TECHNICAL REPORT 353-7
DRAG REDUCTION BY EJECTING ADDITIVE SOLUTIONS INTO A PURE-WATER BOUNDARY LAYER
By
J i n Wu and M a r s h a l l P. T u l i n June 1970
T h i s document has been a p p r o v e d f o r p u b l i c r e l e a s e and s a l e ; i t s d i s t r i b u t i o n i s u n l i m i t e d P r e p a r e d f o r O f f i c e erf N a v a l Research Department o f t h e Navy Under C o n t r a c t No. N o n r - 4 l 8 l ( O O ) NR 062-325
HYDRONAUTICS, I n c o r p o r a t e d i -TABLE OF CONTENTS Page ABSTRACT 1 INTRODUCTION 2 EXPERIMENTAL TECHNIQUE 4 Measurements o f T u r b u l e n t F r i c t i o n 4 E j e c t i o n o f A d d i t i v e S o l u t i o n s 5 RESULTS 5 DISCUSSION 7 A d d i t i v e R e q u i r e m e n t s and E j e c t i o n Techniques f o r Smooth Boundary 7 A d d i t i v e R e q u i r e m e n t and E j e c t i o n Techniques f o r Rough B o u n d a r i e s 13 CONCLUSIONS 15 ACKNOWLEDGMENT 15
ABS TRACT
Drag r e d u c t i o n caused by e j e c t i n g a d d i t i v e s o l u t i o n s f r o m
a s l o t i n t o a p u r e - w a t e r boundary l a y e r on a f l a t p l a t e has
been s y s t e m a t i c a l l y s t u d i e d . R e s u l t s i n c l u d e d r a g measurements f o r a p l a n e b o u n d a r y , smooth and rough,, w i t h v a r i o u s openings o f t h e s l o t and w i t h v a r i o u s c o n c e n t r a t i o n s and d i s c h a r g e s o f t h e e j e c t e d a d d i t i v e s o l u t i o n . C o n c l u s i o n s have been drawn on t h e a d d i t i v e r e q u i r e m e n t i n e x t e r n a l f l o w s and on t h e e j e c t i o n , t e c h n i q u e f o r an optimum d r a g r e d u c t i o n .
HYDRONAUTICS, I n c o r p o r a t e d
-.11-L I S T OF FIGURES F i g u r e 1 - G e n e r a l View o f Equipment
F i g u r e 2 - Drag R e d u c t i o n o f Smooth and Rough B o u n d a r i e s w i t h . Homogeneous A d d i t i v e S o l u t i o n s
F i g u r e 3 - Drag R e d u c t i o n by E j e c t i n g A d d i t i v e S o l u t i o n s I n t o A Pure-Water Boundary L a y e r o f a Smooth S u r f a c e
( S l o t Opening 0,022 I n c h e s )
F i g u r e ^1- Drag R e d u c t i o n by E j e c t i n g A d d i t i v e S o l u t i o n s I n t o A Pure-Water Boundary L a y e r o f a Smooth S u r f a c e
( S l o t Opening 0.042 I n c h e s )
F i g u r e 5 - D r a g R e d u c t i o n by E j e c t i n g A d d i t i v e S o l u t i o n s I n t o A Pure-Water Boundary L a y e r o f a Smooth S u r f a c e
( S l o t Opening 0,093 I n c h e s )
F i g u r e 6 _ D r a g R e d u c t i o n by E j e c t i n g A d d i t i v e S o l u t i o n s I n t o A Pure-Water Boundary L a y e r o f a Rough S u r f a c e
( G l a s s Beads, S l o t Opening 0.022 I n c h e s )
F i g u r e 7 - Drag R e d u c t i o n by E j e c t i n g A d d i t i v e S o l u t i o n s I n t o A Pure-Water Boundary L a y e r o f Rough S u r f a c e (Rub-b e r Mats, S l o t Opening 0.022 I n c h e s ) F i g u r e 8 - Drag R e d u c t i o n by E j e c t e d A d d i t i v e S o l u t i o n s Over A Smooth Boundary F i g u r e 9 - T y p i c a l D r a g - R e d u c t i o n Curve o f a P l a n e Boundary w i t h U n i f o r m A d d i t i v e S o l u t i o n o r by E j e c t i o n F i g u r e 10 - Drag R e d u c t i o n by E j e c t i n g A d d i t i v e S o l u t i o n s Over A Rough Boundary
INTRODUCTION
Many e x p e r i m e n t s show t h e c a p a b i l i t y o f a d d i t i v e s o f h i g h m o l e c u l a r w e i g h t t o r e d u c e t u r b u l e n t f r i c t i o n . Most measurements r e f e r t o t h e p r e s s u r e d r o p i n t u r b u l e n t p i p e f l o w s w i t h a d d i t i v e s homogeneously mixed i n w a t e r . These a r e t h e I n t e r n a l f l o w c a s e S j
where t h e homogeneous a d d i t i v e s o l u t i o n f l o w s c o n s t r a i n e d i n a f u l l y d e v e l o p e d b o u n d a r y l a y e r . However, t h i s does n o t r e s e m b l e t h e case f o r e x t e r n a l f l o w s , where t h e a d d i t i v e s o l u t i o n has t o be e j e c t e d i n t o a d e v e l o p i n g b o u n d a r y l a y e r o f p u r e w a t e r . T h e r e e x i s t s u n c e r t a i n t y a b o u t t e c h n i q u e s f o r t h e most e f f i c i e n t e j e c -t i o n i n -t o e x -t e r n a l f l o w s . I -t may n o -t be r e q u i r e d i n e x -t e r n a l f l o w cases t h a t t h e e n t i r e b o u n d a r y l a y e r s h o u l d be f i l l e d w i t h p o l y m e r s o l u t i o n , because t h e m a j o r e f f e c t s due t o t h e p r e s e n c e o f a d d i t i v e s o l u t i o n s o c c u r v e r y c l o s e t o t h e w a l l and c e r t a i n l y w i t h i n t h e i n n e r b o u n d a r y l a y e r ( R e f e r e n c e l ) . F o r v e r y d i l u t e s o l u t i o n s t h i s i s e s p e c i a l l y t r u e , as s h e a r - s t i f f e n i n g o c c u r s i n t h e t u r b u l e n t r e g i o n c l o s e s t t o t h e w a l l and, i t i s b e l i e v e d , a c c o u n t s f o r t h e r e d u c t i o n o f t u r b u l e n t s k i n f r i c t i o n due t o i t s a c t i o n t h e r e . I t i s n o t a d v i s e d t h a t a h i g h l y c o n c e n t r a t e d a d d i t i v e s o l u t i o n be e j e c t e d a t t h e w a l l and t h e n t o l e t t u r b u l e n t m i x i n g I n s i d e t h e b o u n d a r y l a y e r d i l u t e t h e e j e c t e d s o l u -t i o n . S i n c e -t u r b u l e n -t m i x i n g be-tween -t h e e j e c -t e d s o l u -t i o n and t h e p u r e - w a t e r s u r r o u n d i n g may be h i g h l y s u p p r e s s e d ( R e f e r e n c e 2 ) , t h e e j e c t e d s o l u t i o n may r e m a i n t o o c o n c e n t r a t e d and may t h e r e -f o r e l o s e i t s e -f -f e c t i v e n e s s .
