Helicopter rotor trailing edge noise

of 6 w a s n o t a v a i l a b l e p o s s i b l y due t o t h e asymptotic shape of t h e i r v e l o c i t y p r o f i l e n e a r t h e edge of t h e boundary l a y e r . D e t a i l e d d i s c u s s i o n s of t h e procedures used t o p r e d i c t 6 i n each of t h e above s t u d i e s are g i v e n i n Appendix D. Tables I11 and I V list t h e a v e r a g e v a l u e s of 6 c a l c u l a t e d i n each c a s e .

F i g u r e 26 shows t h e measured t r a i l i n g edge n o i s e sound p r e s s u r e l e v e l s o b t a i n e d from t h e p r e s e n t s t u d y f o r a = 7.6' a n g l e of a t t a c k . The s p e c t r a were measured a t d i f f e r e n t r e t a r d e d a n g l e s b u t were n o t converted t o a common r e t a r d e d a n g l e . T h i s w a s , however, done when t h e s p e c t r a were normalized t o check f o r t h e e x i s t e n c e of a s c a l i n g l a w . Note t h a t a l l a c o u s t i c s p e c t r a r e p r e s e n t t h e a c o u s t i c r a d i a t i o n from a u n i t l e n g t h ( 1 f t o r 0.3 m) of t h e a i r f o i l .

F i g u r e s 27 and 28 p r e s e n t t h e a c o u s t i c s p e c t r a measured by p r e v i o u s i n v e s t i g a t o r s .

Frequency i n f o r m a t i o n i n each case i s g i v e n i n terms of a S t r o u h a l number based on t h e boundary layer t h i c k n e s s v a l u e s l i s t e d i n T a b l e s I11 and I V . These s p e c t r a r e p r e s e n t t r a i l i n g edge n o i s e measurements from a i r - f o i l geometries and chord l e n g t h s d i f f e r e n t from t h e p r e s e n t s t u d y . The follow- i n g d i s c u s s i o n d e v e l o p s t h e s c a l i n g l a w and tests i t a g a i n s t t h e d i f f e r e n t d a t a s o u r c e s .

- Dependence of t r a i l i n g edge n o i s e o n Mach number

S c a l i n g Law Development Comparisons between and d i r e c t i v i t y were a s s e s s e d i n t h e p r e v i o u s s u b s e c t i o n s .

t h e o r y and experiment i n d i c a t e d t h a t t h e v e l o c i t y dependence can b e modeled as 5 5 M o r as U f o r i n c o m p r e s s i b l e flow. I n a d d i t i o n , t h e n o i s e d i r e c t i v i t y p a t t e r n c a n be r e p r e s e n t e d by e q u a t i o n (32) i n t h e p l a n e normal t o t h e a i r f o i l model. However, t h e i n f l u e n c e of a i r f o i l p r o f i l e shape and a n g l e of a t t a c k have n o t y e t been q u a n t i f i e d . These parameters are considered t o i n f l u e n c e t h e n o i s e i n d i r e c t l y by a l t e r i n g t h e t u r b u l e n t boundary l a y e r t h i c k n e s s a t t h e a i r - f o i l t r a i l i n g edge.

Noise dependence on boundary l a y e r t h i c k n e s s w a s modeled as a l i n e a r func- t i o n of 6. A l i n e a r dependence on 6 a l s o f o l l o w s from t h e t h e o r e t i c a l t r a i l -

*

i n g edge n o i s e f o r m u l a t i o n . S i n c e 6 is p r o p o r t i o n a l t o 6 f o r t h e f l a t p l a t e

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geometry used i n t h e t h e o r e t i c a l d e r i v a t i o n , 6 c a n b e r e p l a c e d by 6.

The t h e o r e t i c a l dependence on 6 w i l l become more e x p l i c i t i n t h e n e x t sec- t i o n t i t l e d T r a i l i n g Edge Noise P r e d i c t i o n s . There t h e h i g h frequency l i m i t of e q u a t i o n (21) w i l l b e d e r i v e d t o show t h e dependence on 6 as w e l l as t h e o t h e r p h y s i c a l parameters. The r e s u l t i n g e x p r e s s i o n guided t h e s e l e c t i o n of t h e s p e c i f i c p a r a m e t r i c dependence f o r u s e i n t h e s c a l i n g l a w . It should be noted t h a t t h e l i n e a r dependence on 6 a g r e e s w i t h t h e d e r i v a t i o n of Ffowcs W i l l i a m s and H a l l ( r e f . 1 6 ) i n a d d i t i o n t o t h e a n a l y s i s of Howe (eq. (7), r e f . 11).

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Based on t h e above arguments f o r t h e p a r a m e t r i c dependence on M, D and 6, t h e o v e r a l l sound p r e s s u r e l e v e l f o r a two-dimensional i s o l a t e d a i r f o i l s e c t i o n i s g i v e n by Here t h e parameter s d e f i n e s t h e a i r f o i l span and re r e p r e s e n t s t h e a c o u s t i c source-to-microphone d i s t a n c e i n t h e r e t a r d e d c o o r d i n a t e system. I n l o g a r i t h - mic form t h e above e q u a t i o n becomes OASPL = 50 loglo 1 0 0 + 1 0 log,o 2 '' + IO loglo 6 + K , , re

u i n knots

where K 1 i s t h e unknown c o n s t a n t of p r o p o r t i o n a l i t y .

A r e f e r e n c e v e l o c i t y of 100 k n o t s w a s s e l e c t e d f o r t h e v e l o c i t y s c a l i n g term t o p e r m i t comparing t h e value of K1 o b t a i n e d f r o m the p r e s e n t s t u d y w i t h t h e v a l u e p r e v i o u s l y d e t e r - mined i n t h e a i r f r a m e n o i s e s t u d y by F i n k ( r e f s . 6 and 7). For t h i s r e a s o n t h e v e l o c i t y i n e q u a t i o n ( 6 3 ) must b e i n terms of k n o t s . Note t h a t e q u a t i o n s ( 6 2 ) ( 6 3 ) a p p l y t o a n a i r f o i l w i t h z e r o sweepback a n g l e a t t h e t r a i l i n g edge.

and I f a u n i v e r s a l spectrum e x i s t s t h e n t h e OASPL and 1 / 3 o c t a v e band sound p r e s s u r e l e v e l are r e l a t e d by a S t r o u h a l dependent f u n c t i o n where Here, t h e parameter SPL r e p r e s e n t s t h e 1 / 3 o c t a v e band sound p r e s s u r e l e v e l i n dB and F1 d e s c r i b e s t h e spectrum shape. Solving e q u a t i o n s ( 6 3 ) and ( 6 4 ) f o r t h e SPL dependence g i v e s

u in knots

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Recognizing t h a t D = 1 a t 8, go", and i s o l a t i n g b o t h F1(St) and K1 g i v e s U in knots By s u b t r a c t i n g t h e second and t h i r d terms on t h e r i g h t s i d e of e q u a t i o n from t h e d i f f e r e n t 1 / 3 o c t a v e band s p e c t r a i n f i g u r e s 26 t o 28, t h e e x i s - (66) t e n c e of a u n i v e r s a l spectrum shape c a n b e t e s t e d . I f t h e r e s u l t i n g c u r v e s of F1(St) + K1 f o r each d a t a s e t c o l l a p s e on a s i n g l e c u r v e t h e n t h e s c a l i n g l a w s i n e q u a t i o n s ( 6 4 ) and (65) w i l l have been v e r i f i e d . Furthermore, t h e e x i s t e n c e of a normalized spectrum shape w i l l have been confirmed.

Normalized S p e c t r a - F i g u r e 29 shows t h e normalized a c o u s t i c s p e c t r a ob- t a i n e d from t h e p r e s e n t s t u d y . The n o r m a l i z a t i o n i n c l u d e s c o n v e r s i o n of t h e s p e c t r a measured a t d i f f e r e n t r e t a r d e d a n g l e s i n f i g u r e 26 t o a common a n g l e of 8, = 90" where t h e d i r e c t i v i t y f u n c t i o n , 5 , i s u n i t y . T h e o r e t i c a l d i r e c - t i v i t y c a l c u l a t i o n s were used f o r t h e d a t a c o n v e r s i o n .

T r a i l i n g edge n o i s e s p e c t r a i n f i g u r e 29 tend t o c o l l a p s e o n t o a s i n g l e c u r v e when normalized by t h e p a r a m e t e r s on t h e r i g h t s i d e of e q u a t i o n (66).

Although a d e f i n i t e spectrum peak c a n n o t b e determined from t h e d a t a shown h e r e , t h e c u r v e s u g g e s t s t h a t t h e peak is n e a r S t = 0.1. T h i s i s similar t o t h e v a l u e of S t = 0 . 1 determined by Fink ( r e f s . 6 and 7) i n t h e s t u d y of t r a i l i n g edge n o i s e g e n e r a t e d by f u l l s c a l e c l e a n a i r f r a m e c o n f i g u r a t i o n s .

Normalized a c o u s t i c s p e c t r a o b t a i n e d from t h e earlier d a t a r e p o r t e d by S c h l i n k e r are shown i n f i g u r e 30.

The d a t a c o l l a p s e s o n t o a s i n g l e c u r v e w i t h t h e spectrum peak o c c u r r i n g n e a r = 0.1. Values of t h e p a r a m e t e r s used i n S t t h e n o r m a l i z a t i o n are g i v e n i n Table 111.

F i g u r e 3 1 shows t h e normalized a c o u s t i c s p e c t r a o b t a i n e d from t h e d a t a r e p o r t e d by Brooks and Hodgson f o r a = 5". The spectrum peak i n f i g u r e 3 1 o c c u r s n e a r S t = 0.14 which i s c l o s e t o t h e S t r o u h a l peak s u g g e s t e d by f i g u r e s 29 and 30.

A t a b l e of t h e peak S t r o u h a l numbers a s s o c i a t e d w i t h t h e d i f f e r e n t d a t a s o u r c e s d e s c r i b e d above g i v e s I n v e s t i g a t o r s Peak S t V a l u e Based on 6 P r e s e n t Study 0.1 Brooks and Hodgson 0.14 S c h l i n k e r 0 . 1 Based on t h e t a b u l a t e d v a l u e s t h e S t r o u h a l peak a s s o c i a t e d w i t h t r a i l i n g edge n o i s e l i e s between S t = 0 . 1 and 0.14. This is c o n s i s t e n t w i t h t h e v a l u e of S t = 0 . 1 o b t a i n e d from t h e c l e a n a i r f r a m e t r a i l i n g edge n o i s e s t u d i e s of Fink ( r e f s . 6 and 7) b u t d i f f e r s from t h e v a l u e r e p o r t e d by Brooks and Hodgson ( r e f . 10). T h e i r s t u d y based t h e S t r o u h a l number on t h e measured v a l u e of 6* i n s t e a d of 6 as i n t h e above t a b u l a t i o n . eak S t r o u h a l num- T h e i r r a n g e of

E

b e r v a l u e s w a s c l o s e t o t h e v a l u e s t a b u l a t e d above w i t h S t ( 6 ) v a r y i n g from

* *

0.07 t o 0.1. Here S t ( 6 ) d e s i g n a t e s a S t r o u h a l v a l u e based on 6 . It i s n o t

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clear why t h e S t r o u h a l v a l u e s would b e similar when 6 i s s i g n i f i c a n t l y smaller.

*

It i s p o s s i b l e t h a t t h e v a l u e of 6 w a s t o o l a r g e as d i s c u s s e d i n Appendix D.

The measurements of Brooks and Hodgson can a l s o be compared w i t h t h e peak

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S t r o u h a l v a l u e (based on 6 ) o b t a i n e d from t h e s t u d y of Heller and Dobrzynski ( r e f . 8). The latter s t u d y p r e s e n t e d f a r - f i e l d t r a i l i n g edge n o i s e s p e c t r a o n l y as a f u n c t i o n of frequency. 6* = 5 mm, p r e s e n t e d However, t h e v a l u e of i n r e f e r e n c e 8 to nondimensionalize t h e s u r f a c e p r e s s u r e s p e c t r a , c a n a l s o b e used t o form a nondimensional S t r o u h a l number f o r t h e f a r - f i e l d r a d i a t i o n .

Based on t h e spectrum peak o c c u r r i n g a t f = 200 Hz when U = 50 m/sec ( s e e

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f i g . 1 4 , r e f . 8 ) , t h e peak S t r o u h a l number becomes S t ( 6 ) = 0.02. T h i s is a p p r o x i m a t e l y a f a c t o r of 4 t o 5 smaller t h a n t h e peak S t r o u h a l v a l u e r e p o r t e d i n r e f e r e n c e 10.

The S t r o u h a l peak a s s o c i a t e d w i t h t h e measurements of Heller and Dobrzynski (ref. 8) a g r e e s with t h e a v e r a g e v a l u e determined from t h e p r e s e n t s t u d y . I f

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S t = 0.11, based on t h e a v e r a g e v a l u e of 6 , t h e n u s i n g 6 = 6 / 8 , t h e S t r o u h a l number based on d i s p l a c m e n t t h i c k n e s s is St(6*) = 0.014. T h i s is similar t o

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t h e v a l u e of S t ( 6 ) = 0.02 c a l c u l a t e d f o r t h e s t u d y of Heller and Dobrzynski.

Generalized S c a l i n g Law Approach - The g e n e r a l c o n c l u s i o n from f i g u r e s 29 t o 3 1 i s t h a t f o r a g i v e n a i r f o i l geometry, 1 / 3 o c t a v e band t r a i l i n g edge n o i s e s p e c t r a c o l l a p s e o n t o approximately a s i n g l e c u r v e when normalized by t h e s c a l i n g l a w g i v e n i n e q u a t i o n ( 6 6 ) . It now remains t o d e t e r m i n e i f t h e normalized s p e c t r a o b t a i n e d from t h e d i f f e r e n t a i r f o i l g e o m e t r i e s c a n b e r e p r e s e n t e d by a s i n g l e spectrum f u n c t i o n , F1(St), and a c o n s t a n t , K1. For t h i s purpose, t h e s p e c t r a i n f i g u r e s t h e same graph as shown i n f i g u r e 32. Only s e l e c t e d 29 t o 3 1 were p l o t t e d on s p e c t r a are shown t o a v o i d crowding t h e d a t a .

Development of Equation - The s u c c e s s of n o r m a l i z i n g t h e s p e c t r a from d i f f e r e n t a i r f o i l g e o m e t r i e s d e m o n s t r a t e s t h a t t h e r e e x i s t s a u n i v e r s a l t r a i l i n g edge n o i s e spectrum. To q u a n t i f y t h e spectrum f o r n o i s e p r e d i c t i o n s r e q u i r e s a n a l y t i c a l l y d e s c r i b i n g t h e f u n c t i o n a l form f o r F1(St). T h i s c a n b e achieved by f i t t i n g a n e q u a t i o n t o t h e nondimensional spectrum such as t h e s o l i d 32. I n t h i s c a s e . t h e a n a l y t i c a l e q u a t i o n c o r r e s p o n d s t o s o l i d l i n e i n f i g u r e t h e f u n c t i o n p r e s e n t e d by Fink i n r e f e r e n c e 6 and 7 f o r f u l l - s c a l e a i r f r a m e t r a i l i n g edge n o i s e . The f u n c t i o n i s c u r r e n t l y used i n t h e NASA ANOPP T o t a l A i r c r a f t A n a l y s i s .

The e q u a t i o n d e s c r i b i n g t h e r e l a t i o n s h i p between 113 o c t a v e band sound p r e s s u r e l e v e l s and t h e o v e r a l l sound p r e s s u r e l e v e l is

6 (f) = SPLIl3 - OASPL = 1 0 I O Q , ~ f 0.613 ( f L ) ' - [(&)y2+ Q5]'\ (67)

where f i s t h e frequency a s s o c i a t e d w i t h t h e spectrum peak. Replacing f r e q u e n s y S t r o u h a l number g i v e s t h e s o l i d l i n e i n f i g u r e 32.

I n t h i s case, = 0 . 1 w a s s e l e c t e d based on t h e a v e r a g e peak S t r o u h a l v a l u e determined StMAX from t h e d i f f e r e n t d a t a s o u r c e s d e s c r i b e d i n t h e t a b l e i n t h e p r e v i o u s sub- s e c t i o n . I n a d d i t i o n , a v a l u e of S t = 0 . 1 provided t h e b e s t agreement w i t h MAX t h e d a t a p o i n t s i n f i g u r e 32.

It now remains t o d e t e r m i n e t h e r e l a t i o n s h i p between t h e spectrum shape The l i n k between t h e s e p a r a m e t e r s i s and t h e a b s o l u t e sound p r e s s u r e l e v e l .

c o n t r o l l e d by t h e unknown c o n s t a n t , K1, i n e q u a t i o n ( 6 6 ) . Based on t h e d e c i b e l l e v e l c o r r e s p o n d i n g t o t h e v a l u e a t t h e maximum of t h e s o l i d l i n e shown i n But F1(St = 0.1) = -9.16 dR i n e q u a t i o n f i g u r e 3 2 , F1(St = 0.1) + K1 = 84.0.

(67). Thus, K1 = 93.2 dB.

The f i n a l e q u a t i o n s f o r p r e d i c t i n g b o t h o v e r a l l sound p r e s s u r e l e v e l s and 113 o c t a v e band sound p r e s s u r e l e v e l s are t h e n K , = 93.2, U h knots and = 0.1. Here St MAX E f f e c t s of d i r e c t i v i t y have been i n c l u d e d i n e q u a t i o n (68) t o g e n e r a l i z e t h e r e s u l t s f o r a p p l i c a t i o n t o a l l r a d i a t i o n a n g l e s . It should be emphasized t h a t t h e c o n s t a n t , K1, w a s determined from v a r i o u s i s o l a t e d a i r f o i l d a t a sets w i t h t h e a i r f o i l s a t a f i n i t e a n g l e of a t t a c k (a 6'). Thus, i n t h e strictest test c o n d i t i o n s .

s e n s e , t h e above e q u a t i o n s cannot b e a p p l i e d t o t h e a = 0 ' F o r t u n a t e l y , changes i n a n g l e of a t t a c k can b e accounted f o r by i n t r o d u c i n g t h e c o r r e c t v a l u e of 6 , as shown by t h e good c o l l a p s e of d a t a i n f i g u r e 21.

