APPENDIX I
APPENDIX I NUMERICAL INTEGRATION ESTIMATE OF UNSTEADY LOAD The p u r p o s e of t h e s t r a i n g a g e b a l a n c e s y s t e m was t o o b t a i n a d i r e c t m e a s u r e o f t h e i n d u c e d u n s t e a d y a e r o d y n a m i c l o a d , i n c l u d i n g t h e n o r m a l and c h o r d f o r c e c o m p o n e n t s , and t h e moment. The n o r m a l and c h o r d f o r c e components would t h e n b e u s e d t o compute t h e i n d u c e d l i f t and d r a g f o r c e s . However, b e c a u s e t h e b a l a n c e e l e m e n t r e s p o n s e s were c o n t a m i n a t e d w i t h a h i g h f r e q u e n c y s i g n a l , t h i s p a r t o f t h e t e s t p r o g r a m was n o t s u c c e s s f u l l y c o m p l e t e d . T h e r e - f o r e , a n a t t e m p t was made t o e s t i m a t e t h e u n s t e a d y c h o r d f o r c e component v i a a n i n t e g r a t i o n o f t h e i n d u c e d c h o r d w i s e p r e s s u r e t r a n s d u c e r r e s p o n s e d i s t r i - b u t i o n .
F o r t h e r e a s o n s c i t e d i n Appendix 11, t h e i n t e g r a t i o n was p e r f o r m e d v i a t h e t r a p e z o i d a l r u l e r a t h e r t h a n t h e more p o w e r f u l segmented G a u s s i a n q u a d r a - t u r e a p p r o a c h . The a c c u r a c y o f t h e t r a p e z o i d a l r u l e a p p r o a c h was examined by u s i n g i t t o compute t h e i n d u c e d l o a d i n g f r o m a known i n t e g r a b l e p r e s s u r e d i s t r i b u t i o n f u n c t i o n and t h e n c o m p a r i n g t h e r e s u l t w i t h a n a c c u r a t e a p p r o x i - m a t i o n o f t h e e x a c t v a l u e o f t h e i n d u c e d l o a d . F o r t h e s a k e o f s i m p l i c i t y t h i s e v a l u a t i o n was r e s t r i c t e d t o t h e s u c t i o n s u r f a c e l o a d r e s p o n s e and t o a s i m p l e a i r f o i l s h a p e . I t i s f u r t h e r n o t e d t h a t t h e t e s t f o r a c c u r a c y was p e r f o r m e d u s i n g o n l y o n e s p e c i f i c 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 f u n c t i o n and no a t t e m p t w a s made t o f o r m a l l y e v a l u a t e t h e a c c u r a c y o f t h e p r e s e n t t r a p e z o i d a l r u l e i n t e g r a t i o n scheme i n t h e g e n e r a l i z e d s e n s e .
The 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 f u n c t i o n t h a t w a s u s e d ( c f R e f .
7 ) i s g i v e n by and i s shown p l o t t e d i n F i g . 6 8 . The f u n c t i o n g(X) r e p r e s e n t s t h e e x t r e m e s of a t y p i c a l 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 w i t h l i t t l e o r n o s e p a r a t i o n ; t h a t : i s , a s h a r p l e a d i n g e d g e r e g i o n p e a k r e s p o n s e f o l l o w e d by a n o n - n e g l i g i b l e r e s p o n s e t o w a r d t h e t r a i l i n g e d g e . The s i m p l e a i r f o i l s h a p e t h a t was u s e d i s g i v e n by 4 3 I n t h i s e q u a t i o n t h e f o r w a r d 60 p e r c e n t c h o r d i s r e p r e s e n t e d by a n e l l i p s e and t h e a f t 40 p e r c e n t c h o r d i s assumed t o b e a l i n e a r t a p e r t o w a r d t h e t r a i l i n g e d g e . The a i r f o i l s h a p e h a s a t h i c k n e s s t o c h o r d r a t i o o f 0 . 1 2 , and h a s c o n t i n u o u s d e r i v a t i v e s a t t h e 60 p e r c e n t c h o r d m a t c h i n g p o i n t . I t s h o u l d b e n o t e d t h a t t h e o n l y c r i t e r i a u s e d i n c h o o s i n g t h e f u n c t i o n a l forms g i v e n by E q s . (20) and ( 2 1 ) i s t h a t t h e y a r e r e a s o n a b l e , s i m p l e r e p r e s e n t a t i o n s o f t h e i n d u c e d l o a d d i s t r i b u t i o n and t h e a i r f o i l s h a p e .
The e x a c t v a l u e s o f t h e normal f o r c e , c h o r d f o r c e , and moment were com- p u t e d from E q s . ( 2 0 ) and ( 2 1 ) a n d a r e g i v e n below t o f o u r p l a c e a c c u r a c y : Normal F o r c e = g ( x ) dX = 0.4150 ( 2 2 )
g ( x ) 2 d x = 0.0588
Chord F o r c e = ( 2 3 )
s
a x
Moment = f g ( x > ( x - 1 / 4 ) dx = 0.0120 By u s i n g t h e s u c t i o n s u r f a c e c o o r d i n a t e s g i v e n by x = 0, . 0 0 4 , .010, .019, . 0 4 5 , . 0 7 3 , . 0 9 8 , . 1 1 4 , . 1 4 9 , .268, . 4 5 4 , . 6 5 8 , . 8 5 1 , . 9 7 1 , and 1 . 0 0 0 , t h e t r a p e z o i d a l r u l e y i e l d s t h e f o l l o w i n g computed r e s u l t s : Normal F o r c e = . 4 1 3 0 ; e r r o r = 0 . 5 % Chord F o r c e = . 0 5 7 4 ; e r r o r = 2.4% Moment = . 0 0 9 4 ; e r r o r = 21.7% i n t h e The m a j o r s o u r c e o f e r r o r i n t h e c o m p u t a t i o n of t h e moment o c c u r s r e g i o n ,454 < x < .851, and i s m a i n l v a c o n s e q u e n c e of t h e c o a r s e n e s s of t h e g r i d . However, t h e a b s o l u t e v a l u e of t h e moment is s m a l l ( c o m p a r a b l e t o a s t e a d y - s t a t e c o n d i t i o n b e l o w s t a l l ) and t h e e r r o r i s w i t h i n t h e r a n g e o f n o r m a l e x p e r i m e n t a l a c c u r a c y . Compared w i t h a t y p i c a l maximum moment v a l u e o f 0.1 t h e computed e r r o r i s more l i k e 2 p e r c e n t of f u l l s c a l e . F u r t h e r - o r d e r m o r e , i t i s i m p o r t a n t t o n o t e t h a t t h e e s t i m a t e o f b o t h n o r m a l f o r c e and c h o r d f o r c e i n t h i s c a s e i s e x c e l l e n t .
A l t h o u g h t h i s p r e d i c t i o n was made f o r o n l y one s p e c i a l s i t u a t i o n , i t i n d i c a t e s t h a t a s a t i s f a c t o r y m e a s u r e o f t h e i n d u c e d u n s t e a d y c h o r d f o r c e c a n g e n e r a l l y be o b t a i n e d by t h i s m e t h o d .
F i n a l l y , i f t h e s e g m e n t e d G a u s s q u a d r a t u r e a p p r o a c h i s u s e d ( c f R e f . 7 ) w i t h t h e f o l l o w i n g t r a n s d u c e r l o c a t i o n s : , 0 0 4 , . 0 2 0 , .045, . 0 7 3 , . 0 9 8 , . 1 1 4 , . 1 4 8 , . 2 6 8 , . 4 5 4 , . 6 6 4 , . 8 5 1 , and . 9 7 0 , t h e computed v a l u e s become Normal F o r c e = . 4 1 5 0 ; E r r o r = 0% Chord F o r c e = . 0 5 9 4 ; E r r o r = 1 . 0 % Moment = . 0 1 2 0 ; E r r o r = 0% T h e s e r e s u l t s a r e a p r o m i s i n g i n d i c a t i o n t h a t p r e s e n t t e c h n i q u e s a r e c a p a b l e of y i e l d i n g a c c u r a t e c a l c u l a t i o n s o f a l l f o r c e s and moments on b o t h s t e a d y and o s c i l l a t i n g a i r f o i l s , p r o v i d e d t h a t an a p p r o p r i a t e i n t e g r a t i o n scheme i s u s e d w i t h a n a d e q u a t e number o f m e a s u r i n g s t a t i o n s . However, a d d i t i o n a l c a l c u l a t i o n s w i t h a c o a r s e r t r a p e z o i d a l g r i d h a v e shown a s i g n i f i - c a n t d e t e r i o r a t i o n i n a c c u r a c y f o r t h e s p e c i f i c f u n c t i o n a l d i s t r i b u t i o n of E q .
( 2 0 ) . I t i s e x p e c t e d t h a t t h i s work w i l l b e p u r s u e d f u r t h e r t o p e r f o r m t h e f o l l o w i n g t a s k s : 1 ) Modify t h e a n a l y t i c a l form o f Eq. ( 2 0 ) t o s i m u l a t e c h a n g e s i n l o a d d i s t r i - b u t i o n s o t h e p r e s e n t t r a n s d u c e r a r r a n g e m e n t c a n be e v a l u a t e d i n g r e a t e r d e p t h .
2 ) Expand t h e t e c h n i q u e t o a s s i s t t h e e x p e r i m e n t a l i s t i n s e l e c t i n g b o t h t h e number and p l a c e m e n t o f m e a s u r i n g s t a t i o n s t o m i n i m i z e e r r o r .
