s p e c -i f -i c p r o b l e m s c o n n e c t e d w i t h t h e use o f c o m p r e s s e d a i r a r e n o t p r e s e n t . Pumps a r e s t a n d a r d and e a s i l y a v a i l a b l e , w h i l e o t h e r a e r a t o r s a r e m o s t l y s p e c i a l d e v i c e s . In t h i s way p l u n g i n g j e t a e r a t o r s can a l s o e a s i l y be added t o e x i s t i n g b a s i n s t o i m p r o v e p e r f o r m a n c e .
In c h o o s i n g an a e r a t i o n d e v i c e a good b a l a n c e has t o be made between o p e r a t i o n c o s t s , m i x i n g q u a l i t i e s , c a p i t a l c o s t s and e n v i r o n m e n t a l o u t p u t . F o r a l l t h e s e r e q u i r e m e n t s t h e d i f f e r e n t a e r a t i o n d e v i c e s have t h e i r s p e c i f i c a d v a n t a g e s and d i s a d v a n t a g e s i n t h e p a r t i c u l a r s i t u a t i o n , where t h e w a s t e w a t e r t r e a t m e n t p l a n t s have t o be b u i l t .
1.4. STRUCTURE OF THE THESIS
We can c o n s i d e r t h r e e p r i n c i p a l a s p e c t s o f t h e o p e r a t i o n o f a p l u n g i n g j e t c o n -t a c -t o r : -t h e e n -t r a i n m e n -t o f a i r by -t h e j e -t , -t h e h y d r o d y n a m i c s o f -t h e -two phase f l o w r e g i o n , e n c l u d i n g i t s i n t e r a c t i o n w i t h t h e a m b i e n t l i q u i d , and t h e mass t r a n s f e r a s p e c t s . C h a p t e r 2 i s c o n c e r n e d w i t h t h e a i r e n t r a i n m e n t . A r e v i e w w i l l be g i v e n o f p r e -v i o u s e x p e r i m e n t a l and t h e o r e t i c a l r e s e a r c h . I t a p p e a r s t h a t t h e e x p e r i m e n t a l work has been l a r g e l y r e s t r i c t e d t o s m a l l d i a m e t e r j e t s ( dn < 1 c m ) . An e x p e r i
-mental p r o g r a m was s e t up t o become l a r g e s c a l e d a t a f r o m j e t s w i t h d i a m e t e r s o f up t o 10 cm. The volume o f a i r e n t r a i n e d i s shown n o t t o be a s i m p l e f u n c -t i o n o f -t h e j e -t p a r a m e -t e r s , b u -t i s a l s o i n f l u e n c e d by -t h e geome-try o f -t h e n o z z l e . T h i s e x p l a i n s t h e d i f f i c u l t i e s i n coming t o a g e n e r a l q u a n t i t a t i v e m o d e l , t o p r e d i c t t h e a i r volume r a t e . F o r a p a r t i c u l a r n o z z l e p a t t e r n w i t h a c o n i c a l
e n t r y t o t h e n o z z l e and r e l a t i v e s h o r t n o z z l e t u b e l e n g t h , an e n t r a i n m e n t r e l a t i o n s h i p was e s t a b l i s h e d f o r j e t s w i t h d i a m e t e r s between 1 and 10 cm, v e l o -c i t i e s up t o 10 ms 1 and o f l e n g t h up t o 1 m. O t h e r e x p e r i m e n t s were a l s o done
w i t h s p e c i a l n o z z l e d e s i g n s g i v i n g a s p r e a d i n g o f t h e l i q u i d j e t , and a c o n -s i d e r a b l e i n c r e a -s e i n t h e e n t r a i n m e n t c o u l d be a c h i e v e d , u -s u a l l y a t t h e c o -s t o f i n c r e a s e d p r e s s u r e l o s s a c r o s s t h e n o z z l e .
C h a p t e r 3 d e a l s w i t h t h e h y d r o d y n a m i c s o f t h e p l u n g i n g j e t s y s t e m . A t h e o r e t i c a l model i s p r e s e n t e d , w h i c h p r e d i c t s t h e d i m e n s i o n s , v e l o c i t i e s an g a s f r a c -t i o n s i n -t h e -two phase r e g i o n below -t h e w a -t e r s u r f a c e . T h i s makes i -t p o s s i b l e t o e s t i m a t e t h e r e s i d e n c e t i m e o f t h e b u b b l e s and t h e l i q u i d r a t e t h r o u g h t h i s a e r a t i o n z o n e , w h i c h a r e i m p o r t a n t p a r a m e t e r s f o r mass t r a n s f e r r a t e c a l c u l a -t i o n s . B u b b l e cone h e i g h -t , b u b b l e v e l o c i -t y and h o l d up measuremen-ts were made t o v e r i f y t h e model .
