NOVEMBRE 1 9 6 3 - № 7 L A H O U I L L E B L A N C H E 7 5 7
Densimetric exchange flow in rectangular channels
11.—SOME OBSERVATIONS OF THE STRUCTURE OF LOCK EXCHANGE FLOW
B Y
D. I . H . B A B E , AND A. M. M. HASSAN,
DEPARTMENT OF CIVIL ENGINEERING PORT OF BASRAH, IRAQ
THE ROYAL COLLEGE OF SCIENCE AND TECHNOLOGY, GLASGOW (RESEARCH STUDENT AT ROYAL COLLEGE, 1960-62)
77ii's second paper of the series describes how greater understanding of the varying mechanisms of ex
change flow was obtained from relatively simple experiments involving the colouring of ' blocks ' of wa
ter before the start of an experiment. It became apparent that capacity for the fronts of an exchange flow of large densimetric Froude-Reynolds number to maintain almost the initial velocity for conside
rable relative distance (i.e. for a travel distance of many times the depth) depended on the continual dis- cardment of the diluted water at the front and its replacement by more or less undiluted wafer which overtook the front. Although with decreasing densimetric Froude-Reynolds number the rate of entrain- ment at the fronts decreased, the rate of discardment decreased more rapidly and the velocity of the fronts diminished in a relatively shorter distance. At very small densimetric Froude-Reynolds numbers when the flow was basically laminar, dilution of the fronts became the dominant factor in the lock exchange flow phenomenon.
Attempts to obtain recordings of the velocity and dilution structure were only moderately successful in illustrating the effects of variation of scale because of the combined limitations imposed by the size of the flumes used and by the recording techniques available. However, taken together with some previous observations, and with observations made of dye streaks injected into the moving bodies of water—a modification of the original block colouring method—the combined evidence is considered to be suffi
cient to support the contentions.
1. I N T R O D U C T I O N
I n t h e first p a g e u n d e r t h e g e n e r a l t i t l e of t h e s e r i e s ( B a r r , 1963) w h i c h w i l l b e r e f e r r e d t o a s I, v a r i o u s p u r e d e n s i t y c u r r e n t c a s e s of d e n s i m e t r i c e x c h a n g e flow i n w a t e r w e r e l i s t e d , a n d i n f o r m a t i o n o n t h e i r o v e r a l l c h a r a c t e r i s t i c s w a s g i v e n . I t w a s d e m o n s t r a t e d t h a t t h e s c a l e of s u c h p h e n o m e n a s h o u l d b e d e t e r m i n e d o n t h e b a s i s of t h e d e n s i m e t r i c F r o u d e - R e y n o l d s n u m b e r . D e t a i l s w e r e g i v e n of t h e v e l o c i t i e s of t h e f r o n t s , b o t h i n r e s p e c t of c h a n g e s i n t h e coeffi
c i e n t of p r o p o r t i o n a l i t y w i t h v a r i a t i o n of s c a l e a n d b e t w e e n d i f f e r e n t t y p e s of f r o n t a n d a l s o i n r e s p e c t of t h e p a t t e r n of d i m i n u t i o n of v e l o c i t y of a f r o n t . U s i n g t h i s k n o w l e d g e , a d e s i g n m e t h o d for h y d r a u l i c m o d e l s t u d i e s i n v o l v i n g d e n s i m e t r i c s p r e a d h a d b e e n d e v i s e d . T h i s s h o w e d t h a t t h e p r a c t i c a l r e l e v a n c e of t h e i d e a l i s e d t w o d i m e n s i o n a l e x c h a n g e o r s p r e a d s t u d i e s w a s n o t c o n f i n e d t o t h e u n d e r s t a n d i n g of s m a l l d e n s i t y d i f f e r e n c e effects i n c a n a l a n d l o c k s y s t e m s a n d t h e l i k e , b u t e x t e n d e d t o t h e m u c h m o r e c o m m o n o c c u r r e n c e of t h e t h r e e d i m e n s i o n a l s p r e a d of a b u o y a n t d i s c h a r g e . I t
Article published by SHF and available athttp://www.shf-lhb.orgorhttp://dx.doi.org/10.1051/lhb/1963053
w a s s a i d i n I t h a t t h e n e x t s t a g e i n t h e p r o g r a m m e of s t u d y of e x c h a n g e flow s h o u l d b e t o a t t e m p t t o l e a r n m o r e of t h e s t r u c t u r e — t h e i n t e r n a l velocities a n d t h e d i l u t i o n p a t t e r n s . T h i s p a p e r is c o n c e r n e d w i t h s u c h o b s e r v a t i o n s .
2. N O T A T I O N S (as used in I)
B is t h e b r e a d t h of t h e r e c t a n g u l a r flume;
H is t h e p r i m a r y c h a r a c t e r i s t i c v e r t i c a l d i s t a n c e ; i n t h e c a s e of l o c k e x c h a n g e flow t h e d e p t h ;
L is a l e n g t h a l o n g t h e flume—measur
ed f r o m t h e r e m o v e a b l e b a r r i e r ; L0 is t h e d i s t a n c e f r o m t h e r e m o v e a b l e
b a r r i e r t o t h e fixed b a r r i e r i n t h e c a s e of a " s h o r t " l o c k .
V is t h e v e l o c i t y of a f r o n t a f t e r s o m e e x t e n s i o n ;
V0 i s t h e i n i t i a l v e l o c i t y of a f r o n t i m m e d i a t e l y a f t e r t h e r e m o v e a b l e b a r r i e r is l i f t e d ;
Ap/p is t h e n o n - d i m e n s i o n a l d e n s i t y differ
e n c e o r t h e d e n s i t y difference r a t i o ; Ap = px — p2 w h e r e pj a n d p2 a r e t h e d e n s i t i e s of t h e t w o b o d i e s of l i q u i d ; a n d it is a s s u m e d px i=.p2 p;
V A is [(Ap/p) . < 7 - H ]1 / 2 o r t h e c h a r a c t e r i s t i c v e l o c i t y s u c h t h a t t h e d e n s i m e t r i c F r o u d e n u m b e r (g?A) e q u a l s o n e ; g;h = V , / [ ( A p / p ) . ^ H ] w h e r e Yc is a c h a
r a c t e r i s t i c v e l o c i t y ; K i s t h e r a t i o V0/ VA;
g«A 0\ is t h e d e n s i m e t r i c F r o u d e - R e y n o l d s n u m b e r [(Ap/p)<71 / 2 H3 / a/ v ] , "where v is t h e k i n e m a t i c v i s c o s i t y (see I for t h e l i m i t a t i o n s o n t h i s n u m b e r ) .
3. S O M E F U R T H E R D E T A I L S O F P R E V I O U S L O C K E X C H A N G E E X P E R I M E N T S
B e f o r e t h e p r e s e n t p r o g r a m m e of s t u d i e s wras i n i t i a t e d a t t h e R o y a l College of S c i e n c e a n d T e c h n o l o g y , G l a s g o w , a t t e n t i o n h a d b e e n , i n g e n e r a l , d i r e c t e d t o w a r d s t h e u n d e r f l o w . I t w a s t h e r e f o r e u s u a l l y f o u n d c o n v e n i e n t t o c o l o u r t h e m o r e d e n s e w a t e r i n i t s o r i g i n a l p o s i t i o n a n d t h u s see c l e a r l y t h e p r o g r e s s of t h e u n d e r f l o w a f t e r t h e r e m o v a l of t h e b a r r i e r . T o t h e eye, a n d t o t h e c a m e r a , t h e c o l o u r e d wrater is d o m i n a n t over u n c o l o u r e d w a t e r . T h e d i l u t i o n of t h e p r o g r e s s i n g u n d e r f l o w c a n b e q u i t e a d v a n c e d b e f o r e i t is v i s u a l l v o b v i o u s . O n t h e o t h e r h a n d if a n
u n c o l o u r e d f r o n t p r o g r e s s e s i n t o c o l o u r e d w a t e r i t s f o r m m a y b e difficult t o d i s t i n g u i s h b e c a u s e of t h e c o l o u r e d w a t e r w h i c h is d r a w n i n t o i t s s w i r l i n g t i p . B y c o l o u r i n g first t h e m o r e d e n s e a n d t h e n t h e l e s s d e n s e w a t e r a n d t a k i n g s e t s of s i m u l t a n e o u s p h o t o g r a p h s a t s e l e c t e d s t a g e s of d e v e l o p m e n t of t h e e x c h a n g e flow i n b o t h c a s e s , K e u l e g a n (1957) b u i l t u p a c o m p o s i t e p i c t u r e of e x c h a n g e flow for o n e c h o s e n c a s e . H i s c o n f i g u r a t i o n , i n f l u e n c e d b y a n i n t e r e s t i n t h e m o t i o n of s a l t w a t e r r e l e a s e d i n t o a c a n a l f r o m a s h o r t lock ( l e n g t h L0) w a s B / H = 0.5, L0/ H = 7, a n d t h e r e w a s sufficient c a n a l l e n g t h for L / H for t h e u n d e r f l o w t o r e a c h 4 0 . W i t h H = 10 i n c h e s , Ap/p = 0.020, K . g T ^ t f l w a s 23,800. A l t h o u g h t h e l a t t e r s t a g e s of d e v e l o p m e n t w e r e n a t u r a l l y m u c h affected b y t h e reflection ( F i g . 1) r e s u l t i n g f r o m t h e overflow^
s t r i k i n g t h e e n d of t h e l o c k t h e e a r l y r e c o r d i n g s f r o m t h e s e e x p e r i m e n t s f i r s t d e m o n s t r a t e d t h a t t h e d e v e l o p m e n t of t h e overflow a n d u n d e r flow i n f r e e s u r f a c e l o c k e x c h a n g e flow a r e n o t s y m m e t r i c a l . B a r r (1959) s t u d i e d b o t h o v e r f l o w a n d u n d e r f l o w a n d f o u n d a s s h o w n o n F i g u r e s 1, 2 a n d 4 of I t h a t t h e i n i t i a l t i p v e l o c i t y of t h e overflow e x c e e d e d t h a t of t h e u n d e r f l o w b y
a b o u t 12 % t h r o u g h o u t t h e r a n g e of W^GX a t t a i n a b l e i n a m o d e r a t e l y sized flume. N o m e a s u r e m e n t s of wra t e r v e l o c i t i e s w e r e m a d e b y K e u l e g a n o r B a r r , n o r h a v e s u c h b e e n r e p o r t e d for c o n t r o l l e d c o n d i t i o n s b y a n y o t h e r w o r k e r s , so f a r a s is k n o w n (Allen a n d P r i c e , 1959, h a v e c o m p a r e d s o m e v e l o c i t y m e a s u r e m e n t s f o r a c o m p l e x a n d u n s y m e t r i c a l l y n o n - p r i s m a t i c p r o t o t y p e c o n f i g u r a t i o n a n d a m o d e l t h e r e o f ) . I n d e e d t h e t o t a l c o l o u r i n g of o n e o r o t h e r of t h e b o d i e s of w a t e r t o a l l o w e a s y o b s e r v a t i o n of t h e tip v e l o c i t i e s h a s t e n d e d t o p r e v e n t a n y v i s u a l i m p r e s s i o n of t h e i n t e r n a l v e l o c i t i e s being- o b t a i n e d . P r a n d t l (1952) h a s i n d i c a t e d t h a t
FIG. 1
Diagramatic illustration of reflection effects in lock exchange flow-overflow reflected.