4 5 A P P E N D I X 11 N U M E K I C A L INTEGRATION METHODS D u r i n g t h e p l a n n i n g s t a g e s o f t e s t p r o g r a m , t h e i n t e n t i o n was t o l a y o u t t h e p r e s s u r e t r a n s d u c e r a r r a y i n s u c h a way a s t o p e r m i t i n t e g r a t i n g t h e i n d u c e d p r e s s u r e d i s t r i b u t i o n v i a t h e segmented G a u s s i a n q u a d r a t u r e a p p r o a c h d e s c r i b e d i n R e f . 7 . By d e s i g n , w i t h t h e a i d o f G a u s s i a n q u a d r a t u r e t h e o r y , t h e u p p e r and lower s u r f a c e d i s t r i b u t i o n s were t o b e m o n i t o r e d w i t h 12 and 8 p r e s s u r e t r a n s d u c e r s , r e s p e c t i v e l y . However, t h e p r e c i s e l o c a t i o n o f t h e t r a n s d u c e r s i s c r u c i a l t o t h e s u c c e s s o f t h e a p p r o a c h and t h e m a c h i n i n g e r r o r s made d u r i n g t h e p r e s s u r e t a p d r i l l i n g p r o c e s s were l a r g e enough t o c a u s e t h e c o n c e p t t o be abandoned f o r t h e time b e i n g . T h e r e f o r e , a n e x t r a t a p was i n t r o d u c e d a t t h e o n e p e r c e n t c h o r d l o c a t i o n ( r e l a t i v e t o t h e l e a d i n g e d g e ) t h u s i n c r e a s i n g t h e number o f t a p s on t h e u p p e r s u r f a c e t o 13 and t h e i n t e g r a t i o n o f t h e p r e s s u r e d i s t r i b u t i o n was c a r r i e d o u t u s i n g t h e s t a n d a r d f o r c o m p l e t e n e s s ( a n d f o r f u t u r e r e f e r e n c e ) a b r i e f t r a p e z o i d a l r u l e . However, summary o f t h e two-segment G a u s s i a n q u a d r a t u r e a p p r o a c h f o l l o w s .
of t h e i n t e g r a t e d The two-segment G a u s s i a n q u a d r a t u r e r e p r e s e n t a t i o n d i s t r i b u t i o n f u n c t i o n F ( x ) i s I n m w h e r e A i a r e w e i g h t i n g c o n s t a n t s , x i a r e t r a n s d u c e r l o c a t i o n s , and y i s some p a r t i t i o n p o i n t w i t h i n t h e n o n d i m e n s i o n a l a i r f o i l c h o r d r a n g e [ 0 , 1 ] . The f i r s t and s e c o n d G a u s s i a n q u a d r a t u r e s o f Eq. ( 2 5 ) o p e r a t e i n t h e c h o r d r a n g e s [ O , y ] and [ y , l ] , r e s p e c t i v e l y . The t r a n s d u c e r l o c a t i o n s , x i , a r e d i r e c t l y r e l a t e d t o t h e G a u s s p o i n t s , y i , o f e a c h q u a d r a t u r e w h e r e x i = yyi and x i = y + ( l - y ) y i a r e t h e r e l a t i o n s c o r r e s p o n d i n g t o t h e f i r s t and s e c o n d q u a d r a t u r e s , r e s p e c t i v e l y . The main a d v a n t a g e o f t h e s e g m e n t e d G a u s s i a n q u a d r a t u r e o v e r t h e u s e o f o n e q u a d r a t u r e a p p l i e d o v e r t h e e n t i r e c h o r d i s t h e f r e e d o m t o c h o o s e t h e p r e c i s e l o c a t i o n o f a n y o n e t r a n s d u c e r s t a t i o n a l o n g t h e c h o r d . The s p e c i f i c a t i o n o f t h i s t r a n s d u c e r s t a t i o n d e t e r m i n e s t h e v a l u e o f t h e c o n s t a n t This f e a t u r e l e a d s t o t h e m a i n l i m i t a t i o n o f t h e t h e o r y which i s t h a t A i y .
and y i a r e e x c l u s i v e l y d e t e r m i n e d by t h e c h o s e n o r d e r o f t h e q u a d r a t u r e . I t f o l l o w s , t h a t o n c e y i s known, t h e l o c a t i o n s o f a l l o t h e r t r a n s d u c e r s a r e a u toma t i c a1 l y s p e c i f i ed .
The a c c u r a c y o f t h e G a u s s i a n q u a d r a t u r e a o p r o a c h i s d i r e c t l y r e l a t e d t o t h e a c c u r a c y o f t h e s t a t i o n p o i n t l o c a t i o n s . F i n a l l y , i t i s p o i n t e d o u t t h a t t h e s u p e r i o r i t y of t h i s a p p r o a c h o v e r c o n v e n t i o n a l methods s u c h a s t h e t r a p e - z o i d a l r u l e i s d e t e r m i n e d b y t h e f a c t t h a t a much s m a l l e r number o f t r a n s - d u c e r s i s n e e d e d t o a c h i e v e t h e same a c c u r a c y i n t h e i n t e g r a t e d r e s u l t .
4 6
APPENDIX I11
APPENDIX I11 W I N D TUNNEL WALL CORRECTIONS DUE TO A LIFTING SURFACE I N OBLIQUE FLOW The w a l l c o r r e c t i o n s p r e s e n t e d b e l o w a r i s e b e c a u s e t h e l i f t i n g s u r f a c e i s immersed i n a bounded f l o w and t h e n o r m a l - t o - s p a n c h o r d l i n e s a r e skewed a t a n a n g l e , A , r e l a t i v e t o t h e f r e e s t r e a m . T h e s e c o r r e c t i o n s do n o t i n c l u d e t h e e f f e c t s o f s o l i d and wake b l o c k i n g , and buoyancy which a r i s e s i f t h e t u n n e l h a s a l o n g i t u d i n a l s t a t i c p r e s s u r e g r a d i e n t . Tl~ese e f f e c t s a r e c o n s i d e r e d i n R e f . 11 and must be added t o t h e f o l l o w i n g c o r r e c t i o n s . Ttle p r e s e n t a n a l y s i s w i l l f o l l o w t h e a p p r o a c h d e v e l o p e d i n R e f . 12 w i t h some m o d i f i c a t i o n s a s n o t e d be low.
I n o r d e r t o compare t h e s t e a d y - s t a t e t e s t r e s u l t s f o r t h e s w e p t wing w i t h t h o s e f o r t h e unswept w i n g , i t i s n e c e s s a r y t o c o n s i d e r t u n n e l - w a l l i n t e r f e r e n c e e f f e c t s on b o t h w i n g s . A n a l y s i s o f t h e p r o b l e m f o r t h e swept w i n g i n d i c a t e s t h a t i t i s n e c e s s a r y t o d e t e r m i n e t h e e x t e n t t o which t h e t u n n e l w a l l s a l t e r t h e i n c i d e n c e a n g l e from what i t would b e i f t h e w a l l s were n o t p r e s e n t . T h i s d i s c u s s i o n i s l i m i t e d t o swept w i n g s p l a c e d midway b e t w e e n t h e u p p e r and l o w e r t u n n e l w a l l s . Hence, t h e c o r r e c t i o n t o t h e i n c i d e n c e a n g l e i s c o n s i d e r e d t o b e d e p e n d e n t upon t h e m a g n i t u d e o f t u n n e l - w a l l - i n d u c e d v e l o c i t y a t t h e h o r i z o n t a l c e n t e r p l a n e o f t h e wind t u n n e l .
For a n i n f i n i t e yawed w i n g i n p o t e n t i a l f l o w , l i n e s o f c o n s t a n t p r e s s u r e a r e p a r a l l e l t o t h e l e a d i n g e d g e o f t h e w i n g . I d e a l l y , t h e f l o w o v e r t h e s w e p t wing o f t h i s t e s t p r o g r a m s h o u l d c o r r e s p o n d t o t h e f l o w o v e r t h e i n f i n i t e yawed w i n g . However, b e c a u s e t h e v e r t i c a l t u n n e l w a l l s f u n c t i o n a s r e f l e c t i o n p l a n e s , t h e a c t u a l w i n g c o r r e s p o n d s more n e a r l y t o a p a n e l o f a " k i n k e d " w i n g , a s i l l u s t r a t e d i n t h e s k e t c h b e l o w . I n t h e c o m p u t a t i o n o f t h e t u n n e l - w a l l c o r r e c t i o n s , t h e l i n e s of c o n s t a n t p r e s s u r e a r e c o n s i d e r e d p a r a l l e l t o t h e l e a d i n g e d g e s o f t h e r e s p e c t i v e wing p a n e l s . I t i s r e a l i z e d t h a t a d j a c e n t t o t h e v e r t i c a l w a l l s , t h e l i n e s o f c o n s t a n t p r e s s u r e are n o l o n g e r p a r a l l e l t o t h e l e a d i n g e d g e b u t a r e c u r v e d and become n o r m a l t o t h e w a l l s a t t h e w a l l s .
With t h i s d i s c r e p a n c y i n f l o w a l i g n m e n t , t h e computed c o r r e c t i o n s a r e n o t e x p e c t e d t o be a d e q u a t e a d j a c e n t t o t h e v e r t i c a l w a l l s . The c a l c u l a t e d c o r r e c t - i o n s s h o u l d b e s a t i s f a c t o r y f o r c o r r e c t i n g t o a p p r o x i m a t e l y f r e e - a i r c o n d i t i o n s f o r s e c t i o n s of t h e wing more t h a n o n e c h o r d l e n g t h from e i t h e r w a l l .
