densimetric exchange flow in rectangular channels

densimetric exchange flow in rectangular channels

NOVEMBRE 1 9 6 3 - № 7
LA H O U I L L E
BLANCHE
757
Densimetric exchange flow
in rectangular channels
11.—SOME OBSERVATIONS OF THE STRUCTURE OF LOCK EXCHANGE FLOW
BY
D. I. H. BABE,
DEPARTMENT OF CIVIL ENGINEERING
THE ROYAL COLLEGE OF SCIENCE AND TECHNOLOGY, GLASGOW
AND
A. M. M. HASSAN,
PORT OF BASRAH, IRAQ
(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 discardment 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 entrainment 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.
INTRODUCTION
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
information on their overall characteristics was
given.
It w a s d e m o n s t r a t e d t h a t t h e scale of
s u c h p h e n o m e n a s h o u l d be d e t e r m i n e d on 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 .
Using this knowledge, a design
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 spread h a d been devised.
This
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
the
idealised two dimensional exchange or spread
studies w a s not confined to the 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 difference effects i n c a n a l a n d
lock s y s t e m s a n d t h e like, b u t e x t e n d e d to 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 .
It
Article published by SHF and available at http://www.shf-lhb.org or http://dx.doi.org/10.1051/lhb/1963053
№
LA HOUILLE BLANCHE
758
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 the 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 to
a t t e m p t to 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.
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;
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 case of l o c k e x c h a n g e
flow t h e d e p t h ;
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 ;
H
L
L
is t h e d i s t a n c e from 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 in t h e case
of a " s h o r t " lock.
is t h e velocity of a f r o n t a f t e r s o m e
extension;
is t h e i n i t i a l velocity 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
lifted;
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 = p — p w h e r e pj a n d p 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 p i=.p p;
0
V
V
N O T A T I O N S (as used in I)
0
Ap/p
x
2
2
x
2
1/2
VA
is [(Ap/p) . < 7 - H ]
or the characteris­
t i c velocity 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? ) e q u a l s o n e ;
g; = V , / [ ( A p / p ) . ^ H ]
w h e r e Y is a c h a ­
racteristic velocity;
K is t h e r a t i o V / V ;
A
h
c
0
g« 0\
A
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)<7 H / 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
limitations on this n u m b e r ) .
A
1/2
3 / a
7 - NOVEMBRE 1 9 6 3
uncoloured front progresses into coloured water
its f o r m m a y be difficult to 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 its
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 less 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 selected 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
cases, 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 , influenced b y a n i n t e r e s t i n t h e
m o t i o n of salt 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 L ) w a s B / H = 0.5,
L / 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 to r e a c h 40.
With
H = 10 i n c h e s , Ap/p = 0.020, K . g T ^ t f l
was
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 (Fig. 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 first 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 free 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 overflow
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. No m e a ­
s u r e m e n t s of w ater velocities 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 velocity m e a s u r e m e n t s for a
complex a n d unsymetrically non-prismatic pro­
totype configuration and a model thereof). In­
deed 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 velocities 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 velocities beingobtained.
P r a n d t l (1952) h a s i n d i c a t e d t h a t
0
0
r
3.
SOME FURTHER DETAILS
O F PREVIOUS LOCK
EXCHANGE EXPERIMENTS
r
Before 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 w as
i n i t i a t e d a t t h e R o y a l College of Science a n d
T e c h n o l o g y , Glasgow, a t t e n t i o n h a d b e e n , in
general, directed towards the underflow. It w a s
therefore usually found convenient to colour the
m o r e dense w a t e r in its original position 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 after 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 w ater 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 before it
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
r
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
f o l l o w - u p velocities a p p r o a c h i n g t w i c e t h e fron­
tal velocity m a y occur in analogous cold-warm
air p h e n o m e n a (truly analogous to d a m burst
a n a l o g y e x c h a n g e flow).
As 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 ,
there w a s a rolling u p process similar to 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 .
This
was observed w h e n the interface w a s otherwise
completely smooth, suggesting practically lami­
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 least.
