ENERGY DISSIPATION OF FREE FALLING JETS LITERATURE REVIEW

REPORT NO SR 63 OCTOBER 1985

This report describes work carried out under Contract No DGR PECD

7/6/29 - 204183, Hydraulic structures and alluvial processes funded

by the Department of the Environment. The D 0 E nominated officer

was Dr R P Thorogood. The work was carried out by E Whitehead and

P M Brown in the River Engineering Department of Hydraulics

Research Ltd. Dr W R White was the Company's nominated project

officer.

Any opinions expressed are not necessarily those of the Department

of the Environment.

Crown Copyright 1985

CONTENTS

Introduction

Scope of review

High level jets

Scour under jets

Aeration

Conclusions

References

Bibliography

Page

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2

3

4

5

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11

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Many modern dams a r e of t h i n c o n c r e t e a r c h c o n s t r u c t i o n . T h i s

d e s i g n of dam i s no t normal ly compat ib le w i t h h y d r a u l i c jump b a s i n s

f o r f l o o d energy d i s s i p a t i o n and t h e u s u a l methods used a r e

ski-jump o u t l e t s o r c h u t e s , and v e r t i c a l d r o p s from t h e c r e s t of

t h e dam. The l a t t e r method i s a t t r a c t i v e because t h e s t r u c t u r e is

compact and means can r e a d i l y be i n c o r p o r a t e d t o b reak up t h e j e t

and d i s s i p a t e s u b s t a n t i a l amounts of energy by a i r r e s i s t a n c e .

However, a n e g a t i v e f e a t y r e of t h i s method of ene rgy d i s s i p a t i o n i s

t h a t i t t a k e s p l a c e c l o s e t o t h e dam and i t i s e s s e n t i a l t o p r o v i d e

a p r o t e c t i v e a p r o n under t h e j e t . E x i s t i n g dams u s i n g t h i s method

may o r may n o t have w a t e r p o o l s on t h e apron ; t h e r e has been

l i t t l e i n f o r m a t i o n a v a i l a b l e a s t o t h e b e n e f i t s of e i t h e r approach.

T h i s review s e e k s o u t t h e a v a i l a b l e i n f o r m a t i o n on t h i s s u b j e c t and

p roposes s t e p s t o be t a k e n t o augment i t .

SCOPE OF REV-

The range of i n f o r m a t i o n r e l a t e d t o j e t s f a l l i n g on f i x e d s u r f a c e s ,

and t h e i n f l u e n c e of t a i l w a t e r p o o l d e p t h on t h e f o r c e s g e n e r a t e d ,

is r a t h e r smal l . There i s however, a wider r ange of i n f o r m a t i o n on

t h e s c o u r developed by f a l l i n g j e t s on e r o d i b l e s u r f a c e s . There

a r e f e a t u r e s t h a t a r e common t o both s i t u a t i o n s and i n f o r m a t i o n

ga ined on one h a s r e l e v a n c e t o t h e o t h e r . Papers on t h e

development of s c o u r under f a l l i n g j e t s a r e t h e r e f o r e inc luded .

Also i n c l u d e d i n t h e b i b l i o g r a p h y a r e a number of p a p e r s no t

s p e c i f i c t o t h e t o p i c under review bu t of background i n t e r e s t .

EIGE LEVEL JETS

The head ing r e f e r s t o t h e j e t from over f low c r e s t s o r o u t l e t s h igh

i n a dam and t h e r e f o r e n o t under h igh p r e s s u r e . The throw i s

r e l a t i v e l y s h o r t and t h e j e t on impact w i t h t h e ground o r ap ron

below t h e dam w i l l have a v e r t i c a l o r n e a r v e r t i c a l t r a j e c t o r y .

The p r i n c i p l e papers t h a t r e f e r t o t h e s e c o n d i t i o n s a r e t h o s e by

Ishikawa and H a u s l e r and Hartung.