Equation ( 6 8 ) , t h e r e f o r e , is a g e n e r a l e q u a t i o n .

Comparison With E x i s t i n g S c a l i n g Law - The above f o r m u l a t i o n can now be compared t o t h e e q u a t i o n s developed by Fink ( r e f s . 6 and 7) t o p r e d i c t air- frame t r a i l i n g edge n o i s e . The f u n c t i o n a l dependence on M, 6 , and S t is 5 1 However, t h e d i r e c t i v i t y f u n c t i o n i d e n t i c a l t o t h e f o r m u l a t i o n g i v e n by Fink.

used by Fink f o r a wing w i t h z e r o sweep-back a n g l e w a s d i f f e r e n t from t h a t g i v e n by e q u a t i o n ( 3 2 ) . Fink proposed t h a t Here 8, i s t h e a n g l e between t h e f l i g h t p a t h and t h e o b s e r v e r p o s i t i o n measured Recall t h a t B e i n t h e p r e s e n t s t u d y i s measured from t h e approach d i r e c t i o n .

from t h e o p p o s i t e d i r e c t i o n so t h a t c o s (ee/2) i n t h e above e q u a t i o n becomes s i n 2 ( e e / 2 ) . Thus, e q u a t i o n (70) is similar t o t h e numerator of e q u a t i o n (32) b u t l a c k s t h e Mach number dependent terms. T h i s i s because t h e d i r e c t i v i t y (70) r e p r e s e n t s a low Mach number r e s u l t which w a s p a t t e r n g i v e n by e q u a t i o n based on t h e e a r l y t h e o r y of Ffowcs W i l l i a m s and H a l l ( r e f . 1 6 ) . I n c o n t r a s t t h e p r e s e n t ( 3 2 ) . T h i s s t u d y p r o v i d e s a g e n e r a l e x p r e s s i o n given by e q u a t i o n f u n c t i o n a l form i n c l u d e d i n t h e p r e s e n t s c a l i n g l a w , i s c o n s i d e r e d t o b e t h e c o r r e c t f o r m u l a t i o n f o r t r a i l i n g edge n o i s e .

Another d i f f e r e n c e between t h e p r e s e n t s c a l i n g l a w and t h e r e s u l t of Equation ( 6 8 ) Fink becomes e v i d e n t when comparing t h e v a l u e of t h e c o n s t a n t K 1 .

The u s e s a v a l u e of K1 = 93.2 dB w h i l e Fink r e p o r t e d a v a l u e of K 1 = 101.5 dB.

l a t t e r v a l u e i s based on measurements u s i n g microphones on p o s t s 1 . 2 m above t h e ground. Accounting f o r ground r e f l e c t i o n s , which c a u s e measured l e v e l s t o b e approximately 3 dB above f r e e - f i e l d c o n d i t i o n s a t h i g h f r e q u e n c i e s , r e s u l t s i n K1 = 98.5. Hence, t h e v a l u e of K1 a s s o c i a t e d w i t h t h e s c a l i n g l a w i n r e f e r e n c e s 6 and 7 was h i g h by approximately 5 dB when compared t o t h e p r e s e n t s t u d y . T h i s d i f f e r e n c e w a s e v i d e n t e a r l i e r when S c h l i n k e r compared h i s t r a i l i n g edge n o i s e measurements w i t h t h e p r e d i c t i o n developed by Fink.

The comparisons r e p o r t e d i n r e f e r e n c e 5 i n d i c a t e d approximately a 4 dB d i f f e r e n c e between measured and p r e d i c t e d viilues.

I TRAILING EDGE NOISE PREDICTIONS Objective Two different trailing edge noise prediction methods were developed in the previous sections of this report consisting of a fundamental theoretical approach with no adjustable constants and a scaling law approach based on experimental data. Each approach modeled the noise as radiating from a stationary two-dimensional isolated airfoil segment.

It now remains to assess the accuracy of the two prediction methods.

Following this the stationary two-dimensional isolated airfoil formulation will be extended to the rotating coordinate system. Transformations de- scribed in the section titled Theoretical Formulation of the Trailing Edge Noise Mechanism will be used for this purpose. Sound pressure levels will be calculated and compared to specific full-scale helicopter test data.

Assessment of Isolated Airfoil Noise Prediction Procedures

Scaling Law Approach - It would appear that selecting values for

K based on experimental data removes any discrepancy between the StMAX and scaling law prediction and experimental measurements. Supposedly this would provide an accurate scaling law method for predicting the trailing edge noise.

The accuracy of the scaling law approach, however, is limited by how closely the initial data collapses onto a single curve. Although the solid line in figure 32 represents the average of the experimental data, the curve should be compared to the individual data sets used to generate this figure.

Figure 29 compares the scaling law with the experimental results of the present study. Measurements at Strouhal numbers below unity show reasonable The Strouhal number agreement with the solid line representing equation ( 7 0 ) .

= 0.1 associated with the spectrum peak is close to the value of St MAX Data from the study of Schlinker (ref. 5) is compared to the scaling law in figure 30. Again the sound pressure levels are in good agreement with the measured values while the spectrum peak occurs near the value of StMAX selected for the scaling law. Comparing the scaling law with the measurements of Brooks and Hodgson in figure 31 indicates a difference in Strouhal number associated with the spectrum peak. This difference was not apparent in figure 32 due to the heavy concentration of data points.

The detailed comparison available in figures 29, 30, and 31 emphasizes that the scaling law represents the average of the data points in figure 32 Such differ- and specific data sets can be different from the average line.

ences define the accuracy of the scaling law approach when compared to the isolated airfoil studies conducted by different investigators.

Theoretical Approach - Figure33(a)compares the first principles trailing

edge noise theory given by equations (21) and (22) with the measurements Note that the power spectral density form- obtained from the present study.

Also ulation in equation 21 has been converted to one-third octave band form.

*

needed in equation (22) was determined from figure 19 using' the value of 6

*

Recall the flat plate boundary layer approximation 6 = 6/8 = d i / ( 1 . O 7 ) ( 8 ) .

that the accuracy of modeling the flow field a s a flat plate boundary layer was discussed earlier in the section titled Airfoil Boundary Layer Character- istics. Additional discussions are given in Appendix D.

A comparison of the predicted and measured spectra in figure 3(a) shows good agreement at high frequencies but poor agreement at low frequencies.

A similar comparison with the narrowband spectra of Brooks and Hodgson, given in figure 3 4 , also shows poor agreement. In the latter case the value of 6" needed as an input to the present prediction was based on Table IV and the relationship 6* = 6/8.

Predictions in figure 33(a) and 34 are based on a flat plate surface pressure field model with the spectrum shape, S given by equation (22).

9 ' It was postulated that better agreement at low Brequencies could be obtained by replacing the flat plate convecting surface pressure model with the pres- sure field existing at the trailing edge of an airfoil. Justification for this approach was based on the normalized surface pressure spectrum measure- ments of Yu (ref. 9) as well as Brooks and Hodgson (ref. 1 0 ) . The experi- mental results obtained from reference 9 are plotted in figure 35(a) as a

function of 2 for two freestream velocities. These measurements correspond

to an airfoil at zero degrees angle of attack. Also shown in the same figure is the normalized surface pressure spectrum for a flat plate given by equation 22.

Comparison of the airfoil and flat plate spectra in figure 3 5 ( a ) indicates a definite difference in the spectrum shape and absolute level for these two geometries. Qualitatively, the fluctuating surface pressure spectrum near the airfoil trailing edge is seen to be about 7 dB higher than the zero pres- sure gradient flat plate result. This contrast is presented quantitatively in figure 35(b) where the abscissa represents the difference between the average of the airfoil data (see figure 3 5 ( a ) ) and the flat plate spectrum.

Representing the difference function in figure 35(b) a s DIFF (5) results in

a modified expression for the surface pressure.spectrum given by Applying S' t o t h e i s o l a t e d a i r f o i l n o i s e p r e d i c t i o n p r o v i d e s t h e modified t h e o r e t y z a l p r e d i c t i o n shown i n f i g u r e 33b) f o r t r a i l i n g edge n o i s e measurements conducted d u r i n g t h e p r e s e n t s t u d y . A comparison of t h e modified I n t h e o r y and experiment now shows b e t t e r agreement a t low f r e q u e n c i e s .

p a r t i c u l a r , p r e d i c t e d n o i s e levels are w i t h i n 3 dB of measured levels over most of t h e spectrum range from M = 0 . 1 t o 0.5. The need t o i n c l u d e t h e air- f o i l s u r f a c e p r e s s u r e spectrum h a s , t h e r e f o r e , been demonstrated.

A similar c o n c l u s i o n i s o b t a i n e d from f i g u r e 34 where t h e modified t h e o r y i s compared t o t h e measurements of Brooks and Hodgson. The improvement i n t h e p r e d i c t e d sound p r e s s u r e levels i s e v i d e n t when t h e c i r c l e and s q u a r e symbols are compared a t M = 0.2.

A f i n a l demonstration of t h e a b i l i t y t o c a l c u l a t e t r a i l i n g edge n o i s e r a d i a t i o n u s i n g t h e modified f i r s t p r i n c i p l e s t h e o r y is g i v e n i n f i g u r e 3 6 .

Here t h e p r e s e n t a n a l y s i s i s compared t o t h e d a t a r e p o r t e d by S c h l i n k e r ( r e f . 5). Again t h e comparison between t h e o r y and experiment shows good agreement i n a b s o l u t e sound p r e s s u r e l e v e l s .

F i g u r e 34 a l s o shows t h e t r a i l i n g edge n o i s e p r e d i c t i o n c a l c u l a t e d by Brooks and Hodgson f o r t h e i r own d a t a . A b r i e f d i s c u s s i o n of t h e d i f f e r e n c e between t h e i r p r e d i c t i o n and t h e p r e s e n t c a l c u l a t i o n i s warranted. The pre- d i c t i o n i n r e f e r e n c e 10, which i s based on t h e measured s u r f a c e p r e s s u r e s p e c t r a and c h a r a c t e r i s t i c l e n g t h scales, does n o t r e q u i r e a v a l u e of 6* as a n i n p u t . I n c o n t r a s t , t h e p r e s e n t approach u s e s a n a n a l y t i c a l model f o r t h e s u r f a c e p r e s s u r e c h a r a c t e r i s t i c s and r e q u i r e s a knowledge of 6" which is c a l c u l a t e d from f l a t p l a t e boundary l a y e r t h e o r y . A s noted i n Appendix D , t h e c a l c u l a t e d 6* v a l u e d i f f e r s from t h e measured v a l u e r e p o r t e d by Brooks and Hodgson by a f a c t o r of approximately 2.5. It is n o t clear which v a l u e should b e used. However, Appendix D d i s c u s s e s t h e above d e s c r i b e d d i f f e r -

* *

e n c e s i n 6 and p r e s e n t s t h e r e a s o n s f o r u s i n g t h e v a l u e of 6 o b t a i n e d from f l a t p l a t e boundary l a y e r t h e o r y .

M o d i f i c a t i o n of t h e f i r s t p r i n c i p l e s t r a i l i n g edge n o i s e t h e o r y focused on r e p l a c i n g t h e e x p r e s s i o n f o r Sqq on a f l a t p l a t e w i t h a measured a i r f o i l s u r f a c e p r e s s u r e spectrum. A similar m o d i f i c a t i o n w a s considered f o r t h e spanwise l e n g t h scale, %, which i s d e r i v e d i n e q u a t i o n (19) from t h e span- w i s e cross-spectrum Sqq (w,yo). Based on t h e comparisons of Sqq and SIqq t h e f u n c t i o n a l form of t h e parameter, lly, would mt b e expected t o b e t h e same f o r an a i r f o i l s u r f a c e and a f l a t p l a t e . However, Brooks and Hodgson showed t h a t , indeed, t h e normalized a i r f o i l and f l a t p l a t e s p e c t r a are i d e n t i c a l .

Consequently, i f w a s n o t n e c e s s a r y t o alter t h e e x p r e s s i o n f o r lly and t h e f l a t plate boundary layer length scale was considered to be representative of the flow field modeled here.

Comparison of Scaling Law and Theoretical Approach - It is worthwhile

to compare the analytical and the scaling law approach for calculating trail- ing edge noise. For comparison purposes the theory will be simplified by re- moving the dependence on the ratio of acoustic wavelength to airfoil chord.

Letting the ratio of chord-to-wave-length approach infinity, and letting Mch = M in the expression f o r 1 in equation (21) gives for the far-field narrow band sound pressure level

where 6 ( e e , $ ) is given by equation (32 ). Note that the modified surface

pressure spectrum given by S' in equation ( 7 1 ) has replaced the flat plate surface pressure spectrum teAqin equation (21).

Putting this in third octave form using equation ( 2 4 ) gives approx-

+ 126.8 0.1 < Q) < 20

where F(:) represents the frequency dependence given by equation (22b). Here the value K follows strictly from the theoretical noise model proposed and the values of the parameter S'qq and R obtained after assuming that surface Y pressures near the trailing edge can be modeled by equation ( 7 1 ) and ( 2 4 ) .

It should be noted No adjustment of the value of K exists in equation ( 7 3 ) .

that there is a factor of 8n difference between equations ( 7 2 ) and ( 7 3 ) . This change occurs because a factor of 2 is needed to account for both sides of 2, the airfoil, a second factor of 2.rr accounts for changing from an w spectrum to a frequency spectrum, and an additional factor of 2 is needed to convert 2, % a two-sided spectrum ranging from w = -00 to w = +oo to a one-sided spectrum % % ranging from w = 0 to w = +-.

Before the above theoretical result can be compared to the scaling law equation it is necessary to convert the equation to a form similar to that given by equation (69). This requires replacing the Mach number dependence by

*

velocity and letting 6 =6/8. Equation ( 7 3 ) then becomes

+ I O loglo [F(Q)DIFF (G)] + K

(74) Now the constant, K, contains the conversion which changes Mach number dependence to a velocity dependence in knots. The constant also contains the factor of 8 which links 6* and 6.

For comparison to the above expression, equations (68) and (69) are combined into one similar equation which is where K1 = 93.2.

The form of equations (74) and (75) now permit direct comparison. The parametric dependence on U, 6, and b (€le,$)is similar. However, the peak value in addition to the frequency dependence appear to be different in each equation. These differences are best evaluated by isolating the frequency and amplitude dependent terms in a form similar to equation (661, thereby, permitting direct comparison of the normalized spectrum shape. The result "is shown in figure 37 where the abscissa represents either: a) for the first principles theory, F(St)DIFF(St)+K for the scaling law, F1(St)+K1 b) Figure 37 shows that the spectrum peak amplitudes for the two prediction methods are approximately the same. However, the Strouhal numbers associated with each peak differ by a factor of two even though the spectrum shapes are similar (see shifted curve in figure 3 7 ) . In the case of the scaling law the peak occurs at St = 0.1 while the theoretical result gives a value of approx- imately St = 0.2. This explains why the peak Strouhal number in the analytical prediction shown in figure 33(b) occurs near St = 0 . 2 while the scaling law (based on figure 3 2 ) peaks near St = 0.1.

Summary and Evaluation - The above discussions assessed the accuracy of

the scaling law and theoretical approach for predicting trailing edge noise levels. Based on the comparisons between predictions and experiment both methods give approximately the same sound pressure level at the spectrum peak and predict approximately the same spectrum shape. However, the fundamental theory predicts a larger value for the Strouhal number associated with the spectrum peak. Thus, for the purpose of predicting trailing edge noise radiation from rotating blades the scaling law is considered presently to be the most reliable. This conclusion applies for a range of Mach numbers up to a maximum of M = 0 . 5 5 . Furthermore, this result applies to Reynolds numbers representative of full-scale helicopter main rotor operating conditions.

For those cases in which the Mach number is above the highest value investigqted here the fifth power Mach number scaling continues to be This follows from the fundamental theory which includes the applicable.

Based on equation compressibility effects occurring at high Mach numbers.

( 7 2 ) SppaMU4. For a rotor operating in a constant atmospheric propagation Thus, the Mach number dependence is the same speed given by coy SppaM5.

at low speeds and high speeds.

Trailing edge noise directivity dependence in the scaling law is also considered to remain the same at high rotor Mach numbers. This follows again from the theoretical directivity function which was incorporated directly into the scaling law. Similarly the spectrum shape is considered to remain unaltered based on the theoretical normalized spectrum.

Recall that the analytical and empirical spectrum shapes given by F(St)*DIFF(St) and F1(St) have approximately the same shape although they peak at a different Strouhal number (see Fig.

3 7 ) .

There are two limitations to the applicability of the trailing edge noise prediction procedures developed here. The first requirement is that the air- foil section Mach number must be below the condition at which impulsive noise is generated due to locally supersonic flow.

In this case the shock boundary layer interaction increases the trailing edge boundary layer thickness making the flat plate boundary layer calculation unreliable for determining the value of 6 needed as an input to the scaling law. It should be noted that based on the scaling law dependence trailing edge broadband noise would increase sig- nificantly under this operating condition.

The second requirement applies to model noise tests and the location of the laminar to turbulent transition point on the airfoil. To simulate full scale trailing edge noise radiation it is required that turbulent boundary layer develop over a sufficient distance to ensure an equilibrium boundary layer at the airfoil trailing edge.