HYDRONAUTICS, I n c o r p o r a t e d
-3-I n a p r e v i o u s s t u d y ( R e f e r e n c e 3 ) ^ t h e t u r b u l e n t f r i c t i o n o f a p l a n e b o u n d a r y i n f l o w s o f homogeneous s o l u t i o n s o f h i g h -m o l e c u l a r - w e i g h t a d d i t i v e s was -measured and co-mpared w i t h t h a t p r o d u c e d by e j e c t i n g a d d i t i v e s o l u t i o n s i n t o t h e p u r e w a t e r boundary l a y e r o f a f l a t p l a t e ( R e f e r e n c e 4 ) . The r e s u l t s i n -d i c a t e t h a t t h e e j e c t e -d s o l u t i o n is-'mixe-d b u t v e r y p o o r l y w i t h i t s p u r e w a t e r s u r r o u n d i n g s . V i s u a l s t u d i e s c o n c e r n i n g d i f f u s i o n and e n t r a l n m e n t o f j e t s w i t h a d d i t i v e s o l u t i o n s f l o w i n g i n t o a t u r b u l e n t s t r e a m o f p u r e w a t e r c o n f i r m t h a t a d d i t i v e s suppress t u r b u l e n t d i f f u s i o n . Based on t h e s e r e s u l t s , i t was s u g g e s t e d ( R e f e r e n c e 4 ) t h a t f o r d r a g r e d u c t i o n i n e x t e r n a l f l o w s t h e s o l u t i o n e j e c t e d i n t o t h e b o u n d a r y l a y e r s h o u l d be d i l u t e , t h a t t h e r a t e o f e j e c t i o n s h o u l d be comparable t o t h e d i s c h a r g e w i t h i n t h e i n n e r b o u n d a r y l a y e r ( t h e w a l l c o n t r o l l e d r e g i o n ) , and t h a t t h e n o r m a l component o f t h e e j e c t i o n v e l o c i t y as w e l l as t h e d i f f e r e n c e between t h e e j e c t i o n v e l o c i t y and t h e s t r e a m v e l o c i t y s h o u l d be m i n i m i z e d . I n t h e p r e s e n t s t u d y , t h e f r i c t i o n o f a p l a n e b o u n d a r y , smooth and r o u g h , has been s y s t e m a t i c a l l y measured w i t h a d d i t i v e s o l u t i o n s ( P o l y e x WSR301) o f v a r i o u s c o n c e n t r a t i o n s and d i s -c h a r g e s , e j e -c t e d f r o m a s l o t o f a d j u s t a b l e w i d t h . The r e s u l t s n o t o n l y c o n f i r m t h e p r e v i o u s s u g g e s t i o n s b u t f u r t h e r i n d i c a t e i n a q u a n t i t a t i v e f a s h i o n optimum t e c h n i q u e s o f a d d i t i v e e j e c t i o n r a t e . I t i s shown t h a t u n d e r t h e c i r c u m s t a n c e s o f t h e p r e s e n t t e s t s , a v e r y s m a l l amount o f a d d i t i v e i s a c t u a l l y needed f o r
t h e most e f f e c t i v e a p p l i c a t i o n t o a c h i e v e d r a g r e d u c t i o n i n e x t e r n a l f l o w s : c o n c e n t r a t i o n s o f between 100 and 1000 ppmw a t t h e v i s c o u s - s u b l a y e r d i s c h a r g e f o r a smooth s u r f a c e , and a t t h e m i x i n g - l a y e r d i s c h a r g e f o r a -.riaugh! s u r f a c e . I t r e m a i n s t o be seen w h e t h e r t h e s e c o n d i t i o n s a r e a l s o optimum i n t h e case o f l a r g e r p l a t e s and h i g h e r Reynolds numbers t h a n were s o f a r c o n s i d e r e d .
EXPERIMENTAL TECHNIQUE Measurements o f T u r b u l e n t F r i c t i o n
The e x p e r i m e n t s have been p e r f o r m e d i n a c i r c u l a t i n g w a t e r c h a n n e l w i t h a c l o s e d t e s t s e c t i o n 44 i n . l o n g , 15 i n . w i d e , and 7-5 i n . deep. A p a r t o f t h e c o v e r p l a t e a t t h e t e s t s e c t i o n , 10 i n c h e s w i d e and 21 i n c h e s l o n g , i s c u t f r o m t h e r e s t w i t h a c l e a r a n c e o f l/lOO i n . a l o n g f o u r s i d e s ; see F i g -u r e 1. T h i s p a r t o f t h e c o v e r p l a t e i s h e l d by a s t r a i n - g a g e s u p p o r t whose o u t p u t i s i n d i c a t e d on a d i g i t a l r e a d o u t d e v i c e . A s t r i p o f No, 32 sand b l a s t , 1 i n c h i n w i d t h , was p l a c e d 3/8
i n . u p s t r e a m f r o m t h e l e a d i n g edge o f t h e e j e c t o r . T h e r e f o r e , t h e sand s e r v e s f o r t u r b u l e n c e s t i m u l a t i o n , b u t i t s r e s i s t a n c e i s e x c l u d e d i n t h e d r a g measurements.
The d r a g - m e a s u r i n g p l a t e was a l s o roughened by g l u i n g t o i t s s u r f a c e s p h e r i c a l p a r t i c l e s h a v i n g a d i a m e t e r o f 0.108 i n , and a r r a n g e d i n a random and i n t h e most compact f o r m , o r h a r d -r u b b e -r mats w i t h p y -r a m i d a l -r o u g h n e s s , h a v i n g a h e i g h t o f O.062 i n . and a t a s p a c i n g o f O.I69 i n .
HYDRONAUTICS, I n c o r p o r a t e d 5 -E J e o t i o n o f A d d i t i v e S o l u t i o n s The t e s t f l u i d c o n s i s t s o f aqueous s o l u t i o n s o f v a r i o u s l y c o n c e n t r a t e d p o l y e t h y l e n e o x i d e ( P o l y e x WSR-301) a d d i t i v e . The a d d i t i v e s o l u t i o n i s e j e c t e d f r o m a s l o t e j e c t o r , shown i n F i g -u r e 1. The e j e c t o r i g i n s t a l l e d t r a n s v e r s e l y -u p s t r e a m f r o m t h e p l a n e b o u n d a r y , h a v i n g t h e s l o t a t 1-3/16 i n , f r o m t h e l e a d i n g edge o f t h e p l a n e boundary. Near t a n g e n t i a l e j e c t i o n i s
a c h i e v e d as t h e p l a n e c o n t a i n i n g t h e s l o t i s a t a n i n c l i n a t i o n , o f 7° f r o m t h e p l a n e boundary., The w i d t h o f t h e s l o t o p e n i n g i s a d j u s t a b l e ; t h i s a d j u s t m e n t and t h e use o f a d d i t i v e s o l u t i o n s o f v a r i o u s c o n c e n t r a t i o n s and o f v a r i o u s d i s c h a r g e s e n a b l e us t o o b t a i n d i f f e r e n t i n i t i a l v e l o c i t y and c o n c e n t r a t i o n d i s t r i b u t i o n s o f t h e e j e c t e d a d d i t i v e s o l u t i o n , RESULTS A s e r i e s o f measurements o f t h e t u r b u l e n t f r i c t i o n on t h e p l a n e b o u n d a r y , smooth and r o u g h , u s i n g homogeneous s o l u t i o n s o f p o l y o x a d d i t i v e s were c o n d u c t e d e a r l i e r . . The r e s u l t s , p o r t i o n s f r o m R e f e r e n c e 4, a r e shown I n F i g u r e 2. The d r a g r e d u c t i o n o b -t a i n e d f r o m -t h e r o u g h s u r f a c e w i -t h g l a s s beads i s seen -t o be s i m i l a r t o t h a t f r o m t h e smooth s u r f a c e . . A c o n t i n u o u s c u r v e , drawn t h r o u g h t h e d a t a p o i n t s , w i l l be used t p compare, w i t h t h e d r a g r e d u c t i o n o b t a i n e d I n e j e c t i o n s t u d i e s , .