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I I
The a n a l y s i s p r o c e e d s by a s s u m i n g t h a t t h e bounded wing and a l l image w i n g s a r e s m a l l compared t o t h e t e s t s e c t i o n and e a c h may be a p p r o x i m a t e d by a s i n g l e v o r t e x a t i t s q u a r t e r c h o r d l i n e . The a n a l y s i s f o r c a l c u l a t i n g t h e c h a n g e i n i n c i d e n c e a n g l e d u e t o t h i s a r r a y o f v o r t i c e s i s t h e method o f i m a g e s . B e c a u s e t h e wing i s skewed, t h e c l a s s i c a l image s y s t e m which e x t e n d s above and b e l o w t h e t e s t s e c t i o n t o i n f i n i t y and which r e p r e s e n t s t h e t u n n e l f l o o r and c e i l i n g f o r an a i r f o i l i n bounded f l o w , must be e x t e n d e d t o i n c l u d e a n i n f i n i t e s p a n w i s e image s y s t e m t o t h e r i g h t and t h e l e f t of t h e t e s t s e c t i o n .
i s shown i n F i g . 69 t o g e t h e r w i t h t h e a r r a n g e m e n t f o r a s s i g n i n g T h i s s y s t e m d i r e c t and i n v e r t e d v o r t e x s y s t e m s and a l s o t h e a r r a n g e m e n t f o r a s s i g n i n g p o s i t i v e and n e g a t i v e sweep a n g l e s t o r e p r e s e n t t h e k i n k e d wing s y s t e m . T h e r e a r e t h r e e e f f e c t s t h a t a r e r e p r e s e n t e d by t h i s image s y s t e m : f i r s t , t h e m i s s i n g downward c u r v a t u r e ( i n d u c e d v e r t i c a l v e l o c i t y ) o f t h e a i r s t r e a m t h a t i s r e a l i z e d i n f r e e - a i r and r e d u c e d d u e t o t h e c e i l i n g and f l o o r b o u n d a r i e s ; s e c o n d and t h i r d l y , t h e i n d u c e d l o n g i t u d i n a l and l a t e r a l v e l o c i t i e s which a r e i n d u c e d by t h e t u n n e l w a l l s . The v e r t i c a l v e l o c i t y e f f e c t i s t h e most s i g n i f i - c a n t ; i t i n d u c e s a n upwash a n d , h e n c e , a l o c a l i n c i d e n c e a n g l e c h a n g e , Aa. The l o n g i t u d i n a l and l a t e r a l v e l o c i t y e f f e c t s a r e much s m a l l e r and a r e i g n o r e d f o r p r e s e n t a t i o n . T h i s i s a m o d i f i c a t i o n t o R e f . 1 2 , where t h e l o n g i t u d i n a l v e l o c i t y i s p r e s e n t e d a s more s i g n i f i c a n t .
A p p l i c a t i o n o f t h e B i o t - S a v a r t law t o d e t e r m i n e t h e t o t a l v e l o c i t y o f o n e bound image v o r t e x a t t h e 50 p e r c e n t c h o r d s t a t i o n o f t h e t e s t wing g i v e s r i s e t o t h e f o l l o w i n g e q u a t i o n :
n C O S ~ A - y/a - 112
-
+ 1/21 t a n h + ~ / 4 a ] ~ + [ y / a + I / 2 - n t ( ~ / 4 a ) s i n A ] ~ + m ~ ( h / a ~ ] ” ~ E q u a t i o n ( 2 6 ) f o r t h e e f f e c t of a bound v o r t e x i n skewed f l o w c a n be d e v e l o p e d from t h e unskewed c a s e p r e s e n t e d i n s t a n d a r d a e r o d y n a m i c t e x t s s u c h a s R e f . 20 ( E q . ( 1 1 . 1 0 ) p . 2 1 9 ) . It i s e v a l u a t e d a t t h e s e m i - c h o r d i n a c c o r d a n c e w i t h s t a n d a r d p r a c t i c e , r e p r e s e n t i n g t h e a v e r a g e e f f e c t o f t h e i n d u c e d f l o w f i e l d o v e r t h e a i r f o i l c h o r d . T h i s i s a m o d i f i c a t i o n t o t h e method o f R e f . 1 2 w h e r e t h e i n d u c e d f l o w i s e v a l u a t e d a t t h e w i n g q u a r t e r c h o r d . I f t h e q u a r t e r c h o r d i s u s e d , t h e summation of t h e i n d u c e d f l o w e f f e c t s from a l l t h e image v o r t i c e s i s z e r o . C l a s s i c a l , unswept t h e o r y a l s o p r e d i c t s n o e f f e c t when e v a l u a t e d a t t h e q u a r t e r c h o r d . The s e m i - c h o r d s h o u l d b e u s e d a s i n c l a s s i c a l t h e o r y f o r t h e r e a s o n n o t e d a b o v e .
R e s o l u t i o n o f t h e t o t a l v e l o c i t y , q , i n t o i t s v e r t i c a l component i s a c h i e v e d by m u l t i p l y i n g by t h e d i r e c t i o n c o s i n e :
n sin A + c/4a
r z
'> ( 2 7 ) 2 1/2
[(n sin A - ~ / 4 a ) ~ + rn2(h/a) ]
A c c o r d i n g l y , The c i r c u l a t i o n , r , i n Eq. ( 2 6 ) i s r e l a ed t t h e wing l i f t c o e f f i i e n t , C L , b y : T h e r e f o r e , c o m b i n i n g E q s . ( 2 6 ) t h r o u g h ( 2 9 ) a n d m u l t i p l y i n g by t h e a p p r o p r i a t e s i g n f o r t h e a s s i g n e d c i r c u l a t i o n d i r e c t i o n , t h e e q u a t i o n f o r t h e i n d u c e d f l o w w , r a t i o e d t o t h e f r e e s t r e a m v e l o c i t y becomes: i n t h e t u n n e l , 4 9
n C O S ~ A - y/a - 3
I
-
C L 2 2
+ [y/a + 3 - n +(c/4a)slnA] + rn2 (h/a)2]h 1 [[(y/a + $) tan A +
( 3 1 )
w / V = K I C L = a Q
But w / V i s t h e c h a n g e i n i n c i d e n c e a n g l e , Aa, d u e t o t h e t u n n e l b o u n d a r i e s , and Aa ( d e g r e e s ) = 5 7 . 3 2
v
When summed o v e r t h e e n t i r e l a t t i c e , t h e r e s u l t i n g w i s n e g a t i v e , which is a n upwash. T h e r e f o r e , t h e c o r r e c t e d or f r e e stream i n c i d e n c e a n g l e becomes, i n t h e p l a n e of t h e f r e e stream:
Qoir = Q tunnel + A a
( 3 2 ) "air = atunnel + K , C , or i n t h e p l a n e n o r m a l t o s p a n : REFERENCES 1. Halfman, R. L . , H. C. Johnson, and S. M. Haley: Evaluation of High- Angle-of-Attack Aerodynamic-Derivative Data and Stall Flutter Predic- tion Techniques. NACA Technical Note TN2533, November 1951.
2. Carta, F. 0.: Experimental Investigation of the Unsteady Aerodynamic Characteristics of an NACA 0012 Airfoil. United Aircraft Research Laboratories Keport M-1283-1, August 1960.
3. Carta, F. O., G . L. Commerford, R. G. Carlson, and R. H. Blackwell: Investigation of Airfoil Dynamic Stall and its Influence on Helicopter Control Loads. USAAMRDL Technical Report 72-51, U . S. Army Air Mobility Research and Development Laboratory, Fort Eustis, Virginia, September 1972.
Liiva, J., F. J. Davenport, L. Gray, and I. C. Walton: Two-Dimensional 4.
Tests of Airfoils Oscillating Near Stall. Vol. I, Summary and Evaluation of Results. USAAVLABS Technical Report 63-13A, Vol. 11, Data Report.
USAAVLABS Technical Report 63-13BY U. S. Army Aviation Material Labora- tories, Fort Eustis, Virginia, April 1968.
5. Jepson, W. D: Two Dimensional Test of Four Airfoil Configurations with an Aspect Ratio of 7.5 and a 16 Inch Chord up to a Mach Number of 1.1.
Sikorsky Engineering Report SER-50977, April 5, 1977, performed under Contract No. N60921-73-C-0057.
6. Carta, F. O., and A. 0. St. Hilaire: An Experimental Study of Sweep Effects on the Unsteady Aerodynamics of a Pitching Airfoil. United Technologies Research Center Report R76-411931, March 1976.
7 . St. Hilaire, A. 0.: The Segmented Gaussian Quadrature and its Applica- tion for Optimizing Airfoil Instrumentation Arrays. United Technologies Research Center Report UTRC76-150, October 5 , 1976.
8. McCroskey, W. J., and E.J. Durbin: Flow Angle and Shear Stress Measure- ments Using Heated Films and Wires. Trans. ASME, Journal of Basic Engineering, Vol. 94, No. 1, March 1972, pp. 46-52.
Bellinger, E. D., W. P. Patrick, L. E. Greenwald, and A. J. Landgrebe: 9.
Experimental Investigation of the Effects of Helicopter Rotor Design Parameters on Forward Flight Stall Characteristcs. Report USAAMRDL-TR -74-1, April 1974.
REFERENCES (cont'd) 10. Phillipe, J. J. and M. Sagner: Calcul et Mesure des Forces Agrodynamiques sur un Profil Oscillant avec et sans Dgcrochage.
Presente; la rGunion du Groupe Dynamique des Fluides de 1'AGARD.
Marseilles, 1972. (O.N.E.R.A. Report No. T.P. 132, 1972).
Allen, H. J. and W. G. Vincenti: Wall Interference In a Two-Dimensional 11.
Flow Wind Tunnel, with Consideration of the Effect of Compressibility.
NACA Report 782, 1944.
Dannenberg, R. E.: Measurements of Section Characteristics of a 12.
45' Swept Wing Spanning a Rectangular Low-Speed Tunnel as Affected by the Tunnel Walls. NACA TN 2160, August 1950.
13. Carr, L. W., K. W. McAlister, and W. J. McCroskey: Analysis of the Development of Dynamic Stall Based on Oscillating Airfoil Experiments.
NASA Technical Note, TN D-8382, January 1977.
McAlister, K. W., L. W. Carr and W. J. McCroskey: Dynamic Stall Experi- 14.
cal Paper 1100. January ments on the NACA 0012 Airfoil. NASA Techn 1978.
on the Aero- 15. St. Hilaire, A. 0.and F. 0. Carta: The Inf uence of Sweep Airfoil. Vol. I1 - Data dynamic Loading of an Oscillating NACA 0012 Report. NASA CR-145350, 1979.
16. Carta, F. 0. and C . F. Niebanck: Prediction of Rotor Instability at High Forward Speeds, Vol. 111, Stall Flutter. USAAVLABS Technical Report 68-18C, U.S. Army Aviation Material Laboratories, Fort Eustis, Virginia, February 1969.
ROOS, F. W. and D. W. Riddle: Measurements of Surface-Pressure and 17.
Wake-Flow Fluctuations in the Flow Field of a Whitcomb Supercritical Airfoil. NASA TN D-8443, August 1977.
Carlson, L. A.: TRANDES: A Fortran Program for Transonic Airfoil 18.
