drag and lift on hydrofoil

8/18/2019 drag and lift on hydrofoil

1/7

ft E f f e c ts A s s o c i a t e d w it h D r a g - R e d u c i n g P o l y m e r I n je c tio n

T w o - D i m e n s i o n a l H y d r o f o ils

H . F r u m a n 1

T h e ef fect of a b o u n d a r y - l a y e r in j e c t io n o f d r a g - r e d u c i n g a d d i t iv e s o l u t i o n s o n t h e l if t a n d d r a g o f a 1 0 - c m

c h o r d , N A C A 6 3 A 0 2 0 s y m m e t r i c a l tw o - d i m e n s i o n a l h y d r o fo i l w a s i n v e s t ig a te d fo r v a r i o u s fr e e s t r e a m a n d

i n je c t i o n v e l o c i t ie s , f o i l i n c i d e n c e s , a n d a d d i t iv e c o n c e n t r a t i o n s r a n g i n g fr o m 5 0 t o 4 0 0 p p m o f P O L Y O X

W S R 3 0 1 . T h e e x p e r i m e n ta l re s u l t s d e m o n s t r a te t h a t t h e l i f t o f t h e h y d r o fo i l c a n e i t h e r i n c r e a s e o r d e -

c r e a s e d e p e n d i n g u p o n w h e th e r t h e p o l y m e r i n j e c t i o n i s m a d e o n t h e s u c t i o n o r p r e s s u r e s id e o f t h e f o i l

s u r f a c e , re s p e c t i v e l y . I n b o th c a s e s , h o w e v e r , t h e d r a g i s r e d u c e d . T h e n e t re s u l t o f t h e in j e c t io n o f t h e

d r a g - r e d u c in g a g e n t i s a n a u g m e n ta t i o n o f t h e l i f t- d r a g r a ti o . T h e m a g n i t u d e o f t h i s a u g m e n ta t i o n a n d it s

d e p e n d e n c e o n t h e f r e e s t r e a m v e l o c i t y , t h e i n j e c t i o n v e l o c i ty , t h e c o n c e n t r a t i o n o f p o l y m e r , a n d t h e i n c i-

d e n c e o f t h e f o i l a r e a n a l yz e d .

I n t r o d u c t i o n

.FOLLOWING AN EARLIERPUBLICATION y W u [1] ,2 the ef fects

c i n g p o l y m e r s o l u ti o n s o n t h e l i ft o f h y d r o f o i ls a n d

s t o f p r ope l le r s have b een inv es t iga ted by sever a l au thor s,

t r ad ic tor y resul ts . Sa r pk aya [2] and F r um an e t a l [ 8]

r ev iew of pr ev ious w or ks . I n subs tance ,

t c a s e o f a t w o - d i m e n s i o n a l s y m m e t r i c a l h y d r o f o i l w i t h

ndar y- lay er in jec tion of a d r ag- r educ ing addi t ive , the l i f t -d r ag

lly increases regardless of wheth er th e injection is m ad e

ion or p r es sur e s ide of the f o i l sur f ace. The m agn i tud e

n d s o n t h e f r e e s t r e a m a n d i n j e ct i o n v e lo c i ti e s,

nc idence , and on the po lyme r concent r a t ion of the

so lu t ion .

T h e p r e s e n t p a p e r d e s c r ib e s t h e e f f e c t o f a b o u n d a r y - l a y e r i n -

a d d i t i v e s o l u ti o n o n t h e l if t, d r a g , a n d

- Th e h y d r o f o i l , p r o v i d e d w i t h a n i n -

ed in a r ec i r cu la t ing h igh- speed channe l w i th

am veloci ties of 7, 9 an d 11 m/se e. Th e inject ion rate , the

8 , w hi le the concen t r a t ion of po lym er ( PO LY O X

R 8 0 1 ) 3 i n t h e e j e c t ed s o l u t i o n r a n g e d f r o m 5 0 t o 4 0 0 p p m .

Th e in jec t ions w er e pe r f or me d, f or each inc idence , on the

d pr es sur e s ides o f the f o i l sur face .