C h a p t e r 4 c o n s i d e r s t h e mass t r a n s f e r a s p e c t s . In a model o f a k i n d o f a e r a t i o n b a s i n t h e i n f l u e n c e o f t h e d i f f e r e n t j e t p a r a m e t e r s on t h e oxygen t r a n s f e r p r o -c e s s i s i n v e s t i g a t e d : v e l o -c i t y , d i a m e t e r , j e t l e n g t h , i n j e -c t i o n a n g l e and j e t i n t e r a c t i o n have been s t u d i e d . In t h e l i t e r a t u r e o n l y a few e m p i r i c a l c o r r e l a -t i o n s f o r a e r a -t i o n by a p l u n g i n g j e -t a r e a v a i l a b l e . A more -t h e o r i c a l a p p r o a c h w i l l be p r e s e n t e d h e r e . F o r p r a c t i c a l a p p l i c a t i o n s and a l s o i n o r d e r t o s t u d y s c a l e up e f f e c t s , e x p e r i m e n t s have been c a r r i e d o u t w i t h l a r g e r d i a m e t e r j e t s and d i f f e r e n t n o z z l e d e s i g n s .
C h a p t e r 5 l o o k s a t t h e i n f l u e n c e o f d i f f e r e n t c o n t a m i n a n t s l i k e s a l t s , a l c o -h o l s , soaps and o i l on t -h e oxygen t a k e u p .
In c h a p t e r 6 some d e t a i l s o f t h e p r e f o r m a n c e o f l a r g e r s c a l e p l u n g i n g j e t a e r -a t o r s -a r e p r e s e n t e d -and r e l -a t e d t o t h e r e s u l t s o f t h e p r e s e n t r e s e -a r c h .
C H A P T E R 2
AIR E N T R A I N M E N T
2 . 1 . INTRODUCTION T h e r e a r e s e v e r a l r e c e n t i n v e s t i g a t i o n s o f a i r e n t r a i n m e n t by a p l u n g i n g j e t . A r e v i e w o f t h i s r e s e a r c h w i l l be g i v e n i n s e c t i o n 2 . 2 . Some a t t e n t i o n w i l l be g i v e n t o t h e minimum e n t r a i n m e n t v e l o c i t y , t h i s i s t h e j e t v e l o c i t y below w h i c h no e n t r a i n m e n t t a k e s p l a c e . The measured e n t r a i n m e n t r a t e s a r e o f t e n n o t v e r y r e p r o d u c i b l e between d i f f e r e n t a u t h o r s , even though a p p a r e n t l y t h e e x p e r i -mental c o n d i t i o n s a r e c l o s e l y r e p r o d u c e d . There i s a d i f f e r e n c e t o o i n t h e way t h e v a r i o u s a u t h o r s d e s c r i b e t h e e n t r a i n m e n t p r o c e s s i t s e l f . With t h e a i d o f h i g h speed p h o t o g r a p h i c and f i l m t e c h n i q u e s i t has been shown t h a t d i s t u r b a n c e s on t h e j e t s u r f a c e a t t h e p l u n g i n g p o i n t a r e i m p o r t a n t i n t h e mechanism o f t h e e n t r a i n m e n t p r o c e s s . T h i s r o u g h n e s s o f t h e j e t s u r f a c e i s i n f l u e n c e d n o t o n l y by t h e v e l o c i t y and d i a m e t e r o f t h e j e t b u t i s a l s o s t r o n g l y dependent on t h e d i s t u r b a n c e s o f t h e j e t s u r f a c e a t t h e n o z z l e o u t l e t and how t h e s e d e v e l o p i n t h e d i s t a n c e between t h e n o z z l e o u t l e t and t h e p l u n g i n g p o i n t ( t h e j e t l e n g t h ) . N o z z l e d e s i g n i s an i m p o r t a n t p a r a m e t e r and s p e c i a l a t t e n t i o n w i l l be g i v e n t o t h i s a s p e c t . The r e v i e w ends w i t h a c o m p a r i s o n o f t h e d i f f e r e n t e x p e r i m e n t s and t h e e s t a b l i s h e d e m p i r i c a l c o r r e l a t i o n s . I t w i l l be shown t h a t t h e d i f f e r e n c e s i n n o z z l e geometry e x p l a i n t h e l a r g e d i f f e r e n c e s between t h e r e s u l t s o f d i f f e r e n t a u t h o r s .Because t h e s e r e s u l t s a r e l i m i t e d t o r a t h e r s m a l l d i a m e t e r j e t s ( m a i n l y d^ < 1 c m ) t h e r e was a need f o r d a t a p e r t i n e n t t o l a r g e s c a l e o p e r a t i o n . An e x p e r i m e n t a l programme was u n d e r t a k e n t o measure e n t r a i n m e n t r a t e s f o r j e t d i a -m e t e r s up t o 10 c-m. The e n t r a i n -m e n t r a t e a p p e a r s t o be o f t h e sa-me o r d e r o f m a g n i t u d e as t h e j e t l i q u i d volume r a t e and a s i m p l e c o r r e l a t i o n c o u l d be e s -t a b l i s h e d f o r r e l a -t i v e s h o r -t n o z z l e s w i -t h a c o n i c a l e n -t r y .