Representation schématique des phénomènes de réflexion intéressant un écoulement d'échange en écluse, avec réflexion de l'écoulement « par en-dessus ».
NOVEMBRE 1 9 6 3 - № 7 D . I. H . B A R R AND A . M. M. H A S S A N 7 5 9
f o l l o w - u p v e l o c i t i e s a p p r o a c h i n g t w i c e t h e f r o n t a l v e l o c i t y m a y o c c u r i n a n a l o g o u s c o l d - w a r m a i r p h e n o m e n a ( t r u l y a n a l o g o u s t o d a m b u r s t a n a l o g y e x c h a n g e f l o w ) .
A s r e g a r d s m i x i n g a c t i o n s , t w o t y p e w e r e n o t e d . At t h e t i p , e s p e c i a l l y t h e u n d e r f l o w t i p , t h e r e w a s a r o l l i n g u p p r o c e s s s i m i l a r t o t h a t s h o w n i n P r a n d t l ' s (1952) i l l u s t r a t i o n s . T h i s w a s o b s e r v e d w h e n t h e i n t e r f a c e w a s o t h e r w i s e c o m p l e t e l y s m o o t h , s u g g e s t i n g p r a c t i c a l l y l a m i n a r c o n d i t i o n s of flow a t t h e i n t e r f a c e a t l e a s t . I n s o m e c a s e s t h e s p i r a l w a s s e e n q u i t e a s d i s t i n c t l y a s i n P r a n d t l ' s i d e a l i s e d f i g u r e ( B a r r , 1959). A s t h e i n c r e a s i n g of t h e d e p t h o r of i n i t i a l d e n s i t y d i f f e r e n c e , o r b o t h , l e d t o w a r d s m o r e t u r b u l e n t c o n d i t i o n s , t h e s p i r a l l i n g l a y e r s n o l o n g e r a p p e a r e d t o h a v e d i s t i n c t e x i s t e n c e , b u t t h e g e n e r a l p a t t e r n of m o v e m e n t s e e m e d t o b e t h e s a m e .
T h e o t h e r t y p e of m i x i n g a c t i o n w h i c h w a s c l e a r l y o b s e r v e d , o c c u r r e d b e h i n d t h e t i p of t h e u n d e r f l o w w h e n t h e d e p t h a n d d e n s i t y difference w e r e s u c h a s t o give v a l u e s of K.g>Adl of t h e o r d e r of 5,000 o r r a t h e r l e s s . I n t e r f a c i a l w a v e s , o n t h e p o i n t of b r e a k i n g , w e r e o b s e r v e d i n t h e r e g i o n b e h i n d t h e u n d e r f l o w f r o n t i n e x c h a n g e flowrs of t h e o r d e r of 3 i n c h e s t o t a l d e p t h i n a n 18 i n c h w i d e f l u m e a n d w h e n t h e e x t e n s i o n t o d e p t h r a t i o of t h e f r o n t , L / H , w a s of t h e o r d e r of 20 t o 3 0 . W h e n K.W^bX w a s s l i g h t l y i n c r e a s e d , b r e a k i n g of t h e w a v e s c o u l d b e s e e n a n d o n f u r t h e r i n c r e a s e t h e i n d i v i d u a l waA'es c o u l d n o l o n g e r b e d i s t i n g u i s h e d , t h e g e n e r a l i m p r e s s i o n g a i n e d b y t h e first a u t h o r a f t e r w a t c h i n g m a n y e x p e r i m e n t s , b e i n g t h a t t h e t u r b u l e n t m i x i n g b e t w e e n t h e t w o l a y e r g r e w m o r e i n t e n s e w i t h i n c r e a s i n g v a l u e s of K.&'^Ol-
T h e a p p e a r a n c e of t h e t w o c o n d i t i o n s of n o n b r e a k i n g a n d j u s t b r e a k i n g w a v e s w a s v e r y s i m i l a r t o t h e p h o t o g r a p h s g i v e n b y I p p e n a n d H a r l e m a n (1952) f o r a s i m i l a r , t h o u g h s t e a d y s t a t e , c i r c u m s t a n c e . T h i s t y p e of i n t e r f a c i a l w a v e f o r m a t i o n w a s a l s o n o t e d b y E l l i s o n a n d T u r n e r (1959) a s o c c u r r i n g b e h i n d t h e n o s e of a n u n d e r f l o w l a y e r p r o g r e s s i n g d o w n a s l i g h t s l o p e .
It s e e m e d r e a s o n a b l e t o a s s u m e t h a t s i m i l a r w a v e s c o u l d b e o b t a i n e d b e h i n d a n "overflow f r o n t , t h o u g h s u c h w e r e n o t a c t u a l l y o b s e r v e d . T h u s t h e o v e r a l l i m p r e s s i o n a t t h e e n d of t h e first s t a g e of t h e i n v e s t i g a t i o n of l o c k e x c h a n g e flows w a s t h a t t h e t w o m i x i n g a c t i o n s , p a r t i c u l a r l y t h e s e c o n d , i n t e n s i f i e d w i t h i n c r e a s i n g v a l u e s of K.g>Adl a n d t h a t i n t e r f a c i a l d r a g p r o v i d e d t h e e x p l a n a t i o n f o r t h e r e l a t i v e l y m o r e p r o n o u n c e d d i m i n u t i o n of v e l o c i t y of l o w v a l u e s of K . $ iA 01. W i t h o u t a n y a c t u a l m e a s u r e m e n t s
h a v i n g b e e n t a k e n , t h e i m p r e s s i o n of a n i n t e r face m o r e o r less d i s t i n c t , d e p e n d i n g o n t h e d e g r e e of t u r b u l e n c e , a n d w i t h t u r b u l e n t o r l a m i n a r t y p e v e l o c i t y d i s t r i b u t i o n p a t t e r n s a b o v e a n d b e l o w t h e i n t e r f a c e w a s a l s o p r e s e n t .
4. T H E F L U M E S ( A , B a n d C )
It is c o n v e n i e n t t o briefly d e s c r i b e t h e f l u m e s u s e d for t h e e x p e r i m e n t s c o n s i d e r e d h e r e , a n d w h i c h w e r e u s e d i n o b t a i n i n g t h e r e s u l t s given i n I. S o m e d e t a i l s p e r t i n e n t t o t h e n e x t p a p e r (.III) a r e i n c l u d e d .
