I AI A A-88-0365 EXPERIMENTAL INVESTIGATION OF LOAD EFFECTS ON SIMULATED COMPRESSOR AIRFOIL TRAILING-EDGE FLOWFIELDS NG D.C. McCormick and R.W. Paterson United Technologies Research Center East Hartford, CT H.D. Weingold Pratt & Whitney Aircraft East Hartford, CT AIM 26th Aerospace Sciences Meeting January 11-14, 1988/Reno, Nevada For permission to cop or republish, contact the American Institute of Aeronautics and Astronautics !XI L'Enfant Promenade, S.W., Washington, D.C. 20024
Transcript
I AI A A-88-0365 EXPERIMENTAL INVESTIGATION OF LOAD EFFECTS ON SIMULATED COMPRESSOR AIRFOIL TRAILING-EDGE FLOWFIELDS
NG
D.C. McCormick and R.W. Paterson United Technologies Research Center East Hartford, CT
H.D. Weingold Pratt & Whitney Aircraft East Hartford, CT
AIM 26th Aerospace Sciences Meeting January 11-14, 1988/Reno, Nevada
For permission to cop or republish, contact the American Institute of Aeronautics and Astronautics !XI L'Enfant Promenade, S.W., Washington, D.C. 20024
BXPERIHENTAL INVESTIGATION OF LOADIRG EFFECTS ON SIMlLATED COHPBESSOR AIRFOIL TRAILING-EDGE PLOWFIELDS
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T h i s report. d e s c r i b e s an e x p e r i m e n t a l i n v e s t i - g a t i o n o f t h e f l o w f i e l d d e v e l o p m e n t i n t h e t r a i l i n g - e d g e r e g i o n of a s i m u l a t e d compresso r a i r f o i l h a v i n g p r e s s u r e - t o - s u c t i o n s u r f a c e l o a d i n g . The Study r e p r e s e n t s a c o n t i n u a t i o n o f an e f f o r t t o s t u d y t u r b u l e n t , s e p a r a t e d a i r f o i l t r a i l i n g - e d g e f l o w s . P r e v i o u s e x p e r i m e n t a t i o n had a d d r e s s e d a i r f o i l t r a i l i n g - e d g e s e p z r e t i o n phenomena i n the: a b s e n c e o f p r e s s u r e l o a d i n g . T"r o b j e c t i v e o f t h e c u r r e n t s t u d y w a s t o e x p l o r e t h e e f f e c t s o f l o a d i n g and t h e r e b y p r o v i d e a more r e a l i s t i c s i m u l a t i o n o f t h e compressor a i r f o i l f l ow e n v i r o n m e n t . The p r e s - e n t a p p r o a c h was t o conduc t a l a r g e - s c a l e c a s c a d e s i m u l a t i o n o f t h e a i r f o i l t r a i l i n g - e d g e f l o w f i e i d f o r b o t h a nominal d e s i g n c o n d i t i o n and a h i g h e r l o a d i n g o f f - d e s i g n c o n d i t i o n . For t h e d e s i g n con- d i t i o n , t h e a i r f o i l boundary l a y e r s e p a r a t e d a t t h e t r a i l i n g e d g e . For t h e o f f - d e s i g n c o n d i t i o n , s e p a - r a t i o n o c c u r r e d on t h e s u c t i o n s u r f a c e u p s t r e a m o f Lhe t r a i l i n g e d g e . A p r i n c i p a l r e s u l t o f t h e s t u d y - w a s t h a t p r e s s u r e l o a d i n g was found t o a l t e r t h e t r a i l i n g - e d g e t i m e mean v e l o c i t y f i e l d from t h a t o b s e r v e d i n p r e v i o u s un loaded a i r f o i l e x p e r i m e n t . The r e l a t i v e b a s e p r e s s u r e f o r t h e nominal d e s i g n c o n d i t i o n was u n a l t e r e d from t h e un loaded e x p e r i - ment b u i s i g n i f i c a n t l y lower f o r t h e o f f - d e s i g n c o n d i t i o n . I n c r e a s e d l o a d i n g was found t o i n d u c e g r e a t e r c a s c a d e e x i t f l ow d e v i a t i o n from t h e e x i t m e t a l angle, t h u s r e d u c i n g t h e r e l a t i v e c a s c a d e f l o w t u r n i n g .
I n t r o d u c t i o n
The overall r e s e a r c h p rob lem a d d r e s s e d i n t h i s s t u d y was t u r b u l e n t boundary l a y e r s e p a r a t i o n i n t h e t r a i l i n g - e d g e r e g i o n o f compresso r a i r f o i l s . Because of t h e t h i c k , b l u n t t r a i l i n g - e d g e geome- t r i e s r e q u i r e d f o r s t r u c t u r a l and d u r a b i l i t y rea- sons, s u r f a c e c u r v a t u r e - i n d u c e d s e p a r a t i o n i n v a r i - a b l y o c c u r s i n t h i s r e g i o n a t d e s i g n c o n d i t i o n s . Under h i g h e r l o a d i n g c o n d i t i o n s a s s o c i a t e d w i t h o f f - d e s i g n o p e r a t i o n , t h e s u c t i o n s u r f a c e s e p a r a - t i o n l o c a t i o n moves fo rward r e s u l t i n g i n a larger s p a t i a l e x t e n t o f t h e s e p a r a t e d f low r e g i o n .
* A s s o c i a t e R e s e a r c h E n g i n e e r , Member AIM. ** Manager Cas Dynamics and l b e r m o p h y s i c s ,
***Senior R e s e a r c h S c i e n t i s t , A s s o c i a t e F e l l o w v A s s o c i a t e F e l l o w A I M .
A I M .
One u n d e s i r a b l e consequence of t r a i l i n g - e d g e s e p a r a t i o n i s f a i l u r e t o recover t o t a l p r e s s u r e a t t h e r e a r w a r d s t a g n a t i o n p o i n t . T h i s r e s u l t s i n a d e p r e s s e d b a s e p r e s s u r e and a d r a g c o n t r i b u t i o n wh ich can b e an a p p r e c i a b l e p o r t i o n of t h e o v e r a l l d r a g f o r an o t h e r w i s e w e l l d e s i g n e d a i r f o i l . A s econd u n d e s i r a b l e Consequence i s t h a t SepBrat i o n c o n t r i b u t e s t o a r educed l i f t , t h e r e b y d e c r e a s i n g f l o w t u r n i n g . I n more e x t r e m e l o a d i n g s i t u a t i o n s , t h e s u c t i o n surface s e p a r a t i o n c a n m o w f o r w a r J f rom t h e t r a i l i n g e d g e , r e s u l t i n g i n s t a l l and a
c a t a s t r o p h i c loss o f l i f t . The c a s c a d e s t u d y o f Hobbs e t a l . ' and t h e
un loaded b l u n t - b a s e d a i r f o i l s t u d y o f P a t e r s o n and Weingo ld2 a r e examples of p r e v i o u s e x p e r i m e n t a l programs d i r e c t e d toward improv ing u n d e r s t a n d i n g o f t h e compressor a i r f o i l t r a i l i n g - e d g e s e p a r a t i o n p r o c e s s . Complementary t r a i l i n g - e d g e f l o w f i e l d a n a l y t i c a l s t u d i e s a r e a l s o b e i n g c o n d u c t e d . 3-5 R e l a t i v e t o f u n d a m e n t a l s e p a r a t e d f l a w s t u d i e s , an e x p e r i m e n t a l i n v e s t i g a t i o n o f t u r b u l e n t s e p a r a t i o n and r e a t t a c h m e n t on a f l a t - p l a t e t e s t s u r f a c e , r e p o r t e d by P a t r i c k , 6 h a s been found t o b e r e l e v a n t t o t h e p r e s e n t p rob lem.
P r e v i o u s compresso r c a s c a d e s t u d i e s such as t h a t o f Hobbs e t a i . ' h a v e p r o v i d e d i n f o r m a t i o n on o v e r a l l t r a i l i n g - e d g e f l o w c h a r a c t e r i s t i c s . Because o f t h e s m a l l s c a l e o f such e x p e r i m e n t s , t h e d e t a i l e d d e f i n i t i o n of t h e s e p a r a t e d f low r e g i o n r e q u i r e d f o r code a s s e s s m e n t and deve lopmen t e f f o r t s was no t p r o v i d e d . T h i s l e d t o a p r e v i o u s l y r e p o r t e d e x p e r i m e n t i n which B large-scale a i r f o i l model was used t o p r o v i d e d e t a i l e d i n f o r m a t i o n r e g a r d i n g t r a i l i n g - e d g e pressure d i s t r i b u t i o n s , v e l o c i t y f i e l d s and u n s t e a d y f low ( v o r t e x s h e d d i n g ) c h a r a c t e r i s t i c s . The f o c u s o f t h a t s t u d y was a t es t c o n d i t i o n where t h e e f f e c t o f t u r b u l e n t bound- a r y l a y e r t o t r a i l i n g - e d g e t h i c k n e s s r a t i o c o u l d be e x p l o r e d w i t h o u t t h e p r e s e n c e o f p r e s s u r e l o a d i n g e f f e c t s . The t e s t c o n d i t i o n s were near e q u i l i b r i u m b o u n d a r y l a y e r s i n t h e one t o two t r a i l i n g - e d g e t h i c k n e s s range, t y p i c a l o f s u p e r c r i t i c a l compres- sor a i r f o i l s , w i t h a zero p r e s s u r e g r a d i e n t f r e e - stream boundary c o n d i t i o n . The s t u d y p roduced t h e d e s i r e d d e t a i l e d f l o w f i e l d i n f o r m a t i o n and i d e n t i - f i e d vortex s h e d d i n g a6 an i m p o r t a n t f l o w f e a t u r e . It vas f u r t h e r found t h a t unsymmet r i c b o u n d a r y layers w i t h a t h i c k n e s s r a t i o o f 1.8 ( i n d i s p l a c e - m e n t , wmen tum, and boundary l a y e r t h i c k n e s s ) , b u t s i m i l a r s h a p e f a c t o r s , had a n e g l i g i b l e i n f l u e n c e on t h e f l o w f i e l d .
"Copyright < 1988 by Uoitcd T&nologies Corporation. PubBshed by thr ~ ~ ~ r i ~ ~ ~ ~ ~ t i t ~ t ~ m ti^^ and ~ ~ t ~ ~ n ~ ~ t i c r . In<. a i th penni~rion."
1
The overall goal of t h e p r e s e n t e f f o r t w a s t o e x t e n d t h e p r e v i o u s r e s e a r c h t o i n c l u d e r e a l i s t i c t r a i l i n g - e d g e l o a d i n g c o n d i t i o n s , t h e r e b y i n c l u d i n g t h e r e m a i n i n g m a j o r e f f e c t e x p e c t e d t o i n f l u e n c e s e p a r a t i o n c h a r a c t e r i s t i c s . The a p p r o a c h was t o c o n d u c t a l a r g e - s c a l e c a s c a d e s i m u l a t i o n u s i n g c o n t o u r e d wind t u n n e l walls t o s i m u l a t e midgap s t r e a m l i n e s . The p r e s s u r e d i s t r i b u t i o n w a s d e s i g n e d t o d u p l i c a t e t h a t which would be o b t a i n e d i n a C o n t r o l l e d D i f f u s i o n A i r f o i l c a s c a d e . C o n t r o l l e d D i f f u s i o n A i r f a i l r e f e r s t o a s u p e r - c r i t i c a l c o m p r e s s o r a i r f o i l d e s i g n d e s c r i b e d by Hobbs and Weingold . ' Two c o m p r e s s o r o p e r a t i n g c o n d i t i o n s w e r e i n v e s t i g a t e d . The f i r s t , t e rmed t h e low l o a d i n g c a s e , a d d r e s s e d o n - d e s i g n o p e r a t i o n v h r r e s e p a r a t i o n occurs on t h e t r a i l i n g - e d g e c i r c l e . T h e s e c o n d , h i g h l o a d i n g c a s e was c o n c e r n e d w i t h o f f - d e s i g n o p e r a t i o n , where t h e s e p a r a t i o n r e g i o n e x p a n d s t o i n c l u d e a p o r t i o n of t h e s u c t i o n s u r f a c e j u s t u p s t r e a m of t h e t r a i l i n g e d g e . T h i s i s an i n t e r m e d i a t e c o n d i t i o n i n t h e a p p r o a c h t o a i r f o i l t r a i l i n g - e d g e s t a l l .
Approach
AS i n t h e p r e v i o u s s t u d y Z a l a r g e - s c a l e p l a t e o f C o n s t a n t t h i c k n e s s was used t o s i m u l a t e t h e c o m p r e s s o r a i r f o i l . The s c a l e of t h e e x p e r i m e n t ( c i r c u l a r t r a i l i n g - e d g e d i a m e t e r o f 2 . 5 4 cm) was s e t by t h e need t o a c q u i r e a d e t a i l e d d e f i n i t i o n of t h e v e l o c i t y and p r e s s u r e f i e l d s i n t h e v i c i n i t y o f t h e t r a i l i n g e d g e . The l e n g t h of t h e p l a t e w a s s e l e c t e d t o p r o v i d e r a t i o s of t r a i l i n g - e d g e t u r b u - l e n t b o u n d a r y l a y e r t h i c k n e s s t o t r a i l i n g - e d g e t h i c k n e s s r e p r e s e n t a t i v e o f a c t u a l s c a l e a p p l i c a - t i o n s . T y p i c a l b o u n d a r y l a y e r c h a r a c t e r i s t i c s f o r s u p e r c r i t i c a l a i r f o i l s are g i v e n by t h e B u i l d I c a s c a d e d a t a r e p o r t e d by Hobbs e t a l , ' A t a p o s i - t i o n 0.032 chord u p s t r e a m of t h e t r a i l i n g - e d g e , r a t i o s of p r e s s u r e s u r f a c e and s u c t i o n s u r f a c e momentum t h i c k n e s s t o t r a i l i n g - e d g e d i a m e t e r were 0.09 and 0 . 2 6 r e s p e c t i v e l y . TO a c h i e v e r e l a t i v e t h i c k n e s s i n t h i s r ange , a p l a t e l e n g t h on t h e o r d e r of 2 m e t e r s was r e q u i r e d . A c u r v e d p l a t e c o n t a i n e d w i t h i n a c o n t o u r e d wind t u n n e l d u c t was u s e d t o g e n e r a t e p r e s s u r e g r a d i e n t h i s t o r i e s t y p i c a l o f a CDA ( C o n t r o l l e d D i f f u s i o n A i r f o i l ) c a s c a d e . R e l a t i v e t o f l o w c o n d i t i o n s , t h e 8 p p r o a c h w a s t o c o n d u c t t h e e x p e r i m e n t a t low s u b s o n i c Mach number i n a two-dimens iona l f l o w e n v i r o n m e n t . M o d e l i n g o f c o m p r e s s i b i l i t y e f f e c t s w a s n o t c o n s i d e r e d t o be o f f i r s t o r d e r i m p o r t a n c e .
The p r e s s u r e d i s t r i b u t i o n of t h e CDA c a s c a d e "B", one of e i g h t CDA c a s c a d e s d e s c r i b e d by Hobbs and Weingold , ' w a s s e l e c t e d f o r use i n t h e p r e s e n t s t u d y . T h i s d e s i g n i s t y p i c a l o f t h a t employed i n t h e r o t o r t i p r e g i o n of a c o m p r e s s o r m i d d l e s t a g e .
T r a n s l a t i o n of t h i s d e s i g n i n t o a wind t u n n e l c o n f i g u r a t i o n p r o c e e d s as f o l l o w s : The t h i c k n e s s of the p l a t e was s e l e c t e d as 2 . 5 4 cm. c a s c a d e "B" v a s t h e n s c a l e d t o t h i s s i z e and t h e f l o w f i e l d c a l c u l a t e d a t Uach 0 . 1 , u s i n g t h e i n v i s c i d , two- d i m e n s i o n a l p o t e n t i a l f l o w c a s c a d e a n a l y s i s of C a s p a r , Hobbs, and D a v i s . * A P r a t t 6 W h i t n e y ,
s e m i e m p i r i c a l d e v i a t i o n s y s t e m f o r CDA c a s c a d e s was used t o d e t e r m i n e t h e downstream f l o w a n g l e f o r t h e p o t e n t i a l f l o w c a s c a d e a n a l y s i s . The same a n a l y s i s was used t o d e t e r m i n e t h e f l o w f i e l d f o r t h e c u r v e d p l a t e . The p l a t e c u r v a t u r e was v a r i e d t o f i n d a -' g e o m e t r y h a v i n g s i m i l a r p r e s s u r e g r a d i e n t s b o t h along t h e s u r f a c e s and normal t o t h e a i r f o i l i n t h e t r a i l i n g - e d g e r e g i o n . An u p s t r e a m e x t e n s i o n l e n g t h o f t h e p l a t e ( f o r boundary l a y e r g r o w t h ) was s e l e c t e d t o s i m u l a t e the r a t i o s of t h e boundary l a y e r p a r a m e t e r s t o t r a i l i n g - e d g e t h i c k n e s s c a l c u - l a t e d f o r t h e u n s c a l e d c a s e a d e "8". A boundary l a y e r a n a l y s i s was t h e n a p p l i e d t o t h e midgap s t r e a m l i n e s ( f r o m t h e p o t e n t i a l f l o w c a s c a d e a n a l y s i s ) t o c a l c u l a t e boundary l a y e r deve lopment a s i f t h e midgap s t r e a m l i n e s were s o l i d v a l l s . The wind t u n n e l d u c t was t h e n d e s i g n e d t o b e d i s p l a c e d from t h e c a l c u l a t e d midgap s t r e a m l i n e s by an amount e q u a l t o t h e b o u n d a r y l a y e r d i s p l a c e m e n t t h i c k n e s s . The s y s t e m was t h e n r o t a t e d t o a h o r i z o n t a l i n l e t o r i e n t a t i o n c o r r e s p o n d i n g t o t h e wind t u n n e l i n l e t d u c t . T h i s o v e r a l l c a l c u l a t i o n was r e p e a t e d far a model w i t h i n c r e a s e d t u r n i n g ( h i g h e r l o a d i n g ) t o p r o v i d e a c o n f i g u r a t i o n p r e d i c t e d t o produce suc-
t i o n s u r f a c e s e p a r a t i o n u p s t r e a m of t h e t r a i l i n g e d g e . F i g . 1 shows t h e r e l a t i o n s h i p of t h e o r i g i n - a l a i r f o i l and c a s c a d e a r r a n g e m e n t ( d a s h e d l i n e s ) t o t h e c u r v e d - p l a t e s i m u l a t i o n .