E x p e r i m e n t s were a l s o done w i t h o t h e r n o z z l e d e s i g n s t o show t h e c o n s i d e r a b l e e f f e c t o f promoted d i s t u r b a n c e s o f t h e j e t s u r f a c e on t h e e n t r a i n m e n t r a t e . T h i s c o u l d e a s i l y i n c r e a s e t h e e n t r a i n m e n t r a t e 2 o r 3 t i m e s compared w i t h t h e measured e n t r a i n m e n t r a t e s f o r r e l a t i v e l y smooth j e t s . However, o n l y a l i m i t e d p o s i t i v e e f f e c t on t h e oxygen t r a n s f e r i s r e a l i s e d . In the f i r s t p l a c e a r e m a r k a b l e d e c r e a s e i n t h e b i p h a s i c p l u n g i n g d e p t h a c c o m p a n i e s t h e i n c r e a s e i n a i r e n t r a i n m e n t . T h i s r e d u c e s t h e r e s i d e n c e t i m e o f t h e b u b b l e s . S e c o n d l y , t h e d e l i b e r a t e i n d u c t i o n o f j e t d i s t u r b a n c e s demands an e x t r a power i n p u t . T h i s a s p e c t w i l l be t r e a t e d i n more d e t a i l i n c h a p t e r 4 . 2 . 2 . LITERATURE REVIEW 2 . 2 . 1 . The minimum e n t r a i n m e n t v e l o c i t y
L i n and D o n n e l y (1966) were t h e f i r s t a u t h o r s to make a d e t a i l e d s t u d y o f t h e a i r e n t r a i n m e n t p r o c e s s . W i t h t h e a i d o f h i g h speed p h o t o g r a p h y t h e y s t u d i e d v i s c o u s j e t s o f 2-12 mm d i a m e t e r a t r e l a t i v e l y low v e l o c i t i e s .