Ishikawa ( 1 ) a d d r e s s e s t h e q u e s t i o n of f o r c e s on a f i x e d s u r f a c e

benea th a s t e e p l y f a l l i n g j e t d i r e c t l y and i d e n t i f i e s two types of

f low. Type A o c c u r s when downstream t a i l w a t e r d e p t h i s l e s s than

sequen t d e p t h and downstream f low i s t h e r e f o r e s u p e r c r i t i c a l .

Upstream f low i s submerged and c r e a t e s a poo l behind t h e j e t . Th i s

i m p l i e s a s h e e t j e t and two d imens iona l f l o w w i t h v e r y l i t t l e space

around t h e s i d e s of t h e j e t . Type B f low o c c u r s when downstream

d e p t h i s g r e a t e r than sequen t d e p t h and downstream f low i s

t h e r e f o r e submerged. The a u t h o r makes assumpt ions on energy

c o n s e r v a t i o n and momentum ba lance t o d e r i v e a n e q u a t i o n f o r dynamic

p r e s s u r e on t h e f i x e d bed. Theory is compared w i t h model t e s t s and

g i v e s good agreement. The E n g l i s h v e r s i o n of t h i s paper g i v e s o n l y

a c o n t r a c t e d form of t h e t h e o r y and no d e t a i l s of t h e model t e s t s .

A t r a n s l a t i o n of t h e l o n g e r o r i g i n a l v e r s i o n of t h e paper i n

J a p a n e s e i s no t y e t a v a i l a b l e .

H a u s l e r ( 2 ) ( a l s o H a u s l e r and Hartung ( 3 ) ) i s mainly concerned w i t h

s c o u r under a j e t bu t d e a l s w i t h t h e form of a w a t e r jet i n wa te r

a s an ana logy t o t h e t h e o r y of f r e e j e t t u r b u l e n c e founded by

P r a n d t l and t e s t e d i n a i r . The a u t h o r ' s c o n c l u s i o n i s t h a t

d i s p e r s i o n is a lmost comple te ly l i n e a r and t h a t a c o r e i s formed

t h a t h a s t h e same v e l o c i t y a s t h e e n t r y v e l o c i t y t o t h e t a i l w a t e r .

The boundar ies of t h e c o r e a r e a l s o l i n e a r and converge w i t h a h a l f

a n g l e between 4 and 6 d e g r e e s depending on Reynolds No ( 4 ) .

Haus le r assumes t h a t t h e t a n g e n t of t h e h a l f a n g l e can be t aken t o

be 0 .1 (5.7 d e g r e e s ) and t h a t t h e c o r e l e n g t h i s t h e r e f o r e 5 X

d i a m e t e r o r width of t h e e n t e r i n g j e t . He f u r t h e r s t a t e s t h a t a t

t h i s dep th i n t h e t a i l w a t e r 20 p e r c e n t of a r e c t a n g u l a r j e t ' s

ene rgy w i l l have been d i s s i p a t e d and 30 p e r c e n t of t h e energy of a

c i r c u l a r j e t . S ince j e t t h e o r y would on ly p r e d i c t t o t a l

d i s s i p a t i o n a t i n f i n i t e d e p t h , t h e a u t h o r c a r r i e d ou t exper iments

and p r e d i c t e d t h a t i n p r a c t i c e a c i r c u l a r j e t would have a lmos t

comple te ly d i s p e r s e d a t a wa te r d e p t h of 20 X d i a m e t e r of j e t on

e n t r y t o t a i l w a t e r . Model s t u d i e s by Cola (5 ) p r e d i c t e d a s i m i l a r

l e v e l of d i s p e r s i o n f o r r e c t a n g u l a r j e t s a t a d e p t h of 40 X width

of j e t . It i s n o t c l e a r i n r e f e r e n c e s t o r e c t a n g u l a r j e t s which

wid th dimension is be ing r e f e r r e d t o b u t r e a s o n i n g s u g g e s t s i t

would be t h e s m a l l e r .