\ \
STREAMLINES
flg. I Schemaflc of CurVCd~pI~Ie cascade sirnulalion
Experimental Description
Wind T u n n e l Arranscacnt
The e x p e r i m e n t vas c o n d u c t e d i n t h e r e c e n t l y c o n s t r u c t e d , second UTRC Boundary L a y e r Wind Tunnel w i t h a c a s c a d e s i m u l a t i o n t e s t s e c t i o n . The wind t u n n e l is a l o v - s p e e d , c l o s e d - l o o p e d , low t u r b u - lence ( 0 . 2 5 p e r c e n t ) d e s i g n . A s i d e v i e w s c h e m a t i c of t h e f a c i l i t y w i t h t h e c a s c a d e s i m u l a t i o n t e s t - s e c t i o n is shown in Fig. 2 .
w
HONEYCOMB - 0 1 2
METERS
Fig. 2 Wind tunnel arrangement.
The wind t u n n e l b lower is l o c a t e d u p s t r e a m o f t h e s e t t l i n g chamber . C o n v e n t i o n a l , h i g h q u a l i t y f l o w c o n d i t i o n i n g i s p r o v i d e d i n t h e s e t t l i n g cham- b e r . The c o n d i t i o n i n g c o n s i s t s o f p e r f o r a t e d p l a t e , honeycomb, coarse s c r e e a s , and f i n e screens t o p r o v i d e u n i f o r m , low t u r b u l e n c e f l o w . The con- t r a c t i o n from t h e s e t t l i n g chamber t o t h e t e s t - s e c t i o n i s p r o v i d e d i n two s t a g e s , t h e f i r s t i n t h e s p a n w i s e d i r e c t i o n and t h e second i n t h e t r a n s v e r s e d i r e c t i o n . The wall s h a p e f o r each c o n t r a c t i o n w a s
For t h e h i g h l o a d i n g c a s e , t h e l a r g e t r a n s - verse p r e s s u r e g r a d i e n t ( c a u s e d by t u r n i n g ) i n t e r - a c t e d s t r o n g l y w i t h t h e co rne r boundary l a y e r , g i v i n g r i s e t o corner v o r t e x s t r u c t u r e 8 t h a t d e t e r - i o r a t e d t h e t w o - d i m e n s i o n a l i t y o f t h e wind t u n n e l . T h i s problem is t y p i c a l o f c a s c a d e f a c i l i t i e s and i s u s u a l l y s o l v e d by c o r n e r b l e e d on t h e s u c t i o n s u r f a c e . l o The same method w a s used h e r e t o cor- r e c t t h e p rob lem.
d e f i n e d by m a t c h i n g two c u b i c a r c s by t h e merhod of Model D e s c r i p t i o n Rouse and H a ~ s a n . ~ The method n i v e s d e s i g n s which - - a v o i d l o c a l w a l l a d v e r s e p r e s s u r e g r a d i e n t s (and t h u s boundary l a y e r s e p a r a t i o n ) a s deduced from t h e p o t e n t i a l f l o w s o l u t i o n . The o v e r a l l a r ea c o n t r a c - t i o n r a t i o t h r o u g h t h e t w o s t a g e s is 2 . 1 .
Downstream of t h e c o n t r a c t i o n i s a 30.5 cm s t r a i g h t f l o w s e c t i o n w i t h a 78 .7 em span and B
41 .7 cm t r a n s v e r s e d i m e n s i o n . I n t h i s s e c t i o n t h e wall boundary l a y e r s a r e t r i p p e d on a l l f o u r w a l l s w i t h a 6 nm square b a r . T u r b u l e n t wall boundary l a y e r s were d e s i r e d t o min imize end wall i n t e r - a c t i o n s w i t h t h e tes t s e c t i o n ' s pressure g r a d i e n t s ( c a u s e d by t u r n i n g ) . The t e s t s e c t i o n i n l e t refer- ence c o n d i t i o n s were a l s o measured i n t h i s s e c t i o n . The s t r a i g h t flow s e c t i o n i s f o l l o w e d by t h e tes t s e c t i o n i n which t h e i n i t i a l p o r t i o n of t h e model is mounted.
The model c o n s i s t s o f a f l a t p l a t e r e g i o n and a c i r c u l a r arc, t u r n i n g r e g i o n ( d e s c r i b e d in more d e t a i l b e l o w ) . The u p s t r e a m p o r t i o n of t h e f l a t p l a t e was n o m i n a l l y c e n t e r e d i n t h e s t r a i g h t d u c t wh ich i s 55 cm l o n g i n t h e downstream d i r e c t i o n . The s t r a i g h t d u c t is f o l l o w e d by t h e f l e x i b l e po ly - p r o p y l e n e w a l l s , s h o r n i n Fig. 2 , which r e p r e s e n t t h e d i s p l a c e d (boundary l a y e r c o r r e c t e d ) midgap e r r e a r n l i n e s . The midgap s t r e a m l i n e s t e r m i n a t e a t t h e downstream dump r e g i o n . The f low is t h e n d u c t e d i n t o t h e submic ron f i l t e r sys t em and h e a t e x c h a n g e r s e c t i o n o f t h e r e t u r n l o o p .
v
3
The model c o n s i s t s o f two b a s i c s e c t i o n s , t h e u p s t r e a m f l a t p l a t e s e c t i o n and t h e downstream t u r n i n g s e c t i o n a s shown i n F i g . 3. Both s e c t i o n s are o f aluminum r i b c o n s t r u c t i o n w i t h aluminum s k i n . The t h i c k n e s s i s c o n s t a n t a t 2.54 Cm. The l e a d i n g edge s h a p e o f t h e f l a t p l a t e s e c t i o n i s a 3 t o 1 e l l i p s e . The d i s t a n c e from t h e l e a d i n g edge t o t h e end o f t h e f l a t p l a t e s e c t i o n i s 119 cm f o r b o t h l o a d i n g cases.
REFERENCE CONDITIONS
SUICTION SURFACE
Fig. 3 Cascade simulation geometry
The t u r n i n g o r l o a d i n g s e c t i o n o f t h e model is a c i r c u l a r a r c o f 175 cm mean r a d i u s . The low l o a d i n g c n s e h a s a 1 9 . 6 d e g r e e a r c and t h e h i g h l o a d i n g c a s e h a s a 2 9 . 6 d e g r e e a r c . The shape o f t h e t r a i l i n g edge i s a h a l f c i r c l e of r a d i u s 1.27 cm and i s t a n g e n t t o t h e end of t h e t u r n i n g see- t i o n . The t r a i l i n g edge a d d s a n o t h e r 0 . 4 d e g r e e s o f arc t o t h e model t h u s g i v i n g t h e two l o a d i n g c a s e s t o t a l t u r n i n g a n g l e s of 20 and 30 d e g r e e s (low and h i g h l o a d i n g cases r e s p e c t i v e l y ) .
To a v o i d t h r e e - d i m e n s i o n a l t r a n s i t i o n , t h e model b o u n d a r y l a y e r s were t r i p p e d on t h e f l a t p l a t e s e c t i o n 1 5 . 2 cm downst ream of t h e l e a d i n g e d g e . The t r i p was 0 . 3 8 nm t h i c k and o f t h e Hama- t y p e . " T h i s t h i c k n e s s was d e s i g n e d t o be 80 p e r - Cent o f t h e e s t i m a t e d d i s p l a c e m e n t t h i c k n e s s t o p r o v i d e an e f f i c i e n t t r i p .
The model c o o r d i n a t e s y s t e m (n, y ) h a s i t s o r i g i n l o c a t e d a t t h e t r a i l i n g e d g e w i t h t h e x a x i s p a r a l l e l t o t h e e x i t mean camber l i n e as shown i n F i g s . 3 and 4 . T h i s c o o r d i n a t e s y s t e m i s used t o r e p o r t most of t h e measured r e s u l t s . In a d d i t i o n , t h e s u r f a c e c o o r d i n a t e , s , i s measured from t h e t r a i l i n g - e d g e c e n t e r l i n e and i s used t o r e p o r t t h e s u r f a c e p r e s ~ u r e d a t a .
DIMENSIONS IN cm
, ,
CIRCULAR PRESSURE SURFACE -TRAILING EDGE
-r
SUCT~ON SURFACE 19 ~ T A T I C PRESSURE ? N E E "' TAPS AT ' loo (NOMINAL)
STATIC PRESSURE TAPS INTERVALS
Fig. 4 Detail of trailing edge geometry.
C a s c a d e Descr ipt ion
The s i m u l a t e d c a s c a d e geometry f a r t h e low and h i g h l o a d i n g cases a r e l i s t e d below (angles are measured f rom t h e c a s c a d e t a n g e n t d i r e c t i o n )
LOW L o a d i n g - C h o r d f s p a e i n g 2 . 5 3 2.94 I n l e t f l a w a n g l e 38' 38" E x i t f l o w angle 52' 53" Leading-edge m e t a l a n g l e 38" 38' T r a i l ing-edge m e t a l angle 58" 68'
N o t e , t h e e x i t flow a n g l e i s t h e e x p e r i m e n t a l l y d e t e r m i n e d v a l u e .
O p e r a t i n g and R e f e r e n c e C o n d i t i o n s
The e x p e r i m e n t was performed a t a c o n s t a n t R e y n o l d s numbers of 2.64 x 106 s n d 3.08 x IO6 f o r t h e low and h i g h l o a d i n g c a s e s , r e s p e c t i v e l y . T h i s v R e y n o l d s number i s b a s e d on t h e i n l e t v e l o c i t y and t h e camber l i n e l e n g t h . The o p e r a t i n g c o n d i t i o n s o f t h e wind t u n n e l were m o n i t o r e d u p s t r e a m (9 model t h i c k n e s s e s ) of t h e l e a d i n g edge i n t h e s t r a i g h t d u c t a s shown i n Fig. 3 ( l a b e l e d r e f e r e n c e c o n d i - t i o n s ) . I n l e t dynamic head and t o t a l p r e s s u r e were measured w i t h a p i t o t s t a t i c p r o b e . A l s o , t h e i n l e t t o t a l t e m p e r a t u r e was measured . The nominal o p e r a t i n g c o n d i t i o n s a r e t a b u l a t e d be low:
I n l e t dynamic head 3.43 cm w a t e r T o t a l p r e s s u r e 1 0 cm w a t e r gauge T o t a l t e m p e r a t u r e 32" C I n l e t v e l o c i t y 2 4 . 0 m/s E x i t v e l o c i t y 20.8 m / s - low l o a d i n g
18.1 m / s - h i g h l o a d i n g
For t h e most p a r t , t h e c o n d i t i o n s measured a t t h i s l o c a t i o n are used as t h e r e f e r e n c e q u a n t i t i e s f o r n o r m a l i z i n g d a t a a c q u i r e d i n t h e t r a i l i n g - e d g e v i c i n i t y . T h e i n l e t v e l o c i t y i s d e s i g n a t e d U r e f and is used t o n o r m a l i z e t h e v e l o c i t i e s f o r t h e h o t f i l m and LDV s u r v e y s . The i n l e t p r e s s u r e 5 a r e d e s i g n a t e d p r e f ( r e f e r e n c e s t a t i c ) and Q r e f ( r e f e r - ence dynamic h e a d ) and a re u s e d ( e x c e p t where n o t e d ) t o compute t h e s u r f a c e p r e s s u r e c o e f f i c - i e n t s .
I n s t r u m e n t a t i o n V'
L a s e r Doppler V e l o c i m e t r y (LDV) i s t h e p r i m a r y v e l o c i t y measurement t e c h n i q u e u s e d i n t h i s s t u d y . A n o n i n t r u s i v e method was r e q u i r e d t o document t h e s e p s r a t e d f low r e g i o n downst ream o f t h e t r a i l i n g e d g e . The LDV equipment was a TSI (Thermal System3 1°C.) 9100-7, f o u r beam, two c o l o r s y s t e m . T h i s Sys tem m e a s u r e s two m u t u a l l y p e r p e n d i c u l a r compo- n e n t s of v e l o c i t y s i m u l t a n e o u s l y . The two colors are p r o v i d e d by a two w a t t Argon-Ion Laser w i t h a
To o b t a i n a h i g h s i g n a l t o n o i s e r a t i o , a 3 . 7 5 ~ beam e x p a n d e r was Used w i t h a beam s e p a r a t i o n o f 22 m e n t e r i n g the e x p a n d e r . The t r a n s m i t t i n g l e n s was 152 m i n d i a m e t e r w i t h 8 f o c a l l e n g t h of 762 m. The r e s u l t i n g measurement volume dimen- s i o n s ( e l l i p s o i d ) were 2.5 t o 0.133 mm m a j o r t o m i n o r a x i s . The major a x i s o f t h e volume was b a s i c a l l y a l i g n e d w i t h t h e spanwise d i r e c t i o n , t h u s p r o v i d i n g t h e maximum t r a n s v e r s e r e s o l u t i o n of 0 . 5 p e r c e n t o f t h e p l a t e t h i c k n e s s . The f r i n g e e p a c i n g was 4.16 p and 28 f r i n g e s were p r e s e n t in the measurement volume ( w i t h no Bragg s h i f t ) . T h e i n c l u d e d h a l f angle o f t h e laser beams was 3.141 d e g . f o r b o t h components . The s c a t t e r e d l i g h t was c o l l e c t e d i n t h e b a c k s c a t t e r mode. In o r d e r t o d e t e c t r e v e r s e f l o w t h r o u g h t h e measurement volume, b o t h components were Bragg s h i f t e d . Based on t h e o p t i c a l c o n f i g u r a t i o n and t h e f l o w f i e l d c h a r a c t e r - i e t i c s , the p o l a r r e s p o n s e o f t h e measurement "01- - "me was c a l c u l a t e d t o b e a f u l l 360 dewees.'*
c o l o r s e p a r a t o r .
4
A c o u n t e r - t y p e p r o c e s s o r , TSI 1990C, was used t o i n t e r p r e t t h e Dopp le r s i g n a l . For t h e C u r r e n t e x p e r i m e n t , 16 f r i n g e c r o s s i n g s w e r e r e q u i r e d f o r - e a c h r e a l i z a t i o n and 1024 r e a l i z a t i o n s ( f o r each component) were t a k e n f o r e a c h d a t a p o i n t . The p r o c e s s o r was o p e r a t e d i n t h e c o n t i n u o u s mode i n o r d e r t o compensa te f o r some o f t h e i n d i v i d u a l r e a l i z a t i o n b i a s . 1 3
The mean v e l o c i t i e s were c a l c u l a t e d u s i n g t h e s t a t i s t i c a l e d i t i n g c r i t e r i a of ADEC ( d e s c r i b e d i n R e f . 1 3 ) . For t h e g i v e n sample s i z e of 1024, t h e c r i t e r i a r e j e c t s any d a t a o u t s i d e o f a t h r e e s t a n d - a r d d e v i a t i o n ( c a l c u l a t e d from t h e e n t i r e sample p o p u l a t i o n ) a c c e p t a n c e b a n d . The mean v a l u e was t h e n c a l c u l a t e d b y t h e n u m e r i c a l average o f t h e r e m a i n i n g sample p o p u l a t i o n . T y p i c a l l y no or v e r y few d a t a p o i n t s were r e j e c t e d due t o t h e h i g h s i g - n a l t o n o i s e r a t i o .
The d a t a r a t e o f v e l o c i t y r e a l i z a t i o n s was m o d e r a t e l y low ( 1 0 - 50 p e r s e c o n d ) , t h u s s a m p l i n g was done over r e l a t i v e l y l o n g p e r i o d s . T h i s r e s u l t s i n n e a r i n d e p e n d e n t s a m p l i n g w i t h v e r y r e p e a t a b l e mean values. The w o r s t case u n c e r t a i n t y i n t h e mean v a l u e due t o b i a s and random errors ( u s i n g t h e methodology of R e f . 13) was c a l c u l a t e d t o be ?Z p e r c e n t ( i n e a c h component) o f t h e r e f e r - ence ( c a s c a d e i n l e t ) v e l o c i t y . T h i s occur 's where t h e v e l o c i t y g r a d i e n t s a r e h i g h j u t downstream of t h e t r a i l i n g edge on t h e p r e s s u r e s i d e . T y p i c a l l y , however , t h e measu remen t s are b e t t e r t h a n +1 p e r c e n t .