In some cases t h e spiral w a s seen quite as dis­
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 figure ( 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 difference, o r b o t h , led t o w a r d s
more turbulent conditions, t h e spiralling layers
no longer a p p e a r e d to have distinct existence,
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
be 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> dl
of t h e
o r d e r of 5,000 or 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 ,
on 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
region behind t h e underflow front in exchange
flow s 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 30. 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 seen
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
could no longer be distinguished, the general
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
after
watching m a n y experiments, being that the
turbulent mixing between t h e two layer grew
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.&'^OlA
r
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 ­
breaking a n d j u s t breaking waves w a s very
s i m i l a r t o t h e p h o t o g r a p h s given b y I p p e n a n d
H a r l e m a n (1952) for a s i m i l a r , t h o u g h s t e a d y
state, circumstance.
T h i s t y p e of i n t e r f a c i a l
wave f o r m a t i o n w a s also noted b y Ellison 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 underflow layer progressing d o w n a slight
slope.
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
front, 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 lock 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 ­
larly t h e second, intensified w i t h increasing va­
l u e s of K.g> dl
a n d that interfacial drag pro­
v i d e d t h e e x p l a n a t i o n for 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 velocity of l o w v a l u e s
of K . $ i 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
A
A
759
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 or
l a m i n a r t y p e velocity 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
and below t h e interface w a s also present.
4.
THE FLUMES
( A , B and 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 flumes
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
in I. S o m e d e t a i l s p e r t i n e n t to 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 useful scope 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 .
Thus the
flume w a s p l a n n e d to serve 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
these various functions and t h e space available.
It 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 for
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 ­
tant head t a n k a n d a V-notch weir installed as
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
w as 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
adjustable gate at the " d o w n s t r e a m " end w a s
raised.
T h e p o s i t i o n of t h e g r o o v e s for t h e
r e m o v e a b l e b a r r i e r gave a 13 feet l e n g t h b e ­
tween it a n d the end gate. Initially 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
length and latterly 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 side 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
used open, there being no top. It w a s not, in
g e n e r a l , e a s y t o light for p h o t o g r a p h i n g or 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 wall.
r
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
to 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 ­
veable barrier.
After a t e s t t h e w a t e r w a s
quickly d u m p e d into the tank by lowering the
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 for
a n o t h e r test.
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 side t r a n s p a r e n t . I t w a s s i x t e e n
LA H O U I L L E
760
feet long, w i t h t h e r e m o v e a b l e b a r r i e r in t h e
m i d d l e a n d w i t h solid e n d s . It w a s p l a c e d on a
long t a b l e w h i c h could b e r a p i d l y tilted t o aid
e m p t y i n g a n d filling from 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 as u s e d for flume 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 also of t h e enclosed type, 4 feet
long a n d of IVi i n c h by % i n c h section 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 as 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 flume w i t h B / H = 0.167.
5.
OBSERVATIONAL EXPERIMENTS
W I T H BLOCK COLOURING
(Flume A, 1961)
By 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
vertical 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 in 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 , it w a s p o s s i b l e t o
c o l o u r a block 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
experiment. These additional barriers were then
slowly 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 after t h i s t h e e x p e r i ­
m e n t could 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 at 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
next to the m a i n barrier w a s coloured during an
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 > ¿ 1 = 1,000).
Although
upon
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
water was distributed along the extending interface m o s t of it m o v e d a l o n g t h e flume w i t h t h e
underflow. Dilution occurred due to the entry
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 teristic bulge, b u t the diluted water mostly
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 velocity r a p i d l y d i m i n i s h e d a n d it 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
advance. W h e n a block further back from the
m a i n barrier w a s coloured, no coloured 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 observation w h i c h lasted until the frontal velocity h a d
fallen to 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 velocity.
Similar experiments were then u n d e r t a k e n with
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
underflow a n d overflow.
