How are the noise prediction procedures described in the report developed?

The noise prediction procedures are primarily empirical and incorporate techniques from both published literature and internal methods used by Boeing.

What is the significance of the logarithmic nature of noise levels mentioned in the report?

The logarithmic nature of noise levels means that even small errors in noise estimates can result in large errors in the estimated area of noise contours.

Is there a guide available for using the computer programs mentioned in the report?

Yes, a companion report provides a user's guide for the computer programs developed for noise source estimation and contour calculations.

Aircraft noise source and contour estimation — 19730023213 (1973)

Q: What types of aircraft does the report cover for noise prediction?

The report covers five basic types of aircraft: turbojet, turbofan, turboprop, V/STOL, and helicopter.

Q: What is the purpose of the noise contour estimation program?

The noise contour estimation program calculates contours of equal noise level (footprints) and the area within these contours for an airplane during takeoff and approach operations.

Document

NASA CR-! 14649 AIRCRAFT NOISE SOURCE AND CON TOUR ESTI M ATIO N By D. G . Dunn and N. A. Pea lx ' !

i ,: J u l y 1 973 A v a i la bl e to th e pu blic |N A % ;A - C E- 11 _ 0 _9 } AIEC£A ? T NOI S _ 3 OU_C E NI J =3 1 9_5 A N D CONT OU R E S TI H A_I G _ (dO e il_q Com m e c cial Air p lane C o ., Sea t tle) 2 3 3 p H C $ 13 , 75 CSC L 2 _A [ J n c la_ G3 / _ 2 I H1 ¢ _ J Pr ep a r ed u nd e r c on t r a ct NAS2 -6 9 6 9 by Bo eing Comm erci al Ai r plan e Comp a ny .0 . r ' .O. B ox 3707 Sea ttl e , Was hi ng t on 9 8 1 2 4 f or Ames Rese ar c h Center N A/ a u N AL A ERON A U TI CS AND SP AC E AD M I N I STR A T IO N I . Re po r t N o. [ 2 " . Gov er n me n t Acc os s i o n No. 3. R e t:i p ie n t 's Cat a(og No.

NA S A C R - I !464 9

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4. Tit le and Subtitle 5. Report Date AIRCRAFT NOIS E SOU q CE AND CONTOUR ESTIMATIO N J uly 1 . 9 73 6. Performi ngO r g a niz a t i on Cod e 7. Au t hor(sl 8 . P e r f or m ing O rganization Repo r t No .

D. G . Dunn and N. A. P e art D 6 -60233 1 0, Work U r . i t N o.

9. P e rfor m ing Organization Na m e and Add ress Boeing Comm e rcial Ai r p l ane Company 1 1.contr a ct orGr ant No , P.O . BOX37 0 7 Seattl e, Was h ington 98124 NA S 2-69 6 9 t 13. T y pe of Rep o rt and Period Covered 1 2. Spo n soring Agency Name and Address [ Contra c tor Report Nat ion a l Aeron au ti c s a nd S p ac e A dm i n i s t r a tion | 14 , S p o ns o r i ng A g enc y Cod e Wa s h i n gton, D . C . 20546 I 1 , 5 . Supp l e m e n ta ry N o t e s Comp ut er p r o gra ms m a y be o bt a in e d f ro na Project Manager, D. H. Hickey COSMI C , C omputer Software Management Informat i on C enter NASA-Ames Research C e nter 112 Barrow Hall, Univ e rsi ty of Geor g ia Moflk'tt Field, California 94035 Athens, G e orgia 30601 1 6 A b s tract Calculation proceduresare pr e sent e dfor pr e di c tingthe noise-timehistories a nd noisecontours (footprint s ) o f fiv e basictypesof a i rcraft: turbojet, turofan, turboprop, V / STOL, and h e licopter .

Th e pro c e du r e s h av e b e e n c omputeriz e dto facilitate pr e dictionof th e nois e chara c teristics during ta ke o ff s , f lyov e rs,and / or landingoperations.Th e user's guid e for the co m put e r pro g ramsis pr o vid e d i n a c ompanionreport, NASA CR-i 14650 1 / , g e v W o r s t s IS u g l(jcs t ed b v Aueh ot ( s ) ) 1 8. D i s tr i b u t i o n S e a t o , m ent Aircraf t n o i s e pr ed iction Uncla ss ifi e d unlim i t ed Noise ' ;u p pr e ss ion A c o ' e sti c l i ning w_ ll n c la s,_ i fic,I | Unc l ass i f i e d 24 1 53 .00 * For salt? b Y tho Nflfion, 'a r , l_ J ' I n form at i on , '3.3t rice . Sp r in g fl 01d . V ir g i m a 22 1r _1 CONTENTS Pa g e 5.1.2 Geometr y S olut i on ...................... !6 5.1.3 Noise Extra p ola t ion ..................... 2 i 5.2.3 C or e a nd T ur b i ne N ois e .................... 1 0 8 5.2.5 Propeller, Heli c o p ter, and T i lt Rotor Noi s e ............. 14 8 5.3.1 Acousti c D ata ........................ 17 8 5.3 . 4 Ar e a Calculation ....................... 1 8 1 AP P EN D I X A - T heoretical G ro und Re fl ec t i o n Pr ed i c tio p P r o cedure .......... 1 83 REFERENCES .............................. 22 7 AIRCRAFT NOISE SOUHCE AND CONTOUR ESTIMATION By D . G. Dunn end N. A. Peart Bo e ing Commercial Airpl a ne Company

1.0 SUMMARY

Refle c t in g t he need for analyzin g and , if po ss ibl : , re d_) cin g th e community noi se r es ulting f r o m a i r c r af t op e r at io ns , th e Boeing Co m m e r ci al Airp h m e Compan y , under c ont r a c t to NA S A- A m e s , h as de velop ed a c o mp uter program for pr ed i c t i n g the noise g e n e r a t e d by live basictyp es of a ir craf t: t u rbojet , t u rbofan , turboprop, V / S T OL , a nd h e licopt er . A s e c ond p ro g r a m ha s b e e n de v e l oped wh i c h calc u la t es c ontours of e qu a l n ois e lev e l (footprint s ) a nd the a r e a within th e c on tour s for an a irpl a ne d urin g tak e off a nd ap pr o a c h operations. Th e footpri n t p rogra m is c o m p a tible with t he NASA-Ames fl ight sim ulator. T h e fl i ght simulator p rovid e s a e rod y n am ic a n d e n g in e p e r fo rm ance d at a , an d _ he footpr in t pro g ram c al c ul _ es c ontours for equal n oi se l e v e l , t here by p rov iding a n e sti m ate of t h e n oise e xp o su r e p roduced b y a n aircra ft o p erati o n. Typical resul t s from the computer programs are shown in figure 1. These computer programs are intended t o _ssist air, : r aft designers b y identifying the noise characteristics of various aircraft and engine c o nfigu ra ti o _ls. These n o i s e l evel s can the n be c om pa r ed to co mmu ni t y n oise g o als.

Aircraft noise predic t ion techniques used with i n the a viation community arc usually based on emp i rical d;_ta and t he resul t ing procedures var y . These differences arise in numerous ways; e.g., ( I } t he sanlt acoustic data can be formulated into prediction procedures with var y ing degrees of sophistic_ttion and c omplexity , (2) differe n ces in noise measurements do occur in simi l ar te c _ when some of tl,,c important variables can not bc controlled, and ( 3) the complexities in noise _. }.eration a n d propa_.,ation h a v e f o ste r ed more than o a c theoretical view of the phenome n a involved.

l ' hc sour c e noi se pred ic t i o n a n d ex tr a p o l atio n tech n ique s p res e n ted in t h i s r ep o r t re p r esent t he sta t e of the art durii, g the c ontra c t time p eriod. T h e procedures are primar i ly empirical. S o me p a r i s of t he procedu re s w e r e obt a ined f r om publish e d li t er a ture and in s ome inslances unpublished m e lho ds ustd w i thin th e B o e in g C o mme r c i al A ir plane Co m pa ny w ere e mplo y ed. T he s elec t i on of t cchuiqucs wc r c m_lde to pro vi de a b a se fo r compar i sons am o ng a i rcra f t de s ign choices and f or c v ;duatio_ o f ai r c r af t o perati o ns. ItoweveL r esults f ro m th ese procedures can n o t be expected t o agree c×; ' c lly wit h absolute n o i se le v e l s calculated h y ot h er schemes. I n ma ny ins t a n ces , a n cugine / air_rame confi_.,uratio n has its own pecul i ari t ies. These peculiaritie_ ma y re q uire c m x ectio n s Z NOISE $ 3UR C E ESTIMATOR PROGRAM RESULTS • PER I_ EIVED NOI S E LEVEL (P R L) v s . TIUE • EF F ECTIVE PERCEIVED NOI S E LEV E L (E P NL) • S O U _ I D P R E S SU R E LEVEL ( S PL) S PEC T RA v s . T IME _v X Y ¢ / a EERVER NOISE CONTOUR ESTIMATION PROGRAM RESULTS • EPNL OR M A X IMU N PNL CONTOUR P OINT S • A R EA W IT H IN EACH CO N TOUR . _ . _ . / .. j _ TYIqC _ L) • NOISE E STIMAT ES ( E PR L Cw m A X. P N L) ON _ /" "" / " "' _ ' > ' _ """ ' _{"_ ' _ ' _" " " S I D E L I N E S F R Otl FLIGHT TRACK | i 1 !

X R E S ULT S GIVEN FO R EACH NOIS E COIIPO _E NT AT EACH ,. _ / _ ( / Tn _ r,x OBS E RVER / F LIGHT PATH SEGMENT OEF i 01ED BY THE USER. _ _ . . _ _ _ ,, _ ' _ REQUIRES NOI S E S OURCE P R EDICTIO NS OR E E ASURENENT S AI" _ 'Y A SERIE S O F P OINTS A S DI S CUSSED W S E CTI O N 5 .3.

FIGURE 1 .- RE S UL T S FRO M NOI S E S OURCE AND CONTOUR COMPUTER PROGRAMS I obc ap p ; ,c.I t o t h e p r e di c t.' d lev e ls for a pa rt h : u lar m)i s¢ source ¢.'on i p otl ent OI e h ;,I ng¢ , _ ill one o r more of t h e v a ri ous c a i _ : u l.'ltion m e t h ods of 'lur e d i n t his re po rt .

it i s e xtr eme ly difficult to ass e ss t h e , t ¢c uracy of nois e pr e diction procedures. T h is diffic u lty re s ult s fron i i_s uffi c ient data for known sources (individu a l c o m pon e nt sou r ces which combin e to giv e the total noi s_ , of _h e system), an o mali e s in m e asure d data. and th e s m all number of differ e nt e ngine / sour ce configuratio qs . Cem pari s on _ of predicted with m easured noise levels (Ef f e ctive Per ce iv e d Noise L e v e ls, EPNd B ) t or cu,' e .nt airplanes h ave shown tha*. t he tolerance for these m ethods is generally +5 EPNdB. It should be recognized that noise levels are loga r it h mic quantities, and an error in a noi se e sti m at e can result in a large error i n a con tv u: estimate su ch as area. H e n c e, t he tolera nc e for t he co n to u r estim ation pr o cedure largely depends on t he co nfidence level a ss oc iat ed wit h t he ac ousti c data that is used.

A des c ription of h ow to use t h e c o mpu t er progr am s is cont a in e d in a t ompa n ion r e port (r e f . I ) ° T h is portio n o f t h ,: r e port conta i ns t he e ngin ee ring description of t i_ e noise pr e diction procedure s em bodied in t h e , : o m put e r progra m s.

2.0 INTRODUCTION -i ] ' h e in c rease in c omm e rcial aviation i n t he last decade has been accompanied by incr e ased ' _ complaints rro m c o m muniti e s directly exposed to t he h ig h er noise levels as s ociated with aircraft to i nitial community ex p o su re attempts opera tio n s.

reduce t h e n oise h ave included c h anges in tak e o f f a nd a ppro ach proce d ures , develop m ent of a co u stic a lly tre a ted inlets and m ounti n g jet noi se S Ul _ pr e ssor s on t h e ex h aust noz z les . Also, Federal noise reg ul ations (ref. 2) h ave e s tablis h ed noise limi l s for ne w airplanes t ha t a r e significantly lower than first generation jet operation levels . "l _a is rec e nt emphasis on red u ci n g airplane noise h as resulted in considerable acoustics-related researc h _,_, 1d ew / o l _ m ent a ct i v ities _ T hese activities h ave been primarily direct e d tow ar d defining t h e noise t_ , . e rating a_cchan i sm s of a ircraft en gin e s a nd d e fini n g ways of r e ducing nois e at its sourc e t h roug h d es i g n i n novations and suppression d e vices.

T h e implemen t atio n o f noise reductio p tec hn olog y in engine, nacelle , a nd acoustic lini n g de. _ tgn has J es u l h : d i n a ge ne r at ion of qu i e ter a ir p l ane s , e. g ., t h e B oei n g 7 4 7, Do u gl as D C -I O , L o ck h ee a L - 10 1 I , a n d C e s s na C it a tio n. N um e r o u s o th er p rogr a m s ar e c ur re nt ly un der w a y, each wit h t he o b j e ct i v e of eit her r e du ch_g t he noise of cur r e n t a ir p la n es or dev e lo p i n g n oi s e tec hn ology for ap plic tho n to fut u re a i rc ra f t. T h roug h o u t the se re se a rch p rogr am s , t h ere ha s b e e n o n ly m i n i m a : e ffo r t d c vot - d to developing t he m e t h odology r e quired for pr e dict i n g t he tot a l c ommuni t y noi se p _ ' r tb rm a n cc of ne w air p l an es . T h is report r e pre se nts t he state of t he art c a lc u l ation p r o cedure for airc r a ft t ' otmn u nily ,i_ i s e p t 'cd i c tio n.

The current contrac t , NAS2-6969, h a s bee n c omp lete d i n t w 0 p a rts _-ph_ s es A and B (ref. 3).

Phase A (re f. 4) consi s ted of providin g re la_ :ively " crude " c om pu _eJ_ i _ed procedures applying t o noise source estimation of convent i on a l tu r bo je ts or turbof a ns. Also, par t of th e Phase A effort was t he develop m ent of co m p u terized pr oce d u re _F_ rnoise contour esti ma t i on adap ta ble to " r e abti m e" flight simulation. The computer progr a mswere d e signed to op e r a te on t h e IBMSystem 3 60 1 67 w i th th e additional re qui r eme n tt hat th e no is econ e .o ur p r o g ra m w ouldop er a te o n the Xerox SigmaVii an d VIII computers in conjunct i onwi t h th e NASA-Amesfligh t sim ulator, phas eB consisted of supplyi n g m ore advanc e dcomput er izedprocedu r e s f( J r n oi se sourcep re diction. Th e computer progra mf or t hi s p u rpo se hasbeen written to p r ovid e I / 3 octaveband nol l e e _ ti m a t esfor su ch configur a tions asadvanced t e chnolog y " quiet " e n gines, ri ft fans,lift / c ru is e fans,ejector / suppres s or , e - t blown-flap, pro p eller, helicopter , and tilt rotor aircraft , etc. , in addition to that for c onvent i onal jet a i rc ra f t . Al so , the contour pro gr a m h as been updated to be appl i cable for the m ore generalized re q ui r eme nts.

T he discus s i, 3 n _ ection of t hi s report ha s be en di vid e d into thr ee pa r ts. The first d e als with * , h e ove ra ll vi ew of the nois e prediction procedures. Th e second d e als wi th the description of the various co m puter m odules for noise sourc e esti m ation. T = b !e ! li sts the co m puter m odules i nc luded.

In e a ch of the comp u ter modules , th e user h a s the optio n t o s p ecify red u c ti on s on a spectr a l ba s i s wh e n suppre ssi o n device s a r e employ e d. For th ese si tuations wh e r e lining is in s tall e d, a ca lc u l a tio n p roced ur e app lic a bl e to opti m ized, s ingle or double l a y e r li n i n g s i s a v ai l a bl e . The se p ro ce d u r e._a r e i n cluded i n the n oi s e _ o u rce es tim a tio n progr am for tho s e item s n o t ed i n the l is t for th e n oi se s o urc e c o m p u t er m od u l e s i n t ab le ! .

After the in divi dual noise s ou r ce s pe ct ra are comput e d for a datum condition (free-field, 1 meter fro m source), e xt ra polati o n tec hn i que ' a re t hen u s ed t o adju s t the d a t um s pectra to correspond t o t h e noise ob se rved a s the aircraft ,de s by an ob se rver. Th e spectr a obtaine d are functions of t ime and per m it t he c a lcul a tion o f the effective p e rceived noi s e l e vel during t a keoff a nd / or landing.

The t h ird p ar t of the di s c u s si on deals wi th the procedures us ed to c a lc u late noise conto u rs . At t h e discretion of t h e u s er, an a ddition a l output of t h e noise s ou r ce progr am can be a s et of tabul ar dat a on IBM c a rds to define a n a cou s tic data routi n e for the noise contour p r ogra m . The acou st ic fun c tion c a n be eit h er peak perceived noise level or effective perceived noise level versus some engine perfo rm ance par am eter, r a n g e a t t h e closest point of a ppro a ch, a nd elev a tion a ngle . This f unction is t h en us ed fo r calcul a ti n g noi s e contou rs a s d escribe d in sect i o n 5 .3 . Th e co m puter progr am s for t h i s task ar e des i g n e d to r u n i n ' °r e a l ti m e " on the Xerox Si g ma Vll or VIll co m p u ters for flight s i l nulation s a.d in " batch mode " on the IBM System 36 0 / 6 7 .

TABLE I . - NOIS E SOURCEESTIMATION COMPU ' F ER MODUL ES NO. of M od u les • Me a su r e d Dat a 1 ® J et No i s e 5 a . S i ngl e e xhaust nozz l e b. C o - annu lar exh aust n o z zle s

c. Ejector / supp r es s o r*

• , d. Slot no z zle w tth a ug m en t e r ?'l a p* • e. Exte r n a ll y - b l own fl a p • Noise Gene r ated I nside Pri mary Duct 2 : a . C ore* I b . Tur bi ne* ® Co m pr e ssoror F a n No i se 3 a . In ] e t co m p r e sso r _r f an * b. D i scharge f an* c . Lift - fan s* • Pr opelle r, Hel i cop t e r a nd T t l t Roto r 2 a . Emp iri c a l w opelle r proc e du r e b. Theo r et i c a l p r opelle r / r oto r p r ocedu r es Tot a l 1 3 *Den ot e sop ti onal u s e o f l i n ing

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3.0 CONCLU S IONS

Th is is the fi nal repor t fo r c o ntrac t NA$2-6969. It describ e st he rest A tsf o r t he P h ase B portio n o f the contract. Empiric a l procedures are desc ri bed which r epresent t h e s : ate of t he a rt a nd a re t he best approachesreadil y at hand for estimatin g t h e community noise levels fo; the fi ve basic types of _ ircraftmentioned i n t h e su mm ary. At t h e present time , comprehensive the o retical p r o c ed u res do no t exis t f o r n oise prediction for all t he a irc ra ft mentioned. In some cases, t h eo r etical m ethods c a n be co mp uterized, b ut they are computationail y expensive, require m o re detailed i nfor m a tion t han i s r e a dily available,and do not provide signi fi cantl y more accurate absol u te levels t han that obtained _,_,_ by empirical mea n s.

'_ Pas t experi e nce h as s h own t ha t w h en suppr e ssiondevi c es are t _ , s ed to reduce t h e a c oustic lev e ls of major n o ise source(s); new noise sources always a ppear. New predicti o n p r ocedu l e s must b e co n ti n uall y develo pe d to refl e ct the noise contribution of t h e new s o urces. Also, t h e exis ti ng procedu re s m ust be conti n ually re fin ed to reflec _ the c h ange i n engi n e des i gn and t h e dem an d for increasedaccuracy.

4.0 RECOM MENDATI O N

in gener al , aircraft noise prediction met h ods wi l l c h ang e as tec h nology improv e s;therefor e , it is recommended t ha t t h ese procedures and th e corresponding comput e r progra m s be pe riodically revie w ed a nd updated. To provide guidance on futur e dev e lopm e nts and to gain a b e tt e r underst a ndin g of t h e mec h anisms involved, a t he or e tic al analysis s h ould accompany any - _ , visionsof th e e m pirical procedures presented h erein , -i 5.0 DISCUSSION t 5 .1 MAC RO SCOPIC VIEW O F TIlE P R OBL E M Noise p r e d ictionproc e d ure s h a v e b e end e v e loped fo r five b a sictyp e sof a irc r aft : tu r boj e t; turbof a n;turboprop;V / STOL; . _ ndh e licopt e r.Fi gure 2 s howsthesep r op ul sion s y stem_an d the t yp es of noi se sourc e s a ssociat e d wi t h _ ch ty pe . Of t h e fiv e b a sictype so_ [' a ir pl a n e_ ,th e V / STOL aircra ft i s th e m ost co m plicat e d becaus e o f t h e d if f e r e nt hi gh - _t t confi _t ions pg _ . - _ ntgy b ei ng c onsid e r ed - bl own-fl a p, a u g men to r owi n,g , l ift fan / j e t and tilt r o t o r . In 3 d Ji tion , t he V / STOL config u r a tions ma y hav e m or e t ha n on e typ e of pow e rpl an t, L ¢° , conv e ntional t u rbof a n wing , ! , mounting wi th lift fan s in the win8or lift jetsattached t o th e airplan e ' s f us e lage.

i { t In orderto p r ovi de th e fl e xibi fi W r e qui re din predictin g th e no i s _ f r o m th e sev eral source contributors fo r a givenairc r aft, the app r oach s hownin figur e 3 isu se d.Th e p red ictioncon s ist s of _ four s teps: l ) Solutionof th e Rig h t P a th / O b server Geom e t r y: in thi s step th e airpl a n e b _ st _ medto move al onlga straight n ine,i.e., con s t a ntclimb IPm di ent. At an gu la r inc iden t s o _ ' 1 0°, 2 0 _ , o .. 1 70°betw e e nth e flightpath an da lineto the o bs er v e r, sa m p li n g points ,f o r th e ai r c r aft's p os ition ar e taken whic J_ corre s pond t o a s e t of o bs e rv ati o n tim e s duri ng t he fright when the nois e is h e_ d. At each a _r cra f t posi ti on, all geo m etrical terms re q u ired to e xtrapolate th e nois e f r o m the source to t he observer ag e determined . After t h e _ drpl a n e / observer ge o m etry is defi n ed, the next step considers the orient a tio n * of the noise s o urces.

2) Cal c ulatio n a nd Summatio n of th e So u n d lev e ls f o r Each Sou r ce: For each point a lon g the fli gh t path se gm e n t ,spherical coordin a te an g l e s relati v eto th e n ois e source r e fe r ence a xis ar e calc u lated. S ee ( q _ , q _ o, 0 o) in fi gur e4 . Th es e an _ les describe the location on a sphere about a source where the nois e is to be d e termined.

Th us, non - axi al -sy mm et ri c** radiation patte r ns can b e conside re d.

*The a ngu la rori e n ta tionof the gross t l _ ust vect o r fo r a pow e rpl a nt a bo u t t h e alr c e aft' s l a t e r a l a x i s w i t h re spe ctt o t h e ho riz o n .

* _E x ce pt fo r conventional si n gl e e n gi nea ircr0lt,the r a 4i _ tio n p _ tt e rn s will be no noa xip_l° s y mme tric.

T U RB OJET TU RR O; , ' A N _ . PRIMA RY l ET | , PR IM ARY & S E CO NOA R Y " * _ 2 . COR E G TURBI N E 2 . CORE & TUR Bi H _ : " ). COMPI' _E_$ O _ ( If ' _ LEI") ). F A N (INLET & E XIT) ,i " : , i STOL (BLOWN FLAP) -- TURBOFAN 1. P RIM AR Y JET I . PRIMARY& SECONDA R Y , JET M O D IFIE O FOR 2 ° CORE & TUR B INE BLOWN FLAP 3. COM PR E SS O R (INLET) 2. CO R E & TURBINE 4. P R OPELLE R 3. FA N (INLET & EXIT) STO L (AUGMENTOR-WlNG. _ -- TURBOFAN SLOT NOZZLES I o PRIMARY & S E C ONDARY ,JET M ODIFIEG _ - ' O R AUG M ENTO R WING 2. CORE & TUR B IN E ). F AN ( IN L ET & _ XIT) FIGURE 2 .- REPR E SENTA TIVE _ ) ROPULSIO N SYSTEMS AND NOISE SOURCES FI G URE 2 .- CONC I. UDED

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, L , _ H T Cx " - ": Xl o , i_ N XZ _.... .... _E_ M _ ,T . X N , 0 "' " _ -- " 1 " Z RL_t / - - -- Y :, t ( _ CA L CULATION AN D S UMM A TI O N OF S PL _ S NOISE S O URCEP RE_ !CTIO N i ', ii FOil EACHSO UR C E , _ , & X MODULES 3 ) S UM MA TI O N O F SP L e S k _ GEOMETRY FO R E A C, H _ & X OT A , . L K = ! SPHERICALCOORDINATES

......i.... i ; flail?