F l u m e A w a s b u i l t i n 1958 a t t h e s t a r t of t h e p r o g r a m m e of s t u d y of d e n s i m e t r i c effects w h i c h w a s t h e n p r i m a r i l y i n t e n d e d t o give u n d e r s t a n d i n g of t h e u s e f u l s c o p e of h e a t d i s s i p a t i o n m o d e l s a n d of t h e s c a l i n g t h e r e o f . T h u s t h e f l u m e w a s p l a n n e d t o s e r v e v a r i o u s f u n c t i o n s a n d w a s a c o m p r o m i s e b e t w e e n t h e n e e d s of t h e s e v a r i o u s f u n c t i o n s a n d t h e s p a c e a v a i l a b l e . I t w a s 18 i n c h e s w i d e , 10 i n c h e s d e e p a n d h a d a t o t a l l e n g t h of 19 feet. T o g e t h e r w i t h a n 18 feet b y 7 feet b y 18 i n c h e s d e e p t a n k u s e d f o r t h e t h r e e d i m e n s i o n a l s t u d i e s m e n t i o n e d i n I, i t f o r m e d a c i r c u i t i n w h i c h a c o n t r o l l e d flow c o u l d b e o b t a i n e d b y m e a n s of a % c u s e c p u m p , a c o n s t a n t h e a d t a n k a n d a V - n o t c h w e i r i n s t a l l e d a s p a r t of t h e c i r c u i t . T o u s e t h e f l u m e f o r lock e x c h a n g e flow e x p e r i m e n t s , a p e r m a n e n t b a r r i e r wras p l a c e d n e a r t h e " u p s t r e a m " e n d a n d a n a d j u s t a b l e g a t e a t t h e " d o w n s t r e a m " e n d w a s r a i s e d . T h e p o s i t i o n of t h e g r o o v e s f o r t h e r e m o v e a b l e b a r r i e r g a v e a 13 feet l e n g t h b e t w e e n i t a n d t h e e n d g a t e . I n i t i a l l y t h e p e r m a n e n t b a r r i e r w a s p l a c e d t o give a 4 feet s h o r t e r l e n g t h a n d l a t t e r l y a feet s h o r t e r l e n g t h . T h i s flume, w h i c h h a d o n e s i d e t r a n s p a r e n t , is s h o w n i n F i g u r e s 5 a n d 6 of I a n d w a s a l w a y s u s e d o p e n , t h e r e b e i n g n o t o p . I t w a s n o t , i n g e n e r a l , e a s y t o l i g h t for p h o t o g r a p h i n g o r t o p h o t o g r a p h , p a r t of i t s l e n g t h r u n n i n g close t o a w a l l .
At a h i g h e r level i n t h e l a b o r a t o r y t w o b a t c h i n g t a n k s w e r e s e r v e d b y t h e n o r m a l h o t a n d cold w a t e r s u p p l i e s , a n d w e r e of sufficient c a p a c i t y t o p r o v i d e t h e 17 a n d 7 c u b i c feet n e c e s s a r y to fill t h e l a r g e r a n d s h o r t e r l e n g t h s r e s p e c t i v e l y . D u r i n g Jock e x c h a n g e e x p e r i m e n t s t h i s w a t e r w a s fed i n t o t h e l e n g t h s , s e p a r a t e d b y t h e r e m o v e a b l e b a r r i e r . A f t e r a t e s t t h e w a t e r w a s q u i c k l y d u m p e d i n t o t h e t a n k b y l o w e r i n g t h e a d j u s t a b l e g a t e l e a v i n g t h e f l u m e r e a d y f o r a n o t h e r t e s t .
F l u m e B w a s a 4y« i n . b y 4% i n s q u a r e " p i p e , "
a g a i n w i t h o n e s i d e t r a n s p a r e n t . I t w a s s i x t e e n
feet l o n g , w i t h t h e r e m o v e a b l e b a r r i e r i n t h e m i d d l e a n d w i t h solid e n d s . I t w a s p l a c e d on a l o n g t a b l e w h i c h c o u l d b e r a p i d l y t i l t e d t o aid e m p t y i n g a n d filling f r o m t h e s a m e h i g h level b a t c h i n g t a n k s a s u s e d for f l u m e A. F l u m e B c o u l d b e e a s i l y p h o t o g r a p h e d , a n d is s h o w n in F i g u r e s 4 a n d 5 b of I.
F l u m e C w a s a l s o of t h e e n c l o s e d t y p e , 4 feet l o n g a n d of IVi i n c h by % i n c h s e c t i o n w i t h t h e r e m o v e a b l e b a r r i e r i n t h e m i d d l e . It c o u l d b e u s e d a s e i t h e r a " w i d e " flume w i t h B / H — 6 or a s a v e r y n a r r o w f l u m e w i t h B / H = 0.167.
d i a t e l a y e r b e t w e e n t h e m a i n s t r e a m f o l l o w i n g ( a n d f e e d i n g ) t h e f r o n t a n d t h e o p p o s i n g c o u n t e r flow. T h i s i n t e r m e d i a t e l a y e r t h u s s e r v e d t o s e p a r a t e t h e m a i n f o r w a r d t r a n s f e r z o n e f r o m t h e n e c e s s a r y c o u n t e r flow. It i s c o n v e n i e n t t o call t h e m a i n flow t h e s u b - c u r r e n t , w h e t h e r i t b e t h e u n d e r f l o w or t h e overflow c a s e , b e c a u s e i t is d i s t i n g u i s h e d a s b e i n g s o m e d i s t a n c e w i t h i n t h e b o u n d a r y of t h e u n d e r f l o w or overflow a s m i g h t b e defined e i t h e r b y t h e l i n e j o i n i n g z e r o v e l o c i t y p o i n t s o r t h e l i n e of e q u a l m i x i n g of t h e t w o differing b o d i e s of w a t e r .
5 . O B S E R V A T I O N A L E X P E R I M E N T S W I T H B L O C K C O L O U R I N G
( F l u m e A , 1 9 6 1 )
B y i n t r o d u c i n g o n e or m o r e a d d i t i o n a l t h i n v e r t i c a l c r o s s b a r r i e r s i n t o t h e flume o n c e i t h a d b e e n filled i n t h e n o r m a l w a y for a lock type, e x c h a n g e e x p e r i m e n t , i t w a s p o s s i b l e t o c o l o u r a b l o c k of e i t h e r t h e m o r e d e n s e o r t h e less d e n s e w a t e r w i t h o u t o t h e r w i s e affecting t h e e x p e r i m e n t . T h e s e a d d i t i o n a l b a r r i e r s w e r e t h e n s l o w l y w i t h d r a w n , l e a v i n g t h e c o l o u r e d b l o c k m o d e r a t e l y d i s t i n c t a n d s o o n a f t e r t h i s t h e e x p e r i m e n t c o u l d b e s t a r t e d i n t h e n o r m a l w a y b y swift
ly lifting t h e m a i n b a r r i e r . T h i s s i m p l e t e c h n i q u e a t o n c e gave a n e w i n s i g h t i n t o e x c h a n g e flow. F i r s t a b l o c k of t h e m o r e d e n s e w a t e r n e x t t o t h e m a i n b a r r i e r w a s c o l o u r e d d u r i n g a n e x p e r i m e n t of d e p t h a n d d e n s i t y difference s u c h a s t o give a l o w d e n s i m e t r i c F r o n d e - R e y n o l d s n u m b e r ( K . g >A ¿ 1 = 1,000). A l t h o u g h u p o n i n i t i a t i o n of t h e e x c h a n g e s o m e of t h e c o l o u r e d w a t e r w a s d i s t r i b u t e d a l o n g t h e e x t e n d i n g i n t e r - face m o s t of it m o v e d a l o n g t h e f l u m e w i t h t h e u n d e r f l o w . D i l u t i o n o c c u r r e d d u e t o t h e e n t r y of t h e less d e n s e w a t e r j u s t b e h i n d t h e c h a r a c - t e r i s t i c b u l g e , b u t t h e d i l u t e d w a t e r m o s t l y r e m a i n e d i n t h e f o r w a r d p a r t of t h e u n d e r f l o w . T h e v e l o c i t y r a p i d l y d i m i n i s h e d a n d i t a p p e a r e d t h a t t h e d i l u t i o n h a d i n h i b i t e d t h e c a p a c i t y for a d v a n c e . W h e n a b l o c k f u r t h e r b a c k f r o m t h e m a i n b a r r i e r w a s c o l o u r e d , n o c o l o u r e d w a t e r r e a c h e d t h e f r o n t d u r i n g t h e p e r i o d of o b s e r v - a t i o n w h i c h l a s t e d u n t i l t h e f r o n t a l v e l o c i t y h a d fallen t o a s m a l l f r a c t i o n of t h e i n i t i a l v e l o c i t y . S i m i l a r e x p e r i m e n t s w e r e t h e n u n d e r t a k e n w i t h K . S"A. dv v a l u e s of 7,000 u p w a r d s for b o t h underflow7 a n d overflow. B l o c k s of w a t e r i n i - t i a l l y s o m e s m a l l d i s t a n c e f r o m t h e m a i n b a r r i e r w e r e c o l o u r e d . W h e n t h e s e c a m e i n t o m o t i o n m o s t of t h e c o l o u r e d w a t e r w a s s e e n t o m o v e r a p i d l y a f t e r t h e f r o n t , t o o v e r t a k e it, to be d i l u t e d b y t h e p r o n o u n c e d m i x i n g a c t i o n a t t h e n o s e , a n d t o be d i s c a r d e d to f o r m a n i n t e r m e -
6. V A R I O U S R E C O R D I N G S O F T H E S T R U C T U R E O F L O C K E X C H A N G E F L O W
E x p l a n a t o r y n o t e .