B l o c k s of w a t e r i n i tially some small distance from the m a i n barrier
were coloured. W h e n these came into motion
m o s t of t h e c o l o u r e d w a t e r w a s seen to m o v e
r a p i d l y after t h e f r o n t , t o o v e r t a k e it, to be
diluted by the pronounced mixing action at 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 A
7
BLANCHE
№
7 - NOVEMBRE 1 9 6 3
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 following
( a n d feeding) 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.
This intermediate layer t h u s served to
separate the m a i n forward transfer zone from
t h e n e c e s s a r y c o u n t e r flow. It is 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 it
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 it
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 line j o i n i n g z e r o
velocity p o i n t s or t h e l i n e of e q u a l m i x i n g of
the t w o differing b o d i e s of w a t e r .
6.
VARIOUS RECORDINGS
OF THE STRUCTURE
O F LOCK E X C H A N G E F L O W
Explanatory note.
T h e obvious follow 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 1961, s e e m e d to 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 flow—velocities a n d d i l u t i o n —
as 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 in 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 as t h i s p a p e r is
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 for several reasons:
(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 scope 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 to f o r m u l a t e
r u l e s for 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 ing three dimensional spread was the original
m o t i v a t i o n of t h e s t u d i e s . After t h e a t t e m p t s to
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 case d u r i n g 1 9 6 1 , it 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
outfall w a s coloured w i t h a w e a k dye.
Some
t i m e after 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 to 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 to 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 on, say,
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
scale (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 to 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
obtained in internal motions as between small
scale i d e a l i s e d outfall c o n f i g u r a t i o n s u s i n g t h e
congruency d i a g r a m scaling method, a n d did
NOVEMBRE 1 9 6 3 - №
7
D . I. H . B A R R AND A . M. M.
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
velocities.
A g a i n , k n o w i n g n o w w h a t to look for, t h e
overtaking and discardment patterns, which
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 or fluids a r e m i s c i b l e , w e r e
easily a n d reassuringly recognised in the large
heat dissipation models being operated by the
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 , 1962).
(ii) It 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 to 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 detail i n s u c h cases, 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 as t h e y
occur in the non-steady cases a n d certainly
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 to o b t a i n .
F o r t h e s e r e a s o n s it 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 as possible, suffi­
cient additional recordings t h a t the combined
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 facilities b e c o m e a v a i l ­
able 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, it 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 steady cases.
P h o t o g r a p h s of p a i r s of e x p e r i m e n t s w i t h
differencial colouring.
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 typical r e s u l t s
obtained in this way.
D e s p i t e t h e s h o r t lock
l e n g t h ( L / H — 7) a n d t h e n a r r o w flume 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 to
provide" s o m e e v i d e n c e r e l e v a n t to 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 the velocity of a n
u n d e r f l o w f r o n t . I n t h i s case w i t h a
K-3> 6l
v a l u e of 23,800, t h e f r o n t velocity (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 V . At all t i m e s u p to
this extension u n d i l u t e d saline water was found
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
flume a n d r i g h t u p t o t h e v e r y front 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 lay a zone
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 one
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 . It 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 at
K-WTTft of a b o u t 24,000 for V / V = 0.9 is, b y
0
A
0
0
HASSAN
761
e x t r a p o l a t i o n , e s t i m a t e d to 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
case 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 / V = 0.9) for t h e n a r r o w c h a n n e l ( B / H = 0,5)
as 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 L / H
of 7.2 a n d "65 for L / 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! 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
to 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 to 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 velocity, 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 lead one to e x p e c t
t h a t for K . 3< 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 case, 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 velocity
V > 0.9 V for L / H v a l u e s of u p w a r d s of 70 a n d
perhaps m u c h greater.
0
0
0
A
A
0
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 ­
able 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 case 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 at 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 feet).
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 seen to b e
a b o u t 5 feet 5 i n c h e s ( L / H = 16.2)
and
(18-16.2)/16.2 is a b o u t 11 % , v e r y close t o t h e
t y p i c a l 12 % q u o t e d in 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
the fronts despite the comparatively small L / H
r a t i o s ( L / H for F i g u r e 5 a is 3.2 a n d for F i ­
g u r e 5 b is 11.6); 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 to be t h i n n e r t h a n in K e u l e g a n ' s
experiment.