Hans le r e q u a t e s t h e l e n g t h of a j e t i n u n l i m i t e d w a t e r t o t h e

p o t e n t i a l dep th of s c o u r under a j e t and t h e r e f o r e t o t h e d e p t h of

t a i l w a t e r f o r z e r o p r e s s u r e on t h e bed. For lower dep ths he s t a t e s

t h a t i f t h e bed i s w i t h i n range of t h e j e t c o r e (dep th l e s s t h a n 5

X j e t d i a m e t e r ) t h e peak p r e s s u r e w i l l e q u a l t h e e n t e r i n g v e l o c i t y

head and t h e d i s t r i b u t i o n w i l l be Gauss ian t o a d i s t a n c e of one

t h i r d of t h e w a t e r dep th e i t h e r s i d e of t h e c e n t r e .

SCOUR UNDER JETS

Many e q u a t i o n s have been proposed t o c a l c u l a t e t h e depth of s c o u r

t h a t w i l l occur under t h e impact of a j e t . A comprehensive review

and assessment of t h e s e e q u a t i o n s has been made by Mason and

Arumugam ( 7 ) . The s c o u r d e p t h i n most of t h e formulae i s t h e dep th

from t h e w a t e r s u r f a c e , on t h e assumpt ion t h a t t o t a l wa te r d e p t h i s

t h e c r i t e r i o n f o r e n e r g y d i s s i p a t i o n . Only one o r two formulae

assume t h a t t h e p r o p o r t i o n of t o t a l w a t e r d e p t h t h a t is above

bed l e v e l i . e . t h e t a i l w a t e r dep th w i l l i n f l u e n c e t h e t o t a l w a t e r

dep th . The a u t h o r s showed t h a t t h e v a r i o u s fo rmulae gave widely

d i f f e r e n t r e s u l t s when t e s t e d a g a i n s t a wider v a r i e t y of d a t a t h a n

t h a t used i n t h e o r i g i n a l development of a p a r t i c u l a r formula .

Mason t h e r e f o r e proposed a formula i n t h e form t h a t had showed t o

be t h e most s a t i s f a c t o r y .

T h i s was :

where D = dep th of scour

q = u n i t d i s c h a r g e

H = h e i g h t from t a i l w a t e r t o r e s e r v o i r l e v e l

h = t a i l w a t e r dep th

g = a c c e l e r a t i o n due t o g r a v i t y

d = c h a r a c t e r i s t i c p a r t i c l e s i z e (models)

= 0.25m ( p r o t o t y p e s )

K = 6.42 - 3 . 1 ~ ~ ~ ~

X = 0.6 - H/300

y = 0.15 - R/200

T h i s e q u a t i o n does no t r e l a t e d i r e c t l y t o t h e problem of p r e s s u r e s

on a f i x e d bed bu t i s an a l t e r n a t i v e way of e s t i m a t i n g dep th of

t a i l w a t e r f o r h y d r o s t a t i c p r e s s u r e .

A l l t h e f o r e g o i n g papers on p r e s s u r e s on a n apron , d i s p e r s i o n of a

j e t and s c o u r under a j e t assume no s i g n i f i c a n t a e r a t i o n of t h e

j e t . I sh ikawa assumes t h e v e l o c i t y and dimensions of t h e j e t a t

e n t r y t o t h e t a i l w a t e r . Haus le r s u g g e s t s i g n o r i n g a i r en t ra inment

i n o r d e r t o make t h e r e s u l t s c o n s e r v a t i v e o r t o assume a s m a l l

d i s p e r s i o n i n a i r and s l i g h t l y reduced c o r e s i z e on e n t r y t o t h e

t a i l w a t e r . He does n o t , however, g i v e p o s i t i v e guidance on t h i s

p o i n t .

On t h e o t h e r hand t h e r e i s a body of ev idence t o sugges t t h a t

d e l i b e r a t e i n t r o d u c t i o n of a i r i n t o a f a l l i n g j e t can s u b s t a n t i a l l y

reduce p r e s s u r e s / s c o u r on impact.

Johnson ( 8 ) experimented wi th a v e r t i c a l n o z z l e d i s c h a r g i n g o n t o a

g r a v e l bed. The n o z z l e was s l i g h t l y below w a t e r l e v e l t o exc lude

a l l u n c o n t r o l l e d a i r en t ra inment .