, , i T t _ - • _REE-F , ELO

.... • I N DEX SPEC TR A ( _ ) N OISEEXT RA POL A TIO N e ( V J OR ) / ),! OCTA V E B _ k]DS I 1) & SP Le $ F OR EACH _ & X 3 ) I N STALLATION & SUPP P E. _I_ ' _ • S P H E R ICALDIVERGENCE EFFECT S • A TMO S P HERI C _B SO R PTIGN • LINI N G • EG A • SU PPR ESSOR NOZZ L ES • GR O U N D R EF L ECTIO N • O THER (CORR E CTIO NS ) 2 ) TIME NOISEI S HE ARD FOR EACH _ _ X _) F LIGHT E FF ECT S 3) SPL' _ I "SPL' S I " -_ , ' P L't S • VR C A LCU LA TION B AS ED O N I X TRA P ]I N PEX VELOCI ' i Y VECTOR S FOR EA C H _ & X • DO P PLER (O P TI O NAL) ( _ HU M AN RE SPO NSE ME AS URE M ENT V Z ® C ALC . OF PNL VR S . TI M E e , CA L C O F EPNL R _G I ,, p _ _ _ -_ p U OR_ FIGURE 3 °_ COMP U TAT/ON S E QU E NCE

v!

\ I _ . + ,v. ,, ,, , . ANt , o_ _ O , R_CT IO N O _ ' " OT ' ON

\ , (_ _ +++ + ++_ _ ++ .. _.+ . + ++ . . .

_' / _,;++ r _,. +o_. T A W '[I x l/-.< YC O S +E + Z N S IN+E'J

. o, - / _ , _ ...--- _ +. c o_ [- ,_ c o_ +_+ _,_,, +_, / , _ ,]

,, , W Hmm e :_ " - ( X+i+ V i ' +:N _ ) _ . . , MM {U , V) P LAN E + E s ENG IN E ATTITUDE OR FLAP / _I GLE D I RECT I O N OF M OTION

v_ _+.+ : __ _ _-_ ,, o+

V R- CV j 2- 2 V jV 0 C OSa + VO 2 W H E R E: Q +" 6 E - TA N -I(GRAD I A V0 a VE L OCITY VECTOR OF AIR S PEED RELATIVE TO N O ZZ LE SPEED RE L ATIVE _ j m VELOCITY VECT O ( _ FOR JET TO NO Z ZLE A A A V R 8 Vj - V0 m V ELOCITY V ECTOR OF JET + SPEED RELATIVE TO AMBIE N T A IR FIGURE 4 .- ENGINE ORIENTA T/ON A ND FL IGHT CONSIDERATIONS i !

T h e no i s e at tr i b u ted t o ea c h s ou r ce i s th en c al cula t ed and su m m ed t o fo r m a total of al ' th e sound s o urces at e ach aircraf t position. Th e nois e lev e ls thus form e d repres e nt fre e-fi eld, in de : : t l / 3 or I / l ) o c t av e band sp ec tra, on a spher e ( r adius = l meter) radiating t owa r d th e o b s e r v e r at e a c h po s ition c onside re d along the flight path seg m en t .

3) Extrapolati o n of th e Ind e x Nois e Sp e c tra: I n thi s ste p , sound a tt enuation du e to spheri c a l divergence, atmospheri c absorp t ion, and e xtra - ground - at te n u a t i o n is c onside re d (r ef s. 5 th r ough 8). In addition , th e in t er f er enc e phenom e na of g r ound r e flecti o n is included as an option (s ec tion 5.1.3.2 and appendix A). The results from this step r epr e s e nt the total (1 / 3 or l / l) octave b and spectra versus time received b y the observer as the aircraft pa s ses b y .

4) Human Response Measures: _ ' h e extrapolate d spectra ar e u s ed to calc ul ate th e h uman re s pon s e m e a s ures ; Per c eived _it A ois e Lev e l (PNL ) , tone-c orr e c t ed P NL , and E ffect iv e Per cei ved Noi s e Le vel (E P NL ). Th e _!' EPNL is d et ermin e d b y int e g rat ing t h e a nti lo g ari t h m ( Ba s e l 0) of t h e to n e-co rre cte d PNL i l< wi t h resp ec t t o t ime ( r e f s. 2 and 9 ) , n o t f r om a t rans f er curv e as w a s d o n e d u ring P has e A _ : _ of t he curren t cont r ac t ( ref. 4). Since t he r e i s some qu e s t i o n regarding t ile validi t y o f t h_ fl tone- c orrecti o n p r ocedure , an estim at e of the e ffective percei v ed noise le v el EPNL is provided, based on the regular PNL-time history. Occasionally, the procedure gives a tone-correction when in fa c t no tones can be obser v ed in the l / 3 - o ctave or narrow-band spectra . This estimate is denoted in the computer output by an aste ri sk beside the E P NL label. T he omission of a tone penalt y also solves the problem of o btaining an EPNL estimate when only full octave band spectra are available and tone-corrected PNL's can not be calculated. Further detail on each s t ep men t ioned ab o ve is presented in the following sections.

5 .1.1 De fi n it i ons / Lim it ati ons / Assu m pt i o n s 5. 1 . ! . 1 Fl i g ht a nd Wea t her Co nditi o n s T i le noise pred i ction pr o cedures defined herein are limited to fl ight oper a tions, where the airplane speeds are less than M ach 0°35. The SAE procedures ( refs. 5 throu g h 8 ) that are used for noise extrapolation are limited to _he following weather conditions: I Tempera t ure - 10 to 32 ° C (30 ° to q 0 ° F ) Relative humi d i t y 30 % to 100 ' 7,, D o wnwind 0 t o 16 km 9er hr ( I 0 mph ) l I Figure 5 sh o ws the " weather windows " that are curre n t ly recommended b y the SAE for acoustic testing and by the FAA fo r n ois e cert ifi cation of n ew aircraf t° 5. i. 1.2 Index / Free-Field Spec tr a The far- fi eld noise data used to develop t he predic t ion methods in t his repor t contained atm o spheric and groundeffects t h at areinheren t in most acoustic tes t data. Th ese e ff ects have been estimated and rem o ved from t he data, i.e., the da t a was corrected to free- fi eld condi t ions (no reflecting gr ound plane) and extrapola t ed back to a distance of I m e t er from the source (assu m ed a poin t ) in , ." der t o remove a tm ospheric ab s o r ption. T h e resul t i n g spectra are given t he term "Index / Free-Field Spec t ra. " They do not representthe levels which would be observed at one me t er from an en gi ne, bu t rather far- fi eld levels ar ti fi cially synthesized in order t o remove t he effects mentioned above.

5.1. ! .3 Far-Field / Po in t Source(s) ,o Th e a cou s tic far-field i s defined a s tho s e di st a nces gr eate r th an or equ a l to te n t i m es ti l e ..... !1 _ acoustic wavelength of interest , o r ten times t h e c h aracteristicsource dimension. At t h ese distances , the noise obse rv ed m ay be considered t o have origina t ed a t a poin t . Th us, t he spacing between engines , e t c. , can be considered negli gi ble , as th e o b server is suf fi ciently far away fro m t h e airplane such t ha t th e noise appears t o he emi t ting from a single point.

5.1.1.4 Noise Ex t rapolation SAE procedures (ref. 5 t hrough 8) are u s ed for extrapola t ing th e datum spectra (Index, Free-F i eld) to other positions in the acoustic fi eld. T he ex t rapola t ion procedures consider th e attenuat i on of sound due t o spherical divergence , a _i nosp h eric absorption , and the turbulent boundar y layer near t he gr ound.

If the acoustic impedance of t h e ground is known , the in t e r ference phenomena due to ground reflec t ion can be es t i m ated (sec. 5.1.3.2 and app. A ) . O t herwise , it is assu m ed t h a t t h e obse rv ed noise levels will be typically free- fi eld plus 3 dB-the nominal effect of ground reflec t ion.

5. 1 .I .5 Sc a l ing F o r each noise c o mpon e nt, i t is assum e d tha t t he n o ise and t he t hru s t f r om different powe rpl ants can be s c a l ed f or com p arisons , if the powerplan t s pass e q uivalent mass flows when ope r ating at _he same gasd y nami c c onditions. The s c ale fa c tor is de t ermined from mass flo w measu r em e nts: 1 3 SAE " WINDOW" "AA " WINDOW " U J 0 /,/1 ;; .. ,, , - .. ._ ' _ \ / , " i. /// i / " / .. _ // ' , 1 ,, , ,, ".'.. /i ._l ' % \ ., , _ , .' , , /// , . ,/ " , .7 t i , /. d p , ''. . . .. .-.

0 0 ,,;. :,. !)!i iiiiii iii iii !i! ii i ', ii!ii : ' " '"

i * . / ] " . , . _ i_ii;ii}!!!_i_i_i_i_}iiil}iliiiiiii " , , • STANDARD DAY _ .' : '-"-'" .... ; __iiiiii!iili!i!!i : ,i i i!iiiii "' " ( 7 0 %HU MI D I T Y . I S =C) ' • ,. _: : _i_i_i_! _i_iii' i_iiii_ " .'.; X , ! / " / I ll ,. _' /" _ // > _LI ll= _ # ' I '. / ,/ , / ' . I # " '/ ""7 '" . ", ' ,' - ' " . ' i : ; I I . I , I • I • J ,,.., oF • 1 0 20 40 50 8 0 i 00 t [ f

i-_ -l o o l o _, o : l o

A WE N _ " T E MPERAT URE

LEGEN D S MALL(REF. 6) '==1 COU S TI r TE S TING W EATHER:CO R RECTION S T O S TA N DARDDA Y CO NDITION S ARE • : _ ACOUSTIC T ESTING DONE DURINGTHESE C O NDITIONSMAY REQUIRE ATMOS P HERIC ABSORPTIO N CORRECTIONS(RE F . 6 ) DO NOT MAKE ACOUSTICTESTS:DATA CANNOT BE ADEQUATELY CORRECTEDTO STANDARDDAY CONOITIONS(REF. 6 ) _ NOISE CERTIFICATION FLIGHT TESTS M AY BE CONDUCTEDUNDER THESE C OND I TIONS (REF. 2 ) FI GURE 5 .- WEA T HE R " W IND OWS " FO R AC OU S TIC TE STING (!)

Scale F a c t o r = _ml / m2 w h ere Oh ! , t h 2 ) are t h e m ass flows of two different powerplants operatinga t identi c al gasdyna m i c s, i .e . , Ma ch nu m ber and t em perature. Thus, the a co ustic and perfor m ance data for en gine t w o c an b e scaled to en g ine one by multiplying all linear dimensions , including acoust ic wavelength , by t h e scale factor. N ote t h at acoustic frequency is inversely proportional to wavelengt h. S ince t h rust is propo r tional to area, it s c a} _ wi th t h e square of t h e scale fa c tor.

5 . 1.1. 6 Mul tiple E ngin e s F or multiple e ngi ne a i rc r a ft , a n in c rea s e in noi s e i s ob s er v ed over t l w d predi c ted for a s ing l e e n gi n e . I f N ide n ti ca l s o u r c e s a re p re s e n t wi th n o i n ter f er enc e , the i nc re as e is AdB - - " 10 lOgl0(N) (2A) However , it h a s be e n fou n d (re f s. 7 and 10 ) tha t the in c re a se in n o i s e p redic t ed by equation ( 2 A) i s too high for sound which propagatesnear a je t e x hau st of a n ad j ace n t e ngi ne in order to re a ch t he obse rv er. An e m pirical rela t ionsh i p has been de v eloped (ref. 10) for predicting th e c ha nges in ai rcraft-generated sound a t tributed to t h e a t tenuation / scat t ering / refraction effects caused by j e t effiuxes. This effec t is e x pressed as a function of t he n u mber of iden t ical eng i ne s N, azi mu th ang l e ¢ o, and eleva t ion a ngle _ o s h own in figure4. The formul a is (2 B) LOG 10( N ) Th is a ssumes t ha t th e en gi nes ha ve c o - pl a n a re xits a nd t ha t th eir cen t erlines li e on a common pl an e.

S c an t i n for mat io n i s avai l a ble for e s t a bli shin g t h e i n fl u e nc e of f us el a ge / w i n g sh ieldi n g . F or c o n ve n tio na l j e t tr ansp ort s; i . e ., e n gi n e s m o un ted un der t h e w i ngs, t h e effect s ha ve n ot bee n o bs erved . Ot h er ty p e s o f e n gi n e mo un ti n g s re qu ire a dditio nal te s t s.

5. 1 . 1.7 Flig h t E f fe ct s T h e effe ct of a ir c r a f t motio n for j e t noise is acc o m pli ,Jh ed by t h e u se of the jet vel oci ty relative to t he amb ie n t ai r ( te l 7) a s t h e k ey pa r a m e t e r, i n ste a d o f t he j e t velo c it y rel a tive to t h e n o zz le .

How e v e r , an e xc e p t i o n to t h i s ru l e o cc ur s wh e n p redi ctin g t h e j e t n ois e for an au g m e nt er- w i n g (s e e.

5 . 2.2.4 ) . T he ov e r a ll so un d p re ssu r e l e v el d a t a for t his n oise s ou rce ( re f. ! 1 ) i s n o rma li ze d wi th r e s p e ct t o t o t al t em pe ra tur e an d n o z zle p re s s ure ra tio . Th e e f f ect o f a i rpla ne sp ee d o n t h is c o mp o n e n t is a t p r es e n t un kn o wn , be c aus e par t of th e je t n ois e is g en e ra t e d i n sid e the augment er fl ap and part is generated outside. In order to determine t h e e f fects of motion, a fl ight or win d tunnel test is required and the resul t ant acoustic measure m ents s h ould be co m pared to t h at for a n equivalent static tes t , i.e., free-strea m velocit y equals z ero , T h e other noi s e co m ponen t (core , turbine, fan, ro t ors, etc.) procedure s account for th e motion of the source by u t ilizing t h e r e sults from theory (refs. 12 an d 1 3 ). T he sound pressure lev e l spectra i-:!

are Dopp l e r -s h ifted, and a level correction , 10 lOgl0 (1 -M 0 co s _ ) n, is appli e d. Th e v al u e fo r t h e i _J exponen t , n, v a ries wi t h t he type of source being considered. Additional detail on t he co rr ect i o n s i.t for f righ t are presen t ed in sec t ion 5 .2.

i 5 .1.2 G e o me t : y S o lution "! The f i rst step in the procedure is the geometric solution for the air craft / source position versus , , L _'1 tim e. Th is i s require d fo r e xt rapola t in g th e inde x / fr ee- fi eld spectra t o the ob serv er a nd f or comp uti ng the n on-axial-symmetric n oise chara c t e ristics o f each so u rc e . The an al ysis f or t hi s solu ti on is shown below: Required Da ta (see fi g. 6) G RAD Climb gradien t, i . e., tan O for Z _ ZR X Sideline dis t ance Z 0 Airplane h eight a b ove t h e ground w h en at Y = 0 ZR Observer height above the ground / _ Angle between the fli gh t path and sound propagation pat h CA Averag e speed o f sound over t h e propa g ation path. Th is value is approximated by C A _ 0. 5 ( C z0 + C ZR) where C Z0 and C ZR ar e th e local sp e eds of sound at altitud e Z0 and Z R , re s pe c tively C Z Sp e ed of s ound a t a ircr a ft altitud e, Z . Th is v a lue is approximated by CZ _ CZ O M 0 A i r c r a ft Mach numb er 1 6

e

, C ) ) I &T =0 REF ° S OURCE (X , Y ,Z ) e I 10, ZR-Zo ZR)

) , T AN e

. -_ , _ , _ ,'

,. | I ZR & e =O t I I ,t z .

D

_t.

Z R

-T- V -

OBSERVER(O,O , Z R) "_ FIGURE 6 .- F LIGHT PATH SEGMENT GEOMETRY J ) Res u lt s (see fi g . 6) (Y, Z) Ai rcraftcoordi w t es P S ound prop a ga t io r , path di s ta n ce A P / P Relativeincrea s e in path length fo r groun d reflected signal 0 ! Angle of incidence for groundreflected signal r e lative to gr azin g incidenc e / 3 2 Elevationangle used in extra-ground-attenuationforn',ula 1 " Retarded ti m e when sound is gene ra ted relative to t he visual overhead r e ference; i.e., aircr a ftis at Y = 0 _ t Ti m e the observer he a rs tt ; e acoustic signa ), rela t ive to the vi s ual overhe a d i r eference . > , I Unit Vectors AAA (i, j, k ) (X , Y , Z) coordin a te sys te m ^ S Dir ect i on of flight _ =cos O _ + s in O _ N Dir e ction of sound propag a t e d

zN

with ZN = Z - ZR The basic approach in obtaining a solution f or the flight path ge ometry is to solv e the thr e e gov e rning e quations below for the distanc e Y, which yields a valu e of Z gre at er than or e qual to ZR.

if th e solutio n for Y yields a valu e of Z less than ER, it is assumed that the cli m b gradi e nt is z e ro, corresponding to the noise sourc e be i ng at th e obs erv er height.

A A P cos r, = P PN " S = ° [Y cos g + (;_ - Z R) sin g ] ( 3A) p2 = X2 + y2 + (Z . _ Z R)2 ( 3 B) Z = Zo + Y t a ng (3 C) 1 8 i1 ..............

i! J , ) t A value for Y is obtain e d by fo nn ing t he quadrati c e quati o n (4 ) , from th e substitution of e quations ( 3 B) and ( 3C ) into th e sq v are of e quation ( 3 A). Simplifi c ation yi e lds a y 2 . b Y + ¢ = 0 ( 4 ) wh e r e

_ , _,. a = (sin _ / cos O )2

/ ' i b = -2 Zno tan e sin2 _ c = Zno2 sin2 O - (X2 + Zno2) cos2 / _ Zno - Zo - ZR Th e roots of e quation ( 4 ) ar e th e n giv e n by Y=QI _Q 2 with QI = b / (2a) = -0. $ Zno sin (2 O ) Q2 = c os e 6 2 .+ (Zn o c os O )2 / tan / _ Substitution of both roots into e quation ( 3 A) e liminates th e e rron e ous (QI + Q 2) root and gives the solution

Y " Q 1 " Q2

( 5)

' Aft e r Y is det e n n ined, Z and P ar e co m puted using e quations ( 3 C) and (3B) r e spectively. Th e incr ea :, e in path l e ngth for the ground reflected signal is comput e d by A P / P _ _ - _ o I for [r [ > _ e ( 6 A ) I J = It m _ f o r [ r l< e ( 6 B) N... Q o B K K'I _ 19 + where r : _ / 45 BI = 0.St 4Z Z R / P2 i B k - -I" B k ( _ 11 _,; Once the distances are determined, the angles used in the extrapolation formula s are _' " _ def' m edby

° 1 = t an'l [:IZN ( 7 )

with ZN* = Z Z R _2 = s i n'1 [ ZN / p :] (8) Next, t he time that the soundis g ene ra ted and obs e rved i s co m putedr e lativet o the airc ra f t _ f ere nc e pos i ti o n(X , O, Zo), s h o wnin figur e 6. T h e :' e s ulting fo rm u l asa reas f oll o ws;i. e . , let d S z = y Z + (Z - Zo)2 (9A) dS = [sign of Y I _ 1 / _ 1: = dS / ( M o C Z) (9B)

t = 1:+ (P / C A)

This compl etes the geometry analysis requiredfor nois e extrapo h tion° if the o rientation a ngle ( 6 E) of th e noise source referenc e syst e m is give n , (see fi g . 4), the ( :, _ mpleteg e o me t _ for noise is determined u s ing p r , e _ . u-l, ; e, _ + = d_,Pectlvlty angle = cos'l[ =(Y cos 6 E + Z N si n_ E) / I P I ] (IOA) 2 O 1 I i iI _o '= aztm c_ thangle

= _ an'l[ IX I / - (Y cos8E + Z N stn _ )] (lOB)

, %= eleva ti on angle t a n "1 [ IY stn 6 E - Z N cos6EI / IXl ] (IO C )

NOTE 90°< ¢ b < 180° when (Y cQ ' ;a E + ZN stn a E)

t s pos i tive.

4 5 .1.3 Nois e Extr a pol at ion The pr e dict e d nois e components ar e tr e at e d as fr ee -fi e ld (ind e x) sp ec traat a r e fer e nce distan ce of on e m e t e r. The techniqu e s for e xtrapolating from th e sourc e to th e obs e rv e ra re basi c a! ! y th e sa me as thos e us e d durin g Ph ase A of th e c on t r a ct (r e f. 4 ) with t h e exc e ptions list e d b e low.

!) Ext ra -groun d -att e nuation (r e fs. 7 and 8) 2) Multipl e - e ngineeff e ct (s e c. 5 .1.1. 6 ) 3 ) Groundr e fl e ction (r e fs. 14 t h r o ugh 19) A re vision o f th e e xtra- gr ound-att e nuati o n methods was mad e to r e flect information obta i n ed from r e c e nt JTgD flight t e st data (unpub l ish e d) and to match th e standards (r e fs. 7 and 8) mor e _ * clo se ly .

"lhemu l tiple- e n gi ne effect c an caus e non-axia l -symmetric ra diation patterns; therefor e , i t w _ r e moved from th e e xtrapolation st e p a nd included as pa r t of the pr e diction me thods for e ach noi se | comp o nent (s e e.5. 2 ).

A t h e or e ti c alg r ound r e fl e ctio n p r ocedu re ha s b ee ninclud e d as _ us e roption(s e e. 5 .1.3.2). if the im p e dance of the refl e cting ground plan e i s known, the user of the no _ ;e sourc e prediction computer pro gr a m can esti m at e the eff e cts of this int e rf e rence p h eno m en _ inst e ad of using a 3 dB It addition to t h e free-field spectra.

Thus, the noi se extrapolation procedure, _ contain th e following four items (s ee fig. 6 ).

I _ I) Spherical diverg e nce( r ef. 7) 20 IOg l o(P / Po) w h ere Po = ! :net e r II 21 2 ) A tm o spher ic ab . ' ,o rption whe r e _( f ' ) _ ( f ) I P / 1 000l i s _he a v e ra_, _ : loss c o e ffi c i e n t (dB / K M) ov e r ti le pr opa g a t ion p ath .

T h is p a r a m e ter is a function of f requ e nc y , a mb i ent t @ mp c ratur e , a nd h umidit. i (r e f. 5).

3) i"x tra - gro un u -att e nuation EGA (f o P, // 2 )

--)

i " _ 4 ) G rou n d rcll ec tion GR f , P , 8 1 Z! KI w h ere ( ZI / Zo) a h ,a (KI / K o ) are ' ' ZO ' K0 i_ " Ih ,, nor ma liz e d i mp e da n c e and l,i wa ve n u m b e r respectiv e l y fo r t h e gro u nd .

Rcl'ercnc e s 5 an d 7 pr ov i de all nec e s sa r y detail on sp h eric a l divergence a nd at m o s p h eric a b s or p tio n, r e s p ec tivel y. He n c e t h e s e ite m s a re o m itt e d from f u rt he r di scus sio n he r e.

5 . 1 .3 . ! Extr a -Ground-A t tenuat i on (EG A) ' F h c bc :.l a v ail ab l e stam l a rd, in a fo r m us e ful lo t p r edictio n, i s cont a in e d in r eference 8 . T h is repor t (base d on a n a ver a ge of a large number o f measur eme nts) provides a pro c edur e for calculati n g e s tr a -gr ou nd- a tt e nu a tion as a fl m ction o f distan c e, frequency, elevatio n angle , and w ind direc t ion. This a tt e n uat k m is t h oug h t _.o b y d t_e t o a co m bi nat ion of two e ff ec ts: refr ac tion du e to wind a nd te m per atu r e gr a dic n ts : a nd disp e rsion du e to th e tu rb u l ent h _u nd a ry lay er. T h e l a tter i s n ea rly al wa y s pres ent; h ow e v e r, t he form e r do mi nales f o r upwind propagation. Unfortu n ately, t h e r efe r cn c e d ef in es t h e EG _ , for only a single wind v e loci t y _ I0 m p h. In addition , the p he nom e non is d tql n e d o n ly at so urce ] obs ur v e r he ig h ts of i.73 ,n e t e rs ( 6 ft.) for u p-wi n d prop ag ation. Accordi n g t o ref e r ence 8 th e a tte n u a tio n is e ss e ntially constant i n th e down wi n d sec t or (con e a ngles gr e ater t ha n 1 20 °) . Bec a use of t h e limitations , it h as b e en common ind u stry prac ti ce to use downwind pro pa g a tio n t ot w i n d sp ee d o f 1 0 mp h as a sta n dard.