Otherwise the surface pressure spectrum field con- vected over the trailing edge does not possess a universal spectrum shape and becomes a function of the turbulent flow distance on the airfoil surface.

The above criterion is best satisfied by maintaining the same Reynolds number as that expected for a full scale geometry. The length scale in the Reynolds number calculation would be based on the distance from the transition point to the airfoil trailing edge.

It should be noted that differences between the present theoretical approach and the experimental results should not preclude further development and application of the theory. The analytical model of surface pressure spectra convecting past the airfoil trailing edge is basically correct and can be shown to be similar to the formulations of other investigators. The source of the difference in spectrum peak location is, therefore, not the acoustic source model but rather the surface pressure spectra data needed as an input to the prediction. The lack of agreement can be traced to insufficient details in the surface pressure 'field description. Specifically, the pressure spectrum,S' is presently based on measurements obtained for q' an airfoil at a=Oo. DifPerences between the predicted and measured spectrum peak Strouhal number could possibly be removed by incorporating the influence of angle of attack on the surface pressure spectrum. Measurements of both Yu (ref. 9) as well as Brooks and Hodgson (ref. 10) have shown that increas- ing a increases the low frequency portion of the suction side surface pressure spectrum by approximately 3 dB. Conceptually this would increase the absolute sound pressure level of the low frequency side of the predicted spectrum in figure 37 sufficiently to shift the broad spectrum peak by the one octave in figure 3 7 . This could result in total agreement of the first principles trail- ing edge noise theory with the experimental results.

Accurate predictions of the trailing edge noise mechanism may, therefore, require using measured surface pressure data obtained near the airfoil trail- ing edge. Such detailed measurements were conducted by Brooks and Hodgson at low Mach numbers (M50.2) to provide the necessary experimental input to their theoretical noise prediction. This approach should be extended to the higher Reynolds numbers associated with full-scale helicopter rotor operating conditions. I f it can be demonstrated that the surface pressure data at higher Reynolds numbers continues to collapse onto a universal curve, then this curve could be used as a generalized input to the noise prediction.

Rotating Blade Noise Predictions

Approach - For the purpose of predicting trailing edge noise from rotating

blades the scaling law was transformed to the rotating frame. The method employed assumed that the spectrum of a given blade segment is, at any partic- ular instant, given by equation ( 7 5 ) . The local relative velocity of the rotor blade segment determined the boundary layer details and the resulting noise spectrum. The 1/3 octave band spectrum shape, given by equation (75), was converted to a narrowband power spectral density expression by accounting for the filter bandwidth. The spectrum was permitted to vary as the rotor moved about the azimuth.

To obtain the final spectrum, the instantaneous spectrum was averaged around the azimuth, together with a weighting which accounted for retarded time effects. Details of the analysis were described earlier in the section titled Theoretical Formulation of the Trailing Edge Noise Mechanism.

Input to Noise Prediction - Equation 75 requires for each spanwise segment

of the rotor blade a knowledge of a) the local freestream velocity, b) the average of the suction side and pressure side boundary layer thickness, and With the exception of c> the observer position relative to the rotor plane.

t h e boundary l a y e r t h i c k n e s s , 6 , t h e above v a r i a b l e s are e a s i l y determined.

To avoid u s i n g complicated computational f l u i d dynamics methods f o r determin- t h i s parameter was e s t i m a t e d u s i n g t h e f l a t p l a t e boundary l a y e r cal- i n g 6 c u l a t i o n s . T h i s approach w a s j u s t i f i e d earlier by a comparison of t h e f l a t p l a t e c a l c u l a t i o n w i t h t h e average of t h e p r e s s u r e and s u c t i o n s i d e v a l u e s of 6 f o r t h e r o t o r b l a d e segment t e s t e d i n t h e p r e s e n t s t u d y . The comparisons showed good agreement a t small a n g l e s of a t t a c k ( s e e f i g . 1 9 ) .

Recall t h a t t h e d i f f e r e n c e s between f l a t p l a t e boundary l a y e r t h e o r y and experiment were less t h a n 20 p e r c e n t . Based on t h e t r a i l i n g edge n o i s e l a w t h e e s t i m a t e d d i f f e r e n c e i n n o i s e r a d i a t i o n would b e less t h a n s c a l i n g 0.8 dB. T h i s s t a t e m e n t imples t h a t h e l i c o p t e r r o t o r t r a i l i n g edge n o i s e p r e d i c t i o n s based are a c c u r a t e on f l a t p l a t e boundary l a y e r c h a r a c t e r i s t i c s w i t h i n s e v e r a l d e c i b e l s . G r e a t e r accuracy, and t h e r e f o r e , d e t a i l e d boundary w a s n o t r e q u i r e d s i n c e t h e o b j e c t i v e of t h e s t u d y w a s t o l a y e r i n f o r m a t i o n , assess t h e r e l a t i v e importance of t h i s n o i s e mechanism compared t o t h e o t h e r o p e r a t i v e mechanisms on a f u l l scale h e l i c o p t e r .

S i n c e t h e a b r a s i o n s t r i p on f u l l scale h e l i c o p t e r r o t o r s i s known t o t r i p t h e s u r f a c e boundary l a y e r c l o s e t o t h e b l a d e l e a d i n g edge t h e f l a t p l a t e boundary l a y e r c a l c u l a t i o n w a s i n i t i a t e d a t t h e b l a d e l e a d i n g edge. T h i s i s expected t o i n t r o d u c e o n l y a small e r r o r i n t h e c a l c u l a t i o n of 6 .

Test Case - The t r a i l i n g edge n o i s e p r e d i c t i o n method w a s t e s t e d a g a i n s t d a t a measured d u r i n g a f u l l - s c a l e h e l i c o p t e r n o i s e f l y o v e r . Details of t h e h e l i c o p t e r main r o t o r and t a i l r o t o r are t a b u l a t e d below.

Main Rotor T a i l Rotor Number of Blades 4 4 Rotor Radius 6.7 m 1 . 2 m Blade Chord 0 . 4 m .17 m Rotor R o t a t i o n Rate 307 rpm 1689 rpm The main r o t o r b l a d e geometry was i d e n t i c a l t o t h e r o t o r b l a d e segment t e s t e d d u r i n g t h e two-dimensional i s o l a t e d a i r f o i l i n v e s t i g a t i o n conducted i n t h e p r e s e n t s t u d y .

Data p r e s e n t e d h e r e correspond to a l e v e l f l y o v e r c o n d i t i o n of 36 o r 72 m/sec and a n a l t i t u d e of 76 m. Acoustic s p e c t r a were processed when t h e h e l i c o p t e r w a s i n approximately a n overhead p o s i t i o n s o t h a t 8, = 90". Data w a s o b t a i n e d u s i n g microphones on p o s t s 1.2 m above t h e ground. To account f o r t h e ground r e f l e c t i o n e f f e c t 3 dB were added t o t h e f r e e f i e l d t r a i l i n g edge n o i s e p r e d i c t i o n . Weather c o n d i t i o n s d u r i n g t h e h e l i c o p t e r f l y o v e r are t a b u l a t e d below.

I 60

Wind speed - z e r o v e l o c i t y (calm)

Temperature - 77°F

R e l a t i v e Humidity - 90%

The e f f e c t of atmospheric a t t e n u a t i o n due t o humidity was accounted f o r by a p p l y i n g a c o r r e c t i o n t o t h e measured d a t a .

F i g u r e 38 shows t h e narrowband (12.5 Hz bandwidth) t o t a l h e l i c o p t e r n o i s e spectrum measured d u r i n g t h e f l y o v e r . C o r r e c t i o n s f o r ground r e f l e c t i o n s and a t m o s p h e r i c a t t e n u a t i o n have n o t been a p p l i e d h e r e . The o b j e c t i v e of pre- s e n t i n g t h i s f i g u r e i s t o demonstrate t h a t t h e f l y o v e r s i g n a t u r e i s mainly broadband n o i s e above 1 KHz. Apparent d i s c r e t e t o n e peaks i n t h e spectrum are due o n l y t o t h e s h o r t a v e r a g i n g t i m e ( 1 / 2 s e c ) used d u r i n g t h e spectrum a n a l y s i s . Although a l o n g e r a v e r a g i n g time would have provided a smoother spectrum, s p a t i a l d i r e c t i v i t y i n f o r m a t i o n would t h e n be averaged. For example, t h e 1 / 2 second a v e r a g i n g t i m e employed i n t h e above d e s c r i b e d measurements r e s u l t e d i n a v e r a g i n g a n g u l a r i n f o r m a t i o n w i t h i n f 11' about t h e 90" overhead p o s i t i o n d u r i n g t h e 72 m/sec f l y o v e r . F o r t u n a t e l y , d i r e c t i v i t y i n f o r m a t i o n v a r i e d slowly a t t h i s a n g l e as shown by t h e t h r e e d i f f e r e n t s p e c t r a super- imposed on f i g u r e 38. Each spectrum r e p r e s e n t s t h e o u t p u t from a 1 / 2 s e c spectrum a n a l y s i s o b t a i n e d d u r i n g t h e f l y o v e r . One spectrum c o r r e s p o n d s t o t h e 90" overhead p o s i t i o n w h i l e t h e o t h e r two s p e c t r a r e p r e s e n t t h e preceed- i n g and f o l l o w i n g s p e c t r a .

F i g u r e 3 9 ( a ) shows t h e same f l y o v e r c o n d i t i o n measured w i t h a narrowband spectrum i n f i g u r e 38 converted t o 1 / 3 o c t a v e band a n a l y z e r ( c i r c l e symbol).

The s q u a r e symbol i n f i g u r e 3 9 ( a ) represents t h e same d a t a w i t h t h e atmospheric a t t e n u a t i o n c o r r e c t i o n added t o t h e measurement. A d d i t i o n a l c o r r e c t i o n s t o account f o r t h e Doppler s h i f t and r e t a r d e d s o u r c e p o s i t i o n were n o t n e c e s s a r y i n t h e overhead p o s i t i o n .

i s t h e s c a l i n g l a w p r e d i c t i o n f o r t h e h e l i c o p - Also shown i n f i g u r e 3 9 ( a ) t e r main r o t o r t r a i l i n g edge n o i s e . Comparison of t h e t o t a l h e l i c o p t e r n o i s e spectrum and t h e t r a i l i n g edge n o i s e spectrum d e m o n s t r a t e s t h a t a t h i g h f r e - q u e n c i e s t r a i l i n g edge n o i s e can be a s i g n i f i c a n t n o i s e mechanism. In f a c t , a t some f r e q u e n c i e s p r e d i c t e d and measured n o i s e l e v e l s are almost i d e n t i c a l .

Below 2 KHz o t h e r broadband n o i s e mechanisms b e g i n t o dominate o v e r t h e t r a i l - i n g edge n o i s e as shown by t h e d i v e r g e n c e of t h e p r e d i c t e d and measured c u r v e s .

F i g u r e 39(b) shows a second measured spectrum a t a d i f f e r e n t f l y o v e r Again t h e comparison between p r e d i c t e d 113 o c t a v e band l e v e l s and speed.

measured s p e c t r a is good.

Also p r e s e n t e d i n f i g u r e 39 is t h e f i r s t p r i n c i p l e s p r e d i c t i o n f o r t h e main r o t o r t a i l i n g edge n o i s e . The spectrum peak a m p l i t u d e is c l o s e t o t h e measured l e v e l s a l t h o u g h t h e frequency a s s o c i a t e d w i t h t h e peak o c c u r s a t a v a l u e a b o u t t h e dominant p o r t i o n of t h e measured broadband n o i s e spectrum.

T h i s l a t t e r f e a t u r e w a s expected from t h e comparison of t h e s c a l i n g l a w and t h e f i r s t p r i n c i p l e s t r a i l i n g edge n o i s e p r e d i c t i o n s i n f i g u r e 37. It i s f e l t , however, t h a t f u r t h e r development of t h e a i r f o i l s u r f a c e p r e s s u r e spectrum model w i l l p r o v i d e b e t t e r agreement w i t h measured d a t a .

A comparison of t h e p r e d i c t e d t r a i l i n g edge n o i s e f o r t h e h e l i c o p t e r main r o t o r and t h e measured t o t a l h e l i c o p t e r n o i s e spectrum h a s been pre- s e n t e d i n f i g u r e 39. Although n o i s e from t h e t a i l r o t o r w a s a l s o p r e s e n t t h i s c o n t r i b u t i o n w a s expected t o b e weak. T h i s i s due t o t h e smaller bound- a r y l a y e r t h i c k n e s s and r o t o r span v a l u e s which are l i n e a r i n p u t s t o t h e a n a l y s i s according t o e q u a t i o n (75). Also, t h e s m a l l e r boundary l a y e r t h i c k n e s s on t h e t a i l r o t o r c a u s e s t h e spectrum peak t o s h i f t t o a h i g h e r S t r o u h a l number.

Summary and E v a l u a t i o n - The importance of t h e h e l i c o p t e r t r a i l i n g edge n o i s e mechanism h a s been v e r i f i e d by d i r e c t c a l c u l a t i o n of t h e a s s o c i a t e d n o i s e l e v e l s d u r i n g an a i r c r a f t f l y o v e r . P r e d i c t e d n o i s e levels c l o s e t o t h e t o t a l h e l i c o p t e r n o i s e spectrum demonstrate t h a t t r a i l i n g edge n o i s e must b e accounted f o r i n f u t u r e n o i s e p r e d i c t i o n procedures.

S i n c e t r a i l i n g edge n o i s e i s c o n t r o l l e d by t h e i n h e r e n t c h a r a c t e r i s t i c s of t h e r o t o r b l a d e boundary l a y e r , i t i s d i f f i c u l t t o e l i m i n a t e t h i s n o i s e mechanism. Delaying t h e boundary l a y e r t r a n s i t i o n t o r e d u c e 6 i n e q u a t i o n (75) i s a p o s s i b i l i t y b u t t h e b e n e f i t s are m a r g i n a l due t o t h e l i n e a r depen- dency on boundary l a y e r t h i c k n e s s . E f f o r t s t o s h i f t t h e b l a d e s u r f a c e p r e s - s u r e spectrum t o a h i g h e r frequency t o i n c r e a s e atmospheric a t t e n u a t i o n re- p r e s e n t s a p o s s i b l e b u t d i f f i c u l t t a s k of c o n t r o l l i n g d e t a i l s of t h e t u r b u l e n t boundary l a y e r p r e s s u r e spectrum.

The r e d u c t i o n of h e l i c o p t e r r o t o r t r a i l i n g edge n o i s e i s , t h e r e f o r e , l i m i t e d t o changes i n t h e aerodynamic o p e r a t i n g c o n d i t i o n s . A s suggested by t h e p r e d i c t i o n methods presented h e r e , a. r e d u c t i o n of t i p speed would p r o v i d e t h e g r e a t e s t improvement. Reduced speeds would, presumably, re- q u i r e i n c r e a s i n g t h e number of r o t o r b l a d e s t o m a i n t a i n a c o n s t a n t r o t o r t h r u s t . The r e s u l t i n g i n c r e a s e i n t r a i l i n g edge n o i s e would, however, b e less t h a n t h e d e c r e a s e achieved by changing t h e t i p speed.

With t h e e x c e p t i o n of t h e above d e s c r i b e d n o i s e r e d u c t i o n s , t r a i l i n g edge n o i s e r e p r e s e n t s t h e l i m i t i n g a c o u s t i c s o u r c e mechanism f o r t h e t o t a l h e l i c o p t e r n o i s e spectrum. This c o n c l u s i o n i s similar t o t h e c o n c l u s i o n s obtained i n p r e v i o u s s t u d i e s of t h e n o i s e generated by f i x e d wing a i r c r a f t .

This n o i s e , r e f e r r e d t o as "airframe noise", h a s set t h e n o i s e l i m i t f o r of t h e p r e s e n t s t u d y , a similar n o i s e such a i r c r a f t . Based on t h e r e s u l t s l i m i t e x i s t s f o r h e l i c o p t e r r o t o r broadband n o i s e .

Reductions in high frequency helicopter broadband noise have also been achieved by changing the rotor blade tip shape. The source mechanism,in this case,is not the attached boundary layer trailing edge noise investigated in the present study. Instead, the noise is generated by convection of the three dimensional tip vortex flow field over the blade trailing edge. George (ref. 50) provided an approximate model of the noise generated by this separated and highly turbulent flow field as it convects over an airfoil trail- ing edge. His predictions indicated that blade tip vortex noise can be comparable to trailing edge noise. This result explains the broadband noise reduction observed by some investigators after changing the airfoil tip shape.

\ 6 3 CONCLUSIONS AND RECOMMENDATIONS A. F u l l - s c a l e Rotor Noise A . l . Extension of a v a l i d a t e d i s o l a t e d a i r f o i l t r a i l i n g edge n o i s e s c a l i n g l a w t o t h e r o t a t i n g b l a d e case demonstrated t h a t t r a i l i n g edge n o i s e from a f u l l - s c a l e h e l i c o p t e r c o n t r i b u t e s s i g n i f i c a n t l y t o t h e t o t a l broadband n o i s e spectrum a t h i g h f r e q u e n c i e s . T h i s n o i s e mechanism is expected t o c o n t r o l t h e minimum r o t o r n o i s e l e v e l .

A . 2 . The h e l i c o p t e r r o t o r t r a i l i n g edge n o i s e s c a l i n g l a w f o r s u b s o n i c t i p speeds w a s v a l i d a t e d u s i n g two-dimensional i s o l a t e d a i r f o i l r e s u l t s a t f u l l - scale Reynolds numbers. Knowledge o f t h e h e l i c o p t e r a l t i t u d e , s p e e d , a n g u l a r p o s i t i o n , r o t o r t i p s p e e d , b l a d e number, r o t o r chord and s p a n , and r o t o r boundary l a y e r t h i c k n e s s are t h e o n l y p a r a m e t e r s r e q u i r e d i n t h e a n a l y s i s .

