Landing gear and cavity noise prediction

I N A S A C O N T R A C T O R ~- R E P O R T

LANDING GEAR A N D CAVITYNOISEPREDICTION

BOLT BERANEK ANDNEWMAN INC.

Cambridge, Mass. 0 2 1 3 8 for LangleyResearchCenter N A T I O N A L A E R O N A U T I C S A N D S P A C E A D M I N I S T R A T I O N W A S H I N G T P N , D. C. J U L Y 1976 TECH LIBRARY KAFB, NU 1. Report No. 1 -2. Government Accession No. 3. Recipient's C a t a l o g No.

I " NASA . .. . CR-2714

.~ ~ . " - - 4. Title and Subtiile 5. Repon Date July 1976 6. Performing Organization Code Landing Gearand C a v i t y N o i s e P r e d i c t i o n

i - -~ -~ . - ~" ~ . ~ ~~

8. Performing Organlzation Report No.

7. Author(s) - Donald B. B l i s s andRichard E. Hayden 10. Work Unit No.

. ~ ."

1-9. Peri&GgOTganization Name and Address

505-06-23-01 B o l t Beranekand Newman I n c 11. Contract or Grant No.

50 Moulton S t .

Cambridge, Mass. 02138 L18051A 13. Type ofRepon andPeriodCovered I- . - - .- ;i =_ . . .. . . "~ SponsoringAgencyNameandAddress Contractor Report National Aeronautics E Space Administration - 14. SponsoringAgencyCode Washington, D C 20546

I

I .. ~~ .~ .~ SupplementaryNotes Langley technical monitor: Jay C. Hardin ." ." . ~~ . . . .. ~ .. " - ~ 6 ; Abstract Thispaper i s c o n c e r n e dw i t ?p r e d i c t i o no fa i r f r a m en o i s er a d i a t i o nf r o mt h el a n d i n gg e a r and wheel w e l l s o f commercial a i r c r a f t . Measurements o ft h e s e components on t y p i c a la i r - c r a f ta r ep r e s e n t e da n dp o t e n t i a ln o i s es o u r c e si d e n t i f i e d .S e m i e m p i r i c a le x p r e s s i o n sf o r t h e s o u n dg e n e r a t i o nb yt h e s es o u r c e sa r ed e v e l o p e df r o ma v a i l a b l ee x p e r i m e n t a ld a t aa n d t h e o r e t i c a la n a l y s e s . These e x p r e s s i o n sa r ee m p l o y e dt oe s t i m a t et h en o i s er a d i a t i o nf r o m t h el a n d i n gg e a r andwheel w e l l s f o r a t y p i c a l a i r c r a f t and t o r a n k o r d e r t h e component

-I(FIWord.ggested by Authoris))

10. Distribution Statement A i r f r a m eN o i s e , Component Sources Unclassified - Unlimited Subject Category 71 - 19. Security Classif. (of this report) 22. Rice' 21. NO. of pages 20. Security Classif. (of this p a g e ) $ 4 . 2 5 56 U n c l a s s i f i e d U n c l a s s i f i e d ~~ * For sale by the National Technical Information Service, Springfield, Virginia 22161 T A B L E OF C O N T E N T S L I S T O F F I G U R E S A N D T A B L E S .............................

N O I S E S O U R C E I D E N T I F I C A T I O N ............................ 1 3

C a v i t y D i s c r e t e Pressure O s c i l l a t i o n s ............. 1 3

C a v i t y T r a i l i n g Edge N o i s e ........................ 1 3

C a v i t y and G e a r Wake I n t e r a c t i o n s w i t h t h e Wing

C A V I T Y L E A D I N G E D G E N O I S E .............................. 3 2

L A N D I N G G E A R D I R E C T R A D I A T E D N O I S E ..................... 4 1

C A V I T Y A N D G E A R W A K E I N T E R A C T I O N S W I T H T H E W I N G

R E F E R E N C E S ............................................. 5 1

iii " . " L I S T O F F I G U R E S A N D T A B L E S F i g u r e 1. T y p i c a ls e q u e n c e o f gear a n d f l a p 2 . Example a i r c r a f t f o r l a n d i n g g e a r / c a v i t y

Boeing 7 2 7 m a i n l a n d i n g gear ( c o n t i n u e d ) . . . 5

3.

Boeing 7 2 7 m a i n l a n d i n g g e a r ( c o n c l u d e d ) ... 6

3 .

5 .

6 . McDonnell-Douglas D C - 9 m a i nl a n d i n gg e a r 6. McDonnell-Douglas D C - 9 m a i nl a n d i n gg e a r

( c o n c l u d e d ) ................................ 1 0

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7 .

8 . S i m p l er e c t a n g u l a rc a v i t y ..................

T y p i c a lp r e s s u r es p e c t r u mm e a s u r e di n a 9 .

r e c t a n g u l a r c a v i t y ......................... 1 5

10. T y p i c a l o s c i l l a t i o n c y c l e . . . . . . . . . . . . . . . . . . 1 8

11. T y p i c a le x p e r i m e n t a l mode s h a p e sa n d t h e

p s e u d o p i s t o n a n a l o g y ( d a t a for M = 0 . 8 ) . . . . 19

12. S t r o u h a lf r e q u e n c i e s of c a v i t y modes as a

f u n c t i o n of Mach number .................... 2 1

Comparison o f Mach numberdependencies of 13.

r e s o n a n t mode l e v e l s : l e a d i n g - e d g e a r e a ... 2 2

14. Comparison o f Mach number d e p e n d e n c i e so f

r e s o n a n t mode l e v e l s : t r a i l i n g - e d g e area .. 2 3

T y p i c a lc a v i t ye x t e r n a lr a d i a t i o np a t t e r n 15.

16. N o n d i m e n s i o n a ls p e c t r u mf o rt h ec a l c u l a t i o n C a v i t ye d g en o i s em e c h a n i s m sa n dt h e i r 1 7 .

18. Radiated n o i s ef r o ma ne d g ei n a f r e e shear iV L I S T OF F I G U R E S A N D T A B L E S ( C o n t . ) F i g u r e 1 9 . Estimated l a n d i n g gear c a v i t ye d g en o i s e 2 0 .

21. S p e c t r u mr e l a t i v e to o v e r a l l l e v e l f o r

.................... 4 4

n o i s e f r o m b l u f f b o d i e s I l l u s t r a t i o n o f p o s s i b l e c a v i t y a n d g e a r 2 3 wake impingementon t h e w i n g t r a i l i n g edge 2 4 . Composite o f a l l s o u r c e sf o r t h e Boeing 727, 73 m / s e c ( 2 4 0 f t / s e c ) , 112.8 m ( 3 7 0 f t ) a l t i t u d e ...................................

4 9 T a b l e 1. Summary of e x p e r i m e n t a l d a t a ( t u r b u l e n t 2 . C a v i t y g e o m e t r y f o r t h e Boeing 7 2 7 a i r c r a f t . 2 9 V e n t e de n c l o s u r ef r e q u e n c i e sf o rB o e i n g 7 2 7 3.

V L A N D I N G G E A R A N D CAVITY N O I S E PREDICTION By D o n a l d B . B l i s s a n d R i c h a r d E . Hayden B o l t B e r a n e k and Newman I n c .

INTRODUCTION Airframe ( n o n p r o p u l s i v e )n o i s e i s p r e s e n t l y of c o n c e r ns i n c e i t r e p r e s e n t s a p o t e n t i a l b a r r i e r t o s u c c e s s f u l i m p l e m e n t a t i o n of p r o p o s e dn o i s er e g u l a t i o n so nc o m m e r c i a la i r c r a f t .I np a r t i c u l a r , t h em o s t commonly a c c e p t e d f u t u r e n o i s e r e g u l a t i o n s are t h o u g h t t o be 1 0 PNdB b e l o wF e d e r a l A i r R e g u l a t i o n 36 (FAR-36). Meeting t h i s s o - c a l l e d FAR 36-10 c r i t e r i o n c a n n o t be a c h i e v e d by t r e a t i n g i f a i r f r a m en o i s es o u r c e s are a t o r p r o p u l s i o ns o u r c e sa l o n e above t h e FAR 36-10 d B l e v e l .T h u s , i t i s i m p o r t a n tt oi d e n t i f y t h ea i r c r a f tc o m p o n e n t sa n dn o i s em e c h a n i s m sr e s p o n s i b l ef o r a i r - frame n o i s e r a d i a t i o n a n d t o a t t e m p t t o p r e d i c t t h e component n o i s e l e v e l s .

Troublesome airframe n o i s eo c c u r sd u r i n gt h ea p p r o a c hp h a s e o f f l i g h t , when power s e t t i n g s a r e r e l a t i v e l y low and t h e a i r - c r a f t i s i n a h i g h l i f t , h i g hd r a gc o n f i g u r a t i o n by v i r t u e o f d e p l o y m e n to ff l a p s ,s l o t s ,a n dl a n d i n gg e a ra n dt h ep r e s e n c eo f o p e nc a v i t i e s . T h e p r e s e n t work i s c o n f i n e dt o t h e e f f e c to f l a n d i n g gear a n dc a v i t i e so n l y . A b r o a d e rt r e a t m e n t o f t h e p r o - blem c a n be found i n Hayden et aZ. (1974 and 1975) andHardin e t aZ. (1975).

S i n c et y p i c a lg l i d es l o p e sf o r CTOL a i r c r a f t a r e 3" from h o r i z o n t a l , t h e a i r c r a f t f l y a t low a l t i t u d e f o r a l o n gd i s t a n c e , t h u sp o t e n t i a l l ye x p o s i n g a l a r g e area t on o i s e .B e f o r ec o n - s i d e r i n gt h el a n d i n gg e a r / c a v i t yn o i s em e c h a n i s m sa n dp r e d i c t i o n s i n d e t a i l , i t i s i n s t r u c t i v et or e v i e w t h e t y p i c a ls e q u e n c e of e v e n t su n d e r t a k e n by a na i r c r a f tp r e p a r a t o r yt ol a n d i n g ,s i n c e t h e airframe c o m p o n e n tc o n f i g u r a t i o n ,a i r s p e e d ,a n da l t i t u d e a l l p l a y a r o l e i n t h e o b s e r v e d airframe n o i s e ,a n d a l l v a r ys i g - n i f i c a n t l yd u r i n ga na p p r o a c h .F i g u r e 1 shows a t y p i c a ls e q u e n c e o ff l a pa n d gear deployment as a f u n c t i o no fd i s t a n c ef r o m t h e a i r p o r t a l o n g w i t h t h e r e s p e c t i v e a l t i t u d e s a n d a i r s p e e d s f o r CTOL j e t s i n t h e c u r r e n tc o m m e r c i a l f l e e t .

R e d u c e ds p e e da n di n c r e a s e df l a pa n g l ec h a r a c t e r i z et h e e a r l y s t a g e s of f i n a la p p r o a c h ,w h i c h may b e g i n 1 6 k m (10 m i l e s ) from t h e t o u c h d o w np o i n t . A t a l t i t u d e s .of 4 6 0 t o 5 5 0 m ( a p p r o x i - m a t e l y 1 5 0 0 t o 1 8 0 0 f t ) , t h e 3" g l i d es l o p e i s i n t e r c e p t e da n d t h e l a n d i n gg e a r i s d e p l o y e d ,i n v o l v i n g t h e o p e n i n go fv a r i o u s doors i n t h e f u s e l a g ea n dw i n g . On many a i r c r a f t , some o ft h e d o o r s w i l l r e c l o s es h o r t l y a f t e r t h e g e a r d e p l o y m e n t . When t h e FAA F.IIllSE GEAR DOORS CERTIFICATION RECLCSED oOli.>iT FOR (FLAPS FULLY

DEPLOYED) G E A R DEPLOYED/ j FLAPS 1

u = 82mIsec u ~ 9 8 m / s e c ( 3 2 0 f ~ s ) H = kLTITUDE I x Z 1 . 9 km ( 1 NAUTICAL M I L E ) x Z 9 . 3 km ( 5 x Z 9.3-13 km x 18.5 -37 km R U r.1 'a,' '.';Y NAUTICAL ( 5 - 7 NAUTICAL ( 1 0 - 2 0 NAUTICAL T K E S ~ O L D MILES MILES 1 MILES X=DISTb.NCE F R C 3 RUNWAY THRESHOLD USUALGLIDE SLOPE INTERCEPT F I G . 1. T Y P I C A L S E Q U E N C E OF G E A R A N D F L A P D E P L O Y M E N T .

a i r c r a f t c r o s s e s t h e F A A n o i s e c e r t i f i c a t i o n p o i n t , 1 . 8 5 km (1 n a u t i c a l mile) from t h e t h r e s h o l d , i t i s t r a v e l i n g 6 6 t o 73 m/sec (215 t o 2 4 0 f t / s e c ) a t a na l t i t u d eo f 113 m ( 3 7 0 f t ) . The n o i s e i s measured on a d i r e c tf l y o v e r . The a l l o w a b l el e v e l sf o r a i r - c r a f tn o i s e are a f u n c t i o no fa i r c r a f tg r o s s weight. The t y p i c a l componentsofconcern a r e p o i n t e d o u t i n F i g . 2 f o r a t y p i c a l modern a i r c r a f t .

The d e t a i l s o f f l a p g e o m e t r y ,s e t t i n ga n g l e ,l a n d i n g gear a r r a n g e m e n t ,a n de x a c ta i r s p e e dv a r yb e t w e e na i r c r a f tt y p e s ,a n d e v e nb e t w e e nd i f f e r e n ta i r c r a f to f t h e same t y p e ,d u et ol o a d f a c t o r s , weather, t r a f f i c ,a n dp i l o tt e c h n i q u e s .