Usi n g l !i is s t a ndard , E GA is a function o f dista nc e, fre qu ency, and el e v at i o , _ angle . Da t a are s h o w n i n t e K 'r e n c c 8 at e lev at i o n a n gle s o f 0-2 °, 1 0 °, and 20 ° . Dur i ng P ha s e A o| " t he co n tr ac t, t h i s d at a was re pr e, _e nted by a fuaction of the f o ll ow i ng fo rm: E GA (f , P. _ 2 ) = E GA ( I, P . 0 " ) e× p I - K f f ) w he re EGA(f, P, 0°) = EGA a t 0 - 2° ele v ation a n gle f = frequency P = dista nce / 3 2 = elevation a ngle K(f) = is c h osen to fi t the data at IO * and 20° T h is function was modified duri ng t he P h ase B e ffo rt because it pre d icted substantial am ou nts of EGA at h ig h el e vation angl e s , a p h eno me non not observ e d during flig h t t e sts ; e .g., n e arly 2 PNdB . |_ at // 2 = 30° f or 0.25 N .Mi. side l ine nois , , e _ timates. Durin g the JT8D Retro fi t Feasibility Study for DOT / FAA, a large number of nois e measurements were ma de a t va r ious altitudes from 122 M to 2 7 50 M and at several thrus _ values. A minimum of three flig h ts were made at ea ch altitude a nd t thrust. From a p r e lim i n a ry analys i s of t he data, i t a pp ea r 5 t h at EGA approac h es zero a t eleva t ion _ !

angle s g r¢_er th a n 45 : In view o f t h e ab ove , a t h ird fo rmu l a, w h ic h goes to ze ro a t 45 ° an d line a rly c o n n ects the d a t a i n ref e r en ce 8 w as c h os en un til better d ata b ec o m es ava i l a b l e. T he f or mu l a i s O EGA(f, P, _2) = EGA(f , P, 0 ) F(_, f) (I I ) I w h ere EGA(f , P, 0°) is obt a in e d by line a r interpola t io l_ wi th re s pe c t to lo g (P ) and lo g ( f ) on t he d a t a g i ve n in t a ble 2. Th e f un ct i o n F ( _2, 0 i s sh o wn in f i g ur e 7 an d is tabu l at ed in t al ) le 3.

5. 1. 3 . 2 Gro u n d R efle ction

¢

T h e p arti c ular m od e l c o n sid e r ed is a poi n t s o urce , , h o m og ene o us m edi a (a i r a nd grou n d ) , a n d a sm oot h / i n fi n it e / r e fl ect i ng p l an e w i t h co m p l e x ac ou s tic wav e i m ped a nc e b as e d o n t he ac o u sti c anal og _ o t hat in e l ec t r o ma g ne t ic t he o w (re f s. 14 t hr o u g h 1 9 ) . F r o m t h i s m od e l , i t has b een I b u n d th a t t h e r e fl e ction e ff ec ts are q uite sensitive to I he a i rc raft / obse r v e r geo me tr y, t he sour ce 1_ fr eq uency , a nd wave n u m ber r a tio (KI / K 0 ) , ;,nd _h c nor ma l i m peda nc e (ZI /Z O) o f the ground .

Co m plic a tion aris es b e c a u se t h e val u ers of t h e s e i as_; two par a me ters are n ot co mm on know l edg e f or v ariou s types of t e rrain. If t h e par a m et ers Z I /Z n an d KI / K 0 are n o t k n o wn b u t on ly g u es sed , _h e pre _|ic tedgrou n d refl e ction e ffect ca n mak e t he E ffe ct i v e P e r c eivedNoi se Le ve l m or e i n errort han t h at obtained by simply a ddin g 3 d B t o fre e - f ie l d d a ta . tl o w e ve r , t h is p h eno m ena do e s des e r ve study b e ca use i t s s pe c t r al effe cts are s ig n ifi c a n t . A d et ail e d an al y s is f or t h e op t io n al ground reflection proc edure i nc orporat e d in t h e c omput e rprogra m i s p rovidedin app e ndix A .

2 3 v TABLE 2. - TABU L ATION O F DATA FOR COM P UTING EXTRA G ROUND ATT ENUATION AT O O ELEVA T ION ANGLE - EGA (f, P , 0 ° ) in D B R efe re n c e : Figur e 3 o f SAEA | R g7 6 " _ L og ( f ) P in (f t) 10 _! 2 .32 66 . =3,.8318 _ )is t a nc e L o 9 (P) 2 ,9 2 87 . _ _ 3 ,22 9 -7" t -= h ru_ ' ( 1 0 . 0 0 O 0 0 0 i 0 1 00 2. 0 0 .2 0 .3 0.5 0 . 6 0. 7 0 . 8 1 40 2 ,1 761 0 , 3 0, 5 0 , 6 0 , 8 l, 0 1, 1 2 0 0 2, 3 0 1 0 ,5 0 , 7 1 , 0 1 , 2 1 ,5 1 ,7 3 0 0 2 ,4 77 1 0,7 I ,I 1 , 4 1.8 2, 2 2, 4 } 400 2 . 6021 0.8 1. 5 1.9 2 . 4 2 . 7 3.1 600 2.7781 1 . 1 2. 1 2 .6 3 .2 3 . 6 4. 4 80 0 2.9031 1.5 2.5 3.2 4.0 4.8 5 .8 10 0 0 3 .0 2 .0 3.0 4.0 5.0 6. 0 7 . 2 1400 3.1461 3.0 4.3 5 .6 7 .1 8 . 5 = 10 . 1 20 00 3,3010 4 .2 6. 0 7 .7 9. 7 11 .1 13.0 o 3 0 0 0 3.4 77 1 5.0 7 . 0 9.1 11. 2 1 3 .1 1 4. 7 400 0 3 .6 0 2 1 5 .0 7 .1 9. 7 11.8 14 . 0 i 1 5 .4 ! ,

o ooo I

_ 000 _9 0 31 5 0 72 1 00 i 12 0 148 16 0 I

3 7 . 5 /7 5 75 / 1 50 15 0 1 1 0 0 3 00 1 60 0 6 0 0 7i20 0 1 1 7 0 0 - / 24 0 0 t h ru __ 4 8 0 _0 ] _ 9600 "-'I O CTAVE BAND LIMI T S - (H z ) ELEVATION ANGLE _ 2 " (D F .G o } _ , FIGURE 7 .- DE C'A Y FA CT ORS F O R COMP UTING E XT RA - GROUND A TTENUA TION (CO MMERC IAL OC T A VES ) _ 25 TABLE 3. - DA TA POINTS FOR EGA DECAY FACTOR EL E V .

E _ DECAY FACTORS, F _ 2 t _ ) B 2 in DEG 0 1.0 1.0 1.0 1.0 1.0 1.0 2 1.0 1.0 1.0 1.0 1.0 i.0 10_ .18 6 . 2 97 .352 .40 6 .4 68 .534 20 .16 _ . 183 .188 .198 . 214 . 235 45 O. 0 . O. 0 . O. 0 .

g o O. O. O. O. O. O .

1 2 3 4 5 6,7,8 C O MM ERC I A L OCTAVE BAND NU M BER

i

" NOTE* V a lues in T ab le ab o v e w ere o bt ai n e dfr om Fi g ur e wa s minimi z e d by us i ng _ ! -; "_ / ))l 4 (App e ndix 2)o f S AEA I R 9 2 3. T h e &d B error f o r ra nges P = 250, 350, 5 0 0 , 700, 1 000 , 1 _ 00, 2 000, 2 800, 40 0 0 f ee t .

5. 1.4 Lining Treatment Current technology in predicting the attenuation of acoustic lini ngs in c orporates a com b in a - ti on of experimen t al correlation and theore t ic a l analysis . The acoustic wave a tt enuation analysis is based on a rec t angular duct _ ith mean flow and boundary layer effec t s. Equivalen t duc t heigh t s for non-rec tangu lar duct geo m et ri es are o btained by equating flow areas, trea t ed areas , and duct leng t hs. Far- fi eld a t tenuation direc t ivi t y corrections have been ob tain ed from engine ground tes t data.

In t he appl ic ation of t hi s tec h nology, t hree t ypes of prediction pro c edures of d i ffere n t de t ail and complexi t y can be iden t i fi ed. The s e thr ee t ypes are (1) predic t ion of t he a t tenua t ion spec t ru m i for a gi ven lining design, ( 2) predic ti on of the li ning parameter s for a given duct con fig uration where - ' the attenua t ion o f a noise spectrum is maximized, an d (3) prediction of the attenua t ion spec t ru m i_ for a gi ven duct wi t h fi ning para m eters unspecified, but as s u m ed to be chosen such t hat the • _ attenua t ion of a gi ven noise spectru m is maximized.

c a n prediction relatively inexpensive by i i! The first ki n d of (I)be made the s o lu ti on of the equations governing w a ve propaga t ion _ a lined duc t of somewha t idealized geome t ry, leading t o i_1_ s o luti o ns w hic h c om pare reasonably we _ l wit h data . T o acc o mplis h t h e second kind o f predic t ion _, requ i res an opti m iza t ion program. Th e optimiza t ion progra m i ter a tes t he procedures con t ained in t he f' ws t kind of prediction (I)resulting in t h e op t im u m lining para m ete r s t ha t m aximize t he at t enua t ion of a noise spec trum . Althoug h optimization progra m s e x ist, t hey a re t oo cos t ly t o r un, excep t in fi nal design of a lined duct con figu ra t i o n.

T he gr eates t need f or pre di ctio ns ar e of th e thi rd kind , w hi c h a ri se in trade s tudies , w h ere the e ffects of such para m eter s a s inle t leng t h , number of spli t t er rin gs, and engine choic e are inves t igated. For t hese cases, a si m pli fi ed pr o cedure w hi ch uses a tt enua t ion spectra corresponding t o optimized li n i n gs is used. T h ese atte n u a tion spectra ar e somewhat idealized , i .e. , m ade to confor m to a stand a rd s ha pe in order to avo i d t h e expen s e o f an ex ac t c al cul a tion . Experie n ce with th is ap pro ach, t h o u g h app ro x i ma te , sh o ws good c orrel ati o n w ith re su l ts fro m det a iled p redi c tio ns for p er c e i ved n oi s e lev e l red uc tio ns. T h i s a pp ro ach h a s b ee n i n cor p or a t e d i n to t h e c o m pu ter pr og ram . T he fol l o win g di scu ssio n p ert a i ns to t h e t y pe 3 pr edi ct io n p ro c edure .

T h is proc e d u re e n co mpas se s two t yp e s of o p ti m iz e d li ni n g s: s i n gl e -l ay er an d do u ble-l a y e r . T h e s in gle-l aye r p ro c ed u re giv e s t h e u se r two o p tio n s . T h e fi rs t o p tio n co n sider s o n l y a singl e d e sig n p o in t; i. e . , fi x ed e n g ihe c o n d i tions . T h e seco n d o p tio n c o n siders m ulti p le-degig n - p oi n t s ; i . e . , t h e e n gin e conditio n s v a r y over a l i mit e d r an g e . A co mp ro m i se betw e e n peak a tt enua tio n an d b and wi dt h is m a de b ec a u ._ e t h e li n i ng i s e x pecte d to attenu at e tones t ha t t rack w i t h t he en g ines ' shaf t spe e d (rp m ) .

II 2 7 For double-layer linings, an increase in bandwidt h can be rea li zed wit h t h e same peak at t enuation a s t h at given by sing l e-layer li nings. T h u s, double-layer li nings can be use d for t h e m ul ti ple-design-po i nt option described above, to provide t h e sam e perceived noise level reduction for a s li ghtly less amount of l in in g _ , , ea.

Th e source noise computer progra m contains li ni ng attenua ti on calculation procedures as an op ti on for li n in g t reatmen t of t he follo wi ng noise components: 1) Compressor and inle t fan _ 2) Disc h arge fan

: oi

,i'! ,' _ 3) Lift fan 4) Core and turbine 5) Ejec t or-suppressor jet noise 6) Slot nozzle w ith au g mentoroflap jet noise Within t hese procedures, there are several methods available for calcula ti ng the li ni ng attenuation spec t ra. T h ese methods are as follows: I) For e a c h t ar get frequency, the user defines t h e ma gn itude of maximum at t enuation and th e percen t age of t he t ot al area t ha t is t reated. Th e program th en de t ermines t he spectr um shape .

2 ) The user d v fines t h e e ffectiv e duct height, t h e ratio of appa re nt treatment lengt h to effec t ive duc t heigh t , and th e percen t age of th e t o t al area t hat is treated for each targe t frequency. The progra m then dete rm ines t h e spe c tru m shape.

3 ) Th e user defines t h e geo m etry of t h e lin ing in te rm s of the lengt h and r adi i of cylindrical walls, and t h e percentage of the total area that is treated for each target frequency. The pro gr a m t h en determines the s pectru m shape.

The user is lim ited to t h e configuration s shown i n figure 8 when defining the linings I geo m etrically.

| a) CIRCULAR DUCT b) ANNULAR DUCT R i Innermost an d outermost w alls are 11ned on one stde.

i RI _ __ • _ (Numberof walls = 2) (a = R 1 - R 2 ) q - _- --- -- --LI - ---- - - -D - C) " n " CONCENTRIC WA L LS R 1 -___nl R2 (N umber o f walls = n ) ! Inn e rmost and oute rm os t s t d e , tn t e r tor w a lls ar e w a lls a re 11ned o n on e ltn e d on both std e s .

(Hn = 1 = Rn) = Rn ® 1 FIGURE 8. - LINING G EOM E TRY ! 29 T h e lining attenuation prediction proced, _r e involves t h e successive use of five figures. T h ese curves consider duct geo m etry, treat m e _ area, tar ge t frequency, speed of sound , duct Mach number, attenua ti on over a ran ge of power settings, attenua ti on s pectrum s h ape, a nd directivity angle. Depending on user requirement s , an y or all of the pro ce dures may be used. T i-e u s e of each figu re is explained in detail below.

_ a single pow e r set ti ng a nd a z e ro Machnumb e r. Th e re quired da ta are: l Figu re 9 is an estimate of t h e pea k attenua ti on obtainable for an optimum sin gl e-l a yer lining at ?_ 1) L / H One half the ratio of actual treatment are a t o duct cross section al flow area.

i_ Actual tr e atm e nt a re a is typic ai ly about 65 %of t h at which would be calculat e d _ from a nac e ll e h al f-section d ra wing. L is t he appa re nt treatment length. H is th e _ e ff ective duc t height . See s k etch fo r e x ample.

L Inside of outer cyli n d e r i s l i ne d Outside of i nner cyl i nde r ts l tned I t 2) ftH / c Non-dimension al t ar get frequency, where ft is the t a rg e t frequenc y for peak attenuation, and c is the speed of sound.

Figure 10 shows th e v a riat i on of th e sin gl e-de si gn-point peak a ttenuation with the du c t Ma c h nu m ber. However,it shou l d b e rememberedthat these c u rves represent optimum li ni n gs a t the same frequen cy a n d different M ac h nu m bers; not th e same li ni ng at a different Ma c h num b er, as i s th e c as e in typic a l du c t dat a a nd theoretical a n __y sis.

Figure I 1 shows the co m promis e when a lining is designed to operate e ffectively over a range o i ' power settings-the usu a l case. Th e correction fact _ cause a reductio n _:_ in pe ak attenuation, but an inc re ase in band wi dth by an amount (I / K) or (I / K ' ) res pe ctively fo _ " single or double layer li n in gs. The in l et mode attenuation is co m pro m ise d m o re than the exhaust m ode because, as the power setting is changed, the engine blade passage frequencies and the peak lining attenuation frequency shift in opposite directions fo _ " the in l et mode , a nd m _ he s _m e direction for th e exhaust mode.

F i gure 1 2 gives the a ttenuation spect ru m shape. T h is is used to obtain the a ttenuation of s ou nd a t frequenc i es ot h er t h an the tar g e t frequency. I t i s considered repre s entative of an avera g e single-l a ye r -liningcase: t h e reason a bleco _ pro m ise between the m aximum ob t ainabl e attenuation at : _ --' q I | I M- tlACH NUMBER (AdB)M- REALI Z ABLE ATTENUATION _ M (AdB') 0 " , REAUZABLEATTE N UATION {i M- 0 K - MULTIPLE _ NPOINTCORRECTION ( FIGURE1 1 ) FIGURE IO .- A TTENUATI ON CORRECTIONFOR MACH NUMBER EFFECT 3 2 i (K) ..... z . . ., 1.0 r -- . ^_ -- _v_ -_ '-- !

:" : _ i ! _ SI N GLE DESIGN •: _ :. _ - . ..::.-. : . l ...... ,z: . _ :- - - : u.:, - : : .:-..:--- _ .... : : :: " : ' _ MULTIPLE DESIGN L S " _ ; : ....... _ , _ :. _ ....; ................ :." ...... " .... ;.. ; .......... _ . .: ............

_i.:! ::: :l.:ii : : : i:.: . . . :..::i : _. :. i..! ....... : • : .: . : "." : POINT OPTION "" 't' " _ . ; . ,.. , .... ": " . I .. ; . ; :" I :.' : ": " : , . _....I. • i .... i ..... _....I........... _ * .... : ' " " : ' ! :; ; ,' "; : ;.:: ;. :: : " ..: : : : : ' ;: :: " : ": ; .... i :.: : _:: ' ; : :| : : . . '::- ' : -. ; : . : _. : ..........

• _ :T _ . , : : _ .. . _. . : : . _ • . ; ; ; : : " .! _ : ." '. ; " , .i ' t I , . • |: ' : 1:',,i " ; ;" I ' " " ''! .... I" "I : r ; " I ( M ) -1.0 -0.5 0 0.5 1.0 OPTIMI ZED-SINGLE- LAYER LINING S I NLET MODE - ] - EXHAUST MODE -!

i (K') _ "i:' - ;_-.; ; n _ " : " :i ; 1 ;: : (0.4 , 0.9) _ : :: ........ NOTE _: : i4i : !! : !;!i: :. ,F : ., :. i . ! :-:. ! . i : ii:: . _! :- :;. . ,n . i! : : .:- ::. [ :: .. : . , .[ . . .! . :. . ; .... : .... U S E K" 1. 0 FOR A dB i., . . .... , ., , ........ , ..... ; I • : I ..... : ., : ; -. .

.............. i ... I....... I ....................

t o ........ I ...... }..... I .. I " ..... CORRECTION FORMULA .......... " ' q ' ............. I " " " I ..... ' ' k ' _ :: -_.. : _t! - ..i--.!t, : ,.h _..i , .,;i_!,.i;. 0.5 / - . !: i - :: ,i. : i-. ! ...!. : :. . - !_;!-. :, IN FIGURE 10 ' .; '_ I :: ' I; " .I " : ' : I : : . 'l': : • . : .... :; :: ':I. : '. ' : I ' _ ] _.;- . ,i .... I. :- ; _ ' . . .--I- . .; . ;--.- I . --; L .;,_;.I.; .L.: ; -. _ .; .;' ;. . . i ,;; . i _ , : ;;.. . " .... _ . ; ." .... 1 ; , . . , . .. - ..

..... | , ......... i . . , . • . • . . , ..... I... l ......... , . . l .'I ....... I . , ................

• ', ' , : .'.l' . " .I ' : ': 'I". I: : ;;_ ; :: '. ; ; ". : ; : ', ' :" '. " ' .. . _ " i' :: .............. I ........................ x...................... I....._ ....... I ....... ).........

1:: !.: ".:l : :I:: : l ; I :' . : : .::I ; ". : - ": : .;: _, - , . ; ; " : ]. : "- .. L ' . . .I . " ' ...... I .... L .............. I ' : • ' .... t ..... ": _ :' " [' _ ' ._" . ""_' ""_ .- '; ' _ I '" - : '. _.:_ ..... ";' ? "" '"", , "" T ........... , ..... : ' ? ' " , ..... : " " : '_." , • "I "_.I_" ;| • " ' : :..; 111 ".: :. : .1" . :_,:: .; . . _ : ; ' ;. " : . " .... .

: .i !; !" i :":l : i"ii : :::'_'; i I i i ' : ; ! i" : " I , I .... I • I (M) -1 . 0 -.0.5 0 0.5 1.0 OPTI MIZED - = DOUB L E -LA YER L I NIN GS !

FIGURE I L - BANDWIDTH CORRECTION FACTORS l

:ii- / f-7 / _ ':- ::. iill _ - .i- .......... _:-: ....... _" ..... _ - --_

| | the targ e t fr e qu e ncy a nd th e r e quir e m e nt for att e nuation bandwidt h using th e sin gle -d e sig n - point t option . To approxi m at e th e us e of th e m ultipl e -d e sign-point o pti o n or th e us e of doubl e lay e r linings, th e band wi dth i s inc re as e d by multiplying th e ar gu me nt in octav es , Io g 2(f / fT), by th e factor (K or K e ), show n in fi gur e 11.

0 Figur e i 3 gives th e f ar field dir e ctivity corr e ction to apply to the att e nuation sp e ctrum. F igu r e 1 4 sh o ws a c o m p a ri s o n be tw ee n th e pr e dict e d a tt enua tion an d the exp erime n t a l da t a .

5. 1. 5 Configur a tion Corrections i Th e e ff e cts of fu s el a g e / wi ng shi e lding a nd r e fl e ction hav e not b ee n d eflat ed du e to th e s ca r c ity _ of in for m a ti o n on the i nfl u e nc e 'of eng in e pl a c e ment a nd , f u rthex m or e , it is e x pe cted that th ese z_ eff e cts ar e smal l for conv e n t ional j e t t ran sp orts . How e ver , any ra di cal ch a nge in e ngi ne location , i _ e . g., o ve r-th e -win g -mou ntin g , or us e of supp res sio n d e vic e s , e tc., c o uld res u lt in a sub s tanti al ch a nge _i _ in nois e lev e l a nd r e quir e co rre ctions to b e employ e d. Sinc e the r e is no w a y to anticipat e the change s in airplane / engine con fi guration s , the approach taken here is to let t he u s er of the progra m de fi ne co rr ections for each nois e componen t .

Th e c orrect i o ns pre s c ri bed by the user for each noi se component ca n b e use d for : (!) a A dB !

to be subtracted fro m the overall s ound pre ss urelevel or (2) A dB 's t o be subtr a c te d from the n oi se spect rum . The progra m pe_m i ts the correc t ions t o vary wi th the direc t ivity angle, _ . If the Doppler - s hi f t option is s el,.'cted in predicting a n oise componen t , th e program assumes the correc ti ons are repre s enta ti ve of that obtained fro . n a sta ti c tes t and it will Doppler- s hif t t he | pr e scrib e dcorrec t io n s pec t ra.

5 .1.6 Summation of C o m p on e nt Nois e _ t e probl e m is st ru ctur e d to permit th e calculatio n of th e da tum s pe ctr a for ea ch noi s e c ompo nen t o n a c o mm o n re f e ren ce sp her e a t an gle s 1 0° , 2 0° , ..... , ! 70 '_ rel a tiv e to th e f ri g h t pa th .

Thus, i n di vi du a l n oi se c o mp o n e n ts a re a dd e d togeth e r m th e u s ual m anne r for log a rithmi c q uanti tie s. As e a ch n oi se c o m po n e n t i s d e t e r m i ne d , t h e tot a l n oi s e for a ll the s o u r c e s i s a c c m _ m l at e d us i n g e qua tio n ( I 2) b elo w. T h e r es ult repre s e n t s the tot a l s o un d r a diati n g tow a rd t he ob se rv e r a t e a ch aircr a ft position considered . Further det a il on the pr edi ctio n of th e component noi se fo r each s ource is gi ve n in sec t io n 5.2 .

_= I (12) II ) TOTA L E A CH CO / 4 P, g 35 .L1.7 Output fo r Nois e Contour Esti ma tion On e of th e r e quirem e nt s of t h e nois e predi c tion c omput e r progra m is the linkag e of it s o u tp u t.

a data tab le , with t he nois e c ontour progr a m. T he o utput v a riabl e s for t h e data t a bl e ar e li s ted be lo w an d ill u s t r a t e d i n fig u re ! 5 . The _ orm a t use d f or the out pu t fil e is (I PE ! 2 .3 , 3 E | 2. 3 ).

i N L Noi se l e vel ( E P NL o r P h IL m ax im u m ) corre s po n di n g to e a c h d is tric t co m b in a tio n o f v a l u es fo r Epp,o t , LR . ; EPP E n gi n e p erform anc e p a r a m eter . T hi s v a ri ab le i s to be s p ec ified by t h e us er as a corr e l a t i on i li p a r am eter f or no, s¢ and m ay corr e spo n d to e ngin e pr es sure ratio, jet velocity , e ngin e : _ ' s peed (r p m) , etc . D u ring P has e A of th e contract , thi s p a ramet e r w as e n gi ne pr e s su r e ratio (ref . 4) .

a Elevatio n a n gle i n degrees0 ' ef . 4). It i s comp u ted a s | a = cos " 1 ( X / P)I w h ere P i s the ra n g e a t t h e clo s e s t poi n t of a p p ro ac h (fig . 6).

LR Logarithm (b as e !0) of th e range a t th e c lo se st point of a pp r o ac h (CP A). It is co m p u t e d as IOg l 0 ( P ) w h e n g i s eq u a l to 9 0° ( fig . 6).

5 .2 NOISE SOURCE E S T I M A TION Th e comp u ter program ha s b e en gene ra liz e d to accomodate se v eral different types of n oise so u rc e s associated with c u rrent and futu re aircraft. Th e follo w i n g list describ e s t h e typ es of no i s e sourc e prediction modul es that hav e b ee n inc l uded in th e "N oise Source C omp u t e r Progra m."

