hydrodynamics effect pipe

8/8/2019 Hydrodynamics Effect Pipe

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Hydrotechnical Construction, Vo l. 29, No. 7, 1995

E X P E R IM E N T A L IN V E S T I G A T I O N S O F H Y D R O D Y N A M I C E F FE C TSIN A P IP E D U R I N G C O N N E C T I O N O F FR EE A N D P R E S S U R EF L O W S B Y A H Y D R A U L I C J U M P

G . A . S u d o l 's k i i a n d A . M . S h v a i n s h t e in

T h e h y d r a u l i c j u m p o c c u r r i n g d u r i n g c o n n e c t i o n o f f r ee a n d p r e s s u r e f lo w s i n a c l o s e d c o n d u i t i s a s p e c ia l t y p e o fh y d r a u l i c j u m p . A c h a r a c te r i st i c f e a t u r e o f t h is j u m p i s t h a t i t c a n o c c u r w i t h o u t p a s si n g t h r o u g h t h e c r i t ic a l d e p t h . I n t h epr es sur e sec t ion of the f low i t s r o l le r en t r a ins a cons ider ab le amou nt of a i r , w hich on a r e la t ive ly smal l d i s tance co l lec t s neart h e c e i l in g o f t h e c o n d u i t a n d m o v e s a l o n g i t t o w a r d t h e l o w e r p o o l . T h e i n d i c at e d fe a t u re s o f s u c h a j u m p c o m p a r e d w i t ha j u m p c o n n e c t i n g a r a p i d f l o w w i t h a t r a n q u il f l o w s u g g e s t t h e p o s s i b il i ty o f a d i f f e r e n c e o f t h e i r h y d r o d y n a m i ccharacter is t ics .

T h e t y p e o f ju m p u n d e r c o n s i d e r a t io n o c c u r s m o s t o f t e n i n d i s c h a rg e p i p e s a n d t u n n e l s w h o s e m a i n g a t e s a r e l o c a t eda t the en t r ance and a r e in tended f or oper a t ing f u l l s ec t ion a t des ign d i schar ges . O n the pa th of such s t r uc tur es a hydr au l icj u m p w i t h a p r es s u r e r e g i m e d o w n s t r e a m ( H J P R ) c a n f o r m w i t h p a rt i a l o p e n i n g o f t h e g a t e s. I n t h e j u m p z o n e s u b s t a n ti a lp r e s s u r e f l u c t u a ti o n s c a n b e o b s e r v e d o n t h e p a t h o f th e c o n d u i t , d i s r eg a r d o f w h i c h c a n b e h a z a r d o u s f o r d i s c h a r g e t u n n e l s[ 1] and the mor e so f o r d i schar ge p ipes , e spec ia l ly those cons t r uc ted in the body o f ea r th dams . Th e f luc tu a t ion e ff ec t s ont h e p i p e s u r f ac e s a n d t h e v i b r a t i o n o f t h e c o n c r e t e s tr u c t u r al m e m b e r c a u s e d b y t h e m a r e t r a n s m i t t e d t o t h e e a r t h m a s s o fthe dam, w hich makes i t necessa r y to eva lua te i t s s tab i l i ty . The f i r s t s tep of such an eva lua t ion i s a de te r mina t ion of thef luc tua t ion e f f ec t s on the f low sur f aces of such a condui t . T he l i t e r a tur e conta ins few such d a ta [ 2 , 3 ] .

E x p e r i m e n t a l i n v e s t i g a ti o n s to d e t e r m i n e p r e s s u r e f l u c tu a t i o n s o n t h e p a t h o f t h e d i s c h a r g e p i p e w i t h p a r t i a l o p e n i n g, ;i ' " e ga t~ and con nec t ion of the f r ee and pr es sur e f low by a hyd r au l ic jum p w er e ca r r ied ou t on a mo de l a t a s ca le of 1 :40

: ~a_,,inationo f o n e o f t h e i n t e r m e d i a t e v a r i an t s o f t h e c o m b i n e d d i v e r s i o n a n d s e r v ic e p i p e o u t l e t s o f t h e U s t ' - S r e d n e k a n',~SJJ~ociectlic station.