The f o l l o w i n g l i s t i s b e l i e v e d t o i n c l u d e a l l t h e majorcon- t r i b u t o r s t o airframe n o i s e : Wings a n d s t a b i l i z e r s , F l a p s , Landing gear " s e l f - n o i s e , " L a n d i n g g e a r c a v i t y (wheel w e l l ) o s c i l l a t i o n s , Separated f l o wi n t e r a c t i o no f edges o fc a v i t i e s , D o o r s a s s o c i a t e d w i t h gear deployment, I n t e r a c t i o no f gear a n dc a v i t y wakes w i t h t r a i l i n g edges and f l a p s .

I np r a c t i c e ,o n ef i n d sv a r i o u sc o n f i g u r a t i o n so f f l a p s , e . g . , o n e - , t w o - , or t h r e e - f l a p s y s t e m s , l e a d i n g - e d g ed e v i c e s , a n dl a n d i n g gear ( s i n g l ec a r r i a g e ,m u l t i p l ec a r r i a g e ,i n - l i n e s t r u t s ,e t c . ) . The c o m p o n e n t n o i s e p r e d i c t i o n m e t h o d e n a b l e s o n et oa c c o u n tf o r t h e d i f f e r e n c e sb e t w e e nc o n f i g u r a t i o n s ; t h i s method may b e i m p o r t a n ti nd e t e r m i n i n ga n dr e d u c i n g t h e o v e r a l l n o i s e s i g n a t u r e o f t h e a i r c r a f t .

T Y P I C A L C O N F I G U R A T I O N S I n o r d e r t o d e t e r m i n e t h e g r o s sg e o m e t r ya n dc h a r a c t e r i s t i c s o f t y p i c a l l a n d i n g gear c o n f i g u r a t i o n s ,m e a s u r e m e n t sa n dp h o t o - g r a p h s were made o f a Boeing 7 2 7 and a McDonnell-Douglas DC-9 (see F i g s . 2 t h r o u g h 7 ) . The l a n d i n g gear a r r a n g e m e n ti nb o t h a i r c r a f t i s s e e nt o b e q u i t e similar. S i n c e t h e measurements were made on a c t u a ls e r v i c ea i r c r a f t ,a n dn o tt a k e nf r o m d e t a i l e d e n g i n e e r i n gd r a w i n g s , t h e i n f o r m a t i o ng i v e nm u s t b e viewed as a p p r o x i m a t e . It i s , h o w e v e r , q u i t e a d e q u a t e for p r e s e n t p u r p o s e s .

r . . - -.i;;,.*"?. u -._ q,-, ". ','.';' ,.<<\>?*,:

BOEING 727- 200

SPAN: 32.9 m ( 108')

LENGTH: 48.0 m (157'7")

'LEFT MAIN GEAR NOSE GEAR (LOOKING AFT) F I G . 2. E X A M P L E A I R C R A F T F O R L A N D I N G G E A R / C A V I T Y N O I S E C A L C U L A T I O N S .

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B o t ha i r c r a f th a v e a two-wheelnose gear s u p p o r t e d by a s i n g l es t r u t . When t h eg e a r i s lowered two s e t s o fd o o r so p e n .

The l a r g e r f o r w a r dd o o r sr e c l o s eo n c et h e gear i s i n p l a c e .

D u r i n gt h el o w e r i n gp r o c e s s , t h e l a r g er e c t a n g u l a rc a v i t yw h i c h h o u s e st h en o s eg e a r i s open and exposed t ot h ef l o w . However, t h i s c a v i t y i s s e r i o u s l yd i s t u r b e dd u r i n gp a r t of t h ef l o wo v e r t h i s time by t h el a n d i n gg e a r i t s e l f . Once t h e gear i s i n p l a c e , t h e rear d o o r sr e m a i no p e n ,p r o d u c i n g a r e l a t i v e l y small o p e n i n g i n t o a l a r g ei n t e r n a le n c l o s u r e . T h e f l o wo v e rt h i so p e n i n g i s s e r i o u s l yd i s t u r b e d by t h e p r e s e n c eo ft h es t r u tw h i c h i s t y p i - c a l l yv e r yc l u t t e r e dw i t hb r a c e s ,l i g h t s ,e t c . The small d o o r s o nt h eB o e i n g 727 a r e a l s o f i t t e d w i t hl a r g ec u r v e df l o wd e - f l e c t o r s , w h o s ep u r p o s ea p p e a r st o b e t o f o r c e a i r i n t o t h e c a v i t y .

On e a c h s i d e , t h e m a i nl a n d i n g gear o f b o t h a i r c r a f t h a s a s i n g l em a i ns t r u tt os u p p o r t two wheels. T h e r e i s a d i a g o n a l b r a c er u n n i n gf r o m t h e m a i ns t r u t ,j u s ta b o v et h ew h e e l s ,t ot h e f u s e l a g ei n t e r i o r .I n t h e i r r e t r a c t e dp o s i t i o n ,t h e wheels are c o n t a i n e di nt h ef u s e l a g e ,a n dt h em a i ns t r u ta n d i t s p i v o t p o i n t a r e l o c a t e di n t h e wing. Thus, t h e r e i s a small wing c a v i t ya n d a r e l a t i v e l yl a r g ef u s e l a g ec a v i t y . The d o o rf o rt h e w i n gc a v i t y i s openandexposed t o t h e flowwhenever t h e g e a r i s i np l a c e . On t h e Boeing 7 2 7 , t h i s d o o ra l s oc o v e r s a small p o r - t i o no f t h e f u s e l a g ec a v i t y .T h ef u s e l a g ec a v i t yd o o ro p e n s when t h e g e a r i s b e i n gl o w e r e da n dt h e nr e c l o s e so n c et h e gear i s i np l a c e . W h i l e it i s open, t h e l a r g ee s s e n t i a l l yr e c t a n g u l a r f u s e l a g ec a v i t y i s e x p o s e dt o t h e f l o w . F o rp a r to ft h i s time, as t h eg e a rl e a v e s t h e c a v i t y , t h e f l o wo v e rt h ef u s e l a g ec a v i t y w i l l b e s e r i o u s l yi n t e r r u p t e d . The e n t i r ep r o c e s so fl o w e r i n g t h em a i ng e a ra n dr e c l o s i n gt h ef u s e l a g ed o o r s takes a b o u t 1 0 s e c o n d s . Once t h e g e a r i s i np l a c e , t h e l a r g ef u s e l a g ec a v i t y i s v e n t e d t o t h e e x t e r n a lf l o wo n l yt h r o u g h t h e w i n gc a v i t ya n d , p e r h a p s , a small o p e n i n go nt h ea d j a c e n tf u s e l a g es u r f a c e . The w i n gc a v i t y i s bounded i n t h e s p a n w i s ed i r e c t i o n b y t h e main s t r u t( w h i c he x t e n d si n t o i t s volume) a t one end and the opening i n t o t h e f u s e l a g ec a v i t ye n c l o s u r e a t t h e o t h e re n d .E x c e p t f o rt h em a i ns t r u ta n db r a c e ,f l o wo v e r t h e w i n gc a v i t ys p a n i s r e l a t i v e l yu n i m p a i r e d .T h e s t a t e o f t h e u p s t r e a m b o u n d a r y l a y e r i s somewhat u n c e r t a i ns i n c et h ew i n gl e a d i n ge d g ed e v i c e s a r e u s u a l l yd e p l o y e d when t h i sc a v i t y i s open. The r e l a t i v el o c a - t i o n s a r e s u c h t h a t t h ei n b o a r dt e r m i n a t i o no ft h el e a d i n ge d g e d e v i c e may b e d i r e c t l yu p s t r e a mo ft h ew i n gc a v i t y ,s u g g e s t i n g t h a t a v o r t e x may p a s so v e rt h ec a v i t ym o u t h .

NOISE S O U R C E IDENTIFTCATION I n t h i s s e c t i o n ,t h es o u r c e so fl a n d i n gg e a r / c a v i t yn o i s e a r e i d e n t i f i e d .I nt h ef o l l o w i n gs e c t i o n s ,t h e s en o i s es o u r c e s are d i s c u s s e d i n g r e a t e r d e t a i l to show q u a n t i t a t i v e l y t h e i r dependenceongeometryandflowparametersand t o show q u a l i t a - t i v e l yt h e i re x p e c t e dd i r e c t i v i t yp a t t e r n s .S a m p l ec a l c u l a t i o n s w i l l be c a r r i e d o u t f o rt h eB o e i n g 727 a i r c r a f t . The n o i s e s o u r c e s c l a s s i f i e d below are e s s e n t i a l l yd u et of o u rm e c h a n i s m s : m o d a lp r e s s u r eo s c i l l a t i o n phenomena, t h e edge noisemechanism, v o r t e xs h e d d i n g ,a n dt h ei m p i n g e m e n to ft u r b u l e n tf l o wo ns u r - faces a n db o d i e s .

CavityDiscretePressureOscillations F l o wo v e ro p e nc a v i t i e s or c u t - o u t s i n t h e s u r f a c e s o f a i r - c r a f t o f t e n p r o d u c e s i n t e n s e p r e s s u r e o s c i l l a t i o n s i n t h e c a v i t y which r a d i a t e s d i s c r e t en o i s e . The n a t u r eo ft h ec a v i t yr e s p o n s e dependson t h e c o m p l e x i n t e r a c t i o n o f t h e c a v i t y i n t e r n a l wave s t r u c t u r ea n d t h e e x t e r n a ls h e a r l a y e r . The mean f l o ws u p p l i e s t h e e n e r g y to s u s t a i n t h e o s c i l l a t i o np r o c e s s . A s i n d i c a t e di n t h e p r e v i o u ss e c t i o n ,l a n d i n gg e a rc a v i t i e s may b e e i t h e r a l m o s t t h e f l o wo no n ef a c e or c l o s e de x c e p tf o r a small e n t i r e l y o p e n t o o p e n i n gt o t h e f l o w ,o rt oa n o t h e rc a v i t y . The o c c u r r e n c eo f o s c i l l a t i o n sd e p e n d s on t h e c a v i t yc o n f i g u r a t i o n , t h e f l o ws p e e d andupstreamboundary l a y e r , and t h e p r e s e n c e o f s t r u t s , e t c . , w h i c h . m a yd i s t u r b t h e f l o w . The c a v i t yo s c i l l a t i o np r o c e s s seems t oc a u s em o n o p o l er a d i a t i o n , a t l e a s t a t lowspeeds.

Cavity Leading Edge Noise A s t h e t u r b u l e n tb o u n d a r y l a y e r f l o w passes o v e rt h ec a v i t y l e a d i n ge d g e s , i t e x p e r i e n c e s a sudden change i ns u r f a c ei m p e d a n c e a n ds u b s t a n t i a ls o u n d i s r a d i a t e d . T h i s s o u r c e b e h a v e s as a s p a n w i s e array o fi n c o h e r e n ta c o u s t i cd i p o l e s , whose d i r e c t i v i t y i s m o d i f i e d by t h e b a f f l i n g e f f e c t o f t h e e d g e .

CavityTrailing Edge Noise Whether o rn o t t h e c a v i t y o s c i l l a t e s , t h e c a v i t y t r a i l i n g edge i s s u b j e c t e d to a nu n s t e a d yi n f l o wd u et o i t s i n t e r a c t i o n w i t h t h et u r b u l e n t shear l a y e r o v e r t h e c a v i t ym o u t h . The re- s u l t i n g f l u c t u a t i n g f o r c e s w i l l a g a i np r o d u c ed i p o l e - l i k ea c o u s t i c r a d i a t i o n .T h i sn o i s es o u r c e w i l l b e a f f e c t e d b y t h e p r e s e n c e o f s t r u t s or p r o t u b e r a n c e si n t h e c a v i t y shear l a y e r .

L a n d i n g Gear Direct R a d i a t e d Noise The s t r u t s , wheels, b r a c e s ,a n dd o o r so f t h e l a n d i n g gear w i l l radiate n o i s e d i r e c t l y d u e t o t h e f l u c t u a t i n g l i f t a n dd r a g f o r c e sp r o d u c e d by v o r t e xs h e d d i n gf r o m t h e s e e s s e n t i a l l y b l u f f bodies. The c h a r a c t e r i s t i c so f t h e s h e d d i n g may b e a f f e c t e d b y t h e m u t u a li n t e r a c t i o nb e t w e e nb o d i e s and by t h e p r e s e n c eo f t h e c a v i t y shear l a y e r .

C a v i t y a n d G e a r Wake I n t e r a c t i o n s w i t h t h e Wing T r a i l i n gE d g ea n dF l a p s T h e t u r b u l e n t wakes b e h i n dt h el a n d i n g gear c a v i t i e sa n d s t r u t s may i n d u c eu n s t e a d yl o a d so n t h e w i n g t r a i l i n g edge and t h e f l a p s y s t e m . These l o a d s a r e produced by d i r e c tt u r b u l e n c e impingement and by t h e e f f e c to ft u r b u l e n tf l o wo v e r edges. The r e s u l t i n gi m p i n g e m e n tn o i s ea n d edge n o i s e w i l l dependon t h e t u r b u l e n c es p e c t r u mo f t h e wakes andon t h e i n t e r a c t i o ng e o m e t r y L a n d i n gG e a rW a k e / L a n d i n gG e a rI n t e r a c t i o n s On some l a n d i n gg e a rc o n f i g u r a t i o n s , t h e wakes of some gear components may i m p i n g eo no t h e r gear componentsandproduceun- s t e a d y l o a d s . T h i s t y p eo fi n t e r a c t i o nc a n b e e x p e c t e do n t h e i n - l i n em a i ns t r u t sa n d wheels o f some l a r g e a i r c r a f t . The i m p o r t a n c eo f t h i s n o i s es o u r c e w i l l s t r o n g l yd e p e n do n t h e p a r t i c u l a rl a n d i n g gear geometry.