R efe r ence I) M eas ur e d D a t a 2) J e t Nois e a ) Singl e e x ha u st nozzl e 7, 20, and 2I b ) Co - annu l ar e xh aust nozzl e s 2 2 c) E je ctor / Sup p r ess or nozzle (JT 8 D d e sign ) 2 3, 2 4 , end 25 d) S lot n ozzle wit h aug m entor fl a p ( S TOL ) I I , 2 6 . and 27 c ) Externally -blown fl a p (STO L ) 2 8 and 2 9 3) Co r e a n d Turb i ne N o i se (Tu r boj e ts / T u r bo f a ns) VARIABLES 1) IlL A THREE- - DIM EN SIO N ALDATA A RRAY OF NO I S E LEVEL AS A F UNCTIO M O F (EP P , L R . Q ). TH E NOISE LEVEL VAL U ESREPRESE N TEP NL OR PEAK PNL , ETG .

2) EPP A ONE=DIME N SION A LDATAARRAY OF ENGINE PER F ORMANGE PARAMETERVALUES FO R THE (N L ) ARRAY, 31 LR A O N E-DIMENSIONALDATA ARRAYOF LOG10( R ANGE AT CPA) VALUESFOR T HE (NL) ARRAY.

--- _ 4) a A OdE-DIM EN Si ON AL DATA ARRAYOF ELEVATION ANGLES FOR T H E (NL) ARRAY .

llrgiOTE _ DATAARRAY S (NL , EPP, L R , Q ) DEFINE THE THREE-DI M ENSIONAL TABULA R FUNCTION. NL • fI(EPP, L R , _ ) T H E DATA CO R RE S PONDS TO LEVEL FLIGHT AT A NOMINALAIRCRAFT VEL O CITY , AND !l DIRECTIVITY ANGLE @ O F PEAKNOISE RADIATION.

t _ LEVEL :!

i'il )

_! NL

t

_il_ . OIR E CTIVITY C ON E / " V_ - V _!i INTERSECTION _ , ,, ,/ _ Cli

--- E

. .. . _ - _ ' OBS ER VE R /

P u

"-'_ L R EeP1 G_ FIGURE 15 .- ACOU S T IC DATA FOR NOISE CONTOUR COM PUT E R PROGRAM 4) Co m pre ss or a nd F a n Noise a ) Con v er , t io na l tu rbojet s / turbof a n s b) L i ft- fans 3 0 a n d 31 5 ) Propell e r,Heli c opter an ti Ti l t Rotor Nois e a ) Empiric a l p ropell e r proc e dures 3 2 b) Theoretical propeller / rotor p rocedures 33 through38 All , or a ny s ub s e t, of the m odule s av a il a blec a n be u s ed for noi s e predic t ion . E a c h m odule ma y be called up t o a m ax imum of t h r ee t ime s , corres p ondingto a n aircraftha v ing thr ee differen t t ype s of engines mounted on it. Thi s restr i ction does not apply to the nu m ber of en gi nes of the s ame t y pe a nd o ri entation angle, 6E" I n e a ch n oise predictio n m o dule, the kno w n no n -axial-sy mm et ri c c har ac te ris tic s in the r a diation patterns ar e considered in the calculation of the da t um spectra (free-field , index); e . g., the multiple-en gin e correctio n formula equation (2B) in sec t io n 5 .1.1. 6 . This also includes ar t y u s er speci fi ed installa t ion effect s (see. 5.1.4 an d 5.1.5) on t he r adiat ion p att e rn s. Other fac t o _ cons i dere d are f ligh t vers u s s t a t ic conditi o ns; rela t ive ve l oci t T , Dop p ler-shift, etc., (see. 5.1.1.7 and fi g. 4) . T h e optional use of lining as a s u ppressio n device can be incl u ded in the modules; 2 c, 2d , 3 , a nd 4 li s ted above.

:l As evide n t from t h e options av a il a ble, t h e user of t h e progr a mc a n predict t h e n oi s e f or a l m o s t _l. an y air craft presen t l y fly ing, a nd some w hich h a ve not b e e n built yet. Howeve r, e m p irical p r oce dur e s ha ve their l_mits and failure is antici p ated. ( The complexity of the t y pes o f aircraft presentl y being studied co uld a l so be the limit. ) For t hese c ases, a modul e ha s b ee n in c lud e d to a cc ept measured data to p ro v i de more a cc ura te r e sul t s wh e n on e or more of the models p res e nted are c o nsid e red in a dequat e .

$.2 . 1 MeasuredNo i se Dat a S in ce m e a s u red d a t a is gener al ly mo r e reli a ble t han that o b t a i n ed f r o m cu rr ent predictio n p ro c ed u res, t he cap ab il it y of i n cl u di n g m e a s u red d a ta i n the co m p u ter pro gr am is a v a ilable. T he m e a s ur ed noi s e is a ss um ed to be so u nd pres sur e l evel spectra, SPL S , gi ven in dB re 20 I JN / M 2 a s a f u nc t ion of thr ee o r fo u r v ar i a ble s fo r ax i al-s y mm et ri c or no n - axia l-sy mm e t ric type so ur ces , r espect i vely . T h e ind epe n de nt v m' i a ble s ar e f requ en c y (e i gh t p r efe r re d ! / I oct a ve b a n ds or t we nt y -f o ur 1 / 3 o c t a v e band s d efi ned i n t ab l e 4) , so me presc rib ed e n gi ne p e r tbrma nc e p a r a m ete r, d i rec t i v ity a ngle (_) , and ele v ati o n a ng le ( 0 o). Pr e sc ribed s p ectra a r e assumed to r e pre s ent far-field noise ex t rap o lated back to a free- fi e l d, inde x con d i ti on. Thus, the le v e ls can be treated as independent of l o c al ambient c o nditions.

4 O J TABLE 4. - FIL TER BAND DEFINITION AND ATM OSPHERIC ABSORPTION AT 45.7 m (150 FT ' ) FROM A SOUND SOURCE ANALYS I S I NO . FRE Q UENCY LIH|TS COE _ FFI C |ENT ABSORPTION i (Hz) (Hz) (dB / 1 0 4) (J8) I . PREFERRED 17-19 63.1 44.7 1 89.1 0 . 2 O .

FULL 20-22 126. 8 9 .1 / 178 0.6 O .

OCTAVES i 23-25 251. 178 / 355 1.2 O.

i 26-28 501. 355 / 708 2,4 0,1 29 - 31 1 00 0 708 / 1410 4 . 9 0.2 32-34 2000 1 4 10 / 2820 10 . 2 0.5 35-37 3980 2820 / 5620 25.7 1 . 2 38-40 7940 5620 / 1 1 200 47 . 3 2 . 2 2. P RE F ERRE D 1 7 50 .1 44. 7 / 5 6. 2 O . 2 O . ( ' (1 1 31 1 8 63 . 1 5 6 .2 / 70 . 8 0 . 3 O.

OCTA V E S 19 79 4 70 8/89 1 0 4 0

i_ 20 100 . 89 . 1 / 112 0.5 O.

21 126. 112 / 141 0.6 O.

23 200. 178 / 224 1.0 O.

i1 2 2 158. 1 4 1 / 178 0 . 8 O.

24 251. 224 / 282 1.2 0.1 25 31 6 . 282 / 35 5 1 .5 0 . 1 2 6 398. 355 / 447 1 . 9 0.1 27 501. 447 / 562 2. ¢ 0.1 28 6 31. 5 6 2 / 708 3.0 0.1 29 794. 708 / 891 3.9 0.2 30 1000 8 9 1 / 1120 4.9 0.2 31 1260 1120 / 1410 6.2 0.3 32 1580 1410 / 1780 7 . 9 0.4 33 2000 1780 / 2240 10.2 0,5 34 2510 2240 / 2820 13. _ 0.6 35 31 6 0 2820 / 3550 18.4 0 . 8 36 3980 3550 / 44 7 0 25.7 1.2 37 5010 4470 / 562 0 3C.5 1.4 38 6310 5620 / 7080 43. 2 2.0 39 7940 7080 / g910 63.8 2.9 40 10000 8910 / 11200 91.8 4 .2 i .] "_ 15°C, 70 % Rel att ve Hum t dt t y _ 2 > _ ( f ) x 0.0 4 5 7 fre que ncl e slistedar e e xact to thre e significant d igit s. Often c o nv e ntional llstingsround to t wo s lgnlflc a nt digit s f o r conveni e nce(AS A SI . II - 1966) .

Th e comput e r program'sfunction i s to int e rpolat e on thes e data at sp e cifi e d aircraftop e ra t ing conditions and extrapolat e th e sp e ct ra to th e observ e r. No e ffort is made to scale, correct for airc r aft sp e ed, e tc., b e caus e no infor m a ti on is known about the ty pe of sound source the noise repr e sentsor th e m easur eme nt conditions in which th e data wer e ob ta in e d.

5 .2.2 J et Noise For the v roc e dur e s pr ese nt e d in t hi s r e port, j e t noi se is def ine d as th e nois e g e n e rat e d by j e t flows as th e y e xhaust into th e atmospher e . Th e actual noi se g e n e ration is thought to tak e plac e in th e flow r e gions wh e r e th e j e t flow int era cts with th e atmosph e r e . The noi se g e n e rat e d upstr e am -'-., _ d e th e e ngin e is discussed in sec ti on s 5 .2.3 through 5 .2Jlt, q , In the c ase o f a s in gle j e t , the noise pr o duc in g r e gions ar e sho wn sh a _ . " in figur e 16. In the pas t , the noise produced by t hi s jet was correla t ed wi t h three pa ra meters-densi t y, ar ea, and v e loci ty rela ti v e to the ambi e nt a i r, yi e l di ng consid e rabl e success in p re dicting maximum pa ss by _ noise of turboje t engines (refs. 4 and 7).

Howev e r, turbofan engines hav e r e plac e d t h e turbojet e ngin e s as t h e most common powe r plant for to da ys air transport fle e t. The n e w turbofan e n gi n e s ar e consid e rably qui e t e r than th e turboj e ts and t h e j e t noi se produc e d by the n e w e r engin e s has be e n ob se rved to diff e r from tha t pr edi ct e d by th e SAE proc e dur e (r e f. 7). C l ear ly, a r e vis e dproc e dur e was n e c e ssary. DuringPhas e A of th e curr e nt contract , a relativ e ly " crude " revi s ion was mad e (r e f. 4) , but th e subj e ct d e man de d b e tt e r pr e cision for e stimating ti me -int e grat e d subj e ctiv e measur e s, as pr e scrib e d for th e Phas e B part of the contrac t . This req u ir e d predic t ion of nois e at severala ngu l ar positions r e la t ive t o t he inl e t ce n terline, instead of just at that angle where the maxi m u m noise o ccurs. F or the case of lif t jets attached to an aircraft s fuselage, it was of particular i m port an ce to calcula t e th e relative jet velocity vecto ra ll y as sho wn in fi gure4, section 5 .1 because an incre as e in jet noise oc c u rs wit h crossflow imposed on the jet, i.e., the rela ti ve je t veloci t y is gr eater than tha t without crossflow.

Th e proced ure s pr e s e nted he re for jet nois e are empirical and repr e sent th e stat e -of-art in solving this problem.

Before the noise pre di ction procedure for a si n g le jet is presented, it is wo rt h noting som e technolo gi cal developments (ref. 39 through 4 1) that ar e t aki n g plac e at this tim e which could , _ result in a m ore co m pre h ensive pre d iction proced u re . Figure 16 shows the noise producing shear re g ions in a sin g le jet a n d the co rr espond i n g relative a cous t ic power level as a func t ior, of distance from the nozzle exit plane. T his distrib u tion of energy can be f u rther bro k en down with respec t to freq u ency f / fo a n d position X / Xo a s was do n e ! , r _ references 39 and 40. Hence the noise producing 7_ r e gi ons a ppe ar to be str u ct u re d and no t ran d o m a s previously believed. Thus, i t ma y be possible t ha t a one-di m e , sion a l source distributio n m odel can be developed for pre d icti n g the noise in a far- fi eld.

4 2 I i This math m od el cou l d then be us e d to correct gr o und st at i c nois e data to a po i nt source, a n d e liminat e th e paralla x e rrors th a t occur in extrap o latin g the data to otl _ ., posi ti ons in th e aco w , _ c fi e ld. Th e mod e l c o uld _lso b e us e d t o si m ulat e fright co ndi ti ons from ground static t e s t _ by accounti n g for th e chang e in pot e ntial cor e , v e l oc it y , e tc., that caus e a spectrum shift with fli gh t sp ee d. Th e pr e s e nt SAE ? r acti ce (r e f. 7) giv e s two s pe ctrum s ha p e curv e s f ,'r f righ t and gr ound s ta tic p re dic ti ons wh e n in theory th e r e should only b e one.

In addition to th e a bc _ v e , a b e tter normalization of jet nois e r e m its w he n the acous ti c pow e r is r e l a t e d to the m e chanical pow e r, conv e ction Mac h nu mbe r, d e nsity and t e mperatur e ra ti os as outlin e d b e low in e quation fo rm and illustrat e d in fi gure 17.

Total acoustic pow e r, x 'r_ / c (1 3)

w A W o( )

wh e r e th e on e -d i m e n si onal j e t flow para me t ers ar e Wo = m e c ha nic a l power - ( _ g) I _ j- _ O [ P = m e an d e nsity ra tio Po TS = m e an static tem pe ratur e ratio T so Mc = m e an conv e ction Mach numb e r

= 0 .5 10j - o I / C j

m = 5 for quadrupol e sources ^ Vj - j e t v e locity v e ctor r ela tiv e to th e nozzl e ^ VO = n ozzle velocity v ec tor relative to ambi e nt air • Cj = m e a n speed of so un d in t h e jet = m a ssflo w = P A I_ j I A = dis cha r g e area 4 4

U A C. NO. - v y, c !

FIGURE 17 .- S PACE - AVERAGED OVERALL SOUND PRESSURELEVEL AS A ) FUNCTION OF MACH NUMBER 4 5 Equivalentfo rm s o f equation (13) ar e : (" " f T.. _ . 5 _"_ " I VJ'V° ---- 01: _ A A iS ^ ^ . , q "

~ W o k_' o C . J t_ ) c - o "

The above suggestions ar e p re l iminaryand further work is requiredp ri or t o i_, rporation in t o the e m pirical proced ur es curre , n t] y used. This should not be interpreted to imply t hat th e methods n o w us e d are inadequate and c a use gross errors;but it d o es suggest that they will requireaddition al ref' m ementto increase the rang ,_ of application.

°_ 5.2.2. I Sin gl e Exha u st Nozzle In th e p rese nt proc e dure ( ref. 20), the nois e produc e d by th e jet of a sin gle noz zle has b ee n A A corre lat e d wi th re lativ e j e t v e locity (Vj - VO) as s h_,y n i n fi gur e 18. Thi s curv e was d e v e lop e d fro m the data giv e n in re f e r e nc e 20 for a 2. 54 cm di am et e r noz zle and was e xt e nd e d to n - . at c hth e pr edi ct e d re sults of r e f ere nc e 7 for v e lociti e s gr e at e rthan 760 mps (2 5 00 fps). In formula fo rm , i h e s p a c e -av e rag e , ov e rallsound pr e .;sur e l e v e l is _ ' _ " "" F ( VR)+ 10 L°gIO [ ( _ R )n _ R I (1 4 ) wh e r e P is th e j e t density and t h e r e f ere nc e d e n sity, P R, is 1 6 .02 K G/ M 3 ( 1 I b m / ft 3 ) A is th e fully- e xpand e d discharg e ar ea and the re f e r e nc e ar e a, , _ ) . ; " 0.0929 M2 (1 ft2) VR is th e m agnitud e of ( _ f j - _ f O) n vari e swith VR as shown in fi gure !9 Previous d efinit i o n s ( r ef. 7 ) fo r the ov e r a l l SPL us e d a p 2 norm e lization instead of a p n t erm used h e r e . Th e v a k , e of n w as determined by " force - fitt in g " th e for m ul a to e xpe ri m_ t al d a t a (r e f.

20) so that the term , F(VR), was a pproxi ma tel y proportional to VR8 for velocities less than 760 ra ps.

i I VR FIGURE 18. - _ 'A ' S - P _ , SPACE - A VERAGED OVERALL SOUND PRESSURE L r-:VEL VERSUS t f ELA TI VE JET VEL OCI TY v.

FIGURE Ig .- D E NSITY EXPONENT (n) VERSUS RELA TIV E JET VELOCITY t 1 Th e free-field, spac e -av erd ge, S _ sp e ctru m for (1 / 3 )octaves is d e t e rmin e d from figure 20 as a func ti on of Strouhal Nu m b e r.

S-"_ C (f) = _ + F(S N) ( 15 ) wh e r e f = geome tri c- m e an fr e quency for a pass b an d

SN = f / fo

: _ f o = characteristic freque n cy = VR / D o Do2 -- (_-_) A T wo sp e ct ru m sha p ing curv e s h av e bee n p r o vid ed in fi gure 20 co rre s p on din g to the flight a n d gro u nd curves given by SAE (ref. 7).

t_ N ex t , th e SPL sp e ctrum at a particular dir e ctivity angl e ( _ b ) is o btain e d by int e rp o lating fr o m th e data shown in tabl e 5 . T his tabl e was dev e lo pe d from data gi v e n in ref ere nc e 21 and pro vi d e s a corr e ction to add to th e spac e -av e rag e SPL for th e d e sir e d sp e ctru m .

SPL(f ) - S-' ] _ [ '(f ) + F( S,V R , tp ) ( 1 6) i wher e S = an e ff e ctive Str o uhal n u mber t o en t e r th e tabl e = f Do / U o t Uo = 3 0 4 .8 m / s = 1 000 fp s The r e sults from equation (16) re pr e sent th e f re e-field levels for a si agl e engine at 4 5 .7 M | (1 50 ft) fr om the so u rce . The s p ectru m is corrected to the datum c o n d ition (P = I M) thr o ugh use of t a ble 4 .

S PL( f )[ = SPL(f ) i + 33 .2 +,'X d B( f ) 1 M 4 5.7 M (1 7 ) The effect o f multiple engine s of the sam e type a n d o rie n t a tion i s a ccompli sh ed by a dd i n g the co rr ectio n (eq. (2B), s ac. 5 .I . I.6) to the result gi v e n by equ a ti o n (1 7 ). T hi s co mp lete s the pre d icti o n of jet noise f o r a s ingle noz z le .

r _ 5 !

i

J i t

!

A I 5 4

' J J

' "- . '::] : _:-.. I.!]o:!_o ' .:_ :!: .

t _ * * " * ' q .......... , *_ " I " ..... "' _" ' ::! !:: I:::_ ::: 2 :::ol::t: . . .

t , ., • - -, , . o.,:.,, - J, , , ",,, , ,,, , - ,,-" - - ' "M o' ." ° ..

--_ _! !!!!i! !: 2 i!::_ !J::::: !:::t:!: . _ .* ,4 -* .* ._ .* - * -*.* I_ _* * I I * I I * I I I Ill .,i,• i..I i_ _ I_ •.11 _1 _1 _ I I I I ' l I I I I_ I "_l'lI i ' ,, - *1.I _ = l. - l .' l _., - I . .. I ..-. I_ .,-I I I I I l I I l I I I ,,, ' I ,,_, ,,, I .... t I ' , - _; t I i i I _ I I I I ) i i I I i I !_ I ! i I I ! I I I I |' I I * I * I ! I ! I ! I *, _'_ I 1 ! I I ! I I t I 1 I ! I I I I • i I i I i t t I

_ ,,, ,,_, , ,, ,, , , , , I, , i , I !_

• . - _ o. _ _ _ -. _ . _ I ,_, ,, _ _ , 1_ ,,,. _, _ "_ - I_ t " ''_ . _" , - _lr l ' ' _ ,L ,,.I , , I , ,1, I , I' I , I Ill ,, I IS l b -

{ .., ; I ' I i I I I ! / !-_

........... , _, ......... , . , _ , ,_ ,, , , _ _, i:, _, , ,, " , ,, .... . , "t" ....... F"_' ° _'"; _ ......

i i I ; I I

+ I ..... +_+ +'C+ , +,; _.. :; i. _ +.. Z _Lu ' .;+_+ t .......... ; " :+ ....

I I •

I II +J

¢ I I # | I I I ! | # Q • •

.... " "l ' _ , __

; ...... . _

'" i"', _ j_ ._g

Ii la, o ,+ I I | ] , 4 p ,,i, : +, I + , r + +_ , I +. +. +. I+.+. +.

"+" +'++' 1 22 +'tl

+-I I I I / '_ .+_ _'.';, ,,., +,,.,_ . . . , .,, ....... .,.... ,. ......

I • I I I , , -+ ' .4 - -I_,..l , q ' "lII I I I I+I I I I l I I I o 'I ' , , , _, 'I I I I I l I I I , _ 1 _

_ ...... .1 , ,_ "'t" i°

i i I I I I , !i_ + -, - +-, "°. ' + ++ , ,+ , ,.+, ,. '+. , . .... I, •.li._. 4 m,t.,+ ._+ I . _I, . I II l III II I e I o I I l e ll

+ + +"

o + -j .ill ..,i • ,_., ¢ _i _ . 1 3 "o l'.ll = l_ ' l 1. 4 ,10 J l_l * _ • ¶ * * • • | , _ • , q* '_ _ * I * • * " * I" I I I1 9 I I I+ I I i, l I +I ii i o: I o o • • + ,i , • • • ii • • • + + I • i + • + . l - - f ,,,,+ . - I - I_ i , ,,+ . , .+ _i , ,,,+ - I++ .-ll + +I I I I III ' 'I ' ' ' ° I ' ' ' + '' I ' " 1 I l, J . * d • * I a I i _ i 1,411, ,i • . , • i . . _| l ° ' _ ' °' ° ' .... I' ' ' I ! {_ ......_ _ ........ _1 .... , .... _ ....

" " ' "" "1 ' .... '1 ' _'_

I I ,

.... ' + ....... ..+ ..... I..,,= . +,.,+..... , + ...... 2.+ ' _

: : .. , :: , ., ._, _ ; , , ,,, ,, , , 71 .-,. + +: , -,,,++ 77+ - , ..??_ +_? o ,.-+ ' 4 ...... +- ...... _ ' _ ' +_'" "_i"+" I I_I:_'' . ' ......'"I '+'_ .... ........ " " "" ' = I"'i"" '+ : + ; _"""i "" " '7 - :" "" " + ' g_ '' =, ' : _ _"' +" " ""+'"' " i . 5 8 i r 5 .2.2.2 Co-Annul a r Exh a a st Nozzles For a co-annul ar jet, i.e., a jet w ith both p ri m ary and seconda ry flows, the noise producing r e gio n s are sho w n in figu re 21 a n d are defi n ed as: (l) the i nn e r sh ear layer, w h i ch is du e to the inte r act i on bet w ee n the p rim ary an d s e co n da ry flo w s; (2) the outer she ar layer, w hi ch i s du e to the in t e raction of th e secondary wi th the surrounding air; an d ( 3 )th e mixed flow region where the comb ine d j e t flows hav e b e com e f ul ly dev e lop e d turbul e nc e .

For nois e pr edi ction purpos e s, th e co-annular j e t is consid e r ed to ha v e the nois e gen e rating c hara c t e risti c s of two ind e p e nd e nt singl e j e t flows; on e r e pr e s e nt e d by th e inn e r sh ear layer and th e second r e pr e s e nt e d by th e summation of th e out e r sh ear lay e r and th e mix e d flow r e gion.

_ The nois e characteri s tics of th e inner sh ear lay e r alone ar e pr e dicted r trst as though th e s e con dary flow w as abs e nt, i. e ., the sa me a s in s e ction 5 .2.2.1 , e x ce pt that th e lev e ls ar e th e n _ , adjust e d to accou n t for the pr ese nc e of th e s eco ndary fl ow su rr oun di n g th e p rim ary fl ow. To pr edi ct th e nois e of th e out e r she ar lay e r and mix e d flow r e gion , it is n ece ssary to calculate th e o _ ' ous # cal e quiv ale nt flow p a ra me t e rs for th e se condary str e am of th e co-ann ul ar flow syst e m. This is a ph e no me nolo gi c al , forc e -fit approach and it has no ph y sical i m plications to th e m e an on e -dim e n si onal flow p ar am e t e rs for the flow r egi on b e ing consid e r e d. The s e calculat e d p ar a me t e rs are th e n us e d to pr e dict th e s e co n dary flow j e t nois e as though it was a single j e t. The predict e d noi se of th e tot al co-annular j e t is th e e n e rgy su m of that produc e d by th e two flows m e ntion e d abov e (r e f. 22).

| Noise prediction for inner shear layer .- Th e noise from th e inn e r she ar lay e r is predicted in the same m anner as t h at described in the previous se ction 5 .2.2. I wit h the follo wi ng exception. In the s t ep where t he space-averaged SP L spectrum is c al cul a ted, (eq. 1 5 ), a corr e c t ion term is inser t ed I S-E( f ) = S ' _ (_' ) + A_B ( f) ( 1 8 ) wh e r e [Vjl "Vj2 1 m AdB(f) = 10 IO g l0 I _ / -J]

$

m = e x pe rim ent a lly d e ter m ined e xponen t (ref. 22) shown in figure 22 = F(A2 / A I ' [ ] fl ) VjI, Vj 2 = pri m ary / se condary velocities relative to the nozzle 5 9 FI G URE 21. - IDEALIZED NOISE SOURCE REGIONS FOR CO - ANNULAR JETS 6 1 A1, A 2 = p r i m ary / secondary discharge ar e as fl - VjI / D!