Analysis or Design. NASA CR-2821, June 1977.
Uns t e ady 19. Levy, L. L.,Jr.: Experimental and Computational Steady and 6 , No. 6 , Transonic Flows About a Thick Airfoil. AIAA Journal, Vol.
June 1978, pp 569-572.
20 * Pope, A.: Basic Wing and Airfoil Theory, 1st Ed. McGraw-Hi 1 Book Company, New York, 1951.
T A B L E I NACA 0012 A I R F O I L C O O R D I N A T E S x I C y l c Upper 0 0 .005 .0121 .010 .0170 .020 .0235 .040 -0321 .080 .0429 .120 .049 7 .180 .0559 .250 .0592 .350 .0593 .500 .0528 .600 .0455 .700 .0365 .800 .0261 .9 0 0 .0144 .950 .0080 1.000 .0013 y / c lower = - y / c u p p e r T h i c k n e s s distribution = 2 ( y / c u p p e r ) 5 3 TABLE 11 PRESSURE AiiD HOT FILM MEASUREMENT STATIONS ( A l l c o o r d i n a t e s i n p e r c e n t c h o r d . For n o n - t n e t r i c s e c t i o n , f i r s t c o o r d i n a t e a f t of l e a d i n g e d g e , s e c o n d c o o r d i n a t e s p a n w i s e from r e f e r e n c e l i n e . For m e t r i c s e c t i o n , c h o r d w i s e c o o r d i n a t e only).
& 1 Succ ion S u r f a c e _____________________----_------_-----_---------- P r e s s u r e s Hot F i l m s
I r
Chordwise Kef e r e n c e Line o r L . E . Region 2 . 1 , 1 0 . 0 7 . 4 , 1 0 . 0 Chordwise Array 1 4 . 8 , 1 0 . 0 Array 2 5 . 0 , 1 0 . 0 0 . 4 , 0 . 0 2 . 0 , 0 . 0 0 . 4 , 2 6 . 0 4 5 . 4 , 10.0 4 . 5 , 0 . 0 4 . 5 , 2 3 . 6 8 5 . 1 , 1 0 . 0 7 . 3 , 0 . 0 1 4 . 8 , 1 7 . 7 F i r s t Swept Array ( 4 5 . 4 , O.O)* 2 . 1 , 3 5 . 0 9 . 8 , 0 . 0
-
1 1 . 4 , 0 . 0 Second 2 5 . 0 , 2 1 . 8 ( 4 5 . 4 , 1 0 . 0 ) * 1 4 . 8 , 0 . 0 Swept 2 6 . 8 , 0 . 0 Array Second Swept 4 5 . 4 , 0 . 0 0 . 4 , 5 5 . 8 Array 6 6 . 4 , 0 . 0 4 . 5 , 5 3 . 4 2 . 1 , 5 7 . 9 8 5 . 1 , 0 . 0 2 6 . 8 , 4 0 . 5 4 1 . 8 , 3 5 . 0 5 7 . 0 , 0 . 0 ( 9 7 . 0 , 0.0)* ( 8 5 . 1 , 1 0 . 0 ) * 1 - ~ I ( )* - L o c a t i o n a l s o i n c h o r d w i s e a r r a y P r e s s u r e S u r f a c e , P r e s s u r e s
_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ - - - - - - -
0 . 5 , 0 . 0 1 . 5 , 0 . 0 5 . 2 , 0 . 0 1 8 . 5 , 0 . 0 3 9 . 2 , 0 . 0 6 2 . 7 , 0 . 0 8 3 . 4 , 0 . 0 9 6 . 7 , 0 . 0 5 4 TABLE I 1 1 UNSTEADY TEST MATRIX FOR NACA0012 AIRFOIL - f ( c p s ) - a M, M C ( d e g ) 4 5 . 3 3 8 10 1 0 . 6 7
- - -
. 3 . 3 X X X . 4 .4 X X X . 3 . 3 X X X .4 .4 X X X . 3 . 3 X X X . 4 . 4 X X X . 3 X . 3 X X .4 .4 X X X . 3 . 3 X X X .4 .4 X X X . 3 . 3 X X X .4 .4 X X X . 3 . 3 X X X . 4 . 4 X X X - - - 8 0 . 3 4 6 . 3 X X X . 4 6 2 .4 X X X X 9 . 3 4 6 . 3 X X X t u . 4 6 2 . 4 X X X X 12 . 3 4 6 . 3 X X X I 1 . 4 6 2 .4 X X X X . 3 4 6 1 5 . 3 X X X . 4 6 2 .4 X X X X I 10 9 . 3 4 6 . 3 X X X ,I . 4 6 2 .4 X X X X 12 . 3 4 6 . 3 X X X II . 4 6 2 .4 X X X X 1 5 . 3 4 6 . 3 X X X ,I
I
. 4 6 2 .4 X X X X
- - -
A d d i t i o n a l T e s t P o i n t s :
I f ( c p s )
I l A C A O O 1 2 3 0 10 15 . l o 4 .09 2.5 3.75 5 6.25 TABLE I V NOMINAL VALUES OF kC FOR B A S I C TEST PROGRAM I I I J N o t e s : 1. A l l v a l u e s d i s p l a y e d were r u n a t l e a s t o n c e .
2 . H o r i z o n t a l a r r o w s on r i g h t column d e n o t e n o m i n a l v a l u e s u s e d f o r u n s w e p t r u n s .
3 . Boxed numbers d e n o t e n o m i n a l v a l u e s u s e d f o r s w e p t r u n s .
4 . D i a g o n a l a r r o w s i n d i c a t e m a t c h e d v a l u e s of kC.
5 6 0 0.2 0.4 0.6 0.8 1 .o MACH NUMBER Figure 1 Operating Envelope F R E E STREAM V E L O C I T Y 180'
- S K E W A N G L E S
- - - - - - M A C H N U M B E R
p-0.39 V 1 Mgo =0.924 270'
s i B L A D E
Figure 2 Contours of Sweep Angle and Mach Number m Q) C I L L A T O R Y C R A N K I L L O W BLOCK Y L l N D R l C A L SHAFT BASE SUPPORT (BLADE I N UNSWEPT POSITION) UTRC Main Wind Tunnel Oscillatory Model System Figure 4 , .'.
I m I f . .
(D Q I- a J C
.-
-I a UJ I J W u z W CT W LL W a -I a
:-- P
w l- a n
z
c 9 - UJ N l-
/
b i b 2
/ s2
.
a ) SINGLE ELEMENT SCHEMATIC B A L A N C E CENTER L I N E
_I -
CHORD L I N E d -
- - _ -
x 2 QUARTER CHORD L I N E b ) B L A D E FORCE SYSTEM Figure 8 Balance Schematic (0.4. 26) L E A D I N G EDGE ( 0 . 4 . 5 5 8 ) 1 -
- - - 9 2 . 1 , 35)- .- - - - - -
>
I E #,-PRESSURE T R A N S D U C E R L O C A T I O N - H O T F I L M L O C A T I O N
( X I C . SIC) - CHORDWISE A N D SPANWISE
C O O R D I N A T E I N PERCENT / CHORD. R E L A T I V E T O L E A D I N G EDGE, A N D R E L A T I V E T O R E F E R E N C E CHORDWISE PRESSURE A R R A Y I / A L L O T H E R C O O R D I N A T E S I N PERCENT C H O R D ! ,
i
3 6 T O EDGE O F - T R A I L I N G EDGE M E T R I C SECTION figure 9 Pressure Transducer and Hot Film Layouts on Airfoil Suction Surface 6 5 SUCTION SURFACE 0.04 0.02 -0.02 I I 1 I I -0.04 0 0.02 r). 04 0.06 0.08 0.10 0.12 0.14 0.16
DIMENSIONLESS CHORD POSITION, x = x / c
Figure 10 Section View Showing Suction Surface Instrumentation (Schematic) T A R E FOR B A L A N C E ELEMENT NO. 3 - 1.0 - 2.0
n n
M O M E N T T A R E
- 1 .o
c
-2 .( -
I 4
1 5 6 7 2 8 9 10 1 1 12 FREQUENCY RATIO, f/f 1 Figure 11 Typical Harmonic Content of No-Flow Balance Response I I I
J
L _ _ _ _ _ - - J L _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ . _ _ _ _ _ _ _ _ _ _
ARES D A T A S T A D A S D A T A I PROCESS T I M E CODE
I
I DONE A F T E R
DETECTOR I I I SAMPLE A N D I I H O L D I I I I A N A L O G I I M U L T I P L E X E R I I I I I A N A L O G TO
I
D I G I T A L I D I G I T A L I CON V E R T E R I TAPE I I I I WISARD I D A T A
- - - - - - - - - - - - -,J SYSTEM
L - - - -
Figure 12 Block Diagram for Data Acquisition and Digitizing a Figure 13 Airfoil Force Schematic
I I
__()_ L I F T COEFFICIENT D R A G COEFFICIENT
I I
F L A G G E D SYMBOLS I N D I C A T E REPEAT POINTS 0.56
- 0.52
+'
J z w -
+-
z U w
0.4 t - - L L
w U
s
U
o.2 t
w U a [r I - U
d
-0.2 - J
1 o.20
-0.4 t
-1.0
-1.2 L
0.1
+
5 s
5 O O
o c
5 2
u + 4 . 1
g s x u
(2 % 4 . 2
L O a 0 -0.3 -6 -4 -2 0 2 4 6 8 10 12 14 16 18 2 0 22 24 26 28 INCIDENCE ANGLE, u , ( D E G ) Figure 14 Steady-State L i f t , Drag, a n d Pitching M o m e n t Coefficients for t h e N A C A 0012 A i r f o i l a t Mc = 0.3 a n d A = 0 Deg.