A f t e r b r i e fl y d e s c r i b i n g t h e e x p e r i m e n t a l p r o c e d u r e , s o m e s e -

u l t s a r e pr esen ted and d iscussed . Th e d i f f e r en t f or ce

uced by the pu r e so lvent ( w a te r) in jec t ions and the

m e r i n j e ct i o ns a t z e r o i n c i d e n c e a n g l e a r e c o n s i d e r e d f i rs t a s

e f f e c t o f a c h a n g e o f t h e f o i l i n c i d e n c e o n t h e l i f t - d r a g r a t i o

t h e p o l y m e r c o n c e n t r a t i o n a n d o f t h e f r e e -

v e l o c i t y o n t h e i n c r e a s e o f t h e l i f t- d r a g r a t i o a r e p r e s e n t -

i Hydronautics, Incorporated, Laurel Maryland.

2 Num bers in brackets designate References at end o f paper.

3 Poly(ethylene oxide), manufactured by the Union Carbide Co.

Manu script received at SNAM E headquarters August 21, 1975; revised

A l t h o u g h t h e s e re s u lt s a r e l i m i t e d t o t h e c a s e o f a t w o - d i m e n -

s i on a l h y d r o f o i l , t h e y c l e a r l y u n v e i l s o m e p r a c t i c a l a p p l i c a t i o n s

o f t h e d r a g - r e d u c i n g a d d i t i v e s o l u t i o n s f o r i m p r o v i n g t h e p e r -

form an ce of pract ical und erw ater l i f t ing bodies, such as hydrofoils ,

f ins , and propellers .

E x p e r i m e n t a l p r o c e d u r e

T h e t e s t s w e r e p e r f o r m e d i n t h e H y d r o n a u t i c s H i g h S p e e d

C h a n n e l [ 5 ], F i g . 1 , m o d i f i e d t o o b t a i n a t w o - d i m e n s i o n a l f l o w ,

thus e l imina t ing the f r ee - sur face e f f ec ts w hich m ay h ave o the r w ise

occ ur r ed a t the h igh speeds used in the tes ts . This modi f ic a t ion

incor por a tes a r oof w i th a spec ia l ly des igned t r ans i t ion w hich w as

a t tached to the or ig ina l f r ee -sur f ace s lu ice ga te of the channe l. A n

over s ized hole a llow s f r ee passage of the m ode ls th r ou gh the r oof .

T h e f oi ls w e r e s u p p o r t e d v e r t ic a l l y b y m e a n s o f a b l o c k g a g e a r -

r a n g e m e n t a n d a n i n c i d e n c e - c o n t r o l sy s t em , a s in d i c a t e d i n F i g .

2 . I n o rd e r t o m i n i m i z e a ir e n t ra i n m e n t , w h i c h m a y b e i n d u c e d

by the low pr es sur es on the suc t ion s ide of the f o i l, the up pe r s ide

o f t h e r o o f w a s fl o o d e d . T o c r e a t e t h e b e s t c o n d i t i o n s f o r a t w o -

F ig . 1 Hydronau t i cs , Inc. h igh -spee d chan ne l

1 9 7 6 1 4 5


2/7

\

. ~ . f f C U O N

FC'~ ,

; U T

F ig . 2 B lock gages a r rangemen t w i th mounted hydro fo i l

d i m e n s i o n a l f l o w a n d t o a v o i d s e c o n d a r y f lo w s b e t w e e n t h e l o w e r

a n d u p p e r s e c ti o n s o f t h e r o o f , a n e n d p l a t e w a s f i tt e d t o t h e c r os s

sec t ion of the f o il , be ing f r ee to mo ve w i th i t ( F ig . 2 ). S ince the

t es ts w e r e d e s i g n e d t o o b t a i n c o m p a r a t i v e m e a s u r e m e n t s o f t h e

h y d r o d y n a m i c c h a r a c t e ri s t ic s o f t h e f o il s w i t h a n d w i t h o u t i n j e c-

t ion, no specif ic invest igat ion of the end ga p ef fect , tunnel block age

ef f ec t , e tc . , w as mad e dur in g th i s s tudy . Th e l if t cur v e s lope of

the r aw da ta w as 8 .6 . This va lue i s low er than the one tha t can be

expec ted f r om a t ru ly tw o- d imens iona l fo i l. Th e e f fec t ive aspec t

r a t io o f t h e f o i l c a n b e e s t i m a t e d b y u s i n g t h e c o r r e c t i o n f a c t o rs

given in [6] .