DI2 = _ -A 1 Not e: A singularity e xists wh e n e v e r Vj2 approach e s VjI. In tb . _ p r ogram wh e n e v e r ](VjI - Vj2) / VJ 1[ is l e ss than 0.1, th e inn e r sh e ar lay e r is a _s um e dto v an ish and h e nc e produc e s no'nois e .

Furth e r, th e above proc e dur e ha s not b eer v e rifi e d for th e c as e of Vj2 >VjI, but th e comput e r programstill c o nsid e rs this a valid case.

Noise p r edi ction f o r outer shear la y e r and ,nixed flow reg i on . - ln this step, the nois e is pr e dict e d in th e sam e mann e r as that d e sc ri b e d for a sin gle e xhaust, s e ction 5 .2.2. i, e xc e pt th e para me t e rs( P , A, VR) ar e th e acoustical e qui, _ al e ntterms d e fin e d b e low.

P = me an on e -dim e nsionalflow density of s _: ondary disch ar g e A = AI +A 2

vj2- vji 2 /

VR2- Vj 2 - 2 Vj VO co s at + VO2 ¢ _ = angl e b e tw _ ':n gr oss thru s t v e c t or and th e dir e ction of motion 'i 5 .2.2. 3 Ej e ctor / Su p pr ess orNozzl e s A m ulti- e l e m e nt suppr e ssor n ozzle is sh own in figur e 2 3 . This m o di fi c ation (lob e or t u b ul ar nozzl es ) of t he ex it h a rdw a r e of j e t e ngines c an yield a co ns id e rabl e a m ount of noise s uppr e_ on when c o m pared to a c onv e ntio n al c ir cu lar dis c harg e nozzle. T h e suppre ss ion is b e li e v e d to r e s u lt from th e ch a n g e i n turbul e nt m ixing- an al tern a tion of th e turb ule n ce s c al e an d a r e du c tion in th e m ean re l ative jet ve l ocity gra d i e nt s (ref. 2 4 ), since an increa se in induced s e con d ary air is obs e rved.

Thi s i m p li es an integr a tion ov e r the tot al volume of the j e t. Ho we v e r, this is just a gros s observation of a v,, _ ,ry compli c ated phenomena. In fact , the pro c es se s a re so c ompli c ated that they defy ,, theoretical an a lysi s . Only e m piricalmethods ha ve yielded feasible de sig ns (ref. 2 5 ).

l | FI G URE23 .- MUL TI - ELEMENT S UPPRES S OR ON TEST ST AND !

For the purpose of jet noi se prediction, the noise fro m a m ulti-ele m ent n ozzle can c o nside r ed t o c o nsist o f two parts-(l ) pr e mergingnoise and (2) po s t m ergin g n o ise. The pre-mergin g noise i s generated in t h e region close t o th e nozzle where the s t,.uctureof the individualjets can be iden tifi ed. Th e p o stm e rging noise i s generated in a region dow rstrea m from t he nozzle, after the indivi dual j e ts and induced s e condary air has me rg e d into a sh t gle " unifor m " jet of lower bulk v e locity. The high-fr e quenc y porti o n of th e r e sultant total j e t n ois e spectrumis usuall y do mi nated b y the p rem er gi ngn o ise, while that of th e low-frequency port , on is asso c i at e d with the post me rging n o is e . Th e noise for e ach component is pre dic ted in a manner s _ dlar t o that of a roun d nozzle. Th e total jet noise is t hen obtain e d by su mmi ng , on an energy basis, th e spectra for premer gi n g and postmer.c in gnoise.

Wh e n a shroud , co m monly c a ll e d an ej ector, is add e d to th e multi- e l e m e nt suppr e ssor, an in c re as e in suppr e ssion can occur, provic _e dtha t th e shroud l e ngth to diam e ter ra ti o, L / D, is larg e .

How e v e r , long e jectors ha v e consi de rabl e w ei ght, an d loss e s in f righ t associated with th e m; h e nc e , th e y hav e not b e en stu die d in d e pth as a nois e suppr ess ion item. Anoth e r approach (ref . 2 5 ) us e s a s hort e r e j e ctor which incorporat e s lining to achi e v e th e sa me result. Ev e n this approach hasits limits b e c a u se al l th e pr eme rgingnois e do e s not propagat e no rm a l to th e eje c t o r wa l Rs,a nd on l y part of th e nois e i s int e rc e pted by t h e lining. Furth e r,only limi t e d ty pes of li ning mat e rialscan b e used du e to th e th e rmal e nvi ro nm e n t o f th e ex hau s t.

For short shrouds, L / D l ess t h an 2. 5 , without lining, no significant r e duction in pr eme rging noi se has b ee n observed wh e n co m par e d to th at of a " b are" suppr ess o r configuration. This l e ads to th e assu m ption that th e nois e from a sho rt , hardw al l e j e ctor / suppre ss or can be pr e dict e d in a man n e r similar to t ha t for a " b are " suppressor.This requiresknowl e dg e of the e jector p e rfo rm anc e , however, b e cause t he pr e s e nc e of a shroud ( e jector) impo se s a constraint on the boundariesof th e pre m ergingand post m erging r e gions. Ej e ctor p e rfo rman ce can be obt a ined by us e of a t heoretic al , one-di m ension a l, flow analy si s if on e a ss u me s 100% m ixing in side t h e shroud. Appendix B cont a ins an ex am pl e of th e para me triccurv e s that can be o b tain e d from th e configuration shown in fi gu re 24, taping t his approach.

The pres e nt noise prediction proced ur e is e ss entially e mpirical. It is bas e d on the an alysis of an e xtensive amount of round nozzl e and supp re ssornoi s e data from th e followin g type s of tests: I) F u ll sc a le JT8D, JT 3C , JT4 / J7 5 and JT! 2 static engine tests.

2) Modelscale hot flow t e st (A -- 45 . 6 c m 2).

3 ) F l i g ht te s t for th e 707, 727, and 7 3 7 ai rp l a nes .

6 4 !

i : I The re su lt s of t h e p roce d ure a re I / 3 oc t a ve b and s p ectr a a t the free- fi el d, ind e x co nd it i o n

I

p red i ct t h e p re m erg in g noi s e s pectru m . Thi s , in t u r n , d epen d s up o n the con fig uration of s t udy. F or _l desc ri bed in sect i on 5.1.1.2. Th e overall acc u rac y o f the p r ocedure i s depe n de n t up o n th e ab i lity to in cre a s es the tu r bulence in the jet for the JT8D con figu ra ti on and hence in cr ease s t h e pre m er gi ng 5 dB. Apparently t here is a velocity defec t up s trea m fro m the s uppre ss or nozzle exit which no i se. The li s t i n table 6 represent the tolerances in PNdB b a sed o n ob s ervatio n s from g round s tatic l turbofan e ngines , e.g., th e JT8D, th e proc e dure pr e dicts this co m ponent low by approximately tests, t hat can be expec t ed for the procedure, provided that t he ar ea ratio _ for the suppressor is between 1.5 and 4.5. The area ra t io is defined as tot a l flow area (p rim ary plus induced secondary) / ili divided by the primary di sch ar ge area a t the suppressor exit plane.

Figure 25 shows a comparison of a sample prediction with measured da t a.

Postmerging n oise predic tion .-Con _ der the e j ector / suppressor confi gu ration shown in figure 2 4 , Th e post m e rgi ng noise for t he e j ector exhaus t is assumed t o be si m ilar to that of a conventional circular j e t . The techn i ques descr ibe d in secton 5.2. 2 .1 could b e app l ied ; however, a sli g htl y di ff e r ent appro a ch is t a ken here. Th e overa ll sound pressu re level for a single eng i ne is related t o t he re l at ive j e t velocity , densi t y of the exh a ust, stati c t e m pe ra t u re and di s ch ar ge ar e a . Th e relation is OASPL(_ / ,) = FI(V R, _ , ) 10 log10 LI _R ) _ SR ( - ARR ) J (19) where F !(V R, _ ) is obtained from fi gure 26.

VR = re lati v e jet velocity = j - VO

I ^1

Vj -- mean on e -di m ension a l flow velocity for the ejector exh a us t P = m ea n o n e- d ime n s i o na l fl ow density for t h e ejector exhau : t P R = refe _n ce dens i ty = 1 6 .02 KG / M 3 (1 I bm / ft 3) TS = mean one-di m e n s i onal flow sta t ic te m per a ture TSR = refe r ence te mpe ratu r e fro m fi g ure 27 TABLE _ . - TOLERANCES C o nfiguratio n Engine type 8are st,ppressor Ejector / suppressora Turboj e t + 2 PNd B ' ' + _ 3 P NdB Turbofans -5 + 2 PNdB -2 + 3 PNdB aSho r L hardwall shrouds: L I D < - 2.5.

J

14 0 I ! | I S !

1_ o 1ooo 1oooo FREQUENCY IN HERTZ NUMBE_ OF TUBES 3 '/ TOTAL TEMPERATURE 703°K ( U bSeR) AREA RATIO 3 .3 AREA 0.352 M2 (3 , 78 FT 2 ) AIRPLA N E SPIED 0 ENGINE PRESSURE RATIO 2 , 04 DIRECTIVITY ANGLE 120° ENGINE YJ75 FIGUR E 2 5 . - FREE . FIELD SOUND PRESSURE LEVEL S P E CTRA NORMALIZED TO 1 METER RADIUS , l REFERENCE , COND I T I O NS • D IST AIiCE R " 1 ME TE R • AR - 0 .0 _ 20N2 ( 1 FT 2) • T S R -REFERENCE TE MP • ,o R - 10,02 KG / M3 (1 LBM / FT 3 ) • FREE-FIELD (F I GURE 27 ) 2OO dl "- DEGREES 1 30 600 800 1000 150 0 200 0 3 000 ( F I' / 3 E C) R E t. A T IVE JE T V E LOCI T Y V R 'l' I " | | | I | | | I | I i| 200 400 600 800 (M / 3E C ) FIGURE 2 6. - NORMALIZED OV E RAL L SOUND PRESSURE LEVEL VS .

R E LA T IVE JE 7 VELOCITY _, 69 FIGURE 27. - REFERENCE STATIC TEMPERATURE VS JET VELOCITY

ii i

ii

0 A -- dischargearea of t h e ejector AR = referencearea -- 0.0929 M2 (1 ft2) The 1 / 3 oc t ave band SPL spectrum is calcula t ed by ad 0 ing t he following correc t ions t o the | OASPL, i.e. , S PL ( f , _ ) = O AS P L (' _ ' )+ F 2 ( f / f o ) + F3( f / fo , ' _ ) ( 2 0) i, wh e re F2(f / f o) is obtain e d from figur e 28 F 3 (f / f o, _ ) is obtained from fi gu r e 29 t fo = characteristicfr e qu e ncy = ( vVj _ 2D ) F4(VR, O ) f rom figu re 3 0.

t D = e jector e xit diameter= ( _3_ -))A b When the shroud is removed, t he one-di m ensional flow paramet e rsfor the postme r ging noise region are di f fi cul t to de fi ne. Th is problem has bee n avoided through use of the one-di m ensional flow parameters for t he suppressor exhaus t . This appro a ch resul t ed in an empirical correction term being added to equa t ion (19). The correction t erm is de fi_ , _ ed as a func t ion of ar ea ratio, AR, and relative velocity, i.e., AdB = 0.34 _ F 5 (VR) from figure 3 1, a nd the " effe c tive " one-d im ensional _ ow pa ram e te rs to u se in e quat i ons ( 19)and (20) above are: Vj = velocity for t h e suppressorex h aust P = density for t h e suppre ss or e x h aust T S = st a tic t emp e r a tur e for t he s uppr e sso r exha u s t N o o : . ,!

7 3 FIGURE 30 .- FREQUENCY SHIFT DUE TO CONVECTION DATA SOURCE PR TT-OK1,T.I. ' °R _ MAE-. _ 21 / 7 th SCALE JT 3 C 2.2 868 1 _ 0 ! FULL SCALE JTI D 1.8 750 FULLSCALE J75 2.0 b 95 ]250 i i i i

|

L_ : ; : -40 = e _ ,-. 20 L

N

200 3 00 400 $ 00 500 (M , SEC) RELATIVEVELOCITY,VR I_ I I 1.._ I I ! I J 400 800 1200 1500 2000(FT / SEC) FI GUR E 31. - PO S T - M ER GING NOI SE SUPP R E SS IONV E RSU SR E I A TIVE V E L OCITY • FOR BARE SUPPRESSOR CONFIGUR A TIO N A = disc h ar ge ar e a of s uppr e ss o r D = q (4) A AR J Premergin g noise pred i c ¢ io n .-Consid e r th e " ba r e" suppr ess or configuration s hown in fi gu r e - i 2 3 . Th e p re mer gl ng nois e of a singl e el e m e nt, tub e or lobe, e tc., i s assum e d to b e similar to t h at of a . . conv e ntional circula _ j e t O f the sa m e discharge ar e a. How e v e r, the individual j e ts for th e mul ti - e l em ent suppr e ssor int e rf e re with e ach other and alt e r the turbul e nt structur e ( re f . 2 4 ). By dime nsion al an al ysis, th e . _ ff e cts of the interf e rrrin g je s ts hav e b e en r e lat e d to th e numb e r of _Ii e l e m e nts and th e area raft t ) for the suppr ess or. From this an al y si s th e spac e av e rage, ov era ll sound _l p re ssu re l e v e l for this com l )on e nt is d e fin e d em piri c ally a _ i

= l lv r , 1 : o')+ l o l O ga o L N / ( 2 1 )

+ F6(N) + FT (AR) where FI(V R, 120°) i s obtain e d from fi gure 2 6 F 6 (N) is obtain e d from figure 3 2 F7(AR) is obtained from figur e 33 V R _ V j - (V S - 0 . 2 C O ) VS = induc e d s e condary v e locity _ CO ground static { _ C o in fl i g h t CO = ambi e nt sp ee d of sound N = number o f elem e nts AR = area ratio: (primary + i nduced s e c ond a ry) / pri ma ry 7 6 . 7 .

? ' 7 1=4

? _ r ? " t 't ' _ " " "

gp ~ NOl1331JtlO_) OIIV _ I V3 _ IV " / 8 a nd the m ean on e -di m ension a l flow param e ters Vj, P_ TS , A repre se nt ve lo c it y , d e n s it y . :_ tati e , " t e mp e ratur e, and disc h arg e area for t he s u pp r es s or, r e spectiv e ly.

T he ov e rall SPL vari e s wit5 t he dir ec tivit y angl e , ¢ J , and is defin e d by G ASPL ( ' _ ') = _ + FO( _ ) (22) wk ere F8( ¢ ) is obtained from figure 3 4 .

Finally , t h e | / 3 octave band SPL sp e ctrura is obtained in a mann e r si mil a r to t h at for t h e post m e r ging p ois e , ex ce pt t h at th e c hara c teristi c frequen cy , f n , is t y picall y hig her and an apparent o S k D l _ P ei_ !0 r elative to the post m erging noise must be added to the directivitv angle, fhat is SPL(f,'_ ' ) = O AS P L( _ b ) + F2(f / f o) + F 3 (f / f O, _ + 10°) (2 3 ) wh ere F2(f / f o) is ob t ained from figure 28 .

F3(f / f o, ¢ J °) is obtained from figure 29 ( VJ2 _ F4(VR , _ )F9(M J)

fo -- VRD /

D = e ff e ctiv e ele m e nt diam e t e r = F4(VR, _ b ) is obtain e d from figur e 3 0 F9(M J) is obtained from figur e 35 Mj = Mach numb e r of th e suppr e ssor exhaust.

W h en a ha rdwall shroud, L / D less than 2. 5 , is placed on the exhaust system, t he p e rforman c e of the configur a tion c h anges and t h e induced se c ond ar y Mat h nu m ber i ncreases and typically var i e s between 0.4 a nd 0.6 for t h e configuration studied in appendix B. For t h is s h ort s hr oud, no apparent s h iel d ing takes place and t h e pre m er g ing no i se level h as not been observed to c h ange significant i y.

Ho w ever . t hi s w ill not be th e case w h en th e s hr oud i s l ined (see se c. 5.1.4).

_ L 8 0 TE S T D A T A : • 2 . 54 CM DIAMETERMODEL( B SRL) A JT 8 D F U L L SCALE E N GI N E • J93 ENGINE 1 o 4 T h e tot a l noi s e l e vel for t he " bare " s uppressor, or t h e e j ector / s u ppre s sor c onfig u ratio n i s t he e n erg y s um of the s pe c tr a for t h e p r eme rging an d p ost m ergi n g n oi s e c om p o n e n t s. T h e effe ct of m u ltiple e ng i n e s wit h t h i s ty p e of e xhaus t ha rd wa r e is e s t imat ed by us e o f equa tio n (2B) i n sc c to n 5 . I . i .6.

5. 2 .2.4 S lo t No zz l e Wi th an Au g me nter Fl a p An e mp iri ca l nois e p red i ct i o n p roced u re h as bee n devel o ped f or a typ ical s l ot nozz le / au gme n ter fl ap c o n fig u r a tio n sh o wn i n fig a re 3 6. T h e au gme nt e r fl ap i s un li n e d, b ut it s geo m etry i s co nsi dered r ep re s e nta tive of t h at whi c h w o u ld b e u s ed o n an au g ment er- w i n g S T O L a ir c r a f t. T he pr oced u r e is bas ed o n t h e d a t a o b t a i n ed from model te s t s ( ref . I 1 ) c o nduc t e d un der N ASA c o n tr act NA S2- 6 3 44.

U nfo rt u n a t e ly , d u r i ng t h e ti m e t his pr o c edure wa s b e ing de ve lop ed, t h e re c o mm ended noz z l e con fi gura t ion fo r an augmen t o r -wing ai r c r af t d mn g ed ( re f . 2 6). Thi s new nozzl e was s t ill a slo t , bu t inco r po r a te d a ser i es of sc ree ch s hie l d s in t h e flow. Th e co rresp onding acous t ic da t a wa s" no t available fo r anal ys i s du r ing t he p re s en t con tr ac t per iod and, t h eref o re , t h e app l ica t ion o f t h e p r o ce du re given h ere i s l imi te d. It s hou l d ser ve a s a ba s e l in e fo r fu rt he r d e v el opm e n t in nois e pr e dic t ion pr ocedu res f o r an au g m e n t o r -wing a irc ra f t .

T h e c urrent pro c e du re i s b a sed on a s t a tic te s t p rogr am wh ere t h e m o d el was a 1 0 0 to 1 sl ot n o _ le w i th an au g men ter fl ap p o si tio n ed a t a corre sp o ndi ng fl ap an gle of 35 ° du ri ng takeoff .

T ab l e 7 gi v es t he pa rt icula r ra n ge of te s t cond i tio ns c o ns i d ere d an d a l s o inc l ud e s t ha t of a fu ll- sca l e e qu iv a lent au g m e nt e r win g c o n fig u r a tio n.

l' h e f u ll s ca le equiv a le n t a c o us t i c d a ta w a s extr a pol at ed to t h e index c o n diti o n (R = 1 M) and 3 dB w as subt r ac te d to app ro x i m a te fr e e-fi el d level s. Th e v a lidit y o f t h e te s t d a t a c orre sp o n d in g to e le v a t i o n an gle s , 13 o= 3 0 ° , an d 60 ° , was do ub t fu l . For t h e s e da t a, an a v e r a ge bet w ee n the l e v e l s me a. su red o n each s id e o f t h, . model was a s ed to appr o x i m ate t he f ree-fi e ld p lu s 3 dB c ondit i o n. T he ov er a ll s o u nd p re ssu r e le v el d ata w e r e t hen nor m ali z ed w it h re sp e c t to total te mp er a t u r e r a tio , n o zz le p r essu r e r at io, an d n o zz l e di schar ge a re a f o r each _a l ue o f the d i r e c ti v ity a n gle ( q, ) an d el e v at io n an gle (Be ) " T h i s nor ma l iza t i o n y i eld e d a s c des o f st ra i gh t l in e p l ot s wi t h r e spec t to t he l o g a r i t h ms of t he i ndep_ ' n d _,n t v a r i ab l es: PT / Pso , TT / TT o . an d a r ea. lle n ce, a si mpl e r eh tio n f or t he ov e r a ll s o un d pressu r e l evel w as o b tai tRe d by a l e ast- squ ar es-fi t to t he d a t a w i t h an R-M- S e r r o r of 1. 7 d B. T he relati on i s

OASPL(_. / 3 _ ) = _ o * _ , 0 log 1 0 L\TT o , / No N

O SLOT NOZZLE EXIT !

i' !.

._ _ 7i FIGURE 36 .- SLOT NOZZLE WITH AUGMENTOR FLAP 8 3 i • TABLE Z- RANGE OF TEST CONDITI ONS i1 : _ Test Condi t ion Hodel Full-Sc a le Eq.

(Scale Factor=6.4) l ......

a . Nozzle Press ur e Ra tl O ( PT / P S O) 1.6 t o 3.0 S a me b. Tot a l Tempe r a t u r e Ratto (TT / TTo) 1.0 to 1. 4 3 Same ft 2) !_tl C. Nozzle D i sch ar ge Area ( A ) 1 20.6 c m 2 (1 8 . 7 t n 2) 0 .494 R z (5.32 d. Rtcr ophoneR a dtus (R) 1 5.2 R (50 f t) 97 . 5 H (320 f t ) e. Geom e t rt c - Ke a n Frequenc y (f) 315 Hz t o 64 K Hz 50 Hz t o 10 KHz * NOTE * PSO 1 . 0 S . ATH , _ 2116 psfa TTO _ 296 ° K = 5 32 _ R with the para m eters: ao = function of 0 and _ o from table 8 al = fu nction of _ b fr o m table 8 a2 = functi o n of _ and B o from table 8 AR = r eference area = 0.494 M2 (5.32 ft2) { This relation is s h own in figure 37 along wi th t h e co rr esponding data u s ed to develop it. Th e nozzle confi gu ration upon w h ich t hi s analyses is b ased produced screech at no z zle pressureratios e xce ding t w o. No co rr ection w as made to t h e OASPL to eli m inate t h e effects of s c reec h . However, . * ' :i!ii, the irre gul arities it produced in the spectra were " s m oothed " in the development of a spectrum | shap e formula.

The 1 [ 3 octave band, s pe ct rum shape fo rm ula was obtained by plotting (SPL - OASPL)ve rs us Strou h al number (ref. 7). Th e characteristic dimension of the slot t h at was used to calculate the Strouhal numbe r co rr esponded to the hydraulic diameter f or the flow. However, a temperature !

stratificat i on was observed between the hot, TT / TTo = 1.4 _ , and the cold, TT / TTo = 1.0, flow data. To furt h er collap se the data, a modified Strouh m number w a s used w hi ch included the total t e mpe rature ratio as a factor. That is i S P L ( f . _ , _ o ) = O A S PL(' _ ] Y , _ o) + F( S ) (25 ) w here F(S) = spectrums h ape ca r ve s ho wn in figure 38 S = mo dified Strou hal nu m ber = f / fo f o = chara c te r i s tic fre t ; u ency _ D / _r TO ] D = h ydraulic diameter = 4 A / Perimeter = 2 H / (! + H / L) ( H, L) = sl o t heigh t an d l e n g t h, re s p ec t i v e ly TABLE 8. - FORMULA CONSTANTS t ( _ _j % al o 2 (d e g) (de9) (de) 90 • 1i8.9 1_ : . 57 6.38 _ 60 120.4 6.16 1 _ 30 121. 4 5 . 22 0 117.1 I' 5.13 90 119.9 i _.: 93 6.48 i 60 122.3 5.80 i_ 110 30 122.0 5.25 _ / 11 0 1 17.2 I' 5.31 ° ; i" -- I 6.49 90 121. I 2.._. _ 95 ( l 60 124.1 ' S. 52 120 J 30 12 2 ,3 ; 5.07 I 0 118.6 ', 5 . 04 d 90 120.9 _ 4 3 [ 6.1 7 -' -,-- f • ' 60 123 . 8 I J 5.67

' I

13 o 3 0 12 o. 7 5 . 23

I 0 118. 7 I i 5 . _ 4 i 90 1 2 8 . 6 2 .53 4.83 --" ' r--" 60 127.6 | a 4.88 0 122. 9 4 . 60 140 3 0 126 . 1 _ 4 . 62 90 122.8 Z.1I 4.95 60 1 23 . 4 t ' 4.73 150 3 0 1 2 2 .4 ! 4. 63 0 118. 8 t 5. 15 90 11 9 .5 ' 2 . 0 5 5. 18 60 _ 1 9.8 5. 17 16 0 3 0 1 2 1.4 | 4.5 4 0 118.2 _r 5.33 P SO / AR W HERE ( _ , a lo _ ) = LEA S T - S Q UA R E S- FIT CON S TANT S FROM TABLE 8 ,¥ • REFERENCE C O NDITIONS: TT O = 2 % u K 1532 °R) PS O = STANDARD ATMOSPHERE (21 16 psfa) AR = 11 . 4 94 M2 1 5 . 3 2FT _ 1 • F R EE-FIELD , INDEX(R = 1 M ) i SYM _ 0 x 0° ® Q 0 30 = • 3 0.