- , L I F T COEFFICIENT
A D R A G COEFFICIENT
, - $ - M O M E N T COEFFICIENT A L L D A T A UNCORRECTED F L A G G E D SYMBOLS I N D I C A T E REPEAT POINTS 1.6
1 0.56
1.4 0.52 1.2 0.48 1.0 0.44 n 0.8 u -I 0.40 u n I-- z I- z 0.6
0.36 w
w
u
L L 0.4 L L U 0.32 w LL w 0 0.2 0.28 u a
t B
a - n -I -0.2 0.20 -0.4 0.16 -0.6 0.12 -0.8
- 0.08
-1.0
- 0.04
-1.2 1 1 1 1 1 1 1
F O . ' '
O i 0
-+ .:-
' 5
u -
z u -
-
-0.1 5 ;
-
0 -0.2 9 - 0 -0.3 I 1 1 1 I 1 I 1 1 1 1 1 1 1 1 Figure 15 Steady-State Lift, Drag, and Pitching Moment Coefficients for the NACA 0012 Airfoil at Mc = 0.4 and A = 0 Deg.
L I F T COEFFICIENT
, - A - D R A G COEFFICIENT
MOMENT COEFFICIENT A L L D A T A UNCORRECTED F L A G G E D SYMBOLS I N D I C A T E REPEAT POINTS I 0.64 - 0.60
- 0.56
- 0.52
1.4
- 0.48
1.2
- 0.44
- 0.40
- 0.36
- 0.32
- 0.28
I 0.24 -1 0.20
-
0.16
-
0.12
- 0.08
- 0.04
1 I I I I 0 0.1 I I-
t = o
z
O I -
= 5 -0.1
u -
z o
- L L
6 ; -0.2
k 0 a o -0.3 -6 -4 -2 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 ~ INCIDENCE A N G L E , a, ( D E G ) Figure 16 Steady-State Lift, Drag, and Pitching Moment Coefficients for the NACA 0012 Airfoil a t M, = 0.3 and A = 30 Deg.
7 2 L I F T COEFFICIENT M O M E N T COEFFICIENT A L L D A T A UNCORRECTED
I- FLAGGED SYMBOLS I N D I C A T E REPEAT POINTS I
O. 56 0.52 0.48 0.44 0.40 n 0.36 u I-- z 0.32 W
-
LL 0.28 U W 0.24 U a oc 0.20 n 0.16 0.12
- 0.08
-0.8 -
- 0.04
-1.0 -
-1.2) 1 I I I I I I I I 0
0.1 I
1 1
I- A
$ > A &
r", 0 '
O F z z
-
u w -0.1
2 0 - U
-
3 -0.2
k 0 1 1 1 1 I I I I 1 I I I I I I " -0.3, INCIDENCE ANGLE, a , (DEG) Figure 17 Steady-State Lift, Drag, and Pitching Moment Coefficients for the NACA 0012 Airfoil at Mc = 0.4 and A = 30 Deg.
7 3 M cos A = 0.30 , f 10 CPS, k = 0.124 0 454 # 1 0 658 0 851 0 971 1 2 3 DIM ENS1 ON LESS TIM E, PERIODS Figure 18 Unsteady Pressure Time History for Potential Flow, a~ = Oo Mcos , \ = 0 . 3 0 , f = l O c p s , k = 0 . 1 2 4 1 2 3 DIMENSIONLESS TIME, PERIOD Figure 19 Unsteady Pressure Time History for Stalled Flow Penetration, a =120 d
z
v) z 4 8 12 16 20 4 8 12 16 20 O . l I 0 V - O . ' t - O . ' i -0.2
-o,2L--- 4 8 12 16 20
Illllrllrrlll
4 8 12 16 20 O t
-o.2 t
- o . 4 L t 1 ' ' ' ' '
-0.5 0 4 8 12 16 20 24 0 4 8 12 16 20 24 INCIDENCE ANGLE, a, (DEG) Figure 20 Contribution of CN and C c Components to the Pressure Drag Comoonent, CD, for A = 0 Deg, ?i= 10 Deg, Mc = 0.40, C I M = 12 Deg, and f = 10 cps 7 6 I - -2.0
-0.1 -
I
I I I l l l l l l l l i 1 1 1 1 1 1 1 1 1 1 1 -8 -4 0 4 8 12 -8 -4 0 4 8 12 0.1 0.1
wi i o
V -0.1 -0.1 -0.2 -0.2 1 1 1 1 1 1 l 1 1 1 1 -0.3
1 1 1 1 1 1 1 1 1 1 1 1 -0.3
-12 -8 -4 0 4 8 12 -12 -8 -4 0 4 8 12
-0.2 -O.I 1
-12 -8 -4 0 4 8 12 ANGLE OF INCIDENCE, a, DEG Figure 21 Chttribution of CN and C c Components to the Pressure Drag Component,
CD, for A = 0 Deg, a =IO Deg, M , = 0.40, U M = 0 Deg, and f = 10 cps
7 7 F= 10 DEG 2 . 0 1 2.0 -
-
1.5 1.5
I ,- . -&'
-
-
1.0 1.0 -
-
0.5 0.5 f = 4.0 0 - k 0.045
1 1 1 1 1 1 1 1 1 1 1 1
~ 4 8 12 16 20 4 8 12 16 20 I' f = 8.0 4 8 12 16 20 0.5 f = 10.0 k = 0.124 k = 0.124 - 0 . 5
( ( 1 1 1 1 1 1 1 1 1 1
-0.5 0 4 8 12 16 20 24 0 4 8 12 16 20 ANGLE OF INCIDENCE, a , DEG Figure 22 Effect of Sweep, Amplitude and Frequency on the Induced Lift Response
for M c = 0.30 and UM = 12 Deg, - 1 = 0 Deg; ---,I = 30 Deg
- -
a = 10 DEG a = 8 DEG
0.6 -
-
0.4
-
0.2
-
0.0
LJ
4 8 12 16 21) I-- z
-
W 0.6 - LL L L
-
0.4 W
-
c3 0.2 Q U
-
w 0.0 U v) I 1 I 1 1 1 1 1 1 I l l
1 1 1 1 1 1 1 1 1 1 1 1 )
W 4 8 12 16 20
4 a 12 16 20
a n
-
-
0.6 0.6
-
-
0.4 0.4
-
-
0.2 0.2
-
-
0.0 0.0 k = 0.124 k = 0 . 1 2 4
-0.2 1 1 1 1 1 1 1 1 1 1 1 1 1
- 0 . 2 1 1 I I ' I I I '
0 4 8 12 16 20 24 0 4 8 12 16 20 24 ANGLE OF INCIDENCE, a, DEG Figure 23 Effect of Sweep, Amplitude and Frequency on the Induced Pressure Drag Response
for Mc = 0.30 and U M = 12 Deg, - A = 0 Deg;---A = 30 Deg
7 9 .- a = 10 DEG 0.1 0 -
-
-0.1
-
-0.2
. 7 1
f = 4.0
-0.3 - f - 4.0
ks0.049 k= 0.049 I I 1 1 1 1 1 1 1 ~ ~ 4 8 1 2 16 20 0 - -0.1 -
-
-0.2
-
-0.3 k= 0.099 4 8 12 16 20 4 8 12 16 20 -0.1 -0.2 -0.3 1 1 1 1 1 1 1 1 1 1 1 -0.4 I 0 4 8 12 16 20 : ANGLE OF INCIDENCE, a, DEG Figure 24 Effect of Sweep, Amplitude and Frequency on the Induced Moment Response f o r M c = 0 . 3 0 a n d a ~ = 12Deg-A=ODeg; - - - - - A = 3 0 D e g I 80
-
?i= 8 DEG U = 1 0 D E G 2.0
2.0 I
1.5 1 .o 0.5 f - 4.0 k = 0.03 k = 0.037 O t
u-u-
4 3 12 16 20 -I 1.5 u 1.5 I-- z 1 .o
w 1.0
L!
U U 0.5 W 0.5 I- f = 8.0 f = 8.0 U - k = 0.075 k = 0.075 -J O t I r l r l l r r l r l l L I ~ ~ I I I I I I I I J 4 8 12 16 20 4 8 12 16 20 I 1.5 1.5 1 .o 1 .o 0.5 0.5 f = 10.0 0 0 k = 0.093 k = 0.093 1 1 1 1 1 1 1 1 1 1 1 -0.5 0 4 8 12 16 20 24 ANGLE OF INCIDENCE, a, DEG Figure 25 Effect of Sweep, Amplitude and Frequency on the induced Lift Response for M c = 0.40 and a M = 12 deg, - A=Odeg; - - - - A = 3 0 d e g .
- ?i= 10 DEG a = 8 D E G . . ^ .
0.8 0.6 0.4 0.2 0.2
::I 0
k = 0.037 k = 0.037 1 1 1 1 1 1 1 1 1 1 1 1 1 ~ 1 1 1 1 1 1 1 4 8 1 2 16 20 4 8 12 16 20 I - - z
w
0.6 U U Lu 0.4 u 0.2 n Lu LI v) k = 0.075 k = 0.075 v) Lu 1 1 1 1 1 1 1 1 1 1 1 l l l l l l l l l l l l LI a 4 8 12 16 20 4 8 12 16 20 k = 0.093 -v. L 0 4 8 12 16 20 24 ANGLE OF INCIDENCE, a, DEG Figure 26 Effect of Sweep, Amplitude and Frequency on the Induced Pressure Response
for M c = 0.40 and QM = 12 Deg- A = 0 Deg;- -- A = 30 Deg
- - a = 10 D E G a - 8 D E G 0 . 1 ___--.
0 . 1 *e--, 0 r-% <-- _ _ _ _ _ - - ---:-.