Th e cross section of the foi l was a NA CA 6 3 sym me tr ical profi le,

10 .16 cm in cho r d w i th 20 pe r c ent r e la t ive th ickness . Th e in jec -

t ion s l i t w as s i tua ted a t a 10 pe r cent chor d d i s tance f r om the

lead ing edge so tha t the ac tua l d i s tance w as 1 .016 cm.

Th e inject ion s l i t was design ed so as to decrea se the poss ible local

p e r t u r b a t i o n s w h i c h m a y b e p r o d u c e d b y t h e e je c t e d f l ui d . A s

show n in Fig. 3, the in cl inat ion of the s l it , re lat ive to the foi l tangen t

a t the in jec t ion s tat ion , w as 7 deg . Based on the emp i r ica l r e la -

t ionsh ip desc r ib ing the d i f f us ion of a d i lu te po lym er so lu tion over

a f l a t p la t e o b t a i n e d b y F r u m a n a n d T u l i n [ 7] , t h e g a p o f th e i n -

jec tor w as se lec ted to be 0 .0127 cm.

T h e f r e e s t r e a m v e l o c i ty i n t h e t e st s e c t io n w a s m e a s u r e d w i t h

a 3- m m- dia P r andt l tube p laced ahead of the hydrof oi ls . A l though

it is kno wn that , in gen eral , the s tagnation p ressure readings of such

tubes a r e a f f ec te d by the p o ly me r so lut ions, i t is be l ieve d tha t in

t h e p r e s e n t c a s e th e r e l a t iv e l y s m a l l b u i l d u p o f p o l y m e r c o n c e n -

t ra t ions in the r ec i r cu] a t ing w a te r an d th e r e la t ive ly la r ge d iam ete r

o f t h e p r o b e m a k e a n y s i g n i f i c a n t er r o rs h i g h l y i m p r o b a b l e .

T h e l i f t a n d d r a g f o r c e s w e r e m e a s u r e d b y m e a n s o f f o u r r e -

luc ta nce - typ e b lock gages a t tache d to the f o i ls a s show n in F ig . 2 .

T h e t o t al l if t a n d d r a g l o a d c a p a c i t i e s o f t h e s e g a g e s w e r e 9 0 a n d

1 6 k g , r e s p e c ti v e l y . T h e e l e c tr i c a l o u t p u t s i g n a l f r o m t h e g a g e s

w a s i n t e g r a t e d o v e r a t e n -s e c o n d p e r i o d a n d t h e a v e r a g e v a l u e s

Fig. 3

. _ _ ~ .

Design of the in ject ion s l i t (a l l indicated dimensions are in

cen t imete rs )

w e r e r e c o r d e d . T h e f o r c e s o n t h e fo il , m e a s u r e d b e f o r e e a c h o f

t h e i n je c ti o n s, w e r e u s e d t o c o m p u t e t h e c h a n g e s i n t r o d u c e d b y

t h e i n j e c t io n o f b o t h t h e w a t e r a n d t h e p o l y m e r s o lu t io n .

T h e i n j e c te d f l u id s w e r e c o n t a i n e d i n a n i n e - g a l l o n r e s e rv o i r ,

w hich w as pr es sur ized so as to dr ive the f lu ids in to the in jec t ion

s li t th r oug h a p ipe system. Th e in jec tion f low r a te w as de te r m ined

b y w e i g h t i n g t h e a m o u n t o f s o l u t i o n d i s p e n s e d i n a g i v e n t i m e

i n te r v a l. H e n c e , t h e c o m p u t a t i o n o f t h e in j e c t io n v e l o c i ty a n d

the in jec t ion r a te w as s t r a igh t f or w ar d .