A measured amount of a i r was i n t r o d u c e d t o t h e j e t such t h a t t h e

j e t c o n t a i n e d 50 p e r c e n t a i r a t a tmospher ic p r e s s u r e . When t h e

u n a e r a t e d j e t was g i v i n g maximum scour d e p t h , t h e a e r a t e d j e t under

t h e same t a i l w a t e r c o n d i t i o n s was s c o u r i n g t o o n l y h a l f t h e depth.

A f u r t h e r t e s t is a l s o of i n t e r e s t . The u n a e r a t e d j e t was s p l i t

i n t o 32 f i n e j e t s of t h e same t o t a l a r e a . The j e t s were p a r a l l e l

b u t t h e s e p a r a t i o n between t h e j e t s doubled t h e o v e r a l l impact

a r e a . T h i s had v i r t u a l l y no e f f e c t on t h e s c o u r d e p t h compared

w i t h t h e s i n g l e j e t .

A number of model t e s t s of s p e c i f i c p r o j e c t s (e.g. 9 and 1 0 ) have

shown t h a t , d e s p i t e t h e i n a b i l i t y of models t o e n t r a i n a i r on t h e

s c a l e of a p r o t o t y p e , marked g a i n s i n energy d i s s i p a t i o n have

r e s u l t e d from t h e d e l i b e r a t e b reak up of t h e j e t from a n o v e r s p i l l

c r e s t . Although t h e d e t a i l s may d i f f e r , t h e p r i n c i p l e normal ly

used i s t h a t developed by R o b e r t s (11) u s i n g s p l i t t e r s on t h e

c r e s t . McKeogh and Elsawy (12) showed t h a t t h e t u r b u l e n c e

i n t e n s i t y of a j e t a s i t l e a v e s a n o z z l e h a s a pronounced e f f e c t on

t h e behav iour of t h e j e t . Using s m a l l c i r c u l a r n o z z l e s the a u t h o r s

i n v e s t i g a t e d t h e ' d i s i n t e g r a t i o n l e n g t h ' of a v e r t i c a l f a l l i n g j e t

and showed t h a t t h e j e t broke up i n t o s p r a y i n a s l i t t l e a s h a l f

t h e d i s t a n c e when f low i n t h e n o z z l e was d e l i b e r a t e l y made

t u r b u l e n t . I t r a y be t h e r e f o r e t h a t t h e b e n e f i c i a l e f f e c t of

s p l i t t e r s on t h e c r e s t i s due t o an i n c r e a s e i n t u r b u l e n t i n t e n s i t y

r a t h e r t h a n t h e e n t r a i n m e n t of a i r . When R o b e r t s type s p l i t t e r s

a r e o p e r a t i n g a t low d i s c h a r g e i t i s u s u a l l y s e e n t h a t they d i v i d e

t h e f low i n t o i n d i v i d u a l j e t s w i t h o u t promoting a high degree of

t u r b u l e n c e . Under t h e s e c i rcumstances t h e energy d i s s i p a t i o n i s

not n o t a b l y h i g h e r t h a n f o r a s i n g l e j e t . T h i s is i n l i n e w i t h

b o t h t h e o b s e r v a t i o n s of Johnson and of McKeogh and Elsawy.

Whether t h e e f f e c t of s p l i t t e r s is t o b reak up t h e j e t through

t u r b u l e n c e o r i n t r o d u c e a i r t h a t i s c a r r i e d down t h e w a t e r column

t h e e f f e c t i s t o c a r r y e n t r a i n e d a i r i n t o t h e downstream pool .

V o l k a r t (13) showed t h a t f a l l i n g d r o p l e t s e n t r a i n a i r on impact

wi th a pool i n a s t u d y of a i r bubble e n t r a i n m e n t i n s e l f - a e r a t e d

f l o w s u s i n g s t r o b o s c o p i c t echn iques .