T h e o b v i o u s f o l l o w u p t o t h e b l o c k c o l o u r i n g o b s e r v a t i o n s m a d e i n 1 9 6 1 , s e e m e d t o b e t o o b t a i n m e a s u r e m e n t s of t h e i n t e r n a l s t r u c - t u r e of e x c h a n g e f l o w — v e l o c i t i e s a n d d i l u t i o n — a s e v i d e n c e of t h e v a r y i n g m e c h a n i s m s t h a t h a d b e e n o b s e r v e d . T h i s w a s i n fact a t t e m p t e d w i t h o n l y m o d e r a t e s u c c e s s . N o w a s t h i s p a p e r i s b e i n g p r e p a r e d i n 1963, the. s o m e w h a t difficult t a s k of i n t e r n a l s t r u c t u r e m e a s u r e m e n t s i n a n u n s t e a d y s y s t e m s e e m s less i m p o r t a n t f o r seve- r a l r e a s o n s :
(i) A l t h o u g h t h r e e d i m e n s i o n a l s p r e a d is n o t r e a l l y w i t h i n t h e s c o p e of t h e s e p a p e r s , i t h a s b e e n e x p l a i n e d i n I t h a t t h e d e s i r e t o f o r m u l a t e r u l e s f o r t h e s c a l i n g of h y d r a u l i c m o d e l s i n v o l v - i n g t h r e e d i m e n s i o n a l s p r e a d w a s t h e o r i g i n a l m o t i v a t i o n of t h e s t u d i e s . A f t e r t h e a t t e m p t s t o o b t a i n r e c o r d i n g s of t h e s t r u c t u r e i n t h e t w o d i m e n s i o n a l c a s e d u r i n g 1 9 6 1 , i t w a s d e c i d e d t o a p p l y a m o d i f i c a t i o n of t h e b l o c k c o l o u r i n g m e t h o d to t h e simplified o u t f a l l s t u d i e s m e n t i o n - ed i n I. H e r e t h e p r o c e d u r e w a s e x t r e m e l y simple-—the b u o y a n t w a t e r d i s c h a r g e d f r o m t h e o u t f a l l w a s c o l o u r e d w i t h a w e a k d y e . S o m e t i m e a f t e r t h e s t a r t of a n e x p e r i m e n t w h e n a s u r f a c e field h a d f o r m e d , a s e c o n d a n d d o m i n e n t c o l o u r i n g a g e n t w a s a d d e d t o t h e o u t f a l l flow a n d t h e f u r t h e r t i m e i n t e r v a l for t h e s e c o n d c o l o u r t o o v e r t a k e t h e s p r e a d i n g f r o n t o n , s a y , t h e p r o d u c e d c e n t r e l i n e of t h e o u t f a l l w a s n o t - ed. V a r i o u s i n i t i a l i n t e r v a l s w e r e so t e s t e d a n d t h e n t h e w h o l e r e p e a t e d a t a different h o r i z o n t a l s c a l e (on fifth size w i t h a p p r o p r i a t e v e r t i c a l e x a g g e r a t i o n ) . T h i s p r o v e d t o be a v e r y u s e f u l m e t h o d of a s s e s s i n g t h e d e g r e e of s i m i l a r i t y o b t a i n e d i n i n t e r n a l m o t i o n s a s b e t w e e n s m a l l s c a l e i d e a l i s e d o u t f a l l c o n f i g u r a t i o n s u s i n g t h e c o n g r u e n c y d i a g r a m s c a l i n g m e t h o d , a n d d i d
NOVEMBRE 1 9 6 3 - № 7 D . I. H . B A R R AND A . M. M. H A S S A N 7 6 1
n o t i n v o l v e a n y d i r e c t m e a s u r e m e n t of fluid v e l o c i t i e s .
A g a i n , k n o w i n g n o w w h a t to l o o k for, t h e o v e r t a k i n g a n d d i s c a r d m e n t p a t t e r n s , w h i c h m u s t b e g e n e r a l t o all s p r e a d p h e n o m e n a w h e r e t h e t w o l i q u i d s o r fluids a r e m i s c i b l e , w e r e e a s i l y a n d r e a s s u r i n g l y r e c o g n i s e d i n t h e l a r g e h e a t d i s s i p a t i o n m o d e l s b e i n g o p e r a t e d b y t h e Civil E n g i n e e r i n g D e p a r t m e n t of t h e R o y a l College d u r i n g 1962 ( S m i t h , 1 9 6 2 ) .
(ii) I t is n o w k n o w n t h a t t h e r e a r e a t l e a s t t w o m e t h o d s of s e t t i n g u p s t e a d y s t a t e e x c h a n g e flow; t h e first of t h e s e h a s a l r e a d y b e e n d e s c r i b ed ( B a r r , 1962), t h e s e c o n d a n d m o r e i m p o r t a n t c a s e is t o be d e a l t w i t h i n I I I . A l t h o u g h t h e m e c h a n i s m s of e n t r a i n m e n t a n d d i s c a r d m e n t m a y differ i n d e t a i l i n s u c h c a s e s , t h e r e m u s t be basic, s i m i l a r i t y t o t h o s e m e c h a n i s m s a s t h e y o c c u r i n t h e n o n - s t e a d y c a s e s a n d c e r t a i n l y r e c o r d i n g s w o u l d b e m u c h s i m p l e r t o o b t a i n .
F o r t h e s e r e a s o n s i t w a s d e c i d e d (in 1963) m e r e l y t o o b t a i n , a s s i m p l y a s p o s s i b l e , suffi
c i e n t a d d i t i o n a l r e c o r d i n g s t h a t t h e c o m b i n e d e v i d e n c e w o u l d c l e a r l y i l l u s t r a t e h o w v a r i a t i o n of t h e d i s c a r d m e n t t o e n t r a i n m e n t r a t i o affects t h e d i m i n u t i o n of v e l o c i t y p a t t e r n s . If, a s is h o p e d , e n l a r g e d a n d i m p r o v e d f a c i l i t i e s b e c o m e a v a i l a b l e for t h e s t u d y of b o t h n o n - s t e a d y s t a t e a n d s t e a d y s t a t e e x c h a n g e flows, i t c a n t h e n b e d e c i d e d t o w h a t e x t e n t d e t a i l e d o b s e r v a t i o n s of s t r u c t u r e a r e d e s i r a b l e a n d feasible i n t h e n o n - s t e a d y c a s e s .
P h o t o g r a p h s o f p a i r s o f e x p e r i m e n t s w i t h d i f f e r e n c i a l c o l o u r i n g .
K e u l e g a n ' s (1957) u s e of t h e t e c h n i q u e of differencial c o l o u r i n g h a s a l r e a d y b e e n m e n t i o n ed, i n 3 a n d F i g u r e 4 of I s h o w s t y p i c a l r e s u l t s o b t a i n e d i n t h i s w a y . D e s p i t e t h e s h o r t l o c k l e n g t h ( L0/ H — 7) a n d t h e n a r r o w f l u m e w i d t h ( B / H = 0.5) K e u l e g a n ' s r e s u l t s c a n b e h e l d t o provide" s o m e e v i d e n c e r e l e v a n t t o t h e s t a n d a r d c a s e — i t c a n n o t b e t h o u g h t for i n s t a n c e t h a t e i t h e r t h e n a r r o w w i d t h or t h e effect of a reflection of t h e overflow f r o m t h e lock e n d w o u l d a t a n y t i m e i n c r e a s e t h e v e l o c i t y of a n u n d e r f l o w f r o n t . I n t h i s c a s e w i t h a K-3>A6l v a l u e of 23,800, t h e f r o n t v e l o c i t y (V) a t an e x t e n s i o n to d e p t h r a t i o ( L / H ) of 39.3 w a s s l i g h t l y g r e a t e r t h a n 0.9 V0. A t all t i m e s u p t o t h i s e x t e n s i o n u n d i l u t e d s a l i n e w a t e r w a s f o u n d b y K e u l e g a n t o e x t e n d a l o n g t h e b o t t o m of t h e f l u m e a n d r i g h t u p t o t h e v e r y f r o n t of t h e u n d e r f l o w . A b o v e t h i s b o t t o m l a y e r l a y a z o n e of m i x e d w a t e r , t y p i c a l l y o c c u p i n g b e t w e e n o n e fifth a n d o n e s i x t h of t h e t o t a l d e p t h . I t will be s e e n f r o m F i g u r e 8 of I t h a t t h e L / H r a t i o a t K-WTTft of a b o u t 24,000 for V / V0 = 0.9 is, b y
e x t r a p o l a t i o n , e s t i m a t e d t o b e a b o u t 110, n e a r t h e " e s t i m a t e d " l i m i t of 120 for t h e s t a n d a r d c a s e of a w i d e c h a n n e l ( B / H ^ 6) w i t h n o reflection.