Based on two-dimensional i s o l a t e d a i r f o i l r e s u l t s , h e l i c o p t e r r o t o r boundary l a y e r t h i c k n e s s c a n be e s t i m a t e d u s i n g a f l a t p l a t e t u r b u l e n t boundary l a y e r c a l c u l a t i o n . This s i m p l i f i e s t h e flow f i e l d d e t a i l s needed as a n i n p u t t o t h e p r e d i c t i o n procedure.

A.3. A f i r s t p r i n c i p l e t h e o r y f o r t r a i l i n g edge n o i s e p r e d i c t s t h e c o r r e c t a b s o l u t e sound p r e s s u r e l e v e l b u t d o e s n o t p r e d i c t t h e S t r o u h a l v a l u e i d e n t i - f y i n g t h e spectrum peak. The b a s i c n o i s e model of a f r o z e n p r e s s u r e p a t t e r n c o n v e c t i n g p a s t a t r a i l i n g edge, however, a g r e e s w i t h t h e a c o u s t i c s o u r c e models developed by o t h e r i n v e s t i g a t o r s . D i f f e r e n c e s between t h e o r y and experiment are b e l i e v e d t o b e d u e t o t h e a i r f o i l f l u c t u a t i n g s u r f a c e p r e s s u r e f i e l d model used as an i n p u t t o t h e a n a l y s i s . Accurate p r e d i c t i o n s r e q u i r e u s i n g measured s u r f a c e p r e s s u r e d a t a o b t a i n e d n e a r t h e a i r f o i l t r a i l i n g edge.

A . 4 F u t u r e e f f o r t s should b e d i r e c t e d toward d e t a i l e d a i r f o i l s u r f a c e p r e s s u r e measurements a t Reynolds number r e p r e s e n t a t i v e of f u l l scale h e l i c o p t e r opera- t i n g c o n d i t i o n s .

I f i t can b e demonstrated t h a t t h e s u r f a c e p r e s s u r e s p e c t r a d a t a a t h i g h Reynolds numbers c o l l a p s e o n t o a s i n g l e nondimensional c u r v e , t h e n t h i s c u r v e c a n be used as a n i n p u t t o t h e n o i s e p r e d i c t i o n .

B. T r a i l i n g Edge Noise From a Local Blade Segment B . l . Based on two-dimensional a i r f o i l r e s u l t s , t r a i l i n g edge n o i s e r a d i a t i o n p a t t e r n s from a l o c a l b l a d e segment are w e l l p r e d i c t e d by t h e t h e o r y developed i n t h e p r e s e n t s t u d y . D i r e c t i v i t y p a t t e r n s a r e independent of a n g l e of a t t a c k and a c o u s t i c s o u r c e S t r o u h a l number.

6 4 B . 2 . Noise dependence on l o c a l s e c t i o n Mach number varies as M5 and i s independent of a n g l e of a t t a c k and a c o u s t i c s o u r c e S t r o u h a l number.

B . 3 . Local r o t o r b l a d e a n g l e of a t t a c k i n f l u e n c e s o n l y t h e low S t r o u h a l number p o r t i o n of t h e spectrum. I n c r e a s i n g a n g l e of a t t a c k i n c r e a s e s sound p r e s s u r e l e v e l by o n l y a few d e c i b e l s n e a r t h e spectrum peak. The observed t r e n d i s explained by t h e i n c r e a s e i n boundary l a y e r t h i c k n e s s on t h e s u c t i o n s i d e of t h e a i r f o i l .

B.4. T r a i l i n g edge n o i s e 113 o c t a v e band s p e c t r a from a l o c a l b l a d e segment can b e approximated by a u n i v e r s a l spectrum shape. A s c a l i n g l a w c a p a b l e of p r e d i c t i n g t h e a b s o l u t e spectrum l e v e l s depends o n l y on Mach number, boundary l a y e r t h i c k n e s s , and o b s e r v e r l o c a t i o n .

B.5. Boundary l a y e r t h i c k n e s s i n p u t d a t a t o t h e s c a l i n g l a w can be e s t i m a t e d u s i n g f l a t p l a t e t u r b u l e n t boundary l a y e r c a l c u l a t i o n s . Such c a l c u l a t i o n s approximate t h e a v e r a g e v a l u e of t h e p r e s s u r e s i d e and s u c t i o n s i d e boundary l a y e r s . The average v a l u e c o n t r o l s t h e peak S t r o u h a l number of t h e u n i v e r s a l spectrum curve.

APPENDIX A D i r e c t i o n a l Microphone System D i r e c t i o n a l S e n s i t i v i t y and S p a t i a l R e s o l u t i o n - Although t h e d i r e c t i o n a l microphone system is most s e n s i t i v e t o s o u r c e s l o c a t e d on i t s aiming a x i s , it does s e n s e s o u r c e s a t o f f a x i s d i r e c t i o n s d e f i n e d by t h e a n g l e +o i n f i g u r e 1 2 .

The r e s p o n s e of t h e system t o such o f f a x i s s o u r c e s i s c o n t r o l l e d by d i f f r a c - t i o n a t t h e c i r c u l a r a p e r t u r e of t h e r e f l e c t o r . For t h e p r e s e n t geometry t h e d i f f r a c t i o n phenomenon i s governed by t h e nondimensional parameter T I = (nDfsin$o>/co where D i s t h e r e f l e c t o r a p e r t u r e , f is t h e a c o u s t i c f r e - quency, and co is t h e sound speed. Figure 40 shows t h e measured normalized r e s p o n s e from t h e f o c a l p o i n t microphone p l o t t e d as a f u n c t i o n of q . The r e s p o n s e f u n c t i o n , H , d e c r e a s e s as Go i n c r e a s e s demonstrating t h e d e c r e a s e i n s e n s i t i v i t y t o o f f - a x i s a n g l e s . This response, o f t e n r e f e r r e d t o as t h e s p a t i a l d i s c r i m i n a t i o n c a p a b i l i t y , h a s been shown t o a g r e e w i t h t h e Fraunhofer d i f f r a c t i o n p a t t e r n f o r a c i r c u l a r a p e r t u r e system ( s e e F i g . 40 ) . Such agreement p e r m i t t e d using a n a n a l y t i c a l e x p r e s s i o n f o r t h e r e s p o n s e f u n c t i o n i n t h e d a t a r e d u c t i o n .

F i g u r e 40 demonstrates t h a t d i f f r a c t i o n c a u s e s t h e system t o have a f i n i t e s p a t i a l r e s o l u t i o n i n s t e a d of t h e i d e a l d e l t a f u n c t i o n r e s o l u t i o n . Thus, w h i l e t h e system i s most s e n s i t i v e t o s o u r c e s l o c a t e d on i t s aiming a x i s , it does s e n s e s o u r c e s a t o f f a x i s d i r e c t i o n s . The "sharpness" of t h e r e s o l u t i o n , however, i n c r e a s e s w i t h t h e a c o u s t i c frequency, f , which a p p e a r s i n t h e numer- a t o r of t h e parameter, q . Thus, f o r a f i x e d o f f - a x i s s o u r c e p o s i t i o n d e f i n e d by + o , t h e r e s p o n s e H d e c r e a s e s as f i n c r e a s e s .

One parameter which q u a n t i f i e s t h e d i r e c t i o n a l microphone frequency dependent s p a t i a l d i s c r i m i n a t i o n is t h e d i f f r a c t i o n p a t t e r n half-width, AW.

The half-width, d e f i n e d as t h e s p a t i a l d i s t a n c e between t h e n e g a t i v e 3 dB p o i n t s i n t h e d i f f r a c t i o n p a t t e r n of f i g u r e 40 corresponds t o t h e p o i n t s

+

rl = - 1.66. A 3 dB d e c r e a s e i n s e n s i t i v i t y t o o f f - a x i s s o u r c e s , t h e r e f o r e , o c c u r s f o r d i s p l a c e m e n t s given by x = 1.66 coR/fD where x corresponds t o t h e o f f - a x i s d i s t a n c e shown i n f i g u r e 12. h a s been employed i n Here s i n Go 'L x/R t h e e x p r e s s i o n f o r TI. The r e s o l v i n g half-width i s t h e n AW = 2x = 3.32 coR/fD.

T h i s r e s u l t i s shown i n f i g u r e 4 1 i n a d d i t i o n t o t h e e x p e r i m e n t a l l y determined v a l u e f o r a s o u r c e situat.ed a t a d i s t a n c e of R = 2.81 m from t h e r e f l e c t o r The good agreement between t h e o r y and experiment confirms t h e accuracy of t h e Fraunhofer d i f f r a c t i o n p a t t e r n d e s c r i p t i o n f o r t h e r e f l e c t o r s p a t i a l d i s c r i m i n a - t i o n c h a r a c t e r i s t i c s .

Gain - The d i r e c t i o n a l microphone system a l s o h a s a s i g n i f i c a n t g a i n . A g a i n e x i s t s because t h e l a r g e c o l l e c t i n g area of t h e r e f l e c t o r f o c u s e s t h e s m a l l f o c a l p o i n t microphone. I n a n i d e a l system without d i f - sound o n t o t h e f r a c t i o n t h e g a i n , G , depends on t h e s o l i d a n g l e subtended by t h e r e f l e c t o r and t h e f o c a l p o i n t microphone s o t h a t G = (D/d)2 where D = 1.067 m and d = 0.635 c m . However, t h e frequency dependent d i f f r a c t i o n c h a r a c t e r i s t i c s smear o u t t h e f o c a l p o i n t image s o t h a t o n l y p a r t of t h e a c o u s t i c energy i n c i d e n t on t h e r e f l e c t o r i s c o n c e n t r a t e d on t h e f o c a l p o i n t microphone.

The d i r e c t i o n a l microphone g a i n i n , t h i s case, can b e determined e x p e r i m e n t a l l y ( r e f . 5 ) . The sound p r e s s u r e l e v e l generated by a p o i n t s o u r c e of sound i s measured w i t h t h e r e f l e c t o r and w i t h a n o m n i d i r e c t i o n a l microphone. S o u r c e - t o - r e f l e c t o r and source-to-omnidirectional microphone d i s t a n c e s are i d e n t i c a l d u r i n g t h e measurements. The r a t i o of t h e s e two measurements r e p r e s e n t s t h e g a i n , G ,

-

- 2 where pDM d e f i n e s t h e f o c a l p o i n t microphone sound p r e s s u r e l e v e l and po r e p r e s e n t s t h e o m n i d i r e c t i o n a l microphone sound p r e s s u r e level. The g a i n measurement, which was r e p e a t e d i n t h e p r e s e n t s t u d y as a check on t h e d i r e c t i o n a l microphone system, i s shown i n f i g u r e 4 1 f o r two s o u r c e d i s t a n c e s corresponding t o R = 2 . 8 1 m and 2.07 m. The l a r g e g a i n w a s b e n e f i c i a l a t h i g h f r e q u e n c i e s because t u r b u l e n t boundary l a y e r n o i s e d e c r e a s e s r a p i d l y w i t h i n c r e a s i n g frequency.

The d i r e c t i o n a l microphone g a i n must be determined b e f o r e a b s o l u t e s o u r c e l e v e l s can b e c a l c u l a t e d . A t low f r e q u e n c i e s t h e g a i n f u n c t i o n c a n b e c a l c u l a t e d e x p l i c i t l y ( r e f . 5 ) based on t h e Fraunhofer d i f f r a c t i o n t h e o r y g i v i n g t h e r e s u l t which i s p l o t t e d i n f i g u r e 41.

D i f f e r e n c e s between t h e measured and t h e o r e t i c a l g a i n s a t high f r e q u e n c i e s i n f i g u r e 4 1 a r e a t t r i b u t e d t o s p h e r i c a l a b e r r a t i o n s a t t h e f o c a l p o i n t a r e n o t included i n t h e a n a l y t i c a l c a l c u l a - microphone. These c h a r a c t e r i s t i c s t i o n s of t h e g a i n . Thus, t h e e x p e r i m e n t a l l y determined g a i n was used a t h i g h f r e q u e n c i e s f o r a l l d a t a r e d u c t i o n .

APPENDIX B Forward F l i g h t E f f e c t s Shear Layer R e f r a c t i o n - A s shown i n f i g u r e 13, r e f r a c t i o n changes b o t h t h e a c o u s t i c r a y p a t h as w e l l as t h e p a t h l e n g t h of t h e sound waves a r r i v i n g a t a microphone s t a t i o n o u t s i d e t h e flow. I n a d d i t i o n , t r a n s m i s s i o n of sound a c r o s s t h e open j e t s h e a r l a y e r changes ehe divergence r a t e of t h e a c o u s t i c r a y t u b e s . These l a t t e r changes i n p a t h l e n g t h and d i v e r g e n c e r a t e r e q u i r e c o r r e c t i n g t h e measured sound p r e s s u r e l e v e l s .

The d e t a i l e d a n a l y t i c a l s t u d y and experimental v e r i f i c a t i o n by S c h l i n k e r and Amiet ( r e f . 47) formed t h e b a s i s of t h e c o r r e c t i o n s a p p l i e d t o t h e p r e s e n t d a t a . The c o r r e c t i o n s were used t o c o n v e r t measurements a t t h e o b s e r v e r s t a t i o n ( 0 ) , i n f i g u r e 1 3 , t o t h e c o n s t a n t s i d e l i n e s t a t i o n ( D ) on t h e non- r e f r a c t e d path. The c o r r e c t e d sound p r e s s u r e l e v e l r e p r e s e n t s an e q u i v a l e n t measurement i n t h e absence of t h e s h e a r l a y e r . I n o t h e r words, t h e s h e a r l a y e r i s considered t o b e l o c a t e d a t i n f i n i t y w i t h uniform flow e x i s t i n g between t h e s o u r c e and t h e f a r f i e l d microphone a t s t a t i o n D. A s concluded i n t h e s t u d y of Sctilinker and Amiet, t h e f i n i t e t h i c k n e s s s h e a r l a y e r can b e r e p l a c e d by a n i d e a l i z e d v o r t e x s h e e t . S p e c i f i c d e t a i l s of t h e s h e a r l a y e r mean v e l o c i t y p r o f i l e are, t h e r e f o r e , n o t needed.

An example of t h e magnitude of t h e a n g l e and amplitude changes i s g i v e n i n f i g u r e 42 f o r a n open j e t Mach number o f M = 0.5, corresponding t o one of t h e o p e r a t i n g c o n d i t i o n s t e s t e d i n t h e p r e s e n t s t u d y . The d i s t a n c e t o t h e s i d e l i n e microphone measurement s t a t i o n is g i v e n by h/yl = 0.14 where h r e p r e s e n t s t h e source-to-shear l a y e r d i s t a n c e and y1 i s t h e s i d e l i n e d i s t a n c e

i n f i g u r e 13. A s shown by f i g u r e 42 , sound i n i t i a l l y propagating a t

8, = 80" i n s i d e t h e open j e t i s r e f r a c t e d t o 8, = 113' o u t s i d e t h e airstream.

Also, t h e sound p r e s s u r e l e v e l measured on t h e r e s u l t i n g r e f r a c t e d p a t h a t s t a t i o n 0 i n f i g u r e 13 should b e i n c r e a s e d by 4 dB according t o f i g u r e 42.

Note t h a t t h e amplitude c o r r e c t i o n is always added t o t h e measured d a t a .

Apparent Source Location - The above d e s c r i b e d r e f r a c t i o n a n g l e changes c o n t r o l t h e p r o p a g a t i o n of a s i n g l e r a y through t h e s h e a r l a y e r and a r r i v i n g a t t h e f a r f i e l d microphone s t a t i o n (0) i n f i g u r e 13. I n c o n t r a s t , t h e d i r e c t i o n a l microphone system s e n s e s r e f r a c t e d a c o u s t i c r a y s propagating w i t h i n t h e a n g l e , d e t , as shown i n f i g u r e 1 4 ( a ) . Transmitted r a y s , A and B, each of which are r e f r a c t e d d i f f e r e n t l y , d e f i n e t h e a n g l e , det, i n t h e h o r i - z o n t a l p l a n e . S i n c e t h e d i r e c t i o n a l microphone system s e n s e s o n l y t h e r e f r a c t e d r a y s o u t s i d e t h e flow, it must b e focused on t h e "apparent" s o u r c e l o c a t i o n d e f i n e d by r a y s A and B. The i n t e r s e c t i o n of t h e s e r a y s i n s i d e t h e f l o w c o n t r o l s t h i s a p p a r e n t s o u r c e l o c a t i o n SH, i n f i g u r e 1 4 ( a ) .

G9 P o s i t i o n S w a s determined a n a l y t i c a l l y u s i n g t h e r e f r a c t i o n a n g l e H c o r r e c t i o n c o n t r o l l i n g r a y s A and B. (See Appendix C f o r a d e t a i l e d evalua- t i o n . ) For each Mach number, M, and d i r e c t i v i t y a n g l e , B C , a unique a p p a r e n t s o u r c e p o s i t i o n was c a l c u l a t e d . A s shown by t h e a n a l y t i c a l d e r i v a - t i o n , t h e apparent s o u r c e l o c a t i o n i s independent of t h e d i s t a n c e t o t h e re- f l e c t o r s u r f a c e .

Once t h e a p p a r e n t s o u r c e l o c a t i o n w a s c a l c u l a t e d , t h e s i d e l i n e d i s t a n c e , yl, f o r t h e d i r e c t i o n a l microphone t r a v e r s e could be s e l e c t e d . T h i s d i s t a n c e w a s c o n t r o l l e d by t h e a p p a r e n t s o u r c e - t o - r e f l e c t o r d i s t a n c e , R , i n f i g u r e 1 2 .