I t h a s been shown e x p e r i m e n t a l l y (Homma (14) ) t h a t when a i r i s

e n t r a i n e d i n a j e t , t h e j e t d i s p e r s e s on e n t e r i n g a poo l i n a

s h o r t e r d i s t a n c e than a non-aerated j e t .

It i s a p p a r e n t t h a t a e r a t i o n of a j e t both above and i n t h e

t a i l w a t e r poo l can p o t e n t i a l l y reduce t h e p r e s s u r e s on t h e bed of

t h e p o o l by such a n e x t e n t t h a t t o i g n o r e a e r a t i o n i n o r d e r t o

p r o v i d e a s a f e t y margin could l e a d t o e x c e s s i v e overdes ign o r t o

t h e r e j e c t i o n of a v i a b l e d e s i g n o p t i o n .

CONCLUSIONS

I t i s e s s e n t i a l t o model t e s t f a l l i n g j e t ene rgy d i s s i p a t o r s

t o e n s u r e t h a t f low c o n d i t i o n s a r e s a t i s f a c t o r y i n every r e s p e c t .

The t e s t e d d e s i g n w i l l be t h e outcome of p r e l i m i n a r y desk s t u d i e s

and g iven t h e c o s t of model s t u d i e s and t h e t ime t aken t o e x e c u t e

them, r a d i c a l v a r i a t i o n s a r e u n l i k e l y t o be made u n l e s s t h e i n i t i a l

d e s i g n i s t o t a l l y unaccep tab le .

I t i s t h e r e f o r e of g r e a t advantage i f i n i t i a l d e s i g n o p t i o n s can be

compared on a b a s i s of sound knowledge of t h e behaviour of f a l l i n g

j e t s from o u t l e t t o t a i l w a t e r poo l t o pool bed.

A t p r e s e n t t h e i n f o r m a t i o n a v a i l a b l e i s more q u a l i t a t i v e t h a n

q u a n t i t a t i v e . Only one s t u d y h a s been found t h a t s p e c i f i c a l l y

a t t e m p t s t o de te rmine t h e focus on a c o n c r e t e a p r o n under a f a l l i n g

j e t by t h e o r e t i c a l means. The t h e o r y assumes t h a t t h e v e l o c i t y of

t h e j e t on e n t r y t o t h e poo l i s known and t h a t t h e j e t is c o h e r e n t

and n o t a e r a t e d . The e f f e c t of n a t u r a l o r d e l i b e r a t e d i s p e r s i o n o r

a e r a t i o n of t h e j e t canno t t h e r e f o r e be a s s e s s e d . The remainder of

t h e a v a i l a b l e i n f o r m a t i o n c o n s i s t s of i s o l a t e d s t u d i e s of

i n d i v i d u a l a s p e c t s of j e t behaviour .

There i s a need t o draw t o g e t h e r t h e s e v a r i o u s a s p e c t s and r e l a t e

them t o t h e p r a c t i c a l problem of d e s i g n i n g e f f e c t i v e and s a f e

f a l l i n g - j e t energy d i s s i p a t o r s . I m p l i c i t i n t h i s i s t h e need t o

r e l a t e , a s a c c u r a t e l y a s p o s s i b l e , model performance t o p r o t o t y p e

performance.

P a r t i c u l a r q u e s t i o n s t o be answered a r e :

a ) The behav iour of r e c t a n g u l a r o r s h e e t j e t s i n a t a i l w a t e r pool.

Most work has been done s o f a r w i t h c i r c u l a r j e t s . Occas iona l

r e f e r e n c e s t o r e c t a n g u l a r j e t s s u g g e s t t h a t t h e i r behav iour may

be q u i t e d i f f e r e n t and t h i s is t h e form most o f t e n o c c u r r i n g i n

p r a c t i c e .

b ) The c h a r a c t e r i s t i c s of j e t s i n poo l s w i t h f i n i t e boundar ies .

Most work on j e t s r e l a t e s t o poo l s of u n l i m i t e d e x t e n t .

c ) The e f f e c t of a i r e p t r a i n e d i n t h e j e t o r by t h e j e t on t h e

d i s p e r s i o n w i t h i n t h e t a i l w a t e r pool .

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