T h e c o m p a r a b l e l i m i t s of L / H (i.e. L / H for V / V0 = 0.9) for t h e n a r r o w c h a n n e l ( B / H = 0,5) a s f o u n d b v K e u l e g a n w e r e a b o u t 50 for L0/ H of 7.2 a n d "65 for L0/ H of 14.4. D a t a for t h e s t a n d a r d c a s e a t K.<J!A Jl v a l u e s f r o m 20,000 u p w a r d s is v e r y m u c h n e e d e d — i t is n o t p o s s i b l e t o fully d i s t i n g u i s h b e t w e e n t h e effects of t h e n a r r o w c h a n n e l a n d of t h e reflection w h i c h m u s t o b v i o u s l y c o m b i n e t o r e d u c e t h e c a p a c i t y of t h e u n d e r f l o w to m a i n t a i n t h e i n i t i a l v e l o c i t y , b u t t h e r e s u l t s of K e u l e g a n q u o t e d l e a d o n e t o e x p e c t t h a t for K . 3<A oX v a l u e s of 24,000 u p w a r d s a n d p r e s u m i n g t h e s t a n d a r d c a s e , u n d i l u t e d w a t e r w o u l d b e p r e s e n t a t t h e f r o n t m o v i n g a t v e l o c i t y V > 0.9 V0 for L / H v a l u e s of u p w a r d s of 70 a n d p e r h a p s m u c h g r e a t e r .
F i g u r e 4 a n d 5 of I p r o v i d e r o u g h l y c o m p a r a b l e i n f o r m a t i o n for K.W^lJL v a l u e s of a b o u t 5,000. I n t h e c a s e of F i g u r e 4 t h e L / H v a l u e for t h e overflow w a s 18 a t t h e t i m e e a c h p h o t o g r a p h w a s t a k e n (i.e. a n e x t e n s i o n of 6 f e e t ) . T h e e x t e n s i o n of t h e u n d e r f l o w is s e e n to b e a b o u t 5 feet 5 i n c h e s ( L / H = 16.2) a n d ( 1 8 - 1 6 . 2 ) / 1 6 . 2 is a b o u t 11 % , v e r y c l o s e t o t h e t y p i c a l 12 % q u o t e d i n I. T w o t r e n d s c a n b e o b s e r v e d : firstly t h e r e a r e s i g n s of d i l u t i o n a t t h e f r o n t s d e s p i t e t h e c o m p a r a t i v e l y s m a l l L / H r a t i o s ( L / H for F i g u r e 5 a i s 3.2 a n d for F i g u r e 5 b is 1 1 . 6 ) ; a n d s e c o n d l y t h e z o n e s of m i x ed w a t e r a p p e a r t o be t h i n n e r t h a n i n K e u l e g a n ' s e x p e r i m e n t .
F o r t h e n e x t t w o s t a g e s of d e c r e a s e of K . 9<A o\ w h i c h a r e t o be d e s c r i b e d , n o a t t e m p t h a s b e e n m a d e t o o b t a i n p h o t o g r a p h s ; it w a s t h o u g h t t h a t it w o u l d be difficult t o o b t a i n m e a n i n g f u l r e s u l t s . F u r t h e r t h e t r e n d s b e c o m e m o s t p r o n o u n c e d a n d , b e c a u s e of t h e g r e a t i n c r e a s e i n t i m e a v a i l a b l e for v i s u a l o b s e r v a t i o n , e a s i e r t o d e s c r i b e . T h e s a m e flume (B) a s is s h o w n i n F i g u r e 4 of I w a s filled to 1 i n c h d e p t h o r V2 i n c h d e p t h ( K . ^A (R. i n t h e r e g i o n 2 0 0 - 6 0 0 ) . T h u s a m u c h g r e a t e r r e l a t i v e e x t e n s i o n w a s p o s s i b l e t h a n w h e n it w a s full o r n e a r l y full.
F i g u r e 8 of I s h o w s h o w p r o n o u n c e d d i m i n u t i o n of v e l o c i t y o c c u r r e d a t r e l a t i v e l y s m a l l e x t e n s i o n s . I t w a s m o s t n o t i c e a b l e t h a t a c o l o u r e d f r o n t b e c o m e c o n s i d e r a b l y d i l u t e d a n d t h a t t h i s d i l u tion e x t e n d e d b a c k for s o m e d i s t a n c e ; m o r e o v e r it w a s n o w p r a c t i c a l l y i m p o s s i b l e t o o b s e r v e a n u n c o l o u r e d f r o n t p e n e t r a t i n g i n t o a c o l o u r e d z o n e b e y o n d t h e i n i t i a l s t a g e s of d e v e l o p m e n t .
T h e final s t a g e of d e c r e a s e of K . " pA ol w a s r e a c h e d i n F l u m e C. T h i s % i n c h d e e p e n c l o s e d f l u m e w a s c o n s t r u c t e d e n t i r e l y of p e r s p e x a n d
t h e f r o n t s w e r e o b s e r v e d b y v i e w i n g f r o m a b o v e w i t h a w h i t e b a c k g r o u n d b e l o w . A l t h o u g h t h e i n i t i a l Yi i n c h of p o t a s s i u m p e r m a n g a n a t e c o l o u r e d w a t e r a p p e a r e d a s a d e n s e c o l o u r , t h e d i l u t i o n w a s so p r o n o u n c e d t h a t i t b e c a m e difficult t o o b s e r v e e v e n t h e c o l o u r e d f r o n t a t L / H v a l u e s of 30 a n d a b o v e . I n o n e e x p e r i m e n t ( K . &>A 6X, = 45.5) w h i c h w a s c o n t i n u e d l o n g after t h e s t a g e r e q u i r e d t o o b t a i n d a t a f o r F i g u r e 8 of I, t h e f r o n t w a s still j u s t visible a t L / H of 6 2 , m o v i n g a t a b o u t 0.005 i n c h e s p e r s e c o n d (0.017 V0) a n d w i t h t h e c o l o u r d e e p e n i n g o n l y g r a d u a l l y w i t h d i s t a n c e b a c k t o w a r d s t h e b a r r i e r . T h e i m p r e s s i o n w a s g a i n e d t h a t t h e m e c h a n i s m of e x c h a n g e w a s c o m p l e t e l y r e v e r s e d f r o m t h a t o b t a i n i n g i n t h e t u r b u l e n t r e g i o n . I n s t e a d of u n d i l u t e d w a t e r c o n t i n u a l l y o v e r t a k i n g t h e f r o n t
— a n d t h u s n e c e s s i t a t i n g g r e a t e r i n t e r n a l velo
cities t h a n t h a t of t h e f r o n t — t h e w a t e r t o t h e r e a r a p p e a r e d t o h a v e a l m o s t c o m e t o r e s t , w i t h the f r o n t m a i n t a i n i n g i t s a d v a n c e o n l y b y c o m p l e t e l y e n t r a i n i n g t h e w a t e r i n t o wdiich i t m o v e d .
D y e i n j e c t i o n o b s e r v a t i o n s .
T o o b t a i n s o m e definite r e s u l t s i l l u s t r a t i n g t h e e n t r a i n m e n t a n d d i s c a r d m e n t p r o c e s s a s i m p l e d y e i n j e c t i o n s y s t e m w a s a r r a n g e d for flume B . E x p e r i m e n t s w e r e c o n d u c t e d b y c o l o u r i n g o n e of t h e d i s s i m i l a r b o d i e s of w a t e r w i t h f l u o r i s e n e a n d b y i n j e c t i n g p o t a s s i u m p e r m a n g a n a t e s o l u t i o n o n c e t h e e x c h a n g e flow h a d b e e n i n i t i a t e d . T w o c o m b i n a t i o n s of d e p t h a n d of d e n s i t y difference •were c h o s e n t o b e close t o t h e l i m i t s of K.~$>A (R. t h o u g h t r e a s o n a b l e i n t h e c i r c u m s t a n c e s
D e p t h (H) Ap/p ( a s s u m i n g K = 0.5)' (£) 3 i n . 0.032 5,650 (if) l i n . 0.005 4 3 0 A 0.03 i n c h b o r e s t a i n l e s s steel t u b e w a s u s e d t h e i n j e c t t h e d y e ; o n e e n d wras b l o c k e d a n d a c i r c u l a r h o l e of s l i g h t l y s m a l l e r d i a m e t e r w a s d r i l l e d a t r i g h t a n g l e s t o t h e axis of t h e t u b e a n d j u s t a b o v e t h i s e n d . T h e t u b e w a s i n s e r t e d i n t o t h e flume t h r o u g h h o l e s d r i l l e d v e r t i c a l l y i n t h e t o p b o a r d o n e i n c h f r o m t h e p e r s p e x side a n d w a s a l w a y s p o s i t i o n e d so t h a t t h e a x i s of t h e o u t l e t h o l e w a s n o r m a l t o t h e l e n g t h of t h e flume.