The e j e c t i o n s t u d i e s were c o n d u c t e d a t a c o n s t a n t c h a n n e l v e l o c i t y o f 8 f t / s e c . The Reynolds number d e f i n e d w i t h t h e
l e n g t h o f t h e p l a n e boundary i s 1.3 x 10^. F o r each s l o t o p e n i n g o f t h e s e s t u d i e s , a s e r i e s o f e x p e r i m e n t s , e j e c t i n g a d d i t i v e s o l u t i o n s o f v a r i o u s c o n c e n t r a t i o n s , were s y s t e m a t i c a l l y con-d u c t e con-d . D i f f e r e n t con-d i s c h a r g e s o f a con-d con-d i t i v e s o l u t i o n s were e j e c t e con-d f o r each a d d i t i v e c o n c e n t r a t i o n t o c o v e r t h e most i n t e r e s t i n g r a n g e , showing a r a p i d v a r i a t i o n o f d r a g r e d u c t i o n w i t h d i s c h a r g e . D u r i n g t h e e x p e r i m e n t , t h e t u r b u l e n t f r i c t i o n o f t h e p l a n e bound-a r y wbound-as mebound-asured on t w o o c c bound-a s i o n s , one b e f o r e bound-and t h e o t h e r d u r i n g e j e c t i o n . The d r a g r e d u c t i o n o b t a i n e d by t a k i n g t h e d i f -f e r e n c e o -f two r e a d i n g s was -f u r t h e r c o r r e c t e d t o e l i m i n a t e t h e r e d u c t i o n due t o e j e c t i o n i t s e l f and t o r e t a i n o n l y t h e i n f l u e n c e o f a d d i t i v e s o l u t i o n s . T h i s c o r r e c t i o n was based on a p r e - t e s t c a l i b r a t i o n o b t a i n e d by e j e c t i n g p u r e w a t e r a t v a r i o u s d i s c h a r g e s u n d e r t h e same e x p e r i m e n t a l c o n d i t i o n . Because t h e e j e c t i o n d i s c h a r g e i s v e r y l i t t l e i n comparison w i t h t h e b o u n d a r y - l a y e r d i s c h a r g e , t h i s c o r r e c t i o n i s g e n e r a l l y s m a l l , and does n o t exceed a b o u t 5 p e r c e n t o f t h e t o t a l t u r b u l e n t f r i c t i o n o f t h e smooth s u r f a c e and i s n e g l i g i b l e f o r t h e r o u g h s u r f a c e .
A s e t o f sample r e s u l t s f o r t h e smooth s u r f a c e f o r one s l o t o p e n i n g , i s shown i n t h e upper h a l f o f F i g u r e 3. F o r each c o n c e n t r a t i o n , t h e d r a g r e d u c t i o n was p l o t t e d v e r s u s t h e d i s -c h a r g e o f a d d i t i v e s o l u t i o n . A -c o n t i n u o u s -c u r v e was t h e n f i t t e d t o smooth t h e d a t a and t o r e l a t e t h e d r a g r e d u c t i o n w i t h t h e
HYDRONAUTICS, IncorporatecS -7-e j -7-e c t l o n d i s c h a r g -7-e . Prom t h -7-e f a i r -7-e d d a t a , t h -7-e d r a g r -7-e d u c t i o n o b t a i n e d w i t h d i f f e r e n t a d d i t i v e c o n c e n t r a t i o n s a t any g i v e n e j e c t i o n d i s c h a r g e c a n be d e t e r m i n e d ; s e e t h e l o w e r h a l f o f F i g u r e 3, where Q , as shown l a t e r , i s t h e v i s c o u s s u b l a y e r s d i s c h a r g e . T h i s p r o c e d u r e i s n e c e s s a r y because i t i s I m p r a c • t l c a l t o i n t r o d u c e t h e a d d i t i v e s o l u t i o n s o f v a r i o u s c o n c e n t r a -t i o n a -t any d e s i r e d d i s c h a r g e . F o l l o w i n g t h e same p r o c e d u r e o u t l i n e d i n t h e f o r e g o i n g p a r a g r a p h , d r a g - r e d u c t i o n r e s u l t s w i t h o t h e r s l o t openings and f r o m d i f f e r e n t s u r f a c e s can be o b t a i n e d ; see F i g u r e s 4, 3> 6 and 7. I t i s n o t e d i n t h e l a s t f i g u r e t h a t a d d i t i v e s o l u t i o n s o f h i g h e r c o n c e n t r a t i o n s were e j e c t e d . The r e s u l t s o v e r a smooth s u r f a c e w i t h v a r i o u s openings o f t h e e j e c t o r and w i t h
t h e e j e c t i o n d i s c h a r g e a t v a r i o u s m u l t i p l e s o f t h e v i s c o u s sub-l a y e r d i s c h a r g e a r e compared i n F i g u r e 8. The r e s u sub-l t s f r o m smooth and f r o m r o u g h s u r f a c e s a r e compared i n F i g u r e 10.
DISCUSSION
A d d i t i v e R e q u i r e m e n t s and E j e c t i o n Techniques f o r Smooth Boundary The n o m i n a l t h i c k n e s s o f a v-is.cous' s u b l a y e r , 5 , i s
g e n e r a l l y c o n s i d e r e d t o be ( R e f e r e n c e 5 )
where u^^ i s t h e s h e a r v e l o c i t y , ''•q/p ^'^q w a l l s t r e s s and p i s t h e d e n s i t y o f t h e f l u i d ) ; and v i s t h e k i n e m a t i c v i s c o s i t y o f t h e f l u i d . A v i r t u a l l y l i n e a r v e l o c i t y g r a d i e n t , T^/pv, p e r s i s t s w i t h i n t h e s u b l a y e r , o f w h i c h t h e d i s c h a r g e p e r u n i t w l d t h j Q , can be f o u n d as
s
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I ^ V = 67.3 V [ 2 ] I t i s seen t h a t t h e n o r m a l v i s c o u s s u b l a y e r d i s c h a r g e I s i n d e -pendent h o t o n l y o f t h e b o u n d a r y shear b u t a l s o , more I n t e r e s t i n g , o f t h e d i s t a n c e f r o m t h e l e a d i n g edge o f t h e s o l i d boundary. T h i s I m p l i e s t h a t t h e v i s c o u s s u b l a y e r i s e n c l o s e d b y a s t r e a m l i n e ,or t h e v i s c o u s s u b l a y e r f l o w s i n s i d e a s t r e a m t u b e . C o n s e q u e n t l y , t h e mass t r a n s f e r between t h e v i s c o u s s u b l a y e r and i t s s u r r o u n d -i n g s I n v o l v e s d -i f f u s -i v e r a t h e r t h a n c o n v e c t -i v e p r o c e s s e s . The d i s c h a r g e o f t h e v i s c o u s s u b l a y e r I s seen i n E q u a t i o n [2] t o v a r y w i t h t h e s q u a r e o f t h e d i m e n s i o n l e s s v i s c o u s s u b -l a y e r t h i c k n e s s a n d w i t h t h e k i n e m a t i c v i s c o s i t y o f t h e f -l u i d . W i t h a d d i t i v e s o l u t i o n , d r a g r e d u c t i o n i s g e n e r a l l y accompanied by an i n c r e a s e o f t h i s d i m e n s i o n l e s s t h i c k n e s s ( R e f e r e n c e 6 ) . I n a d d i t i o n , t h e v i s c o s i t y o f d i l u t e a d d i t i v e s o l u t i o n s I n c r e a s e w i t h t h e a d d i t i v e c o n c e n t r a t i o n . C o n s e q u e n t l y , t h e d i s c h a r g e o f t h e v i s c o u s s u b l a y e r w i t h e j e c t i o n o f a d d i t i v e s o l u t i o n s i s