8 60 = 0 A 9 0 `0 z 2 5 _ Q

o

:O % : 1 2O O !

..I O .

< 15 o n .

5 i ............. i .

5 10 1 5 20 2 5 30 35 10L OG 10( 4 _ ) FIGU _3 E 37 . - OV ERALL SOUND PRES _ SU RE LEV EL CORRELA " l ION 8 7 o.

41_ D.

I • I I ! ! !

9P ~ ( 3 dSVO - 'IdS )

v R = IL 0o l

- r j = j e t v e locity relativ e to th e nozzl e Although figur e 38 shows a c e rta i namount of data scatt e r, the scatt e r is l arg e ly due t , ground re flection and to screech for p re ssur e _ atios great e r than two. The dependenc e with resp e ct to variation s in th e angl e s , q , , an d 1 _ o is we ak. H e nc e , th e us e of a singl e curv e is not e xpect e d to caus e s eri ous e rrorin humanr e s p ons e e stimat e s, such as p e rc e iv e d nois e l e v e l.

Multiple slo f /flap confi f urat ions . - The use of multipl e slot / fl ap c o nfigu r a tion s by STOL air c r aft c an b e bro ke n down in t o a singl e " a c ousti c e quival e nt " slot / fl ap c on figu ratio a , provid e dth e spa c ing b e tw ee n th e slots is small c ompar e d to th e slot dim e nsions , i. e . , l e ss than T 0%. The sk e tch b e low illustrat e show thi s can b e don e .

I I l I* " "I I T - T -- X' , .... , , , .... ,' " r IIH SI _ OT-- HOZZLES @ I I I I " " , " " I" " " | " " " l _ ' _ ' X SL O T -_l NOZZLES "Aco us tica lly " t hi s i s app r oxi ma t e ly eq ui v al e nt to

".1 I

where He = M H Le = N L Thus, t he u se of multipl e s lot / fl a p co n figur a tions r e q ui r e s th e c han ge of o nl y two input v a ria b l es i n t h e b as i c pred i c tio n d efine d p r e vi ous ly, tha t i s r : A= M NHL D = 2 M H / I ! + (MH) / (N L)] w he re H i s t h e typi c al slot he i , _ t t , and L i s t h e t ypical s lo t leng th , _ Req u ired additional wo r k .-Reflecting on _ om e of th e recent deve l opments m entio n ed in s e c t '_ on5 . 2.2.1, it is believed that a better formulation c ould result through u se o f diff e r e nt indt; p - n dent variab l es than nozzle pressurerat i o (PT / Pso) and total tem pe = ature ra t i o ( T T / TTo) used in e quations (24) and ( 2 5 ) abov e -nam e ly _ tat _ c t em peratur e ratio and c onv e c tion Ma c h nu m b e r. T h e pr e s e nt proc e dur e h as not be e n validat e d for pr e dicting th e nois e of an aircraft in fl i ght. T he s e n e w va ri abl e s would giv e mor e insi gh t as to h ow t he eff e cts of fli gh t could b e , predicted. Furth e r work is recomm e nd e dusing this approach in th e analysisof the da t a obtain e d from the testsd e scrib ed in ref e renc e sI 1 and 27.

_i_! 5.2.2.5 Extern a lly Blo w n-Flap Configuration _II A model of an extern a lly blown-flap configuration is shown i n figur _ ; s 39 a nd 40 . The engine it_t ex ha us t is re dire cte d by the fla p(s) a nd an incre as e i n lift occurs . This l i ft- a ugmentat i on ma kes the devi c e des i r ab le for ST O L ai r c r a ft . However, the b low n flap has a pe na lty - more n oi s e i s p rod uc ed t han th a t fro m a c o n ve nt io na l w i n g mo unt i n g such as th a t o n the cu t ' re n t c o m mer c i a l a ir p l an e fl eet ( r e f . 2 9) .

T h e i v . c rea s e in noise c an be a ttributed to t wo item s . T h e first is t he pre se nce of an a¢ l dition a l n oi s e s o u r c e, i m pin g e m en t of the t u rb ulen t j et produ c i n g a fl u c t ua ti n g for c e o n th e fl ap(s), w hich has " di p ole " c h a r ac teri s ti cs. T h i s for ce i s t h e sour c e for t h e di p ole c o m p o n e n t an d has b e en gi ven t h e ter m " imp i n geme n t n oi se" i n ref e r enc e 2 8 an d t h i s te rm i n ology wi i ! b e us ed here . T h e s e c o n d it e m car : s i n g an i nc re ase i n noi se is due t o a cha nge i n t he jet s tr uc t u re . T h i s r esu Rs E r o m t he p r es e n ce of th e fl ap w h i ch a lte rs f c h er _: di a tio n patte rn of je t n oi s e . A l s o , t he j e t v e lo c ity gr a die n ts a t t he traili n g edge of the fla p can prod uc e more n oi s e t han t ha t tbr a f r e e jet . Ho w ever ., w h e n t he fl aps a re e x_ e n ded, t h e im p ingeme n t n oise u s ually domin a te s in t h e f ar -field , t h erefore th is report " d ea l s w ith t he noi s e p redi c tio n f o r thi s cas e . Wh e n t h e fla p( s) are r e tr ac ted , th e jet n oi s e c o mp o n e n t domi na te s over th e im p i n g emen t no i se, bu t t h e a dd i tio na l n oi s e p rod u ced a t t he tr a ili n g edge of the flap(s) is ass u m ed to b e i ns ig n i fic a n t , i .e., it i s co n ve c ted an d refra c ted a f t an d doe s n ot c o n trib u te to the no ise ob s erved belo w the aircr af t. T h us , the t ,-c h ni q u es pres en ted for s i ngl e a nd c o -an nu lar = R k ex h aus t n o zz le s in sec tio n s 5 . 2 . 2 . 1 an d 5 . 2 . 2 . 2, ca r _ e ap pl i ed to the exh a u s t as tho u g _h it we re a t ree jet .

The acou s tic d a ta used to develop t h e no s ie prediction procedure _ or t h e blown-flap c onf i g u r a ti on w e re obt a in e d ,_' o m ref ere n ce 2 8 . Th e c onditions fo r th e s tat ic t e_ t w e r e as l i st e d in t a ble 9 , an d show n in fi g u re 41.

9 O NOTES: W ING P L A N E RAD IUS, R " 3.05 M (10 FT ) V ER TICAL P LA N E ELEVATION ANGLE, 1 _ o - 90"-. _ w FIGUR E 39 .- MICROPHONE SETUP AND WING, FLAP ARRANGEMENT NOTES: D - 5.2CM (2.05 INCHES) NOMINAL F LAP ANGLE a n - (L / O) r : ?.|, (LL / O |r :|.|6, (H / D) r :1o5, lint =4 _ * FIGURE 40 .- BASIC CONFIGURA T/ON OF EX TERNALL Y BLOWN FLAP MODEL 9 1 TABLE 9. - TE S T CONDITIONS(REFER TO FIGS. 39 AND 4 0) i I te m $ ,ym. _ ..... Cond t tt on a. Stattc temperature Ts Ftgure 41 b. Jet veloc|t y V j 150 to 350 Iq / S c . Nozzle dt a meter D 5.2 cm (2. 0 5 tn.)

l d. Relat t ve nozzle pos t t t on H / D 0.2 to 1.5 when _N = 45° LL / D - 3.9 to 1 .2 • _! L / O 3.3 to 7.1 e. Nomt nal Flap Angle o _ N 0° to 45° f. D t r ect t v t t y Angl e _ 10 ° to 180° g. Elevat i on Angle / 30 0° to 90° h. X t crophone Ra d't us R 3. 0 5 H ( 10 ft) t , G e o me tr i c-mean - fre q uenc i es f 0 .2 to 2 0 KHz | | 300 !_ 7 2 4 6 8 2 (FT / S EC) 100 1000 JET VELOCITY, Vj __ • I| _ -- | • ' " ' I 2 4 600 (M / SEC) 30 4 6 8 100 NOTE: DATAWERE C ALCULATED USING PRESSURE RATIO ANDVELOCIT Y' DATAG I VENIN REF o 28 " FIGURE 4 1 .- REFERENCE STA TIC TEMPERATURE VS . JET V E L OCITY 9 3 In ord e r to e x ter, d th e rang e of application to hot flows, a static t e mp e rature ratio term h as b ee n in c l u d e d ( se e s ec . 5 .2.2). Nois e l e v e l s for flight co n ditions ar e e st im at e d b y r elatin g th e overall sound pr es sur e lev e l to th e imping e m e nt v e locity on th e flaps and applying th e Doppl e r corr e ctio n for a r a ndo m dipol e source. Fi g ur e 4 2 shows the variation in th e ov e rall sound pr e ssure level with th e imping e m e nt veloc i ty and flap an g l e . Th e approxi m at e 5 t h to 6 th pow e r slop e with r e sp e ct to v e locity impli e s th e do m inanc e of th e dipol e sourc e for th e r e f e r e nc e confi g uration, i. e ., L / D = 7. I, H / D = !. 5 . At high e r j e t v e lociti e s and / or lar ge r valu e s of L / D and H / D, th e j et noise compon e nt may do m inat e ov e r th e im p ing e m e nt noise. But for th e r e ported t e st confi gur ation, the imp i ng e m e nt nois e e xc ee ds th e j e t nois e by 10 to 7 dB for a j e t v e locity rang e , 1 5 0 to 3 2 5 lVl / S.

' , i_ , H e nc e , th e jet nois e e mitt e d from a STOL airc ra ft using th e blown-flap during tak e off will contribut e typically l e ss than 0. 5 dB to th e total nois e obs e rv e d in th e far fi e ld.

In e quation form, t h e ov e rall sound pr e ssure level at t h e datum condition (fr e e-field , index: R = I M) is g i v e n by

Ii I

+ F3C ' I j/ . j oCH, V1 ) _ - F4( /' 3 o, "_ , C _ . N ) + FSfX N , l p ) F6( _N ) (2 6 ) whe r e VF = flap i m p i n geme nt v e loc i ty (_l " Vo) F2(L / D) + VO

I ^ ^ l

F I thro u gh F 6 r e pr e s e nt th e em pirical cu rve s show n in figur e s 4 2 t hr ou g h 4 7, r e sp e ctiv e ly ^ Vj = c e nter fi ne jet veloc i ty vector at the nozzle exit ^ VO = velocity vector of the ambient a ir relat i ve to the nozz l e and flap f s) c_ N = nominal fla p angle ( ' ; ig.40 } (a, b) = emp iric a l cons t an _ ( 0. 0526, 1.05 2 6) chos en t o fit th e data in figur e 42 T S = _ t; q i c t emp eratur e o f t h e jet ( abso l ute u n its) _ N 170 ' " • i m , o N M

3 1 4o

_ N _ J

t _

_ O , 1 3 0

:_I 15 o 2 00 3 00 _ oo 5 00 (,, , s e c )

; I I M PI N GE M ENT VELO C ITY,VF REFERENCE CONDI T I O N S : FREE-FIELD,INDEX(R - 1 M) STATICT EST , Mo - 0 TSR '-REF . STATICTEMP E RATU R E FROM FIGURE4 _ , P R -REFERENCE DEN S ITY = 16o02 KG / M 3 11LBM / FT 3) AR = R_IE RENCEAREA " 0.0929 M2 1 1 FT2) - 80 " _ o "90° FIGURE 42 .- 0 VERALL SOUND PRESSURE LEVEL VERSUS IMPINGEMENT VELOCITY 9 5 • | II II l II I | e II ! | | ! 6 1o o ....... x .9 - . , , , r -.-- --5 . 77 / { X / D) F O R -- : >7 0 5.

•O " .7 " o5 i w >, >, ° 4 " NOTES 1) S TATIC C ON DITIOI , _ 2) FREE JET •2 " 3 ) JET MACH NUMBER <: 1.0 O_ ' i ! I , 1 4 I I It i . , , , * O 5 10 15 AXIAL DIS TANCE FR O M JET NOZZLE , X / D VF = CENTERLINE VELOCITY AT AXIAL DISTANCE (X) F ROM N O ZZLE EXIT Vj =CENTERLINE VELOCI T Y AT NO Z ZLE EXIT D =NOZZLE DIAMETER FIGURE _ 3. - VARIA TION OF EXHAUST JET VELOCITY WIT H AXIAL DISTANCE FROM NOZZLE EXIT 9 6 NO M INAL FLAP ANGLE ( I N=O ° a) Yj=19 0 M / S (524 FPS) !, FIGURE 44 .- CHANGE IN OVERALL SP L WITH DIRECTI VITY ANGLE RE LATIVE TO _ = 80 ° N O MINAL FLAP ANGLE GN =0 ° 4 r"T'!'FT"! ' "I:T _.T ' -'T:-_I''-I'. : ; ..... I """

""'T _ " "'_i' T i11.177 7Til

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FIGURE 4 4 . - CONCI = UDED

4 i i I ' 1 I , . , .I I : !. . _

: I t , ! ' , i I _ | . _"SJI "I i. , ._._, i _J_!.

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I ! i / ; / . : ! / . 4 " . I l l - _ / - X _' ' i.... I I '. / _ , _ _ 3 0 0 _ 60 30 0 ELEVATION ANGLE , 8 0, IN OE G R _ E5 a) I // = DIRECTIVITY ANGLE RE, INLET : 0° TO 70° F IGURE 45 o - VA RI A T ION IN OA SPL WITH ELEV ATION A NGLE I00 FI G UR E 45. - CONTINUED i01 + 1I' = 140" 1 O : 1. _ 0 ° -6 I ................ _ " °r . :_ . ". " t • ". f.: . _:: v "l ' " l ..... I r , '::'": .: :_. : ..... .... : ' : ..... ::¶: : I _ .. _l , l ' ' :' ": ............. .... _:" :' " ' !: ...... :; -"': ' _: ' : : " ' 4'r ' i .... S S''' : _ ' _ '" : - ': " ' '. ' I ' ' !

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0 _, _ - , _ : :. _._ i..i::.i__ : ,: i _ 90 60 30 0 9 0 6 0 30 0 ELEVATION ANGLE, p o, I N DEGREE S C) _ = DIR E CTIVITY ANGLE RE, INLET = 140° TO 180° FIGURE 4 5. - CONCL UDED I t V BDIR E CTIVITY ANGU[ REFE RE NCEINLET T, 30 " T_O " . ', : ! ! T

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' e l # 0 .Z .4 1_ } _ • i_ .6 • | XN m | Ooa' I ' v-*o * ! , , . I. _.....,

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_- v - _ m* v--o *

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*NOTE* XN.(_ " , OZ, / [,L, m, ) '" , / On'] _! _- o '_ T O _r : , o " ! FI G URE 46. - CH Ah G E I N OVE R AL L S P L RE LA TI VE TO BASICCONFIGURA TION FO R NOMINA L FLAP CON D ITION ( _ N = 45 ° i0_ 3 FIGURE 46. - CONCL UDED 1 . 0 . 9 10 20 3 0 40 NOMINALFLAP ANGLE .Ci N( D E G R E ES) NOTE ° " ENGINE PI _ ACEMENTEFFECT = F5(XN _ Y) F6(a N) SEE FIGURE 4116 FOR F5 (XN, T ) FIGURE 47 . - FLAP ANGLE CORRECTION 7" O E N GINE PLACEMENT EFFECT !

l 1 0 5

00000002-TSA12

I

TS R _ - re f eren ce _ t at i _ l cm l _r_l u f c l_b_ olul, a m l _ ) l _e_n fi _ ic 4 1 P _ d ens it y o f t _t_ . _ j et PR = r ef e rence d en si t y = I 0. 02KG / I ',_i 3 _ IIb m l f t31 _1 A = di sc har g e a re a o f n o zzl e : :! A R = r e fer e nc e a res -- - 0 . 09 29 M 2 (!f t 2) il Mo = ai r craft Ma c h nu m b er g = ang le betw ee n direction of ak c ra t' t moti o n and s o und p r opa ga tion path q J = dire ctiv i t y an gle relative to engin e inl et _ o = el e v a tion a n gl e (figs. , _ an d 3 9) X N = dim e n s i on l e ss en gin e l oc at io n w he n o t N = 4 5 ° = (L / D ) ( H / D ) / _ aD .t,b- D = no zzle d i ameter, If the nozzle i s not c ircular, us e th e h ydrauli c dia m eter, 4A / peri me t e r.

Th e overa ll SPL for N ide nti c al bl o wn - flap c onfi g urations is estimated by adding the m tdti- e n gi n e corr ec tion, e quation (2B) in s ec tion 5 .1.1.6 , to th e r e sult from e quation (2 6 ) abov e .

Th e I / 3 oc tav e b a nd s pec tr um e ha_ i s shown in figur e 4 8. Using this c urv e , th e s ound pr e_ u re l e vel s p ec t r u m is d efin ed as SPL(f) _ 0 ASPL + FT(f / f o) (27) wh e re F 7 is an e m pi rical ly d e ri ved curv e (fig. 48) fo = the cha r ac t eri sti c S trouh a ] fr e qu e n c y in l |z (VF / D) _ ( I + s in 2 e t N ) / (I - M o cos_ ) .

T he fact or, VO.5 ( I + sin2 t _N ), res ult s fr o m file c h an ge i n t he h ydra u lic di ameter of t he flow proje c t ion on the flap(s) as the flap angle , aN , is va r i e d. This exp r ession a ss u m e s t ha t the im p in g e, , _;ent area is an ellipse f or t he discharge f r om a ci r cula r nozzle. I n r ealit y , the impingeme n t a r ea is a h y perbolic sec t ion , an d t he resu l ting formula is consid e rab ly more complica t ed. However , t h e sca tt e r in t h e d a t a (ref. 2 8 ) , does no t me r it such ,_: fi nemen t . The term, ( ! - Mo co s _ ), represen t s the Doplrler shift fo r an aircraft in fl ight.

A few c on c luding remarks about this p ro c ed u re a r e: a) The da t a ana ly sis wo u ld be simplified if t he refe r e nc e c oordina t e s y s t em was rela t i v e t o the f l a p(s ) ins t ead of t he center l ine of t he nozzle. "lhis w ould permit the same da t a to be represen t ed by fewer c u rves.

_ ' _ b) Addi ti o nal h ot flo w tests are re q u i re d t o v erif y t he m eth o ds use d to ext r a p olate the tes t o! ( c o ld fl ow) data (r ef . 2 8) to tha t applying to r eal engin e s.

c ) For cold flow models, it is expected that the p rocedure presented above will p redict the OASPL within +- 3 dB provided t he j e t Mach nu m ber is less t han one.

d ) A compariso n of predicted value s with a set of tes t data taken from r e ference 28 is shown in fi gu r es 49 and 50.

5.2. 3 Core and T ur bin e Nois e The g oa l of re(i a cing s u b s o n ic a irc ra ft no ise h a s le d to the c o nsi d era t io n o f engi n es wi t h l o wer jet velocities when comp a red to turbojets. The S A E jet noise procedure (ref. 7) when a pplied to t hese newer engines results in lower levels t h a n th at observed-e v en when efforts are m a de to elimin a te the fan noise componeJ,lt. Recent jet model tests ( ref. 20 ) . in which care was ta k en to keep upstream nomscto a min i mum, h a ve shown that a trend similar to that g i ven by ref. 7 is valid at veloci t ies less than 305 M / S ( 1000 fps). T his obser va tion became more a p pa l enc a l ter appropriate moditications to lhe density correc t ion exponent or the inclusion of a ( p2 T S 1.5 ) f a ctor was used to ct_ li apsc the nlodel dala (se e . 5,2.2), [ : ull scale _n g inc le : d_ al h : , _vpower se t tings , however , exhibit a signi l ic a nt ly different t rend a t jet ve l ocitie s below 31)5 M / S t[l_ t| , , . _bscr v edfrom t he jet mode l te s ts. App a rentl y there are a ddi t ion a l noise sourc_,s w h ich produce more I_w frequenc y noise t han i_ predicted for jet noise. Also. discrete ton e s due to _he la , '_t f urbinc _ ,; tagch_a v e bccn identified. T hese sources a re believed to be gcnerated u pst r e a m fro l n t h e nozz h : c×i_ ;.l l ld can be a tlribnted to v ar iou_ items: N OTES: 1) PRESSURE RATIO = 1 . 7 , TOTAL TEMPERATURE = 2 83 °K 2) MEASUREMENT RADIUS = 3 . 05 M 3) E L EVATION ANGLE _ o = 900 4 ) L / D = 7.1, H / D = 1 . 5 FIGURE ,4 9 . - PREDICTED VERSUS MEASURED 0 VERA L L SPL FOR BLOWN-FLAP MODEL !0 9 " I _'''_ :' ....... i .................... i¸ LEGEND CONDITIONS PREDICTED PT / P s o - 1o7 MF J _ SURED ¢ - 80° • o_ N , _ 45° fl o,,90 o w o_ N = 0 ° FIGURE 50. - SAMP LE FLAP t MPIN C E MENT N OIS E P REDICTION I10 a) Combu s ti o n b ) Static pres s ure fluctuations for flow through the turbine rotors c) Turbulen t flow impinging on t he turbine rotors and sta t ors d) Turbulent fl o w al o ng the inner surfa c e o f t h e en gi n e and nozz l e walls e) Separated fl ow on the tailpipe cone and / or turbine exi t struts Of the items mentioned, those associated wi t h the t urbine produce high frequency, broadband and t one noise. The low frequency broadband noise is probably due to combustion. For the purpose of noise prediction two co m ponents will be identified-(' _ ) core noise for the low frequency and (2) turbine noise for the high frequency contributo rs .

Th e present noise prediction procedures for these components are based on da t a provide d by various engine ma nufacture rs , research institutes, a nd NASA. Most of t h e data is proprieta _ and t hus little substantiating data can be presen t ed at t hi s time to justify the procedures. In fact, the procedures are not a ll that good ; th e tolerance is approximately +_.7 PNd B . A more detailed analysis of available engine data could result in a better core noise prediction procedure. Particular attention should b e given to th e progress m a de by various govern m ental contracts with industr y , e.g., GE / FAA.

5.2.3. I Core Noise Prediction ! The fo ll owing p r ediction procedure for core noise h as been deve l oped f r om f ull scale en gin e l acoustic measurements (primarily from hi gh bypass ratio turbofans). Th e noise source is assumed to t be a m onopole. The strength of th e so ur ce i s r e lat e d t o th e engine's co m b u stor a nd t u rbine inlet a n d.

e xi t parame ter s. Th e or e ti ca lly , a mo n o p ol e s o u r c e h as a u n ifor m o mn i- d ire c t i on al r a di a tio n patt er n, but f ar -field e n gi n e d a t a i n dic a te s th a t th e s o und is a tte nua t e d i n the i n let qua d ran t (s e e fi g . 51 ).

The r eas o ns for thi s a tt enua t i o n a c e p ro bab l y d u e to a c o m b i na t i o n o f effec t s: ( I ) the s o u r ce i s ge n er a te d i ns ide a d uc t , ( 2) c o n vection , a nd (3) refr a ction . In m athe ma ti ca l ter m s , the ove ra ll so un d p r essu re lev e l for a si n g le e ngin e , at t he fre e -field, i n de x c o n ditio n i s give n by 0A $P L = 10 Log10 _ p, ] _ T _ ] k_ " M O (28)

+ F

FIGURE 51 .- CORE NOISE DIRECTI VI TY PA TTERN !1 2 wh e r e _h c = combus t or corr e c t ed ma s s flow = _ '_ / TT x / T sR / ( P T c / P s R ) I / I = p li m a r y m ass flo w r h R = refere nc e ma s s flow = 0 . 453 6 K G / S ( I l b m / se c ) TT X = comb ust or e x i t total t emperat u re ( ab s ol u te unit s ) T S R = refere n ce te m per a t u re = 288° K ( 518 . 7° R ) PT I = tu rbi n e i n let tot a l pre ssu re ( a b s olu t e un it s) PT X - tu rbi n e e x it t ot a l pre ssu re ( a b s ol u te unit s ) PTC = co m bu s to r total pressure (ab s olute unit s ) ! PSR = re fere n ce pressure = I S . A T M . (211 6 ps f a ) : t M o = air c r a ft Ma ch numb er = a ngle betwee n direction of aircraft motion and soun d propagation path = dir e c t ivit y angle re inlet a xis F I = e m piric a l c u rve (fig . 5 1 ) a = c orrec t ion for the type o f bur n er = 0 f or annul a r types = + 9 tot c an t y p e s , i .e., JT 8 D K = specifi c engi n e co r rectio n ( see table I0 ) T h e use of m ul t i p le e ngi nes is i o be es t i m atcd b y adding e quation (2 B) in section 5 . 1. 1.6 t o e q u a tio n ( 28 ) above .

I i TABLE IO .- SPECIFIC ENGINE CORRECTION TYPEOF ENGINE K_ CF6-6 -1 _ , _ JTSD- 1 -3.5

ii!i _T9O - 7 , 2

RB.211-22B +4 RB.211 - 22B +1 (l_ tth Revtsed Strut Oestgn) TF34-GE-2 -2 Pap e r Engtne S t udtes 0 9 !