S i n c e d e t a i l e d c a l i b r a t i o n s of t h e d i r e c t i o n a l microphone s p a t i a l r e s o l u t i o n and g a i n were o n l y a v a i l a b l e f o r two s p e c i f i c v a l u e s of R , t h e v a l u e of y1 w a s s e l e c t e d t o p r o v i d e a d i s t a n c e of R = 2.07 m o r 2.81 m between t h e r e f l e c t o r and t h e a p p a r e n t s o u r c e p o s i t i o n . R e c a l l t h a t t h e v a l u e of R con- t r o l l e d t h e f o c a l p o i n t microphone l o c a t i o n ri, i n f i g u r e 1 2 .

A s shown by f i g u r e 1 4 ( a ) , t h e d i r e c t i o n a l microphone s e n s e s sound w i t h i n a s o l i d a n g l e . I n t h e h o r i z o n t a l p l a n e , r a y s A and B ( f i g . 1 4 ( a ) ) d e s c r i b e t h e l i m i t s of t h i s s o l i d a n g l e i n a d d i t i o n t o determining t h e a p p a r e n t s o u r c e p o s i t i o n . I n t h e v e r t i c a l p l a n e ( f i g . 1 4 ( b ) ) r a y s C and D define similar limits of t h e s o l i d a n g l e . According t o t h e arguments p r e v i o u s l y p r e s e n t e d , t h e d i r e c t i o n a l microphone system must b e focused on t h e a p p a r e n t s o u r c e p o s i t i o n d e f i n e d by t h e i n t e r s e c t i o n of r a y s C and D i n s i d e t h e flow. These r a y s e x p e r i e n c e i d e n t i c a l r e f r a c t i o n a n g l e changes i n t h e v e r t i c a l p l a n e i n c o n t r a s t t o t h e h o r i z o n t a l p l a n e where r a y s A and B are r e f r a c t e d d i f f e r - e n t l y as t h e y propagate through t h e s h e a r l a y e r . Thus, t r a c i n g r a y s C and D back i n t o t h e f l o w f i e l d r e s u l t e d i n a d i f f e r e n t a p p a r e n t s o u r c e p o s i t i o n i n t h e v e r t i c a l p l a n e when compared t o t h e h o r i z o n t a l p l a n e . Details of t h e a n a l y s i s used t o p r e d i c t t h e a p p a r e n t s o u r c e p o s i t i o n , Sv (see f i g . 1 4 ( b ) ) i n t h e v e r t i c a l p l a n e a r e included i n Appendix C.

Both S and S are s i t u a t e d on t h e r e f l e c t o r c e n t e r l i n e b u t a t d i f f e r e n t H V d i s t a n c e s from t h e open j e t s h e a r l a y e r . F i g u r e 1 4 ( a ) shows t h a t SH i s s i t u a t e d a t a d i s t a n c e , a , from t h e s h e a r l a y e r w h i l e f i g u r e 1 4 ( b ) i n d i c a t e s t h a t Sv is l o c a t e d a t a d i s t a n c e of bl. The s i g n i f i c a n c e of t h e s e d i f f e r e n t a p p a r e n t s o u r c e l o c a t i o n s i s b e s t demonstrated by a numerical example. For M = 0.5 and B C = 50°, t h e d i r e c t d i s t a n c e between SH and Sv is 1 6 c m .

The a b i l i t y t o s e n s e t h e a c o u s t i c r a d i a t i o n from t h e s e d i f f e r e n t s o u r c e r e g i o n s depends on t h e d i r e c t i o n a l microphone d e p t h of f i e l d . T h i s parameter, shown i n f i g u r e 4 3 r e p r e s e n t s t h e frequency dependent d e c r e a s e i n t h e measured d i r e c t i o n a l microphone o u t p u t as a s o u r c e i s moved c l o s e r o r f u r t h e r from t h e r e f l e c t o r . In each case t h e f o c a l p o i n t microphone d i s t a n c e , ri, i s f i x e d by t h e d i s t a n c e R shown i n f i g u r e 1 2 . Consequently, s o u r c e p o s i t i o n v a r i a t i o n s about R, r e p r e s e n t e d by R 2 A , r e s u l t i n a d e c r e a s e i n t h e measured response.

The d i f f e r e n t s o u r c e l o c a t i o n s g i v e n by SH and S r e p r e s e n t t h e extremes V of t h e a p p a r e n t s o u r c e p o s i t i o n i n t h e open j e t . I d e a l l y , t h e d i r e c t i o n a l microphone should have a l a r g e depth of f i e l d t o s e n s e t h e d i s t r i b u t e d a p p a r e n t s o u r c e r e g i o n . Oddly, t h i s c o n t r a d i c t s t h e u s u a l requirement f o r s h a r p s p a t i a l r e s o l u t i o n demanded of d i r e c t i o n a l microphone systems.

The f i n a l c r i t e r i a s e l e c t e d f o r f o c u s i n g t h e d i r e c t i o n a l microphone s y s - t e m on t h e a p p a r e n t t r a i l i n g edge n o i s e s o u r c e r e g i o n was based on t h e d i s t a n c e t o t h e midpoint between Sv and SH. A s shown i n f i g u r e 4 4 , t h e s i d e l i n e d i s - t a n c e , yl, w a s s e l e c t e d t o p r o v i d e %ID = R. Here R = 2.81 m o r 2.07 m c o r r e s p o n d i n g t o t h e two d i s t a n c e s f o r which d e t a i l e d d e p t h of f i e l d c a l i b r a - t i o n s were a v a i l a b l e . Most important of a l l , w i t h t h e s y s t e m focused on %ID, t h e d e c r e a s e i n t h e system o u t p u t due t o t h e s o u r c e a t R M I D f A R / 2 , where AR r e p r e s e n t s t h e d i s t a n c e between SH and Sv, could n o t exceed 0.5 dB.

T h i s t i g h t t o l e r a n c e a s s u r e d t h a t t h e a p p a r e n t s o u r c e r e g i o n w a s d e f i n i t e l y w i t h i n t h e r e f l e c t o r d e p t h of f i e l d . All d a t a r e p o r t e d i n t h e p r e s e n t s t u d y s a t i s f i e d t h i s c o n d i t i o n .

It should b e n o t e d t h a t a s t h e measurement a n g l e , Bc, approached t h e open j e t a x i s , t h e d i s t a n c e between SH and Sv i n c r e a s e d t o t h e p o i n t where t h e d e p t h of f i e l d w a s i n s u f f i c i e n t f o r s e n s i n g t h e e n t i r e s o u r c e r e g i o n a t h i g h w a s considered u n a c c e p t a b l e and measurements a t Mach numbers. T h i s s i t u a t i o n s u c h c o n d i t i o n s were n o t conducted a t h i g h Mach numbers f o r a n g l e s c l o s e t o t h e open j e t axis. Other i n v e s t i g a t o r s should b e aware of t h i s l i m i t a t i o n when u s i n g a d i r e c t i o n a l microphone t o i n v e s t i g a t e a c o u s t i c s o u r c e d i s t r i b u t i o n s a t h i g h Mach numbers i n an open j e t t e s t s e c t i o n .

S c a t t e r i n g E f f e c t on D i r e c t i o n a l Microphone Measurements - The d i r e c t i o n a l microphone s p a t i a l r e s o l u t i o n and g a i n c h a r a c t e r i s t i c s shown i n f i g u r e s 4 0 and 4 1 a p p l y o n l y i n t h e absence of flow between t h e a c o u s t i c s o u r c e and t h e d i r e c - t i o n a l microphone system. In r e a l i t y , t h e d i r e c t i o n a l microphone, s i t u a t e d outside t h e flow, c o l l e c t s t h e sound t r a n s m i t t e d through t h e t u r b u l e n t s h e a r l a y e r . T u r b u l e n t e d d i e s i n t h e s h e a r l a y e r can s p a t i a l l y s c a t t e r t h e sound s u f f i c i e n t l y t o r e d u c e t h e measured a c o u s t i c s o u r c e s t r e n g t h and broaden t h e s o u r c e d i s t r i b u t i o n p a t t e r n . For example, i f t h e d i r e c t i o n a l microphone were scanned p a s t an i d e a l p o i n t s o u r c e of sound i n s i d e t h e open j e t t h e I 1 a p p a r e n t " g a i n of t h e system would be reduced w h i l e t h e d i f f r a c t i o n p a t t e r n These changes must be accounted f o r s i n c e t h e d a t a would be broadened.

r e d u c t i o n procedure i n c l u d e s t h e d i r e c t i o n a l microphone g a i n and s p a t i a l r e s o l u t i o n c h a r a c t e r i s t i c s . A summary of t h e e f f e c t s of s c a t t e r i n g on t h e measured sound p r e s s u r e l e v e l s i s provided h e r e .

To h e l p understand t h e s c a t t e r i n g e f f e c t on t h e measured d i r e c t i o n a l microphone sound p r e s s u r e l e v e l s , t h e f o l l o w i n g t e n t a t i v e p h y s i c a l explana- t i o n i s p r e s e n t e d . The argument is based on a p o i n t s o u r c e of sound s i t u a t e d i n t h e open j e t p o t e n t i a l c o r e . I n i t i a l l y , a wavefront o r i g i n a t i n g from t h e a c o u s t i c s o u r c e h a s a smooth s p h e r i c a l shape as shown i n f i g u r e 45. While p a s s i n g through t h e s h e a r l a y e r l o c a l s c a t t e r i n g by t h e t u r b u l e n c e s t r u c t u r e r e o r i e n t s small segments of t h e a c o u s t i c wavefront. The a n g l e between t h e normal t o each wavefront segment and t h e r e f l e c t o r a x i s i s no l o n g e r z e r o .

Thus, t h e wavefront segment a r r i v i n g a t t h e r e f l e c t o r a p p e a r s t o o r i g i n a t e from an o f f - a x i s s o u r c e . S i n c e t h e r e s p o n s e t o o f f - a x i s s o u r c e s i s d i m i n i s h e d , t h e d i r e c t i o n a l microphone o u t p u t i s decreased. I n t h i s manner, t h e e f f e c t i v e g a i n of t h e system i s reduced. A t t h e same t i m e , t h e d i f f r a c t i o n p a t t e r n f o r t h e p o i n t s o u r c e i s broadened g i v i n g t h e appearance of a d i s t r i b u t e d a c o u s t i c s o u r c e r e g i o n i n s t e a d of a p o i n t s o u r c e i n s i d e t h e open j e t . T h i s .

i s similar t o t h e appearance of a l i g h t observed through f r o s t e d g l a s s .

The s i z e of t h e l i g h t a p p e a r s t o be much l a r g e r .

The e f f e c t s c a n be demonstrated q u a n t i t a t i v e l y u s i n g t h e s o u r c e d i s t r i - b u t i o n measurements shown i n f i g u r e 4 6 . The experiment w a s conducted d u r i n g t h e p r e s e n t s t u d y w i t h t h e a i d of a p o i n t s o u r c e of sound l o c a t e d i n s i d e t h e open j e t test s e c t i o n . I n each c a s e t h e d i r e c t i o n a l microphone w a s scanned p a s t t h e s o u r c e p r o v i d i n g 1 1 3 o c t a v e band s o u r c e d i s t r i b u t i o n c u r v e s l i k e t h o s e shown f o r 1 0 kHz and 40 kHz. The a b s c i s s a i n each f i g u r e represents t h e r a t i o of t h e d i r e c t i o n a l microphone sound p r e s s u r e l e v e l t o the o m n i - d i r e c t i o n a l sound p r e s s u r e l e v e l . The l a t t e r microphone was p l a c e d a t t h e d i r e c t i o n a l microphone s t a t i o n corresponding t o t h e peak i n t h e measured a c o u s t i c s o u r c e d i s t r i b u t i o n . Apparent s o u r c e - t o - r e f l e c t o r and a p p a r e n t souce-to-omnidirectional microphone d i s t a n c e s were i d e n t i c a l . The r a t i o of t h e sound p r e s s u r e l e v e l measurements a t t h e s o u r c e d i s t r i b u t i o n peak r e p r e s e n t e d t h e d i r e c t i o n a l microphone g a i n d e f i n e d earlier.

A t M = 0, scanning t h e d i r e c t i o n a l microphone p a s t t h e a c o u s t i c s o u r c e provided t h e expected p o i n t s o u r c e d i f f r a c t i o n p a t t e r n and system g a i n . T h i s i s v e r i f i e d by comparing t h e measured half-width, AW i n f i g u r e 46, w i t h t h e t h e o r e t i c a l v a l u e i n f i g u r e 4 1 a t t h e corresponding frequency. Also, a comparison of t h e g a i n r e p r e s e n t e d by t h e peak v a l u e s i n f i g u r e 46 shows agreement w i t h t h e p r e v i o u s l y measured v a l u e s d e s c r i b e d i n f i g u r e 41.

A s t h e open j e t Mach number i n c r e a s e d t h e peak a m p l i t u d e s i n f i g u r e 4 6 d e c r e a s e d w h i l e t h e s o u r c e d i s t r i b u t i o n became broader. These changes were more pronounced a t t h e h i g h e r frequency of 40 kHz s i n c e t h e a c o u s t i c wave- l e n g t h was t h e n comparable t o t h e t u r b u l e n t eddy s i z e , Turbulence scatter- i n g of sound has been shown t o b e s t r o n g e r under t h i s c o n d i t i o n ( r e f . 4 7 ) .

The above d e s c r i b e d changes, r e p r e s e n t e d by t h e p a r a m e t e r s AMP and AW, were monitored o v e r t h e r a n g e of 1 1 3 o c t a v e band c e n t e r f r e q u e n c i e s from 1.25 kHz t o 50 kHz. Measurements were conducted u s i n g t h e p o i n t s o u r c e of sound a t each Mach number and d i r e c t i v i t y a n g l e i n v e s t i g a t e d i n t h e a i r f o i l t r a i l i n g edge n o i s e s t u d y . A s an example, t h e f i n a l e f f e c t i v e g a i n , Ge, a p p l i e d t o t h e r e f l e c t o r measurements o b t a i n e d a t M = 0.5 and 8, = 90" i s 7 2 given by f i g u r e 4 7 . Here t h e v a l u e of Ge a t f = 1 0 kHz, M = 0.5, and R = 2 . 0 7 m , is o b t a i n e d from t h e corresponding peak value i n f i g u r e 4 6 .

Also shown i s t h e d i f f r a c t i o n p a t t e r n half-width f u n c t i o n , AW, which i n c r e a s e s as frequency i n c r e a s e s . These measured v a l u e s o b t a i n e d i n t h e p r e s e n c e of flow, can be compared w i t h t h e M = 0 measurements i n f i g u r e 4 1 . The d i f f e r e n c e i n t h e d i r e c t i o n a l microphone response demonstrates why s c a t t e r i n g e f f e c t s must b e accounted f o r . Knowing t h e e f f e c t i v e g a i n , G e , t r a i l i n g edge n o i s e sound p r e s s u r e levels can b e c a l c u l a t e d from t h e d i r e c t i o n a l microphone measurements.

7 3

APPENDIX C Apparent Source P o s i t i o n Beneath Shear Layer a sound r a y as i t p a s s e s through t h e Because of t h e a n g l e change of s h e a r l a y e r , t h e a p p a r e n t p o s i t i o n of a sound s o u r c e , from a n a c o u s t i c a l s t a n d p o i n t , i s n o t t h e same as i t s t r u e s o u r c e p o s i t i o n . The a p p a r e n t s o u r c e p o s i t i o n can b e r e a d i l y c a l c u l a t e d .

Consider r a y s i n t h e p l a n e d e f i n e d by t h e v e c t o r normal t o t h e two-dimen- s i o n a l s h e a r l a y e r and t h e flow v e c t o r and d e f i n e t h i s t o b e t h e xy p l a n e ( s e e f i g . 4 8 ( a ) ) . The a c t u a l s o u r c e p o s i t i o n i s S and t h e a p p a r e n t s o u r c e p o s i t i o n i s SH. The f o l l o w i n g g e o m e t r i c a l r e l a t i o n s h i p s f o l l o w immediately: s = h/sin 0, (C.1) d l = sd8,/sin 9 , Thus , dB hd 8 , /sin2 8 , (C. 3)

Likewise, i n terms of et r a t h e r t h a n 8

C dB = od8,/sin2Bt (C. 4) Combining e q u a t i o n s (C.3) and (C.4) sin2 8, de,

a = h - - (C.5)

sin28c de, Equation (1) of Amiet ( r e f . 34) i s

tan ec = [ , / ( p 2 c o s e, + M )

Taking t h e d e r i v a t i v e g i v e s de, sine,

- -

- -

sin2 eC

(c. 7)

dot c: which combined w i t h e q u a t i o n ( C . 5 ) g i v e s f i n a l l y For 8, = 90°, t h e a c t u a l and a p p a r e n t s o u r c e p o s i t i o n s w i l l c o i n c i d e , b u t a t o t h e r a n g l e s they w i l l d i f f e r .

An apparent s o u r c e p o s i t i o n can a l s o b e c a l c u l a t e d based on t h e r a y p a t h s i n o t h e r p l a n e s . I n p a r t i c u l a r , c o n s i d e r a p l a n e p e r p e n d i c u l a r t o t h e above p l a n e and containi,ng a ray i n t h e xy p l a n e a f t e r r e f r a c t i o n by t h e s h e a r l a y e r .

Thus, t h e p l a n e makes an a n g l e B t w i t h t h e s h e a r l a y e r . T h i s p l a n e i s shown i n f i g u r e 48(b) which i s b a s i c a l l y t h e same a s f i g u r e 11 o f r e f e r e n c e 53. The a c t u a l s o u r c e p o s i t i o n i s n o t shown, b u t i s a g a i n t a k e n t o b e a d i s t a n c e h i n s i d e t h e s h e a r l a y e r .