CAVITY DISCRETE PRESSURE OSCILLATIONS High speed f l o wo v e rc a v i t i e s or c u t - o u t s i n t h e s t r u c t u r a l s u r f a c e so fa i r c r a f to f t e np r o d u c e si n t e n s et o n a lp r e s s u r ef l u c - t u a t i o n s . A b a s i cr e c t a n g u l a rc a v i t yc o n f i g u r a t i o n i s shown i n F i g . 8 . A t y p i c a lp r e s s u r es p e c t r u mm e a s u r e di ns u c h a c a v i t y i s shown i n F i g . 9, where t h r e e d i s c r e t e peaks can b e s e e n .

S u b s t a n t i a lr e s e a r c h has a l r e a d y g o n ei n t o t h e s t u d yo fc a v i t y o s c i l l a t i o n s , b u t most o f t h e work has c o n c e n t r a t e do n h i g h sub- s o n i c a n d s u p e r s o n i c Mach numbers. A s a r e s u l t , l e s s d e t a i l e d i n f o r m a t i o n i s a v a i l a b l e f o r t h e low Mach numbersubsonicflow c a s e (e.g. M < 0 . 3 ) o f i n t e r e s t i n c o n n e c t i o n w i t h airframe n o i s e , a l t h o u g h t h e u n d e r l y i n go s c i l l a t i o nm e c h a n i s ms h o u l d b e e s s e n - t i a l l y t h e same. A m a j o r i t y o f t h e work has f o c u s e do ns i m p l e r e c t a n g u l a rg e o m e t r y ,w h i c h i s sometimes, b u t n o t always, an F I G . 8 . S I M P L E R E C T A N G U L A R C A V I T Y .

I 8 0 I I I I I I THIRD OCTAVE BAND CENTER FREQUENCY IN kHz F I G . 9 . T Y P I C A L P R E S S U R E S P E C T R U M M E A S U R E D I N A R E C T A N G U L A R C A V I T Y .

a p p r o p r i a t er e p r e s e n t a t i o n of l a n d i n gg e a rc a v i t yg e o m e t r y . The r e c e n t work o f Heller and Bliss (1974 and 1975) p r o v i d e st h e basis f o r much o f t h e f o l l o w i n g d i s c u s s i o n .

I n g e n e r a l , c a v i t i e s o s c i l l a t e d u e to a c o u p l i n gb e t w e e ni n - t e r n a l p r e s s u r e modesand t h e m o t i o no ft h es h e a r l a y e r o v e r t h e c a v i t ym o u t h .S h e a rl a y e rd e f l e c t i o n s a t t h ec a v i t y mouth t r a i l i n g e d g ep r o d u c e mass a d d i t i o na n dr e m o v a l a t t h i s p o i n t i n t h e c a v i t y .

T h i sp e r i o d i c mass a d d i t i o na n dr e m o v a lf o r c e st h ea c o u s t i c modes i n t h e c a v i t y , w h i c h f o r c e t h e s h e a rl a y e ra n dt h e r e b yp r o v i d e t h e r e q u i r e ds h e a r l a y e r d e f l e c t i o n a t t h e t r a i l i n ge d g e . Ac- t u a l l y , t h e i n t e r n a l modes and t h e s h e a rl a y e rm o t i o n are c o u p l e d a n d c a n n o t b e c o n s i d e ' r e d s e p a r a t e l y . F o r m a l l y , t h e s h e a r l a y e r must b e t r e a t e d as a boundaryof t h e s y s t e m s u b j e c t t o t h e a p p r o - p r i a t e material s u r f a c ea n dp r e s s u r eb o u n d a r yc o n d i t i o n s ,w h i c h c o u p l e t h e i n t e r n a l wave m o t i o nt ot h ec o r r e s p o n d i n g wave p a t t e r n i n t h e e x t e r n a lf l o w . The i m p o r t a n c eo fp r o p e r l yt r e a t i n g t h e s h e a r l a y e r c o u p l i n g i s i l l u s t r a t e d b y t h e f a c t t h a t measured m o d a lf r e q u e n c i e si no p e nr e c t a n g u l a rc a v i t i e sd i f f e rs u b s t a n t i a l l y from t h e c o r r e s p o n d i n g h a r d box modes. If t h e mouth area i s a small f r a c t i o n o f t h e t o t a l c a v i t y s u r f a c e area, t h e n ,o fc o u r s e , t h ee f f e c to f shear l a y e r couplingbecomes l e s s i m p o r t a n t ,a n d i t may b e p o s s i b l e t o estimate t h e f r e q u e n c i e s by s i m p l e rm e a n s .

S h a l l o wr e c t a n g u l a rc a v i t i e s , L/D > 2 . 0 , t e n d to r e s p o n dp r i m a r i l y i nl e n g t h w i s e m o d e s ,w h e r e a sd e e pc a v i t i e s , L/D < 2 . 0 , t e n d to r e s p o n d i n d e p t h m o d e s . For o t h e rc a v i t yc o n f i g u r a t i o n s ,t h e i n t e r n a l modes may b e q u i t ec o m p l e x ,b u t t h e o s c i l l a t i o n mechanism j u s td e s c r i b e d s t i l l a p p l i e s .

T h es h e d d i n go fd i s c r e t ev o r t i c e sf r o m t h e c a v i t yl e a d i n g edge, a n dt h e i rs u b s e q u e n ti m p i n g e m e n t on t h e t r a i l i n ge d g e , has s o m e t i m e sb e e nc o n s i d e r e de s s e n t i a lt ot h ec a v i t yo s c i l l a t i o n p r o c e s s .D i s c r e t ev o r t i c e sh a v eo f t e nb e e no b s e r v e de x p e r i - m e n t a l l yi n t h e s u b s o n i cf l o wc a s e . V e r y l i k e l y , t h e r o l l i n g up of t h e s h e a rl a y e ri n t ov o r t i c e s i s a m a n i f e s t a t i o no f t h e f o r c i n g d u e to t h ec a v i t yi n t e r n a lp r e s s u r em o d e s .I nf a c t , t h i s non- l i n e a r b e h a v i o r may p r o v i d ea ni m p o r t a n ta m p l i t u d el i m i t i n g mecha- nism for t h e o s c i l l a t i o n p r o c e s s .

S i n c es i m p l er e c t a n g u l a rc a v i t i e s will beused a s t h e b a s i s f o r some o f t h e n o i s ep r e d i c t i o n si n t h i s r e p o r t , i t i s worth- w h i l e to r e v i e wt h eo s c i l l a t i o np r o c e s sf o r t h i s c a s e i n some d e t a i l . A s mentioned, shear l a y e rd e f l e c t i o n leads t o a p e r i o d i c mass a d d i t i o na n dr e m o v a l a t t h ec a v i t yt r a i l i n ge d g e .I n a s h a . l l o wc a v i t y , t h i s mass a d d i t i o na n dr e m o v a lp r o d u c e sa ne f f e c t t h a t i s similar to r e p l a c i n g t h e c a v i t y r e a r b u l k h e a d w i t h a n o s c i l l a t i n gp i s t o n . (For d e e p e rc a v i t i e s , a monopole source a t t h e t r a i l i n g e d g e would b e more a p p r o p r i a t et h a n a p i s t o n . ) T h i s" p s e u d o p i s t o n " e f f e c t g e n e r a t e sf o r w a r dt r a v e l i n gw a v e si n t h e c a v i t y t h a t r e f l e c t from t h e f r o n t b u l k h e a d t o become rear- ward t r a v e l i n gw a v e s .T h er e s u l t i n g wave s t r u c t u r e i n t h e c a v i t y f o r c e s t h e s h e a r l a y e r i n a n u n s t e a d y m a n n e ro v e rt h e e n t i r ec a v i t yl e n g t h . T h i s s h e a rl a y e rm o t i o n ,i nt u r n , i s r e s p o n s i b l e f o r t h e t r a i l i n g e d g e mass a d d i t i o na n dr e m o v a l t h a t o r i g i n a l l y p r o d u c e d t h e c a v i t y i n t e r n a l wave s t r u c t u r e ; t h u s , t h ef e e d b a c kl o o p i s c o m p l e t e .

F i g u r e 1 0 shows a t y p i c a l o s c i l l a t i o n c y c l e as d e r i v e df r o m water t a b l e f l o wv i s u a l i z a t i o nt e c h n i q u e s . *I n ( A ) a nu p s t r e a m t h e f r o n tb u l k h e a dw h i l e a downstreamwave t r a v e l i n g wave r e a c h e s a p p r o a c h e s t h e r e a r b u l k h e a d .T h er e f l e c t e d wave p r o c e e d s rear- ward i n ( B ) and ( C ) , w h i l e a new u p s t r e a m wave i s formed a t t h e rear as t h e s h e a r l a y e r d e f l e c t sb e l o w t h e t r a i l i n g c a v i t y edge.

The waves i n t e r a c tn e a rt h ec a v i t yc e n t e r as shown i n (D) and ( E ) .

I n (F), t h e w a v e sa g a i na p p r o a c h t h e f r o n ta n d r e a r b u l k h e a d s , a n dt h e shear l a y e r i s above t h e t r a i l i n g e d g e l e v e l as mass i s e f f e c t i v e l y removed from t h e c a v i t y .N o t i c ei n t h i s i l l u s t r a t i o n t h a t t h e u p s t r e a mt r a v e l i n g wave radiates i n t o t h e e x t e r n a l f l o w whereas t h e downstream wave does not. T h i s o c c u r s b e c a u s e t h e u p s t r e a m wave p r o d u c e s a d i s t u r b a n c ew h i c h moves s u p e r s o n i c a l l y r e l a t i v e t o t h e e x t e r n a lf l o w , w h i l e t h e r e l a t i v ev e l o c i t yo f t h e downstream wave i s s u b s o n i c . The p h a s es p e e d so f t h e u p s t r e a m anddownstreamwaves may b e c o n s i d e r a b l yd i f f e r e n tf r o m t h e sound s p e e d i n t h e c a v i t yb e c a u s eo f t h e e f f e c t i v e 'c o m p l i a n c eo ft h e s h e a r l a y e r . F u r t h e r m o r e , t h e p h a s e s p e e d s a r e a l s od i f f e r e n t f r o me a c ho t h e rb e c a u s et h e shear l a y e r a p p e a r s s t i f f e r t o t h e u p s t r e a m wave t h a n it d o e s t o t h e downstreamwave; t h e s p e e do f t h e u p s t r e a m wave i s t h e r e f o r eg r e a t e r . S i m i l a r l y , t h e s p a t i a l e n v e l o p e so f t h e upstreamanddownstreamwaves a r e d i f f e r e n t .

T y p i c a l l y , t h e u p s t r e a m wave r a d i a t e s anddecaysand t h e down- stream wave draws energyfrom t h e e x t e r n a lf l o wa n da m p l i f i e s .

If t h e e n e r g ya d d i t i o no f t h e downstream wave e x c e e d st h ee n e r g y loss o f t h e u p s t r e a m wave b y a na m o u n ts u f f i c i e n tt oo v e r c o m e a l l o t h e r s o u r c e s o f e n e r g y loss i n t h e s y s t e m , t h e n t h e o s c i l l a - b t i o np r o c e s s w i l l s u s t a i n i t s e l f . The a c t u a la m p l i t u d eo f o s c i l l a t i o n i s c o n t r o l l e d by t h e l e v e lo fd a m p i n gi n t h e s y s t e m and by t h e e f f e c to fn o n l i n e a r i t y ,w h i c hu l t i m a t e l y limits t h e r a t e of energy removal from t h e e x t e r n a lf l o w . It i s p r e c i s e l y t h e b e h a v i o ro f t h e c a v i t y as a v e r yc o m p l e xo s c i l l a t o r whose a m p l i t u d e i s c o n t r o l l e d b y many f a c t o r s t h a t makes even t h e semi- e m p i r i c a l p r e d i c t i o n o f o s c i l l a t i o n a m p l i t u d e s d i f f i c u l t .

The c o m b i n a t i o no f t h e upstreamanddownstreamwaves i n t h e c a v i t yp r o d u c e s a s t a n d i n g wave p a t t e r n whosepeakpressure a m p l i t u d e si n c r e a s et o w a r d t h e t r a i l i n ge d g e .T y p i c a le x p e r i - m e n t a l mode s h a p e s a r e shown i nF i g . 11. A p r e s s u r ea m p l i t u d e *Although s t r i c t l y s p e a k i n g , t h e water t a b l e s i m u l a t i o n a p p l i e s t o Mach numberflows, t h e p r o c e s s e s i l l u s t r a t e d are b e l i e v e d t o be e s s e n t i a l l y t h e same f o rl o w Mach numberflow.

A

-1 t

.

F I G . 10. T Y P I C A L O S C I L L A T I O N C Y C L E .

L / D = 4 . 0 1 1 1 1 1 1 1 1 1 MODE 1 \\\\\ \\\\ PSEUDOP 'ISTON

1 ~~~~,\\\\\\\\\\,\\\\~~

T l

F I G . 11. T Y P I C A L E X P E R I M E N T A L M O D E S H A P E S A N D T H E P S E U D O P I S T O N A N A L O G Y ( D A T A F O R M = 0 . 8 ) .

maximum a l w a y so c c u r s a t t h e f r o n tb u l k h e a d ,b u to f t e n t h e c o r - r e s p o n d i n g maximum a t t h e r e a r d o e sn o to c c u re x a c t l y a t t h e wall.

T h i s d i s p l a c e m e n to f t h e rearward maximum i s a m a n i f e s t a t i o n of t h e p i s t o n - l i k e e f f e c t o f p e r i o d i c mass a d d i t i o na n dr e m o v a l a t t h e t r a i l i n g e d g e .