HYDRONAUTICS, I n c o r p o r a t e d -9-c e r t a i n l y g r e a t e r t h a n t h a t I n d i -9-c a t e d by E q u a t i o n [ 2 ] . However, o u r method h e r e i s t o c o r r e l a t e t h e e j e c t i o n d i s c h a r g e w i t h t h e s u b l a y e r d i s c h a r g e f o r a p u r e w a t e r boundary l a y e r . T h i s s t u d y was p l a n n e d s p e c i f i c a l l y t o i n v e s t i g a t e r e q u i r e ments and t e c h n i q u e s f o r e j e c t i n g a d d i t i v e s o l u t i o n s i n t o a p u r e -w a t e r b o u n d a r y l a y e r f o r t h e most e f f i c i e n t d r a g r e d u c t i o n . R e l e v a n t q u e s t i o n s and answers a r e :
( l ) F o r an i d e a l e j e c t i o n , what i s t h e most economic way o f u s i n g a d d i t i v e f o r d r a g r e d u c t i o n i n ex-t e r n a l f l o w s ? The d r a g r e d u c t i o n w i t h v a r i o u s s l o t openings> c o n c e n t r a t i o n s , and e j e c t i o n d i s c h a r g e s shown I n t h e l o w e r h a l v e s o f F i g u r e s 3^ 4 and 5 c l e a r l y d e m o n s t r a t e t h e f o l l o w i n g t r e n d s : ( a ) F o r a g i v e n s l o t and w i t h a d d i t i v e s o l u t i o n s o f a g i v e n c o n c e n t r a t i o n , t h e d r a g r e d u c t i o n g e n e r a l l y I n c r e a s e s w i t h t h e d i s c h a r g e when t h e e j e c t i o n r a t e i s s m a l l Or comparable w i t h t h e s u b l a y e r d i s c h a r g e ; t h e r a t e o f I n c r e a s e s l o w s down when t h e e j e c t i o n r a t e i s g r e a t e r t h a n t w i c e t h e s u b l a y e r d i s c h a r g e ; t h e d r a g r e d u c t i o n no l o n g e r i n c r e a s e s , o r even d e -creases when t h e e j e c t i o n r a t e i s g r e a t e r t h a n a b o u t f i v e t i m e s t h e s u b l a y e r d i s c h a r g e .
( b ) The d r a g r e d u c t i o n a t v a r i o u s c o n c e n t r a t i o n s w i t h t h e a d d i t i v e s o l u t i o n e j e c t e d a t 1, 2, and 4 t i m e s t h e v i s c o u s s u b l a y e r d i s c h a r g e s a r e shown i n t h e l o w e r h a l v e s o f F i g u r e s 3> 4 and 5. I t i s seen t h a t a s i g n i f i c a n t d r a g r e d u c t i o n i s p r o v i d e d by e j e c t i o n a t t h e v i s c o u s - s u b l a y e r d i s c h a r g e . The g a i n o f d r a g r e d u c t i o n w i t h h i g h e r e j e c t i o n r a t e i s n o t o v e r w h e l m i n g . These t r e n d s i n d i c a t e t h a t t h e e j e c t i o n r a t e a t t h e v i s c o u s s u b l a y e r d i s c h a r g e i s p r o b a b l y c l o s e t o t h e most e f f e c t i v e ( e c o n o m i c ) way t o use a d d i -t i v e f o r d r a g r e d u c -t i o n i n e x -t e r n a l f l o w s . T h i s i s s u b s t a n t i a t e d by t h e r e s u l t s showing t h a t r e l a t i v e l y l i t t l e g a i n i s o b t a i n e d when t h e e j e c t i o n d i s -c h a r g e i s i n -c r e a s e d by t w o o r f o u r t i m e s t h e v i s c o u s s u b l a y e r d i s c h a r g e . Sometimes even l e s s d r a g r e d u c t i o n was o b t a i n e d a t h i g h e r e j e c t i o n r a t e s , e s p e c i a l l y w i t h h i g h a d d i t i v e c o n c e n t r a t i o n s , p r o b a b l y because t h e e j e c t e d s o l u t i o n s f a i l e d t o mix w i t h t h e s u r r o u n d i n g p u r e w a t e r and r e s u l t e d i n l e s s d r a g r e d u c t i o n , see a l s o F i g u r e 2. ( 2 ) What s l o t c o n f i g u r a t i o n s h o u l d be adopted? The s l o t c o n f i g u r a t i o n i s d e f i n e d by two p a r a m e t e r s , namely, t h e a n g l e o f i n c l i n a t i o n and t h e o p e n i n g o f t h e s l o t . I t i s o b v i o u s t h a t t h e
HYDRONAUTICS, I n c o r p o r a t e d -11-a n g l e o f i n c l i n -11-a t i o n o f t h e s l o t s h o u l d be s m -11-a l l so t h a t t h e e j e c t e d a d d i t i v e s o l u t i o n w i l l be k e p t n e a r t h e w a l l . The e f f e c t o f e j e c t i o n a n g l e on d r a g r e d u c t i o n was n o t i n v e s t i g a t e d h e r e . The e j e c t i o n a n g l e was l i m i t e d by t h e c o n v e n i e n c e o f c o n s t r u c t i n g t h e e j e c t o r . The w i d t h o f t h e s l o t o p e n i n g s h o u l d be comparable w i t h t h e t h i c k n e s s o f t h e s u b l a y e r . However, t h e v e l o c i t y o f t h e e j e c t i o n s h e e t i s a l s o r e l a t e d t o t h e s l o t o p e n i n g . The c o m p a r i s o n o f t h i s v e l o c i t y w i t h b o u n d a r y - l a y e r v e l o c i t i e s g o v e r n s t h e m i x i n g between t h e e j e c t e d a d d i t i v e s o l u t i o n and t h e s u r r o u n d i n g p u r e w a t e r . The r e s u l t s o b t a i n e d f r o m a g i v e n e j e c t i o n a n g l e b u t w i t h d i f f e r e n t s l o t openings a r e compared i n F i g -u r e 8. The v e l o c i t y o f t h e e j e c t i o n s h e e t i n t h e p r e s e n t e x p e r i m e n t i s g e n e r a l l y l e s s t h a n t h e a v e r a g e v i s c o u s - s u b l a y e r v e l o c i t y . C o n s e q u e n t l y t h e n a r r o w e s t s l o t p r o v i d e s t h e b e s t m a t c h i n g o f t h e e j e c t i o n v e l o c i t y w i t h t h e b o u n d a r y - l a y e r f l o w . I n a d d i t i o n , t h e t h i c k n e s s o f t h e v i s c o u s s u b l a y e r i s a b o u t 0.005 i n . The s l o t o p e n i n g s h o u l d n o t be t o o much g r e a t e r t h a n t h i s t h i c k n e s s ( w i t h i n an o r d e r o f m a g n i t u d e ) i n o r d e r t o a v o i d t h e d i f f u s i o n o f a d d i t i v e s o l u t i o n away f r o m t h e w a l l . The r e -s u l t -s -shown i n F i g u r e 8 a r e v e r y much i n l i n e w i t h our d i s c u s s i o n s p r e s e n t e d h e r e .
( 3 ) What s h o u l d t h e c o n c e n t r a t i o n be o f t h e e j e c t e d a d d i t i v e s o l u t i o n ?