F o r t h e n e x t t w o stages of d e c r e a s e of
K . 9< 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 to o b t a i n m e a n ­
ingful 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
to 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
V i n c h d e p t h ( K . ^ (R. in t h e r e g i o n 200-600).
T h u s a m u c h greater relative extension w a s
possible t h a n w h e n it w a s full or 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 at 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 .
It 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
become considerably diluted and t h a t this dilu­
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
uncoloured front penetrating into a coloured
zone 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 .
A
2
A
T h e final s t a g e of d e c r e a s e of K . " p ol w a s
r e a c h e d in 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
flume 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
A
762
LA
HOUILLE
t h e f r o n t s w e r e o b s e r v e d b y viewing f r o m above
w i t h a w h i t e b a c k g r o u n d below.
Although
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 colour, 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 even 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 above. I n o n e e x p e r i m e n t
(K. &> 6X, = 45.5) w h i c h w a s c o n t i n u e d long after
t h e stage 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 62,
m o v i n g a t a b o u t 0.005 i n c h e s p e r second
(0.017 V ) a n d w i t h t h e colour d e e p e n i n g only
gradually with distance back towards the barrier.
The impression w a s gained that the mechanism
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
obtaining in t h e turbulent region.
I n s t e a d of
undiluted water continually overtaking t h e front
— 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 to 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 rest, w i t h
the front 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
moved.
№
BLANCHE
7 - NOVEMBRE
1963
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 " .
Results were obtained as
s h o w n i n T a b l e 1.
TABLE
1
A
Details
of overtaking
K.#A~tfl =
observations
5,650
0
D y e injection observations.
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
the entrainment a n d discardment process 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.
Experiments were conducted by
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 fluorisene 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 once 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.~$> (R. t h o u g h t r e a s o n a b l e i n t h e
circumstances
A
Depth
(£)
(if)
(H)
3 in.
lin.
Ap/p
(assuming
K = 0.5)'
0.032
0.005
5,650
430
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 inject t h e d y e ; o n e e n d w as b l o c k e d a n d a
c i r c u l a r h o l e of slightly 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 above 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 drilled 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 axis of t h e outlet
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.
TYPE OF FRONT
Inches
Relative
Inches
Relative
Underflow.
.
9
3 H
36
12
H
Underflow.
.
18
6 H
69
23
H
Overflow.
. .
9
3 H
36
12
H
Overflow.
. .
18
6 H
84
28
H
Figure 2 shows photographs taken during 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 lines 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 also b e e n
re-touched.
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 seen 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
colour 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 set of p h o t o g r a p h s of a n overflow e x p e riment, which were obtained b y t i m e lapse cine
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 over t h e
desired 3 H a n d t h e relative distance to t h e
o v e r t a k i n g p o i n t w as a b o u t 13 H — t h i s b e i n g
in reasonable agreement with t h e visual observation.
r
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< 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,
the tube being placed in t h e same relative position.
A
r
Considering t h e experiments with t h e larger
v a l u e of K . g r (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 half 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 overflow r e s p e c t i v e l y . T h e f r o n t w a s allow-
OVERTAKING POINT
(distance from tube)
PASSING DISTANCE
TABLE
Details
2
of overtaking
K.Wa~üZ
=
observations
430
PASSING DISTANCE
OVERTAKING POINT
(distance from tube)
TYPE OF FRONT
Inches
Relative
Inches
Relative
A
7
Underflow.
.
3
3 H
15
15 H
Underflow.
.
6
6 H
45
45
H
. .
6
6 H
45
45
H
Overflow.
NOVEMBRE 1 9 6 3 - №
7
D . I. H . B A R R AND A . M. M. H A S S A N
763
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)
Dye stream in the process of overtaking.
Débit colore rattrapant
le «front».
(d)
Intensity of dye at front building-up.