If t h e o s c i l l a t i o n f r e q u e n c i e s a r e r e - e x p r e s s e d as a S t r o u h a l number based on f r e e stream s p e e da n dc a v i t yl e n g t h ,a n dt h e n p l o t t e d a g a i n s t Mach n u m b e r ,t h e yo r d e rt h e m s e l v e sa l o n gc e r t a i n l i n e s t h a t c a n b e a s s o c i a t e d w i t h r e s o n a n t modes as shown i n F i g .

1 2 . The s o l i dl i n e sc o r r e s p o n dt o t h e s e m i - e m p i r i c a le q u a t i o n P T mu m-a

s = - -

m ' 0 0 [M/dl+P M 2 ] + l / k v

where m i s t h e mode number ( e q u a lt o 1, 2 , 3 , . . . ) , y = 1 . 4 i s t h e r a t i oo fs p e c i f i c h e a t s . The q u a n t i t i e s a and kv a r e e m p i r i c a l c o n s t a n t s ; t h e c h o i c eo f a = 0 . 2 5 and kv = 0.57 i s i n goodagree- ment w i t h t h e e x p e r i m e n t a l d a t a . A s e m i - e m p i r i c a l f r e q u e n c y f o r m u l a similar to t h e above was f i r s t g i v e n b y R o s s i t e r ( 1 9 6 6 ) .

The p r e s e n tf o r m ,p r e s e n t e d b y H e l l e r e t aZ. (1970), c o r r e c t sf o r t h e h i g h e rs o u n ds p e e di n t h e c a v i t y ,w h i c hn e a r l ye q u a l s t h e f r e e - stream s t a g n a t i o n s o u n d s p e e d . U n f o r t u n a t e l y , E q . (1) agrees l e a s t w e l l w i t h t h e data a t low Mach number. Furthermore, t h e d a t a b e g i n st o show some l e n g t h - t o - d e p t hr a t i o , L/D, dependence a t low Mach number as e v i d e n c e d b y t h e s y s t e m a t i cs p r e a d i n gf o r e a c h mode number. T h i s dependence i s n o ta c c o u n t e df o r b y E q .

(1). N e v e r t h e l e s s , E q . (1) w i l l p r o v i d e a s a t i s f a c t o r y r o u g h e s t i m a t e o f f r e q u e n c yi nt h el o w Mach number r a n g e as l o n g as t h e c a v i t y r e m a i n s s h a l l o w . It can, however, b e s e r i o u s l yi ne r r o r for d e e p c a v i t i e s .

F i g u r e s 13 and 1 4 i l l u s t r a t e c a v i t y p r e s s u r e l e v e l s a t t h e f r o n ta n dr e a rb u l k h e a d s ,r e s p e c t i v e l y , as a f u n c t i o no f mode number, length-to-depth r a t i o , and Mach n u m b e r . D i f f e r e n t modes a r e s e e nt od o m i n a t ed e p e n d i n go n t h e p a r t i c u l a rc o n d i t i o n s . For t h e c a s e s where t h e r e i s a d e q u a t e data, t h e l e v e l s a r e s e e n t o d r o pv e r yd r a m a t i c a l l y a t low Mach number. Experiments show t h a t t h e r e i s u s u a l l y a Mach numberbelowwhich a g i v e n c a v i t y will n o t e x h i b i t d i s c r e t e o s c i l l a t i o n s , i . e . , a n i n i t i a l o n s e t speed. A i r c r a f tl a n d i n g gear c a v i t i e s may w e l l f a l l i n t h e v i c i n i t y o f i n i t i a lo n s e t . The data d o e sc l e a r l yi l l u s t r a t e t h a t no simple r e l a t i o nb e t w e e nl e v e la n d speed i s e v i d e n t .A g a i n , t h i s c o m p l i c a t i o n a r i s e s b e c a u s et h ec a v i t yb e h a v e s as a no s c i l - l a t o r whoseamplitude i s c o n t r o l l e d b y c o m p l e xp r o c e s s e s .

2 0 CURRENT BBN TESTS = 4.0 L = 91.44 cm (35")

=5.5-5.1 I W=25.4cm (10

3.2 F I G . 1 2 . S T R O U H A L F R E Q U E N C I E S O F C A V I T Y MODES A S A F U N C T I O N O F M A C H N U M B E R .

L/D 4.0 5.1 0 .5 1 1.5 2 2.5 3 MODE 1 Ma 0 I I I I I I I I I I

m -10- - c -

CI

- -

,Q -30

-

8 -50- -

I I I I I 1 I I I I -60 0 .5 1 1.5 2 25 3 0 .5 1 1.5 2 2.5 3 0 5 1 1.5 2 2.5 3 MODE 2 M o o 0 LE RC 8x6 FOOT

I TUNNEL

I

o MIT NAV SUP SON

I TUNNEL

I

I o AF FLIGHT TEST I

V SMALL-SCALE MODEL

I TEST I

0 .5 1 1.5 2 2.5 3 0 .5 1 1.5 2 2.5 3 Ma'J MODE 3 Ma'J F I G . 1 3 . C O M P A R I S O N OF M A C H N U M B E R D E P E N D E N C I E S OF R E S O N A F I T M O D E L E V E L S : L E A D I N G - E D G E A R E A .

2 2 L/D 2.3 4.0 5.1 - 6 0 - 0 .5 1 15 2 2.5 3 0 .5 1 1.5 2 2.5 3 MODE 1

E -50

-60 U 0 5 1 1.5 2 2.5 3

0 .5 1 1.5 2 2 5 3 MaD MODE 2 LE RC 8 x 6 FOOT TUNNEL o MIT NAV SUP SON TUNNEL o AF FLIGHT TEST V SMALL-SCALE MODEL TES?

0 .5 1 1.5 2 2.5 3 0 .5 1 1.5 2 2.5 3 Map MODE 3 Moo F I G . 1 4 . C O M P A R I S O N O F M A C H N U M B E R D E P E N D E N C I E S O F R E S O N A N T M O D E L E V E L S : T R A I L I N G - E D G E A R E A .

I

The e x t e r n a l r a d i a t i o n p a t t e r n f o r h i g h speed s u b s o n i cf l o w i s shown i n F i g . 1 5 . T h i s s k e t c h i s c o n s i s t e n t w i t h b o t h t h e o s c i l l a t i o n p r o c e s s d e s c r i b e d p r e v i o u s l y a n d t h e f l o w v i s u a l i z a - t i o np h o t o g r a p h sa v a i l a b l ei n t h e l i t e r a t u r e .D i r e c t i v i t ym e a s u r e - m e n t st a k e no n a small s c a l ec a v i t ym o d e li n a wall j e t f a c i l i t y s u g g e s t t h a t a t verylow Mach numbers t h e r a d i a t i o n p a t t e r n i s n o t as d i r e c t i o n a l as i n d i c a t e da n d i s , f o r a l l p r a c t i c a lp u r p o s e s , t h a t o f a simple monopole ( H e l l e r , 1 9 7 4 ) . It c a n be c o n c l u d e d t h a t t h e d i r e c t i o n a l s t r u c t u r e i n d i c a t e d i n F i g . 1 5 becomes less pronounced w i t h d e c r e a s i n g Mach number. T h i s t r e n d i s s u p p o r t e d by t h e p h o t o g r a p h s o f K a r a m a c h e t i ( 1 9 5 5 ) . The s t r e n g t ho f t h e m o n o p o l er a d i a t i o n w i l l b e d i r e c t l y r e l a t e d t o t h e t r a i l i n g edge mass a d d i t i o na n dr e m o v a lp r o c e s s .

Assuming a c a v i t y r a d i a t e s as a simple monopole,* where r i s t h e d i s t a n c ef r o m t h e s o u r c ea n d Q i s t h e a m p l i t u d eo f t h e u n s t e a d y mass f l o w . B e c a u s e Q must b e d i r e c t l yr e l a t e dt o e t h e u n s t e a d y mass a d d i t i o na n dr e m o v a lp r o c e s s a t t h e c a v i t y t r a i l i n g e d g e , we c a n w r i t e where Um/2 is t h e a v e r a g ev e l o c i t yi n t h e shear l a y e r , W i s t h e c a v i t y w i d t h , q i s t h e shear l a y e r p e r t u r b a t i o na m p l i t u d e a t t h e t r a i l i n ge d g e ,a n d f3 i s a c o r r e c t i o nf a c t o rd i s c u s s e db e l o w . T h e shear l a y e r a m p l i t u d ec a n b e n o n d i m e n s i o n a l i z e d b y t h e c a v i t y l e n g t h : where q i s t h e d y n a m i cp r e s s u r ea n d S i s t h e S t r o u h a ln u m b e r , g i v e na p p r o x i m a t e l y by E q . (1) as a f u n c t i o n of mode number and Mach number. The c o r r e s p o n d i n gt o t a lp o w e r i s g i v e n b y *Due t o t h e f a i r l y low f r e q u e n c i e s w i t h c o r r e s p o n d i n g l yl o n g wave- l e n g t h s ,a n d t h e a c t u a l l o c a t i o n s o f c a v i t i e s on t h e a i r c r a f t , we h a v ec h o s e nt on e g l e c ta n ye f f e c to f t h e a i r c r a f t as a na c o u s t i c b a f f l e .

2 4

// /

/

DIRECT EXTERNAL WAVE FROM TRAILING EDGE UPSTREAM T 'RAVELING WAVE

'Y

F I G . 15. T Y P I C A L C A V I T Y E X T E R N A L R A D I A T I O N P A T T E R N I N H I G H S P E E D S U B S O N I C FLOW (Mm>0.5).

I h

The nondimensional shear layer amplitude, n , may depend on

a number of parameters, but primarily The dependence on fD/a, contains information on the ratio of wavelength t o depth. Dependence on M y L/D, and fD/ac is indicated by the analytical work of Heller and Bliss (1974). The'ratio of upstream boundary layer thickness to cavity length, 6/L, is an important parameter for the shear layer thickness. The other non- dimensional term in Eq. (5) is the f l o w rate correction factor, 1 3 . This factor accounts for thenonuniform shear layer velocity profile, amplitude variations across the cavity width, and other effects associated specifically with the fluid mechanical details of the mass addition and removal process. The most important functional dependences are expected to be Notice, inAparticular, that B may depend on the nondimensional amplitude 0 . In spite of this complexity, we can expect B to be of order unity, the the other terms in Eq. (3) s h o u l d constitute a proper order-of-magnitude estimats for Q. It is now apparent that the complicated dependence of Q limits the usefulness of E q . ( 5 ) .

A rough estimate of levels can be made assuming the shear layer displacement cannot greatly exceed its half thickness.

Then, f o r a turbulent shear layer, let A rl = 0.1 and assume that B = 1.0. Because we are interested in the low Mach number limit, Eq. (1) is approximately 2 6 Then, E q . ( 4 . 5 ) becomes which w i l l u s u a l l y be a h i g h estimate, andwhich i s a p p l i c a b l e o n l y for low Mach n u m b e r .T h ed i r e c td e p e n d e n c eo n mode number i s a r e s u l t of the a p p r o x i m a t i o n s made andmustnot be t a k e n t o o s e r i o u s l y .C l e a r l y , i t s h o u l dn o t be u s e df o rh i g h mode numbers ( e . g . , m > 4 ) .

When some e x p e r i m e n t a l data i s a v a i l a b l e , t h e dependence of ( G B ) i n E q . ( 5 ) c a n b e estimated. The dependences on M and L/D are p r o b a b l y s t r o n g e s t . T h e r e f o r e , where k i and k 2 a r e c o n s t a n t s w h i c h d e p e n d o n L/D. The a p p r o x i - m a t i o no fE q .( 8 ) i s u s e f u l when some data i s a v a i l a b l e a t two Mach numbers t h a t a r en o tt o ow i d e l ys e p a r a t e d . It i s t h e n p o s - s i b l e t o s o l v e for k , and k 2 a n du s eE q s .( 8 )a n d( 5 )t op r e d i c t t h e r a d i a t i o nf r o mo t h e rc a v i t i e sa s s u m e d similar t o t h e s e f o r which d a t a i s a v a i l a b l e . T h i s i s t h ea p p r o a c hu s e dt op r e d i c t d i s c r e t et o n en o i s ef r o ml a n d i n gg e a rc a v i t i e s .S u b s t i t u t i n g E q . ( 8 )i n t o Eq. ( 5 ) g i v e s The c o r r e s p o n d i n gt o t a l power l e v e l i s T h e c a v i t yt o n ef r e q u e n c i e sa n dl e v e l sf o rt h eB o e i n g 7 2 7 a i r c r a f t w i l l n o t b e estimated. T a b l e 1 summarizes data o b t a i n e d b y H e l l e r ( 1 9 7 4 ) ,w h i c h i s u s e f u lf o r t h e e s t i m a t i o np r o c e d u r e .

I na d d i t i o n ,F i g s . 1 2 , 13, and 1 4 w i l l be u s e d as r e q u i r e d . Table 2 summarizes t h e c a v i t yg e o m e t r yf o r t h e m a i nl o a d i n gg e a rf u s e - l a g ea n dw i n gc a v i t i e sa n d t h e n o s eg e a rc a v i t y . The a i r c r a f t a p p r o a c hs p e e d i s assumed t o be 73 m/sec ( 2 4 0 f t / s e c ) , w i t h M = . 2 1 5 and q = 3280 N / m 2 ( 6 8 . 5 l b / f t 2 ) . S P L i s r e f e r r e dt o 20 v N / m 2 and PWL i s r e f e r r e d to 10-l2 watts. SPL i s d e t e r m i n e d a t 1 5 2 . 4 m (500 f t ) below and 1 5 2 . 4 m ( 5 0 0 f t ) t o t h e s i d e of t h e a i r c r a f t ( r = 1 5 2 . 4 x J 2 m ) a s s u m i n gm o n o p o l ed i r e c t i v i t y .