Th e po lym er used in these te s ts w as po ly( e th y len e oxide) , PO -

L Y O X W S R 3 0 1 , w h i c h h a s b e e n d e m o n s t r a t e d t o b e a h i g h l y

e f f ic i e n t d r a g - r e d u c i n g a g e n t. T h e m e t h o d o f p r e p a r a t i o n o f t h e

d i l u t e p o l y m e r so l u ti o n s h a s b e e n d e s c r i b e d e ls e w h e r e [ 7 ] . F o u r

d i f f e r e n t p o l y m e r c o n c e n t r a t i o n s - - 5 0 , 1 0 0, 20 0 , a n d 4 0 0

p p m - - w e r e t e s t e d .

P r e s e n t a t i o n o f r e s u lt s

The e f f ec t o f an in jec tion o f w a te r on the l i ft and dr ag o f the f o il

a t ze r o inc id ence i s show n in F igs . 4 and 5 as a f unc t io n of the in -

ject ion rate . No twiths ta ndin g a conside rable dispersion of the data

poin t s , it is c lea r tha t the w a te r in jec t ion pr o duc es a nega t ive l i f t

a n d g e n e r a l l y a n i n c r ea s e o f t h e d r a g o f t h e fo il . T h e p o l y m e r

inject ion, on the othe r hand, in trodu ces a posi t ive l i ft , F ig. 6, wh ile

s ign i f ican t ly r educ ing the dr ag , F ig . 7 . Th e e f f ec t o f the po lym er

i n j e c ti o n b o t h o n t h e l i ft a n d o n t h e d r a g i n c r e a s es w i t h t h e i n j e c-

t i o n ra t e. T h e r e i s a n o r d e r o f m a g n i t u d e c h a n g e o f t h e l i ft

c o e f fi c ie n t s a n d t h e d r a g r e d u c t i o n f o r r o u g h l y t h e s a m e o r d e r o f

m a g n i t u d e c h a n g e o f t h e in j e c t io n r a t e .

Th e f i r s t conc lus ion to be dr a w n f r om these r esu l ts is tha t , in -

d e e d , t h e i n j ec t i o n o f d i l u t e p o l y m e r so l u ti o n s i n t o t h e b o u n d a r y

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

t o w a r d t h e s i d e o f t h e f oi l w h e r e t h e i n j e c t io n i s b e i n g m a d e a n d

a s ign i f ican t r educ t ion of the dr ag . The w a te r in ject ion in t r oduces

the oppo s i te e f f ec t s in the f o i l f o r ces .

Th e inf luenc e of the w a te r in jec t ion on the l i f t - d r ag r a t io of the

f o il f o r d i f f e r e n t i n c i d e n c e s a n d c o n s t a n t f r e e s t r e a m v e l o c i ty , 9

m / s e e , is s h o w n i n F i g . 8 . W h e n t h e i n j ec t i o n is m a d e o n t h e

pr es sur e s ide of the f o i l , the l i f t - d r ag r a t io i s inc r eased , w hi le i t i s

dec r e ased f or an in jec t ion on the suc t ion s ide of the f o il .

F igu r e 9 pr esen ts ' the e f f ec t o f the in jec t ion of 100- ppm poly mer

so lu t ion on the l i f t - d r ag r a t io of the f o i l a t a f r ees t r eam ve loc i ty

of 9 m/see . For the in jec t ion on the pr es sur e s ide , the l i f t -d r ag

r a t io i s gener a l ly augm ented and inc reases w i th the inc idence angle

and th e in jec tion ra te . A t low inc ide nce angles and in jec t ion ra tes

t h e l i f t -d r a g r a t i o is r e d u c e d w h e n c o m p a r e d w i t h t h e z e r o i n j e c-

t i o n v al u es . T h e p o l y m e r i n j ec t i o n o n t h e su c t i o n si d e p r o d u c e s

a s i g n i f ic a n t a u g m e n t a t i o n o f t h e l i f t -d r a g r a t i o a s o p p o s e d t o t h e

t r end obse r ved in the case of w a te r in jec t ion .