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
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 in
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 slight 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 to i n t r o d u c e a n
error.
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
show a m a r k e d divergence from the correspondi 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 cases, it
was noted t h a t w h e n the dye did reach the
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 viously. 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.
Internal velocity
1961).
measurements
(Flume
A,
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 developed 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 King, 1954) w a s a v a i l a b l e a n d it s e e m e d
barrière.)
w o r t h w h i l e to a t t e m p t to u s e it for velocity
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 velocities d o w n to 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 velocities 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 in 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
through the water.
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
fresh or salt 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
was employed, though this m e a n t t h a t the inst 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 to 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 or
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
764
LA HOUILLE BLANCHE
• №
7 - NOVEMBRE 1 9 6 3
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 ative 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
found t h a t the m e a n velocity indicated 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 velocity — w h i c h
did not in 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 at t h e K.gi cK. v a l u e s of a b o u t
10,000.
To obtain roughly comparable 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 . & d l w i t h velocities 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 , dye 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 .
Typical results,
s h o w i n g c o m p a r i s o n of front 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 less sign
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> éí
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.ff
<Ji v a l u e s a b o u t 10,000.
A
O Run I - Essai /
•
Run 2 -
Essai?
A
_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.<F £fl about 10,640,
rotor 6 ft. from removeable barrier.
A
Résultats typiques de mesures de vitesses au micro-moulinet,
avec K.& u\
égal à environ 10 640, le rotor du moulinet
étant à environ 1 pied de la barrière amovible.
A
every 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 lock e x c h a n g e flow a n d t h e relatively
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 tent setting was discarded on the ground that
half t h e p o t e n t i a l velocity m e a s u r e m e n t s w o u l d
be missed.
Two longitudinal positions were
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 line 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 below 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 respectively, 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 to t h e face w a s also 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
A
A
¿i 5
g I
f t
4
Front ; repeat runs
"Front ", essais de répétition
X Oye splotch - Tache de colorant
0
20
I
40
60
80
.100
120
140
Time from lifting of borner ( seconds)
Temps compté à partir du soulèvement de la barrière
160
(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.£ïï <Jl égal à environ 2 400.
A
A t t e m p s at dilution measurement.
• 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)
Fie. 4
Typical results of velocity measurement
with miniature current meter, K.ff oX about 8,420,
rotor 6 ft. from removeable barrier.
A
Résultats
typiques de mesures de vitesses au micro-moulinet,
avec K. & ûX égal à environ 8 420,
rotor à 6 pieds de la barrière amovible.
A
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 case.
W h a t s e e m e d d e s i r a b l e w a s to
obtain simultaneous vertical traverses at 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
with oscillograph recording h a d been developed
(Barr, 1962) a n d successfully 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
was used w i t h the four thermo-junctions p r o t r u d ing 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
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 cooler b o d i e s of w a t e r . By 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
the t i m e average t e m p e r a t u r e at a point in 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
steady state.
R e c o r d s f r o m eight m e a s u r i n g
points could be obtained in one second. But
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
turbulence transients on longer period transients
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 to 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
flume 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
vertical traverse with an angled bulb t h e r m o m e ­
ter lowered vertically into the tubes using a
ratchet mechanism which incorporated a depth
scale. 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 often t o o k p l a c e d u r i n g
or 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 ,
although the records from the subsequent down­
w a r d s t h e n u p w a r d s traverses were fairly con­
s i s t e n t . T h e o n l y definite 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.$ dl
w a s i n t h e r e g i o n of 10,000 w a s
observably greater t h a n in a corresponding
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 » (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 .
A
A
765
i n c r e a s i n g scale t h e s t a g e is r e a c h e d well 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 to v e r y
m u c h greater relative extensions.
Exchange
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 two layer system but a three layer system.
During the early stages the intense mixing
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 velocity. Of c o u r s e d i m i n u t i o n of velocity of
the fronts eventually does occur.