T h e w i d t h a n d h e i g h t o f t h e c r o s s s e c t i o n o f th e m o d e l o f t h e d i s c h a r g e s e c t io n o f t h e p a t h o f t h e p i p e o u t l et o nw h i c h t h e m e a s u r e m e n t s w e r e t a k e n w e r e 1 7 .5 a n d 3 2 . 5 c m . T h e p r e s s u r e f l u c tu a t i o n s w e r e r e c o r d e d b y m e a n s o f D D T - 1t r a n s d u c e rs a n d t h r o u g h a s t ra i n - g a u g e a m p l i fi e r w e r e r e c o r d e d o n a B r u e l l a n d K j a e r m e a s u r i n g m a g n e t i c t a p e r e c o r d e r.T h e e x p e r i m e n t a l d a t a w e r e p r o c e s se d o n a t y p e D V K c o m p u t e r . I n t h e m e a s u r i n g a n d p r o c e s s i n g s y s t e m h i g h - f r e q u e n c ynoise gr ea te r than 50 H z w as suppr es sed by means of spec ia l f i l t e r s . This c i r cums tance w as impor tan t , s ince the na tur a lf r e q u e n c y o f t h e f i rs t m o d e o f v i b r a ti o n s o f t h e 1 . 4 - cm - t h i c k o r g a n ic g l a s s s id e w a l l o f t h e m o d e l w a s a b o u t 8 0 H z . T h es c o p e o f r e a li z a t io n s o f t h e f l u c t u a t i o n p r o c e s s d u r i n g p r o c e s s i n g w a s a b o u t 3 3 0 s e c , t h e d i s c r e t i z a t io n i n t e r v a l w a s 0 . 0 2 s e c .

The exper imenta l inves t iga t ions of the char ac te r i s t i c s o f p r es sur e f luc tua t ions in the inves t iga ted condui t conduc teda t v a l u es o f t h e F r o u d e n u m b e r f o r t h e c o n t r a c t ed s e c t i o n in f r o n t o f th e j u m p e q u a l t o 5 . 6 a n d 9 . 5 s h o w e d t h e f o l l o w i n g .

1 . The in tens i ty of p r es sur e f luc tu a t ion (the r a t io of the s tand ar d devia t ion o to the ve lo c i ty head f o r the con t r ac tedsec t ion in f r on t o f the jum p in w hic h the ve loc i ty i s equa l to V c) d i f f e r s ins ign i f ican t ly ove r the length o f the cond ui t (F ig .l a ) . H e r e g i s th e a c c e l e r a ti o n o f g r a v i t y . T h e m a x i m u m v a l u e s o f t h is i n t e n s i t y r e a c h 0 . 0 7 - 0 , 0 9 ; t h e y a r e c l o s e t o t h e d a t ai n [ 3 ], b u t s l i g h t ly h i g h e r t h a n i n t h e e x p e r i m e n t s w i t h H J P R g i v e n i n [ 2 ]. T h e p o s i t i o n o f t h e m a x i m u m v a l u e s o f t h ein tens i t ie s o f p r es sur e f luc tua t ions over the length of the jum p in these inves t iga t ions d i f f e r somew hat , bu t f or x /h i > 8 theva lues of the in tens i t i e s a re c lose ( x i s the long i tud ina l coor d ina te r ead f r om the s ta r t o f the jum p; h j i s the h e igh t o f the jum pde te r mined as the d i f f e r ence of the he ight o f the p ipe and de pth in the cont r ac ted sec t ion hc) . The ind ica ted d i f f e r ence s canb e d u e t o c o n d i t i o n s o f s u b m e r g e n c e o f t h e j u m p a n d s h a p e o f t h e c r o s s s e c t io n o f t h e c o n d u i t s i n t h e s e i n v e s ti g a t io n s .Chan ges in f luc tua t ion in tens i ti e s a long the length of the H JPR and jump in an open chan ne l [ 4-6] d i f f e r subs tan t ia l ly . Int h e l a t te r c a s e t h e m a x i m u m i n t e n s it y v a l u e i s s l i g h t ly lo w e r a n d i t s d e c a y l o n g t h e l e n g t h o c c u r s m u c h m o r e r a p i d ly . T h es m a l l e r v a lu e o f t h e m a x i m u m v a l u e o f t h e i n t e n s i t y o f p r e s s u re f l u c t u a t io n s fo r a h y d r a u l i c j u m p i n a n o p e n c h a n n e lc o m p a r e d w i t h t h e H J P R c a n b e d u e t o t h e lo w e r v a l u e s o f t h e F r o u d e n u m b e r i n e x p e r i m e n t s c o n d u c t e d i n c lo s e d

Translated f rom Gidrotekhnicheskoe Stroi te l 's tvo , No. 7, pp. 3-6, July, 199 5.