A d i s t i n c t i o n was made between l a m i n a r and t u r b u l e n t j e t s . L a m i n a r j e t s were c h a r a c t e r i s e d as j e t s w i t h a n o n - d i s t u r b e d smooth s u r f a c e . T h i s c o u l d o n l y be a c h i e v e d w i t h a v i s c o u s l i q u i d ; t h e y used a w a t e r - g l y c e r o l m i x t u r e o f 300 mPas and v e l o c i t i e s j u s t above t h e minimum e n t r a i n m e n t v e l o c i t y (Re^ < 1 5 0 0 ) . I t was seen t h a t a c o n t i n u o u s t h i n gas f i l m was p r e s e n t between t h e p l u n g i n g j e t and t h e r e c e i v i n g l i q u i d , w h i c h was b r o k e n up i n t o f i n e b u b b l e s as a r e s u l t o f j e t i n s t a b i l i t y . V e r y l i t t l e a i r i s e n t r a i n e d i n t h i s r e g i m e : l e s s t h a n 1% o f t h e l i q u i d volume r a t e . Such e n t r a i n m e n t by l a m i n a r j e t s i s t h e r e f o r e o f l i t t l e i n t e r e s t f o r a e r a t i o n p u r p o s e s , b u t may be i m p o r t a n t i n some i n d u s t r i a l p r o -c e s s e s where a i r e n t r a i n m e n t s h o u l d be p r e v e n t e d , f o r example i n t h e f i l l i n g o f b o t t l e s w i t h v i s c o u s l i q u i d s o r i n t h e c a s t i n g o f m o l t e n s t e e l ( S z e k e l y , 1 9 6 9 ) . F o r t h e s e s i t u a t i o n s t h e minimum e n t r a i n m e n t v e l o c i t y i s t h e c e n t r a l p a r a m e t e r . L i n and D o n n e l y (1966) d e r i v e d an e m p i r i c a l c o r r e l a t i o n : (W ej ) m i n = l ° ( R e / -7 4 (2-D w h i c h i s v a l i d f o r t h e Re. range o f 8 t o 1 5 0 0 , w i t h v i s c o s i t i e s f r o m 50 t o 400 J _ -J _ "i mPas and s u r f a c e t e n s i o n s f r o m 30 t o 6 3 . 1 0 Nm . F o r t u r b u l e n t j e t s , e x p e r i m e n t a l d a t a were g i v e n by S h e r i d a n (1966) and C i b o -r o w s k i and B i n ( 1 9 7 2 ) . The l a s t one s u g g e s t e d a s i m p l e -r e l a t i o n :
We. • = 400 J ,min ( 2 . 2 )
v a l i d f o r r e l a t i v e l y s h o r t n o z z l e s ( Ln/ dn < 1 0 ) . A more t h e o r e t i c a l a p p r o a c h
i s g i v e n by Cumming ( 1 9 7 5 ) , w h i c h a g r e e s w e l l w i t h ( 2 . 1 ) as was shown by B i n ( 1 9 7 6 ) .
The r e l a t i o n s g i v e n above a r e r e s t r i c t e d i n t h e s e n s e t h a t d i s t u r b a n c e s on t h e j e t s u r f a c e and t h e i r i n t e r a c t i o n w i t h t h e p o o l l i q u i d s u r f a c e p l a y a r o l e , even though v e l o c i t i e s a r e v e r y l o w . F o r e x a m p l e : w i t h an o b l i q u e p l u n g i n g j e t a i e n t r a i n m e n t w i l l o f t e n o c c u r , whereas f o r a c o r r e s p o n d i n g v e r t i c a l j e t i t w o u l d n o t . I t has t o be remarked h e r e t h a t t h i s minimum e n t r a i n m e n t v e l o c i t y o f j e t s i s r e l a t e d t o t h e e n t r a i n m e n t o f a m b i e n t a i r by s o l i d b o d i e s as may o c c u r d u r i n g t h e c o a t i n g o f f i l m s , f i b r e s , t e x t i l e s o r p a p e r when drawn t h r o u g h a l i q u i d b a t h ( B u r l e y and Kennedy, 1 9 7 6 ) . 2 . 2 . 2 . The mechanism o f a i r e n t r a i n m e n t by a t u r b u l e n t j e t L i n and D o n n e l y (1966) o b s e r v e d t h a t as t h e v e l o c i t y o f a l a m i n a r j e t i n c r e a s e s , d i s t u r b a n c e s a p p e a r on t h e j e t s u r f a c e and t h e e n t r a i n m e n t becomes i r r e g u l a r : o n l y t a k i n g p l a c e when d i s t u r b a n c e s h i t t h e pool l i q u i d s u r f a c e . A t h i g h e r v e -l o c i t i e s (Re^ > 1 8 . 0 0 0 ) t h e y o b s e r v e s t h a t t h e j e t s u r f a c e i s no -l o n g e r smooth b u t i l l d e f i n e d , a i r i s t a k e n up i n t h e j e t s u r f a c e and t h e e n t r a i n m e n t i s i n -c r e a s i n g l y v i g o r o u s .