A m o r e d e t a i l e d p i c t u r e o f t h e p o l y m e r i n j e c ti o n e f f e ct s o n t h e

hyd r of o i l fo r ces i s p r esen ted in F igs . 10 th r o ug h 18 . F igu r e 10

show s the r e la t ive chang es of the l if t and d r ag f or ces f or an in jec -

1 4 6 J O U R N A L O F S H I P R E S E A R C H


3/7

L~

O


4/7


5/7

A C L / C L

o

V

z~

V = 7m/s

I - 100 ppm

0 . 5

.01 0 .05 0 . I

I N J E C T I O N R A T E , V / V

. 10 Re la t i v e ch an g e o f l i f t an d d r ag fo r ce s fo r an in jec t io n o f a

0 0 - p p m P O L Y O X W S R 3 0 1 s o lu t io n o n t h e p r es s u r e s id e o f t h e f o il

=u


6/7

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Z

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Fig. 14

20

I0

I I I I I I I

L I F T ~ , I n j e c t i o n I

P O L Y O X W S R 3 0 1

V I I rn / s

V i = 0 . (

5 0 1 0 0 5 0 0 1 0 0 0

C O N C E N T R A T I O N , p p m

I n f l u e n ce o f co n ce n t ra t io n o n

the relat ive change of the

l i f t -d rag

ratio

C o n c l u s i o n s a n d r e c o m m e n d a t i o n s

S e v e ra l i m p o r t a n t c o n c l us i o n s c a n b e d r a w n f r o m t h e r e s u lt s

p re s en ted in the p rev ious s ec t ion . Thes e a re :

( i) W i t h p o l y m e r in j e c ti o n t h e d r a g i s g e n e r a l l y r e d u c e d r e -

ga rd le s s o f whe th e r the in j ec t ion i s on the s uc t ion o r p re s s u re s ide

o f the fo il s u r face . Fo r the s ame fo il ang le , f r e e s t ream ve loc i ty ,

and po lymer concen t ra t ion , t he d rag reduc t ion inc rea s e s w i th the

in jec t ion ra t e. Fo r the s ame f ree s t ream ve loc i ty , po l ym er con-

cen t ra t ion , and in j ec t ion ra t e , l a rge r d rag reduc t ion e f fec t s a re

a c h i e v e d w i t h i n je c ti o n s m a d e o n t h e p r e s s u re r a t h e r t h a n o n t h e

suction side.

( ii ) W he n the po lym er so lu t ion i s i n j ec ted on the suc t ion s ide

o f the hyd ro fo i l , t he re i s, i n gene ra l , a s ubs tan t i a l i nc rea s e o f the

l if t. As fo r the d rag , t he ma gn i tude o f the l i f t e f fec t i s s t rong ly

d e p e n d e n t o n t h e r a te o f i n j ec t io n . H o w e v e r , t h e l if t a u g m e n t a -

t i o n is m o r e p r o n o u n c e d f o r i n je c t io n s m a d e o n t h e s u c t i o n s id e

o f the fo i l a t l a rge inc iden ce ang le s and d ec rea s e s whe n the inc i -

den ce ang le dec rea se s .

( i i i ) W hen the po lym er is e j e c ted in to the p re s su re s ide o f the

fo i l s u r face , i nc rea s e s o r dec rea s e s in li f t occu r dep end ing on the

fo i l ang le , t he f ree s t ream ve loc i ty , and the in j ec t ion ra t e .

( iv ) W a te r in j ec t ion und e r cond i t ions co r re s p ond in g to thos e

tes ted prod uces e i ther negl igible effec ts or e ffec ts oppos i te to those

wi th po lymer in j ec t ion .

(v ) S ign i f i c an t inc rea s e s o f the l i f t -d rag ra t io o f the hydro fo i l

a re a ch ieved th rough po ly me r in j ec tion on the suc t ion s ide . The

a b s o lu t e c h a n g e o f t h e l i f t - d r a g r a t io a p p e a r s t o b e q u i t e i n d e -

p e n d e n t o f t h e i n c i d e n c e a n g l e f o r c o n s t a n t f re e s t r e a m v e l o c i t y

and in j ec t ion ra t e.