The Seed m a t e r i a l used f o r t h i s e x p e r i m e n t was
Duke S c i e n t i f i c polymer m i c r o s p h e r e s w i t h a q u o t e d '-~ mean d i a m p t e r o f 1.07 p and d e n s i t y of 1.05 gJml
( S . G . r e l a t i v e t o w a t e r o f nearly one). The micro - s p h e r e s a r e quo ted t o have a low v a r i a n c e i n dism- e t e r . T h i s was c o n f i r m e d w i t h a Ryco LAC 226 l a s e r - i l l u m i n a t e d a e r o s o l p a r t i c l e c o u n t i n g and s i z i n g s y s t e m . The s i z e a n a l y s i s w a s per fo rmed u n d e r normal r u n n i n g c o n d i t i o n s , t h u s a l s o conf im- i n g t h e i n j e c t i o n t e c h n i q u e d i d n o t p roduce s i g n i f - i c a n t a l g o m e r a t i o n s .
The seed w a s d i l u t e d w i t h e t h y l a l c o h o l and
i n j e c t e d i n t o t h e wind t u n n e l w i t h e TSI 9302 Model a t o m i z e r . The a t o m i z e r is a Wrigh t j e t b a f f l e t y p e which g e n e r a t e d 2 pm s i z e d r o p l e r s o f t h e s o l u t i o n . Due t o t h e low v a p o r p r e s s u r e o f a l c o h o l , t h e alco- h o l r a p i d l y e v a p o r a t e s l e a v i n g t h e polymer mic ro - s p h e r e s . The r ake t y p e i n j e c t i o n p robe was i n s t a l l e d i n t h e l o w v e l o c i t y , f i r s t s t a g e c o n t r a c - t i o n , i n o r d e r t o min imize t h e f low d i s t u r b a n c e . I t s l e n g t h was i n t h e t r a n s v e r s e d i r e c t i o n and was c e n t e r e d s p a n w i s e . The probe was a d j u s t e d up and down i n t h e t r a n s v e r s e d i r e c t i o n u n t i l equal d a t a r a t e s were a c h i e v e d above and be low t h e t r a i l i n g e d g e . T h i s c o n f i r m e d t h a t t h e f low was e q u a l l y s e e d e d on b o t h s i d e s o f t h e m o d e l .
~
5
R e s u l t s and D i e c u s s i o n
O v e r a l l S t a t i c P r e s s u r e D i s t r i b u t i o n s
Model s u r f a c e p r e s s u r e d i s t r i b u t i o n s , p r e s e n t - e d i n t e r m s o f t h e p r e s s u r e c o e f f i c i e n t , f o r t h e low and h i g h l o a d i n g cases are shown i n F i g . 5 . T h e p r e s s u r e c o e f f i c i e n t , C i s b a s e d on t h e r e f - e r ence ( i n l e t ) c o n d i t i o n s a n g ' i s p l o t t e d versus t h e u p s t r e a m s u r f a c e c o o r d i n a t e , s i t , measu red from t h e t r a i l i n g edge (where t i s t h e t r a i l i n g - e d g e t h i c k - ness). The s q u a r e symbols a re f o r t h e p r e s s u r e s u r f a c e and t h e c i r c l e s a re f o r t h e s u c t i o n sur- f a c e . The open symbols a r e f o r low l o a d i n g and t h e c l o s e d a r e f o r h i g h l o a d i n g . For r e f e r e n c e p u r p o s e s , s k e t c h e s o f t h e low and h i g h l o a d i n g model g e o m e t r i e s are g i v e n below t h e f i g u r e . N o t e , t h e o v e r a l l l e n g t h of t h e h i g h l o a d i n g case i s l o n g e r d u e t o t h e l a r g e r t u r n i n g a r c .
OPEN SYMBOLS - LOW LOADiNG CLOSED SYMBOLS - HIGH LOADING
Low loading - For t h e low l o a d i n g case t h e f l o w over t h e p r e s s u r e s u r f a c e h a s e x p e r i e n c e d a n e t a c c e l e r a t i o n from t h e l e a d i n g edge s t a g n a t i o n p o i n t (C = 1) t o t h e f i r s t p r e s s u r e t a p ( c - -0 .3) . ?he f i r s t t a p i s a p p r o x i m a t e l y 4 t down- stream of t h e l e a d i n g e d g e . The p r e s s u r e t h e n b e g i n s t o rise r a p i d l y , well u p s t r e a m o f t h e a c t u a l model t u r n i n g . The i n c r e a s i n g p r e s s u r e i s d u e t o t h i s s u r f a c e b e i n g on t h e c o m p r e s s i o n s i d e o f t h e t u r n i n g . About h a l f w a y t h r o u g h t h e t u r n i n g s e c t i o n t h e p r e s s u r e r e a c h e s a maximum and t h e n b e g i n s t o d rop as t h e flow accelerates to match t h e t r a i l i n g - edge p r e s s u r e .
On t h e s u c t i o n surface t h e flow e x p e r i e n c e s a
n e t a c c e l e r a t i o n from t h e l e a d i n g edge t o t h e f i r s t t a p ( c p - - 0 . 2 ) . The p r e s s u r e t h e n r ises s l i g h t l y b e f o r e d r o p p i n g i n r e s p o n s e t o t h i s s u r f a c e b e i n g on t h e e x p a n s i o n s i d e of t h e t u r n i n g . J u s t dawn- stream o f t h e f l a t p l a t e l t u r n i n g l i n e t h e pressure b e g i n s t o rise as t h e f l o w d e c e l e r a t e s t o ma tch t h e t r a i l i n g - e d g e p r e s s u r e .
P
Righ L o a d i n g - The b e h a v i o r of t h e h i g h l n a d i n g p r e s s u r e d i s t r i b u t i o n i s n e a r l y i d e n t i c a l e x c e p t f o r t h e a b s o l u t e l e v e l and t h e manner i n which t h e s u c t i o n s u r f a c e p r e s s u r e d i s t r i b u t i o n a p p r o a c h e s t h e t r a i l i n g e d g e . A s i s e v i d e n t by t h e a r e a between t h e s u r f a c e p r e s s u r e d i s t r i b u t i o n s , t h e l i f t i s larger f o r t h e h i g h l o a d i n g c a s e . Upstream o f t h e t r a i l i n g - e d g e t h e s u c t i o n s u r f a c e p r e s s u r e d i s t r i b u t i o n becomes f l a t over t h e l a s t 4 t o 5 t r a i l i n g - e d g e t h i c k n e s s e s . T h i s c o n s t a n t p r e s s u r e is i n d i c a t i v e of boundary l a y e r s e p a r a - t i o n . Flow v i s u a l i z a t i o n a l s o conf i rmed t h i s o b s e r v a t i o n ( and t h e l o c a t i o n i s shown w i t h an a r r o w i n t h e f i g u r e ) . Thus t h e a d v e r s e p r e s s u r e g r a d i e n t on t h e s u c t i o n s u r f a c e i s s u f f i c i e n t t o s e p a r a t e t h e boundary l a y e r .
The b a s e p r e s s u r e a t t h e t r a i l i n g edge f o r t h e l o w l o a d i n g i s C = 0 . 1 0 4 . The e x i t p r e s s u r e of t h e c a s c a d e ( b a d o n t h e a s y m p o t i c p r e s s u r e on t h e midgap s t r e a m l i n e s l w i n d t u n n e l w a i l s ) i s 0.250. Thus t h e p r e s s u r e from t h e t r a i l i n g edge h a s t o e v e n t u a l l y r i s e t o t h e f i n a l c a s c a d e p r e s s u r e v a l u e a t some d i s t a n c e downstream. For t h e h i g h l o a d i n g
P c a s e , t h e b a s e p r e s s u r e a t t h e t r a i l i n g edge i s C
0.245. The e x i t p r e s s u r e v a l u e , which t h e t r a i l i n g - e d g e p r e s s u r e m u s t r i s e t o , i s C = 0.430. P
The l oca l d i f f u s i o n f a c t o r is d e f i n e d a s
w h e r e U m a x i s t h e maximum v e l o c i t y on t h e s u c t i o n s u r f a c e and Ue i s t h e c a s c a d e e x i t v e l o c i t y . It i s a measure of t h e s u c t i o n s u r f a c e d i f f u s i o n and r e s u l t i n g wake momentum t h i c k n e s s . Us ing t h e sur- f a c e p r e s s u r e d a t a and c a s c a d e e x i t v e l o c i t i e s , t h e l o c a l d i f f u s i o n f a c t o r was c a l c u l a t e d t o be 0 . 2 6 1 and 0 .369 f o r t h e low and h i g h l o a d i n g cases r e s p e c t i v e l y . A s e x p e c t e d , t h e h i g h l o a d i n g v a l u e i s h i g h e r and t h e f l o w e x p e r i e n c e s s u c t i o n s u r f a c e s e p a r a t i o n due t o t h e i n c r e a s e d d i f f u s i o n .
Boundary L a y e r s Upstream o f T r a i l i n g Edge
The boundary l a y e r s a p p r o a c h i n g t h e t r a i l i n g e d g e on t h e s u c t i o n and p r e s s u r e s u r f a c e were d e f i n e d i n d e t a i l w i t h h o t f i l m anemometry. Bound- a r y l a y e r c h a r a c t e r i s t i c s were measured 8 to 9 t r a i l i n g - e d g e t h i c k n e s s e s u p s t r e a m o f t h e t r a i l i n g e d g e where s u r f a c e s t a t i c p r e s s u r e s i n d i c a t e d t r a i l i n g - e d g e e f f e c t s were small. T h e s e p r o f i l e s a r e i n t e n d e d t o p r o v i d e a s t a r t i n g c o n d i t i o n or c h e c k p o i n t f o r c o m p u t a t i o n a l a n a l y s i s . Also, p r o f i l e s were d e f i n e d j u s t u p s t r e a m o f t h e t r a i l i n g e d g e t o p r o v i d e i n f o r m a t i o n on boundary l a y e r deve lopmen t u n d e r t h e i n f l u e n c e o f t h e f r e e s t r e a m p r e s s u r e g r a d i e n t s and t o d e f i n e t h e boundary l a y e r C h a r a c t e r i s t i c s j u s t u p s t r e a m o f t h e t r a i l i n g edge. T h i s also p r o v i d e s a second c o m p u t a t i o n a l check p o i n t .
A t a b u l a r l i s t i n g o f t h e boundary l a y e r Char- a c t e r i s t i c s i n t e r m s o f d i s p l a c e m e n t and momentum t h i c k n e s s and s h a p e f a c t o r a re g i v e n below ( n o t e
t h e a p p r o x i m a t e s u r f a c e c o o r d i n a t e , s i t , c a n he found by a d d i n g 0 .29 t o t h e a b s o l u t e v a l u e of x i t ) .
l o w Load ing S u c t i o n S u r f a c e pressure S u r f a c e
x i t $It e l t H X i t 6 * i t e i t 11 ~ __-- -8.75 0.656 0 .394 1 .67 17 9 . 1 0 0 . 1 0 8 0.0683 1 .58 -0 .90 0 .216 0.166 1 . 3 1 1 - 1 . 0 0 0 .344 0 , 1 9 4 1 77
High Load ing pressure S u r f a c e S u c t i o n S u r f a c e
x . t 6* i t e i t H x i t 6*/ t e l l H - 8 . 1 5 0 . 4 9 3 0.330 1.50 17 9.40 0 .443 0 .225 1 .97
The r e s p e c t i v e boundary l a y e r p r o f i l e s , b o t h i n p h y s i c a l and l aw-of - the -wa l l c o o r d i n a t e s , a r e g i v e n i n R e f . 12 .
Low Load ing - The p r e s s u r e s u r f a c e boundary l a y e r s a re n o m i n a l l y 1 . 8 t t h i c k f o r t h e low l o a d i n g c a s e . The u p s t r e a m survey h a s a r e l a t i v e l y l a r g e s h a p e f a c t o r ( 1 . 7 ) due t o t h e a d v e r s e p r e s s u r e g r a d i e n t h i s t o r y (see F i g . 5 , SIC > 10). From t h e u p s t r e a m s u r v e y l o c a t i o n t o t h e t r a i l i n g edge t h e f l o w a c c e l e r a t e s t o meet t h e t r a i l i n g - e d g e c o n d i - t i o n . I" response t o t h e f a v o r a b l e p r e s s u r e g r a - d i e n t , t h e shape f a c t o r d e c r e a s e s t o 1 . 3 , i n d i c a t - i n g a h e a l t h i e r boundary l a y e r . The boundary l a y - e r s on t h e s u c t i o n s u r f a c e were somewhat t h i n n e r in boundary l a y e r t h i c k n e s s a t 1 . 3 t - l . 5 t . Note t h a t b o t h e u r v e y s are i n t h e d e c e l e r a t i n g ( a d v e r s e pres- sure g r a d i e n t ) p o r t i o n of t h e s u c t i o n s u r f a c e ( F i g . 5 , s / t < 10) . h e r t h i s r e g i o n t h e s h a p e f a c t o r i n c r e a s e s from a r e l a t i v e l y h i g h v a l u e of 1 .6 t o a h i g h e r v a l u e of 1.8, i n d i c a t i v e of a boundary l a y e r a p p r o a c h i n g s e p a r a t i o n .
F o r t h e low l o a d i n g , b o t h f a r u p s t r e a m pro- f i l e s on t h e p r e s s u r e and s u c t i o n s u r f a c e s d i s - p l a y e d a s u b l a y e r , l o g - l i n e a r ( i n t e r i a l s u b l a y e r ) , and wake b e h a v i o r i n l aw-of - the -wa l l c o o r d i n a t e s .
The n e a r t r a i l i n g - e d g e p r o f i l e s m a i n t a i n e d s i m i - l a r i t y i n t h e s u b l a y e r and p a r t o f t h e l o g - l i n e a r r e g i o n b u t v a r i e d c o n s i d e r a b l y i n t h e wake r e g i o n . For t h e a u c t i o n s ide p r o f i l e , t h e wake roe= f a r above t h e l o g - l i n e a r curve f i t , t y p i c a l o f a t u r b u - l e n t boundary s u b j e c t e d t o an a d v e r s e g r a d i e n t . For t h e p r e s s u r e s i d e p r o f i l e t h e wake r e g i o n was
' s u p p r e s s e d be low t h e l o g - l i n e a r curve f i t . presum- a b l y t h e wake h a s not r e s p o n d e d t o t h e r a p i d i n c r e a s e in t h e f r i c t i o n v e l o c i t y d u e t o t h e accel- e r a t i o n .
I n terms o f t h e r a t i o o f momentum t h i c k n e s s t o t r a i l i n g - e d g e t h i c k n e s s , t h e p r e s s u r e and s u e t i o n s u r f a c e v a l u e s a t X / t - -1.0 were 0.166 and 0.194 r e s p e c t i v e l y . These v a l u e s are close t o t h e R e f . 2 u n l o a d e d case v a l u e s (0.1 t o 0 .17) and w i t h i n t h e R e f . 1 b u i l d I c a s c a d e (CDA c a s c a d e ) range (0 .09 t o 0 .26 ) .
W
sigh Load ing - The h i g h l o a d i n g p r o f i l e s on t h e p r e s s u r e s u r f a c e werd q u a l i t a t i v e l y v e r y s i m i l - BT t o t h e low l o a d i n g p r o f i l e s , b u t somewhat t h i c k - e r a t 2 . l t . A s seen i n t h e t a b l e , t h e p r e s s u r e s u r f a c e d a t a a r e c o n s i s t e n t w i t h t h e low l o a d i n g r e s u l t s . For t h e s u c t i o n s u r f a c e boundary l a y e r s , an i n t e r m e d i a t e p r o f i l e was t a k e n a t x f t = - 4 . 9 t o d e t a i l t h e r a p i d g rowth of t h e boundary l a y e r . The c o r r e s p o n d i n g p r e s s u r e g r a d i e n t , shown i n F i g . 5 ( s l t < IO), d i s p l a y s d e c e l e r a t i n g f low f o l l o w e d by a f l a t r e g i o n i n d i c a t i v e of boundary l a y e r s e p a r a - t i o n . The g rowth o f t h e boundary l a y e r t h i c k n e s s o v e r t h e l a s t n i n e t r a i l i n g - e d g e t h i c k n e s s e s is
t o t h e p r e m a t u r e boundary l a y e r s e p a r a t i o n . I n t e r m s o f t h e r a t i o of momentum t h i c k n e s s t o t r a i l i n g - e d g e t h i c k n e s s , t h e p r e s s u r e s u r f a c e v a l u e a t x l t = -1 was 0 . 2 0 4 . Ups t ream of s e p a r a t i o n on t h e s u e t i o n s u r f a c e ( x / t = - 9 . 4 ) t h e r a t i o was 0 .225 . These values, a s i n t h e case o f low load - i n g , a r e w i t h i n t h e R e f . 1 C D A c a s c a d e range.