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e x / h j f r j g , z / h jF i g. 1 . V a r i a t i o n o f p r e s s u r e f l u c t u a t i o n i n t e n s i t i e s o n t h e b o t t o m a n dc e i l in g o f t h e c o n d u i t o v e r t h e l e n g t h o f t h e j u m p (a ) a n d h e i g h t o f t h e s i d ew a l l f o r x / h i = 3 . 3 ( b ) , v a r i a t i o n o f t h e c o e f f ic i e n t s o f s k e w n e s s a n dk u r t o s i s o v e r t h e l e n g t h o f t h e j u m p (c ) a n d ( d ), e x a m p l e s o f s p a t i a lc o r r e l a t i o n s o f p r e s s u r e f l u c t u a t i o n s o v e r th e l e n g t h o f t h e ju m p ( e) , h e i g h to f t h e s i d e w a l l f o r x /h j = 3 . 3 ( f ) , a n d a c r o s s t h e f l o w f o r x / h j = 3 . 9 ( g ).I a n d I I) c a l c u l a t e d c u r v e s f o r h i g h a n d l o w l e v e l s o f t u r b u l e n c e [ 4 ] ; 1 a n d2 ) e x p e r i m e n t a l d a t a fo r b o t t o m a n d ce i l i n g o f c o n d u i t f o r Fr c = 9 . 5 ; 3a n d 4 ) s a m e f o r F r c = 5 . 6 ; 5 a n d 6 ) s a m e o n s i d e w a l l f o r F r c = 9 . 5 a n d5 . 6 , r e s p e c t i v e l y ; 7 , 8 , a n d 9) e x p e r im e n t a l c u r v e s a c c o r d i n g t o d a t a [ 2 ,5 , 6 ] , r e s p e c t i v e l y .

c o n d u i ts t h a n a c c o r d i n g t o t h e d a t a [ 4 - 6] . W i t h a d e c r e a s e o f t h e F r o u d e n u m b e r f o r t h e c o n t r a c t e d s e c t i o n o f a j u m p i n a nopen channe l , a s the inves t iga t ions exam ined in [7 , 8 ] ind ica te , an inc rea se , o f the ma x im um in tens i ty o f the p re s s u ref luc tua t ions to 0 . 08 -0 . 01 occu rs .2 . T h e v a l u e s o f t h e i n t e n si t ie s o f p r e s s u r e f l u c t u a ti o n s o n t h e b o t t o m a n d c e i l in g o f t h e p i p e a t t h e s a m e s i tep r a c t ic a l l y c o in c i d e , o n t h e s i d e w a l l t h e y i n c r e a s e i n th e z o n e o f " d i sp l a c e m e n t " b e t w e e n t h e f o r w a r d s t r e a m a n d r o l l e r o ft h e h y d r a u l i c j u m p ( F i g . l b ) .

3 . T h e d i s t r i b u t io n o f t h e p r e s s u r e f l u c t u a t io n s i n t h e H J P R d i f f e r s f r o m t h e n o r m a l . T h e c o e f f i c i e n ts o f s k e w n e ssa s and ku r tos i s E reco rde d in the exp e r ime n t s ac tua l ly co inc ide on the pe r im e te r o f the condu i t . T he v a lue s o f a s a re pos i t ivea n d d e c r e a s e o v e r t h e l e n g t h f r o m t h e s t a r t o f th e j u m p , a s d i st a n c e g r e a te r t h a n ( 8 - 1 0 ) hi t h e y d o n o t e x c e e d 0 . 2 5 .A p p r o x i m a t e l y t h e s a m e c h a r a c t e r o f v a r i a t i o n o f a s w a s r e c o r d e d i n t h e i n v e s t ig a t i o n s g i v e n i n [ 5 ]. P o s i t i v e v a l u e s o f Ei n c r ea s e s o m e w h a t a l o n g t h e l e n g t h o f t h e j u m p , w h i c h i s r e la t e d t o a n i n c r e a s e o f t h e c o n t r i b u t i o n t o t h e p r e s s u r e f l u c t u at i o nb y t h e e n d o f t h e j u m p o f t h e c o m p o n e n t s f r o m d i s t u r b a n ce c a u s e d b y t h e m o v e m e n t a n d o u t f l o w o f a i r c a v i t i e s in t o t h el o w e r p o o l .