( vi ) T h e d e p e n d e n c e o f th e li f t -d r a g r a t io a u g m e n t a t i o n o n

t h e p o l y m e r c o n c e n t r a t i o n i s s i m i la r t o t h e o n e o b s e r v e d f o r d r a g

reduc t ion e f fec t s on f l a t p l a t e s and p ipe f lows.

T h e p r e s e n t c o n c l us i o n s a r e i n g e n e r a l q u a l i t a t iv e a g r e e m e n t

wi th thos e o f Le hm an an d Sues s mann [4 ] . Spec i f i c a l ly , t he l if t -

i n c r ea s e a n d d r a g - r e d u c t i o n e f f e ct s a ss o c ia t e d w i t h p o l y m e r i n -

j e c t io n o n t h e s u c t i o n s id e o f a t w o - d i m e n s i o n a l h y d r o f o i l h a v e

been f i rm ly e s t ab l i shed . Th e re s u l ts p re s en ted by the au th o r in

[3 ] fo r two NAC A 68 s e r i e s hydro fo i l s w i th d i f fe ren t r e l a t ive

th icknes s e s demons t ra t ed tha t t he l a rge r l i f t - inc rea s e e f fec t s a re

1

J - =

0 . 1 - - 1 0 0 p p m

- - - - - - 2 0 0 p p m

<

°\ V

20

..%

a = 5 °

Fig . 15

10 11

FREE STREAM. VEL OCI TY, m /sec

I n f l u e n ce of freestream veloc i ty and concentration on relat ive

chang e of the l if t -drag rat io

ob ta ined w i th the th i cke r fo il . Th e th i cke r fo il s tud ied ea r l i e r [3

was iden t i c a l t o the N AC A 68A 020 fo il u s ed in the p re s en t inves -

t iga t ion. There fore , based on the exist ing da ta , the most favorable

in jec t ion cond i t ions , a s we l l a s the mos t de s i rab le fo i l s hape , c an

be de f ined .

S ince the da ta s uppor t ing the l i f t- inc rea s e e f fec t we re ob ta ined

fo r the ca s e o f a two-d imens iona l hydro fo i l , fu r the r r e s ea rch i , ,

nece s s a ry to a s s e s s the app l i c ab i l i t y o f th i s l i f t augmen ta t ion

phe nom eno n to three-dime ns ional l if t ing bodies . Fu rthe r researclq

i s a l so neces s a ry to a ch ieve a be t t e r un de rs t a nd in g o f the fund a -

men ta l s o f the phenom enon . In th is r ega rd , p re s s u re d i s t r ibu t io r

me asurem ents un der various in jec tion condi t ions as wel l as de ta i led

visual iza tions of the f low pa t te rn chan ges should be ca rr ied o ut a ,,

pa r t o f fu tu re re s ea rch e f fo r t s .

A c k n o w l e d g m e n t

T h e w o r k r e p o r t e d h e r e i n w a s s u p p o r t e d b y t h e U . S . D e p a r t .

m e n t o f th e N a v y , O f f i c e o f N a v a l R e s ea r c h , u n d e r C o n t r a c t N o

N 0 0 0 1 4 - 7 1 - C - 0 0 6 8 , N R 0 6 2 -8 2 5 .

Th e au tho r w i s hes to expre s s h i s app rec ia t ion to M es sr s. R . J

A l t m a n n a n d R . D . B a t e m a n f o r t h e i r h e l p i n t h e p e r f o r m a n c e o t

the te st s. M r . P . R oge rs was in cha rg e o f the da ta comp ute1

analysis.

R e f e r e n c e s

1 Wu, J ., "Lifting Reduction of Additive Solutions,"

Journal o f Hy.

dronautics

Vo l. 8, No. 4, O ct. 1969.

2 Sarpkaya ,T., "On the Performance o f Hydrofoils in Dilute Polyo~

Solutions," Paper presented at the International C onference on Dra~

Reduction, Cambridge, England, Sept. 1974.