I f dzl i s t h e r a y tube w i d t h j u s t a t t h e s h e a r l a y e r and dz2 i s t h e width a t a d i s t a n c e of y1 from t h e s o u r c e , t h e n e q u a t i o n (A.19) of r e f e r e n c e 5 3 g i v e s From t h e geometry of f i g u r e s 1 4 ( b ) and 48(b)

( c . l o )

S u b s t i t u t i o n f o r dz2/dz f r o m e q u a t i o n ( C . 9 ) gives ( C . 11) t, = h/{, However, t i s n o t t h e d i s t a n c e measured normal t o t h e s h e a r l a y e r ( f i g . (14b)) s i n c e t h e p l a n e considered makes an angle B t w i t h t h e s h e a r l a y e r . The d i s - t a n c e b l normal t o t h e s h e a r l a y e r i s sin 8 ,

b, = t, sin 8, = h -

(C.12) 5 , = h , b u t i n g e n e r a l bl # h . Note t h a t f o r 8, # 9 0 ° , Again, f o r 8, = 9 0 ° , b from e q u a t i o n s ( C . 8 ) and (C.12), a # bl s o t h a t t h e apparent s o u r c e p o s i t i o n depends on which p l a n e i s b e i n g considered.

7 5

APPENDIX D Boundary Layer Thickness Boundary Layer Thickness C a l c u l a t e d f o r t h e Study of S c h l i n k e r ( r e f . 5 ) - For t h e NACA 0012 symmetric a i r f o i l (22.9 cm chord) measurements r e p o r t e d by S c h l i n k e r , t h e boundary l a y e r t h i c k n e s s w a s e s t i m a t e d u s i n g t h e f l a t p l a t e boundary l a y e r t h e o r y . It should b e noted t h a t a boundary l a y e r t r i p w a s needed only on the p r e s s u r e s u r f a c e of t h e a i r f o i l t o e l i m i n a t e d i s c r e t e vor- t e x shedding t o n e s when t h e a i r f o i l w a s a t a n g l e of a t t a c k . The t r i p w a s l o c a t e d a t t h e 30 p e r c e n t chord s t a t i o n , I n c o n t r a s t , n a t u r a l t r a n s i t i o n w a s p e r m i t t e d t o occur on t h e s u c t i o n s i d e of t h e a i r f o i l . Based on t h e e x p e r i - mental d a t a t r a n s i t i o n on t h e s u c t i o n s u r f a c e o c c u r s a t x / c = 0.05 when the a i r f o i l o p e r a t e s a t a = 6" a n g l e of a t t a c k . A knowledge of t h e t r a n s i t i o n l o c a t i o n on each s u r f a c e w a s t h e n used i n t h e f l a t p l a t e p r e d i c t i o n f o r 6 .

The cumulative l e n g t h over which t h e boundary l a y e r developed corresponded t o t h e d i s t a n c e f r o m t h e i n d i v i d u a l t r a n s i t i o n p o i n t s t o the a i r f o i l t r a i l i n g edge. C o n t r i b u t i o n s from t h e upstream laminar boundary l a y e r were assumed n e g l i g i b l e . The f i n a l v a l u e of 6 l i s t e d i n T a b l e I11 r e p r e s e n t s t h e a v e r a g e of t h e p r e s s u r e and s u c t i o n s i d e boundary l a y e r s e s t i m a t e d f o r t h e s t u d y i n r e f e r e n c e 5. The c r e d i b i l i t y of such average v a l u e p r e d i c t i o n s was demon- s t r a t e d by t h e c l o s e agreement between f l a t p l a t e p r e d i c t i o n s and measurements o b t a i n e d i n t h e p r e s e n t s t u d y f o r a n a i r f o i l a t small a n g l e s of a t t a c k ( f i g .

1 9 ) . Included i n Table I11 are t h e a i r f o i l geometric parameters.

A check on t h e a b i l i t y t o p r e d i c t 6 u s i n g t h e f l a t p l a t e boundary l a y e r i s o b t a i n e d by comparison w i t h t h e NACA 0012 measurements r e p o r t e d by t h e o r y von Doenhoff ( r e f . 5 1 ) . Logarithmic p l o t s of t h e boundary l a y e r v e l o c i t y pro- f i l e s were o b t a i n e d f o r a = 0" w i t h n a t u r a l t r a n s i t i o n o c c u r r i n g i n t h e boundary l a y e r . Considering t h e R e = 2.67 x l o 6 c a s e shown i n f i g u r e 19 of r e f e r e n c e 50, s k i n f r i c t i o n measurements i n d i c a t e d t h a t t r a n s i t i o n occurred a t approximately 50 p e r c e n t chord when a = 0 " . C a l c u l a t i n g t h e e q u i v a l e n t f l a t p l a t e t u r b u l e n t boundary l a y e r which starts developing a t t h i s s t a t i o n g i v e s 6 / c = 0.022 a t the a i r f o i l t r a i l i n g edge. I n comparison, t h e measure- ments of von Doenhoff i n d i c a t e t h a t t h e v e l o c i t y p r o f i l e a t 97 p e r c e n t chord a s y m p t o t i c a l l y approaches u n i t y n e a r y / c = 0.02. Thus, t h e c a l c u l a t e d f l a t p l a t e r e s u l t i s i n good agreement w i t h t h e e x p e r i m e n t a l r e s u l t . I n a d d i t i o n , 50 shows t h a t a t t h e 52 p e r c e n t chord s t a t i o n 6 / c = 0.0025 v e r i f y i n g r e f e r e n c e t h a t t h e l a m i n a r boundary l a y e r upstream of t h e t r a n s i t i o n p o i n t r e p r e s e n t e d o n l y 10 p e r c e n t of t h e f i n a l t r a i l i n g edge boundary l a y e r t h i c k n e s s .

Boundary Layer Thickness C a l c u l a t e d f o r t h e Study of Brooks and Hodgson ( r e f . 1 0 ) - The t r a i l i n g edge t u r b u l e n t boundary l a y e r t h i c k n e s s f o r t h e NACA 0012 a i r f o i l (60.96 cm) chord was c a l c u l a t e d u s i n g t h e f l a t p l a t e boundary l a y e r t h e o r y . The approach was s i m i l a r t o t h a t used i n c a l c u l a t i n g 6 / c f o r t h e s t u d y of S c h l i n k e r ( r e f . 5 ) . S i n c e a boundary l a y e r t r i p was a p p l i e d a t t h e 15 p e r c e n t chord s t a t i o n i n t h e s t u d y by Brooks and Hodgson, t h e c a l c u l a t i o n was i n i t i a t e d a t t h i s s t a t i o n .

Table I V g i v e s t h e c a l c u l a t e d v a l u e of 6/c i n a d d i t i o n t o t h e parameters d e s c r i b i n g t h e a i r f o i l . The v a l u e of 6 / c = 0.0166 r e p r e s e n t s t h e average of t h e p r e s s u r e s i d e and s u c t i o n s i d e boundary l a y e r t h i c k n e s s v a l u e s .

It i s worthwhile t o compare t h e measured v a l u e s of displacement t h i c k n e s s ,

*

6 / c y r e p o r t e d by Brooks and Hodgson w i t h t h e v a l u e of 6 / c c a l c u l a t e d h e r e .

This comparison w i l l b e needed i n a f u t u r e d i s c u s s i o n of t h e S t r o u h a l v a l u e The p r e s e n t d i s c u s - a s s o c i a t e d w i t h t h e spectrum peak r e p o r t e d i n r e f e r e n c e 10.

*

s i o n w i l l apply t o t h e 6 / c d a t a r e p o r t e d f o r t h e a = 0" angle-of-attack geometry. Data f o r t h e a = 5" a n g l e of a t t a c k w a s n o t provided by Brooks and Hodgson.

*

For t h e range of Mach numbers i n v e s t i g a t e d a t cx = 0 " , 6 / c w a s approxi- mately c o n s t a n t and e q u a l t o 0.0065 i n r e f e r e n c e 10. Then 616" 2 2 based on t h e v a l u e of 6 / c c a l c u l a t e d above. This r a t i o i s d i f f e r e n t from t h e t y p i c a l v a l u e of 6 / 6 * = 8 measured i n a two-dimensional f l a t p l a t e boundary l a y e r theory. One p o s s i b l e e x p l a n a t i o n could b e t h e b a s i c d i f f e r e n c e between t h e f l a t p l a t e geometry used t o c a l c u l a t e 6/c and t h e a i r f o i l geometry f o r which

*

6 / c w a s measured. T h i s , however, would imply t h a t t h e f l a t p l a t e boundary l a y e r c a l c u l a t i o n f o r 6/c i s i n e r r o r by a f a c t o r of approximately f o u r . Yet, measurements o b t a i n e d by von Doenhoff ( r e f . 52) showed good agreement w i t h t h e f l a t p l a t e c a l c u l a t i o n f o r 6/c at a = 0" as noted i n t h e previous s u b s e c t i o n .

*

i t i s p o s s i b l e t h a t t h e v a l u e of 6 / c i s h i g h i n t h e s t u d y r e p o r t e d by Thus, Brooks and Hodgson.

A q u a n t i t a t i v e j u s t i f i c a t i o n f o r t h e above s t a t e m e n t is a v a i l a b l e from t h e r e c e n t s t u d y of D'Ambra and Damongeot ( r e f . 53) u s i n g a NACA 0012 a i r f o i l .

T h e i r i n v e s t i g a t i o n of t h e a i r f o i l f l u c t u a t i n g s u r f a c e p r e s s u r e s and broadband n o i s e p r e s e n t e d frequency i n f o r m a t i o n i n terms of a S t r o u h a l number based on T h e i r displacement t h i c k n e s s w a s determined through s o p h i s t i c a t e d calcu- 6*/c.

l a t i o n s based on t h e p o t e n t i a l flow f i e l d method of Garabedian and Korn com- a v i s c o u s boundary l a y e r c a l c u l a t i o n . The f o l l o w i n g s i m p l e r e l a t i o n - bined w i t h s h i p w a s o b t a i n e d t o e v a l u a t e t h e e f f e c t s of t h e v a r i o u s parameters: (D.1)

log,, B* = -3.775 + 1.1 f -k 0.12 M -k 0.8 log,, C + 0.775 Q

Here, x / c r e p r e s e n t s t h e d i s t a n c e from t h e a i r f o i l l e a d i n g edge t o t h e s t a t i o n a t which 6* i s t o b e c a l c u l a t e d . The a i r f o i l chord l e n g t h i s s p e c i f i e d i n meters w h i l e a i s given i n d e g r e e s .

The above e q u a t i o n i s s p e c i f i c t o t h e NACA 0012 a i r f o i l and i n c l u d e s t h e l o c a t i o n of t h e t r a n s i t i o n p o i n t and s e v e r a l o t h e r parameters. The e q u a t i o n r e p r e s e n t s t h e b e s t c u r v e f i t d e r i v e d from t h e t h e o r e t i c a l computations and i s a p p l i c a b l e f o r t h e compressible flow range of 0.3 C M 2 0.84 and -4" I a I 6'.

Extending e q u a t i o n 62 t o t h e incompressible flow test c o n d i t i o n g i v e n by M = 0.2 i n t h e s t u d y by Brooks and Hodgson g i v e s 6*/c = 0.00247 f o r a = 0 " .

I n comparison t h e v a l u e r e p o r t e d i n r e f e r e n c e 1 0 i s 6*/c = 0.0065. D i f f e r e n c e s between t h e s e v a l u e s s u g g e s t t h a t t h e displacement t h i c k n e s s i n r e f e r e n c e 1 0 may b e l a r g e by a f a c t o r of approximately 2.5.

REFERENCES 1. George, A. R . : H e l i c o p t e r Noise-State-of-the-Art. AIAA Paper 77-1337, 1377.

2. Schmitz, E. H . , Boxwell, D . A . : I n F l i g h t Far F i e l d Measurement of H e l i c o p t e r Impulsive Noise. J o u r n a l of t h e American H e l i c o p t e r S o c i e t y , Vol. 24, No. 4 , October 1976.

3. Munch, C . L . , P a t e r s o n , R. W . , Day, H . : Rotor Boradband Noise R e s u l t i n g from TiplVortex Blade I n t e r a c t i o n . Sikorsky A i r c r a f t Report S e r . 50909, Contract DAHC04-72-C-0040, February 1975 ( A v a i l a b l e from D T I C as AD A020-692).

4. P a t e r s o n , R. W . , Vogt, P. G . , Fink, M. R . , Munch, C . L . : Vortex Noise of I s o l a t e d A i r f o i l s . J. of A i r c r a f t , Vol. 1 0 , No. 5 , 1973, pp 296-302.

S c h l i n k e r , R . H . : A i r f o i l T r a i l i n g Edge Noise Measurements w i t h a D i r e c t i o n a l 5.

Microphone. A I A A Paper 77-1269, 1977.

6. Fink, PI. R. : Airframe Noise P r e d i c t i o n Method. F e d e r a l A v i a t i o n Administra- t i o n Report No. FAA-RD-77-29, March 1977 ( A v a i l a b l e from D T I C as A039-664).

7. Fink, M. R . : Noise Component Method f o r Airframe Noise. AIAA Paper 77-1271, 1977.

8. H e l l e r , H . H . , Dobrzynski, W. M . : Unsteady S u r f a c e P r e s s u r e C h a r a c t e r i s t i c s on A i r c r a f t Components and Far F i e l d Radiated Airframe Noise. J. o f A i r c r a f t , Vol. 1 5 , No. 1 2 , December 1978, pp 809-515.

9. Yu, J. C . , J o s h i , M . C . : On Sound R a d i a t i o n from t h e T r a i l i n g Edge of a n I s o l a t e d A i r f o i l i n a U n i f o r m F l o w . A I A A Paper N o . 79-0603, 1979.

10. Brooks, T. F . , Hodgson, T . H . : P r e d i c t i o n and Comparison of T r a i l i n g Edge Noise Using Measured S u r f a c e P r e s s u r e s . AIAA Paper 80-0977, 1980.

11. M. S . : A Review of t h e Theory of T r a i l i n g Edge Noise. J. of Sound Howe, and V i b r a t i o n , Vol. 61, No. 3 , 1978, pp 437-465.

1 2 . Yu, J. C . , Tam, C. K . : An Experimental I n v e s t i g a t i o n of t h e T r a i l i n g Edge AIAA Paper 77-1291, 1977.

Noise Mechanism.

13. Olsen, W . , Boldman, D . : T r a i l i n g Edge Noise Data w i t h Comparison t o Theory.

A I M Paper 79-1524.

REFERENCES (Cont ' d ) 1 4 . Fink, M . R . : P r e d i c t i o n of E x t e r n a l l y Blown F l a p Noise and Turbomachinery S t r u t Noise. NASA CR-134883, August 1975.

15. L i g h t h i l l , M. J.: On Sound Generated Aerodynamically - P a r t I: General

Theory. Proceedings of t h e Royal S o c i e t y , London, Vol. A211, 1952, pp 564-587.

1 6 . Ffowcs W i l l i a m s , J . , Hall, L. H . : Aerodynamic Sound G e n e r a t i o n by Turbulent Flow i n t h e V i c i n i t y of a S c a t t e r i n g Half P l a n e . J. F l u i d Mech., Vol. 4 0 , P a r t 4 , March 1970, pp 657-670.

1 7 . C r i g h t o n , D . G . , Leppington, F. G . : S c a t t e r i n g of Aerodynamic Noise by a S e m i - I n f i n i t e Compliant P l a t e . J o u r n a l of F l u i d Mechanics, Vol. 43, 1970, pp 721-736.

18. C r i g h t o n , D . G . : R a d i a t i o n From Vortex Filament Motion Near a Half-plane J o u r n a l of F l u i d Mechanics, Vol. 51, 1970, pp 357-362.

19. Howe, M. S . : C o n t r i b u t i o n s t o t h e Theory of Aerodynamic Sound w i t h Applica- t i o n t o Excess Jet Noise and t h e Theory of t h e F l u t e . J o u r n a l of F l u i d Mechanics, Vol. 71, 1975, pp 625-673.

20. Howe, M. S . : The I n f l u e n c e of Vortex Shedding on t h e G e n e r a t i o n of Sound by Convected Turbulence. J o u r n a l of F l u i d Mechanics, Vol. 76, 1976, pp 711-740.

21. Howe, M. S . : The E f f e c t of Forward F l i g h t on t h e D i f f r a c t i o n R a d i a t i o n of a High Speed J e t . J o u r n a l of Sound and V i b r a t i o n , Vol. 50, 1977, pp 183-193.

22. Chase, D . M . : Sound Radiated by Turbulent Flow Off a Rigid Half-plane as Obtained from a Wavevector Spectrum Hydrodynamic P r e s s u r e . J o u r n a l of A c o u s t i c a l S o c i e t y o f America, Vol. 52, 1972, pp 1011-1023.

23. Chase, D . M . : Noise Radiated From a n Edge i n Turbulent Flow. American I n s t i t u t e of A e r o n a u t i c s and A s t r o n a u t i c s J o u r n a l , Vol. 1 3 , 1975, pp 1041- 1047.

24. Chandiramani, K. L . : D i f f r a c t i o n of Evanescent Waves w i t h A p p l i c a t i o n s t o Aerodynamically S c a t t e r e d Sound and R a d i a t i o n from Unbaffled P l a t e s . J o u r n a l of t h e A c o u s t i c a l S o c i e t y of American, Vol. 55, 1974, pp 19-29.

REFERENCES (Cont ' d )

25. Amiet, R. K . : Noise Due t o Turbulent Flow P a s t a T r a i l i n g Edge. J o u r n a l of Sound and V i b r a t i o n , Vol. 47, 1976, pp 387-393.