4 . S t a b l e c o r r e l a t i o n s o f p r e s s u r e f l u c t u a t i o n s a r e t r a c e d i n t h e H J P R z o n e . T h e c o e f f i c i e n t s o f l o n g i t u d i n a lco r re l a t ions o f p re s s u re f luc tua t ions r l app roa ch ze ro on ly a t a d i s t ance g rea te r than 8h i (F ig . l e ) . T h e va lue s o f thec o r r e l a t i o n c o e f f i c i e n t r h o v e r t h e h e i g h t o f t h e c o n d u i t ( F i g . l f ) d e c r e a s e s o m e w h a t w i t h i n t h e f o r w a r d f l o w ( y i s t h ec o o r d i n a t e o r t h o g o n a l t o t h e b o t t o m o f t h e c o n d u i t ) a n d t h e n r e m a i n p r a c t i c a l ly c o n s t a n t i n t h e r o l l e r o f t h e h y d r a u l i c j u m p .T h e v a l u e s o f t h e c o r r e l a t i o n c o e f f i c i e n t o n t h e b o t t o m a n d c e i li n g o f th e c o n d u i t a t t h e s a m e s i te a r e u p t o 0 . 6 - 0 . 7 . T h ep r e s s u r e f l u c t u at i o n s o v e r t h e w i d t h o f t h e c o n d u i t a r e p r a c t i c a ll y i n p h a s e , a n d t h e v a l u e s o f t h e c o r r e l a t i o n c o e f f ic i e n tsac ros s the f low r b in F ig . t g (z i s a coo rd ina te t r ans ve rs e to the d i rec t ion o f the f low) a re c los e to u n i ty . In a l l d i rec t ionst h e v a l ue s o f t h e c o r r e l a t i o n c o e f f ic i e n t s in t h e z o n e o f t h e H J P R i n th e c o n d u i t i n v e s t i g a te d b y u s w e r e h i g h e r t h a n i n t h eU-s haped condu i t [2 ] .

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F i g . 2 . G e n e r a l i z e d g r a p h o f t h e s p e c t r a l d e n s i t y o f p r e s s u r e f l u c t u a t i o n so n t h e b o t t o m o f t h e c o n d u i t : 1 ) z o n e o f e x p e r i m e n t a l p o i n t s f o r s i te s int h e i n i ti a l s e g m e n t o f th e j u m p b e f o r e c o n t a c t o f t h e ju m p r o ll e r w i t h t h ec o n d u i t c e i l in g ; 2 ) e x p e r i m e n t a l p o i n t s i n s e g m e n t o f c o n d u i t o p e r a t in g f u l ls e c t i o n ; 3 , 4 , a n d 5 ) c u r v e s p l o t t e d f r o m d a t a [ 7 , 9 , a n d 1 0 ] ; 6 ) c a l c u l a t e dc u r v e in a c c o r d a n c e w i t h A . M . O b u k h o v ' s d e p e n d e n c e .

5. Th e gene r a l char ac te r o f the spec t r a l dens i ty f unc t ion of the pr es sur e f luc tua t ions g ive n in F ig . 2 in g ener a l izedcoor d in a tes i s com par able to the da ta of o the r jum p inves t iga t ions . The f o l low ing nota t ions a r e u sed in F ig . 2 : u k is theconvec t ive ve loc i ty ( eddy t r anspor t ve loc i ty) ; s i s the nor mal ized spec t r a l dens i ty ; f i s the l inea r f r equency . The va lues ofthe gene r a l ized spec t r a l dens i ty f unc t ion of p r es sur e f luc tua t ions in the in i t i a l s egm ent of the jump in F ig . 2 a r e loca ted ins idea b a n d b o u n d e d b y i t s e x t r e m e v a l u e s . I n t h e s e g m e n t l o c a te d d o w n s t r e a m o f t h e s e c t i o n i n w h i c h t h e r o l l e r o f t h e j u m p[ ou~ :e ,_ the ce i l ing and the con dui t oper a tes f u l l s ec t ion , the spec t r a l dens i ty f unc t ion i s r epr esen ted b y f i l l ed c ir c les. A s ar csa i~ ~ f ana lyz ing these da ta and compar ing them w i th the r esu l t s o f the exper iments of o the r inves t iga tor s , i t i s poss ib le:,~ de tec t ce r ta in co mm on f ea tur es and char ac te r i s t ic s o f the spec t r a l dens i ty f unc t ions o f p r es sur e f luc tua t ions :