8 Fruman ,D. H ., Sundaram , T. R., and D augard, S. J., "Effect of Dra~

Reducing Polymer Injection on the L ift and D rag of a Tw o-Dimensional

Hydrofoil," Paper presented at the International Conference on Dra~

Reduction, Cambridge, England, Sept. 1974.

4 Lehman, A. F. and Suessmann, R. T., "An Experimental Study ot

1 5 0 J O U R N A L O F S H I P R E S E A R C t


7/7

i f t and D rag of a Hydrofo i l wi th Po lymer Eject ion ," Oceanics, Inc.

port No. 72-94, N ov. 1972.

5 Johnson , V. E ., J r . and Goodman, A. , "Th e HYD RONA UTICS,

rpora ted Variable-Pressure, Free-Surface, H igh-Speed Chann el,"

American Society of

Engineers, New York, 1964, p. 49.

6 Etter, R. J. and H uang, T. T., " 'An Exp erim ental Investigation of

dyna mic Characterist ics of Several Fai red Cables Having

me trical NA CA Airfoil Sections," Hydronautics, Inco rpora ted

hnical Re port 530-1, July 1967.

7 Frum an, D. H. and Tulin, M. P., "Diffusion of a Tangential Dra g-

Polymer Injection on a Fla t Plate at High R eynolds Num bers,"

ncorp orate d Tec hnical Report 7101-3, 1973.

A d d e n d u m

S i n ce t h e su b miss io n o f t h i s p ap er , t wo o t h e r r ep o r t s4 ,5 hav e bee n

4 Frum an, D. H., Tulin, M. P., and Liu, H.-L., "Lift, D rag, and Pressure

bution Effects Accompanying D rag-Reducing P olym er Injection

o-Dimensional Hydrofo i l s ," Paper p resen ted at the 1975 Annual

Command Hydromechanics Committee

i ss u e d. T h e s e r e p o r t s c o n t a i n s o m e o f t h e a d d i t i o n a l in f o r m a t i o n

t h a t t h e a u t h o r c o n s i d e r e d n e c e s s a ry t o a c h i e v e a b e t t e r u n d e r -

s t a n d i n g o f t h e f u n d a m e n t a l s o f t h e p h e n o m e n o n . I n p a r t i c u l a r ,

t h e m e a s u r e m e n t s o f t h e p r e s s u re d i s t r ib u t i o n o n t h e f o i l s u r f a c e

h a v e d e m o n s t r a t e d t h a t t h e p o l y m e r i n je c t i o n d e c r e a s e s th e v a l u e

o f t h e l o c a l p r e s s u r e o n t h e s i d e o f th e f o i l w h e r e t h e i n j e c t i o n i s

p e r f o r m e d . O n t h e o p p o s i te si d e, t h e r e is a s li g h t a u g m e n t a t i o n

o f t h e p r e s s ur e . B a s e d o n t h e s e r e s u lt s , F r u m a n e t a l4 h a d s u g -

g e s t e d t h a t t h e l i ft a n d p r e s s u re c h a n g e s d u r i n g p o l y m e r i n je c t io n s

a r e d u e t o a n e l o n g a t i o n a l v is c o e l a s t ic e f f e c t o f t h e i n j e c t e d f l u i d .

T h i s e f f e c t i s r e s p o n s i b l e f o r a n a l t e r a t i o n o f t h e f o i l s h a p e i m m e -

d i a t e l y d o w n s t r e a m o f t h e i n je c t io n s li t. H o w e v e r , t h e d e t a i l e d

n a t u r e o f t h e i n t e r a c t i o n b e t w e e n t h e v i s c o e l as t ic e f f e c t a n d t h e

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

(SEAHA C), Monterey, C alif. , Oct. 1975.

5 Lehm an, A. F . , "Ad di t ional Invest igations o f the Hyd rodyna mic

Characteri s tics o f a H ydrofo i l Em ploying Polymer Eject ion , ' Paper

prese nted at the 1975 SEAHA C Meeting, Monterey, Calif . , Oct. 1975.

M B E R 1 9 7 6 1 5 1

drag and lift on hydrofoil

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