T A B L E 1. SUMMARY O F E X P E R I M E N T A L D A T A ( T U R B U L E N T B O U N D A R Y L A Y E R ) " d M i c .

L e v e l , M i c . L e v e l , Urn m/sec q . N / m 2 P r e d . E q . (7)+ N o . 1 , dB? N o . 4 , d B * * M ( 1 b / f t 2 ) f ,Hz S=fL/U,* R u n N o . ( f t / s e c ) L/D

-

1200 81 97.2 .125 1116 (23.3) 98 1.79 10 42.7 (140) 1.0 1116 (23.3) 1000 99 2.08 98.5 .125 42.7 (140) 1.4 11 81 100.1 1.6 1116 (23.3) 1050 2.50 96 .125 42.7 (140) 12 108.8 4462 (93.2) 1150 109 1.71 95 ' 2.0 .251 85.3 (280) 13 106 105.7 4462 (93.2) 1000 120 .251 85.3 (280) 1.6 14 1.19 126 108 104.5 1.4 4462 (93.2) 1000 1.04 .251 85.3 (280) 15 1250 106 90 1 0 3 . 5 , .251 4462 (93.2) 0.93 1.0 85.3 (280) 88 111.4 4452 (93.2) 2000 106 85.3 (280) .251 2.98 Note: W = 2.54 cm f o r a l l c a s e s . D = 6.35 cm e x c e p tf o r Run No. 17 where D = 3.18 cm.

*Dominant mode.

?Microphone 1 was l o c a t e di nt h ec a v i t yf r o n tb u l k h e a d .

**Microphone 4 was l o c a t e d 86.4 c n d i r e c t l y a b o v e t h e c a v i t ym o u t h .

+ U s i n gm e a s u r e d S .

TABLE 2 . C A V I T Y GEOMETRY FOR THE BOEING 727 AIRCRAFT L,m (ft) D,m (ft) Main Gear Fuselage Cavity Fuselage door open 1 . 6 8( 5 . 5 ) 2.04 ( 6 . 7 ) Fuselage door closed 1.74(5.7)1.28 ( 4 . 2 ) Main Gear Wing Cavity Innermost 0.61 ( 2 . 0 ) 1 . 4 3( 4 . 7 )

-

Outermost 0.61 ( 2 . 0 ) 0.88(2.9) -t 0.61 ( 2 . 0 ) 1 . 1 6( 3 . 8 ) Average 1 . 0 1 ( 3 . 3 ) 1 . 9 0.89 ( 31.3) 1.16 (12.5) Nose Gear Cavity All doors open 0.85(2.8) 2.68(8.8) 1.07(3.5) 3.2 2.41 ( 85.0) 2.86(30.8) Main doors closed - 2.41 ( 85.0) 0 . 8 5( 2 . 8 )1 . 3 1( 4 . 3 ) 1.01 ( 3 . 3 ) 1.32 (14.2) *Includes opening into wing cavity; values of L and W are averages.

'Excludes portion occupied by main gear strut.

M a i nG e a rF u s e l a g eC a v i t y When t h ed o o r s are o p e n ,t h em a i nf u s e l a g ec a v i t yh a sa n L/D = 1.2. By a p p r o x i m a t i n gt h i s as L/D = 1.0, r u n s 1 0 and 1 6 c a n be u s e di n Eq. ( 9 ) to f i n d k , = 0.0388and k 2 = 0 . 4 4 2 .

Because t h i s i s a d e e pc a v i t y ,t h ef r e q u e n c y i s n e a r l yi n d e p e n d e n t ofspeed, s o t h eS t r o u h a ln u m b e rb e h a v e s as t h ei n v e r s es p e e d ; i n t e r p o l a t i n g , w e f i n d S = 1 . 0 5 a t Urn = 7 3 . 2m / s e c( 2 4 0f t / s e c ) .

From Eqs.. ( 1 0 ) and ( 9 ) : For comparison, Eq. (7) p r e d i c t s SPL = 9 4 d B , u s i n g S = 1 . 0 5 .

Main Gear W i n g C a v i t y The a v e r a g e L/D i s 1 . 9 , b u t we assume 1 . 6 t o u s e t h e d a t a of T a b l e 1. U s i n g r u n s 1 2 and 14 w i t h Eq. ( 9 ) g i v e s k l = 9 . 1 and k , = 3 . 2 3 .I n t e r p o l a t i n gt h e data o f T a b l e 1 g i v e s S = 1 . 6 5 .

From Eqs. (10) and (9): PWL = 138 d B , SPL = 8 3 d B , f = 1 0 4 Hz.

For comparison, Eq. (7) p r e d i c t s SPL = 93 d B .

N o s e G e a r C a v i t y When a l l t h ed o o r s a r e o p e n ,t h en o s eg e a rc a v i t y has a n L/D = 3 . 2 . From t h e d a t a f o r L/D = 3 . 3i nF i g . 1 2 , we h a v e S = 1.05 f o r Mode 2 and S = 1 . 5 f o r Mode 3 .S i n c e T a b l e 1 has no e x t e r n a lr a d i a t i o nl e v e l s for t h i s c a s e i t i s n e c e s s a r yt o i m p r o v i s e .U s i n gF i g .1 3w i t h L/D = 4 . 0 , t h e l e v e l a t t h ec a v i t y l e a d i n ge d g eb u l k h e a d i s a p p r o x i m a t e l y P 2 0 l o g - = -53 d B f o r Mode 2 P 20 l o g - = - 4 7 dB f o r Mode 3 Observefrom T a b l e 1 t h a t t h e r e was a b o u t a 1 5 d B a v e r a g e d i f - f e r e n c eb e t w e e nt h el e v e l s a t microphones 1 and 4. Using t h e a b o v e ,t h ee q u i v a l e n tl e v e l s a t microphone 4 can b e estimated as 9 6 d B f o r Mode 2 and 1 0 2 d B for Mode 3 A Then, using Eq. ( 5 ) , c a l c u l a t e 6 : = 0.038 f o r Mode 2, and Bn = 0 . 1 1 8 f o r Mode 3 .

A p p l y i n g E q s . ( 5 ) and ( 6 ) t o t h e a c t u a l c a s eg i v e s

Mode 2 : PWL = 1 4 1 d B , SPL = 77 d B , f = 2 9 H z

Mode 3: PWL = 153 d B , SPL = 90 d B , f = 4 1 H Z .

F o r c o m p a r i s o n ,E q .( 7 )p r e d l c t s 77 d B f o r Mode 2 , 8 1 d B f o r Mode 3 , and 84 d B f o r Mode 4 . U s i n gt h e data o f T a b l e 1 d l - r e c t l y ( a s s u m i n g L/D = 4 . 0 )g i v e sa n estimate of SPL = 7 0 d B and f = 8 1 H z , w h i c hc o r r e s p o n d st o Mode 4 .

C l e a r l y , t h e above estimates are veryapproximateand some- what a r b i t r a r y . E q u a t i o n ( 7 ) c a n p r o v i d e a s i m p l e f i r s t e s t i - mate w i t h t h e u n d e r s t a n d i n g t h a t t h e a c t u a la n s w e r may be as much as 2 0 d B l o w e r . The last column of T a b l e 1 s u g g e s t s t h a t Eq.

( 7 ) i s m o s ta c c u r a t e when t h e c a v i t yo s c i l l a t e si n t e n s e l y .

Beyond t h i s , t h e a b o v e i l l u s t r a t e s t h a t o b t a i n i n g more a c c u r a t e estimates i s d i r e c t l y r e l a t e d t o t h e a v a i l a b i l i t y of r e l e v a n t e x p e r i m e n t a l data. A l l t h e d i f f e r e n t modes t h a t m i g h t o c c u r were n o t e s t i m a t e d . T h e e x p e r i m e n t a l e v i d e n c e s u g g e s t s t h a t Modes 2 , 3, and 4 are most commonly o b s e r v e d a t d o m i n a n tl e v e l s i n t h i s Mach number range. The f i r s t t w oc a l c u l a t i o n si l l u s t r a t e t h e p o i n t t h a t c a r e m u s t b e t a k e n t o estimate t h e p r o p e rS t r o u h a l number when t h e c a v i t y i s n ol o n g e rs h a l l o w ,e . g . , L/D < 2 . A s t h e d e p t hs c a l eb e c o m e si m p o r t a n t , t h e S t r o u h a ln u m b e r sc a nb e g i nt o d i f f e r f r o mt h o s e o f F i g . 1 2 . D e c r e a s i n g Mach number seems t o a c c e n t u a t et h i sd i f f e r e n c e .

The d i s c u s s i o na n d estimates s o f a r h a v ea s s u m e dc l e a nr e c - t a n g u l a rc a v i t i e s . I n f a c t , t h e l a n d i n gg e a rc a v i t i e so n r e a l a i r c r a f t a r e n o t a l w a y s s i m p l yr e c t a n g u l a ra n d a r e u s u a l l yc l u t - t e r e d w i t h s t r u t s ,b r a c e s ,a n dd o o r s . The w i n gc a v i t i e so f t e n have a s u b s t a n t i a ll e a d i n ge d g eo v e r h a n ga n dn o n c o n s t a n tl e n g t h .

A t o n ee n d , t h e w i n gc a v i t yo p e n si n t o a l a r g ef u s e l a g ev o l u m e , and a t t h e o t h e r e n d it i s d i s t u r b e d b y t h e m a i nl a n d i n gg e a r s h a f t . The s t a t e o f t h e u p s t r e a mf l o w may b e u n c e r t a i nb e c a u s e l e a d i n ge d g ed e v i c e s a r e o f t e nd e p l o y e d when t h e c a v i t y i s open.

A s mentioned e a r l i e r , d u r i n gp a r to f t h e s h o r t time t h a t t h e main d o o r so n t h e f u s e l a g ea n dn o s e a r e open, t h e gear i s i n t h e p r o - c e s so fb e i n gd e p l o y e d ,a n d t h e f l o wo v e r t h e c a v i t ym o u t h i s s e r i o u s l yi n t e r r u p t e d .

A l l o f t h e a b o v ef a c t o r sc a n be e x p e c t e d t o r e d u c e t h e l e v e l of o s c i l l a t i o n sa n d ,i n some c a s e s ,s u p p r e s st h e me n t i r e l y . R e - c e n t l y , Heller and B l i s s ( 1 9 7 4 ) s t u d i e d a n u m b e ro fp o s s i b l e o s c i l l a t i o ns u p p r e s s i o nd e v i c e s . Much o f t h i s r e s e a r c h c o n c e n - t r a t e d o nt h eh i g hs u b s o n i ca n ds u p e r s o n i c Mach numberrange, w h e r ec a v i t yo s c i l l a t i o n s a r e p a r t i c u l a r l yi n t e n s e . One way found t o r e d u c e t h e o s c i l l a t i o n l e v e l s was t o d i s t u r b t h e u p s t r e a mf l o w a n dc a v i t ys h e a rl a y e rw i t hs p o i l e r s or v o r t e xg e n e r a t o r s .T h e s e r e s u l t ss u g g e s tt h a ta n yd i s t u r b a n c e st ot h ef l o wo v e rt h ec a v i t y mouth may l e a d t o a s u b s t a n t i a l r e d u c t i o n i n o s c i l l a t i o n l e v e l s .

Very l i t t l e i s known a b o u tt h ee f f e c to fv e n t i n ga no p e nr e c t a n g u - l a r c a v i t y t o a large i n t e r n a l volume l i k e t h e t y p i c a l w i n g c a v i t yc o n f i g u r a t i o n . A t t h ev e r y l e a s t , t h e m o d a lp a t t e r ni n t h e o p e nc a v i t y w i l l b e a l t e r e d and a r e d u c t i o n i n o s c i l l a t i o n s a s s o c i a t e dd i r e c t l yw i t ht h eo p e nc a v i t yc a n be e x p e c t e d . One e f f e c to ft h ef r o n to v e r h a n go nw i n gc a v i t i e s w i l l be to a l t e r t h eo s c i l l a t i o nf r e q u e . n c y .S i n c e wave s p e e d s w i l l b e h i g h e r u n d e r t h e ( n o n c o m p l i a n t )o v e r h a n g , a f r e q u e n c yi n c r e a s e i s e x p e c t e d .

The e f f e c t o f a f r o n to v e r h a n go nl e v e l s i s unknown; e x p e r i m e n t s have shown t h a t a rear o v e r h a n go f t e ni n c r e a s e sl e v e l s .

I n summary, t h e estimates show t h a t o p e nr e c t a n g u l a rc a v i t i e s c a n be a s i g n i f i c a n t airframe n o i s es o u r c e ,b u to n l y i f r e a l i s t i c l a n d i n gg e a rc a v i t i e sa c t u a l l yd oo s c i l l a t e .D u r i n ga p p r o a c h , once t h e m a i nd o o r sh a v er e c l o s e d , t h e l a r g ef u s e l a g ea n dn o s e c a v i t i e s become e s s e n t i a l l yv e n t e de n c l o s u r e s ,r a t h e rt h a no p e n r e c t a n g u l a rc a v i t i e s .T h ef l o wo v e r t h e o p e n i n g s w i l l b ed i s - t u r b e d by t h eg e a rs t r u t sa n db r a c e s . The o p e n i n go ft h en o s e g e a rc a v i t y i s p a r t i c u l a r l yc l u t t e r e d .T h e r e i s p r e s e n t l y no r e l i a b l e way t o estimate t h eo s c i l l a t i o nl e v e l sf o rt h e s ee n - c l o s u r e s . However, o s c i l l a t i o nf r e q u e n c i e s w i l l be a p p r o x i m a t e l y g i v e n b y t h e H e l m h o l t zr e s o n a t o rf r e q u e n c ya n d by t h e h a r d modes.