De F r a t e and Rush (1969) i n v e s t i g a t e d t u r b u l e n t j e t s i n more d e t a i l . They d i s -t i n g u i s h e d -t h r e e v e l o c i -t y r e g i m e s . A -t l o w e r v e l o c i -t e s a s m a l l i n d e n -t i s formed i n t h e w a t e r s u r f a c e a r o u n d t h e p l u n g i n g p o i n t . By a t h i c k e n i n g o f t h e j e t t h i s i n d e n t i s deepened t e m p o r a r i l y and a i r i s e n c l o s e d by t h e n e x t t h i c k e n i n g . A t s t i l l h i g h e r v e l o c i t e s t h e j e t s t a r t s t o make an o s c i l l a t i n g movement and t h e d e n t deepens t o f o r m an o s c i l l a t i n g c a v i t y : a i r e n t r a i n m e n t t a k e s p l a c e when t h e j e t l i q u i d c l o s e s t h e u p p e r end o f t h e c o n t r a c t i n g c a v i t y , r e s u l -t i n g i n c a p -t u r e o f -t h e a i r . The d i s r u p -t i o n o f -t h e j e -t s u r f a c e c a u s e d by a i r f r i c t i o n a t h i g h e r v e l o c i t i e s c a u s e s t h e c o n t i n u a l f o r m a t i o n o f l a r g e c a v i t i e s a t t h e p l u n g i n g p o i n t , w h i c h do n o t c l o s e so r e a d i l y and i n d e e d can sometimes be s t a b i l i s e d by v o r t e x a m p l i f i c a t i o n o f any c i r c u l a t i o n i n t h e r e c e i v i n g v o l -ume. H a u x w e l l (1972) made h i g h speed f i l m s o f e n t r a i n m e n t p r o d u c e d by t u r b u l e n t j e t s , and a g r e e s w i t h De F r a t e and R u s h ' s o b s e r v a t i o n s o f t h e o s c i l l a t i n g c a v -i t y a r o u n d t h e j e t .
H e n d e r s o n , M c C a r t h y and M o l l o y (1970) g i v e a d i f f e r e n t d e s c r i p t i o n o f t h e e n -t r a p m e n -t p r o c e s s . They c a l l -t h e den-t a r o u n d -t h e j e -t a -t -t h e p l u n g i n g p o i n -t -t h e " i n d u c t i o n t r u m p e t " . Here t h e pool l i q u i d s u r f a c e and t h e j e t s u r f a c e form a k i n d o f v e n t u r i w i t h i n w h i c h t h e a i r i s s u c k e d down by t h e downward movement o f t h e j e t , as i n a w a t e r j e t pump. To e x p l a i n t h e i r r e g u l a r e n t r a i n m e n t o b -s e r v e d a t l o w e r v e l o c i t i e -s , t h e y -s u g g e -s t t h a t t h e i n d u c t i o n t r u m p e t i -s a w h i r l w h i c h i s sometimes a m p l i f i e d by e d d i e s i n t h e r e c e i v i n g l i q u i d . A t h i g h e r j e t v e l o c i t i e s , when a i r e n t r a i n m e n t becomes r e g u l a r , t h e y assume t h a t t h e e n t r a i n -ment becomes i n d e p e n d e n t o f t h e move-ments i n t h e r e c e i v i n g l i q u i d .
Van de Sande (1974) a l s o makes a d i s t i n c t i o n between l o w and h i g h v e l o c i t y r e g i m e s . The l o w v e l o c i t y regime e x t e n d s t o a b o u t 5 ms , below w h i c h t h e e n -t r a i n m e n -t i s i r r e g u l a r and c a u s e d by -t h e d i s -t u r b a n c e s on -t h e j e -t s u r f a c e . Some-what c o n t r a r y t o t h e d e s c r i p t i o n o f De F r a t e and R u s h , Van de Sande c o n c l u d e d f r o m h i g h speed f i l m t h a t even a s i n g l e d i s t u r b a n c e i s s u f f i c i e n t t o c a u s e a i r e n t r a i n m e n t . A s k e t c h o f t h i s e n t r a i n m e n t i s g i v e n i n f i g u r e 2 . 1 .
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f i g . 2.1 e n t r a i n m e n t mechanism f o r low v e l o c i t y j e t s (Van de Sande,1974)
In t h e h i g h v e l o c i t y r a n g e , c h a r a c t e r i s e d by a c r i t i c a l Weber number, p v2d
We = a g n n > 1 0 , t h e s h e a r f o r c e s o f t h e a m b i e n t a i r d i s r u p t t h e j e t s u r f a c e
and a i r e n t r a i n s i n t h e j e t w h i c h l e a d s t o a w i d e n i n g o f t h e j e t . T h i s a i r i n the j e t i s c a r r i e d downwards, t o g e t h e r w i t h t h e a i r i n t h e d e v e l o p i n g boundary l a y e r . Around t h e j e t a t t h e p l u n g i n g p o i n t a c o n t i n u o u s gas r i n g i s f o r m e d . In t h e t r a n s i t i o n r e g i o n between t h e l o w and h i g h v e l o c i t i e s t h e e n t r a i n m e n t i s more r e g u l a r t h a n i n t h e l o w v e l o c i t y r e g i o n , a l t h o u g h i t i s s t i l l n o t t r u l y c o n t i n u o u s . The g e n e r a l f o r m o f t h e e n t r a i n m e n t c u r v e p r o p o s e d by Van de Sande was as drawn i n f i g . 2 . 2 .