T y p i c a l r e s u l t s o b t a i n e d f r o m t h e p r e s e n t ( e j e c t i o n ) s t u d y a r e compared i n F i g u r e 9 w i t h e a r l i e r r e s u l t s w i t h u n i f o r m s o l u t i o n s o v e r t h e same p l a n e b o u n d a r y . These curves a r e d i f f e r e n t i n shape: t h e d r a g r e d u c t i o n c u r v e w i t h u n i f o r m a d d i t i v e s o l u t i o n s i s seen t o be r a t h e r peaked, w h i l e t h e c u r v e w i t h e j e c t i o n f e a t u r e s a p l a t e a u . The f o r m e r i n d i c a t e s t h a t h i g h l y c o n c e n t r a t e d a d d i t i v e s o l u t i o n s a r e r e l a t i v e l y i n e f f e c t i v e f o r d r a g r e d u c t i o n . The l a t t e r r e v e a l s t h a t t h e e j e c t e d a d d i t i v e s o l u t i o n i s d i l u t e d by t h e b o u n d a r y l a y e r f l o w . I t i s e x p e c t e d t h a t w i t h f u r t h e r i n -c r e a s e o f e j e -c t e d a d d i t i v e -c o n -c e n t r a t i o n , o r o f e j e c t i o n d i s c h a r g e , t h e b o u n d a r y l a y e r f l o w n e a r t h e w a l l w i l l f a l l t o d i l u t e s u f f i c i e n t l y t h e a d d i t i v e s o l u t i o n , and a d r o p o f d r a g r e d u c t i o n w i l l r e s u l t . The d i l u t i o n o f t h e e j e c t e d a d d i t i v e s o l u t i o n i s i n d i c a t e d by t h e s h i f t t o w a r d h i g h e r concentra-^ t i o n s o f t h e e j e c t i o n c u r v e r e l a t i v e t o t h e c u r v e w i t h u n i f o r m s o l u t i o n . The d i l u t i o n i n t h e p r e s e n t case i s deduced t o be about one t o t e n . As t h e l e n g t h o f t h e b o u n d a r y I n c r e a s e s , i n c r e a s i n g d i l u t i o n a l o n g t h e l e n g t h o f t h e p l a t e s h o u l d
HYDRONAUTICS, I n c o r p o r a t e d -13-cause t h e d r a g r e d u c t i o n c u r v e t o s h i f t f u r t h e r t o w a r d t h e h i g h c o n c e n t r a t i o n end. More s t u d i e s a r e needed I n o r d e r t o i n v e s t i g a t e i n d e t a i l t h e d i l u t i o n p r o c e s s w h i c h i s o f much i m p o r t a n c e f o r t h e p r a c t i c a l a p p l i c a t i o n o f a d d i t i v e s f o r d r a g r e d u c t i o n . ( 4 ) I n w h i c h p o r t i o n o f t h e boundary l a y e r do a d d i t i v e s a c t t o cause d r a g r e d u c t i o n ? T h i s q u e s t i o n can o n l y be answered a d e q u a t e l y by a d e t a i l e d s u r v e y o f a d d i t i v e c o n c e n t r a t i o n w i t h i n t h e boundary l a y e r and a s y s t e m a t i c com-p a r i s o n o f t h e measured com-p r o f i l e s w i t h t h e d r a g r e d u c t i o n r e s u l t s . However, i t i s c l e a r f r o m F i g u r e s 3^ 4 and 5 t h a t an i n c r e a s e i n e j e c t i o n d i s c h a r g e f a i l e d t o cause s i g n i f i c a n t i n c r e a s e i n d r a g r e d u c t i o n . T h i s i n d i c a t e s t h a t a d d i t i v e s o l u t i o n need o n l y t o f i l l t h e v i s c o u s s u b l a y e r and t h e i n n e r m o s t r e g i o n o f t h e t u r b u l e n t bound-a r y l bound-a y e r i n o r d e r e f f e c t i v e l y t o cbound-ause d r bound-a g r e d u c t i o n .
A d d i t i v e R e q u i r e m e n t and E j e c t i o n Techniques f o r Rough B o u n d a r i e s A d e t a i l e d b o u n d a r y - l a y e r measurement o v e r t h e same r o u g h s u r f a c e w i t h g l a s s beads was c o n d u c t e d by Wu ( R e f e r e n c e 7 ) . ]|fc was shown t h a t a c o n s t a n t v e l o c i t y p e r s i s t s i n a r e g i o n w i t h i n a q u a r t e r o f t h e p a r t i c l e s i z e f r o m t h e t o p o f t h e bead. A v e r y s t r o n g t u r b u l e n t m i x i n g u n d o u b t e d l y e x i s t s i n t h i s r e g i o n , whici!
p r e s u m a b l y erases t h e u s u a l s t r o n g v e l o c i t y g r a d i e n t near t h e w a l l . T h e r e f o r e , t h e roughness n o t o n l y d i s r u p t s t h e v i s c o u s s u b l a y e r b u t a l s o i n t r o d u c e s a v e r y s t r o n g m i x i n g l a y e r n e a r t h e w a l l . The d i s c h a r g e o f t h e m i x i n g l a y e r i s a b o u t t e n t i m e s t h a t o f t h e v i s c o u s s u b l a y e r ( R e f e r e n c e 7 ) . The a d d i t i v e s o l u t i o n e j e c t e d a t t h e w a l l i s t h e n d i f f u s e d v e r y r a p i d l y i n t h i s m i x i n g l a y e r . C o n s e q u e n t l y , more a d d i t i v e i s r e q u i r e d ; h i g h e r e j e c t i o n r a t e s o r a d d i t i v e s o l u t i o n s o f h i g h e r c o n c e n t r a t i o n s s h o u l d be e j e c t e d t o be s t r o n g l y d i l u t e d by t h e m i x i n g due t o r o u g h n e s s . No d e t a i l e d boundary l a y e r s u r v e y was p e r f o r m e d o v e r t h e r o u g h s u r f a c e on t h e r u b b e r mats. The roughness elements i n t h i s case were somewhat s m a l l e r i n h e i g h t , b u t t h e elements somewhat more w i d e l y spaced. Moderate s p a c i n g i s known ( R e f e r e n c e 8 ) t o make t h e s u r f a c e r e l a t i v e l y r o u g h e r i n c o m p a r i s o n w i t h t h e same r o u g h -ness elements p l a c e d i n t h e most compact a r r a n g e m e n t , i n o t h e r words, t h e f l o w c o n d i t i o n over t h e s e two r o u g h s u r f a c e s may n o t be a p p r e c i a b l y d i f f e r e n t .