I n summary, h o t f i l m measuremen t s t a k e n up- s t r e a m o f t h e t r a i l i n g edge showed boundary layer c h a r a c t e r i s t i c s c o n s i s t e n t w i t h t h e imposed p r e s - sure g r a d i e n t h i s t o r i e s . Momentum t o t r a i l i n g - e d g e t h i c k n e s s r a t i o h e r e i n t h e range t y p i c a l o f C D A c a s c a d e s used i n f u l l scale a p p l i c a t i o n s .
f rom a p p r o x i m a t e l y 1 . 5 t t o 2 . 7 t . T h i s i s f i v e times t h e r a t e f o r t h e low l o a d i n g c 8 5 e . The s h a p e f a c t o r s t a r t s a t a v e r y h i g h v a l u e o f 2 . 0 and i n - creases t o 3 . 2 , i n d i c a t i v e of boundary l a y e r s e p a r - a t i o n . T h i s is c o n s i s t e n t w i t h f low v i s u a l i z a t i o n which showed an u n s t e a d y ( i n t e r m i t t e n t ) f low s e p a r - a t i o n e x i s t e d over t h e l a s t 5 - 6 t r a i l i n g - e d g e
V o r t e x s h e d d i n g from t h e model t r a i l i n g edge was p r e s e n t f o r b o t h t h e low and h i g h l o a d i n g cases a s i n d i c a t e d by h o t f i l m a u t o s p e c t r a l d e n s i t y func- t i o n s t a k e n i n t h e wake. R e s u l t s a r e g e n e r a l l y s i m i l a r t o t h e p r e v i o u s un loaded e x p e r i m e n t ( f l a t
~r~~~ ~~
~~~~ ~~ - - ~ ~ I~
~uremenfs occur i n t h e x / t = - 4 . 9 and x / t = -0.8 peaked cha rac t e r i s t i c s '
p r o f i l e s . T h e r e f o r e , t h e i n t e g r a l q u a n t i t i e s a r e Low Loading - The c e n t e r o f F i g . 6 d i s p l a y s somevhar a f f e c t e d by t h e s e errors, b u t n o t s i g n i f i - L D V and h o t f i l m mean v e l o c i t y wake p r o f i l e s t a k e n c a n t l y , s i n c e t h e d i f f e r e n c e between t h e measured a t x l t = 6.0 f o r t h e low l o a d i n g case (where and c o r r e c t v e l o c i t y i s sma l l r e l a t i v e t o t h e f r e e - in the s t r e a m v e l o c i t y . p r o f i lcs i l ? u u s t r a t e where t h e c o r r e s p o n d i n g L D V
In law-of-the-wal' coo rd ina te s , the p re s su re h i s t o g r a m s and h o t f i l m s p e c t r a ! d i s t r i b u t i o n s were s u r f a c e boundary l a y e r s were Very t o the t a k e n (shown On t h e l e f t and r i g h t o f t h e f i g u r e ) . low l o a d i n g p r o f i l e s . However, none o f t h e s u c t i o n s u r f a c e p r o f i l e s d i s p l a y e d l o g - l i n e a r b e h a v i o r due
=ds2 + u 2 1. The l o c a t i o n s ( a )
i,
U - a Uy Uy+o
o - LDV 0 - HOT FILM
10
Yl f 0 b- z W
W Q
Y2 D
0
10 0
-5
0 -0 5 05
250 500 UyJ'JreI
0 FREQUENCY (Hr)
Fig. 6 Spectrallhistogram distributions at x / t =6.0
7
The agreemen t be tween LDV and h o t f i l m mean v e l o c - i t y i s r e a s o n a b l e d e s p i t e a h i g h l o c a l t u r b u l e n c e i n t e n s i t i e s o f 40 p e r c e n t . On t h e l e f t - h a n d s i d e o f F i g . 6 are t h r e e s p e c t r a l d i s t r i b u t i o n s ( h o t f i l m ) c o r r e s p o n d i n g t o l o c a t i o n s ( a ) - ( c ) . The a n a l y z e r bandwid th i s 1 . 8 Hz. Eacep t f o r t h e spec - t r a l d i s t r 4 b u t i o n s n e a r t h e maximum wake d e f e c t , a l l t h e S p e c t r a showed a 130 Hz d i s c r e t e f r e q u e n c y s i g n a l r e l a t i v e t o a broadband ( r a n d o m ) , t u r b u l e n t wake s i g n a l . T h i s d i s c r e r e f r e q u e n c y i s a s s o c i a t e d w i t h t h e fundamen ta l p e r i o d o f t h e s h e d d i n g c y c l e f rom one s i d e o f t h e t r a i l i n g e d g e . A t t h e wake e d g e ( n o s p e c t r a shown) , where t h e b roadband random s i g n a l i s small and t h e e n t i r e v o r t e x s h e d d i n g s p i k e can be seen, i t i s e v i d e n t t h a t t h e " d i s c r e t e " f r e q u e n c y i s q u i t e v i d e and i s t h u s a c t u a l l y a narrow band random s i g n a l . T h i s sug- g e s t s t h e s h e d d i n g f r rq i l ency m o d u l a t e s , p re sumab ly d u e t o random v a r i a t i o n s o f t h e i n l e t boundary
.At t h e manimun d e f s c t l o c a t i o n ( b ) , t h e spec - t r a l d i s t r i b u t i o n c o n t a i n s an a d d i t i o n a l d i s c r e t e f r e q u e n c y o f t w i c e t h e f u n d a m e n t a l . T h i s i s due t o t h e h o t f i l m s e n s i n g s h e d d i n g f r m b o t h s i d e s . The r e l a t i v e b roadband random s i g n a l i s g r e a t e r a t t h i s l o c a t i o n . These o b s e r v a t i o n s a r e c o n s i s t e n t w i t h t h e un loaded c a s e o f R e f . 2 .
T h e c o r r e s p o n d i n g t r a n s v e r s e (E ) v e l o c i t y component h i s t o g r a m s (LOV) a t l o c a t i o n s ( a ) - ( c ) a r e shown on t h e r i g h t - h a n d s i d e o f F i g . 6 . Each h i s t o g r a m p l o t s t h e p e r c e n t a g e o f r e a l i z a t i o n s w i t h i n a b i n v e r s u s v e l o c i t y . A t t h e edge of t h e wake ( n o t shown) t h e t r a n s v e r s e component i s c h a r - a c t e r i z e d by a m a l l m s v a l u e w i t h a s l i g h t l y n e g a t i v e mean v a l u e . The n e g a t i v e mean v a l u e i s due t o t h e f l o w d e v i a t i o n from t h e e x i t m e t a l a n g l e ( x a x i s ) a s d i s c u s s e d l a t e r . Ha l fway t h r o u g h one s i d e o f t h e wake , ( a ) and ( c ) , t h e e f f e c t o f t h e v o r t e x s h e d d i n g i s a p p a r e n t . Examining t h e ( a ) l o c a t i o n , t h e h i s t o g r a m i s skewed , c h a r a c t e r i z e d by a s h a r p peak on t h e l e f t s i d e o f t h e mean v a l u e and a l o n g t a i l on t h e r i g h t s i d e o f t h e mean. The ( c ) l o c a t i o n i s s i m i l a r t o t h e ( a ) l o c a t i o n e x c e p t t h a t t h e o r i e n t a t i o n o f t h e peak and t a i l r e l a t i v e t o t h e mean v a l u e a re r e v e r s e d . These o b s e r v a t i o n s a r e c o n s i s t e n t w i t h t h e u n l o a d e d c a s e of R e f . 2 .
l a y e r s .
Y
A t t h e c e n t e r o f t h e wake, ( b ) , t h e h i s t o g r a m is n e a r l y f l a t . T h i s i s i n c o n t r a s t t o t h e un load- e d ease which showed a d e f i n i t e d o u b l e peaked h i s - t o g r a m w i t h v e r y few near-mean r e a l i z a t i o n s . The s o l i d l i n e in t h e ( b ) h i s t o g r a m i s t h e a p p r o x i m a t e d i s t r i b u t i o n o f t h e un loaded c a s e . P e r h a p s t h e d i f f e r e n c e i s due t o more t u r b u l e n t mix ing o f t h e v o r t e x s t r u c t u r e f o r t h e l o a d e d c a s e .
High L o a d i n g - The c o r r e s p o n d i n g s p e c t r a l d i s t r i b u t i o n s and h i s t o g r a m s f o r t h e h i g h l o a d i n g case ( n o t shown) a r e s i m i l a r t o t h e low l o a d i n g c a s e e x c e p t f o r one n o t a b l e change . The fundament - al s h e d d i n g f r e q u e n c y i s less t h a n h a l f t h e low l o a d i n g v a l u e . I t a p p e a r s t h a t t h i s change i s r e l a t e d t o t h e boundary l a y e r d i s p l a c e m e n t t h i c k - ness o f t h e a p p r o a c h i n g boundary l a y e r s .
To c o r r e l a t e t h e shedd ing f r e q u e n c i e s o f t h e d i f f e r e n t c a s e s , t h e S t r o u h a l number , S t = f l / U , was c a l c u l a t e d . Here f is t h e v o r t e x s h e d d i n g
t h e a v e r a g e f r e e s t r e a m v e l o c i t y i n t h e t r a i l i n g - e d g e r e g i o n . Us ing t h e t r a i l i n g - e d g e t h i c k n e s s as t h e c h a r a c t e r i s t i c l e n g t h g i v e s values of 0 . 1 6 and 0 . 0 8 f o r t h e l o w and h i g h l o a d i n g c a s e s , r e s p e c t - i v e l y . However, u s i n g a c h a r a c t e r i s t i c l e n g t h b a s e d on t h e t r a i l i n g - e d g e t h i c k n e s s p l u s t h e b o u n d a r y l a y e r d i s p l a c e m e n t t h i c k n e s s e s ( p r e s s u r e and s u c t i o n ) , c a l c u l a t e d j u s t u p s t r e a m o f t h e t r a i l i n g e d g e , y i e l d s S t r o u h a l numbers o f 0 . 2 3 and 0 . 1 9 . These v a l u e s a re more t y p i c a l o f b l u f f body s h e d d i n g . For t h e un loaded c a s e t h e S t r o u h a l number ( w i t h d i s p l a c e m e n t t h i c k n e s s e s a d d e d ) w a s 0 . 2 2 which is i n good ag reemen t w i t h t h e c u r r e n t r e s u l t s . No te , u s i n g t h e momentum t h i c k n e s s t o c a l c u l a t e t h e e f f e c t i v e t h i c k n e s s d i d no t c o l l a p s e t h e d a t a ( t h e v a l u e s were 0 . 2 0 and 0.12 f o r t h e low and h i g h l o a d i n g , c a s e s r e s p e c t i v e l y .
f r e q u e n c y , 1 i s t h e c h a r a c t e r i s t i c l e n g t h , and U i s L,
Plow Visualization
Flow v i s u a l i z a t i o n was used t o d e f i n e t h e two- d i m e n s i o n a l i t y o f the f low and t h e l o c a t i o n O f
s e p a r a t i o n l i n e s . The main t e c h n i q u e u s e d i n t h i s e x p e r i m e n t was a form o f t h e a m n o n i d r e a c t o r met!iod f o r s u r f a c e flow v i s u a l i z a t i o n . Smoke v i s u a l i z a - t i o n was used t o b e t t e r d e f i n e t h e s e p a r a t i o n on t h e s u c t i o n s u r f a c e o f t h e h i g h l o a d i n g c a s e .
D e t a i l e d r e s u l t s a r e shown i n Ref . 12 and a r e b r i e f l y d i s c u s s e d h e r e . ,d
Low L o a a i n g - The f low on t h e p r e s s u r e s u r - f a c e w a s o b s e r v e d t o b e two-d imens iona l over n e a r l y t h e e n t i r e s p a n o f t h e model . On t h e s u c t i o n s u r - f a c e t h e r e was a n o t i c a b l e m i g r a t i o n of t h e f low t o w a r d s t h e c e n t e r o f t h e s p a n d u e t o c o m e r bound- a r y l a y e r i n t e r a c t i o n w i t h c a s c a d e p r e s s u r e g r a d i - e n t s . Such m i g r a t i o n i t t y p i c a l of e x p e r i m e n t a l c a s c a d e s where corner s u c t i o n i s u s u a l l y a p p l i e d t o r e d u c e t h e i n t e r a c t i o n . 1 u For t h i s c a s e , no c o r n e r s u c t i o n was a p p l i e d s i n c e t h e f low w a s two- d i m e n s i o n a l over 65 p e r c e n t o f t h e s p a n . For b o t h s u r f a c e s , t h e f l o w was found t o s e p a r a t e on t h e t r a i l i n g - e d g e c i r c l e . a t a p p r o x i m a t e l y a n 1 R d e g r e e a n g u l a r l o c a t i o n (measu red f rom t h e p r e s s u r e s u r f a c e l t r a i l i n g - e d g e i n t e r f a c e ) . It i s presumed t h a t s e p a r a t i o n p o i n t s are u n s t e a d y due t o t h e v o r t e x s h e d d i n g and l a c k o f a s a l i e n t edge . The p r e s s u r e s u r f a c e s e p a r a t i o n l i n e was n o t i c e a b l y more d e f i n e d t h a n t h e s u c t i o n s u r f a c e ( i . e . , t h e p r e s s u r e s u r f a c e t r a c e ended more a b r u p t l y ) . T h e r e f o r e , t h e s u c t i o n s u r f a c e s e p a r a t i o n l i n e a p p e a r s t o be more u n s t e a d y r e l a t i v e t o t h e p r e s - sure s u r f a c e s e p a r a t i o n .
It was o b s e r v e d t h a t t h e s u c t i o n s u r f a c e f low t u r n s o n t o t h e t r a i l i n g edge a p p r o x i m a t e l y one d e g r e e f u r t h e r t h a n t h e p r e s s u r e s u r f a c e f l o w . The b o u n d a r y l a y e r measurements from t h e h o t f i l m and LDV d a t a c l e a r l y show t h e pressure s u r f a c e boundary
f a c t o r d i s t r i b u t i o n t h a n t h e s u c t i o n boundary l a y e r ( d u e t o t h e f a v o r a b l e and a d v e r s e p r s s s u r z g r a d i e n t
l a y e r t o b e c h a r a c t e r i z e d by a much h e a l t h i e r s h a p e ..-
h i s t o r i e s a c t i n g on t h e p r e s s u r e and s u c t i o n sur- f a c e s , r e s p e c t i v e l y ) . Thus b a s e d on t h e boundary l a y e r d a t a , t h e p r e s s u r e s u r f a c e boundary l a y e r
-' v o u l d be e x p e c t e d t o t u r n more t h a n t h e s u c t i o n s u r f a c e boundary l a y e r (which i s n o t t h e ease) . T h i s s u g g e s t s t h a t h i g h s u r f a c e C u r v a t u r e on t h e t r a i l i n g - e d g e c i r c l e overcomes t h e e f f e c t o f a h e a l t h i e r b o u n d a r y l a y e r .
a L o a d i n g - L i k e t h e low l o a d i n g c a s e ,
t h e f l o w on t h e p r e s s u r e s u r f a c e was o b s e r v e d t o b e t w o - d i m e n s i o n a l ove r n e a r l y t h e e n t i r e s p a n . For t h e ' s u c t i o n surface i t wes n e c e s s a r y t o a p p l y corn- er s u c t i o n t o a c h i e v e any semblance o f a two- d i m e n s i o n a l r e g i o n . W i t h corner s u c t i o n i t was p o s s i b l e t o a c h i e v e a two-dimens iona l r e g i o n over 35 p e r c e n t o f t h e s p a n .
The p r e s s u r e s u r f a c e s e p a r a t i o n w a s v e r y s i m - i l a r t o t h e low l o a d i n g case. The f l o w a P p e a r e d t o n e g o t i a t e t h e t r a i l i n g - e d g e c i r c l e s l i g h t l y f u r t h e r t o a 19 - 20 d e g r e e ailgular l o c a t i o n . On t h e suc- t i o n s u r f a c e , t h e f l o w was o b s e r v e d t o S e D a r a t e 5 - 6 t r a i l i n g - e d g e t h i c k n e s s e s u p s t r e a m o f t h e t r a i l - i n g e d g e . The s e p a r a t i o n l i n e , however, was n o t c l e a r l y d e f i n e d and t h u s i s a p p a r e n t l y i n t e r m i t t e n t i n n a t u r e . I n t e r m i t t e n t s u c t i o n s u r f a c e s e p a r a t i o n h a s a l s o b e e n o b s e r v e d by Deutsch and Z i e r k e . "
The reason f o r t h e o b s e r v e d p r e m a t u r e boundary l a y e r s e p a r a t i o n i s t h e a d v e r s e p r e s s u r e g r a d i e n t on t h e s u c t i o n s u r f a c e . The i n c r e a s e d l o a d i n g ( a n d t h u s a d v e r s e p r e 5 s u r e g r a d i e n t ) f o r t h i s c a s e h a s b e e n s u f f i c i e n t t o cause t h e boundary l a y e r t o s e p a r a t e p r i o r t o t h e t r a i l i n g e d g e .
w Smoke Plow V i s u a l i z a t i o n - A S d i s c u s s e d i n
t h e LDV r e s u l t s , t h e r e i s an a b s e n c e o f t ime mean r e v e r s e d f low i n t h e s u c t i o n s u r f a c e s e p a r a t i o n b u b b l e f o r t h e h i g h l o a d i n g c a s e a s measured w i t h Lnv. S i n c e surface f l o w v i s u a l i z a t i o n c m n o t pro- v i d e i n f o r m a t i o n on i n t e r m i t t e n t s e p a r a t i o n s t a t i s - t i c s , smoke v i s u a l i z a t i o n u s i n g s t r o b o s c o p i c v i d e o
w a s employed . A smoke g e n e r a t i n g probe ( h e a t e d oil, a t o m i z a t i o n t y p e ) was f l u s h mounted t o t h e s u c t i o n s u r f a c e a p p r o x i m a t e l y 0 . 4 t r a i l i n g - e d g e t h i c k n e s s e s u p s t r e a m of t h e t r a i l i n g e d g e . S t r o b e l i g h t s w e r e S e t a t 30 Hz t o match t h e f r a m i n g of t h e v i d e o camera.
I n a r e a l - t i m e mode ( i . e . , normal v i d e o p lay- b a c k ) t h e flow was c l e a r l y r e v e r s e d ( u p s t r e a m ) t h e m a j o r i t y of t h e t i m e ( a p p r o x i m a t e l y 80 p e r c e n t o f t h e t i m e ) . Smoke f l o w v i s u a l i z a t i o n a n a l y z e d f rame-by-f rame showed t h a t t h e f l o w w a s c l e a r l y u p s t r e a m 50 p e r c e n t o f t h e time, i n d e t e r m i n a t e 40 p e r c e n t o f t h e t ime, and downstream 10 p e r c e n t o f t h e t i m e . However, t h e LUV d a t a i n d i c a t e d maximum r e v e r s e d f l o w r e a l i z a t i o n s of o n l y 20 p e r c e n t o f t h e s a m p l e . I n c o n c l u s i o n , t h e LUV d a t a i s c l e a r l y b i a s e d i n t h i s r e g i o n .