C o n s i d e r i n g t h e e x p e r i m e n t s w i t h t h e l a r g e r v a l u e of K . g rA (Jl (5,650) first, t h e i n j e c t i o n t u b e w a s p o s i t i o n e d 9 i n c h e s (3 H ) i n f r o n t of t h e b a r r i e r a n d e i t h e r h a l f a n i n c h . f r o m t h e b o t t o m or j u s t b e l o w t h e w a t e r s u r f a c e for underflow' a n d overflow7 r e s p e c t i v e l y . T h e f r o n t w a s a l l o w -
ed t o p a s s t h e t u b e b y s o m e p r e d e t e r m i n e d d i s - t a n c e t h e n d y e w a s i n j e c t e d a n d t h e e x t e n s i o n of t h e t i p of t h e f r o n t a t t h e p o i n t w h e n t h e i n j e c t - ed d y e r e a c h e d t h e t i p w a s n o t e d — t h e p o i n t of " o v e r t a k i n g " . R e s u l t s w e r e o b t a i n e d a s s h o w n i n T a b l e 1.
TABLE 1
Details of overtaking observations
K . # A ~ t f l = 5 , 6 5 0
TYPE OF FRONT
PASSING DISTANCE OVERTAKING POINT ( d i s t a n c e f r o m t u b e ) TYPE OF FRONT
I n c h e s R e l a t i v e I n c h e s R e l a t i v e
U n d e r f l o w . . 9 3 H 3 6 1 2 H
U n d e r f l o w . . 1 8 6 H 6 9 2 3 H
O v e r f l o w . . . 9 3 H 3 6 1 2 H
O v e r f l o w . . . 1 8 6 H 8 4 2 8 H
F i g u r e 2 s h o w s p h o t o g r a p h s t a k e n d u r i n g a n e x p e r i m e n t of t h i s t y p e . T h e fluorisene j u s t s h o w s o n t h e o r i g i n a l p r i n t a n d d o t t e d l i n e s h a v e b e e n a d d e d t o d e l i n e a t e the. t i p . T h e n u m b e r s i n d i c a t i n g feet f r o m t h e b a r r i e r h a v e a l s o b e e n r e - t o u c h e d . I n t h i s case t h e p a s s i n g d i s t a n c e e s t i m a t e d f r o m F i g u r e 2 a w a s 3.5 H o r s l i g h t l y m o r e a n d i t , c a n b e s e e n t h a t o v e r t a k i n g h a d o c c u r r e d b y 16 H (c) b u t t h a t t h e full d e n s i t y of c o l o u r a t t h e t i p h a d n o t y e t b e e n r e a c h e d . I n a n o t h e r s e t of p h o t o g r a p h s of a n overflow e x p e - r i m e n t , w h i c h w e r e o b t a i n e d b y t i m e l a p s e c i n e c a m e r a , t h e p a s s i n g d i s t a n c e w a s j u s t o v e r t h e d e s i r e d 3 H a n d t h e r e l a t i v e d i s t a n c e t o t h e o v e r t a k i n g p o i n t wras a b o u t 13 H — t h i s b e i n g i n r e a s o n a b l e a g r e e m e n t w i t h t h e v i s u a l o b s e r v - a t i o n .
R e s u l t s for s i m i l a r e x p e r i m e n t s a t t h e l o w e r K . W<A 61 v a l u e s (430) w e r e a s s h o w n i n T a b l e 2, t h e t u b e b e i n g p l a c e d i n t h e s a m e r e l a t i v e p o s i - t i o n .
TABLE 2
Details of overtaking observations
K.Wa~üZ = 4 3 0
TYPE OF FRONT
PASSING DISTANCE OVERTAKING POINT ( d i s t a n c e f r o m t u b e ) TYPE OF FRONT
I n c h e s R e l a t i v e I n c h e s R e l a t i v e
U n d e r f l o w . . 3 3 H 1 5 1 5 H
U n d e r f l o w . . 6 6 H 4 5 4 5 H
O v e r f l o w . . . 6 6 H 4 5 4 5 H
NOVEMBRE 1 9 6 3 - № 7 D . I. H . B A R R AND A . M. M. H A S S A N 7 6 3
Just after start of injection-front well ahead.
Juste après le début de l'injection.
Le « front » précède de beaucoup le débit coloré.
(c)
Dye has reached front, but not a full intensity.
Le débit coloré a rattrapé te « front »,
mais le colorant n'a pas encore atteint sa pleine intensité.
(b) (d) Dye stream in the process of overtaking. Intensity of dye at front building-up.
Débit colore rattrapant le «front». Augmentation de l'intensité du colorant au front.
Fia. 2
Views of dye injection experiment. (The figures indicate distance in feet from the barrier.)
Essai avec injection de colorant. (Les chiffres visibles sur les photos donnent la distance, en pieds, à partir de la barrière.) A l t h o u g h t h e i n c r e a s e i n r e l a t i v e d i s t a n c e i n
t h e first of t h e s e o b s e r v a t i o n s w a s s l i g h t c o m p a r - ed w i t h t h e c o r r e s p o n d i n g e x p e r i m e n t i n t h e m o r e t u r b u l e n t r a n g e , it a p p e a r e d t h a t t h e u s e of t h e s a m e t u b e w i t h t h e s a m e i n t e n s i t y of s p u r t of d y e i n t o t h e m u c h s h a l l o w e r a n d m o r e s l o w l y m o v i n g f r o n t t e n d e d t o i n t r o d u c e a n e r r o r . T h e s e c o n d a n d t h i r d o b s e r v a t i o n s do s h o w a m a r k e d d i v e r g e n c e f r o m t h e c o r r e s p o n d - i n g t e s t s i n t h e p r e v i o u s set, a n d i n all c a s e s , it w a s n o t e d t h a t w h e n t h e d y e d i d r e a c h t h e f r o n t it w a s c o n s i d e r a b l y m o r e d i l u t e d t h a n p r e - v i o u s l y . T h e i m p r e s s i o n of a definite o v e r t a k i n g p l a c e w a s c e r t a i n l y lost.
I n t e r n a l v e l o c i t y m e a s u r e m e n t s ( F l u m e A , 1 9 6 1 ) .
A m i n i a t u r e c u r r e n t m e t e r of t h e t y p e d e v e l o p - ed b y t h e H y d r a u l i c R e s e a r c h S t a t i o n ( D e d o w a n d K i n g , 1954) w a s a v a i l a b l e a n d i t s e e m e d
w o r t h w h i l e t o a t t e m p t t o u s e it for v e l o c i t y m e a s u r e m e n t s . T h e i n s t r u m e n t w a s c a p a b l e of r e c o r d i n g v e l o c i t i e s d o w n t o a b o u t 1 i n c h p e r s e c o n d . A l t h o u g h f r o n t v e l o c i t i e s m u c h g r e a t e r t h a n t h i s c o u l d b e o b t a i n e d i n t h e flume u s i n g a s a l i n e d e n s i t y difference, t h i s w a s n o t f o u n d p r a c t i c a b l e . T h e c o u n t of r e v o l u t i o n s of t h e t i n y r o t o r (1 c m ) d e p e n d s o n p a s s a g e of c u r r e n t t h r o u g h t h e w a t e r .
P r o v i s i o n is m a d e for b a l a n c i n g t h e c i r c u i t w i t h f r e s h or s a l t w a t e r , b u t difficulty w a s e x p e r i e n c - ed w i t h t h e c h a n g i n g c o n c e n t r a t i o n a t t h e r o t o r . T h e m a i n t a i n e n c e i n b a l a n c e w a s f o u n d t o be m u c h e a s i e r w h e n t h e r m a l d e n s i t y difference w a s e m p l o y e d , t h o u g h t h i s m e a n t t h a t t h e i n s - t r u m e n t w a s a l w a y s u s e d v e r y n e a r t o t h e l o w e r l i m i t of effective m e a s u r e m e n t .
T h e c o u n t of r o t o r r e v o l u t i o n s s h o w n o n t h e d e c a t r o n d i s p l a y c a n b e e i t h e r c o n t i n u o u s o r i n t e r m i t t e n t (i.e. t h e c o u n t l a s t i n g 10 sec. is m a d e
O Run I - Essai /
• Run 2 - Essai?
_ L
O 10 20 30 40 50 60 70 80 90 Time from lifting of barrier (seconds?
Temps compté à partir au soulèvement de ia barrière (secondes) FIG. 3
Typical results of velocity measurement with miniature current meter, K.<FA£fl about 10,640,
rotor 6 ft. from removeable barrier.