The r e s u l t s o b t a i n e d w i t h t h e r o u g h b o u n d a r i e s a r e shown i n F i g u r e s 6 and 7. Compared t o t h e d a t a o v e r t h e smooth b o u n d a r y , t h e s e r e s u l t s show a l a r g e e f f e c t o f e j e c t i o n d i s c h a r g e o v e r t h e r a n g e t e s t e d . The r e s u l t s o b t a i n e d f r o m t h e r o u g h s u r f a c e a r e compared w i t h t h o s e f r o m t h e smooth s u r f a c e i n F i g u r e 10. I t i s i n t e r e s t i n g t o see t h a t t h e d a t a f r o m t h e r o u g h s u r f a c e i s g e n -e r a l l y s h i f t -e d w i t h r -e s p -e c t t o t h -e d a t a f r o m t h -e smooth s u r f a c -e , t o w a r d t h e h i g h c o n c e n t r a t i o n end. The r a t i o , seen i n F i g u r e 10,
HYDRONAUTICS, I n c o r p o r a t e d
-15-o f t h e a d d i t i v e c -15-o n c e n t r a t i -15-o n s r e q u i r e d f -15-o r t h e m-15-ost e . f f l c l e n t d r a g r e d u c t i o n seems t o be a b o u t one t o f i v e o r t e n , t h e same o r d e r as t h e r a t i o between t h e v i s c o u s - s u b l a y e r d i s c h a r g e and t h a t o f t h e roughness m i x i n g l a y e r
CONCLUSIONS
A s y s t e m a t i c d r a g r e d u c t i o n s t u d y was c o n d u c t e d by e j e c t i n g P o l y o x (WSR 301) a d d i t i v e s o l u t i o n s i n t o a p u r e w a t e r boundary
l a y e r o v e r b o t h smooth and r o u g h s u r f a c e s . The r e s u l t s were compared w i t h an e a r l i e r s t u d y i n v o l v i n g u n i f o r m a d d i t i v e s o l u -t i o n s , . I -t i s recommended -t h a -t f o r -t h e mos-t e f f e c -t i v e d r a g r e d u c t i o n w i t h a d d i t i v e i n e x t e r n a l f l o w s , t h e s l o t e j e c t i o n a n g l e s h o u l d be s m a l l w i t h r e s p e c t t o t h e f l o w d i r e c t i o n and t h e s l o t o p e n i n g s h o u l d be comparable l y l t h t h e t h i c k n e s s o f t h e v i s c o u s s u b l a y e r . I t was shown t h a t a l a r g e d r a g r e d u c t i o n was o b t a i n e d by e j e c t i n g t h e a d d i t i v e s o l u t i o n a t a r a t e c o m p a r a b l e tO' t h e n o r m a l v i s c o u s s u b l a y e r d i s c h a r g e . T h i s r a n g e o f d i s -charges I s recommended t o be t h e most economic. The c h o i c e o f a d d i t i v e c o n c e n t r a t i o n o f t h e e j e c t e d s o l u t i o n i s g o v e r n e d by t h e l e n g t h o f t h e boundary and, i t s r o u g h n e s s . I n t h e p r e s e n t case ( s h o r t p l a t e ) , optimum a d d i t i v e c o n c e n t r a t i o n s were f o u n d t o be 10^ = 10^ ppm f o r t h e smooth p l a t e and an o r d e r o f magnit u d e l a r g e r f o r r o u g h s u r f a c e s where a w a l l mixing; due magnit o r o u g h -ness causes i n c r e a s e d d i l u t i o n o f t h e e j e c t i o n s o l u t i o n .
ACKNOWLEDGMENT
The a u t h o r s a r e t h a n k f u l t o Mr. N. Lewis f o r p e r f o r m i n g ' t h e measurements.
HEFERENCES 1. T u l l n , M. P., "Hydrodynamic A s p e c t s o f M a c r o m o l e c u l a r S o l u t i o n s , " P r o c e e d i n g s o f S i x t h ONR Symposium on N a v a l Hydrodynamics, pp. 3-18j 19d6. 2.. Wu, J i n , " E x p e r i m e n t s on F r e e T u r b u l e n c e i n V i s c o e l a s t i c F l u i d s , " HYDRONAUTICS, I n c o r p o r a t e d T e c h n i c a l R e p o r t 353-1. 1965.
3, Love, R, H,, "The E f f e c t o f E j e c t e d Polymer S o l u t i o n s on
t h e R e s i s t a n c e and Wake o f F l a t P l a t e i n a Water Flow," HYDRONAUTICS, I n c o r p o r a t e d T e c h n i c a l R e p o r t 353-2, I 9 6 5 . 24. Wu, J i n , "Drag R e d u c t i o n i n E x t e r n a l Flows o f A d d i t i v e
S o l u t i o n s , " V i s c o u s Drag R e d u c t i o n , ed. C. S. W e l l s , Plenum P r e s s , New York-, p p , 331-350, 1969¬
5. Rouse, H., " E l e m e n t a r y Mechanics o f F l u i d s , " John W i l e y
and Sons, I n c o r p o r a t e d , New Y o r k , 1957¬
6. E l a t a , C , L e h r e r , J . a n d K a h a n o v i t z , A., " T u r b u l e n t Shear
Plow o f Polymer S o l u t i o n s , " I s r a e l J o u r n a l o f T e c h n o l o g y , V o l , 4, No,. 1, pp. 87-95. 1966.
7, Wu, J i n , "Boundary L a y e r Over U n i f o r m Roughness,"'
HYDRONAUTICS, I n c o r p o r a t e d T e c h n i c a l R e p o r t 353-8 ( i n p r e p a r a t i o n ) .
8. S c h l l c h t l n g , H.., "Boundary L a y e r Theory," M c G r a w - H i l l Book Company, New York, 1968.
H Y D R O N A U T I C S , J N C O R P O R A T E D
Rough pfate Slot Strain-gage support (w.itin gloss beads )
Concentration öf Additive Solution, c (ppmw)
FIGURE 2 - DRAG REDUCTION O F SMOOTH AND ROUGH BOUNDARIES WITH H O M O G E N E O U S ADDITIVE S O L U T I O N S .
H Y D R O N A U T I C S , I N C O R P O R A T E D
Additive Concentration of Ejected Solution , c (ppmw)
Discharge, q (cfs/ft) o, 20 0 • • • * 1 9 a
•
Discharge: • ° s O 2 Q s €> 4 Q s f a o o ••
C 1 1 • 1 c <1
3 )Additive Concentration of Ejected Solution, c ( ppmw)
FIGURE 3 - DRAG REDUCTION BY E J E C T I N G ADDITIVE SOLUTIONS I N T O A PURE-WATER BOUNDARY LAYER O F A SMOOTH SURFACE (SLOT O P E N I N G 0.022 I N C H E S )
240
r
300 Discharge, q (cfs/ft) -4 ,„-3 ,„-21
-« O1
J O ^• •
•
Discharge: • Q 5 O 2 Q s <» 4 Q s • a -< >•
i 1 >0" iO 10 10Additive Concentration of Ejected Solution , c
(ppmw)-HGURE 4 - D R A G REDUCTION BY E J E C T I N G ADDITIVE SOLUTIONS ilNTO A PURE-WATER BOUNDARY •LAYER O F A SMOOTH SURFACE ( S L O T O P E N I N G 0.042 J N C H E S )
H Y D R O N A U l I C S . r N C O R P O R A T E D
Additive Concentration of Ejected Sofi/tion,c (ppmw)
Discharge, q (cfs/ft)
Additive Concentrotion of Ejected Solution, c (ppmw)
FIGURE 5 - DRAG REDUCTION BY E J E C T I N G ADDITIVE SOLUTfONS INTO A PURE-WATER BOUNDARY l A Y E R O F A SMOOTH SURFACE (SLOT O P E N I N G 0.093 I N C H E S )
Discharge, q ( cfs/ft)
1
i Discharge; • Q: s O 2<Q a 4 Q -S » c O'\
i j ^ •-8 i
1, J g ° '«
2•
) 10 10Additive Concentration of Ejected Solution, c (pprnw)
10^
FIGURE 6 - DRAG REDUCTION BY E J E C T I N G ADDITIVE SOLUTIONS I N T O A PURE-WATER BOUNDARY LAYER.OF A ROUGH SURFACE ( G L A S S BEADS, SLOT O P E N I N G 0.022 I N C H E S )
H Y D R O N A U T I C S , INCORPORATED
Additive Concentration of Ejected Solutioni, c (ppmw)
'fo"'*)0"-'lo-'^ io"*50"^ro"^ lo"* lo'^to'^ no"* lo'^ lo"^ w"* 10"^ lo'^ 10"* 10'^ 10"^ jo"''lo"^ 10"^
P'scharge, q (cfs/ft) 6 0 : iO Discharge; • Qs O 2 Q s « 4.Q '9
0 8
9 •» O O ^ O T O ' 10" Additive Concentration of Ejected Solution, c (ppmw)10"
FIGURE 7 - DRAG REDUCTION BY E J E C T I N G ADDITIVE SOLUTIONS INTO A PURE-WATER BOUNDARY LAYER O F A ROUGH SURFACE ( RUBBER MATS, SLOT O P E N I N G 0.022 I N C H E S )
60
30
0 60
ction disc :harge;
• 2 ' 1 f < <
•
• . 3 o o 30 0 60 30 Slot Width: ( 1 / 1 0 0 0 i n . ) • 22 — » 42 O 93 2 Q O O O O 8 a 9 O 9 O • » O 4 Q ^ • O ^ O O 1 C c ; 01