.=- --: c
0 -
q*
' - 3
-
-0.1 -0.1
%
U
' 9
-o.2 t
-Oe2 t
- -0.3 f = 4.0 f = 4.0 k = 0.037 k = 0.037 1 1 1 1 1 1 1 1 1 1 1 4 8 12 16 20
>f _ _ * - - -
V 2 t - - 0 - 0 z w - ' L
- !\
0 -0.1 - 0 . 1 U U w *I
-
8 -0.2 -0.2
i - z
-
Lu -0.3 f = 8.0 E t = 8.0 k = 0.075 k = 0.075 1 1 1 1 1 1 1 1 1 1 1 4 8 12 16 20 0 - - -0.1 - - 0 . 2
-0.3 1
f = 10.0 f 10.0
-0.3 t k = 0.093
k = 0.093
- 0 . 4 1 ' I I I I I I I '
0 4 8 12 1 6 20 24 ANGLE OF INCIDENCE, a , DEG Figure 27 Effect of Sweep, Amplitude and Frequency on the Induced Moment Response for Mc = 0.40 and U M = 12 Deg,-A = 0 Deg;------ A = 30 Deg
-
-
a = 10 DEG n = 8 DEG
-2.0 t
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 -8 -4 0 4 8 -8 -4 0 4 8 1.5 1.5
1 .o
1.0 0.5 0.5 tlM = 120 4 3 12 16 20 0 - UM = 150 -0.51 I I I I ' I 4 8 12 16 20 24 28 ANGLE OF INCIDENCE, a, DEG Figure 28 Effect of Sweep, Amplitude and Mean Incidence Angle on the Induced Lift Response
for Mc = 0.30 and f = 8 cps, (k = 0.099), - A = 0 Deg; _ _ _ _ _ _ A = 30 Deg
8 4
a= 8 DEG
- a = i o D E G
- 0 . 2 1
- 8 --4 0 4 8 0.4 n a2 I-- Z w - U LL w -0.2 0 = 90 aM = 90
-o.2 t
(3 Q I I I I I I I I I I I I ]
1 1 1 1 1 1 1 1 1 1 1 1
cc 0 4 8 12 16 n 0 4 8 12 16 w KK v) w 0.6 KK a 0.4 0.2 aM= 120 1 1 1 1 1 1 1 1 1 1 1 4 8 12 16 20 4 8 12 16 20 0.8 0.8 0.6 0.6 0.4 0.4 0.2 0.2 aM = i 5 O I l l 1 1 1 1 1 1 1 1 -0.2 -0.2 4 8 12 16 20 24 28 4 8 12 16 20 24 28 ANGLE OF INCIDENCE, a, DEG Figure 29 Effect of Sweep, Amplitude and Mean incidence Angle on the Induced Pressure Drag
Response for M c = 0.30 and f = 8 cps, (k = 0.099), - A = 0 Deg; - - - -
A = 30 Deg a 5
-
-
a = 10 DEG U = 8 DEG 0.1 0.1 -0.1 -0.1 -0.2 -0.2 -0.3 -0.3 cl, =oo 1 1 1 1 1 1 1 1 1 1 1 -8 - 4 0 4 8 _ _ _ _ . - - - - - h.,
~ - - - -;>-
I - -:.--:-.-.--.
C;:. _ _ -_ - - - - -
- _ _ -T,k, I ,
-0.1 0 - - , - '. ! -0.1 0 -
- -0.2 5 -0.2 -
\i
+- -
-0.3 -0.3 - C~ = 90 Lu aM = 90
-
1 1 1 l 1 1 1 1 1 1 1 U 1 1 1 1 1 1 1 1 ~ ~ ~ I- z W 0 - 2 E - -0.1 -0.1 - -0.2 -0.2 -0.3
-0.3 1
a M = 1 2 0 aM = 1 2 O 2 1 1 I 1 I I I I 1
1 1 1 1 1 1 1 1 1 1 1 1
4 8 12 1 6 20 4 8 12 16 20 0.1
01 i
-0.1 -0.2 -0.3
4 a 12 16 20 24 28
4 8 12 16 20 24 28 ANGLE OF INCIDENCE, a, DEG Figure 30 Effect of Sweep, Amplitude and Mean Incidence Angle on the Induced Moment Response
for M = 0.30 and f = 8 cps (k = O.OSS), - A = O D e g ; ---- A = 30 Deg
-
a = 8 D E G
a= 10 D E G
1.5
2.0 I
1 .o
0.5 -0.5 -8 -4 0 4 8 I I
-
1.5 1.5
-
1 .o 1.0
-
0.5 0.5 0 - 0 4 8 12 16 0 4 8 12 16 0 - an)l= 120 1 1 1 1 1 1 1 1 ~ ~ ~ 4 8 12 16 20 4 8 12 16 20
I
1.5 1.0 .:.
,.
p' ' 0.5
0.51 0
% = 1 5 O a~ = 15' l I 1 1 l 1 1 1 1 1 1 - O.!
4 8 12 16 20 24 28 ANGLE OF INCIDENCE, a, DEG Figure 31 Effect of Sweep, Amplitude and Mean Incidence Angle on the Induced Lift Response A = 30 Deg
for Mc = 0.30 and f = 4 cps (k = 0.0491, - A = 0 Deg; ----
8 7
- -
a = 8 DEG C L = 10 D E G 0 6 0.4
0.4 t
0.2
0.2 1
-0.2 -0.2 % = 00 O d -8 -4 0 4 aM 8 = oo 1 1 1 1 l 1 1 1 1 1 ~ -8 -4 0 4 8 0 4 8 12 16 0.4 0.2 -0.2 % = 12' 1 1 1 1 1 1 1 1 1 1 1 4 8 12 16 20 0.4 0.2 -0.2 % = 15' % = 15' -0.4 1 1 1 1 1 1 1 ~ 1 1 1 -0.4 4 8 12 16 20 24 28 4 8 12 16 20 24 28 ANGLE OF INCIDENCE, a, DEG Figure 32 Effect of Sweep, Amplitude and Mean Incidence Angle on the Induced Pressure Drag
Response for Mc = 0.30 and f = 4 cps (k = 0.0491, - A = 0 Deg; ---- A = 30 Deg
-
-
a = 8 DEG U = 1 0 D E G
0.1 I
-0.2
- O . l i
-0.3 ~ % = 00
-a -4 o 4 a
I -0.1
-0.3 L - u - J (LM = 90
U o 4 a 12 16
o 4 a 12 16
w 0 I 0 - 0 W 2 I - z
0 1
, z - -0.1
-0.1 /-
-
-0.2 V
- 0 . 2 , I
T
I
-0.3 c
-0.1 -0.2 % = 15' UM 15' 1.u- -0.4
4 a 12 16 20 24 2a
4 8 12 16 20 24 28 ANGLE OF INCIDENCE, a, DEG Figure 33 Effect of Sweep, Amplitude and Mean Incidence Angle on the Induced Moment Response for Mc = 0.30 and f = 4 cps (k = 0.0491,- A = 0 Deg;---A = 30 Deg * 2.0 1.5.
1.0 -
' . : I
0.5 -
-
-1.0 0 -
-
-2.0 -0.5 - aM = 00 L I I I I I 1 I 1 1 I I 9 O a M =
1 1 1 1 1 1 1 1 1 1 1 1 1
0 4 8 12 16
-
U M = 120
1 1 1 1 1 1 1 1 1 1 1 1
4 8 12 16 20 I O S % = 15' - a5 4 8 12 16 20 24 28 4 8 12 16 20 24 28 ANGLE OF INCIDENCE, a, DEG Figure 34 Effect of Sweep, Amplitude and Mean Incidence Angle on the Induced Lift Response
for M c = 0.40 and f = 8 cps , (k = 0.075),- A = 0 Deg; ------ A = 30 Deg
0 8
-
0.6 1
0.6 - 0.4 - 0.2 0.2
0.4 i
,--_ 0 - “M 0 ’ O F aM = 00 1 I I 1 I l l I 1 1 1 - - 8 -4 0 4 8
0.6 1
n 0 0.4 I - W 0.2 - U U
‘ u o
aM = 90
1 1 1 1 1 1 1 1 1 1 1 1 1
0 4 8 12 16 U v) v)
w 0.6 0.6 1
K a 0.4 0 . 4 1 9 I , 0.2 0.2 ~ ./* ,
--
0 - - _ - - - _ - - 1 20 a M = aM = 1 2 O 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 j ~ ~ ~ ~ 4 8 12 16 20 4 8 12 16 20 0.6 0.4 0.2 QM= 15’ U I I 1 1 1 1 1 1 1 -0.2
-0.2 llllrrllrlrl
4 8 12 16 20 24 28 4 8 12 16 20 24 28 ANGLE OF INCIDENCE, a, DEG Figure 35 Effect of Sweep, Amplitude and Mean Incidence Angle on the Induced Pressure Drag Response
for M c = 0.40 and f = 8 cps, (k = 0.075). - A = 0 Deg; - --- A = 30 Deg
-
-
a = 10 DEG a = 8 DEG o. 2
-
0.1
_ _ - --•
0 -
I e - -
-
-0.1
-0.2 - a M = 0 '
1 1 1 1 1 1 1 1 1 1 1 -8 -4 0 4 8
I I
L Z w - - L L LI 0 4 8 12 16 W I- 0.1 - _.*---.
0.1 - _ _ _ *.--- 0 -
-
-0.1
-
-0.2 1 1 1 1 1 1 1 1 1 1 1 _ * - - _ _
0.1 - 0.1 - _.-e
< - - _ _ _ _ _ _ - - - 2 - f- \.-\ . .
. .
. .
.-a. 0 -
\ \ \ .
-0.1 -
-0.1 0 - - > \ ' J
'% \ \ , \ ','-, aM = 150
I .
Q .