The u p s t r e a m e x t e n t o f t h e u n s t e a d y s e p a r a t i o n b u b b l e o b s e r v e d i n smoke f l o w s t u d i e s w a s 5 t o 6 t r a i l i n g - e d g e t h i c k n e s s e s . T h i s is c o n s i s t e n t w i t h t h e s e p a r a t i o n l i n e deduced from t h e s u r f a c e flow
t/ v i s u a l i z a t i o n . A l s o , t h e s t r o b e f r e q u e n c y was v a r i e d close t o t h e f u n d a m e n t a l s h e d d i n g f r e q u e n c y
i n an a t t e m p t t o b e a t w i t h any p e r i o d i c m a t i o n s . S i n c e no p e r i o d i c S t r u c t u r e was o b s e r v e d , it is c o n c l u d e d t h a t t h e i n t e r m i t t e n t s e p a r a t i o n i s ran- dom i n n a t u r e a n d n o t d r i v e n by t h e v o r t e x s h e d d i n g .
I n summary, smoke f l o w v i s u a l i z a t i o n i n d i c a t e d a t i m e mean s e p a r a t i o n l i n e welt u p s t r e a m of t h e t r a i l i n g edge f o r t h e h i g h l o a d i n g c a s e . T r a c k i n g o f u p s t r e a m c o n v e c t e d e d d i e s c o n f i r m e d t h i s s e p a r a - t i o n l o c a t i o n and d e m o n s t r a t e d t h e i n h e r e n t l y u n s t e a d y , random and i n t e r m i t t e n t n a t u r e of t h e s e p a r a t i o n . I n t e r m i t t e n t s u c t i o n s i l r f a c e s e p s r a - t i o n h a s b e e n o b s e r v e d i n t h e d o u b l e c i r c u l a r a rc a i r f o i l c a s c a d e of Ref . 1 4 . I n t e r m i t t e n t s e p a r a - t i o n of t h e t u r b u l e n t boundary l a y e r s on f l a t p l a t e t e s t s u r f a c e s caused by imposed a d v e r s e p r e s s u r e g r a d i e n t s h a s also been s t u d i e d by p a t r i c k 6 among o t h e r s . Such i n t e r m i t t e n c y a p p e a r s t o be a c h a r a c - t e r i s t i c o f s e p a r a t i o n from s u r f a c e s h a v i n g low s u r f a c e c u r v a t u r e . On t h e t r a i l i n g - e d g e circle, t h e h i g h C u r v a t u r e f o s t e r s s e p a r a t i o n a t a p p r o x i - m a t e l y f i x e d l o c a t i o n .
T r a i l i n g - E d g e Region s t a t i c Pressure U i a t r i b u t i o n
I n o r d e r t o compare t h e t r a i l i n g - e d g e p r e s s d r e d i s t r i b u t i o n s among t h e two l o a d i z g cases and t h e u n l o a d e d c a s e o f Paterson and Weingold, ' i t i s n e c e s s a r y t o s c a l e t h e s u r f a c e p r e s s u r e s i n a d i f f e r e n t manner t h a n used p r e v i o u s l y . Casca6e e x i t s t a t i c p r e s s u r e i s a s u i t a b l e p r e s s u r e r e f e r - e n c e f o r t h e c u r r e n t s t u d y and c a n be c o n s i d e r e d t o c o r r e s p o n d t o t h e c o n s t a n t f r e e s t r e a m s t a t i c p r e s - sure r e f e r e n c e u s e d i n t h e p r e v i o u s u n l o a d e d s t u d y . U s i n g e x i t c a s c a d e s t a t i c p r e s s u r e as a r e f e r e n c e , t h e t r a i l i n g - e d g e p r e s s u r e c o e f f i c i e n t , C t e , i s d e f i n e d as a n d r e l a t e d t o C by ( n o t e , tge sub- s c r i p t " t e " r e f e r s t o t h e t r a i l i n g - e d g e s c a l i n g ) . P .
w h e r e Q,, = ( P t - P t e ) , Pt i s t h e i n l e t t o t a l p r e s - s u r $ , a n d P t e i s t h e c a ~ c a d e e x i t p r e s s u r e . The d y n a m i c h e a d r a t i o , Q r e f / Q t , , i s 1.133 and 1 . 7 5 4 f o r t h e low and h i g h l o a d i n g cases , r e s p e c t i v e l y .
S u r f a c e p r e s s u r e d a t a over t h e l a s t e i g h t t h i c k n e s s e s a r e shown i n F i a . l a and l a s t two t h i c k n e s s e s i n F i g . 7b i n t e rm of t h e a b o v e d e s c r i b e d t r a i l i n g - e d g e s c a l i n g . I n a d d i t i o n t o t h e two l o a d i n g c a s e s of t h e current e x p e r i m e n t , t h e u n l o a d e d c a s e of P a t e r s o n and Weingold i s a150
shown. A s i n d i c a t e d , t h e t r a i l i n g - e d g e s u r f a c e e x t e n d s over t h e r e g i o n s i t < n j 4 . A l s o , p r e s s u r e a n d s u c t i o n s u r f a c e s e p a r a t i o n s a r e i n d i c a t e d by arrows l a b e l e d "Press. S e p . " and " S u e t . Sep." r e s p e c t i v e l y as i n d i c a t e d by s u r f a c e f l o w v i s u a l - i z a t i o n .
9
OPEN SYMBOLS - LOW LOADING CLOSED SYMBOLS - HIGH LOADING
Low L o a d i n g - For t h e low l o a d i n g c a s e , t h e p r e s s u r e s u r f a c e d i s t r i b u t i o n (open s q u a r e s ) over the l a s t 8 t i s c h a r a c t e r i z e d by d e c r e a s i n g p r e s s u r e f r o m a value above t h e c a s c a d e e x i t p r e s s u r e , t h r o u g h t h e e x i t v a l u e a t s / t = 2 . 3 , t o a l o c a l minimum on t h e t r a i l i n g - e d g e c i r c l e . On t h e t r a i l i n g - e d g e c i r c l e t h e p r e s s u r e q u i c k l y r i s e s ( w i t h a s l i g h t o v e r s h o o t ) t o t h e base p r e s s u r e v a l u e ( - 0 . 2 ) . T h e a n g u l a r l o c a t i o n on t h e t r a i l i n g - e d g e c i r c l e of t h e l o c a l minimum p r e s s u r e i s a p p r o x i m a t e l y 8 .5 d e g r e e s measured f rom t h e pressure s u r f a c e i t r a i l i n g - e d g e c i r c l e i n t e r f a c e . Flow v i s u a l i z a t i o n i n d i c a t e d boundary l a y e r s e p a r a - t i o n o c c u r r e d a t a 1 7 d e g r e e l o c a t i o n ( a s shown i n t h e f i g u r e s ) . Based on t h e s e o b s e r v a t i o n s , t h e l o c a l minimum i s d u e t o t h e l o c a l t u r n i n g (expan- s i o n ) on t h e t r a i l i n g - e d g e c i r c l e . When t h e p r e s - sure b e g i n s t o r ise ( t o m a t c h t h e t r a i l i n g - e d g e pressure) t h e a d v e r s e g r a d i e n t q u i c k l y s e p a r a t e s t h e boundary l a y e r . T h i s i s c o n s i s t e n t w i t h t h e u n l o a d e d case 8s d i s c u s s e d s h o r t l y . A s a l i e n t t r a i l i n g e d g e , s u c h 8 s a s q u a r e d o f f c o n f i g u r a t i o n , would n o t e x p e r i e n c e t h i s t y p e of "overspeed" .
The s u c t i o n surface pressure d i s t r i b u t i o n i s : h a r a c t e r i z e d by a r e l a t i v e l y s l o w , m o n o t o n i c p r e s - sure rise t o t h e t r a i l i n g - e d g e v a l u e . It i s n o t e d t h a t f l o w v i s u a l i z a t i o n i n d i c a t e d t h e s u c r i o n sur- face boundary l a y e r s e p a r a t e d a t an a n g u l a r l o c a - t i o n of 1 8 d e g r e e s on t h e t r a i l i n g - e d g e c i r c l e .
Since t h e d i s t r i b u t i o n d i s p l a y s no a p p r e c i a h l e c h a n g e s i n t h e v i c i n i t y o f 1 8 d e g r e e s , i t a p p e a r s t h a t no s i g n i f i c a n t l o c a l t u r n i n g h a s o c c u r r e d .
.-,' Kigh Loading - The h i g h load ing case i s
c h a r a c t e r i z e d by s e v e r a l n o t a b l e d i f f e r e n c e s r e l a - t i v e t o t h e low l o a d i n g c a s e . nos t o b v i o u s i s t h e lower base p r e ~ s u r e value ( -0 .32 ) . The s u c t i o n s u r f a c e d i s t r i b u t i o n ( s o l i d c i r c l e s ) is nearly f l a t over t h e l a s t 5 t r a i l i n g e d g e t h i c k n e s s e s due t o t h e s e p a r a t i o n u p s t r e a m o f t h e t r a i l i n g e d g e , hav- i n g a value e q u a l t o t h e b a s e p r e s s u r e v a l u e . The p r e s s u r e s u r f a c e d i s t r i b u t i o n ( s o l i d squares) , up- s t r e a m 6 t - 8 t , i s t h e same as t h e low l o a d i n g c a s e .
Near t h e t r a i l i n g edge t h e p r e s s u r e b e g i n s t o d r a p more r a g i d l y t o t h e lower base pressure v a l u e . Tne n e a r t r a i l i n g - e d g e d i s t r i b u t i o n d i s p l a y s a more n e g a t i v e l o c a l minimum pressure ( r e l a t i v e t o b a s e p r e s s u r e ) t h a n the l o w l o a d i n g c a s e , a l t h o u e h t h e p r e s s u r e boundary l a y e r s e p a r a t i o n l i n e was n e a r l y t h e same f o r b o t h c a s e s . Thus t h i s h i g h e r "over- s p e e d " i s p r o b a b l y due t o t h e g r e a t e r p r e s s u r e d i f - f e r e n c e be tween t h e u p s t r e a m ( a t s i t = 8 ) p r e s s u r e s u r f a c e and b a s e p r e s s u r e values,
I f t h i s t r a i l i n g - e d g e s c a l i n g is relevant, t h e n presumably d i f f e r e n t l o a d i n g c a s e s (with f i x - same t r a i l i n g e d g e ) f o r w h i c h t h e s u c t i o n boundary l a y e r r e r a i n s a t t a c h e d u p t h e t r a i l i n g e d g e , w m 1 3 c o l l a p s e t o t h e C u r r e n t low l o a d i n g c a s e d i s t r i b u - t i o n . T h u s , i t is s p e c u l a t e d t h a t t h e lower ba!;e p r e s s u r e v a l u e f o r t h e h i g h l o a d i n g c a s e i s due t ? loss i n p r e s s ~ ~ r e r e c o v e r y on t h e s u c r i o n s u r f a c e
s i n p l i f i e d v i e w o f t h i s complex i n t e r a c t i o n p r o c e s s i s t h a t t h e amount of s u c t i o n s u r f a c e pressure r e c o v e r y d e t e r m i n e d t h e b a s e p r ~ s s u r e v a l u e and t h e p r e s s u r e surface f l o w a c c e l e r a r e d t o t h i s v a l u e .
i r o n t h e p r e m a t u r e boundary l a y e r s e j ~ a r a t i o n . 4 W
Unloaded Case - The unloaded case s t u d i a d by Paterson and Weingold' i s compared w i t h t h e c u r r e n t d a t a i n F i g s . 7 . T h e i r e x p e r i m e n t a l model y e s a f l a t p l a t e t e r m i n a t e d w i t h t h e same t r a i l i n g - e d g e g e o m e t r y . Wind t u n n e l s p e e d s and s c a l e s ( t r a i l i n g - e d g e s i r e and r e l a t i v e boundary l a y e r t h i c k n e s s e s ) were similar t o t h e C u r r e n t e x p e r i m e n t . The bound- a r y c o n d i t i o n s on t h e model were c o n s t a n t f r e e - S t r e a m v e l o c i t y u p s t r e a m and downstream o f t h e t r a i l i n g edge . Thus t h i s e x p e r i m e n t i s o l a t e d t h e e f f e c t s of t h e t r a i l i n g e d g e f rom o v e r a l l t u r n i i g e f f e c t s .
The u n l o a d e d c a s e i s shown as t h e d a s h e d l i n e i n t h e f i g u r e s . S i n c e t h i s c a s e was s y m m e t r i c a l , t h e d a s h e d l i n e r e p r e s e n t s b o t h t h e u p p e r and lbwer surfaces. As Shown i n F i g . 7 a , t h e p r e s s u r e a t s / t = 8 i s t h e ( c o n s t a n t ) f r e e s t r e a m va lue . Downstream of t h i s p o i n t t h e e f f e c t s of t h e t r a i l i n g edge b e g i n t o lower t h e p r e s s u r e be low t h i s v a l u e . h a t is , t h e local i n v i s c i d f low b e g i n s t o a c c e l e r a t e . Over t h e l a s t t r a i l i n g - e d g e t h i c k n e s s ( s i t < 1.25) the d i s t r i b u t i o n is r e m a r k a b l y similar t o t h e low l o a d i n g p r e s s u r e surface d i s t r i b u t i o n ( F i g . 7 b ) . The b a s e p r e s s u r e va lues f o r t h e u n l o a d e d and low l o a d i n g c a s e 8 are i d e n t i c a l . -'
The s t a t i c p r e s s u r e d i s t r i b u t i o n downst ream o f t h e t r a i l i n g e d g e f o r t h e u n l o a d e d case was also r e p o r t e d i n R e f . 2 . The d i s t r i b u t i o n from t h e
‘rJ t r a i l i n g - e d g e v a l u e ( -0 .20) d e c r e a s e d r a p i d l y t o B minimum a t x l t = 0 . 4 ( - 0 . 2 9 ) b e f o r e b e g i n n i n g a m o n o t o n i c r i s e t o t h e ( c o n s t a n t ) f r e e s t r e a m v a l u e a t x / t = 3.5. T n i s minimum v a l u e was a s s o c i a t e d w i t h v o r t e x s h e d d i n g f o r m a t i o n , a r e s u l t and con- c l . u s i o n a l s o found by R o ~ h k o l ~ f a r c y l i n d e r wakes .
In b o t h t h e un loaded f l a t p l a t e s t u d y and t h e c y l i n d e r s t u d y i t was shown t h a t s u p p r e s s i o n of v o r t e x s h e d d i n g by i n s e r t i o n of a wake s p l i t t e r p l a t e l a r g e l y e l i m i n a t e d t h i s n e a r wake minimum and r a i s e d b a s e p r e s s u r e s i g n i f i c a n t l y . T h u s , t r a i l i n g - e d g e s e p a r a t i o n c o n t r i b u t e s t o low b a s e pressure f i r s t by p r e v e n t i n g recovery o f p r e s s u r e a t a r e a r s t a g n a t i o n p o i n t and s e c o n d l y by produc- i n g f r e e s h e a r l a y e r s which r i r l l - u p i n t o a v o r t e x s t r e e t . The good ag reemen t be tween low l o a d i n g and u n l o a d e d c a s e b a s e p r e s s u r e s s u g g e s t 5 s e p a r a t i o n l o c a t i o n s ( R e f . 2 r e p o r t e d a 16’ a n g u l a r l o c a t i o n compared t o 1 7 - 18” f o r t h e low l o a d i n g ) and “ o r - t e x s h e d d i n g c h a r a c t e r i s t i c s were s i m i l a r . The f u r t h e r d e p r e s s i o n i n b a s e p r e s s u r e w i t h t h e h i g h l o a d i n g c o n f i g u r a t i o n , which also d i s p l a y e d v o r t e x s h e d d i n g , a p p e a r s t o be due t o f a i l u r s o f t h e s u c - t i o n s u r f a c e f l o w t o t u r n toward t h e t r a i l i n g - e d g e c e n t e r l i n e (and recover p r e s s u r e ) due t o u p s t r e a m s e p a r a t i o n .
T r a i l i n g - E d g e Hem V e l o c i t y F i e l d
Low L o a d i n g - V e c t o r r c p r e s e n t a t i o n o f t h e LDV v e l a c i t y d a t a i s shown i n F i g . 8 f o r t h e low l o a d i n g c a s e . 4 d e t a i l of t h e n e a r t r a i l i n g - e d g e r e g i o n i s s h o r n i n F i g . 9 . S e p a r a t i o n l o c a t i o n s on t h e mode l , d e r i v e d from s u r f a c e f l o w v i s u a l i z a t i o n , a r r i n d i c a t e d i n t h e s e f i g u r e s by arrows. Each v e c t o r r e p r e s e n t s t h e e s t i m a t e d t i m e mean magn i tude a n d f l o w d i r e c t i o n o f t h e v e l o c i t y . The u n i t l e n g t h o f t h e v e c t o r r e l a t i v e t o t h e r e f e r e n c e v e l o c i t y ( U r e f , i n l e t v e l o c i t y ) is shown i n t h e f i g u r e s . The numbers i n d i c a t e t h e f r e e s t r e a n p r e s - s u r e c o e f f i c i e n t s , C t e ( b a s e d o n c a s c a d e e x i t c o n d i t i o n s as d e s c r i b e $ e a r l i e r ) , e s t i m a t e d by t h e v e l o c i t y d a t a a t t h e edges of t h e s u r v e y s . For t h i s s c a l i n g a v a l u e o f zero c o r r e s p o n d s t o a v a l u e equal t o t h e c a s c a d e e x i t v e l o c i t y .