•
) » O » O O 10" •5 10 1 0 'Additive Concentration of Ejected Solution, c (ppmw)
10
FIGURE 8 - DRAG REDUCTION BY EJECTED ADDITIVE SOLUTIONS OVER A SMOOTH BOUNDARY
Concentration of Uniform or Elected Additive Solution, t (ppmw )
FIGURE 9 - TYPICAL DRAG-REDUCTION! CURVE O F A PLANE BOUNDARY WITH UNIFORM ADDITIVE S O L U T I O N OR BY E J E C T I O N
60 30 0 60 Eje. 1 ; t i o n disc \ h a r g e : 9
•
•
1 1•
O•
•
° O 9 ^ ! • 8I
30I
0 60 _ O - » Surface: Smoorti Roughened with gloss beads Roughened with rubber mots 2 Q O 'O ' 8 ° o 9 o 9 9 30-•
' * 1
O O 1 1 <•
a f•
> 8 a 9 8 > 10 10 TO' 1Additive Concentration of Ejected Solution, c (ppraw)
10-^
F I G U R E I O - DRAG REDUCTION BY E J E C T I N G ADDITIVE SOLUTIONS OVER A ROUGH BOUNDARY
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3202 E. F o o t h i l l B o u l e v a r d
Pasadena, C a l i f . 91107 Dr. J . Hoyt
N a v a l Undersea Research and Development Center 3202 E, F o o t h i l l B o u l e v a r d Pasadena, C a l i f , 91107 P r o f e s s o r T.Y. Wu Department o f E n g i n e e r i n g C a l i f o r n i a I n s t , o f Tech. Pasadena, C a l i f . 91109 D i r e c t o r O f f i c e o f N a v a l Research B r a n c h O f f i c e 1030 E. Green S t r e e t Pasadena, C a l i f . 91101 P r o f e s s o r A. A c o s t a Dept. o f M e c h a n i c a l E n g i n e e r i n g C a l i f o r n i a I n s t . o f Tech. Pasadena., C a l i f . 91109 N a v a l Ship' E n g i n e e r i n g C e n t e r P h i l a d e l p h i a D i v i s i o n T e c h n i c a l L i b r a r y P h i l a d e l p h i a , Penn.. 19112 -7-T e c h n i c a l L i b r a r y (Code 249B) P h i l a d e l p h i a N a v a l S h i p y a r d P h i l a d e l p h i a , Penn, 19112 1 1 P r o f e s s o r R, C. MacCamy Dept. o f Mathematics C a r n e g i e I n s t . o f Tech. P i t t s b u r g h , Penn. 15-213 1 1 .Dr. P a u l K a p l a n Oceanlcs, I n c . P l a i n v l e w , Long I s l a n d , New Y o r k l l 8 0 3 l 1 T e c h n i c a l L i b r a r y N a v a l M i s s i l e Center P o i n t Mugu, C a l i f , 93^41 1 T e c h n i c a l L i b r a r y N a v a l C i v i l E n g i n e e r i n g Lab, 1 P o r t Hueneme, C a l i f . 930^1 1 Commander P o r t s m o u t h N a v a l S h i p y a r d Portsm.outh, New Ham.pshlre
1 03801 1 Commander N o r f o l k N a v a l S h i p y a r d P o r t s m o u t h , V i r g i n i a 23709 1 1 P r o f e s s o r F, E. B i s s h o p p D i v i s i o n o f E n g i n e e r i n g Brown U n i v e r s i t y P r o v i d e n c e , Rhode Islan.de 02912 1 " Dr. L. L. H i g g i n s
TRW Space Technology Labs, I n c . One Space P a r k
R e d s t o n e S c i e n t i f i c I n f . Cen. A t t n : C h i e f , Document S e c t i o n Army M i s s i l e Command R e d s t o n e A r s e n a l , A l a . 35809 1 Dr. H. N. Abramson S o u t h w e s t R e s e a r c h I n s t . 8500 C u l e b r a Road • San A n t o n i o , Texas 78228 1 E d i t o r A p p l i e d M e c h a n i c s Review S o u t h w e s t R e s e a r c h I n s t . 8 5 Ö O C u l e b r a Road San A n t o n i o , Texas 78206 1 L i b r a r i a n N a v a l Command C o n t r o l Com-m u n i c a t i o n s Lab. C e n t e r San D i e g o , C a l i f . 92152 1 L i b r a r y and I n f . S e r v i c e s G e n e r a l D y n a m i c s - C o n v a l r P. 0. Box 1128 San D i e g o , C a l i f . 92112 1 Commander (Code 246P) P e a r l H a r b o r N a v a l S h i p y a r d Box 400 , PPO San F r a n c i s c o , C a l i f . 96610 1 T e c h n i c a l L i b r a r y (Code H245C-3) H u n t e r s P o i n t D i v i s i o n San F r a n c i s c o Bay N a v a l S h i p y a r d San F r a n c i s c o , C a l i f . 9^135 1 O f f i c e o f N a v a l R e s e a r c h San F r a n c i s c o A r e a O f f i c e r 50 P e l l S t r e e t San F r a n c i s c o , C a l i f . 94013 1 I Dr. A..- May N a v a i Ordnance L a b o r a t o r y W h i t e Oak S i l v e r S p r i n g , Md. 209IO l ' I P e n t o n Kennedy Document L i b r a r y The Johns H o p k i n s U n i v e r s i t y A p p l i e d P h y s i c s L a b o r a t o r y 8621 G e o r g i a Avenue S i l v e r S p r i n g , Md. 20910 1 L i b r a r i a n N a v a l Ordnance L a b o r a t o r y W h i t e Oak S i l v e r S p r i n g , Md. 20910 l ' ! Dr. B r y n e P e r r y D e p t . o f C i v i l E n g r . S t a n f o r d U n i v e r s i t y S t a n f o r d , C a l i f . 9^305 V P r o f e s s o r M i l t o n Van Dyke D e p t . o f A e r o n a u t i c a l Engr. S t a n f o r d U n i v e r s i t y S t a n f o r d , C a l i f . 94305 1 P r o f e s s o r E. Y. Hsu D e p t . o f C i v i l E n g r . S t a n f o r d U n i v e r s i t y S t a n f o r d , C a l i f . 94305 1 D r . R. L. S t r e e t D e p a r t m e n t o f C i v i l E n g r , S t a n f o r d U n i v e r s i t y S t a n f o r d , C a l i f . 9^305 1 P r o f e s s o r S. E s k l n a z i D e p t . o f Mech. E n g r . S y r a c u s e U n i v e r s i t y S y r a c u s e , New Y o r k I 3 2 I O 1
HYDRONAUTICS, I n c o r p o r a t e d P r o f e s s o r R. P f e f f e r F l o r i d a S t a t e U n i v e r s i t y G e o p h y s i c a l F l u i d Dynamics I n s t . T a l l a h a s s e e , F l a . 32306 1 P r o f e s s o r J,. Foa Dept. o f A e r o n a t u i c a l Engrg. Rennsselaer P o l y t e c h n i c I n s t , T r o y , New- York 12l80 1 P r o f e s s o r R. C. D i P r i m a Dept. o f Mathematics R e n n s s e l a e r P o l y t e c h n i c i n s t . T r o y , New York 12l80 1 Dr, M. S e v i k
Ordnance Research Lab. Penn. S t a t e U n i v e r s i t y
U n i v e r s i t y P a r k , Penn. l6801 1 P r o f e s s o r J . Lumley
Ordnance Res. Lab. Penn. S t a t e U n i v e r s i t y U n i v e r s i t y Park, Penn. I 6 8 O I 1 Dr, M.-, R o b e r t s O T i Dept^ o f T h e o r e t i c a l and A p p l i e d Mechanics U n i v e r s i t y o f I l l i n o i s Urbana, I l l i n o i s 61803 1 S h i p y a r d T e c h n i c a l L i b r a r y Code 130L7 B l d g , 7^6 San F r a n c i s c o Bay N a v a l S h i p y a r d V a l l e j o , C a l L f . 9^592 1
U.S, N a v a l Research Lab. Washington, D. C, 20390
A t t n : Code 2027 6
Commanding O f f i c e r and D i r e c t o r Naval S h i p Research and
Development C e n t e r Washington, D. C. 2003{t A t t n i Codes l4 2 1 800 1 513 1 500 1 901 1 520 1 530 1 521 1 522 1 C h i e f o f N a v a l Research Department o f t h e Navy 800 N. Qulncy S t r e e t A r l i n g t o n , Va. 22217 A t t n : Codes 438 1 461 1 466 1 463 1 481 1 421 1 468 Ï 473 1 S c i e n c e and T e c h n o l o g y Div.. L i b r a r y o f Congress Washington, D. C. 20540 1 Commander
N a v a l Ordnance Systems Com, Washington, D. C. 2036O A t t n : Codes 03 1 ORD 913 ( L i b r a r y) 1 ORD 035 1 ORD 05411 1 N a v a l S h i p E n g i n e e r i n g C e n t e r Concept D e s i g n D i v i s i o n Washington, D, C, 20360 A t t n : Code 6420 1
N a v a l S h i p Systems Command D e p a r t m e n t o f t h e Navy W a s h i n g t o n , D. C.