Amiet, R. K . : E f f e c t of t h e I n c i d e n t S u r f a c e P r e s s u r e F i e l d on Noise Due 26.

t o Turbulent Flow P a s t a T r a i l i n g Edge. J o u r n a l of Sound and V i b r a t i o n , Vol. 57, 1978, pp 305-306.

Amiet, R . K . : High Frequency T h i n - A i r f o i l Theory f o r Subsonic Flow. A I M 27.

J o u r n a l , Vol. 1 4 , 1976, pp 1076-1082.

28. Amiet, R. K . : Acoustic R a d i a t i o n from a n A i r f o i l i n a Turbulent Stream.

J. Sound V i b r a t i o n , Vol. 41, 1975, pp 407-420.

29. Willmarth, W. W . and ROOS, F. W . : R e s o l u t i o n and S t r u c t u r e of t h e Wall P r e s s u r e F i e l d Beneath a Turbulent Boundary Layer. J. of Fluid Mechanics, v o i . 22, 1965, pp 81-94.

30. Hinze, J. 0.: Turbulence. McGraw H i l l Book Co., I n c . , New York, 1975, second e d i t i o n .

31. E c k e r t , E. R. and Drake, R. M . , Jr.: Heat and Mass T r a n s f e r . M c G r a w H i l l Book Co., I n c . , New York, 1959, pp 144.

32. Corcos, G . M . : The S t r u c t u r e of t h e Turbulent P r e s s u r e F i e l d i n Boundary Layer Flows. J. o f F l u i d Mechanics, Vol. 18, 1964, pp 353-378.

33. G o l d s t e i n , M. E . : S c a t t e r i n g and D i s t o r t i o n of t h e Unsteady Motion on T r a n s v e r s e l y Sheared Piean Flows. J . of F l u i d Mechanics, Vol. 91, 1979, pp 602-632.

34. Amiet, R. K . : R e f r a c t i o n of Sound by a Shear Layer. J . Sound and V i b r a t i o n , Vol. 58, 1978, pp 467-482.

35. Amiet, R. K. : Noise Produced by Turbulent Flow i n t o a P r o p e l l e r o r H e l i c o p t e r Rotor. Paper 76-560, A I A A , 1976. (Also published i n s y n o p t i c form i n A I A A J o u r n a l , Vol. 15, No. 3 , March 1977, pp 307-308.)

36. Amiet, R. K . : Noise Due t o Rotor-Turbulence I n t e r a c t i o n . NASA Conference P u b l i c a t i o n 2052, 1978, pp 109-126.

REFERENCES (Cont ' d ) 37. P a t e r s o n , R. W . and Amiet, R. K. : Noise of a Model F e l i c o p t e r Rotor d u e t o I n g e s t i o n of Turbulence, NASA CR-3213, 1979.

38. Bendat, J. S . and P i e r s o l , A. G . : Measurement and A n a l y s i s of Random Data.

John Wiley and Sons, Inc . , 1965.

39. Amiet, R. K . : Frame of Reference C o n s i d e r a t i o n f o r t h e Forward F l i g h t Noise Problem. UTRC Report N212775-1, 1974.

40. P a t e r s o n , R . W . , Vogt, P . G . , Foley, W . If.: Design and Development of t h e United A i r c r a f t Research L a b o r a t o r i e s Acoustic Research Tunnel. J . of A i r c r a f t , Vol. 1 0 , No. 7 , 1973, pp 427-433.

41. S t . Hilaire, A. O . , Carta, F. O . , Fink, M . R . , Jepson, W . D . : The I n f l u e n c e of Sweep on t h e Aerodynamic Loading of a n O s c i l l a t i n g NACA 0012 A i r f o i l .

Volume 1-Technical Report, NASA C R - 3 0 9 2 , May 1 9 7 9 .

42. Hama, F. R . : An E f f i c i e n t T r i p p i n g Device. J. of A e r o n a u t i c a l S c i e n c e s , Vol. 2 4 , March 1957, pp 236-237.

43. S c h l i c h t i n g , H.: Boundary Layer Theory, McGraw H i l l Book Co., 1968.

44. P a t e r s o n , R. W . , Vogt, P. G . , Fink, 11. R . , Munch, C . L . : Vortex Noise of I s o l a t e d A i r f o i l s . 3. A i r c r a f t , Vol. 1 0 , No. 5 , May 1973, pp 296-302.

45. L a u f e r , J . , S c h l i n k e r , R . H . , Kaplan, R . E . : Experiments on Supersonic J e t Noise. A I M J . , Vol. 1 4 , No. 4 , A p r i l 1976, pp 489-497.

46. S c h l i n k e r , R . H . : Supersonic Jet Noise Experiments. PhD D i s s e r t a t i o n , U n i v e r s i t y of Southern C a l i f o r n i a , 1975.

47. S c h l i n k e r , R . H . , Amiet, R . K . : Shear Layer R e f r a c t i o n and S c a t t e r i n g of Sound. A I M Paper 80-0973, 1980.

48. Klebanoff, P. S . : C h a r a c t e r i s t i c s of Turbulence i n a Boundary Layer w i t h Zero P r e s s u r e G r a d i e n t , NACA Rep. 1247, 1955 (Supercedes NACA TN-3178).

49. Schloemer, H. H . : E f f e c t s of P r e s s u r e G r a d i e n t s on Turbulent Boundary Layer Wall P r e s s u r e F l u c t u a t i o n s . J o u r n a l of t h e A c o u s t i c a l S o c i e t y of America, Vol. 42, No. 1, 1967.

8 2 REFERENCES (Cont ' d ) 50. George, A. R . , Najjar, F. E . , K i m , Y . N . : Noise Due t o Tip Vortex Formation on L i f t i n g R o t o r s , AIAA Paper No. 80-1010, 1980.

51. Amiet, R. K . : C o r r e c t i o n of Open-Jet Wind Tunnel Measurements f o r Shear Layer R e f r a c t i o n . P r o g r e s s i n A s t r o n a u t i c s and A e r o n a u t i c s , Vol. 4 6 , 1976, pp 259-280. Also, A I A A Paper 75-532.

52. von Doenhoff, A. E . : I n v e s t i g a t i o n of t h e Boundary L a y e r about a Symmetrical A i r f o i l i n a Wind Tunnel of Low Turbulence, NACA Report No. 4-507, August 1940.

F . , Damongeot, A . : A i r f o i l S e c t i o n F l u c t u a t i n g P r e s s u r e and Rotor 53. D'Ambra, Broadband Noise. Paper No. 64 p r e s e n t e d a t t h e F i f t h European R o t o r c r a f t and Powered L i f t A i r c r a f t Forum, Amsterdam, The Netherlands, September 4-7, 1979.

t 8 3 Table I Mach Number vs Propagation Angle, and Airfoil Angle of Attack GEOMETRIC SYMBOL ANGLE, (Y 0 -0 4 O 7.6 A PROPAGATION ANGLE, O c , deg 50 70 90 110 130 0.1 H E- 0.2 w m 2 0.3

-

J Z 0.43 T

9 0.5

0.55

I

Table II Angle and Amplitude Changes Associated with Refraction and Retarded Source Position Corrections PROPAGATION ANGLE, O , , deg 50 70 90 110 130

- - -

56.6 75.8 95.8 116.6 138.8 54.4 75.4 95.7 115.3 134.3 0.1 -1.21 -0.68 0.2 0.95 2.09 -2.9 -0.45 -0.69 -2.94 -1.06

-

81 .1 80.8

- -

0.2 -0.61 -0.33 66.7 86.4 109.2 133.7 63.3 86.4 107.4 120.3 0.3 -2.40 -0.36 1.95 5.1 9 -2.49 -0.16 -0.99 -5.79 71.9 93.7 121.4 69.3 93.8 115.4 0.43 -2.78 0.57 4.71 0.07 -0.15 -1.6 131.8 7.08 -0.15 -4.80 102.5

0.55 1 - 1 ’01”

2.26 -0.15 1) O t , degrees KEY TO PARAMETERS.

2) @ , , degrees NUMBERS REFER 3) REFRACTION AMPLITUDE CORRECTION, dB TO LISTING IN 4) AMPLITUDE CORRECTION FOR CONVERSION EACH BOX.

TO RETARDED SOURCE POSITION Table 111 Average Boundary Layer Thickness Calculated for the Data of Schlinker AIRFOIL: NACA 001 2 CHORD: c = 22.9 cm SPAN: s = 53.3 c m SOURCE TO MICROPHONE DISTANCE: r e = 2.81 Table IV Average Boundary Layer Thickness Calculated for the Data of Brooks and Hodgson AIRFOIL: NACA 001 2 VE LOCITY CHORD: c = 60.96 cm mlsec SPAN: s = 46 c m SOURCE TO MICROPHONE DISTANCE: re = 1.22 m 0.01 87 69.5 0.2 0.01 66

I 1 I

M ROTOR BLADE

’/ SEGMENT

/

J

fee-\ - --

I I I 1 TRAILING EDGE M- NOISE RADIATION LTWO-DIMENSIONAL AIRFOIL SECTION Figure 1 Simulation of Rotating Blade Trailing Edge Noise Radiation by a Two-Dimensional Airfoil Section a7 L I N E D ACOUSTIC CORNERS TURBULENCE ACOUSTI C WE DG ES COLLECTOR A I R FLOW

c3

TOWER HONEYCOMB HEATER A N D M U F F L E R '

t

HIGH PRESSURE A I R SUPPLY S Y S T E M TOP V I E W

1 1 46m 4

I N L E T A N ECHO1C DIFFUSER M U F F L E R D R I V E R 1

- - I

c - - - - c - +

CHAMBER

n

C E N T R I F U G A L F A N D R I V E MOTOR SIDE V I E W Figure 2 UTRC Accoustic Research Tunnel \ "\ \ \ ' \ \ \ Figure 3 Airfoil in Rectilinear Motion OBSERVER

t

\ 1".

\ \ SEGMENT Figure 4 Rotor Blade Segment Moving in Forward Flight 9 1 Figure 6 Section of Helicopter Main Rotor Blade used for Isolated Airfoil Study SUCTION SURFACE TRIP LOCATION INTERIOR SPAR

-

I

PRESSURE SURFACE TRIP LOCATIONS

i ABRASION STRIP LOCATION ON FULL-SCALE

HELICOPTER ROTOR BLADE SPAN = 53.3cm CHORD = 40.6cm Figure 7 Rotor Blade Cross-section 0.20

. 0 0.15

X ABRASION STRIP JOINT

i i

n ON PRODUCTION ROTOR I -SUCTION AND PRESSURE

[/ SURFACE TRIP LOCATION

z 0.10 SECOND TRIP ON a PRESSURESURFACE W

-

z

-

0 0 0.05 0 0.2 0.4 0.6 0.8 MACH NUMBER, M Figure 8 Location of Minimum Static Pressure Point on Airfoil Suction Side FOCAL POINT MICROPHONE Figure 9 Facility Background Noise Sources SPHERICAL REFLECTOR

I

FOCAL POINT MICROPHONE

L

1 Of cm THREE DIRECTIONAL I ROTATING BASE

r MOTORIZED LINEAR TRAVERSE

Figure 10 Schematic Diagram of Spherical Reflector Directional Microphone System 9 6 Q, C r n

.-

I

U C Q C

.-

c Q, v) LENS EQUATION: 1 1 2 - + - = - IMAGE POINT R ri R ,

I

i- li -I

FOCAL POINT MICROPHONE SOURCE + R 4 Figure 12 Directional Microphone Operating Principles M SHEAR LAYER M = O NON REFRACTED WAVEFRONT, M = 0 SI DELIN E TRAVERSE STATION Figure 13 Geometry for Transmission of Sound Through a Shear Layer M __t M = O TRANSMITTED CENTERLINE ACOUSTIC DIRECTIONAL MICROPHONE REFLECTOR a) HORIZONTAL PLANE SIDEPLATES 7 TRANSMITTED ACOUSTIC RAYS

J

1 S V

SOURCE SOURCE LAYER POSITION. Sv LAYER RAY PLAN VIEW OF RAYS C AND D b) VERTICAL PLANE LOOKING UPSTREAM Figure 14 Apparent Source Position Effects on Directional Microphone Alignment /-INTERMITTENCY INTERFACE, 6 , - CORRESPONDING TURBULENT TO Y = 0.02, BOUNDARY $16 = 1.07 LAYER INTERFACE BOUNDARY MEAN VELOCITY LAYER PROFILE THICKNESS, b 0 0 0 0 0 0 FLAT PLATE Figure 15 Boundary Layer Thickness and Intermittency Interface Measurements on a Flat Plate 0.0' 0.01 0.0: 6.

+-I

C 0 0.0; .

= -

A- -

B

5 0.01

L L w 0 0 z 0

a

c II n n LIJ -0.01

d

z

II:

= -0.02

- 0

-c

0 0 -0.03 ' 0 -0.04 I I I I I -0.05

0.2 0.4 0.6 0.8 1 .o 1

NOR MALI ZE D VE LOClTY a) M = O X Figure 16 Normalized Mean Velocity and Turbulence Intensity Profiles for

Rotor Blade Section, cx = - 0 . 4 O

0.05 0.04 0.03 0.02

--

O0 I

C

o 8 ’

0.01 0 0 -0.01

--

C -0.02 -0.03 -0.04 I t I I

I

-0.05 0.4 0.6 0.8 1.o 1 0.2 N 0 R M AL I Z E D VE LOClTY b) M =0.3

Figure 16 - Continued

0.05 0 UlUO 0 SIMILAR TO @ u ) ' / @ u ) ' ~ ~ ~ 0.04 0.03 0.02 U 0 0 0.01

2 0

€I

n Y -0.01 0 O -0.02 -0.03 -0.04 -0.05

0 0.2 0.4 0.6 0.8 1 .o 1.2

NOR MAL IZE D VE LOC ITY C) M = 0.43

Figure 16 - Continued

0.05 0 U N O 0 SIMILAR TO @ U ) ' / @ U ) ' ~ ~ ~ 0.04 - 0 0.03 - 0 0 0.02 0 0 0 0 0.01 0 0 I D 0 0 -0.01 - 0 -0.02 0 9 - 0 - 0 -0.03 -0.04 I 1 I I 1 1 I I 1 1 1 -0.05

0 0.2 0.4 0.6 0.8 1 .o

NORMALIZED VELOCITY d) M =0.5

Figure 16 - Concluded

0.05 -0- d i k , PRESSURE SIDE

-

43- 6 p , SUCTION SIDE 0.04

-- blC, CALCULATED FROM FLAT PLATE BOUNDARY

LAYER THEORY

-

0.03 0.02

- -- -B------a------Q-- 0

-

0.01 I I 1 I 0.05

-

0.04

-

0.03 0 U U C

-

0.02 A c . # W 0

-

0.01 I I I 1 0 .

0.05 n n

-

0.04

-

0.03

-

0.02 0 n

-

0.01

- 0

1 1 I I 4 0 - Figure 17 Normalized Boundary Layer Interface Distance Versus Mach Number and Angle of Attack for Rotor Blade Section 0.05 0.04 0.03

” 0.02

.

E

5 0.01

w 0 C z n w -0.01 -0.02 -0.04

1 I I 1 I I I I 1 1 I

-0.0:

0.2 0.4 0.6 0.8 1 .o 1.2

NORMALIZED VELOCITY a) M=0.15 Figure 18 Normalized Mean Velocity and Turbulence Intensity Profiles for

Rotor Blade Section, 8 = 7 . 6 O

0.0: 0 UlUO 0 u ’ ~ ~ ~ I U , = 0.049 0.01 0.0: 0.0; 0.01 C -0.01 -0.02 -0.03 -0.04

I 1 I I I I I I I I I

-0.05

0.2 0.4 0.6 0.8 1 .o 1.2

NORMALIZED VELOCITY b) M =0.3

Figure 18 - Continued

0.05 0 UIU, 0 SIMILAR TO ( p ~ ) ' / ( p u ) ' ~ ~ ~ 0.04 0.05 0 0 0.02 O D O m 0 OO 0.01 0 0 D O -0.01 0 O O -0.02 -0.03 -0.04 -0.05

0.2 0.4 0.6 0.8 1 .o 1

NORMALIZED VELOCITY C ) M = 0.43

Figure 18 - Continued

0.05 0 U l U O 0 SIMILAR TO @ U ) ' / @ U ) ' ~ ~ ~ 0.04 O 0.03 D C O 0.02 0 0

c n

0 0 0.01 D C 0 0 -0.01 c - C O O -0.0; -0.0: -0.01 d) M = 0.5 1 1

I I I I I 1 1 1

-0. O!

NORMALIZED VELOCITY d ) M =0.5

Figure 18 - Concluded

0.07 DATA MEAN SYMBOL LINE PARAMETER Q

- 6,IC -04"

0.06

0 - - -- 6,IC 7 6"

A - - - 6,IC 12"

Y 0.05 cg

---- 6,IC FLAT PLATE BOUNDARY

[I LAYER THEORY

-- 0.04

cg L L 0.03

?