As i l l u s t r a t e d i n t h e o v e r a l l v i e w , F i g . 8, t h e b o u n d a r y l a y e r s and f r e e s t r e a m f l o w a p p r o a c h i n g the t r a i l i n g edge are c l e a r l y a t t a c h e d and i n t h e general d i r e c t i o n o f t h e s u r f a c e . The p r e s s u r e surface boundary layer is o b s e r v e d t o be more full a n d h e a l t h i e r t h a n t h a t o f t h e s u c t i o n s u r f a c e . T h i s i s due t o t h e a p p o s i t e s u r f a c e p r e s s u r e g r a d i - e n t h i s t o r i e s u p s t r e a m o f t h e t r a i l i n g edge . The d i f f e r e n c e s i n t h e v e l o c i t y p r o f i l e s a r e q u a n t i f i e d by t h e s h a p e f a c t o r s d e s c r i b e d e a r l i e r . The h o t f i l m s s u r v e y s j u s t u p s t r e a m o f t h e t r a i l i n g e d g e g i v e s h a p e f a c t o r values o f 1 . 1 1 for t h e s u c t i o n s u r f a c e and 1.31 f o r t h e p r e s s u r e s u r f a c e . T h i s d i f f e r e n c e i n v e l o c i t y p r o f i l e s ( s h a p e f a c t o r )
W causes a c o r r e s p o n d i n g l a r g e r v e l o c i t y g r a d i e n t t h r o u g h t h e s h e a r l a y e r on t h e p r e s s u r e s i d e o f t h e wake.
AS o b s e r v e d i n F i g . 8, t h e e n t i r e f l o w f i e l d ( e x c l u d i n g the immedia te wake r e g i o n ) shows a gen- e ra l downward v e l o c i t y companen t . O u t s i d e t h e wake, t h e f l o w angle or t h e p r e s s u r e s i d e i s n e a r l y c o n s t a n t a t 6 degrees f rom the t r a i l i n g - e d g e metal a n g l e . For t h e s u c t i o n s i d e , t h e f l o w a n g l e is n e a r l y c o n s t a n t a t 4 d e g r e e s from t h e m e t a l angle. It i s n o t e v i d e n t what amount o f t he f l o w d e v i a t i o n i s due t o v i s c o u s e f f e c t s s i n c e t h e K u t t a c o n d i t i o n f o r B b l u n t - b a s e d a i r f o i l i s n o t well d e f i n e d .
I t s h o u l d b e n o t e d , t h e e x i t a n g l e o f t h e midgap s t r e a m l i n e s w a s n o m i n a l l y 9 d e g r e e s from t h e m e t a l a n g l e . This i s t h e e s t i m a t e o f t h e e x i t flow d e v i a t i o n t h a t was u s e d i n t h e p o t e n t i a l f l o w cas- c a d e a n a l y s i s ( b a s e d on a s e m i e m p i r i c a l d e v i a t i o n s y s t e m ) . A more a c c u r a t e e x p e r i m e n t a l s i m u l a t i o n would use t h e c u r r e n t f l aw d e v i a t i o n i n f o r m a t i o n t o
11
r e c a l c u l a t e t h e midgap s t r e a m l i n e l o c a t i o n s and t h e n r e p e a t t h e e x p e r i m e n t . T h i s would p resumab ly r e s u l t i n a c l o s e r agreement be tween t h e measu red e x i t f l o w a n g l e and t h e midgap s t r e a m l i n e e x i t a n g l e . However, i t i s b e l i e v e d t h a t t h e e r ror i n t h e midgap s t r e a m l i n e e x i t a n g l e i s o f second o r d e r i n f l u e n c e on t h e near t r a i l i n g - e d g e f l o w f i e l d . The p r i m a r y i n f l u e n c e b e i n g t h e v i s c o u s e f f e c t s on t h e a i r f o i l .
Downstream o f t h e t r a i l i n g edge t h e f low f rom b o t h s i d e s g e n e r a l l y t u r n s i n w a r d s , f i l l i n g i n t h e wake b e h i n d t h e t r a i l i n g edge . From F i g . 9 it i s c l e a r t h a t t h e f l o w from t h e p r e s s u r e s u r f a c e t u r n s more i n t o t h e wake t h a n t h e s u c t i o n s u r f a c e f l o w . T h i s g r e a t e r t u r n i n g i s most l i k e l y due t o t h e l a r g e r v e l o c i t y g r a d i e n t on t h e pressure s i d e s h e a r l a y e r . The p r o b a b l e mechanism i s i n c r e a s e d f l u i d e n t r a i n m e n t (compare t o t h e s u c t i o n s i d e s h e a r l a y e r ) which l o c a l l y r e d u c e s t h e p r e s s u r e on t h e low v e l o c i t y s i d e o f t h e s h e a r l a y e r , t h u s i n d u c i n g t h e p r e s s u r e s i d e s h e a r l a y e r t o t u r n more i n t o t h e wake . T h i s i n c r e a s e d p r r ~ s u r e s i d e t u r n i n g i n d u c e s t h e o u t e r flow on t h e p r e s s u r e s i d e t o d e v i a t e f u r t h e r from t h e m e t a l angle ( 6 d e g r e e s compared t o 4 d e g r e e s f o r t h e s u c t i o n s i d e ) .
Note t h a t a s i g n i f i c a n t normal p r e s s u r e g r a d i - e n t d o e s no t e x i s t i n t h e immedia t e i n v i s c i d r e g i o n downs t r eam of t h e t r a i l i n g e d g e , a 5 shown i n Fig. 9 by t h e f r e e s t r e a m p r e s s u r e c o e f f i c i e n t v a l u e s . Based on t h e s e o b s e r v a t i o n s , i t i s conc luded t h a t t h e i n v i s c i d normal p r e s s u r e g r a d i e n t d o e s not p l a y a r o l e i n t h e i n c r e a s e s p r e s s u r e s i d e t u r n i n g i n t o t h e wake.
I n t h e wake downst ream o f t h e t r a i l i n g e d g e a
s e p a r a t i o n b u b b l e w i t h two r e c i r c u l a t i o n r e g i o n s i s p r e s e n t ( a t l e a s t i n t h e t i m e mean sense) a s shown i n t h e d e t a i l e d v e c t o r p l o t o f F i g . 9. The a x i a l e x t e n t o f t h e s e p a r a t i o n b u b b l e i s a b o u t 1 . 5 c . The two r e c i r c u l a t i o n s a p p e a r t o be asymmetric. T h i s asymmetry i s b r o u g h t o u t i n t h e s t r e a m l i n e a n a l y s i s d i s c u s s e d s u b s e q u e n t l y . The u n l o a d e d case2 i n d i - c a t e d a t i m e mean s e p a r a t i o n b u b b l e w i t h two s p - m e t r i c r e c i r c u l a t i o n s , however , t h e b u b b l e was
s h o r t e r i n t h e a x i a l e x t e n t , c l o s u r e o c c u r r i n g a t 0.Rt . Also n o t e i n t h e f i g u r e , t h e f i r s t s u r v e y s downs t r eam o f t h e s e p a r a t i o n p o i n t s do n o t show r e v e r s e d f low s i n c e t h e s e p a r a t i o n i s v e r y t h i n r e l a t i v e t o t h e LDV s p a t i a l r e s o l u t i o n .
~
12
High L o a d i n g - The v e c t o r r e p r e s e n t a t i o n of t h e overall f l o w f i e l d f o r t h e h i g h l o a d i n g c a s e i s shown i n Fig. 10. A d e t a i l e d p l a t o f t h e n e a r t r a i l i n g - e d g e r e g i o n i s g i v e n i n R e f . 1 2 . I n i t i a l s u r v e y s o f t h e wake showed t h e t r a i l i n g - e d g e i n t e r - a c t i o n r e g i o n t o be l a r g e r t h a n t h a t f o r t h e low l o a d i n g f l o w f i e l d . Thus t h e i n c r e m e n t a l s p a c i n g o f d a t a p o i n t s was r o u g h l y d o u b l e d . C o r r e s p o n d i n g l y , t h e s c a l e an t h i s f i g u r e i s d i f f e r e n t f rom t h e low l o a d i n g case i n o r d e r t o a d e q u a t e l y d i s p l a y t h e f l o w f i e l d . A s c a l e d compar i son o f t h e two c a s e s i s g i v e n s u b s e q u e n t l y i n t e rms of t h e d i s p l a c e m e n t t h i c k n e s $ d i s t r i b u t i o n .
yll 0
- 2
- 4
-6 -6 - 4 4 8 12 O X l t
Fig. 10 Overall velocity vectors, high loading
I n F i g . IO, t h e f l o w over t h e p r e s s u r e s u r f a c e i s c l e a r l y a t t a c h e d , f o l l o w i n g t h e g e n e r a l d i r r c - t i o n o f t h e model . The s u c t i o n s u r f a c e f low d e v i - a t e s s i g n i f i c a n t l y f rom t h e model s u r f a c e d i r e c t i o n d u e t o t h e p r e m a t u r e boundary l a y e r s e p a r a t i o n 5 t t o 6 t u p s t r e a m o f t h e t r a i l i n g edge a s docunei iced b y t h e f l o w v i s u a l i z a t i o n ( and s u r f a c e p r e s s u r e s ) . However, t h e e s t i m a t e d t i m e mean v e l o c i t i e s i n d i - c a t e t h e f low c l o s e t o t h e s u r f a c e t o be i n t h e downst ream d i r e c t i o n . T h i s c o n f l i c t i n g r e su ! t i s d u e t o a l a r g e i n d i v i d u a l r e a l i r a i i o n b i a s c r e a : r d by t h e n a t u r e o f t h e f l o w f i e l d and s e e d d e n s i t y i n t h i s r e g i o n ( a n d t h u s i s r e s t r i c t e d t o t h i s r e d i o n ) .
A s d i s c u s s e d p r e v i o u s l y i n t h e f l o w v i s u n l i r a - t i o n s e c t i o n , t h i s r e g i o n i s c h a r a c t e r i z e d by Q
I a r j r s e p a r a t i o n b u b b l e e x t e n d i n g over t h e l a s t 6 t r a i l i n g - e d g e t h i c k n e s s e s o f t h e s i i c t i o n s u r f a c e f o r a p p r o x i m a t e l y 80 ( o u t no less t h a n 5 0 ) p e r c e n t o f t h e t i m e . The r e m a i n i n g p e r c e n t a g e o f t h e r i m e i s c h a r a c t e r i z e d by " b u r s t s " o f downst ream, c o r * f l o w . The s e p a r a t i o n b u b b l e h a s a low velocity and p resumab ly l o w s e e d d e n s i t y ( a s i s t h e e x p e r i e n c e w i t h s e p a r a t i o n b u b b l e s ) w h i l e t h e core f low i s h i g h i n v e l o c i t y and seed d e n s i t y . The b i a s o c c u r s b e c a u s e a d i s p o r t i o n a t e number o f r e a l i z a t i o n s a r e from t h e downs t r eam, core f l o w . The b i a s i s c l e a r - l y p r e s e n t by t h e o b s e r v a t i o n t h a t a maximum of 20 p e r c e n t o f t h e LDV r e a l i z a t i o n s ( f a r a g i v e n h i s t o - gram i n t h i s r e g i o n ) a r e u p s t r e a m w h i l e t h e smoke v i s u a l i z a t i o n i n d i c a t e d 80 p e r c e n t o f t h e t i m e t h e f l o w vas ups t r eam. This b i a s s h o u l d d e c r e a s e w i t h i n c r e a s i n g d i s t a n c e from t h e s u c t i o n s u r f a c e and d i s t a n c e downst ream o f t h e t r a i l i n g edge s i n c e t h e s e e d d e n s i t y s h o u l d become more u n i f o r m by t h e i n c r e a s e d m i x i n g .
Based on the o u t e r v e l o c i t y v e c t o r s , t h e p r e s - sure s i d e flow h a s a n e a r l y C O n S t m t downward d i r - e c t i o n o f 12 d e g r e e s w h i l e t h e s u c t i o n s i d e f low i s n e a r l y c o n s t a n t a t 6 d e g r e e s (downs t r eam o f t h e t r a i l i n g e d g e ) . Thus t h e p r e s s u r e s i d e f l o w h a s d e v i a t e d s i g n i f i c a n t l y more t h a n i n t h e law l o a d i n g case ( 6 d e g r e e s ) w h i l e t h e s u c t i o n s i d e f low h a s d e v i a t e d o n l y m o d e r a t e l y more t h a n t h e low l o a d i n g case ( 4 d e g r e e s ) . However, u p s t r e a m of t h e t r a i l - i n g e d g e t h e s u c t i o n s u r f a c e f l o w f o r t h e low l oad -
t h e t r a i l i n g e d g e , w h e r e a s , t h e h i g h l o a d i n g ha: d e v i a t e d 10 d e g r e e s f rom t h e s u r f a c e . T h i s i r
v
i n g c a s e i s w i t h i n 2 d e g r e e s of t h e surface n e a r -
o b v i o u s l y due t o t h e p r e s e n c e of t h e s e p a r a t i o n t w i c e t h e t h i c k n e s s of t h e lower s u r f a c e boundary b u b b l e which c h a n g e s t h e e f f e c t i v e s h a p e of t h e l a y e r . Based on t h e C u r r e n t d a t a i t would be a i r f o i l . e x p e c t e d t h a t some e n t r a i n m e n t i n d u c e d wake d e v i a - v
The p r e s s u r e c o e f f i c i e n t values i n F i g . IO i n d i c a t e t h a t t h e f r e e s t r e a m p r e s s u r e s i d e f l o w e x p e r i e n c e s a m o d e r a t e a c c e l e r a t i o n over t h e t r a i l - i n g edge , t h a t vas n o t p r e s e n t i n t h e low l o a d i n g c a s e , b e f o r e q u i c k l y d i f f u s i n g t o w i t h i n a few p e r c e n t o f t h e e x i t v e l o c i t y . T h i s i s b e l i e v e d r e l a t e d t o t h e l a r g e r p r e s s u r e s u r f a c e t o b a s e p r e s s u r e d i f f e r e n t i a l , d i s c u s s e d e a r l i e r , f o r t h e h i g h l o a d i n g p r e s s u r e s u r f a c e . N o t i c e a b l e i s t h e d i f f u s i o n o f t h e s u c t i o n s u r f a c e f r e e s t r e a m f l o w p a s t t h e t r a i l i n g e d g e t o a b o u t x i t = 3 . The low l o a d i n g c a ~ e a b r u p t l y s t o p p e d d i f f u s i n g j u s : d o w n s t r e a m o f t h e t r a i l i n g edge . Due t o t h e con- t i n u e d d i f f u s i o n , t h e r e i s a n a t m a l p r e s s u r e d i f - f e r e n c e b e t w e e n t h e f r e e s t r e a m f l o w s b o v e and be low t h e wake f o r s e v e r a l t r a i l i n g - e d g e t h i c k n e s s e s . T h i s may a c c o u n t f o r some o f t h e wake Or n e a r wake r e g i o n t u r n i n g .
The t i m e mean v e c t o r r e p r e s e n t a t i o n of t h e d a t a d o e s n o t i n d i c a t e any r d c i r c u l a t i o n downstream o f t h e t r a i l i n g edge as i n t h e c a s e of low l o a d i n g . T h e a x i a l e x t e n t o f r e v e r s e d flow ( n e g a t i v a Ux) i s a p p r o x i m a t e l y 3.3: which i s more t h a n t w i c e t h a t of t h e low l o a d i n g . The p r e s s u r e s u r f a c e f l o w c a n b e seen i n F i g . 10 t o t u r n t o f i l l i n t h e wake w h i l e t h e s u c t i o n s i d e f l o w d o e s v i r t u a l l y no t u r n i n g ( n e g l e c t i n g t h e "dead a i r " f rom t h e s u c t i o n s i d e j u s t downst ream o f t h e t r a i l i n g edge t o a b o u t n / t = 3 . 5 ) . A S i n t h e low l o a d i n g c a s e , e n t r a i n - ment e f f e c t s arr b e l i e v e d t o c o n t r i b u t e t o t h e ' l a r g e p r e s s u r e s i d e t u r n i n g i n t o t h e wake. The i n c r e a s e d p r e s s u r e s i d e t u r n i z g i s also r e l a t e d t o t h e i n c r e a s e d d e v i a t i o n of t h e f r e e s t r r a n f low on t h e p r e s s u r e s i d e , 12 d e g r e e s f o r t h e h i g h l o a d i n g compared t o 6 d e g r e e s f o r t h e low l o a d i n g . case .