20360
A t t n : Codes034l 1
2052
( T e c h .L i b r a r y
) 1
03412
J.L. S c h u i e r1
031 J.H. H u t h 16644c
1
63 4
2A1
O f f i c e o f Res. a n d D e v e l o p m e n t M a r i t i m e A d m i n i s t r a t i o n 441 G. S t r e e t NW. W a s h i n g t o n , D, C.20235 1
N a t i o n a l S c i e n c e F o u n d a t i o n E n g i n e e r i n g D i v i s i o n 1800 G. S t r e e t NW. W a s h i n g t o n , D. C.20550
D r . G. K u i m N a t i o n a l B u r e a u o f S t a n d a r d s W a s h i n g t o n , D. C.20234
D e p a r t m e n t o f t h e Army C o a s t a l E n g r g . R e s e a r c h C e n t e r 5201 L i t t l e F a l l s Road, NW. W a s h i n g t o n , D. C, 20011 L i b r a r i a n S t a t i o n 5-2 C o a s t Guard H e a d q u a r t e r s 1300 E. S t r e e t , 'NW. W a s h i n g t o n , D. C.20226
D i v i s i o n o f S h i p D e s i g n M a r i t i m e A d m i n i s t r a t i o n 44l G. S t r e e t NW. W a s h i n g t o n , D. C.20235
HQ USAF (AFRSTD) Room I D 377 The P e n t a g o n W a s h i n g t o n , D. C.2033O
D r . A. P o w e l l (Code 01) N a v a l S h i p R e s e a r c h and i D e v e l o p m e n t C e n t e r W a s h i n g t o n , D. C.20034
i D i r e c t o r o f R e s e a r c h Code RR NASA I 600 I n d e p e n d e n c e Ave, SW || W a s h i n g t o n , D. C.20546
l N a v a l A i r Systems Command i D e o a r t m e n t o f t h e Navy W a s h i n g t o n , D. C. 203 60 ' A t t n : Codes A I R 5301 1 AIR6o4
i Dr. J o h n C r a v e n (PM l l O O ) Deep Submergence S y s t e m s P r o j . ' 1 D e p a r t m e n t o f t h e Navy W a s h i n g t o n , D. C.20360
i Commander 1 N a v a l O c e a n o g r a p h i c O f f i c e -W a s h i n g t o n , D. C.20390 1
C h i e f o f Res. a n d D e v e l o p m e n t O f f i c e o f C h i e f o f S t a f f 1 D e p a r t m e n t o f t h e Army The P e n t a g o n , W a s h i n g t o n , D. C.20310
D i r e c t o r 1 U.S. N a v a l R e s e a r c h L a b . W a s h i n g t o n , D. C. 20390 A t t n : Code 6170 ] N a v a l S h i p E n g i n e e r i n g C e n t e r 1 D e p a r t m e n t o f t h e Navy W a s h i n g t o n , D. C.20360
A t t n : Code 61OO 1'6 l l 4
R a l p h L a c e y1'
HYDRONAUTICS, I n c o r p o r a t e d -.11-Dr.. A. S. I b e r a l l , P r e s i d e n t G e n e r a l T e c h n i c a l S e r v i c e s , I n c , 451 Penn S t r e e t Yeadon,, Penn, 19050 I Dr. H. Cohen IBM Research C e n t e r P.O. Box 218 Y o r k t o w n H e i g h t s , New Y o r k 10598 1,
P l n d e l l S c h o o l Road, Howard County-L a u r e l , Maryland 208lO
UNCLASSIFIED P l n d e l l S c h o o l Road, Howard
County-L a u r e l , Maryland 208lO
2b. G R O U P
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J i n Wu and M a r s h a l l P, T u l i n 1 . R E P O R T D A T E June IQTO 7 « - T O T A I , N O . or P A O E » Jb. N O , O F H E M 29 8 Qa. C O N T R A C T O R G R A N T NO. Nonr 4 l 8 l ( 0 0 ) NR 062-325 b. P R O J E C T N O . c.-9 a . O R t O I M A T O R ' S R E P O R T NUMBER^Sj T e c h n i c a l R e p o r t 353-7 Qa. C O N T R A C T O R G R A N T NO. Nonr 4 l 8 l ( 0 0 ) NR 062-325 b. P R O J E C T N O .
c.- ÊB. O T H E R R E P O R T UO(Si (Any othtr nummrs tft*t mmy bm mmël^mti thim rm port)
10. A V A J L A B I L I T Y / L I M I T A T I O N T I O T I C E S
T h i s document h a s been approved f o r p u b l i c r e l e a s e and s a l e j i t s d i s t r i b u t i o n i s u n l i m i t e d H . S U P P L E M E N T A R Y N O T E S . ( 2 S P O N S O R I N G M I L I T A R Y A C T I V I T Y O f f i c e o f N a v a l R e s e a r c h Department o f t h e Navy 13. A B S T R A C T Drag r e d u c t i o n c a u s e d by e j e c t i n g a d d i t i v e s o l u t i o n s from a s l o t i n t o a p u r e - w a t e r boundary l a y e r on a f l a t p l a t e h a s been s y s t e m a t i c a l l y s t u d i e d . R e s u l t s i n c l u d e d r a g measurements f o r a p l a n e boundary, smooth and rough, w i t h v a r i o u s openings o f t h e s l o t and w i t h v a r i o u s c o n c e n t r a t i o n s and d i s c h a r g e s o f t h e e j e c t e d a d d i t i v e s o l u t i o n . C o n c l u s i o n s have been drawn on t h e a d d i t i v e r e q u i r e m e n t i n e x t e r n a l f l o w s and on t h e e j e c t i o n t e c h n i q u e f o r an optimum d r a g r e d u c t i o n .
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