\ \
. \
'\ ' -0.2 - . --\,
-0.2 - <
a M = i 5 O ',.Y I I . -0.3 1 1 1 1 1 1 1 1 1 1 1 '
I I '
-0.3
-
-
a = 8 D E G a - 10 DEG k=0.099 0 - k=0.099 M= 0.3 M= 0.3 I I 1 1 1 1 1 1 1 1 1 4 8 12 16 20 I 1.5 1.0 0.5 0 k k=0.075
I M= 0.4
M= 0.4
-0.5 1 1 1 1 1 1 1 1 1 1 1 -0.5 1 1
0 4 8 12 16 20 24 0 4 8 12 16 20 2 ANGLE OF INCIDENCE, a, DEG Figure 37 Effect of Sweep, Amplitude and Mach Number on the Induced Lift Response
f o r a ~ = 1 2 D e g a n d f = 8 cps, - A = O D e g ; - - - - - A = 30 Deg
0.8 0.8
0.6 -
0.6 -
- 0.4
0.4 -
d
-
0.2 0.2 I , -v' k= 0.099
- -
_ _ - - 0 -
-_,B - M = 0.3
M = 0.3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 ~ ~ ~ ~ ~ 0.6 0.4 0.2 M = 0.4
-0.2 I ' 1 I I 1 1 ' 1 I I
-0.2 0 4 8 1 2 16 20 24 0 4 8 12 1 G 20 24 ANGLE OF INCIDENCE, a , DEG Figure 38 Effect of Sweep, Amplitude and Mach Number on the Induced Pressure Drag Response
f o r a ~ = 12 Deg and f = 8 cps ,-A = 0 Deg; - - - A = 30 Deg
9 4 - - a = 8 DEG a - 1 0 D E G 0.1 I I 0.1 I
' --0.1 ' -
-0.1 ' ' -0.2 -0.2
k= v 0.099
' k = 0.099 -0.3 k= 0.099 H M = 0.3 M = 0.3 I - . 1 1 1 I 1 I l l I I I 1 w 4 8 12 16 20 4 8 12 16 20 z U L L w I - w H
-0.1 -
-
-0.2 k= 0.075 k= 0.075
-0.3 1
M = 0.4 M = 0.4
-0.3 t
-0.4 4
0 4 8 12 16 20 24 ANGLE OF ATTACK, a. DEG Figure 39 Effect of Sweep, Amplitude and Mach Number Induced Moment Response for
U M = 12 Deg and f = 8 cps, - A = 0 Deg;---A = 30 Deg
k = 0 . 1 5 6 k = 0.106 f = 3.8 f = 2.5 I l l 1 1 1 ' 1 ' ' 1 1 1 I l l
3.0 [
-
-
-
-
k = 0.261 0.21 2 f = 6.3 5.0 -w, I I I I 1 , ANGLE OF INCIDENCE, a, DEG Figure 40 Effect of Frequency on the Induced Lift Response for M c = 0.1, U M = 15 Deg,E= 10 Deg, A = 30 Deg 1 .o 0.8 0.6 0.4 0.2 I-: -0.2 LL1
C !
LL 1 .o
-
0.8
-
0.6
-
0.4 k = 0.261 0.2 f = 6.3 n " 4 8 12 16 20 24 28 32 4 8 12 16 20 24 28 32 ANGLE OF INCIDENCE, a, DEG figure 41 Effect of Frequency on the induced Pressure Drag Response for Mc = 0.1, Q M = 15 Deg, h = 10 Deg, A = 30 Deg
-
-
-
I I
-
k = 0.1 56 k = 0.106
w
f = 3.8 f - 2 . 5
0 2 -0.4 t
- 1 1 1 1 1 1 1 1 1 1 1 1 1 , -0.5 -d U LLI
E
0.1 r c k = 0.261 k = 0.212 f = 6.3 f = 5.0
t
4 . 5 4 8 12 16 20 24 28 32 4 8 12 16 20 24 28 3 2 ANGLE OF INCIDENCE, a, DEG Figure 42 Effect of Frequency on the Induced Moment Pesponse for M c = 0.1, a M = 15 Deg,
-
a = 10 Deg, A = 30 Deg 0.4 - aM = 00 QM = 90
-
0.2 -
' A A
S A
A ! ! A 0 0 u W
-
I- -0.2 -
W I a E a n u
z -0.4 I I I 1 I I
n Q = 1 5 O b
-
g 0.2
w A A Q A 0
A A
0 A A A
t
-0.2 -0.4 1 I I I I I I 0 0.4 0.8 0.12 0.16 0 6 0.4 0.8 0.12 0.
REDUCED FREQUENCY, k Figure 43 Variation of aerodynamic damping parameter with reduced frequency ti= 100 0 A=0°;Mc=0.30 A = Oo; MC = 0.40 A 11 = 30°; MC = 0.30 A A = 3 0 ’ ; MC = 0.40 0.4 aM = 00 0.2 T H E O R Y
LE
I l l a‘ L u -0.2 I- W z Q r x I i 1 -0.4
I
1 1 I -0.4 REDUCED FREQUENCY, k Figure 44 Variation of aerodynamic damping parameter with reduced frequency ( a ) U N S T E A D Y FLOW, INCREASING A N G L E OF A T T A C K B O U N D A R Y L A Y E R EDGE
Yp=c
(b) S T E A D Y M E A N FLOW, SAME A N G L E OF A T T A C K Flow Fields Near an Airfoil a t Steady and Unsteady Angle of Attack Figure 45 CHORDWISE POSITION, x/c, % 0.4 UPPER 1.0 UPPER 7.3 UPPER 15 UPPER 27 UPPER 0 50 100 150 200 250 TIME FROM ARBITRARY ZERO, MtLLESECONDS Absolute-Level Pressure Fluctuations on a Chordwise Line Along a Figure 46 Steady Unswept NACA 0012 Airfoil at 0.30 Mach Number and 150 Angle of Attack. ( a ) Forward Upper Surface C H 0 R DW I S E PO SIT I 0 N, XIC. 96 0.4 UPPER 27 UPPER 66 UPPER
v
85 UPPER 97 UPPER 0 50 100 150 200 250 TIME FROM ARBITRARY ZERO, MILLISECONDS Figure 46 (Concluded) - (b) Forward and Aft Upper Surface CHORDWISE POSITION, XIC. % 97 LOWER 83 LOWER 19 LOWER 1 . 7 LOWER 0.5 LOWER 0 50 100 150 200 250 TIME FROM ARBITRARY ZERO, MILLISECONDS Figure 47 Absolute-Level Pressure Fluctuations on a Chordwise Line Along the Lower Surface of a Steady Unswept NACA 0012 Airfoil at 0.30 Mach Number and 150 Angle of Attack.
CHORDWISE POSITION, XIC. % 97 UPPER 97 LOWER 83 LOWER 63 LOWER 39 LOWER I I 1 I 0 50 100 150 200 250 TIME FROM ARBITRARY ZERO, MILLISECONDS Figure48 Self-Scaled Pressure Fluctuation on a Chordwise Line Along a Steady Unswept NACA 0012 Airfoil a t 0.30 Mach Number and 150 Angle of Attack. (a) Aft Upper and Lower Surfaces CHORDWISE POSITION, x/c. "/o 39 LOWER 19 LOWER 1.7 LOWER 0.5 LOWER 0 . 4 UPPER I I I I 100 150 200 250 0 50 TIME FROM A R B I T R A R Y ZERO, MILLISECONDS (Concluded)-(b) Forward Lower and Upper Surfaces Figure 48 19% CHORD, LOWER SURFACE ORD. LOWER SURFACE 200 250 50 100 150 TIME FROM A R B I T R A R Y ZERO, MILLISECONDS Figure 49 Phase Reversal of Self-Scaled Pressure Fluctuations on Forward Lower Surface of a Steady Unswept NACA 0012 Airfoil at 0.30 Mach Number and 1 5 O Angle of Attack SPANWISE POSITION.
XIC. % (PRESSURE) (HOT FILM, SIGN REVERSED) 26 (PRESSURE) ( H O T FILM, SIGN REVERSED) 56 (PRESSURE) TIME FROM ARBITRARY ZERO, MILLISECONDS Self-Scaled Pressure and Heat Transfer Fluctuations on Spanwise Lines Along Figure ,50 a Steady Unswept NACA 0012 Airfoil at 0.30 Mach Number and 150 Angle of Attack. Pressures at 0.4 % Chord, Hot Films at 2.1 % Chord, Upper Surface.
'E H 0 R D W I S E POS I T I 0 N , X I C , % 0.4 UPPER
p-
1.0 UPPER 2.0 UPPER 4.5 UPPER 15 UPPER I I I I 0 50 100 150 200 250 TIME FROM ARBITRARY ZERO, MILLISECONDS Figure 51 Absolute-Level Pressure Fluctuations on a Chordwise Line Along a Steady Unswept NACA 0012 Airfoil a t 0.30 Mach Number and 190 Angle of Attack. (a) Forward Upper Surface CHORDWISE POSITION, XIC. 46 15 UPPER 27 UPPER 66 UPPER 85 UPPER 97 UPPER 100 150 200 2 50 0 50 TI ME F ROM ARBITRARY ZE RO, M I LLISECON DS
Figure 51 (Concluded) - (b) Aft Upper Surface
CHORDWISE POSITION, X I C . % 97 UPPER 97 LOWER 83 LOWER 1.7 LOWER 0.5 LOWER 0 50 100 150 200 2 50 TIME FROM ARBITRARY ZERO, MILLISECONDS Figure 52 Absolute-Level Pressure Fluctuations on a Chordwise Line Along the Lower Surface of a Steady Unswept NACA 0012 Airfoil at 0.30 Mach Number and 190 Angle of Attack.
CHORDWISE POSITION ', X I C . % 9 7 LOWER 63 LOWER 19 LOWER 1.7 LOWER 0 . 5 LOWER I I 1 I 100 150 200 250 0 50 TIME FROM ARBITRARY ZERO, MILLISECONDS Figure 53 Self-scaled Pressure Fluctuations on a Chordwise Line Along the Lower Surface of a Steady Unswept NACA 0012 Airfoil a t 0.30 Mach Number and 190 Angle of Attack SPANWISE POSITION, X!C. % ( P R ESSUR E) (HOT FILM, SIGN REVERSED) (PRESSURE) (HOT FILM, SIGN REVERSED) 56 (PRESSURE) I I I I TIME FROM ARBITRARY ZERO, MILLISECONDS Figure 54 Self-Scaled Pressure and Heat Transfer Fluctuations on Spanwise I.ines Along a Steady Unswept NACA 001 2 Airfoil a t 0.30 Mach Number and 1 9 Angle of Attack. Pressures at 0.4 % Chord, Hot Films at 2.1 % Chord, Upper Surface.
CHORDWISE POSITION, xic. % a 0.4 UPPER 1.0 UPPER 4.5 UPPER 15 UPPER
I
27 UPPER 150 200 250 50 100 TIME FROM ARBITRARY ZERO, MILLISECONDS Figure 55 Absolute-Level Pressure Fluctuations on a Chordwise Line Along a Steady Unswept NACA 0012 Airfoil at 0.40 Mach Number and 120 Angle of Attack. (a) Forward Upper Surface CHORDWISE POSITION, X I C . % 27 UPPER 66 UPPER 85 UPPER A 9 7 UPPER 9 7 LOWER 0 50 100 150 200 250 TIME FROM ARBITRARY ZERO, MILLISECONDS
Figure 55 (Concluded) - (b) Aft Upper and Lower Surfaces
CHORDWISE POSITION.