These f r e q u e n c i e sh a v eb e e ne s t i m a t e df o rt h eB o e i n g 7 2 7 and are p r e s e n t e di n T a b l e 3 . It i s n o tp r e s e n t l y known w h e t h e r t h e s e v e n t e de n c l o s u r e sc a n b e a s i g n i f i c a n ts o u r c eo f airframe n o i s e .

C A V I T Y L E A D I N G E D G E N O I S E When a t u r b u l e n tb o u n d a r y l a y e r e n c o u n t e r sa na b r u p tc h a n g e i ns u r f a c ei m p e d a n c e ,s u c h as a ne d g e ,s u b s t a n t i a ls o u n d i s r a d i a t e d . T h i ss i t u a t i o no c c u r s when t h e t u r b u l e n t b o u n d a r y l a y e r p a s s e so v e rt h el a n d i n gg e a rc a v i t yl e a d i n ge d g e s . The p r o c e s sc a n b e modeled as a spanwise array o fi n c o h e r e n td i p o l e s whose f o r c e s t r e n g t h i s r e l a t e d t o t h e f l u c t u a t i n g p r e s s u r e a t t h e s u r f a c ea n dt h ec o r r e l a t i o na r e ao ft h el o c a ld i s t u r b a n c e .

The d i r e c t i v i t yo ft h e s ee d g es o u r c e s d i f f e r s from t h e c l a s s i c a l d i p o l e b y v i r t u e o f t h e p r e s e n c e o f a b a f f l i n g s u r f a c e whose d i m e n s i o n s a r e many c h a r a c t e r i s t i cw a v e l e n g t h so ft h ee d g e - g e n e r a t e d s o u n d . The i n t e n s i t y o f t h i ss i m p l em o d i f i e dd i p o l e 3 2 - . ... . . . . . . . . . . . .. . .

T A B L E 3 . VENTED ENCLOSURE FREQUENCIES FOR BOEING 727 LANDING GEAR C A V I T I E S - . I . ~ ~ . ~ .

Cav i t y M o d e Frequency (Hz) - . . - ~- ~ ~ ~ .~ .

.. . - ~ - .- .- . -.

Main Gear Fuselage Cavity Helmholtz. Resonator 30 ( f u s e l a g ed o o r s closed) F i r s t L e n g t h Mode 84 First,Depthand Width Mode 102 Nose Gear Cavity HelmholtzResonator (forwarddoorsclosed.)

F i r s t L e n g t h Mode 6 3 F i r s t Depth Mode 202 F i r s t Width Mode ~ " " " - ..

where ac i s t h e c a v i t y soundspeed, V i s thecavityvolume, A i s t h e mouth area (see Table 2 ) and ( A l ) i s t h e volume a t t h e r e s o n a t o r mouth.

( A l ) : 1.27 m 3 ( 4 5 f t 3 ) main g e a r c a v i t y ( A l ) 2 1 . 3 3 m 3 (47 f t 3 ) n o s eg e a rc a v i t y .

Note 2: General volume mode f r e q u e n c i e s are givenby r where 2 R and RZ are the length, depth, and width dimensions, and the x ' y ' i n t e g e r sn x ,n y ,n Z( n l = 0 , 1, 2,...) arecorresponding mode numbers.

model i s g i v e n by where w i s t h e f r e q u e n c yo f t h e f l u c t u a t i n gf o r c e ,F 2 i s t h e local m e a n - s q u a r ef o r c e , m i s t h e e f f e c t i v e number o fs o u r c er e g i o n s a l o n g t h e s p a n , 0 i s t h e a n g l eb e t w e e n t h e l i n e of t h e t r a i l i n g edgeand t h e o b s e r v e r ,a n d Q i s t h e a n g l eb e t w e e n t h e p l a n eo f t h e s u r f a c ea n d t h e o b s e r v e r . The n u m b e ro fs o u r c er e g i o n sc a n be a p p r o x i m a t e d by t h e s p a no f t h e edge d i v i d e d by t h e s p a n w i s e c o r r e l a t i o n d i s t a n c e i n t h e b o u n d a r yl a y e r .

S u f f i c i e n t l y d e t a i l e d measurementsofnear-edgeflowshave n o tb e e n made t o a l l o w a d i r e c t c a l c u l a t i o n o f radiated sound from t h e s u r f a c e p r e s s u r e s p e c t r u m . H o w e v e r , o n e c a n take ad- v a n t a g eo fe m p i r i c a lp r o c e d u r e st o estimate e d g en o i s es p e c t r a [see Hayden (1972), Hayden e t aZ. (1974), and Hayden e t aZ.

(1975)]. Based on t h e s e s o u r c e s , t h e s p e c t r u mf o r a l i g h t l y l o a d e d a i r f o i l shown i n F i g . 1 6 and t h e c o r r e s p o n d i n ge q u a t i o n givenbelowwereused t o estimate c a v i t yl o a d i n ge d g en o i s ef o r t h e Boeing 727 a i r c r a f t . T h e e q u a t i o nf o ro v e r a l lp o w e rl e v e l i s

PWL ( d B r e 1 0 - l 2 W ) = + 16.3 + 10 l o g (6WU6) . (12)

where 6 i s t h e boundary l a y e r t h i c k n e s s (in), W i s t h e c a v i t y w i d t h n o r m a lt o t h e flow ( m ) , a n d U i s t h e f r e e stream v e l o c i t y( m / s e c ) .

T h i s e x p r e s s i o n i s v a l i d f o r t h e c o n t r i b u t i o no f t h e flowonone s i d e of' t h e edge, as i s a p p r o p r i a t ef o r t h e c a v i t yl e a d i n ge d g e problem.

T h e computed r e s u l t f o r t h e sum o f a l l p o s s i b l ec a v i t y lead- i n g e d g e s e x p o s e d to t h e flow i s shown l a t e r i nF i g . 1 6 . A c a v i t y l e a d i n g edge b o u n d a r yl a y e rt h i c k n e s so f 0 . 0 5 5 m ( 1 . 1 8 f t ) was u s e d , based on a f l a t - p l a t e t u r b u l e n tb o u n d a r yl a y e rf o r m u l aa n d t h e a v e r a g ed i s t a n c et ot h ew i n gl e a d i n g edge. A c t u a l l y , t h e bound- a r yl a y e rp r o p e r t i e s may b e c o n s i d e r a b l yd i f f e r e n t ,s i n c e t h e m a i ng e a rc a v i t y i s l o c a t e d a t t h ew i n g - f u s e l a g ej u n c t i o na n d i s p a r t i a l l yd o w n s t r e a mo f t h e w i n gl e a d i n ge d g ed e v i c e s . .How- e v e r , a more r e l i a b l e estimate o f t h e boundary l a y e r p r o p e r t i e s i s n o ta v a i l a b l e . The same t h i c k n e s s was a s s u m e d f o r t h e n o s e g e a rc a v i t y . No attempt was made t o c o m p u t es e p a r a t e l y t h e c a s e o fm a i nf u s e l a g ed o o r sa n df o r w a r dn o s ed o o r sc l o s e d ,f o rw h i c h t h e l e v e l s w i l l be lower. Because t h i s i s a r e l a t i v e l y weak n o i s e s o u r c e , o n l y a n u p p e r b o u n d estimate i s needed. Note t h a t t h e l e n g t ho fe x p o s e de d g e i s much l e s s t h a n t h e l e n g t ho fw i n g , f l a p , a n d s t a b i l i z e r t r a i l i n g e d g e s t h a t g e n e r a t en o i s e b y t h e same mechanism.

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Urn Urn F I G . 1 6 . N O N D I M E N S I O N A L S P E C T R U M F O R T H E C A L C U L A T I O N OF C A V I T Y N O N D I M E N S I O N A L S P E C T R U M F O R T H E C A L C U L A T I O N OF C A V I T Y L E A D I N G ED-GE N O I S E . L E A D I N G ED-GE N O I S E .

C A V I T Y T R A I L I N G E D G E N O I S E R e g a r d l e s so fw h e t h e r or n o t a c a v i t y o s c i l l a t e s , t h e c a v i t y t r a i l i n g e d g e i s s u b j e c t e d t o a t u r b u l e n ti n f l o wd u et ot h ep r e - s e n c eo ft h et u r b u l e n ts h e a rl a y e ro v e rt h ec a v i t ym o u t h . The r e s u l t i n g f l u c t u a t i n g f o r c e s p r o d u c e d i p o l e - l i k e a c o u s t i c radia- t i o n ,a n d are, n od o u b t , a m a j o rs o u r c eo fc a v i t yb r o a d b a n dn o i s e .

F i g u r e l7a s c h e m a t i c a l l yi l l u s t r a t e st h i si m p i n g e m e n to ft u r b u - l e n ti n f l o w ,a n da l s og i v e sa ni n d i c a t i o no ft h el e a d i n ge d g e s o u r c ed i s c u s s e di n t h e p r e v i o u ss e c t i o n .F i g u r e l 7 b i n d i c a t e s q u a l i t a t i v e l y t h e a n t i c i p a t e d d i r e c t i v i t y p a t t e r n s f o r t h e s e s o u r c e s ,w h i c b ,p r e s u m a b l y , a r e d i s t o r t e d by t h ep r e s e n c eo ft h e c a v i t y .

The sound mechanism i s e s s e n t i a l l y t h e l e a d i n g edge d i p o l e , whose i n t e n s i t y h a s t h e same p a r a m e t e rd e p e n d e n c e s as i n d i c a t e d by Eq. (11). Because of t h e c o m p l e x i t yo ft h ei n t e r a c t i o n p r o - cess, i t i s n e c e s s a r y ,h o w e v e r , to e m p l o ya ne m p i r i c a l scheme.

The d i p o l ee d g en o i s em o d e l was a d a p t e d to t h el e a d i n g - e d g e s i t u a t i o n ,a n d a s e r i e s o fe x p e r i m e n t sp e r f o r m e du s i n g a f r e e j e t as a r e p r e s e n t a t i v es o u r c e o f a f r e e t u r b u l e n t shear l a y e r . The r a t i o n a l e for t h e modeling was t h e same as i n o t h e r e d g e n o i s e m o d e l s ;n a m e l y ,t h a te a c hl o c a lf o r c ef l u c t u a t i o n i s r e l a t e d t o t h ed i f f e r e n t i a lp r e s s u r ea c r o s st h ee d g ea n dt h es c a l eo ft h e d i s t u r b a n c e . To p r e d i c tt h et o t a ls o u n do u t p u t ,o n es i m p l ya d d s up t h ei n d i v i d u a ls o u r c e s ,w h o s en u m b e r s a r e estimated by t h e r a t i o o f t h e wetted s p a n , W , to t h e s p a n w i s ec o r r e l a t i o nl e n g t h .

F i g u r e 1 8 s u m m a r i z e st h er e s u l to fs e v e r a le x p e r i m e n t sp e r f o r m e d by Hayden, Kadman, and Chanaud ( 1 9 7 2 ) . T h e p e a k p o w e r l e v e l o c c u r s a t a S t r o u h a ln u m b e r o f a b o u t 0 . 3 based on t h e l o c a l shear l a y e r t h i c k n e s s , 6 , and t h e maximum mean v e l o c i t y , U .

T h e l / 3 - o c t a v eb a n dp o w e rl e v e l a t t h i s peak i s PWL ( @ f6/U I 0 . 3 ) i n d B r e 1 0 - l 2 w = + 8 . 3 + 1 0 l o g ( 6 W U 6 ) , where 6 i s t h el o c a l shear l a y e rt h i c k n e s si nm e t e r s ( 6 = 0 . 2 ~ ~ where x i s t h ed i s t a n c ef r o mt h ef l o ws e p a r a t i o np o i n t ) , W i s t h e w e t t e d s p a n ( m ) , and U i s t h e f r e e s t r e a m v e l o c i t y ( m / s e c ) . The o n e - t h i r d o c t a v e s p e c t r u m may b e c a l c u l a t e du s i n g F i g . 1 8 . F i g u r e 1 8 a l s o shows v a r i a t i o n se n c o u n t e r e df r o mp o s i t i o n i n ge f f e c t s of t h e e d g ei n t h e shear l a y e ra n d t h e i m p i n g e m e n ta n g l e . T h e WHEEL WELL

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1 DIRECTION OF FLIGHT

( b 1 APPROXIMATE RADIATION PATTERNS FROM EDGE SOURCES F I G . 1 7 . C A V I T Y E D G E N O I S E M E C H A N I S M S . A N D T H E I R A P P R O X I M A T E D I R E C T I V I T Y .

d i r e c t i v i t y o f t h e s o u r c e i s t h e same as t h a tp r e v i o u s l yr e p o r t e d f o rt r a i l i n g - e d g en o i s ef o rt h i ne d g e s . The e f f e c to f a nearby s u r f a c e ,s u c h as c a v i t y walls, f l o o r ,e t c . , w i l l a f f e c t t h e d i - r e c t i v i t y ,b u ts u c he f f e c t sh a v en o ty e tb e e nc o n s i d e r e dq u a n t i - t a t i v e l y .