I n summary, f o r t h e low l o a d i n g c a s e t h e mean wake and p a t t e r n is u n s y m m e t r i c a l and more compl i - c a t e d t h a n t h e u n l o a d e d c a s e . T h i s i s due t o d i f - ferences i n t h e r e l a t i v e s t r e n g t h s of t h e s u c t i o n and p r e s s u r e s u r f a c e b o u n d a r y layers a s q u a n t i f i e d b y t h e Shape f a c t o r d i f f e r e n c e ( 1 . 7 7 and 1 . 3 r e s p e c t i v e l y ) . The t r a i l i n g - e d g e v i s c o u s i n t e r a c - t i o n r e g i o n f o r h i g h l o a d i n g i s much l a r g e r and h a s s i g n i f i c a n t l y r e d u c e d t h e r e l a t i v e f l o w t u r n i n g compared t o t h e low l o a d i n g c a s e . The r e d u c e d t u r n i n g a p p e a r s t o be due t o two f a c t o r s . F i r s t , t h e s u c t i o n s u r f a c e s e p a r a t i o n c h a n g e s t h e a i r f o i l s h a p e s i g n i f i c a n t l y i n a manner which causes f l o w d e v i a t i o n from t h e metal angle. Second, t h e larger v e l o c i t y g r a d i e n t d i f f e r e n c e i n t h e s u c t i o n and p r e s s u r e s u r f a c e b o u n d a r y l a v e r s ( s h a p e f a c t o r s 3.24 and 1 .24 r e s p e c t i v e l y ) i n d u c e s g r e a t e r p r e s - sure s i d e f l o v d e v i a t i o n by e n t r a i n m e n t . A l s o , t h e l e n g t h o f t h e s e p a r a t e d f low r e g i o n i s o b s e r v e d t o i n c r e a s e m o n o t o n i c a l l y f rom u n l o a d e d t o low and h i g h l o a d e d cases . T h i s i s b e l i e v e d t o be c a u s e d b y t h e m o n o t o n i c a l l y d e c r e a s i n g s t r e n g t h of t h e s u c t i o n s u r f a c e s h e a r l a y e r ( r e l a t i v e t o t h e p r e s - sure s u r f a c e ) o b t a i n e d i n t h e t h r e e cases .
N o t e t h a t t h e u n l o a d e d case' also i n v e s t i g a t e d an u n s y m m e t r i c a l boundary l a y e r c o n f i g u r a t i o n . F o r t h i s case t h e u p p e r s u r f a c e boundary was n o m i n a l l y
t i o n would o c c u r . However, t h i s w a s n o t t h e c a s e , i n f a c t , t h e u n s y m m e t r i c a l b o u n d a r y l a y e r f l o w f i e l d was n e a r l y i n d i s t i n g u i s h a b l e froin t h e s y m n e t r i c a l c a s e . T h i s r e s u l t i s r a t i o n a l i z e d by t h e f a c t t h a t , though t h e boundary layer t h i c k n e s s e s were d i f f e r e n t , t h e s h a p e f a c t o r s w e r e n e a r l y t h e s a w ( 1 . 2 8 and 1 . 3 8 ) . mu$, t h e r e l a t i v e boundary l a y e r s t r e n g t h s a s measured by t h e s h a p e f a c t o r s were t h e same and no f l o w d e v i a t i o n i s a c o n s i s t e n t r e s u l t .
S t r e a m l i n e A n a l y s i s
The mean LDV d a t a was used t o c a l c u l a t e t h e s t reamline p a t t e r n . T h i s p a t t e r n can b e compared t o e i t h e r t h e t i m e mean s o l u t i o n of an u n s t e a d y c o d e c a l c u l a t i o n o r a s o l u t i o n o f t h e t i m e a v e r a g e d e q u a t i o n s of m o t i o n . It i s t h e s i m p l e s t method o f c a t e g o r i z i n g t h e wake s t r u c t u r e , however , a s
p o i n t e d o u t i n t h e R e f . 2 s t u d y , t h e t r a n s v e r s e f l o w i n t h e wake c e n t e r l i n e r e s i d e s a t t h e l o c a l mean va l i le o n l y a s m a l l f r a c t i o n o f t h e t i m e due t o t h e p r e s e n c e o f v o r t e x s h e d d i n g . Thus c a u t i o n s h o u l d be e x e r c i s e d when i n t e r p r e t i n g t h e mean pa t : e m s .
Low L o a d i n g - I n F i g . 1 1 t h e overall ~ t r e a i i - l i n e p a t t e r n f o r t h e low l o a d i n g case i s shown. The s t r e a m l i n e p a t t e r n Shows t h a t t h e t i m e mean f l o w follows t h e p r e s s u r e and s u c t i o n s u r f a c e up t o t h e t r a i l i n g edge where t h e f l a w s e p a r a t e s . Down- s t r e a m o f t h e t r a i l i n g edge t h e f l o w from b o t h s i d e s t u r n s i n toward t h e wake w i t h t h e pres sur^
s i d e f l o w t u r n i n g more . T h i s i s c o n s i s t e n t w i t h t h e v e c t o r p l o t s . The $ = 0 s t r e a m l i n e (body v a l u e ) which o r i g i n a t e s f rom t h e p r e s s u r e s i d e of t h e t r a i l i n g edge r e p r e s e n t s t h e " d i v i d i n g s t r e a m - l i n e " which s e p a r a t e s t h e t i m e mean f l o w o f t h e p r e s s u r e s u r f a c e f rom t h e f l o w o f t h e s u c t i o n sur- f a c e . A second $ = 0 s t r e a m l i n e o r i g i n a t e s on t h e s u c t i o n s i d e and t e r m i n a t e s on t h e t r a i l i n g - e d g e c i r c l e . D i s a g r e e m e n t b e t w e e n t h e o r i g i n s of t h e * = 0 s t r e a m l i n e s and t h e s e p a r a t i o n l o c a t i o n s (arrows) shown i n F i g . I 1 i s due t o l a c k of h i g h r e s o l u t i o n LDV d a t a near t h e t r a i l i n g - e d g e s u r f a c e . From t h e f i g u r e i t i s e v i d e n t t h a t u p s t r e a m of X / t = 2 large s t r e a m l i n e t u r n i n g o f t h e near wake i s P r e s e n t . Downstream a l l t h e s t r e a m l i n e s a re i n t h e d i r e c t i o n o f t h e weer flow.
1
-2 '-0.02
I - 2 0 2 4 6 8
Xl t
Fig. 11 Streamline pattern, low loading.
13
A d e t a i l e d v i e w o f t h e t r a i l i n g - e d g e wake r e g i o n i s s h o r n i n F i g . 1 2 w i t h an a d d i t i o n a l s t r e a m l i n e value of -0.013, The c a l c u l a t e d $ = 0 s t r e a m l i n e s l i f t o f f t h e t r a i l i n g edge near t h e s e p a r a t i o n l o c a t i o n s shown by t h e arrows. The p r e s s u r e s i d e s t r e a m l i n e c o n t i n u e s downstream t o i n f i n i t y ( d i v i d i n g s t r e a m l i n e ) and t h e s u c t i o n s u r f a c e s t r e a m l i n e t u r n s u p s t r e a m and s t a g n a t e s a t t h e t r a i l i n g e d g e . The lower s t r e a m l i n e t h u s forms a c l o s e d r e c i r c u l a t i o n b u b b l e t h a t i s a t t a c h e d t o t h e t r a i l i n g e d g e . A m o r e n e g a t i v e S t r eam f u n c t i o n v a l u e , s a y -0 .02 , d e f i n e s a c l o s e d r e c i r c u l a t i o n r e g i o n l o c a t e d downst ream o f t h e t r a i l i n g - e d g e and a s u c t i o n s u r f a c e s t r e a m l i n e t h a t e x t e n d s f rom n e g a t i v e t o p l u s i n f i n i t y . The l a t t e r s t r e a m l i n e i s v e r y close t o t h e s u c t i o n s u r f a c e ups t r eam o f t h e t r a i l i n g e d g e and f o l l o w i n g t h e n e a r wake r e g i o n a p p r o a c h e s c l o s e l y t h e d i v i d i n g s t r e a m l i n e . A s t r e a m l i n e h a v i n g an i n t e r m e d i a t e v a l v e of -0 .013 e x t e n d s from n e g a t i v e i n f i n i t y on t h e s u c t i o n s i d e , t u r n s u p s t r e a m be tween t h e $ = 0 and $ = -0 .02 r e c i r c u l a t i o n s and t h e n t u r n s downs t r eam. Thus, i n t h e mean, t h e f l o w from t h e s u c t i o n s i d e f l o w s u p s t r e a m t o t h e p r e s s u r e s i d e o f t h e t r a i l i n g e d e e .
2( NUMBERS GIVE VALUES OF tp/1
Y l t
- - 0 2 d -04- ! -06- I -08- I
Fig. 12 Streamline pattern in near wake, low loading.
To e x p l o r e t h i s u n u s u a l s t r e a m l i n e p a t t e r n , f i r s t c o n s i d e r t h e s t e a d y , symmet r i c c a s e . Here, two w = 0 s t r e a m l i n e s l i f t o f f t h e s u r f a c e a t t h e b o u n d a r y l a y e r s e p a r a t i o n l o c a t i o n s , enclose two s y m m e t r i c a l r e c i r c u l a t i o n r e g i o n s , j o i n downet ream a t a closure p o i n t a n d t h e r e s u l t a n t s i n g l e s t r eam- l i n e t h e n e x t e n d s t o downst ream i n f i n i t y . A l s o f rom the closure p o i n t , a n o t h e r $ = 0 s t r e a m l i n e e x t e n d s u p s t r e a m and s t a g n a t e s a t t h e t r a i l i n g e d g e . For t h i s s i t u a t i o n t h e two r e c i r c u l a t i o n s a r e c l o s e d a n d a t t a c h e d t o t h e t r a i l i n g e d g e , w i t h n o f l o w f rom t h e p r e s s u r e and s u c t i o n s i d e s e n t e r - i n g t h e r e g i o n . It i s b e l i e v e d (by t h e n a t u r e o f t h e v e c t o r r e p r e s e n t a t i o n ) t h e u n l o a d e d case ' would also g i v e t h i s r e s u l t .
One i n t e r p r e t a t i o n o f t h e f l o w p a t t e r n of F i g . 12 i s t h a t t h e s t r o n g p r e s s u r e s u r f a c e s e p a r a t e d s h e a r l a y e r S e t s u p B c o r r e s p o n d i n g l y s t r o n g c l o c k - w i s e r e c i r c u l a t i o n r e g i o n (+ = - 0 . 0 2 ) w h i c h e n t r a i n s near s t a g n a n t s u c t i o n s i d e F l u i d . T h i s c o u l d c a u s e t h e 0 = -0.013 s t r e a m l i n e t o reverse a n d t h e n p r o c e e d d o w n s t r e a n be tween t h e d i v i d i n g s t r e a m l i n e and t h e + = -0 .02 b u b b l e .
It i s n o t e d t h a t t h i s s t r e a m l i n e p a t t e r n b e a r s a r m a r k a h l e r e s e m b l a n c e t o t h e t r a i l i n g edge f l o w f i e l d p r e d i c t e d by Smith" f o r l a m i n a r , s t e a d y s e p a r a t i o n s f rom s h a r p t r a i l i n g - e d g e a i r f o i l geone- t r i e s . S m i t h ' s "modera t e asymmetry" c a s e showed one a t t a c h e d ( s u c t i o n s i d e ) and one of f -body r e c i r - c u l a t i o n ( p r e s s u r e s i d e ) w i t h s u c t i o n s u r f a c e f low moving u p s t r e a m h e f o r e t u r n i n g downst ream and pass - i n g over t h e t o p o f t h e of f -body r e c i r c u l a t i o n . R e c e n t Nav ie r -S tokes a n a l y s i s by D a v i s , Hobbs , and Weingold'' ' o f t h e CDA c a s c a d e geomet ry r e p o r t e d i n R e f . 1 h a s a l s o d i s p l a y e d t h i s flow p a t t e r n f o r a
n e g a t i v e i n c i d e n c e a n g l e w i t h s u c t i o n s u r f a c e s e p a r a t i o n . C l o s e i n s p e c t i o n o f t h e t r a i l i n g - e d g e r e g i o n ( n o t shown i n R e f . 17 ) h a s r e v e a l e d t h a t t h e s u c t i o n s u r f a c e r e c i r c u l a t i o n i s a t t a c h e d , bounded by t h e body s t r e a m f u n c t i o n v a l u e and t h e p r e s s u r e s i d e r e c i r c u l a r i o n i s o f f - b o d y , e n t r a i n i n g suction s i d e f l u i d . The case i s more r e l e v a n t tha i i
R e f . 1 6 , s i n c e t h e t r a i l i n g edge i s b l u n t and t h e f l o w t u r b u l e n t .
-,
High L o a d i n g - The h i g h l o a d i n g s t r e a m l i n e p a t t e r n i s shown i n F i g . 13. Dashed l i n e s a r e u s e d t o d e p i c t e s t i m a t e d ly = 0 , -0 .02 and -3.05 s u c t i o n s u r f a c e s t r e a m l i n e s i n t h e r e g i o n -6 < x l t < 1 because of u n c e r t a i n i t i e s i n t r o d u c e d by t h e p r e v i - o v s l y d i s c u s s e d LDB b i a s e r r o r i n t h i s r e g i o n . s e p a r a t i o n and c l o s u r e o f t h e $ = 0 s t r e a m l i n e a r e shown b a s e d on s u r f a c e f l o w v i s u a l i z a t i o n T e E u l t S . n u t e r f l o w s t r e a m l i n e s ( $ < -0 .20) a r e b e l i e v e d t o b e less i n f l u e n c e d by t h e b i a s and a r e a c c o r d i n g l y shown a s c a l c u l a t e d from LDV r e s u l t s . On t h e p r e s - sure s i d e t h e s t r e a m l i n e s f o l l o w t h e s u r f a c e close l y . I n c o n t r a s t t h e s u c t i o n s i d e s t r e a m l i n e s d i v e r g e r a p i d l y f rom t h e s u r f a c e due t o t h e bound- a r y l a y e r s e p a r a t i o n .
-'
N Ih.4REllS GIVE VALUES 4 OF t d t
PRESSL - . .._ -ESTIMATED I IRE
STREAMLINES ?s2. I
- 8 - 4 4 8 12 O X I 1
Fig. 13 Streamline pattern, high loading
A s w i t h t h e low l o a d i n g c a s e , t h e I& = 0 __ s t r e a m l i n e t h a t l i f t s o f f t h e p r e s s u r e s i d e i s a d i v i d i n g s t r e a m l i n e . No t i m e mean r e c i r c u l a t i o n s w e r e o b s e r v e d i n t h e wake r e g i o n be low t h i s S t ream-
l i n e , a s p r e v i o u s l y deduced from t h e v e c t o r r r p r e - s e n t a t i o n . s t r e a m l i n e b e h a v i o r i n t h i s r e g i o n was somewhat s c a t t e r e d due t o t h e s u c t i o n s u r f a c e - v e l o c i t y b i a s . However, l a r g e enough v a l u e s d i d p r o v i d e r e a s o n a b l e s t r e a m l i n e p a t t e r n s . F o r e x a m p l e , t h e $ = -0 .02 s t r e a m l i n e t u r n s and p ro - c e e d s u p s t r e a m some d i s t a n c e b e f o r e t u r n i n g toward downs t r eam i n f i n i t y . T h i s i s s t r i k i n g l y s i m i l a r t o t h e b e h a v i o r o b s e r v e d i n t h e low l o a d i n g case and t h a t p r e d i c t e d by Dav i s e t a1.1 ' and S m i t h . 1 6 A l s o , t h e r e g i o n o f l a r g e s t r e a m l i n e t u r n i n g o f t h e n e a r wake i s p r e s e n t u p s t r e a m o f x l t = 6 (compared t o 2 ' f o r low l o a d i n g ) . Downstream o f t h i s l o c a t i o n a l l s t r e a m l i n e s a r e i n t h e general d i r e c t i o n o f t h e o"teT f l o w .
I n sumnary , s t r e a n l i n e p a t t e r n s i n f e r r e d from t i m e mean v e l o c i t y r e s u l t s showed a s i g n i f i c a n t l y more c o m p l i c a t e d , u n s p m e t r i c a l c h a r a c t e r t h a n t h e two eddy p a t t e r n c h a r a c t e r i s t i c o f an un loaded c o n f i g u r a t i o n . The p a t t e r n s a p p e a r t o be g e n e r a t e d by a s t r o n g p r e s s u r e s u r f a c e s h e a r l a y e r i n t e r a c t - i n g w i t h a weake r s u c t i o n s u r f a c e s h e a r l a y e r .
I n t e g r a l Q u a n t i t i e s
T h e d i s p l a c e m e n t a n d momentum t h i c k n e s s (6* and B r e s p e c t i v e l y ) w e r e c a l c u l a t e d from t h e LDV a n d h o t f i l m d a t a u p s t r e a m and downst ream o f t h e t r a i l i n g e d g e u s i n g s r a n d a r d i n c o m p r e s s i b l e f l o w d e f i n i t i o n s . Ups t r eam o f t h e t r a i l i n g edge t h e i n t e g r a t i o n w a s f rom t h e s u r f a c e t o t h e f r e e s t r e a m . Downstream o f t h e t r a i l i n g e d g e , i n t e g r a t i o n as f rom t h e d i v i d i n g s t r e a m l i n e t o t h e l o c a l f r e e - i t r e a m . The n o r m a l i z i n g v e l o c i t y f o r t h e i n t e g r a - t i o n was t h e l o c a l f r e e s t r e a m val i le and t h e i n t e - g r a t i o n l i n e was normal t o t h e t r a i l i n g - e d g e m e t a l
- a n g l e .
D i s p l a c e m e n t T h i c k n e s s - F i g u r e 14 shows t h e d i s p l a c e m e n t t h i c k n e s s d i s t r i b u t i o n a round t h e model and downs t r eam o f t h e t r a i l i n g edge c a l c u - l a t e d from t h e LDV and h o t f i l m p r o f i l e s . The d i s p l a c e m e n t t h i c k n e s s , i s p l o t t e d r e l a t i v e t o t h e model s u r f a c e or t h e d i v i d i n g s t r e a m l i n e .
I DIVIDING STREAMLINE '
- 2
- 4 HIGH LOADING
1 8 4 4 8 12
Fig. 14 Displacement thickness relative to tralling O xll
Y edge and dividing streamline.