[I w

---F --- - m-----R------

# 0.02

--- =--------

0.01 0.1 0.2 0.3 0.4 0.5 MACH NUMBER, M Figure 19 Average of Normalized Boundary Layer Interface Distances on

Pressure and Suction Side of Rotor Blade Section

L c L N I Y Ln I I c h m J J c\l cy 0 a

- 0 0 - 0 4 O

0 7 6 " A 12" O O 0

30 - O 0

8 00

- O Q

rb O

20 -

m -

U i a v) I I I l l l l l I I I I I I l l , n 1 0 1 1 1 1 ' I W >

s 00 A

0 50- 00 A m

-

OOO A

-

40 - % 8

"&&A

- 00 A

A 0 O A

30 -

-

I 1 I I I I d I I P I I I I I , 20 I I l l ' 0.1 1 10

-

O OO

-

00%

- oo&l

C O O

' ' 1 1 ' I I I I I I I l l Q I I I I I l l

55:

- O O O

STROUHAL NUMBER, St e ) M = 0.5, 8, = 98"

Figure 21 - Concluded

NORMALIZED TO Be = 95.7 O

c I

a) M = 0.1 NORMALIZED TO 0, = 86.4' SYM st 0 0.27 e,=500 70" 90" 110" -20. I 1 1 0 20 40 60 80 100 120 140 160 180 RETARDED ANGLE Be, deg b) M = 0.3 Comparison of Measured and Theoretical Source Directivity as a Figure 22

Function of Mach Number for Rotor Blade Section, a = - 0 . 4 O

NORMALIZED TO 0, = 93.8" m -0 1- a CI) w SYM St 0 0.19 I - 0 0.24 W a A 0.30

0 0.599

c ) M = 0.43 m -0 A- a CT) W > - I - w a

I ecj700 910

1 / ,

-20 I i f I

0 20 40 60

Figure 22 - Concluded

NORMALIZE

-

m O - D A- a SYM St c n

-

W 2 0 0 2 5 I-

4 O 0 5 0

-10- A 0 9 9 H,=70" 90"

-

-20, 0 20 40 60 80 100 120 140 160 180 RETARDED ANGLE, B e , deg Comparison of Measured and Theoretical Source Directivity for Figure 23

Rotor Blade Section, M = 0.3, CY = 7 . 6 O

11 7 SYMBOL APPROXIMATE St 0 0 55 A 0 25 V 0 13 I I I I I I 1 I I I I I I I I I I 0.1 0.2 0.3 0.4 0.5 0.6 0.8 1.0 STROUHAL NUMBER, St a) a=-0.4" Figure 24 Variation of 1/3 Octave Band Trailing Edge Noise Spectra with Mach Number for Rotor Blade Section, 8 , = 9 8 O SYMBOL APPROXIMATE St 0 1 .o 0 0 55 A 0 35 0 0 19 0.2 0.3 0.4 0.6 0.8 1.0 0.1 STROUHAL NUMBER, St b) ~ = 7 . 6 "

Figure 24 - Concluded

- CURVE - THEORY NUMBER - 1 PRESENT STUDY. B(He)

--- - 2

BROOKS AND HODGSON. 6(He).

-

BASED ON HOWE

--- 3 GOLDSTEIN. D W , )

-

- - - 4

GOLDSTEIN. b(O,), REFRACTION REMOVED m - -0 A- n v) W

lor

I- W U -20 I l l l l l I 1 1 1 1 1 1 1 1 1 1 -30 a) M = 0.2 m -0 /- I/ v) W I - W CI -1 0

-30L ' I ' ' ' I ' I ' I ' I

0 20 40 60 80 100 120 140 160 1 0 ANGLES, Om, O , , deg (b) M = 0.43 Figure 25 Comparison of Theoretical Trailing Edge Noise Source Directivity Patterns in Measured and Retarded Coordinate Systems -30 0 20 40 60 80 100 120 140 160 180 ANGLES, O Y , Be C) M = 0.86

Figure 25 - Concluded

1 2 1 b

- h h 0 0 1 7 5 4 "

0 0 2 8 0 8 A 0 3 864

O O h

0 0 4 3 938

-

b b h h h05 982 h b h

- h

h h

0 0

0 0

- A o ~ o ~ o o

A A rn

-

-u A A J a A A v3

- D

A A A z a A A A m A

- 0

O O A

40 - 0

0 0

- 0

- 0 0

0 0 0

- 0 0

- 0

Figure 26 One Third Octave Band Trailing Edge Noise Spectra for Rotor Blade

Section, 0 , = 70°, (I! = 7.6O, re = 3m

1 2 2 M 0 0 0 9 0 0 1 3 A 0 1 8

0 0 2 2

h 0 2 6

a 0 3 1

I 0 1 1 1 ' 1 1 I I I I I I l l 1 1 I I I I I I I 0.05 0.1 1 10 STROUHAL NUMBER, St One Third Octave Band Noise Spectra for NACA 0012 Data Reported Figure 27

by Schlinker, 8 , = 90°, a = 6 O , re = 2.81m

1 2 3 M a 0 0 2 0" 0 0.2 5"

-

-

10 1 1 1 1 1 I I I I I I I I I 1 I 1 I 1 1 1 1

Figure 28 - One Third Octave Band Trailing Edge Noise Spectra for NACA 0012

Data Reported by Brooks, 8 , = 90°, re = 1.22m

1 2 4

Figure 29 Normalized 1/3 Octave Band Trailing Edge Noise Spectra for Rotor Blade

Section, Oe=980, cr=7.6', re=3m l o o / M 0 0 0 9 0 0 1 3 A 0 1 8

0 0 2 2

I7 0 2 6

gOl 0

VALUE AT

I r PEAK, St = 0.1

501 I I I l l I I I 1 I 1 1 1 1 I I 1 I I I l l 0.05 0.1 1 10 STROUHAL NUMBER, St Figure 30 Normalize 113 Octave Band Trailing Edge Noise Spectra for NACA 0012 Airfoil Data Reported by Schlinker, de=9O0, a = 6 O , re=2.81 m I I 1 2 6 M

-

0 0.1 0 0.2

-

SCALING LAW

L

VALUE AT PEAK.

S t = O . l 4 50, I 1 1 1 1 I I I 1 1 1 1 1 0.05 0.1 1 10 STROUHAL NUMBER, St Figure 31 Normalized 1/3 Octave Band Trailing Edge Noise Spectra for NACA 0012

Data reported by Brooks, 8 , = 90°, (I! = 5 O , re = 1.22 m

1 2 7 NACA 001 2 DATA OF

17 0 1 1 NACA 0012 DATA OF

0 0 2 B R O O K S , a = 5 " m -0 Y

+

LL STROUHAL NUMBERS AT SPECTRUM PEAK

-

PRESENT STUDY

-

A 0.01 0.1 1 10 STROUHAL NUMBER, St Figure 32 Comparison of Normalized 1/3 Octave Band Trailing Edge Noise Spectra

Measured by Various Investigators, 8e = 90°

a M oe A 0 7 6 " 0 1 75.4 0 7 6 " 0 3 86 4 A a A A 7 6 " 0 5 98.2 A 0 - 0 4 " 0 1 75.4 - 0 4 " 0 3 86.4

- a P A u A - 0 4 " 0 5

98.2 THEORY.

---% M = 0 5

- 0

m r M = 0.3 -0 4c

30 c

I I I I I I I I I I I I I I I I STROUHAL NUMBER, St a) THEORY USING FLAT PLATE SURFACE PRESSURE SPECTRUM Figure 33 Comparison of Measured and Theoretical 1/3 Octave Band Noise Spectra

for Rotor Blade Section, tIc = 70°, C Y = 7 . 6 O , re = 3 m

n z a

-

m W >

2 4 0 -

m .

-

M = O . l -

-

- 0

-

I , , ' I f I 1 I I l l I I I 1 1 1 1 1

0.05 0.1 1 .o 10.0

STROUHAL NUMBER, St b) THEORY USING AIRFOIL SURFACE PRESSURE SPECTRUM

Figure 33 - Concluded

SYMBOL DATA SOURCE EXPERIMENT OF BROOKS AND HODGSON

--- PREDICTION OF BROOKS AND HODGSON

PRESENT THEORY WITH FLAT PLATE Sqq APPLIED TO M = 0.2 CASE PRESENT THEORY WITH AIRFOIL Sqq m -0 1- w > w w a:

g 3c

W [r a n I -

z

/ - \ 0 0 0 20 n

z

\ -5 M = 0 . l J O U - - 0 1c Q z I J I I t I I I I 1 I 1 I I I C

1 .o

0.3 10.0 FREQUENCY. KHz Figure 34 Ccmparison of Present Theory with Results of Brooks and Hodgson,

' O e = 90 O, CY = 0 O, re = 1.22 m, Bandwidth: 1 Hz

SYMBOL M DATA SOURCE 0.09 YU (REF. 9), AIRFOIL DATA, CY = 0 "

-- -- 0.16 YU (REF. 9), AIRFOIL DATA, CY = 0 "

---

AVERAGE OF AIRFOIL DATA, a=Oo

---- - FLAT PLATE CALCULATION BASED ON

EQUATION 22 OF PRESENT STUDY I

-60 I I I I

0.05 0.10 0.20 0.50 1 .oo 2.00 w 6 * I U a) AIRFOIL AND FLAT PLATE SPECTRA 0 MEASURED DIFFEREKE

- EMPIRICAL CJRVE FIT

USED TO DLFINE DIFFLRENCE FUNCTION 1 I I 1 1 1 1 I I I I I I I I I I I I I I l l I 0.10 1.oo 10 0.01 b) DIFFERENCE BETWEEN AIRFOIL AND FLAT PLATE SPECTRUM LEVELS Comparison of Airfoil and Flat Plate Normalized Surface Pressure Figure 35 Spectra, Bandwidth, 1 Hz 1 3 2 8 ( M 0 0.13 0 0.22 A 0.31 7( 6 C THEORY, M = 0.31 m U M = 0.22 i

2 5c

-J ~ M=0.13 CI)

-

v

I I ' I 1 1 I 1 I 1 1 1 I 1 1 I I I l l

0.05 0.10 1 .o

10.0 STROUHAL NUMBER, St Figure 36 Comparison of Measured and Present Theoretical Prediction for NACA 0012

Data Reported by Schlinker, O e =goo, CY = 6 O , re =2.81 m

PRESENT FIRST PRINCIPLES 90 THEORY SHIFTED TO ALIGN THEORY WITH AIRFOIL SPECTRUM PEAK WITH

% SURFACE PRESSURESPECTRA

SCALING LAW

z

tj

z

1 80 LL [r F

Y

a v) SCALING LAW n 70 W E I 1 1 I 1 I I I I I I 1 I I I I 1 I l l

0.10 1 .o 2.0

0.01 STROUHAL NUMBER, St Comparison of Normalized 113 Octave Band Spectrum Functions for First Figure 37

Principles Theory and the Scaling Law, tle = 90°

UJ t

.-

L P N I Y E a L L

i

(r 0 LL 0, n v) c 0 0 0 0 0 0 d 0 m co b (D v) 9 P '1dS CINtlBMOkkJVN 0 MEASURED DATA 0 MEASURED DATA CORRECTED FOR ATMOSPHERIC ATENUATION

- PRESENT SCALING LAW PREDICTION

WITH GROUND REFLECTION ADDED

--- PRESENT THEORETICAL PREDICTION WITH

GROUND REFLECTION ADDED

0 ' g 8

n

Q 0

z

8 0 0 0

7 0 - W >

-

0 T

-

," 60

-

I I 1 1 1 1 1 1 1 1 1 I rn c J- Q n a

Q

" Q

cn n

z

s

w >

7-i 60

z

," 7 I 1 1 1 1 1 1 1 1 I I I 1

0.5 1 .o 2.0 3.0 4.0 5.0 6.0 8.0 10.0

FREQUENCY, KHz b) FLYOVER SPEED OF 36 mlsec, B e = 90" Comparison of Measured 1/3 Octave Band Helicopter Flyover Noise Figure 39 Spectrum and Predicted Trailing Edge Noise Spectrum -4 m U r; -8 c EXPERIMENT

i

A 1 kHz 0 10kHz 0 50 kHz -1 2

- FRAUNHOFER

DIFFRACTION THEORY -1 6 -2 0 2 4 n Df

T ) = - sin @o

cO Figure 40 Diffraction Pattern of the Directional Microphone System for a

Point Source of Sound at M =0, R =2.8m

-

SYMBOL R MEASUREMEN1 Q 0 2.81rn GAIN 0 2.07 GAIN A 2.81 DIFFRACTION PATTERN HALF-W I DTH IO0 m -0 h [r c v (3 E THEORETICAL GAIN, R = 2 81m

\

50 3 Q THEORETICAL GAIN, R = 2.071-11 L J THEORETICAL DIFFRACTION PATTERN HALF-WIDTH,R = 2.81 rn I I I I I I I I I I I I I I I I '1 1.25 1.6 2 2.5 3.15 4 5 6.3 8 10 12.5 16 20 25 31.5 40 50 Figure 41 Gain and Diffraction Pattern Half-width of Directional Microphone

System for a Point Source of Sound at M = O

a) ANGLE CORRECTION 12 '

a !

4 - 0 - -4 .

-a -

-1 20 -

20 40 60 80 100 1 !O RADIATED ANGLE, e , b) AMPLITUDE CORRECTION Figure 42 Refraction Angle and Amplitude Corrections, M = O S ,

Sideline Geometry, hlyl = 0.14

0 SOURCE AT R - A SOURCE AT R + A

- AVERAGE RESPONSE

m -0 W- m a :

Y

d W 2; -I W oc m m w oc a n Z DISPLACEMENT DISTANCE, A, cm C ) f = 50 KHZ Figure 43 Directional Microphone Depth of Field Response to A Point Source of Sound at M = O 14 0 APPARENT SOURCE, SH, IN HORIZONTAL PLANE, @ MID POINT USED TO LOCATE THE DIRECTIONAL MICROPHONE WITH y 1 , VARiES M AND^, LAYER ACOUSTIC RAY O1 WITHOUT FLOW

I

DIRECTIONAL MICROPHONE REFLECTOR AR = R1 .3 - R2,3 R1 ,3 -+ R2,3 2.81 -m

= { OR

R ~ i ~ = 2 2.07 m Figure 44 Locating the Directional Microphone Reflector to Account for the Apparent Source Position ACOUSTIC SOURCE

/-

OPEN JET CONVECTION TRANSLAl INLET WAVEFRONT SHEARLAYER WAVEFRONT WITH SCATTERING WAVEFRONT WITHOUT SCATTERING DIRECTIONAL MICROPHONE CENTERLINE I SOLID ANGLE OVER WHICH DIRECTIONAL MICROPHONE Figure 45 Physics of Scattering 1 4 2 1 = 10 kHz f = 40 kHz

-

Figure 46 Variation of Acoustic Source Diffraction Pattern with Open Jet Mach

Number, OC =goo

R MEASUREMENT SYMBOL

-

0 2.07m GAIN - 0 2.07rn APPARENT DIFFRACTION PATTERN HALF-WIDTH

-

THEORETICAL GAIN, 0 0 FOR M = 0, m R = 2.07m -0

Eo

50 3-

n

c Y Q c ?

THEORETICAL DIFFRACTION HALF-WIDTH, FOR M = 0, R = 2.0711-1 12O I I I 1 I 1.0 1.25 1.6 2.0 2.5 3.15 4 5 6.3 8 10 12.5 16 20 25 31.5 40 50 113 OCTAVE CENTER FREQUENCY, f, kHz Figure 47 Gain and Apparent Diffraction Pattern Half-width of

Directional Microphone System, M = 0.5,8, = 90 O

14 4 APPARENT SOURCE POSITION, SH \ LAYER M = O a) APPARENT SOURCE POSITION IN THE HORIZONTAL PLANE CONTAINING THE SHEAR LAYER NORMAL AND THE FLOW VECTOR LAYER APPARENT SOURCE. Sv b) APPARENT SOURCE POSITION IN THE PLANE NORMAL TO THE X-Y PLANE AND AT AN ANGLE 81 WITH THE SHEAR LAYER Figure 48 Coordinates Defining Apparent Source Position 1. Roport No. 2. Govrrnmrnt k t u i o n No. 3. Raipiont's Cotdog No.

NASA CR-3470 4. Titlo wd Subtitlo 5. A ~ p w r OItr HELICOPTER ROTOR TRAILING EDGE NOISE 7. Author($) 8. Performing Orpnizrtion R . p a c No.

Robert H. Schlinker and Roy K. Amiet

I

10. Work Unit No.

9. k f a m i n g Org8nirrtion Name 8nd Addrrrc United Technologies Research Center 11. Contract or Grrnt No.

East Hartford, CT 06108 NAS1-15730 13. T y p of Report and Puiod Covered 12. Sponsoring Agemy N8mo and Address Contractor Report National Aeronautics and Space Administration 14. Sponwning Agmcy codr Washington, D.C. 20546 15. Supplcmontrry Nota Langley Technical Monitor: Thomas F. Brooks Final Report 16. Abstract An experimental and analytical study was conducted to assess the importance of railing edge noise as a helicopter rotor broadband noise source. To isolate the noise lechanism a two-dimensional section of a helicopter main rotor blade was tested in an coustic wind tunnel at close to full-scale Reynolds numbers to ensure realistic airfoil oundary layers. Boundary layer data and acoustic data were obtained for use in develop- ng an acoustic scaling law and testing a first principles trailing edge noise theory.

.esults obtained from the isolated airfoil study were extended to the rotating frame oordinate system to develop a helicopter rotor trailing edge noise prediction. Compari- ons of the calculated noise levels with helicopter flyover spectra demonstrated that railing edge noise contributes significantly to the total helicopter noise spectrum at igh frequencies. This noise mechanism is expected to control the minimum rotor noise.

7. Key Words (Suggested by Author(a)I 18. Distribution Strtcmont elicopter Rotor Noise Noise

'railing Edge Noise Unclassified - Unlimited I '

boundary Layer Noise /' Subject Category 71 ,, i otor Noise / lade Noise / i 8. ' k w l t y a8d. (of this report) 20. Security ClrJf. (of thii page) 21. No. of P&Jm 22. Rlcr nclassified Unclassified 148 A0 7 m - m s For sale by I h e NaliinaI Technical Informalion Service, Springfield, Virgma 22161 ,, NASA-Langley. 1981