Use o f t h e s p e c t r ao fF i g . 1 8 t op r e d i c ti m p i n g e m e n tn o i s e i s j u s t i f i a b l e ,b e c a u s e t h e t w oo r i e n t a t i o n so f t h e edge,normal to a n da l i g n e dw i t ht h ef l o w ,r e p r e s e n t t h e t w os u r f a c e sw h i c h form t h e c a v i t yt r a i l i n g wedge. Because of t h e e f f e c t so ff l o w s e p a r a t i o n , t h e n o r m a lo r i e n t a t i o np r o b a b l yp r o v i d e s a good re- p r e s e n t a t i o no f t h e c a v i t y rear b u l k h e a d . Use o f t h e data f o r t h e wedge a l i g n e d w i t h t h e f l o wp r o b a b l yo v e r e s t i m a t e sr a d i a t i o n f r o mt h es u r f a c eb e h i n d t h e c a v i t y . Use o ft h e s et w os p e c t r a t o g e t h e r a l l o w s t h e r a d i a t i o n t o be roughlybounded w i t h a band.

The n o i s ed u et os h e a rl a y e ri m p i n g e m e n to n t h e a f t edge of t h e l a n d i n gg e a rc a v i t i e s was c a l c u l a t e du s i n gE q . (13) and F i g . 1 8 . A s e x p l a i n e d e a r l i e r , two s i t u a t i o n st y p i c a l l yo c c u r d u r i n ga p p r o a c h :o n ei nw h i c hb o t hf u s e l a g ea n dw i n gd o o r s a r e o p e n ,a n do n ei nw h i c hf u s e l a g ed o o r s a r e r e c l o s e d . T h e r e s u l t s shown - i nF i g . 19 i n d i c a t e t h a t t h e s e s o u r c e sc o u l d b e a dominant f a c t o r a t l o wf r e q u e n c i e so r a t h i g h e rf r e q u e n c i e s i f t h e s h e a r l a y e r c h a r a c t e r i s t i c s a r e d i f f e r e n tf r o mt h o s em o d e l e d .

The e f f e c t so fo t h e rs o u r c e so fi n f l o wt u r b u l e n c eo nn o i s e r a d i a t i o nf r o m t h e c a v i t yt r a i l i n ge d g eh a v en o tb e e n estimated.

These s o u r c e sw o u l di n c l u d e t h e l a n d i n g g e a r s t r u t when t h e g e a r i s i np l a c e ,a n d t h e e n t i r ea s s e m b l y as t h e g e a r i s b e i n gl o w e r e d .

The m a i n g e a r s t r u t may b e r e l a t i v e l yu n i m p o r t a n t ,s i n c e i t s wake c a no n l yi n t e r a c t w i t h a small f r a c t i o n o f t h e t o t a l l e n g t h o f t h e w i n gc a v i t yt r a i l i n ge d g e .I n t h e a b s e n c eo fd i r e c t l y r e l e - v a n te x p e r i m e n t a l data, t h e e f f e c t o f t h e s e s o u r c e so fi n f l o w t u r b u l e n c eo nt r a i l i n ge d g en o i s ec a n n o t b e estimated w i t h any c o n f i d e n c e .

F i n a l l y , t h e q u e s t i o n a r i s e s as t ow h e t h e r t h e p r e s e n c eo f t h e c a v i t yc a ns e r v et oa m p l i f yt u r b u l e n c ei m p i n g e m e n tn o i s et h r o u g h t h e e x c i t a t i o no fc a v i t ym o d e s .F o r a c l e a nr e c t a n g u l a rc a v i t y ,w h i c h i s a l w a y se x p o s e dt o i t s own t u r b u l e n t shear l a y e r , t h e answer i s l a r g e l yc o n t a i n e di nt h es e m i - e m p i r i c a la n a l y s i so f i t s o s c i l l a t i o n b e h a v i o r , as d i s c u s s e di n t h e s e c t i o no fc a v i t yd i s c r e t ep r e s s u r e o s c i l l a t i o n s . The shear l a y e rt u r b u l e n c e i s p a r t i a l l yr e s p o n s i b l e f o r t h e w i d t h o ft o n a lp e a k s ,b u t i s o t h e r w i s eo fs e c o n d a r yi m p o r - t a n c e to t h e o s c i l l a t i o np r o c e s s .I nf a c t ,c a v i t i e s w i t h l a m i n a r shear l a y e r s t y p i c a l l y o s c i l l a t e more i n t e n s e l y ,s u g g e s t i n g t h a t a n ya d d i t i o n a lf o r c i n gd u et o shear l a y e rt u r b u l e n c e i s more t h a n overcome by t h e e f f e c t s o f i n c r e a s e d shear l a y e rt h i c k n e s sa n d re- duced mean v e l o c i t yg r a d i e n t .S i m i l a r l y ,i n t r o d u c i n gt u r b u l e n c e 7273 LANDING CONFIGURATION

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w z 77 3c 4 0 63 1 0 0 160 250 400 630 1000 1600 2500 4000 31.5 50 EO 125 200 3 1 5 500 800 1250 2000 3150 5000 BOO0 ONE-THIRD OCTAVE BAND CENTER FREQUENCIESINHZ (CPS) F I G . 1 9 . E S T I M A T E D L A N D I N G G E A R C A V I T Y E D G E N O I S E S O U R C E S F O R A B O E I N G 7 2 7 .

u p s t r e a m of t h e c a v i t y w i t h s p o i l e r s raises t h e broadbandand re- d u c e st h et o n e s . W e c a nc o n c l u d et h a tt h ei n c r e a s ei nt h eb r o a d - i s d i r e c t l yd u et oc h a n g i n g t h e i n c i d e n tt u r b u l e n c e b a n dl e v e l i n t e n s i t y r a t h e r t h a n a c o u p l i n g w i t h t h e c a v i t y d y n a m i c s .

However, when t h e c a v i t y i s e s s e n t i a l l y a v e n t e de n c l o s u r e r a t h e r t h a n a n o p e n r e c t a n g u l a r c o n f i g u r a t i o n , i t s modalcharac- t e r i s t i c s are less d e p e n d e n to nt h e mean s h e a r l a y e r p r o p e r t i e s .

I n this case, it c a n be e x p e c t e dt h a ns h e a r l a y e r t u r b u l e n c e , a n d p a r t i c u l a r l y i t s i m p i n g e m e n to nt h ec a v i t yt r a i l i n g edge, w i l l e x c i t e modes i n t h e c a v i t ye n c l o s u r ea n d some a m p l i f i c a t i o n o ft h er a d ' i a t e ds o u n d may o c c u r .N o t i c e t h a t t h es p e c t r a of F i g .1 9 f a l l i n t h e same g e n e r a lf r e q u e n c yr a n g e as t h ev e n t e d e n c l o s u r ef r e q u e n c i e so f T a b l e 3 .

L A N D I N G G E A R D I R E C T R A D I A T E D N O I S E P e r h a p s t h e most familiar aerodynamicnoisemechanism i s r e l a t e d t o t h e g e n e r a t i o n o f a n u n s t e a d y wake b y a b l u f f body i n a na i r f l o w .V o r t e xs h e d d i n g b y c y l i n d e r s a t low Reynolds numbers producesnarrowbandsound r e l a t e d t o t h e f l u c t u a t i n g l i f t a n d d r a gf o r c e s . A s R e y n o l d s n u m b e r i n c r e a s e s , t h e shedding becomes i n c r e a s i n g l y r a n d o m a n d b r o a d b a n d n o i s e i s . p r o d u c e d . S i m i l a r l y , u s u a l l y t h e m o r er o u g ha n di r r e g u l a r t h e bodyshape,themore broadband t h e r e s u l t i n g n o i s e s p e c t r u m .

F l u c t u a t i o n s i n t h e a e r o d y n a m i cf o r c e so c c u ri nb o t ht h e d i r e c t i o nn o r m a lt o t h e f l o w , FN, and t h e d i r e c t i o no f t h e mean flow, FD. The magnitude of t h e f l u c t u a t i n gf o r c e s i s r e l a t e dt o t h e s t e a d y s t a t e d r a go n t h e body,which i s a f u n c t i o no fR e y n o l d s number. V a l u e s o f r m s n o r m a lf o r c et o s t e a d y d r a g a r e g i v e n b y J o n e s e t a Z . ( 1 9 6 9 ) ; t y p i c a l l y , FN " - 0 . 2 a t Reynolds numbers - UD - - l o 6 .

F, V T y p i c a lv a l u e so fd r a gf l u c t u a t i o n s were found b y H e l l e ra n d W i d n a l l ( 1 9 6 8 ) t o b e I ' DSS The f r e q u e n c y , f , f o r t h e f o r c e s a t a givenReynoldsnumber i s a d i r e c t p r o p o r t i o n o f t h e r a t i o o f v e l o c i t y to diameter ( f D / U = c o n s t a n t ) . T h i s Strouhal number, which has b e e ns t u d i e do v e r a wide r a n g e , i s u s u a l l ya b o u t 0 . 2 to 0.25; t h e b a n d w i d t ho f t h e f o r c e f l u c t u a t i o n s a l s o v a r i e s w i t h Reynoldsnumber(Jones e t aZ., 1 9 6 9 ) The r e l a t i o n s h i p b e t w e e n t h e s p e c t r u m o f f o r c e f l u c t u a t i o n s , @F, and t h e s p e c t r u mo f radiated s o u n dp r e s s u r e , O p a , may be g i v e n by f o rf r e q u e n c i e sw h o s ew a v e l e n g t h s a r e much l o n g e rt h a n a d i m e n s i o n t h e s u r f a c e . The a n g l e 8 i s t a k e nf r o m t h e a x i so f t h e f o r c e o f f l u c t u a t i o n s . The sound power spectrum i s F o r a t y p i c a l a i r c r a f t , t h e b l u f f body p r o t r u s i o n s t h a t c a u s e wake-related f o r c en o i s e a r e n o ts i m p l y shapes, as shown i n F i g .

2 0 a n dF i g s . 3 t h r o u g h 7 . N o t i c e t h a t b e c a u s e of t h e i r t h i c k f l a t e d g e s , t h e l a n d i n g gear d o o r s a r e c o n s i d e r e dt ob e h a v es i m i l a r l y t o t h e more b l u n t s t r u t s a n d wheels.

The d i f f i c u l t y i n p e r f o r m i n g a p r e d i c t i o n o f t h e n o i s ef r o m s t r u t s , wheels, b l u f f doors, e t c . , i s t h e e s t i m a t i o n o f t h e a p p r o p r i a t ef o r c e sa n d t h e i r f r e q u e n c ys p e c t r u m . The gear was b r o k e ni n t o small components,and t h e f l u c t u a t i n g l i f t a n dd r a g c a l c u l a t e df o re a c hs e c t i o n .R e y n o l d sn u m b e r s based on s e c t i o n diameter (or, i n t h e c a s eo fw h e e l s , t h e t i r e w i d t h ) were around 1 t o 2 x l o 6 . For c y l i n d e r si n t h i s r a n g e ,J o n e s ' data show t h a t t h e S t r o u h a l number o f t h e peak n o r m a lf o r c ef l u c t u a t i o n i s a b o u t 0 . 2 5 , t h e rms m a g n i t u d eo f t h e n o r m a lf o r c er a n g e sb e t w e e n0 . 0 8 t o 0 . 1 2 times t h e s t e a d yd r a g ,a n dt h es p e c t r u m has a broadband c h a r a c t e r ,u n l i k ev o r t e xs h e d d i n g a t l o w e r or much h i g h e rR e y n o l d s numbers. The o v e r a l ll e v e l for e a c hs e c t i o n was computed u s i n g E q . ( 1 4 ) a n da p p l y i n gH e l l e ra n dW i d n a l l ' s( 1 9 6 8 )b r o a d b a n d s p e c t r u m ( t h e 1/3-octaveband peak o c c u r r i n g a t t h e s h e d d i n g S t r o u h a l number i s 1 5 dB b e l o wt h eo v e r a l ll e v e l ) , shown i n F i g . 2 1 .

4 2 S N FLUCTUATIONS F I G . 2 0 . L A N D I N G G E A R D I R E C T R A D I A T I O N S O U R C E S .

& W I I

16 .025 .OW 063 .I00 . I 6 0 .250 .400 .630 1.00 1.600 2.50 4.00 6.30 10.0

ONE-THIRDOCTAVE BAND STROUHAL NO.

F I G . 2 1 . S P E C T R U M R E L A T I V E TO OVERALL LEVEL FOR N O I S E FROM B L U F F B O D I E S .

The drag f l u c t u a t i o n s were computedusingEq. ( 1 5 ) and Heller a n dW i d n a l l ' sS t r o u h a ls p e c t r u mc e n t e r e d a t f D / U = 0 . 4 .

T h ec o m p o s i t es p e c t r af o rd i f f e r e n tc o m p o n e n t s are shown i n F i g . 2 2 . The drag f l u c t u a t i o n sc o n t r i b u t e l i t t l e t o t h e t o t a l s o u n do u t p u t as e x p e c t e d . The low-frequency area i s dominated by t h e wheels (which were assumed t o u n d e r g of l o ws e p a r a t i o n a t t h e maximum diameter p o i n t ) , a n d s t r u t s d o m i n a t e t h e h i g h - f r e q u e n c y area. The t o t a l power l e v e ld o m i n a t e st h a to f t h e wing edge s o u r c e s a t l o wf r e q u e n c i e s .I nc o n s i d e r i n gt h e f a r f i e l d c o n t r i b u - t i o n o f t h e d i r e c t radiated s o u n d , a f t e r - r e f l e c t i o n e f f e c t s o f d i r e c t i v i t ys h o u l d b e c a r e f u l l y estimated. To o b t a i na n estimate o f t h e d i r e c t radiated n o i s e ( S P L ) o ft h e gears a t t h e same ground o b s e r v e r p o i n t , 50 d B c o u l d be s u b t r a c t e df r o mt h e power l e v e l s .

However, it s h o u l d be r e c o g n i z e dt h a tb e c a u s eo f t h e inhomogeneous n a t u r eo f t h e componentsand t h e l o c a lf l o wa r o u n d t h e gear, t h e s e estimates a r e already g r o s s .