I t was d e r i v e d f r o m e x p e r i m e n t s i n w h i c h dn < 1 cm : f o r a l l c o n d i t i o n s >
v^ and <f>2 > The t r a n s i t i o n r e g i o n was s a i d by Van de Sande t o be d e s c r i b e d w i t h s u f f i c i e n t a c c u r a c y by l i n e a r i n t e r p o l a t i o n .
entrainment
f i g . 2.2 e n t r a i n m e n t v e r s u s j e t v e l o c i t y (Van de Sande, 197*0. Ahmed (1974) and Cumming (1975) a l s o s t u d i e d t h e e n t r a i n m e n t mechanism b u t added no new e l e m e n t s t o t h e d e s c r i p t i o n o f i t . Ahmed was t h e f i r s t a u t h o r t o i n v e s t i g a t e l a r g e r d i a m e t e r j e t s , up t o 3.8 c m , w h i l e o t h e r a u t h o r s have u s u a l l y used j e t s s m a l l e r t h a n 1 cm.
From t h e f o r e g o i n g r e v i e w t h e f o l l o w i n g c o n c l u s i o n s c a n be drawn about t h e way i n w h i c h t h e j e t p a r a m e t e r s i n f l u e n c e t h e e n t r a i n m e n t m e c h a n i s m . A c l e a r d i s -t i n c -t i o n c a n be drawn be-tween -t h e l o w and h i g h v e l o c i -t y r e g i m e s . F o r r e l a -t i v e l y low v e l o c i t y t u r b u l e n t j e t s t h e e n t r a i n m e n t i s i r r e g u l a r and t h e d i s t u r b a n c e s o f t h e j e t s u r f a c e a r e a d o m i n a n t f a c t o r i n t h e e n t r a i n m e n t m e c h a n i s m . F o r r e l a t i v e l y h i g h v e l o c i t y j e t s a i r f r i c t i o n c o n t r o l s t h e s u r f a c e r o u g h n e s s o f t h e j e t . A i r e n t r a i n s w i t h i n t h e j e t and a b o u n d a r y l a y e r i s a l s o d e v e l o p e d , w h i c h i s c a r r i e d down b e l o w t h e w a t e r s u r f a c e . The e n t r a i n m e n t becomes r e g u l a r . D i s t u r b a n c e s o f t h e j e t s u r f a c e a r e a g a i n i m p o r t a n t because o f t h e i n t e r a c t i o n o f t h e j e t w i t h t h e a m b i e n t a i r . The f o l l o w i n g p a r a g r a p h w i l l show t h e way i n w h i c h n o z z l e geometry c a n i n f l u e n c e t h e s e d i s t u r b a n c e s and c o n s e q u e n t l y t h e a i r e n t r a i n m e n t i n b o t h v e l o c i t y r e g i m e s .
2 . 2 . 3 . The i n f l u e n c e o f n o z z l e d e s i g n on t h e e n t r a i n m e n t r a t e
The i n f l u e n c e o f n o z z l e d e s i g n was r e a l i s e d as soon as v e r y d i f f e r e n t e n t r a i n -ment r a t e s were measured f o r j e t s p l u n g i n g w i t h t h e same d i a m e t e r and v e l o c i t y
(Henderson e t a l . 1 9 7 0 ) . These r e s u l t s e s t a b l i s h e d t h a t s u r f a c e r o u g h n e s s i s an i m p o r t a n t p a r a m e t e r , and t h a t n o z z l e d e s i g n c a n i n f l u e n c e t h i s . In t h e l i t -e r a t u r -e a b o u t a i r -e n t r a i n m -e n t s p -e c i a l a t t -e n t i o n has b-e-en g i v -e n t o t h i s a s p -e c t by Van de Sande (1974) and Cumming ( 1 9 7 5 ) .