It s e e m s a
not unreasonable hypothesis that this results
both from m o u n t i n g frictional drag and because
t h e " s u b - c u r r e n t s " will s t a r t to e n t r a i n w a t e r
from t h e intermediate zone. T h u s a front's p r o ­
gress m a y eventually be inhibited not by the
i m m e d i a t e d i l u t i o n d u e to 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
water, t h o u g h initially discarded, r e t u r n s to the
f r o n t in t h e " s u b - f l o w " .
This trend has been
observed in steady state exchange experiments
in the laboratory, where the relative extension
is c o m p a r a t i v e l y s m a l l a n d to 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
diluted w a t e r from the intermediate layer.
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
interface behind a front as observed by Ippen
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
conditions.
The formation
of
considerable
l a y e r s of i n t e r m e d i a t e w a t e r above the e x t e n d ­
i n g m a i n flows at l a r g e v a l u e s of 3> (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
wave action.
A
7.
DAM-BURST ANALOGY
FLOW
EXCHANGE
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
cient 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 velocity 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 , as w o u l d
be expected, 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
and discardment process took place at the fronts
as 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.
CONCLUSIONS
It 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 scales 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 front. W i t h
T h e stage h a s been reached w h e r e experi­
m e n t s of a m u c h l a r g e r scale t h a n so f a r p o s s i ­
ble 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 the
s t e a d y s t a t e cases, b e f o r e a r e t u r n is m a d e to
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 the
non-steady cases.
#
T h e experimental w o r k w a s carried out in the
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 Science 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 facilities g r a n t e d , a n d
for h i s h e l p f u l advice 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.
766
LA H O U I L L E B L A N C H E
№
7 - NOVEMBRE
DEDOW ( H . R.) and KING (R. F . J . ) , 1954. —
178, 4626, 396-398.
REFERENCES
ALLEN ( F . H.) and PBICE ( W . A . ) , 1959. — The Dock
Harbour Authority,
40, 465, 72-76.
and
BARR ( D . I. H . ) , 1959. — Proc. 8th Congress
International
Association
for Hydraulic Research, Paper 6-C.
BARR ( D . I. H . ) 1962 ( A ) . — Civil Engineering
Works Review, 57, 675, 1277-1279.
BARR ( D . I. H . ) , 1962 ( B ) . — Instrument
1355-1361.
and
Practice,
BARR ( D . I. H . ) , 1963 ( A ) . — The Engineer,
352.
Public
16, 11,
215, 55S7, 34a-
BARR ( D . I. H . ) , 1963 ( B ) . — Paper I of this
series.
ELLISON (T. H.) and TURNER
Mech., 6, 423-448.
(J. S . ) , 1959. —
1963
Engineering,
/.
Fluid
HASSAN (A. M. M . ) , 1962. — Scale problems in hydraulic
models where density spread is simulated.
M. Sc.
Thesis, Glasgow University.
IPPEN (A. T.) and HARLEMAN ( D . R. F . ) , 1952. — Steadystate characteristics of sub-surface flow Nat.
Bur.
Standards,
Circ. 521, Gravity Waves, 79-93.
PRANDTL (L.), 1952. — The essentials of fluid dynamics
Blacliie Lond (Translation
of 3rd edition of Führer
durch die Strömungslehre,
1949).
SMITH ( A . A . ) , 1962. — The Engineer,
214, 5566, 532-535.
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 précédent. 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 (underflow ou overflow) a p u être obtenue, qui explique assez bien l'influence du nombre de FroudeReynolds 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 répand 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 barrière (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 observations visuelles. Les figures 3 et 4 portent en abscisse le temps (compté à partir de l'ouverture de
la barrière) et en ordonnée la vitesse mesurée en un point situé à une certaine distance de la
barrière (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 correspond à une faible valeur de K. g ? cK.- On voit en ordonnée, en fonction du
temps, la position du front et celle d'une tache de colorant qui ne semble pas devoir le rattraper.
Les auteurs concluent à la nécessité d'expériences à plus grande échelle, en particulier l'extension du diagramme de la figure 8 de l'article I pour les grandes valeurs de K •W ~ûVA
A