i n t h e i n i ti a l s e g m e n t o f th e i n v e s ti g a t ed j u m p t h e h i g h - f r e q u e n c y m a x i m u m o f t h e s p e c t r u m i s r e c o r d e d i n t h e z o n eo f S t r o u h a l n u m b e r s S h o f a b o u t 2 , b u t i s ex p r e s se d a s v i v i d l y a s f o r t h e g i v e n r e g i m e o f c o n n e c t i o n [ 9] , t h e g e n e r a l o u t l in eof the spec t r a l dens i ty f unc t ion i s even c lose r to tha t ob ta ined in the case of a sur f ace r eg ime of connec t ing f low s [ 10] ;

i n t h e s e g m e n t o f t h e c o n d u i t o p e r at i n g fu l l s e ct i o n t h e m a x i m u m o f t h e s p e c tr a l d e n s i t y fu n c t i o n f o r S h n u m b e ra p p r o x i m a t e l y e q u a l t o 2 d e g e n e r a t e s, w h i c h i s r e l a te d t o s u p e r p o s i t i o n o f d i s tu r b a n c e s o f v a r i o u s o r i g i n ( t u rb u l e n c e c a u s e db y m o v e m e n t o f a i r c a v i t ie s ) . A p r e s s u re f l u c t u a t i o n s p e c t r u m a n a l o g o u s i n f o r m w a s o b s e r v e d i n t h e c a s e o f t h es u p e r p o s i t i o n o f d i st u r b a n c e s c a u s e d b y w h i r l p o o l s w i t h v a r i o u s a x e s o f r o t a ti o n o c c u r r i n g u n d e r c o m p l e x t h r e e -d i m e n s i o n a lcond i t ions [ 7];

t h e m a x i m u m o f t h e s p e c tr a l d e n s i t y f u n c t i o n is r e c o r d e d a l s o i n t h e l o w - f r e q u e n c y r e g i o n f o r S h n u m b e r o f a b o u t0 .1 , bu t the cont r ibu t ion of the low - f r equen cy f luc tua t ions ( Sh < 0 .5) to the ener gy of the spec t r um i s smal l ;

t h e r a t e o f d e c a y o f t h e s p e c t ra l d e n s i t y f u n c t io n in t h e r e g i o n o f h i g h v a l u e s o f t h e S h n u m b e r ( S h > 2 ) o c c u r s a ta s m a l l e r ra t e t h a n a c c o r d i n g t o A . M . O b u k h o v ' s f u n c t i o n a l d e p e n d e n c e F ( S ) = S h - 7 /3 .

W h e n a n a l y z i n g t h e d a t a o n t h e s p e c tr a l d e n s i t y f u n c t io n s o f p r e s s u r e f l u c t u a t io n s , t h e e d d y t r a n s p o r t v e l o c i t y vkf i g u r e s in t h e d i m e n s i o n l e s s c o m p l e x e s l a i d o u t o n t h e c o o r d i n a t e a x e s. I t w a s d e t e r m i n e d o n t h e b a s is o f c o m p a r i n g t h eautoco r r e la t ion f unc t io n and spa t ia l cor r e la t ions of p r es sur e f luc tua t ions [ 4] and f or the g ive n condi t ion s w as about ( 0 .4-0 .6) v c .

T h e d a t a p r e s e n t e d h e r e p e r m i t e v a l u a t in g t h e f l u c t u a t i o n c o m p o n e n t o f t h e l o a d o n t h e f l o w s u r fa c e s o f a r e c t a n g u l a rc o n d u i t i n t h e p r e s e n c e o f a h y d r a u l i c j u m p o n i ts p a t h a n d c o m p l e t e f i l li n g o f th e c o n d u i t i n t h e s t r et c h a f t e r t h e j u m p .

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