Résultats typiques de mesures de vitesses au micro-moulinet, avec K.&Au\ égal à environ 10 640, le rotor du moulinet
étant à environ 1 pied de la barrière amovible.
e v e r y o t h e r 10 s e c ) . B e c a u s e of t h e u n s t e a d y n a t u r e of l o c k e x c h a n g e flow a n d t h e r e l a t i v e l y s h o r t d u r a t i o n of a n y e x p e r i m e n t , t h e i n t e r m i t - t e n t s e t t i n g w a s d i s c a r d e d o n t h e g r o u n d t h a t h a l f t h e p o t e n t i a l v e l o c i t y m e a s u r e m e n t s w o u l d b e m i s s e d . T w o l o n g i t u d i n a l p o s i t i o n s w e r e c h o s e n for t h e r o t o r , a t 1 feet a n d 6 feet f r o m
t h e b a r r i e r , a n d t h e r o t o r a x i s w a s set p a r a l l e l to t h e c e n t r e l i n e of t h e flume b o t t o m a t 0.16 feet f r o m t h e b o t t o m a n d 0.16 feet b e l o w w a t e r s u r f a c e for m e a s u r e m e n t s of u n d e r f l o w s a n d overflows r e s p e c t i v e l y , t h e t o t a l d e p t h b e i n g m a d e 0.8 feet, t h r o u g h o u t . At t h e s t a r t of a n e x p e r i m e n t a s t o p clock w i t h a c i r c u l a r p a p e r d i s k s t u c k t o t h e face w a s a l s o s t a r t e d a n d t h e t i m e s c o r r e s p o n d i n g t o t h e first i n d i c a t i o n of
• Run 3 - Essai 3 o Run 4 - Essai 4 \
0 10 20 30 40 50 60 70 80 90 100 Time from lifting of borner (seconds)
Temps compté à partir du soulèvement de la barrière (secondes)
F i e . 4
Typical results of velocity measurement with miniature current meter, K.ffAoX about 8,420,
rotor 6 ft. from removeable barrier.
Résultats typiques de mesures de vitesses au micro-moulinet, avec K. &A ûX égal à environ 8 420,
rotor à 6 pieds de la barrière amovible.
m o v e m e n t a n d t h e n s u c c e s s i v e c o u n t s of 10 p u l - ses w e r e m a r k e d o n t h e d e s k b y t i c k i n g t h e p o s i t i o n of t h e h a n d . T h e m e t h o d t h u s t e n d e d to give i n d i v i d u a l e r r o r s b u t e l i m i n a t e c u m u l - a t i v e e r r o r . F i g u r e s 3 a n d 4 s h o w t y p i c a l r e - s u l t s ; w h e t h e r a t 1 foot or 6 feet f r o m t h e b a r - r i e r o r for overflow o r u n d e r f l o w , it w a s a l w a y s f o u n d t h a t t h e m e a n v e l o c i t y i n d i c a t e d w a s g r e a t e r t h a n t h e i n i t i a l f r o n t v e l o c i t y — w h i c h did n o t i n fact d i m i n i s h g r e a t l y w i t h i n t h e flume l e n g t h a t t h e K.giAcK. v a l u e s of a b o u t 10,000.
T o o b t a i n r o u g h l y c o m p a r a b l e m e a s u r e m e n t s a t s m a l l v a l u e s of K . &A d l w i t h v e l o c i t i e s b e l o w t h e 1 i n c h p e r s e c o n d m i n i m u m of t h e c u r r e n t m e t e r , d y e s p l o t c h e s w e r e r e l e a s e d s o m e s h o r t d i s t a n c e b e h i n d t h e overflow f r o n t s o o n a f t e r w i t h d r a w a l of t h e b a r r i e r . T y p i c a l r e s u l t s , s h o w i n g c o m p a r i s o n of f r o n t t r a v e l w i t h t h a t of t h e f o r e m o s t p o i n t of t h e d y e t r a c e a r e given on F i g u r e 5. T h e r e w a s c e r t a i n l y m u c h l e s s s i g n of o v e r t a k i n g d u r i n g tjhese t e s t s a t K.g>Aéí v a l u e s a b o u t 2,400, t h a n d u r i n g t h e p r e v i o u s l y d e s c r i b e d t e s t s a t K.ffA <Ji v a l u e s a b o u t 10,000.
¿i 5
g I 4
f t Front ; repeat runs
"Front ", essais de répétition X Oye splotch - Tache de colorant
I
0 20 40 60 80 .100 120 140 160 Time from lifting of borner ( seconds)
Temps compté à partir du soulèvement de la barrière (secondes) FIG. 5
Typical results of velocity measurement by observation of dye splotch, K.g^rJt about 2,400.
Résultats typiques de mesures de vitesses par observation d'une tache de colorant, avec K.£ïïA<Jl égal à environ 2 400.
A t t e m p s a t d i l u t i o n m e a s u r e m e n t .
T h e difficulties i n v o l v e d i n t h e m e a s u r e m e n t of d i l u t i o n i n a n u n s t e a d y t u r b u l e n t s y s t e m a r e not i n c o n s i d e r a b l e , a n d h a v e n o t b e e n o v e r c o m e i n t h i s c a s e . W h a t s e e m e d d e s i r a b l e w a s t o o b t a i n s i m u l t a n e o u s v e r t i c a l t r a v e r s e s a t a r a n g e of p o i n t s a l o n g d e v e l o p i n g e x c h a n g e flows. A r e c o r d i n g s y s t e m b a s e d on t h e r m o p i l e p r o b e s w i t h o s c i l l o g r a p h r e c o r d i n g h a d b e e n d e v e l o p e d ( B a r r , 1962) a n d s u c c e s s f u l l y u s e d ( B a r r , 1963 A) in a s t e a d y s t a t e m i x i n g s t u d y . If t h e s y s t e m w a s u s e d w i t h t h e f o u r t h e r m o - j u n c t i o n s p r o t r u d -
i n g f r o m t h e m e a s u r i n g e n d of e a c h Ys i n . d i a m . p r o b e u n c o v e r e d , localised m e a s u r e m e n t s (to
NOVEMBRE 1 9 6 3 - № 7 D . I. H . B A R R AND A. M. M. H A S S A N 7 6 5
w i t h i n a n Ys i n . c u b e r o u g h l y ) c o u l d b e o b t a i n e d of t h e t u r b u l e n t f l u c t u a t i o n s i n a m i x i n g >:one of w a r m e r a n d c o o l e r b o d i e s of w a t e r . B y f o r m i n g a b l o b of w a x o v e r t h e m e a s u r i n g e n d , t h e s p e e d of r e s p o n s e w a s v e r y m u c h r e d u c e d a n d t h e t i m e a v e r a g e t e m p e r a t u r e a t a p o i n t i n a m i x i n g z o n e c o u l d be f o u n d if t h e s y s t e m w e r e s t e a d y s t a t e . R e c o r d s f r o m e i g h t m e a s u r i n g p o i n t s c o u l d b e o b t a i n e d i n o n e s e c o n d . B u t e v e n t h e a v a i l a b i l i t y of a m o d e r a t e l y s o p h i s t o c a t - ed r e c o r d i n g s y s t e m s u c h a s t h i s w a s n o t r e a l l y h e l p f u l . T h e s u p e r i m p o s i t i o n of s h o r t p e r i o d t u r b u l e n c e t r a n s i e n t s o n l o n g e r p e r i o d t r a n s i e n t s c a u s e d b y t h e r a p i d l y c h a n g i n g s t a t e of d e v e l o p m e n t of t h e e x c h a n g e flow m a d e b o t h c o n d i t i o n s of t h e p r o b e e n d s u n s u i t a b l e . W h a t w a s d o n e w a s t o a t t e m p t t o i s o l a t e v e r t i c a l s a m p l e s b y p l a c i n g IY2 i n c h d i a m e t e r p e r s p e x t u b e s i n t o t h e f l u m e d u r i n g a n e x p e r i m e n t a n d t h e n m a k i n g a v e r t i c a l t r a v e r s e w i t h a n a n g l e d b u l b t h e r m o m e t e r l o w e r e d v e r t i c a l l y i n t o t h e t u b e s u s i n g a r a t c h e t m e c h a n i s m w h i c h i n c o r p o r a t e d a d e p t h s c a l e . T h e m e t h o d w a s n o t v e r y s a t i s f a c t o r y ; s o m e a d d i t i o n a l m i x i n g o f t e n t o o k p l a c e d u r i n g o r i m m e d i a t e l y a f t e r t h e p l a c i n g of t h e t u b e , a l t h o u g h t h e r e c o r d s f r o m t h e s u b s e q u e n t d o w n w a r d s t h e n u p w a r d s t r a v e r s e s w e r e f a i r l y c o n s i s t e n t . T h e o n l y d e f i n i t e c o n c l u s i o n t h a t c o u l d b e d r a w n f r o m t h e r e s u l t s ( H a s s a n , 1962) w a s t h a t t h e n e t t r a n s p o r t of w a t e r i n a u n d e r f l o w w h e r e K.$Adl w a s i n t h e r e g i o n of 10,000 w a s o b s e r v a b l y g r e a t e r t h a n i n a c o r r e s p o n d i n g d e v e l o p m e n t of u n d e r f l o w w i t h K . g »A (R a b o u t 2,000; e s p e c i a l l y i n t h e r e g i o n n e a r t h e t i p .