The c a v i t y t u r b u l e n t shear l a y e r w i l l impingeon t h e l a n d i n g gear s t r u t s and braces, t h e r e b y s u b j e c t i n g a p o r t i o n of t h e s e e l e m e n t st oa nu n s t e a d yi n f l o w . A s a r e s u l t ,a d d i t i o n a ll o a d s w i l l be p r o d u c e di n t h e impingementregion,and t h e v o r t e x shed- d i n gp r o c e s s may b e a f f e c t e do v e r t h e e n t i r e l e n g t h o f t h e e l e m e n t .

If t h e impingementregion i s a r e l a t i v e l y small p o r t i o no f t h e e l e m e n ts p a n ,a n d i f t h eR e y n o l d s number is s u f f i c i e n t l yh i g h s o t h a t t h e s h e d d i n g i s already t u r b u l e n t , t h e s e e f f e c t s may n o t b e t o oi m p o r t a n t . On t h e o t h e rh a n d , i f t h e v o r t e xs h e d d i n g p r o c e s s was i n i t i a l l y d i s c r e t e , t h e a d d i t i o no fi n f l o wt u r b u l e n c e t o a n yp o r t i o n o f t h e s t r u t m i g h t d i s r u p t t h e d i s c r e t es h e d d i n g p r o c e s s .

On some l a n d i n gg e a rc o n f i g u r a t i o n s , t h e wakes o f some g e a r components may i m p i n g eo no t h e rg e a rc o m p o n e n t sa n dp r o d u c e un- s t e a d y l o a d s . T h i s i n t e r a c t i o n may o c c u ro nt h ei n - l i n em a i n s t r u t sa n d wheels o f some l a r g ea i r c r a f t . The i m p o r t a n c eo ft h i s n o i s es o u r c e w i l l s t r o n g l yd e p e n d on t h e p a r t i c u l a r l a n d i n g g e a r g e o m e t r y .L a n d i n gg e a rw a k e / l a n d i n gg e a ri n t e r a c t i o n sh a v en o t b e e nc o n s i d e r e di n t h i s r e p o r t ,a n d it i s b e l i e v e d t h a t d i r e c t l y r e l e v a n t e x p e r i m e n t a l data would b e r e q u i r e d t o make a r e a s o n a b l e estimate o f e f f e c t on r a d i a t e d n o i s e .

C A V I T Y A N D G E A R W A K E I N T E R A C T I O N S W I T H T H E W I N G T R A I L I N G E D G E A N D F L A P S The t u r b u l e n t wakes b e h i n d t h e l a n d i n g g e a r c a v i t i e s a n d s t r u t s may i n d u c eu n s t e a d yl o a d so n t h e w i n gt r a i l i n ge d g ea n d 4 5

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1 100 160- 250 400 630 1000 1600 2500 4000 6300 3 1 . 5 5 0 80 125 200 315 500 800 1250 2000 3150 5 0 0 0 8000 ONE-THIRD OCTAVE BAND CENTER FREQUENCIES IN HZ (CPS) F I G . 2 2 . L A N D I N G G E A R D I R E C T R A D I A T E D N O I S E .

t h ef l a p s y s t e m . T h i s e f f e c t i s i l l u s t r a t e ds c h e m a t i c a l l yi n F i g . 23. These l o a d s a r e produced by d i r e c tt u r b u l e n c ei m p i n g e - mentand b y t h e e f f e c t o f t u r b u l e n t f l o w o v e r t h e wingand f l a p edges. The r e s u l t i n gi m p i n g e m e n tn o i s ea n de d g en o i s e w i l l de- pendon t h e t u r b u l e n c e s p e c t r u m o f t h e w a k e s a n d o n t h e i n t e r a c t i o n g e o m e t r y ;t h e s en o i s es o u r c e sc a n b e e x p e c t e dt oh a v e a d i p o l e - l i k e c h a r a c t e r . The wake b e h i n dt h ew i n gg e a ra n dc a v i t y i s com- p o s e do ft h et u r b u l e n tf l o wf r o m h a l f t h e c a v i t y s h e a r l a y e r as w e l l as t h e wakes o f s t r u t s ,b r a c e s ,a n d wheels. B e c a u s et h e c a v i t y s h e a r l a y e r i s a d j a c e n t t o t h e l o w e r s u r f a c e o f t h e w i n g it m u s t i n e v i t a b l y i n t e r a c t w i t h t h e w i n g t r a i l i n g edge a n d f l a p s y s t e m . T h ed e g r e eo fi n t e r a c t i o nw i t ht h ew a k e s o f o t h e r com- p o n e n t s i s less c e r t a i n ,a n dp r e s u m a b l yd e p e n d so nt h ef l a p s e t t i n g .

R e c a u s eo ft h ec o m p l i c a t e dn a t u r e of t h i s n o i s e s o u r c e , a q u a n t i t a t i v e estimate o f t h e o v e r a l l l e v e l a n d s p e c t r u m has n o t b e e n a t t e m p t e d . It i s b e l i e v e d t h a t a ne x p e r i m e n t a ls i m u l a t i o n o ft h ew a k e / f l a pi n t e r a c t i o nf l o w w i l l be r e q u i r e d t o make a r e l i a b l e n o i s ep r e d i c t i o n .S i n c e a v e r yt u r b u l e n tl a n d i n gg e a r wake i s e x p e c t e d , t h i s i n t e r a c t i o n may p r o v e t o b e a ni m p o r t a n t airframe n o i s es o u r c e .

C O M P O S I T E N O I S E P R E D I C T I O N The r e s u l t s o f t h e p r e v i o u ss e c t i o n sc a n b e combined w i t h t h e p r e d i c t i o no f Hayden e t a Z . (1974) f o r t h e w i n g s ,f l a p s ,a n d s t a b i l i z e r of a Boeing 7 2 7 to o b t a i n a c o m p o s i t eo f a l l n o i s e s o u r c e sd u r i n ga p p r o a c h . The r e s u l t i s shown i nF i g . 2 4 f o r d i f f e r e n tc a v i t ya n dl a n d i n gg e a rs i t u a t i o n s . It a p p e a r s t h a t wing, f l a p , and s t a b i l i z e r s o u r c e sc o n t r o l t h e h i g h - f r e q u e n c y r a n g e ,w h i l eg e a rd i r e c t r a d i a t e d n o i s ea n d shear l a y e r impinge- ment on t h e c a v i t y a f t edgedominate t h e low-frequency a r e a .

The r e g i o n where mostof t h e c a v i t y o s c i l l a t i o n p e a k l e v e l s were e s t i m a t e d t o o c c u r . i s i n d i c a t e d by t h e c r o s s - h a t c h e db o xi n t h eu p p e r l e f t o f F i g . 2 4 . S i n c e t h e s e estimates are v e r y l i k e l y h i g h , t h e a c t u a ll e v e l sp r o b a b l y f a l l below t h e box. The i n d i c a - t i o n i s t h a t c a v i t y o s c i l l a t i o n s c a n b e a n airframe n o i s ep r o b l e m , b u to n l y i f t h e yo c c u rf o r r e a l a i r c r a f tl a n d i n gg e a rc o n f i g u r a - t i o n s .

To estimate t h e l e v e l a t t h e F A A c e r t i f i c a t i o n p o i n t , t h e e f f e c t s must b e c o n s i d e r e d . F i g u r e 24 il- d i r e c t i v i t y a n d p a t h s o u r c e sw h o s ed i r e c t i v i t y i s l u s t r a t e s t h i s l e v e l for t h ee d g e 4 7 TRAILING-EDGE

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.-.-. C A V I T I E S A N D L A N D I N G G E A R ( A L L D O O R S O P E N )

CAVITIES AND LANDING GEAR (FUSELAGE DOORS CLOSED) 1 1 ~ I 1 ~~~~~~~ 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 80 30 40 63 100 160 2 5 0 400 630 1OOO 1600 2500 4000 6300 31.5 SO 80 125 2 0 0 315 5 0 6 -806 ~ -1250- ~ 2000 3150 5000 8000 ONE-THIRD OCTAVE BAND CENTER FREQUENCIES IN HZ (CPS) F I G . 2 4 . C O M P O S I T E OF A L L S O U R C E S F O R T H E B O E I N G 727, 7 3 m / s e c ( 2 4 0 f t / s e c ) , 1 1 2 . 8 m (370 f t ) A L T I T U D E .

4 9 r e l a t i v e l yu n c o m p l i c a t e d . It would be r e a s o n a b l yc o n s e r v a t i v et o s u b t r a c t 50 d B from t h e s o u r c ep o w e rl e v e l so f t h e o t h e rs o u r c e s to o b t a i n t h e SPL a t t h e o b s e r v e r p o s i t i o n shown f o r t h e a p p r o a c h c e r t i f i c a t i o np o i n t( g r o u n dr e f l e c t i o nn e g l e c t e d ) .T h u s ,o n e w o u l de x p e c tt oo b s e r v e1 / 3 - o c t a v eb a n dl e v e l so f 75 t o 78 dB between 60 and 800 Hz, a n d o v e r a l l l e v e l s o f 88 t o 91 d B f o r t h e s i t u a t i o nm o d e l e d . T h ep e r c e i v e dn o i s el e v e l i s a p p r o x i m a t e l y 97 PNdB, which i s a b o v e F A R 36-10 d B f o r t h e Boeing 727.

R E F E R E N C E S 1. H a r d i n , J . C . , F r a t e l l o , D . J . , Hayden, R . E . , Kadman, Y . K . , and A f r i c k , S . , " P r e d i c t i o no f Airframe N o i s e , " NASA TN D-7821.

2 . Hayden, R . E . ( 1 9 7 2 ) . " N o i s e f r o m I n t e r a c t i o n o f F l o w w i t h R i g i d S u r f a c e s : A R e v i e wo fC u r r e n tS t a t u s o fP r e d i c t i o n R e p o r t No. 2 2 7 6 ; a l s o NASA T e c h n i q u e s , " BBN CR-2.126.

3 . Hayden, R . E . ( 1 9 7 2 ) . "Fundamental Aspects of Noise Reduction from Powered L i f t D e v i c e s , "I n v i t e dP a p e r , 1 9 7 3 SAE N a t i o n a l A i r T r a n s p o r t a t i o nM e e t i n g , Miami, F l o r i d a .

4 . Hayden, R . E . , Kadman, Y . K . , a n d A f r i c k , S . ( 1 9 7 4 ) . "An Approach t oD e t a i l e dD i a g n o s t i cC a l c u l a t i o n so f Airframe N o i s e , " BBN R e p o r t No. 2 7 9 1 .

5 . Hayden, R . E . , Kadman, Y . K . , and Chanaud, R . C . ( 1 9 7 2 ) . " A S t u d yo ft h eV a r i a b l eI m p e d a n c eS u r f a c e Concept as a Means f o rR e d u c i n gN o i s ef r o m J e t I n t e r a c t i o n w i t hD e p l o y e dL i f t - AugmentingFlaps," BBN R e p o r t No. 2399; a l s o NASA C R - 1 1 2 1 6 6 .

6 . Hayden, R . E . , Kadman, Y . K . , B l i s s , D . B . , a n d A f r i c k , S . ( 1 9 7 5 ) .

" D i a g n o s t i cC a l c u l a t i o n so fA i r f r a m e - R a d i a t e dN o i s e , "p r e s e n t e d a t t h e A I A A 2ndAero-AcousticsConference,March, Hampton, V i r g i n i a .

7 . H e l l e r , H . H . , Holmes, G . , a n d C o v e r t , E . E . ( 1 9 7 1 ) . "Flow- I n d u c e dP r e s s u r eO s c i l l a t i o n si nS h a l l o wC a v i t i e s , " J . Sound V i b . 18, N O . 4 , 545-553.

8 . H e l l e r , H . H . and Bliss, D . B . ( 1 9 7 4 ) . "Aerodynamically Induced P r e s s u r eO s c i l l a t i o n si nC a v i t i e s :P h y s i c a l Mechanisms and.

S u p p r e s s i o nC o n c e p t s , " AFFDL-TR-74-133.

9 . H e l l e r , H . H . and B l i s s , D . B . ( 1 9 7 5 ) . "The Physical Mechanism o fF l o w - I n d u c e dP r e s s u r eF l u c t u a t i o n si nC a v i t i e sa n dC o n c e p t s f o rT h e i rS u p p r e s s i o n , "p r e s e n t e d a t t h e A I A A 2nd Aero-Acoustic Conference, March, Hampton, Virginia.

1 0 . H e l l e r , H . H . and Widnall, S . ( 1 9 6 8 ) . " C o r r e l a t i o n o f F l u c - t u a t i n gF o r c e sw i t ht h eS o u n dR a d i a t e df r o mR i g i dF l o wS p o i l e r s , " BBN R e p o r t No. 1734; a l s o J. A e o u s t . Soe. A m . 4 7 ( 3 ) ( 1 9 7 0 ) .

11. Heller, H . H . ( 1 9 7 4 ) . Experimental work performed under con- t r a c t t o NASA L a n g l e y ,p r e s e n t l yu n p u b l i s h e d .

12. Jones, G.W., Cincotta, J.J., and Walker, J.W. (1969). "Aero- dynamic Forces on a Stationary and Oscillating Circular Cylinder at High Reynolds Numbers," NASA TR-R-300.

13. Karamacheti, K. (1955). "Acoustic Radiation from Two Dimensional Rectangular Cutouts in Aerodynamic Surfaces," NACA TN 3487.

1 4 . Rossiter, J.E. (1966). "Wind Tunnel Experiments on the Flow Over Rectangular Cavities at Subsonic and Transonic Speeds," Royal Aircraft Establishment ARC R&M 3438.

NASA-Langley, 1916 CR-2714