114 !

i 1 t V e ry littl e data ar e availabl e c o n ce rning th e c o re nois e sp e ctru i_ ] shap e . Ess e nti a lly, n o use fu l _e ctral informa t ion c an b e d e duc e d from conventional e ngin e me asur eme nts (without a significant amount of work) du e to th e ground r e flections at low fr e qu e nci e s. Pr e s e ntly, th e SAE flight Strouhal sp ec tru m is u se d, sinc e cor e nois e has b e en confus e d with j e t nois e in th e past and is assu me d broadband in natur e . Th e I / 3 o c tav e sound pr e ssur e l e v e l s pec t ru m is d e fin e d I t

t

S PL ( f) = O ASPL+ F2( f / fo ) (29) whe r e

I

F2 is the fli gh t Strouhal s pe c t rum shape (fig. 20b) fo = c ha ract e ristic frequency in Hz [ = b / [_c (l - Mo c os / j )] b = 1 246H z -(K G / sec ) 0 "5 = 1 8 5 0 Hz - ( I bm / sec ) 0"5 ! 5 . 2 . 3. 2 T u rb in e N oise Predi c ti on Th e tur b in e noise pr e di c tion pro c edure consid e rs two noise componen t s: broadband and d is crete tone. Both components have been rela t ed to the rela t ive t ip veloci t y of the turbine's last stage, t he p rim ary mass flow, and local speed of sound at the turbine exi t . The effec t s of t starer / rot o r s p a c ing on the discr e te tone levels is also considered.

. _ it has be en assumed t hat both c ompon e nts hav e sp ec tra shap e s t ha t normalize with respe ct t o ' _ , the fundamental blade passage frequency o f the last stag e of the t urbine. Th e p redicted s p ec tra are i | giv e n in te rm s of ! / 3 octave band levels (dB re 20 / aN / M2) at th e fr ee -fi e ld, ind e x (R- I M) =1 c o n di t ion.

Broadba nd comp w: ent . - T h e relation for t h e pe ak I / 3 o c tave band level at a radius o f 45 . 7 M (1 5 0 ft) from t h e source is

!

L0 = ]0 L0910 K,,VI1 CL : i_ ) . ( '1- HO CO,'i_ ) (3 0)

+ I: = l o

!15 ..... 7 ....... , --- " " = _ , _ - - - -* - : " ' ......

.......... ,.............. ,, _o---_ ., : -; : ................... : . - . ....

.................. _-'C,_ , ' ....... _: : "-," ........

r _ w h ere VTR = R e lativ e tip sp ee d of last rotor of th e turbin e . If VTR is unknown _ us e 0.7 times th e ti p sp ee d.

VR = R e fer e nc e v e locity, 0. 3 0 5 M / S (! fps) = Primary mass flow d R = Ref e r e nc e mass flow, 0. 4536 KG / S (I Ib m / s e c) ,i :I C L = Sp ee d of sound at th e turbine ex it. If CL is unknown, use C L :, a _ with a = 19.8 M / S p e r ( ° K)0"5 = 48. 5 fps pe r (*R) 0" 5 TT7 = Turbine exit total t e mperature CR = R e f e r e n c e sp ee d of sound, 34 0. 3 M / S (I 11 6 fps) Mo = Aircraft Mach nu m ber = Angl e betwe e n direction of aircraft motion and sound propagation pat h = Dir e c tivity an gl e r e . inlet axis F I = Empirical curve shown in figur e 5 2 Sa m ple data and predict e d r e sults are shown i n fi gu r e 53 . The I / 3 octav e band sp e ctru m s h ape is shown in , figur e 54 . The sound pr e ssur e lev e l sp e ctru m is d e fin e d as $PL(f) _ L0 + Fz( f / f o) (31) wh er e fo = fund a m e nt a l blade p a ssage fr e q uency of t h e l ast rotor st a g e of t h e turbine = B 0/ 160 (! - Mo co _ , _ )!

!1 6 i I I FIGURE 53 .- CHARACTERI S TIC TURBINE NOI S E LEVELS VS RELA TIVE T IP SPEED F2 = Function shown in figure 54 B - - Numb e r blad e s f o r th e last roto r stag e of th e turbin e = S h aft speed in rp m The use of mu ltipl e en gi n es re qu ire s t h e correction, e q. ( 2 B) i n se c . 5. I. 1 .6, a nd t h e s pectr u m is e x tr ap o l_t ed to a r a d i a s of o n e mete r u sin g S PL( f ) I = SP L( f ) [ + 33. 2 + A dB( f ) I ( 32) 1 H 45.7 H Table 4 Discrete ton e compon ent .- The discr e t e ton e compon e nt of turbin e nois e i s d ¢ fi i t e d in a mann e r s imilar to t ha t for bro a db a nd noi se. The l ev el of t h e fundamental t one a t 4 5 .7 M (1 r50ft) - from the source is giv e n by I ° • i O. 6 -4] + r I ( 4 ) + 56 + K whe r e C / S = s t a tor / roto r s p a cing shown in fig u r e 55 K = correctio n for turbofan s wit h a prim a ry no z zl e exit p lane upstr e a m fro m t h e secondary nozzl e e xit plan e, i. e . , th e JTSD _- -! 0 dB for th e JT8D |, " " 0 dB t b r du a l ex hau st s ystem s with co-pl a nar e x its , or t u rboj e ts The fre q uency o f the fundame n tal ton e corre s ponds to the blade passag e fre q uency , fo , a bove.

The higher har m onic s ar e assum e d to f a ll off at a -!0 dB slope as shown i n figure 5 4. A revi e w of | . av a il _N , _ _e st d a t a indic a tes t h at t he second h ar m onic r a ng e s fro m 8 to 20 dB b e low t he fu n da m e _t tai . In so me cases, th e h armonics for t he second to t h e last tur b in e sta ge w e re dominate .

T he lack of adequate informati o n precluded fur the r study of the p h en o raenon.

in the computer program, th e ton e s ar e a dded to th e bro a dband sp e ctr um (e q. ( 3 1) above) | be fo r e t l_e c o rr e c tions for t he us e of multipl e engines and inde x (R = ! M ) conditions ar _ a p pli e d .

After t h e c orrec t ion s ar e made , t h e resulting s p e c t ru m r e prese n ts t h e t u r b ine noise at t he fr ee -field , index co nditio n .

DISCRETE TON I_ m 0 tl "1 = " ., NOTE: t . = J "%1 _ " "" BLADE PAS S AGE FREQUE N CY , fo ' ..J o10 Q I SDEFINED A S T H E FUNDA M E N TA L -- " ' . HARM O N I C FREQUENCY II z , ..,20 " ll llt l I, , - , " -3 0 _ 1 2 3 4 HARMOM IC NUMBER FIGURE 54 . - T URBINE NOIS E S PECT RUM S HAPE 5TAT O R(NGV) ROTOR S TATOR R O T O R SP ACING EQUA L S C / 5 FIGURE 55 .- DEFINITION OF STATOR . ROTORSPACINGFOR TURBINES i, i 5.2.4 Co m pr ess or o r Fan Nois e Th i s sec tion de al s wit h t h e p re d i ctio n pro ce dur es fo r ] / 3 oct a v e b a n d noi s e du e to rot a ti ng c om p r e ss or a n d fan blades. The procedures p redict t he noi s e s pectr a for the free -fi eld, index co nd itions d i s cus sed in s e c t ion 5.1.1.2 The me t ho ds given are applicable to t urbojet c ompressors.

single o r mu l t i stage tur b ofans w ith or wi t hout i n let guide vanes, and lift fans for S TOL ai r c raft. It is as s umed that the inlets are t he " fi xed 4 nlet t ype," i.e. , no blow - in - d oo rs and the blade / vane number ratios for the fans or compressors are optim um for minimum noise.

The e m p irical noise predi ct ion p r ocedures discussed in this section w ere deri v ed f r om JT9D an d J T3D s t atic eagine t ests. The data was ana ly zed in terms of the following noise components: a) i n l e t f an o r co m pre ss or noise e m i t te d from the in l et duct l) Br o adband n o ise 2 ) Dis c ret e tone noise 3 ) Com bina t ion t on e n oi se ( buzz - sa w) b) F a n dis ch a rg e n o i se emitted from t h e fa n d i sc ha rge d uc t l ) Broadband noise 2 ) D i s c re t e to n e n o ise The c o m p u te r pro gra m pr e di c t s ea c h of t he su bc o m pon e n t ( br o a d ba nd , dis c r ete ton e , and c ombina t i o n tone ) n o ise f o r ite m s a) and b) above and the spectrum levels a re com b i n ed on an energ y bas i s to form a sin g le spe c tr u m. For an engin e w i th m o re t han one fan stage, each stage is treated as an independent so_lrce and the soun d energ y p roduced b y each s tage is ac c umulated acco r dingly. No c orrection i s made fo r bla d e row a tt e n uation. Caution is to be applied in using this p ro ced u r e lot turb o f a ns wi th m ore t han two fa n st ages. I n t he case of a t ur bo j e t , t he noise fro m t h e fi rst c omp r es s o r st age is assum e d t o be r ep r esen t a ti ve of tL e fa r-fi eld n o is e.

5.2.4. I Ba ck gro un d i This discussi on t ou ches bri e fly o n t i le v a riou s i d eas a n d ph i los o ph i es th a t v_e n t in t o t he .... _ dcv e lo pnlent o f t he p ro cedures. Of the i lems d i ._;ct,ssed,the fir st is the d ef i ni t ion o f the so v rc e n o ise i : a ss o ciated wi t h tile t ot a ling blades in side a d uct with i nlet a n d ex it gu i _ ' : vanes. T he sec ond i s a _. [ i 12 2

J

description of s ome o f t h e procedure-rel a ted correc t io ns tha t a re e m ployed . Speci ._ l a ppli, a tio ns an d li m it a tions are noted briefly.

Br oadban d nois e . - The term broadband noise is associated wi t h " whi t e " noise t h at is gener at ed by uns t able a ir fl ow pas t t he ro t ors and s t a t ors of each fan s ta ge. This noise is no t stric t ly whi te r ' it f noise because a t a fr equency o f appr ox i m ate l y t wice t h e fundamen t al blade p a ssage f reque n cy , th e . / :_ spectr a l dens it y levels ha ve bee n o b served to f all o f f at a ppr o xima tely 30 dB per decade. Th e generate t he noise a re no t well u nders t ood, b ut are t hough t t o invo,ve local varia t ions in t he s t a t ic , , , _ pressure fi eld due to : , , " i ) vor t ex s h edding fro m t h e blades a n d va n es, , , , " ii c orr e sponding ! / 3 octave band spe c tru m sh ape is _h ow n in figure 5 6 a . The e xa c t m e ch a n isms w h i c h , 2 ) lif t flu ct uat io n s r e su lti n g fro m a p p roac hin g eddies in un s tab le fl o w , and " | / 3) t u r b ule nt bo und ary layer(s) / s' I n t his proced u re, t he broadb an d noise is sep a ra t ed i nt o t w o com p o _, en t s; o n e radi at i ng u pstrea m a n d o u t t h e i n let , a n d o n e ra d ia t i n g downstrea m a n d o u t t h e f an disc h a r ge n o zz! e . E n gi n e si z e scal ing is acco m plis h ed by n ormali z ing th e inle t co m pone nt wi th r . c g pec t t o the ro t or diame t er and t h e d isch a rge co m po n e nt wit h respect t o t h e exit a re a of th e f a n disc h arge nozzle. This n or m a li za ti o n appr o x i m at es t he more cl a ssical m a ss fl ow sc a ling a s disc u ssed in sectio n 5.1.1.5. The val i dity of the approxi mat ion is due t o t he way t he t u rbo f an engi n es are designed, i.e., t he inle t and _. disc ha rge Mach nu m be r s do n o t vary ap pr ec iably for d iff e rent e n gine s op e rat in g a t t h e s a me f a n p ress u r e ra t io. T h e n or ma l ized l e vel s are t h e n r e l ate d t o th e r i se in p re s s u r e a c r e ss each f a n st age as s h ow n in fig ures 57 a and 57b.

Disc rete to n e no is e .- Di s cre t e t o nes a t in t e g er m u l tiples of th e fu nd am en t al b l ade p a ss age f r eq ue nc y are radia te d from th e fans and compresso rs of a ll j e t engines wh e n o p e rat e d at e ith e r su b soni c o r supersoni c ti p sp ee ds. A major sour c e of th e ton e s fo r fans w ith inl e t g uid e v an es (IGV ' s) i s the st a t i c pressure fi eld d ev elop ed as the blades c hop thr o ugh t h e wak e s from t h e inl e t guide vanes. For fans wi t hout I G V ' _ , inlet flow t urb u len ce p roduces th e s ame e ff e ct, but th e sound p roduce d i s o f a lower l evel.

An a dditi ona l s our ce o f n ea rly eq u a l st re n g t h to t he n oi s e g en e r ate d by th e IGV-ro t o r interac t ion is t he no is e pro d uced by ro tor a n d exi t- guide - vane (EGV) inte r a c tion. A sig t _ificant ! pa r amet er affe, ct in g the roto r - EGV in t e r a ctio n i s t he bl ad e / van e numb er ra t i o. Th is e ff e c t i s i l lustrated in se c tion 5.2.4.4. I n bo t h c ases, I GV- r o to r o r r otor-EGV int er a c tion , t h e noi s e i s ge n e r a ted by a s t atic p r essu r e field which can be r elated t o lif t fluctuations on the blad e s and van e s.

'_' 12 3 t

g

!!i

Ill lT rl___lltilllI_ L ,_!l ,; /1 L I I [ 111 iI III I I I lll l ilili l _l!l_HRl.]_lil_l"_ l _ ,1' • " I I_, : 1"Hl"H11 _ _, _, i I 11 I I lll III li lllllllJllll [ ll]il!_ll ' ]ll_1111!1] 11 11'.] -] !i]-_ --_ ug Tll:ll l ! ' ,l!i l l. , , ] I I i i I I li t l ll ll l jl jH _ L ll]l lli' , l _)l.l__ [ I I I I I tl ll Lllll I t _ ' l_ j j_ j _l [ _ , _ ...........

I l m_ ' _ / _ ;_ ]l ] 1/1 J l II l llItl ][ T. _ ]N ] ] J] _ d _L.'_I_I._. I ,:_ ] /I I I I I l l / l_lllt!lil l T l ',I_l,: t 'l llllllll_ E l;_ I N]_ili i i itl l l l tlll[ l l _ ] _.[l_ E _) l Il l I t I Il tl l 1111 1 1] 1 1 11 hl l U _I_ ', l!li 'l ll[] l lli]]!!];]l! ' . ].L I J II_|. ' _._]1 [ ] I I I IIII I llit_II [T '__ ? ,I]I ]I . I] , ][ I I I I I 11 I|lllllllll_ h' _l ' .I / ll i _]tllll ] !lll_l l _ L .a l _l I,.-. 0.5 .1 .2 .4 .5 1 2 4 6 10 I, k l e L . D I MENSIONLESS FR E QUENCY a) BROADBAND NOISE SPECTRUM SHAPE HARMONIC LEVEL H ARMONICLEVEL = HARMONIC f Lo , K = 11 LEVEL

/

L e " . H M ONI CLEVEL=L o+ 3 - 3K 5 d B 1 2 3 4 5 K 1 2 3 4 5 K HAR M ONICNUMBER HARMONICNUMBER SKETCHNO , 1 FOR 1st FAN STAGE SKETCHNO , Z FOR AL L OTHER WITHOUTIGV ' S CASES b) DISCRETE TONE-RELATIVE LEVEL VS HARMONIC NUMBER FIGURE 56. - FAN NOISE SPECT RUM SHAPES 12 4

!

_ 75 I _ _ 70 N O O _ 65 _ _ i I I ' z _ . _ 0,. 1 0.Z 0.4 0 1 6 0.8 1.0 i FAN PR E S S URE RI S E-, c_ T / PT ..... ( F AN PR E S SURE RATIO M INU SON E) _1 a) N O ISE E M ITTED FR OM THE INL E T DUCT

9 0

_ e 5

_ 80

8 _

N 75

o 70 Z _ I , I ,| J J ___J 0,1 0.2 0. 4 0 , 6 U ]1 . .4) F AN PRE S SURE RiSE - AP,r / Pr | (FAN PRESSURE R A; I0 MINUSONE) b) NOISE EMITTED FROM THE FAN DISCHARGE DUCT FIGURE 57. - BROADBAND FAN NOISE ( P EAK ONE-THIRD | OCTAV E BAND SOUND PRESSURE L E VEl.)

In the prediction procedure, the d isc re t e-tone noise is separa t ed into two noise components in the same manner a s that done for b roadband noise. The normalized levels for t hese componen t s are shown in fi gu r es 58a and 5 8b. For turbofans wi t hout IGV's for the f i rs t fan s t age, e.g., the J T9D, there is an additional noise s ource radia t ing out the inlet as the relative t ip Mach number exceeds unity. This noise is called (o m bination tones and is discussed below. As t h e relative tip Mach number exceeds one , the ha r monic tones at multiples of the funda m ental blade passage f r equency decrease with an increas e in tip speed or fan pressure ra t io. This phenomenon is t hought to be t he resul t of a non-linear trans f orma t ion of acoustic energy from the discre t e-tone noise t o combina t ion t ones. I t is t r ea t ed as foll o ws for noise predic t ion purposes. At low rela t ive tip Mach numbers, t he f un damen t a l t one foll o ws the solid li ne shown i n fi gu re 58b . Th is curve is used un t il the Mach number exceeds uni t y. Af t er this point is reached, noise level decays for an increase in the Mach number cr fan pressur e ra t io as shown by t he dashed fi ne in figu re 58b. It should be remembered, tha t t he inte _ ec tica poin t of t he so li d curve and the dashed line vary wit h differen t engines. T his point corresponds to t he condition where t he rela t ive t ip Mach number j us t exceeds uni t y- 1.025 is used in t he compu t er progra m . T he effect just described applys only to t he fi rs t fan s t age wi t hout IGV's , ot h erwise the solid cu rv e in fi gu re 58b is use d for all fan or compressor s t ages.

B o th the inlet and dis ch arge funda m ental t o n e s are assu m ed t o h av e their peak l evel at the blade passage fre q uency. The relat i ve levels f o r t he hi gh er h a rm onics are shown i n fi gure 5 6 b.

Co m bination tone nois e (buzz - saw] .-When the fi rs t ro t or s t age does n ot have IG V ' s, an additio r,rd source of fan no i se become s sign ifi can t w h en the rela t ive tip Ma c h number g o es superson i c . At th ese h i gh tip speeds, a shock fo rm s on each ro to r b l ade. Th ese s h oc k s move u pstrea m a nd decay i nto a system of Mach waves whic h propaga t e ou t of the i nle t duc t .

Theoret i cally , t hey would be obse rv ed in the far field as a series of to n es at mu l t iples of t h e blade passage f r equency. E x perience indicates t h a t th ere is a redis tri bu t ion o f energ y . Small differen c es within t h e m an u fac t uri n g and assembly t olerances of ro t or blades appear t o affec t t h e de t ailed s h ape of t he sho c ks a t tached t o each blade. T h us, t he Mach wave system repea t s i t self wi th each revol u ti o n of th e r ot or, rather tha n wi th the pas, _ age of eac h blade. T h e resul t ing noise spe c tru m c o n t ain , all h armonics o f t h e s h aft ' s ro t ational speed. This noise h a s been termed combi n a t ion t one !.

:_ nois e for the subj ec tive response it produces.

A n o is e spect ru m, c onsisting of a s e ries o f t ones ea c h with t he same order of m a g n i t ude a n d s ep ar a t_ ; d by a fixed frequen c y , is referred t o as a combi n a t i o n tone. I t is a charac t eris t ic of th e h u man au di tory system to judge t h e pit ch of t h i s typ e of noi s e as t h oug h i t w ere a t o ne at t h e s ep ar a tio n t : -eq u ency, a lt h o u g h t h er e m a y be little s ou n d e n er gy at t h at fr equ e ncy. T h i s t y p e of n o i se i ; f ou n d in al l f a ns an d c o m p ressors wh i ch o p er a t e a t superso n i c ti p spe eds , b u t it m a y b e m ask ed by a lo u der to n e a t t h e b lade-pas s age f r equ e ncy or b y jet n oise . T he p r e s e nc e of i n let-g u ide - van es atte n uat e s t h e M ach w a v e s ys t e m ; henc e , t he c o mb inatio n t o n e n o i se i s 1 27 i in s ignific an t comp a red to the other component s a s i n the c as e of the older byp ass engin es . However , if one observes a 74 7 aircraftdur i ng ta k eoff , the n o i s e e mi tte d fro m the i n le ts of t he JTgD engines is perceived to be s i m ilar to t h a t produced by a buz z -saw, In t he predic t ion procedure , the ca l culat i on of comb i na t ion tone yJ oiseinclude s the following sim p lifying as sump t io n s: 2) I t wil l cont ri bu t e to the t o t al f a n noise onl y if the rel a ti v e t ip Mac h number i s gre at er l) Combin at ion t one noise i s emit t ed only f rom the fan inle t .

th a n one.

3) I t will con tri bu t e t o the t otal f a n noise for fan s wi t ho: _t IGV's.

4) Combina t ion tone noise can be predicted in t erms of three sep ar ate spectrums based on peak noise levels centered at one- h alf , one-four t h , and one-eigh th of t he funda m ental blade pa s s a ge frequency of th e fi rst f a n stage .

The three pe a k noi s e level s are shown i n figu l e 59, plot t ed against the rela t ive tip M ach number. T he spectru m sh a pe s corre s ponding to t h e t hr ee peak noise level s are s hown in fi g u re 60.

Co rr ect ions . - In t h e predict i on procedures , va ri ous correcti o ns are emp l oyed to account for ch a nges in the en gi ne con fi guration from that for th e reference JT3D and JT9D en gi ne s . The c o rr ec t ions ref l ect th e effec t s for v a rying suc h items a s rotor-sta t or spacing, d i rect i vity angle, bypass-ratio , disch a rge duc t length, flight effects, a nd t he use of IG V 's an d mul t iple en gi nes. E a c h of these corrections a re di s c u s s ed below.

! ) Rotor- S ta t or Spacing Correction-This correc ti on a c count s for t he noi s e generated due t o t h e pre s ence of s tator s in front and be h i n d of t h e rotor. Th e correction is s h o wn in fi gure 6 1 and is to be a dde d t o the peak noise levels d escribed above in "Broadban d Noise " a n d " D i s c rete Tone Noise ." F igure 62 illustratesthe de fi nit i on o t "the rotor-stator spacing t h at refer to conditions at the rotor tip.

2) Directi v ity Correction - T h is corre c tion accounts for the fact t h at the radiation pattern for t he fan or compressor noise is not sp h erically sym me tn ,, about t h e source. T h e procedure uses simplified directivity patterns for t h e noise subco m ponents (fig s . 63 and 64). T h ese dir e cti v ity pa l terns s h ow t h at t h e n o ise is maximum a t _ l , = 6 0 ° for t he inlet c ompon e nts a nd at • = I I0 ° for t h e fan di scha rg e components. Engine test data h as l I FIGURE 59 .- INLET FAN COMBINATION TONE NOISE !

m " = PEAK LEVEL AT f ", f o / 4 '" Ii .............. " - i ...... _ 'i ; ! ': i ; : ' ; ! :' ' _ _ lil I i i f ii : ' i : 'iii!i " " :; :" ' 1 7:,' : ' " r ] ' " ' -10 " - :_i * " ;; " : .... N i4 : I'li_ _': : , ' _, O f :: I-,, tu PEAK LEVEL AT f - f o / 8 G .

i t" + . _ , i. _ .... I_- 1 7 ................

, ' , - _ * " -_+ ' .......... r _ '. , i:1 .,.,I = ' , _ !! I ' . T Ji , : ' _ ' _, . _ _, ._ . . , ..... _ - _ -, -_:,, ....

..... ..... iiit

-30 /' "_ '" I _ "' .... _ ' .... ..

. 03 , 0 4 .06 0 °1 0.2 0 , 4 0°6 1.0 2. 0 4.0 DIMENSIONLE SS FREQUENCY, f / fo FIGURE 60 .- CO MBINA TIO N TONE NOISE SPECTRUM SHA PE S 1 3 0 i TURBOFANS WITH INLET GUIDE V A NES ( IGV) I G VSTAT OR ROTOR STATOR S I = C 2 / C | , _ : C4 1 C _ , RSS = MINIMUM OF( Si, S, Z) ,, |00 WHERE R _ I S THE MINIMUM R OI ' OR / STA T OR SPACING IN PE R C E NT FIR$ ' _ ' STAGE OFTURBOFANS WITHOUT IGV'S ROTOR _ RS S = C2 / CI a I00 r rlERERSS IS THE ROTOR / S TAT OR SPACING IN PERCENT t FIGURE 62 .- ROTOR . ST A TOR SPACING

t

t 1 33 gp _ ' NOI . L33 _ N03 AII AI/ 33 _II 1 34 I I s h o wn a variation in d ir ec tivity an g l e lor t he maxi mum no i s e nam e ly .5 0° to 70° _ .nd q O _ t to 1 2 0 ° for t he inlet and disc h arge c o m pon en ts . Since c o mm u ni ty n o is e estimates ar e bas r = don passby c on d itions , t he e_ o l in EPNdB in c ur r ¢ . d by using t h is s i m plifi e d app s' o _ e h is small.