7. D A M - B U R S T A N A L O G Y E X C H A N G E F L O W
T h i s c a s e of p u r e d e n s i t y e x c h a n g e flow w a s defined i n I a n d s o m e a s s e s s m e n t s of t h e coeffi
c i e n t of p r o p o r t i o n a l i t y for t h e i n i t i a l v e l o c i t y of b o t h t h e u n d e r f l o w a n d overflow w e r e given. A few " b l o c k " c o l o u r i n g e x p e r i m e n t s w e r e c a r r i e d o u t for t h i s c a s e a n d it w a s f o u n d t h a t , a s w o u l d be e x p e c t e d , t h e s a m e o v e r t a k i n g , e n t r a i n m e n t a n d d i s c a r d m e n t p r o c e s s t o o k p l a c e a t t h e f r o n t s a s h a d b e e n o b s e r v e d i n l o c k e x c h a n g e flow.
8 . C O N C L U S I O N S
I t h a s b e e n s h o w n t h a t t h e m e c h a n i s m of l o c k e x c h a n g e flow c h a n g e s c o n s i d e r a b l y w i t h c h a n g e of s c a l e — s c a l e b e i n g m e a s u r e d i n t e r m s of t h e W^OZ n u m b e r . A t v e r y s m a l l s c a l e s t h e e x t e n s i o n of t h e f r o n t s is r a p i d l y i n h i b i t e d b y t h e b u i l d u p of d i l u t e d w a t e r a t t h e f r o n t . W i t h
i n c r e a s i n g s c a l e t h e s t a g e is r e a c h e d w e l l w i t h t h e l a b o r a t o r y o r d e r of size w h e n a d i s c a r d m e n t p r o c e s s a l l o w s t h e e x c h a n g e t o c o n t i n u e t o v e r y m u c h g r e a t e r r e l a t i v e e x t e n s i o n s . E x c h a n g e flow i n s u c h c i r c u m s t a n c e s — t h e c i r c u m s t a n c e s p r e s u m a b l y of all full size o c c u r r e n c e s — i s n o t a t w o l a y e r s y s t e m b u t a t h r e e l a y e r s y s t e m . D u r i n g t h e e a r l y s t a g e s t h e i n t e n s e m i x i n g a c t i o n a t t h e f r o n t s does n o t c a u s e d i m i n u t i o n of v e l o c i t y . Of c o u r s e d i m i n u t i o n of v e l o c i t y of t h e f r o n t s e v e n t u a l l y d o e s o c c u r . I t s e e m s a n o t u n r e a s o n a b l e h y p o t h e s i s t h a t t h i s r e s u l t s b o t h f r o m m o u n t i n g f r i c t i o n a l d r a g a n d b e c a u s e t h e " s u b - c u r r e n t s " w i l l s t a r t to e n t r a i n w a t e r f r o m t h e i n t e r m e d i a t e z o n e . T h u s a f r o n t ' s p r o g r e s s m a y e v e n t u a l l y b e i n h i b i t e d n o t b y t h e i m m e d i a t e d i l u t i o n d u e t o t h e f r o n t a l m i x i n g a c t i o n b u t b e c a u s e m o r e a n d m o r e of t h e d i l u t e d w a t e r , t h o u g h i n i t i a l l y d i s c a r d e d , r e t u r n s t o t h e f r o n t i n t h e " s u b - f l o w " . T h i s t r e n d h a s b e e n o b s e r v e d i n s t e a d y s t a t e e x c h a n g e e x p e r i m e n t s i n t h e l a b o r a t o r y , w h e r e t h e r e l a t i v e e x t e n s i o n is c o m p a r a t i v e l y s m a l l a n d t o a m u c h g r e a t e r e x t e n t i n t h e field w h e r e w i t h t h e m u c h g r e a t e r r e l a t i v e e x t e n s i o n s p o s s i b l e , t h e r e is m o r e o p p o r t u n i t y for t h e g r a d u a l e n t r a i n m e n t of a l r e a d y d i l u t e d w a t e r f r o m t h e i n t e r m e d i a t e l a y e r .
It a p p e a r s t h a t t h e f o r m a t i o n of w a v e s on t h e i n t e r f a c e b e h i n d a f r o n t a s o b s e r v e d b y I p p e n a n d H a r l e m a n (1952), E l l i s o n a n d T u r n e r (1959) a n d B a r r (1959) is t o g e t h e r Avith t h e n e x t s t a g e of t h e b r e a k i n g of t h e w a v e s , a t r a n s i t o r y s t a g e i n t h e d e v e l o p m e n t f r o m l a m i n a r to t u r b u l e n t c o n d i t i o n s . T h e f o r m a t i o n of c o n s i d e r a b l e l a y e r s of i n t e r m e d i a t e w a t e r a b o v e t h e e x t e n d i n g m a i n flows a t l a r g e v a l u e s of 3>A (R r e s u l t s f r o m d i s c a r d m e n t of w a t e r f r o m t h e f r o n t s , a n d n o t f r o m t h e i n t e n s i f i c a t i o n of t h e a f o r e s a i d w a v e a c t i o n .
T h e s t a g e h a s b e e n r e a c h e d w h e r e e x p e r i m e n t s of a m u c h l a r g e r s c a l e t h a n so f a r p o s s i b l e a r e r e q u i r e d : i n p a r t i c u l a r t h e e x t e n s i o n of t h e c o n g r u e n c y d i a g r a m for t h e s t a n d a r d c a s e of l o c k e x c h a n g e u n d e r f l o w a n d t h e f o r m a t i o n of a d i a g r a m for t h e overflow is a p r e s s i n g n e e d . It is t h o u g h t t h a t m e a s u r e m e n t s of s t r u c t u r e of e x c h a n g e flow s h o u l d n o w b e a t t e m p t e d for t h e s t e a d y s t a t e c a s e s , b e f o r e a r e t u r n is m a d e t o t h e m o r e difficult e x p e r i m e n t a l p r o b l e m of t h e n o n - s t e a d y c a s e s . #
T h e e x p e r i m e n t a l w o r k w a s c a r r i e d o u t i n t h e Civil E n g i n e e r i n g L a b o r a t o r i e s of t h e R o y a l College of S c i e n c e a n d T e c h n o l o g y , G l a s g o w . T h e a u t h o r s a r e m o s t g r a t e f u l to P r o f e s s o r W i l l i a m F r a z e r for t h e f a c i l i t i e s g r a n t e d , a n d for h i s h e l p f u l a d v i c e a n d c r i t i c i s m .
T h e e x p e r i m e n t s d e s c r i b e d i n 5 a n d 6 (rf) a n d (e) w e r e p e r f o r m e d by t h e s e c o n d a u t h o r u n d e r t h e d i r e c t i o n of t h e first.
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RÉSUMÉ
Courants de densité en canal rectangulaire
II. — QUELQUES EXPÉRIENCES SUR LA STRUCTURE DE L'ÉCOULEMENT CONSÉCUTIF A L'OUVERTURE D'UNE VANNE
PAR D. I. H. BARR ET A. M. M. HASSAN
Cet article, le second de la série, considère le cas de la figure 1 a de l'article p r é c é d e n t . Au moyen d'expériences simples (en particulier la coloration de masses d'eau bien délimitées au départ), une connaissance plus approfondie du mécanisme de l'écoulement des fronts d'onde (under- flow ou overflow) a p u être obtenue, qui explique assez bien l'influence du n o m b r e de F r o u d e - Reynolds densimétrique sur la vitesse de propagation du front. Aux faibles valeurs de ce nombre, l'eau mélangée qui se produit au front y reste et diminue la vitesse de propagation. Aux valeurs élevées de ce nombre, l'eau mélangée se r é p a n d à l'aval du front et forme une troisième couche de densité intermédiaire, si bien que, l'eau du front étant constamment renouvelée à p a r t i r du corps de l'écoulement, la vitesse de propagation du front diminue beaucoup moins vite.
Les tableaux 1 et 2 et la figure 2 illustrent ce phénomène. Une injection de colorant est p r a - tiquée dans l'écoulement, en un point situé à quelque distance de la b a r r i è r e (3 H dans le cas étudié), un peu après le passage du front (celui-ci a dépassé le tube d'injection d'une distance que les auteurs appellent « passing distance »). Le colorant rejoint le front d'onde lorsque celui-ci est arrivé au point appelé « overtaking point », dont la distance au tube d'injection est donnée dans les tableaux.
Des mesures de vitesses au point fixe, dans le corps de l'écoulement, confirment les observa- tions visuelles. Les figures 3 et 4 portent en abscisse le temps (compté à p a r t i r de l'ouverture de la barrière) et en ordonnée la vitesse mesurée en un point situé à une certaine distance de la b a r r i è r e (0,30 m p o u r la figure 3, 1,80 m p o u r la figure 4). La vitesse, plus grande que celle du front, indique bien une réalimentation de celui-ci.
La figure 5 c o r r e s p o n d à une faible valeur de K. g ?A cK.- On voit en ordonnée, en fonction du temps, la position du front et celle d'une tache de colorant qui ne semble p a s devoir le r a t t r a p e r . Les auteurs concluent à la nécessité d'expériences à plus grande échelle, en particulier l'ex- tension du diagramme de la figure 8 de l'article I p o u r les grandes valeurs de K •WA~ûV-