A t t h e t o p o f F i g . 14 , t h e low l o a d i n g c a s e shows t h e d i s p l a c e m e n t t h i c k n e s s d e c r e a s e s a long t h e p r e s s u r e s u r f a c e and i n c r e a s e s along t h e suc- t i o n s u r f a c e . This i s due t o t h e o p p o s i t e p r e s s u r e g r a d i e n t s a c t i n g on t h e r e s p e c t i v e boundary l a y e r s . Downstream o f t h e t r a i l i n g edge t h e d i s p l a c e m e n t s u r f a c e s converge f o r 3 t r a i l i n g - e d g e t h i c k n e s s e s b e f o r e becoming n e a r l y p a r a l l e l w i t h a 0 . 7 t - 0 . 8 t s e p a r a t i o n . Convergence is due t o f l o w f i l l i n g t h e wake . The d i v i d i n g s t r e a m l i n e i s o b s e r v e d t o u n d e r g o a r a p i d change be tween t h e two d i s p l a c e m e n t s u r f a c e s over t h e f i r s t two t r a i l i n g - e d g e t h i c k - nesses. I n i t i a l l y , t h e s t r e a m l i n e i s c l o s e t o t h e p r e s s u r e s i d e d i s p l a c e m e n t s u r f a c e , t h e n i t d e v i - a t e s t oward t h e s u c t i o n s i d e d i s p l a c e m e n t s u r f a c e b e f o r e becoming e s s e n t i a l l y p a r a l l e l w i t h t h e prss- sure s i d e . The r a p i d change i n t h i s s t r e a m l i n e i s b e l i e v e d t o be d u e t o p r e s s u r e s i d e f l o w , a t t h e e x p e n s e o f i t s own momentum, e n e r g i z i n g t h e s u c t i o n s i d e by f l u i d e n t r a i n m e n t . T h a t i s , by t u r h l a n t and v o r t e x m i x i n g , slower f l u i d e l e m e n t s on t h e s u c t i o n s i d e a r e exchanged w i t h f a s t e r e l e n e n t s on t h e p r e s s u r e s i d e . Thus i n o rde r t o m a i n t a i n t h e same mass f l o w be tween t h e d i s p l a c e m e n t s u r f a c e s a n d t h e d i v i d i n g s t r e a m l i n e , t h e d i v i d i n g screain- l i n e must m i g r a t e t o w a r d s t h e s u c t i o n s i d e .
R e s u l t s o b t a i n e d h e r e are s i m i l a r t o t h o s e o f t h e R e f . 2 u n l o a d e d p l a t e s t u d y i n t h a t d i s p l a c e - ment s u r f a c e s e p a r a t i o n approached a c o n s t a n t v a l u e o f 0 . 7 t i n t h r e e t r a i l i n g - e d g e t h i c k n e s s e s .
The h i z h l o a d i n g c a s e , shown a t t h e h o t t o m o f F i g . 1 4 , i l l u s t r a t e s t h e d r a m a t i c g rowth o f t h e s u c t i o n s u r f a c e , s e p a r a t e d boundary l a y e r . The s u c t i o n s u r f a c e d i s p l a c e m e n t t h i c k n e s s a t t h e t r a i l i n g edge i s more t h a n 120 p e r c e n t o f t h e t r a i l i n g - e d g e t h i c k n e s s (compared t o 34 p e r c e n t f o r the low l o a d i n g c a s e ) . The pressure s u r f a c e d i s - p l acemen t t h i c k n e s s i s v e r y s i m i l a r t o t h e low l o a d i n g c a s e . A t t h e t r a i l i n g e d g e , t h e t o t a l d i j p l a c e m e n t t h i c k n e s s i s 1 . 4 t . Downs t r ean o f t h e t r a i l i n g e d g e t h e d i s p l a c e m e n t s u r f a c e s began t o c o n v e r g e a t a r a t e much s l o w e r t h a n f o r low load - i n g . Tne d i s p l a c e m e n t Surfaces a r e s t i l l conve rg - i n g a t t h e end o f t h e measurement domai;, and a p p r o a c h i a g a n a s y m p t o t i c value a round 1 . 3 ~ ( n e a r l y d o u b l e t h a t o f t h e low l o a d i n g c a s e ) . The d i v i d i n g s t r e a m l i n e , s i m i l a r t o t h e low l o a d i n g c a s e , m i g r a t e s s i g n i f i c a n t l y from t h e p r e s s u r e s i d e t o t h e s u c t i o n s i d e b u t over a l o n g e r a x i a l d i s t a n c e ( r o u g h l y 3t f o r low and 6 t f o r h i g h l o a d i n g ) . A f t e r f i v e t r a i l i n g - e d g e t h i c k n e s s e s t h e d i v i d i n g s t r e a m l i n e i s e s s e n t i a l l y p a r a l l e l t o t h e p r e s s u r e s i d e d i s p l a c e m e n t s u r f a c e b u t i s s t i l l c o n v e r g i n g toward t h e s u c t i o n s i d e .
F o r low l o a d i n g , t h e e f f e c t i v e a i r f o i l s h a p e i s a m i l d l y t a p e r e d e x t e n s i o n of t h e a i r f o i l s i m i - l a r t o CDA wake o f R e f . 1. The d i s p l a c e m e n t sur- faces d e v i a t e f rom t h e m e t a l angle 8 s t h e f l o w m i g r a t e s t o t h e c a s c a d e e x i t a n g l e . The d i v i d i n g s t r e a m l i n e d e v i a t e s f rom the m e t a l angle by s i x d e g r e e s . For h i g h l o a d i n g , t h e e f f e c t i v e a i r f o i l s h a p e i s d r a m a t i c a l l y d i f f e r e n t . The d i s p i a c e m m t r e g i o n i s much l a r g e r and i n t h i s c a s e , t h e asymp- t o t i c d i r e c t i o n o f t h e d i v i d i n g s t r e a m l i n e d e v i a t e s f rom t h e metal angle by f i f t e e n d e g r e e s . The
15
e f f e c t o f t h e u p s t r e a m s u c t i o n s u r f a c e s e p a r a t i o n on t h e r e l a t i v e f l o w t u r n i n g i s e v i d e n t i n t h e f i g u r e . Based on t h e d i v i d i n g s t r e a m l i n e s , t h e s e p a r a t i o n causes an a d d i t i o n a l 9 d e g r e e s o f f low d e v i a t i o n ( u s i n g t h e d i v i d i n g s t r e a m l i n e s as an e s t i m a t e o f t h e c a s c a d e e x i t a n g l e ) .
Momentum T h i c k n e s s - The momentum t h i c k n e s s d i s t r i b u t i o n f o r t h e low l o a d i n g c a s e i s shown a t t h e t o p o f F i g . 1 5 i n terms o f n o r m a l i z e d momdntum t h i c k n e s s p o t t e d v e r s u s n o r m a l i z e d a x i a l d i s t a n c e . Hot f i l m d a t a are d i s p l a y e d a s s q u a r e s . The p r e s - s u m s u r f a c e momentum t h i c k n e s s i s seen t o d e c r e a s e t o w a r d t h e t r a i l i n g edge a s t h e s u c t i o n s u r f a c e momentum t h i c k n e s s i n c r e a s e s . T h i s b e h a v i o r i s r e l a t e d t o t h e p r e s s u r e g r a d i e n t h i s t o r y ( i n t h e Same manner as d i s p l a c e m e n t t h i c k n e s s ) . Downstream o f t h e t r a i l i n g edge t h e t o t a l momdntum t h i c k n e s s ( s u c t i o n p l u s p r e s s u r e s i d e ) shows a r a p i d i n c r e a s e f o r 2 - 3 t r a i l i n g edge t h i c k n e s s e s t o a v a l u e e / t = 0.52. T h i s r e g i o n a l s o c o r r e s p o n d s t o t h e a r e a o f r a p i d downward d i s p l a c e m e n t o f t h e d i v i d i n g s t r e a m l i n e . T h i s d i s p l a c e m e n t r e f l e c t s e n e r g i a a - t i o n o f t h e s u c t i o n s i d e f l o w by t h e p r e s s u r e s i d e and f rom t h e momentum t h i c k n e s s d a t a i t can b e i n f e r r e d t h a t s i g n i f i c a n t t o t a l p r e s s u r e 105s o c c u r s d u r i n g t h i s p r o c e s s .
The h i g h l o a d i n g momentum t h i c k n e s s d a t a , g i v e n a t t h e bo t tom o f F i g . 15 , shows s i m i l a r t r e n d s as t h e low l o a d i n g c a s e . The p r e s s u r e sur- f a c e d i s t r i b u t i o n i s o b s e r v e d t o be n e a r l y t h e same as t h e low l o a d i n g c a s e ( a s w a s t h e d i s p l a c e m e n t t h i c k n e s s ) . The s u c t i o n s i d e graws a t a S i m i l a r r a t e t o t h e low l o a d i n g c a s e b u t t o mors t h a n t w i c e i t s v a l u e . Downs t r ean o f t h e t r a i l i n g edge t h e momentum t h i c k n e s s i n c r e a s e s r a p i d l y f o r 6 - 7 t r a i l i n g e d g e t h i c k n e s s e s t o a v a l u e e / t = 0 . 9 ( 7 5 p e r c e n t g r e a t e r t h a n f o r low l o a d i n g ) . This r e g i o n o f i n c r e a s i n g momentum t h i c k n e s s , as i n t h e low l o a d i n g c a s e , i s c o i n c i d e n t w i t h t h e r e g i o n o f d i v i d i n g s t r e a m 1 i n e rn ig ra t i o n .
0.6
0- 0.6
o - LDV
- 8 - 4 0 4 8 12 XJl
Fig. 15. Momentum thickness distribution.
The a s y m p t o t i c v a l u e s of t h e d i s p l a c e m e n t and momentum t h i c k n e s s were used w i t h t h e incompres- s i b l e two-d imens iona l r e l a t i o n g i v e n by L i e b l e i n l e t o c a l c u l a t e t h e mixed o u t t o t a l p r e s s u r e loss
(mass f low a v e r a g e d ) , o t h e r w i s e known a s t h e c a s - c a d e loss c o e f f i c i e n t , w = APt/Qref where a ? , ' i s t h e mass a v e r a g e t o t a l p r e s s u r e l o s s . The e q u a t i o n
ment and momentum t h i c k n e s s , c a s c a d e i n l e t and e x i t f l o w angles, and c a s c a d e geomet ry . F o r t h e low
l o a d i n g case w w a s found t o be 0.0278 and f o r t h e h i g h l o a d i n g c a s e 0 . 0 4 9 7 , Thus t h e h i g h l o a d i n g c a s e t o t a l p r e s s u r e loss i s abou t 80 p e r c e n t g r e a t - e r t h a n t h e low l o a d i n g c a s e .
g i v e n by L i e b l e i n re la tes o t o t h e wake d i s p l a c e - -
C o n c l u s i o n s
The o v e r a l l p roblem a d d r e s s e d i n t h e C u r r e n t s t u d y w a s f l o w s e p a r a t i o n i n t h e t r a i l i n g - e d g e r e g i o n o f compresso r a i r f o i l s . The s p e c i f i c f u c u s o f t h e s t u d y was t o d e l i n e a t e t h e e f f e c t s o f p r e s - sure l o a d i n g , t h e r e b y p r o v i d i n g p h y s i c a l i n s i g h t a 5
w e l l a s e x p e r i m e n t a l d a t a o f use t o code d e v e l o p - ment e f f o r t s . The s t u d y shoved t h a t l o a d i n g e f f e c t s w e r e s i g n i f i c a n t and need t o be c o n s i d e r e d i n t h e n u m e r i c a l mode l ing o f t h e t r a i l i n g - e d g e s e p a r a t e d f l o w f i e l d .
The p r imary e f i e c t o f l o a d i n g i s conc luded t o b e i t s i n f l u e n c e , t h r o u g h d i f f e r e n t p r e s s u r e anii
s t r e n g t h s o f t he boundary l a y e r s a p p r o a c h i n g t h ? t r a i l i n g edge and t h e s t r e n g t h s o f t h e r e s u 1 : i n t s h e a r layers emana t ing from t h e s e p a r a t i o n l o c a - t i o n s . For t h e p r e s e n t low l o a d i n g c a s e , t h e s h a p r f a c t o r s u p s t r e a m o f t h e t r a i l i n g edge were 1.31 and
1 . 7 7 f o r t h e p r e s s u r e and s u c t i o n s u r f a c e s . T h i s
s e p r a t i o n l o c a t i o n s on t h e t r a i l i n g edge and b a s e p r e s s u r e f rom t h e un loaded c a s e . However, t h i s d i f f e r e n c e was s u f f i c i e n t t o cause i n c r e a s e d p r e s - sure s i d e s h e a r layer t u r n i n g inro t h e w a 4 i (by e n t r a i n m e n t ) . T h i s r e s u l t s i n i n c r e a s e d f l o w d e v i - a t i o n from t h e t r a i l i n g - e d g e m e t a l a n g l e and t h u s r e d u c e s a i r f o i l c i r c u l a t i o n .
s u c t i o n s u r f a c e p r e s s u r e g r a d i e n t h i s t o r i e s , on t h e
shape f a c t o r d i f f e r e n c e was n o t s u f f i c i e n t t o a l t e r V'
For t h e h i a h l o a d i n g c a s e t h e s u c t i o n s a r i a c e s e p a r a t i o n l o c a t i o n w a s a l t e r e d by t h e weak bound- a r y l a y e r s t r e n g t h , r e s u l t i n g i n i n t e r m i t t e n t suc- t i o n s u r f a c e s e p a r a t i o n and b a s e p r e s s u r e d e p r e s - s i o n . The l a r g e d i f f e r e n c e i n t h e s h a p e f a c t o r s ( 1 . 2 4 on t h e p r e s s u r e s u r f a c e and 3 . 2 4 on t h e SUC-
t i o n surface) c a u s e d much g r e a t e r p r e s s u r e s i d e f l o w t u r n i n g i n t o t h e wake. T o g e t h e r w i t h t h e s t r e a m l i n e d i s p l a c e m e n t c r e a t e d by t h e s u c t i o n s u r f a c e s e p a r a t i o n , t h i s d r a m a t i c a l l y i n c r e a s e d t h e f l o w d e v i a t i o n f rom t h e metal a n g l e . The r e s u l t i n g e f f e c t i v e s h a p e o f t h e t r a i l i n g e d g e , a s d e f i n e d by d i s p l a c e m e n t s u r f a c e s l o c a t i o n s , was q u i t e d i f f e r - e n t from t h e m i l d l y t a p e r e d e x t e n s i o n o f t h e a i r - f o i l t h a t a p p l i e d t o t h e low l o a d i n g c a s e .
Based on t h e s e f i n d i n g s , i n c r e m e n t a l i n c r e a s e s i n a i r f o i l t u r n i n g f rom t h e low l o a d i n g case t o t h e h i g h l o a d i n g case w i l l p r o b a b l y r e s u l t i n a g r a d u a l i n c r e a s e i n f l o w d e v i a t i o n f rom t h e t r a i l i n g - e d g e m e t a l ang le . T h i s i s p r i m a r i l y d u e t o i n c r e a s i n g l y l a r g e r s h a p e f a c t o r d i f f e r e n c e be tween t h e s u c t i o n and pressure s u r f a c e boundary l a y e r s .
From a compar i son o f previous un loaded and p r e s e n t low l o a d i n g and h i g h l o a d i n g e x p e r i m e n t s ,
-
it is concluded that v o r t e x shedding is a charac- teristic feature of the trailing edge separation process. A Strouhal number based on a lengrh scale equal to the sum of the trailing-edge thickness and boundary layer displacemeat thicknesses was found to correlate widely varying shedding frequencies detected in this and a previous unloaded trailing- edge experiment. For situations where loading c a u s e s separation to occur just upstream of the trailing edge, a s in the present high loading c a s e , the separation displays internittent flow r e v e r s a l . This process is attributed to low surface curva- t u r e , resulting in a sensitivity o f the separation location to random fluctuations in the weak suction surface boundary layer incident on the trailing- edge region. Despite the above un~teady flow fea- tures, a coherent time mean flowfield was found to exist.
Acknowledgements
T h e study reported here was perforaed for Naval Air Systems Command under Contract N00014-83- C-0434. Tne authors wish to acknowledge Raymond P. Shreeve (Naval Postgraduate School), 'lichael J . Werle (UTKC), and Joseph \L. Verdon (UTRC) for t!ieir helpful contributions in the formulation of this research program. Appreciation is also expressed to Josepn E. Garberoglio (Pbh') , David E . Hobbs ( P 6 d ) , Edward H. Greitzer (%IT) and :'alter \L, P r e a z Jr. ('destern N e w England College) for helpful dis- cussions during t!ir c o u r s e of th e invesrigation and review of the final report. The assistance O F iillian P. Parrick (UTRC) in placing a two- c o i i i ~ o n e n c laser velocimetry sysren into operation and Stanley A . Skebe's wind tunnel desion contribu- tions are also gratefully acknowledged. Also, the a u t h o r s wish co acknowledge Charles C. Coffin a n d Keith A . Post for their assistance in conducting the experimen:.
References
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2 . eaterson, R.W., and Weingold, H.D., "Experimental Investigation of a Simulated Compressor Airfoil Trailing-Edge Flowfield," AIAA Journal, Vol. 21, No. 5, Hay 1985, pp. 768-775.
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14, Deutsch, S . and Zierke, W.C., "The Yeasurement o f Boundary Layer on a Compressor Slade in Cascade - Part 2 : Suction Surface Roundary Layers," Presented at the Gas Turbine conference and Exhibition, Anaheim, California, Ma? 31-June 4, 198?, AS,* paper 87-67-249,
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