XIC. % 27 UPPER
I ‘ 1
66 UPPER
I I I I I
50 100 150 200 2 50 TIME FROM A R B I T R A R Y ZERO, MILLISECONDS Figure 56 Self-Scaled Pressure Fluctuations on a Chordwise Line Along the Upper Surface a Steady Unswept NACA 0012 Airfoil at 0.40 Mach Number and 120 Angle of Attack.
2 7 % CHORD, UPPER SURFACE I I
I 66% CHORD, UPPER SURFACE
~~ ~ ~ 27% CHORD, UPPER SURFACE, REVERSED SIGN UPPER SURFACE
I I I, I 1
0 50 100 150 200 250 TIME FROM A R B I T R A R Y ZERO, MILLISECONDS Figure 57 Phase Reversal of Self-scaled Pressure Fluctuations on Mid-Chord Upper Surface of a Steady Unswept NACA 0012 Airfoil at 0.40 Mach Number and 120 Angle of Attack CHORDWISE POSITION, X I C . % 0.4 UPPER 1.0 UPPER 4.5 UPPER 15 UPPER 27 UPPER 0 50 100 150 200 250 TIME FROM ARBITRARY ZERO, MILLISECONDS Absolute-Level Pressure Fluctuations on a Chordwise Line Along a Figure 58 Steady Unswept NACA 0012 Airfoil a t 0.40 Mach Number and 140 Angle of Attack. (a) Forward Upper Surface CHORDWISE POSITION, XIC, ?6 27 UPPER 66 UPPER 85 UPPER 9 7 UPPER 9 7 LOWER 0 50 100 150 200 250 TIME FROM ARBITRARY ZERO, MILLISECONDS Figure 58 (Concluded)- (b) Aft Upper and Lower Surfaces CHORDWISE POSITION, x/c, % 0.4 UPPER 27 UPPER 66 UPPER 85 UPPER 97 UPPER
I I
I 100 150 200 250 0 50 TIME FROM ARBITRARY ZERO, MILLISECONDS Figure 59 Self-scaled Pressure Fluctuations on a Chordwise Line Along a Steady Unswept NACA 0012 Airfoil a t 0.40 Mach Number and 140 Angle of Attack.
(a) Upper Surface CHORDWISE POSITION, X I C . % 97 UPPER 97 LOWER .
I
19 LOWER
w I
1.7 LOWER
' I
A I
0.5 LOWER 1 I I I 50 100 150 200 250 TIME FROM ARBITRARY ZERO, MILLISECONDS Figure 59 (Concluded)-(b) Lower and Aft Upper Surfaces 1 2 1 85% CHORD UPPER SURFACE -66% CHORD, UPPER SURFACE -19% CHORD, LOWER SURFACE
v- 0.5% CHORD, LOWER SURFACE, REVERSED SIGN
I I I I I
0 50 100 150 200 250 TllllE FROM A R B I T R A R Y ZERO, MILLISECONDS Phase Reversal of Self-scaled Pressure Fluctuations on Aft Upper Surface and Figure 60 Forward Lower Surface of a Steady Unswept NACA 0012 Airfoil at 0.40 Mach Number and 140 Angle of Attack.
FREE S T R E A M L E A D I N G V E L O C l T Y 3 0 ' SWEEPBACK S T A G N A T I O N POIN7 UPPER SURFACE
I LOWER SURFACE
S T R E A M L I N E S T R E A M LI N E
I
I
I
I
I
I
I
I
I
I
I
I
I
Calculated Streamline Shapes at Edge of Boundary Layer Figure 61 for NACA 0012 Airfoil with 30° Sweepback. Incompressible Flow, Lift Coefficient = 1.0 Referenced to Streamwise Flow.
12 3 CHORDWISE POSITION, XIC. "0 0.4 UPPER 2.0 UPPER 27 UPPER 97 UPPER 97 LOWER I I I I 50 100 150 200 250 TIME FROM ARBITRARY ZERO, MILLISECONDS Figure 62 Absolute-Level Pressure Fluctuations on a Line Normal to the Leading Edge of a Steady 300 Swept NACA 0012 Airfoil at 0.30 Mach Number and 150 Angle of Attack Normal to the Leading Edge, 1 2 4 CHORDW ISE POSITION, X I C . % 0.4 UPPER 11 UPPER 27 UPPER 66 UPPER
97 UPPER i
I I I I I TIME FROM ARBITRARY ZERO, MILLISECONDS Figure 63 Self-Scaled Pressure Fluctuations on a Line Normal to the Leading Edge of a Steady 300 Swept NACA 0012 Airfoil at 0.30 Mach Number and 150 Angle of Attack Normal to Leading Edge. (a) Upper Surface 1 2 5 CHORDWISE POSITION, XIC. % 97 UPPER 9 7 LOWER 1 9 LOWER 1.7 LOWER 0.5 LOWER I I I I I 100 150 200 250 0 50 TIME FROM ARBITRARY ZERO, MILLISECONDS Figure 63 (Concluded) - (b) Lower and Aft Upper Surfaces 0.4 UPPFR 4.5 UPPER 27 UPPER 9 7 UPPER
I I I I
D 50 100 1 50 200 TIME FROM ARBITRARY ZERO, MILLISECONDS Absolute-Level Pressure Fluctuations on Lines Parallel to the Free Stream Along Figure 64 I the Upper Surface of a 300 Swept NACA 0012 Airfoil at 0.30 Mach Number and 200 Angle of Attack Normal to the Leading Edge. (a) Full Chord Length I 1 2 7 CHORDWI SE POSITION x/c, % 0 . 4 UPPER I 4.5 UPPER UPPER UPPER
I I
I I I
100 150 200 2 50 0 50 TIME FROM ARBITRARY ZERO, MILLISECONDS Figure 64 (Concluded) (b) Line Normal t o Leading Edge 7.3 UPPEP 1 1 UPPER I
I
66 UPPER 0 50 100 150 200 250 TIME FROM A R B I T R A R Y ZERO, MILLISECONDS I Figure 65 Self-Scaled Pressure Fluctuations on a Line Normal to the Leading Edge of a Steady 300 Swept NACA 0012 Airfoil a t 0.30 Mach Number and 200 Angle of Attack Normal to the Leading Edge. (a) Upper Surface CHORDWISE POSITION, XIC, o/b 0.4 UPPER 0.5 LOWER 19 LOWER 83 LOWER 97 UPPER 0 50 100 150 200 250 TIME FROM ARBITRARY ZERO, MILLISECOND Figure 65 (Concluded) - (b) Lower Surface and Extremes of Upper Surface CHORDWISE POSITION, X/C.% 0.4 UPPER 4.5 UPPER 27 UPPER 97 UPPER I I 1 I 50 100 150 200 2!
TIME FROM ARBITRARY ZERO, MILLISECONDS Figure 66 Absolute-Level Pressure Fluctuations on a Line Parallel to the Free Stream Along the Upper Surface of a 300 Swept NACA 0012 Airfoil at 0.30 Mach Number and 160 Angle of Attack Normal to Leading Edge, CHORDWISE POSITION, XIC,% 0.4 UPPER I 2.0 UPPER 4.5 UPPER 9.8 UPPER I 15 UPPER I I I I 50 100 150 200 2 0 TIME FROM ARBITRARY ZERO, MILLISECONDS Figure 67 Absolute-Level Pressure Fluctuations on a Line Normal to the Leading Edge of a Steady 300 Swept NACA 0012 Airfoil a t 0.40 Mach Number and 160 Angle of Attack Normal to the Leading Edge. ( a ) Forward Upper Surface CHORDWISE POSITION, X/C%
1 27 UPPER
66 UPPER 85 UPPER 9 7 UPPER 97 LOWER
--
I 1 I I I 50 100 150 200 2 TIME FROM ARBITRARY ZERO, MILLISECONDS Figure 67 (Concluded)- (b) X Figure 68 Analytical Simulation of Leading Edge Suction Peak.
w N 3. Recipient's Catalog No. 2. Government Accession No 1 . Report No.
NASA CR-3092
I I
5 Report Date 4 Title and Subtitle The I n f l u e n c e of Sweep on t h e Aerodynamic Loading of a n
May 1 9 7 9
O s c i l l a t i n g NACA 001 2 A i r f o i l . Volume I - T e c h n i c a l Report 6 Performing Olganization Code 8 Performing Orynization Report No.
' Author(s) A . 0. S t . H i l a i r e , F. 0. Carta, and M. R . F i n k , U n i t e d T e c h n o l o g i e s Research C e n t e r , and
t
W . D. J e p s o n , S i k o r s k y A i r c r a f t D i v i s i o n , 1J.T.C.
Work No, 9 Perforrning Organization Name and Address U n i t e d T e c h n o l q g i e s Research Center 1 1 Contract or Grant No S i l v e r Lane NASI- 148 7 3 East H a r t f o r d , Conn. 06108 13 Type of Report and Period Covered 12 Sponsoring Agency Name and Address C o n t r a c t o r Report - N a t i o n a l A e r o n a u t i c s and Space A d m i n i s t r a t i o n 14 Sponsoring Agency Code Washington, D . C . 20546 7. Key Words (Suggested by Authorlsll 18. Distribution Statement Aerodynanic Testing Swept W irig Aerodliiar i c s U n c l a s s i f i e d - U n l i m i t e d Dynamic S t a l l T r a i l i n g Edge Noise O s c i l l a t i n p , IIACA 0012 A i r f o i l Turbulence Comection P i t c h i n g O s c i l l a t i o n s Unsteady Aerodynamics Subject C a t e g o r y 02 9 Security Classif. (of this report1 20. Security Classif. (of this page) 22. Rice' 2 1 . NO. of Pages U n c l a s s i f i e d 137 $7.25 U nc 1 ass i f i ed * For s a l e b y the Natlonal T e c h n i c a l Informallon Service, Sorinpfield Virmnta 22161 - NASA-Langley, 1979