' 3) Guide Vane Con'ectio n -T h e presence of inlet-guide-vanesfor t he first fan stage, or e xit guide-v a nes of a procedingstage , alters t h e obse r ved discrete tone c o m ponents for t h e t_a n stag e I _ , _ ing considered. T he broadba n dco m p o nent ra d iating out t h e disc h arg e duct is afr o affected. T h e c h ange in noise is accounted for a s fo U ows : a) Fo ur t h e inlet fan noise - subtract 6 dB from all discrete tones except t h e funda _ nen t ai tone a _ t h e blade passa g e frequency . Co m bination t ones (buzz-saw) are no l considered to b e significantin t h e far field and h ence are not calculated .

b) For th e fan disc h arge noise - add 6 dB to th e fundamental tone and 3 dB to t h e broadbandco m pon e nt .

4) Bypass Ratie and Duct Lengt h Corre c tion-T h is co r rection approximates for the c h ange in t h e fa n disc h ar g e noise t h at would be observed in th e far-field if * , h ebypass ratio and duct leng th w ere varied. At t h e present time , t h e physics for t h is effect are not completely understo o d, b u t a t e iho ug h t to be due to a c h ange in t h e trans mi ssio n coeffi ci ent at t h e end o f t he disc h a rg e duct, i . e. , t h e duct acts as a s h ort-wave-guide.T h e cor r ection is defined as f ollo ws, i . e ., ! et $ , le t _ L = i Oglo(BPR / 10) for' 0.5 < BPR < 10 fo e 8PR 1 > 10 f1 7 8 'fo r BPR _ 0.5 i Update _ L for th e c han g e in du c t len g t h, _ . e ., let & L = ( _ L) C T h e c onstan t . C equals O , ! / 6, 1 / 3, I resp ect iv e ly f o r s h o rt lh n ducts , 3 / 4 le n gt h fan du ct s , long f an du c ts wit h c oplanar pri m ary / sec onda r y no zz le exi t, _,an d long fan du c t s wi t h a ret ra cte d p r i m ary nozzl e , i. e . , t h e JT S O engin e. & L is a d ded to t he discr e te t one l e v e l s and A L / 2 is add ed to t he b roa db and l e v e l _ of t he dis cha r get an n o i se.

$ 1 3 5 5) Flig ht Effec t Cor r ection-T h i s is an optio n al correction co n sis t ing of two p a rt s. T h e E c s t pa rt i s t he Do p pler- shi ft wh ic h i s w ell k n o wn an d r e qu ire s n o ex p l anat io n _. < . . T h e s e c o n d pa rt i nc l u de s a th eoretic a l le v el c or r e c tio n ass u m i n g a di p ole s o u rce . " flae re su lt of t his level c orr ec tion g i ve s a s li gh t inc re as e i n n oi se level i n t h e f or wa rd qua d ran t an d a s li gh t de c r ease m level for t h e a f t qua d r ant .

An a ddition a l flig h t effect a pplie s for a lift fa n mo unted in th e wing of a n aircraft . T h i s ef f ect is due to t h e flow distortion that results from flow separation at t h e inlet lip and t h e work distribution differen c e on t h e fan rotor. S in c e t his effect is p e culiar to t h e lift-fan configuration, it will be discussed furt h er in section 5. 2 .4.4.

6 ) Mult i ple En gi ne s C o r re c tion s- To account for multiple s ource s, t w o cc , rre c tion s a r e em p loy e d - o n e ap pli es to til e i n let f an n oi se compo n e n t s an d t h e s eco n d app lie s to t h e di scha r g e f an n oi s e c o m p o n e nts. E quat io ns ( 2 A) an d ( 2B ) i n s e c tio n 3 . 1 . 1 .6 a re app lied re s pectively for th e inlet a nd disc ha rge fan component s .

7) Index Spectr a Co rr ec t ion - To remove a tmo s p h eri c effect s fro m t h e predicted spe c tr a , t h e spectr a are ex t rapol at ed inward t o a radius of o n e me t er. Th e fan noise p redic t ion procedures a l e b a se d on data ori gi na l ly measured a t a ra dius of 45.7 M (150 f t ) . T h e correc t ion for spher i cal divergence is +33.2 dB and t he a t mos p henc a bsorp t ion correction i is given in table 4 .

i R esu lts . - Before t h e actu a l p r edictio n procedure s for co m pre s sor or f an n oi s e a re p re s e nt ed , it i s ee ms a ppropriate t o s h ow a c o mpari s on o f t h e r es ult s t ha t ha ve been o b t a i n ed wit h mea s ured en gi ne data . Figures 65 and 6 6 s h ow t h e comparison . It is expected t h at t h e observed far-field noise can be predic ; cd wit h in ± 3 PNdB for engines simil a r to t h o s e in current usage .

5. 2 . 4 . 2 I n let Fan and Compre ss or N oise Prediction T h is section de a ls w it h t he prediction of the t h ree noise compo n ents r a di a ti n g o u t th e inlet for c o n v en tio na l t u r b of an an d tu r b ojet en gi n e s. Th e n oise fro m t he c o mp r ess or of a t u r b ojet en gi n e i s predi c t e d as t h o u g h i t wa s a s i n g le - s tage fan. The n oi se f ro m t h e t u rbofa n e n gi ne i s pr e dict e d as t h e e n ergy s u m of t h a t pr od uc ed by e a ch f a n st a ge . T h e p ro ce dur e is ba s ed o n d a t a f rom si ngle an d do u ble s t a g e fan s. H en ce , c a re sh o u ld b e exer c is e d in u sing th e s e p ro ce d ur es f or f a ns w it h mor e t han two s tage s b eca us e bl a de ro w att e nua ti o n is n ot c on s i dere d .

¢, I Br J a dban o c ,, m tpon c ,nt pred ict ion , T he ch a rac t er i s t ic p e a k I / 3 o ct a v e ban d so u n d pr e s sure l e , .'el o f a sing l e f an s t age is de fi ned by _ I N LET FA N COMPO N ENT _ = 6 0° DISCHARG EFA N COMPO N ENT @ =1 10 ° --.,,:+ ........................ -.+L_._ + _+ . ......... +++u • - - " t -_ .......... rl.......... _ . ~, , . _ . _ , _ FIGURE 66, - . TOTA L FAN NOIS E FOR J T "3D-7 EN G I NE , , i A SIDELINE AT61 METERS 1 38 !

m !

Lo = FI(FPR - 1) + F2(RSS) + F3(_ ) + 10 Lo910 (1 - t 4 o cos _ ;) (34 )

-,]

where ill F1, F2 , F3 represent the appropriatec _ rves in figures 57 a, 61, and 63 , respectiv e ly : , _ FPR = Fan pre s sure- a tio, i. e ., total pr e ssure ratio acr o ss th e f a n .l s t age be i ng c on. _ red ' ! RSS = Rotor-S ta tor spacing in %, s e e figu re 6 2 = Directivity angle re. inle t axi s D = Fan di am eter DR = Refere n ce diame t er = 0 . 305 M(1 f t ) ( ! - M o cosl[) = Doppler-s hif t / 'a ctor T h e re su lt , L o , i s a f ree- fi eld level i n dB re . 20 p N / M2 a t a r a di us o f 45 . 7 M from t h e s o u r c e a t s t an d a rd da y c o n dit i o ns (1 5 ° C , 7 0% rel a tive hu m i dit y). Th e s o un d p re ssu re level sp e c tr um i s obt a i n ed fro m fi g u re 5 6 a , i . e ., SPL(f) -' - Lo + F4(f / fo) (35) wher e fo = the fundament a l blade pas s agefreq u ency in H z = B 01 [ 6 0 (! - Mo cos / _ )l B = t h e mu n ber of f a n bl a de s on t h e st ag e bein g consi d ered = th e wh eel s peed in rp m 1 3 9 | I Dis crete tone component pred i ct i on .-T h e c h arac t eristic peak level in dB re 20 # N / M 2 for t h e funda m ental t one of a single f an stage is given b y Lo = FI(FPR - 1) + F2(RSS) + F3(Il J ) (I - Ho cos _ ) "4 ( 36 ) wh ere F 1, F2 , F3 represent t h e appropriate curves in figure 58b, 61, and 63 , respec t ively. Th e solid- fi ne curve in fi gure 58b is to be used for all fan s t ages with t he excep t ion of t he 1s t s t a g e for a turbof a n engine without inle t - gu ide-vanes and operating at a fan pressure ra t io grea t er t han critical.

T h e calcula ti o n for t his case is FI(FPR- 1) = FI(FPR 0 - 1) - 30.4 Loglo _ , FPRo . 1" t FPR- 1 olt d 1 1 ne wh ere FPR o equals th e critical fan pressure ratio wh en the relative tip Mach number jus t exceeds : uni t y. Th e t ypical result of the ca l culat i o n for the JT g D engine is shown as t h e da shed - line in figu re 58b. TI L e characteristic level, L o from equation (36), is at free- fi eld, standard day conditions and 4 5.7 M from t h e source .

t Th e nex t step is the accumula t ion of the harmonic levels to form the aco u stic spectrum. Th e ._ re lat iv e har m on i c levels are s h own in fi gure 56b. The tones ar e added on an energy b a sis to t h e b r oadband spect rum . Th e calculation steps for accu m ulating t h e harmonic levels a r e outlined belo w.

T h e steps c ontain t h e l ogi c for calculating only t h ose h ar m onics t h at ar e necessary to form t h e 1 / 3 octave band spectru m instead of t h e " brute-force " approac h of calculating many h armonic tones and t h en dete rm ining w hi c h tones are contained in eac h pass band. The indicator IG V in t h e logic denotes i f inlet-guide-vanes a re present for t h e first stage, i . e., I G V #=0. The symbols fo ' fl denote t h e fundamental blade passage frequency and t h e cutoff f r equenc i es for t h e filters , respectively.

A lso , t h e equals sign h as been genera liz ed to denote t h at t h e results of t h e rig h t replaces t h e qu a ntity to t h e left of the equals si gn .

F ortrat _ instn 4 ctiot z s . . - ao = 0. 1 (L o -3. ) IF (IGV . EQ. O) ao _ - a o + 0 . _ , 14 0 # t NI = l'+fl / f o DO 3 1 = 1,2 4 t PI - I0 . **(0.1 * SPLI) N 2 -- fl+l / f o IF ((N 2 - N1) .L T. O) GO T O 3 !

DO 2 K=NI,N 2 i ' t .

IF (K .EQ . 1) GO TO 1 |' PI = PI+ 10"**(ao"0. 3 * K) GOTO2 | 1 PI = PI+ 10. ** (0.1 * Lo) 2 C O NTINUE | SPLI -- 10. * AL O GI0(PI) 3 N 1 - N2+ 1 Th e results of th e abov e calculation ar e tw e nty-four 1 / 3 octav e band sound pr e ssur e lev e ls for | the inlet fan sp ec tru m wh ic h in c lud e s th e bro a dbandand dis c r e t e -tone c omponents .

Combination - tone component prediction . - Combination tone noise is calculat e d only for t he firs t fan stage for turbofans wit h out inlet-guide-v a nes.It i s assu m ed that only th i s stage contributes t o buzz-saw noise obser ve d in t h e acou s ti c f ar - fie ld. Fur th er, this noise is a ss um ed to exis t only w h en t h e rela t ive tip M a c h numberis greaterthan one.

The chara c te ri stic peak ( I / 3 ) octav e band so u nd press u re levels i n dB r e 2 0 I J N / M2 at center freq u encies eq ua l to ! / 2, 1 / 4 , a n d I / 8 of t h e f und amental blade pass a ge freq u e n cy f o are give n by I ¸ L1 - a o + F S O _R ) f or f = f o l 2 L 2 = a0 + F5 ( HTR) fo r f = fo / 4 (3 7) L 3 = a o + F S( _R) fo r f = f o / 8 whe_ F 5 are the appropriatecurves in figur e 59 MTR = r e lativ e tip Ma c h number ao = F3 (q,) + !0 IOgl0 (1 - Mo cos _ ) " 4 F 3 = t he dir e ctivity correc t ion shown in fi gu r e 63 The lev e ls (L I , L2, L 3 ) ar e at fr ee -field, standard day conditions at a radius of 45 .7 M from the s ource .

Th e sound pr e s s ur e l e vel s pectru m f or this compone n t i s approx i mat e d by SPL(f) ffi 10 LOglo K _ I where GK represents the sp e ctrum shap e curve s shown in figure60 for K = i, 2, 3 .

5. 2 . 4 .3 Di s ch ar ge F an Noise Prediction Two co m ponents are accumulated to provide the t o tal fan nois e radiatin g from the fan d is charge duct. The s e components are broadband and di s cret e tone noise. The n o ise produced by m ore than one fan stage is esti m ate d by predicting the noise for each sta g e and the results a r e summed o n an energy basis. The c o mpressor noise contributi o n emitting fr o m the engine disch arg e does not appear s igni fi ca n t i n the far-fi e ld ; hence, it can be ignored. The reasons are ( I) it i s mask e d by more do m inent s o urce s, i.e., f a n, jet, core a nd turbine co m pone n t s and (2) it is attenu a ted in its propagation through the hi gher co m pre ss or s ta g e s , th e combu s tor , and turbine stages.

14 2 v k _ k Broadband component pred i ct i on . - Th e c h aract e ristic p e ak 1 / 3 octav e band sound pr e s s ure level of a single f a n stage is defin e d as follows: ;_ Lo = FI(FPR- 1) + F2(RS$) F3( _ ) + C ] t (3 9)

c, " " o |' wh e r e

th e appropriat e curv e s in figur e s 5 7b , 6 1, and 6 4, r e sp e ctiv e ly.

Fan pr e ssur e ratio, i . e . , total pr ess ur e ra tio acro ss th e fan stag e b e ing consid e r e d.

Ro t or-Stator spacing in % , s ee fig ure 62.

Dir e ctivity angl e r e in le t axis.

F an discharg e nozzl e ar e a .

R e ference ar e a = 0.0929 M2 (1 ft 2) Doppler-shift factor.

3 dB for fan stag e s with in l e t-guid e - van es.

0 d B for th e Ist fan stage wi thout IGV's.

Bypass-ratio and duct lengt h correction discuss e d in sect : ion 5 .2.4.1.

level in dB re 20 p N / M 2 at a radius of 4 5 .7 M from t h e source at 70% relati v e h u m idity). The sound pressure level s pectru m is cribed for t h e inlet broadband co m ponent.

icti on . -T h e _h a r acteri s tic p e ak level in d B r e 2 0 P N / M 2 for t h e age is g w en by 1 43 | i• Lo ffi FI(FPR - 1) + Fz(RSS) + F3(I _ ) + C (4O ) + 10 LOglo[( _ RR) ( 1 - M o cos _ ) "4] + _ L whe re F 1, F2, F3 r e pr e s e nt th e approp ri ate curv e s in fi gur e s 5 8a, 6 1, and 6 4, r e,a ctively.

C = 6 dB for fan stag e s with inlet-guide van e s.

= 0 dB for the first fan stage without IGV ' s.

Th e charact e ristic l e v e l , Lo from equation (40), is at fr e e-fi e ld standard day conditions and 4 5 .7 M fro m the sourc e .

Th e next step is the accumulation of th e harmonic lev e ls to form the acoustic spectrum. Th e procedur e for adding the ton e s to th e broadband _ o m pon e nt is the sam e as that describ e d for the inlet di scret e -ton e co m ponent wi th th e e x c e ption that we have a different charact e ristic lev e l, Lo.

5 .2.4.4 Lift Fan Nois e Pr e dictio n Th e lift fan noise pr e diction proc e dur e has b ee n d e velop e d bas e d on th e fan nois e pr e diction proc e du re , d e scrib e d in pr e vious se ctions 5 .2. 4 .2 and 5 .2.4. 3 , and a forward v e locity corr e ction i utilizing e xisting e xp e rimental data (r e f . 3 0). The stat i c n o ise lev e l of an e xistin g lift fan (r e f . 3 ! ) i was compar e d to t he pre dic t e d nois e by th e method outlin e d in the pr e vious two s e ctions and good t , agre e ment was found (fig. 6 7a). It i s assumed that the predicted results corr e spond to a fan design vanes or " leaning " van e s, ar e not con s id e r e d in th e pr e diction.

l wi th an optimum blade / van e nu m b e r ratio; however th e effects of varying th e number of e xit guide Th e noise sources for lift fan propulsion systems are simil ar to that of conv e ntional engin e s .

The f an its e lf constitutes the major noise source. In addition to the fan noise, noise due to the jet a nd turb i ne are a l s o gen e rated by the drive system. The noise of each of these components can b e evaluated by the metho d s descri b ed in sections 5 .2.2 and 5 .2. 3 . Th e total noise is the energy su m of the individual components. For lift fans that are driven by a tip tu rbine, the m axi m u m design tip M a ch n um ber of the f a n will generally be less than one, mainly because of the t u rb i ne stress limit.

Th is limits the fan pre ss ure ra tio to below 1 . 3, which results in low jet v e locities and jet noise.

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o,. :: : : : : ' : :_ " : .... :: , ":_ : : :: : :: : !I! :.:: - _ , ._ _ " ,":. : I ' : ' , :".I I ' " I ' ' , : ' " i ' " : " _ ' I • I " ' • I ' " I " ' " _ - -_-- ' 0 . 1 .2 .3 VELOCITY RATIO V c / VTIP , b) LIFT F A N R O T O R EXIT DIST O RTI O N TEST VERSUS PREDICTI O N & , FIGURE 67 . - LIFT FAN PRED ICTIO NS i 145 _ _ confi _ . , ,_ 'ation. The noise du e to the t ip turbine also is of se condar y i m portance due to t h e la rg e numb e r o f turbin e blad e s , i . e . , th e funda me n ta l b l ad e passag e fr e qu e ncy f o r th e turbin e usually li e s abov e th e audio fr e quency rang e .

Th e e ff e ct of forward m otio tl r e quir e s consid e ration of the flow distortion e ff e ct on nois e g e n e ration. This flow distortion r e sult s m a i nly from two sourc e s. Flow s e paration is possibl e at th e inl e t lip du e to th e s m all radius of curvatur e r e quir e d by wing installations. The second and th e mo re se v e r e disto rti on r e sults from a n o n-uniform loa d in g distribution e xisting on th e fan rot o r.

Figur e 6 8 shows a typical tak e off flight path f o r a lift fan installation in two mod e s of op e ration.

Mod e 1 re pr ese nts v ert ica i tak e off or th e z e ro c ro ssflow ve lo c ity cas e si m ilar to static op e ration , and Mod e 2 r e p re s e nts th e op e r a ti o n with crossfl o w imp o s e d on th e fan.

Th e complet e vector diag ra m for th e " up wi nd " side of th e fan is shown. On this side, the crossflow loads up th e rotor and incr e a se s th e fan pr e ssure ratio; but on th e " downwin d" sid e , th e opposite happ e ns. The diff ere nc e in work that r e sults ca n b e stat e d as follows : AW~ _ c(U2V2-U! V 1) l e t ; U = rotational speed = U I = U2 :!

i

A V --- chang e in fan e xit velocity - V2 - V 1 Th er e for e A W ~ U Upwind: A W ~ U (AV + V c ) _C Down win d:

(Av . vc)

AW _ g c T h e abov e diff e renc e in work ass u mes that no flow entrai n ment take s plac e due to t h e inlet w a lls be t bre t h e air e nters the fan . Th is a ssumption is reason a ble fo r s h allow inlets su ch as a '_ 1 4 6 .... • -- z z .? ,, .......

i _ h , !

_,, Vo ®

FLIGHT PATH I _ ' FIGURE 6 8. - E FF E CT OF CROSSFLOW ON I _ IFT FAN PERFORMANCE | I " fan-in-wing " pr o pulsion system. A ri ft-cruis e fan woul d have a lon g er inlet, and in this c ase , nearly co m plete entrainment of the air would take place before flow incidence on the fan face. Theref c, r e , t h e dis t ortion effec t s o n noise generation could be significantly less than that ci t ed a b ove.

The distortio n for the two lift fans, for which experi _: ental data was available in reference 3 I, have been calcula t ed. Figure 67b compares the measured and calculated distor t ion for t h e X- 535 and LF366 con fi gurati o ns. The calculated trend agrees we ll with the experi m ental data. This in di cates t ha t t he ratio of forward veloci t y to tip speed is indeed a good correlation parameter for distortion effects.

Th e distortion effects on nois e trove b e en reported in reference 31 based on ac t ual lift fan noise tests. A re v iew of o th er l i terature and related da t a has in dicated that the state-of-the-art in pre di c t ing the effec t of dis tortion is be st repre s ented by t _ e da t a presented in reference 31.

Th e correspondin g correction, to be added to the _ isc r ete fan tones, is shown in figure 69 as a function of the v e locity ratio Vc / VTI P.

C oncluding , t h e basic fan nois e proc e dur e d e sc ri b e d in s e ctio n s 5 .2.4.2 and 5 .2.4. 3 i s ad e quat e to p re d i ct th e nois e for a lift fan at static cont t itions. It has b ee n shown t hat forward v e locity is th e ma j or para me t e r producing disto rt ion in lift fans. Th e r e fore, th e incr e as e in discr e t e -ton e nois e c a n b e r e asonabl e r e pr e s e nt e d as a function of Vc / VTI P. Exp erime ntal data is cu rr e ntly th e most reliabl e sourc e for repr e s e nting t he chang e in r , ois e du e to distortion.

5 .2. 5 Prop e ller, H e licopte r , and Tilt Rotor Noise Two predic t ion procedures have been developed for these noise co m ponen t s. One is e m pi ri cal and applies to p r o _e ller aircraft. Th e other ha s a theoretical basis and applies to he li copters and tilt rotor ai r craft, in t il e development of the la t ter procedure, it was found t hat it could also be applied f or propeller noise predic t ion because the acoustic theory for propellers is essen t ially the sa m e as that for rotors.

Bot h procedures consider two subcomponen t s for t h e observed far-field noise. T h e subco m po n en t s are (I)discrete-tone, ro t a t ional noise and (2)broadband vortex noise, in each procedure the vor t ex noise is predic t ed by e m pirical equations because the m o r e re fi ned integration an d bound a ry-valu e p r o b le m a ppro a c h es a re computationall y expensiv e and t h ey re q uire m ore infor m ation t ha n is readily available . T h ese refined approac h es a re important for propeller / rotor design : but t h e increase in accur a cy for absol u te levels is not t h at impressive . T h e two procedures de sc r ib ed h ere differ in only one respect. T h e rotational noise i s pre d icted e m p i rically in one and t h eoretically in t he other.

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i " / MO- AIRCRA=T MACH NUMBER 4

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0 . 05 .10 .15 .20 .25 Vc / Vtip FIGURE 69 .- CORRECTION FOR CROS, S FLOW ON LIFT FAN NOISE i 1 4 9 An e rror a n a l ys i s ha s bee n ma de c o m parin g t h e two p r o c e dur e s wit h da ta g i v en i n r e f eren c e s 3 7 an d 3 8. T he a co u s ti c d a t a was m e asu r e d i nsi de a han g e r at app r o x i ma te l y 3 .9 M fro m t he c e nter o f t h e p ro p e l ler . S i n c e t he p ropell e r diam e ter was 1 . 5 M , i t was not k n o wn i f t he m e asu r e d n oi se r ep r es ent e d f a r-fi e ld lev e ls . A c orr e ctio n o f -l . 1 d B f or grou nd int e rf e r en ce was a dded to t he dat a t o o b t ai n n omi na l f r e e - fi el d c ond i t i o ns. In t he or y t he gro un d reh ec tio n an o mal y v a ri es b et w ee n + 4 d B for the te s t c o n ditio ns w i t h t he fir s t des tr uc tive i n terf e r ence oc cu rri , g be t we e n 5 0 an d 70 H z.

Th e d a t a a n a ly sis is t oo length y to pr esen t h e re , bu t it i s wor t h noti n g t h e r es ul ts t h a t w e re o b t a i ne d lbr a f o u r- b l a ded H .S. 2 12-1 4 p ro p eller . B ase d o n a sa m ple of 9 0 sp e c t ra , t he 9 0 % PNdB fo r t h e rotor an d p ro p eller pr edic tio n p ro c ed u re s , _ co n fid enc e ban d i s -5 "8. PNd B an d -3 1 7 i resp e c tively . He nc e, o n e c a n c onc ! ud e th a t t h e accu r ac y o f e ac h pro c e dur e is r o u g hl y equa l . A t t he p res e n t ti me, o n e pro cedur e ca n n ot be re c o mme n d ed in p re f er e nc e to t h e o ther . M o r e da t a an d i s t ud y a re r e quired. So m e s amp l e p r edicti o ns a r e sh o wn in fi gu re s 7 0 and 7 1.

-f 5. 2. 5 . 1 P rope l ler N o is e Pred ic tio n A s im p lifi e d p re dic t ion p r oc ed u re fo r est ima t ing pro pel l er noi se ha s bee n d e v e lop ed. The p r oc e du re con s id e rs two no i s e co m pon e n t s t ha t ar e g e n er a te d b y a r o t a t ing p r o pe ll er. Th ese compon e n ts are ( 1 ) b r oadband vo rte x noi se and (2) disc rete - t on e , r o t a t ional noi se . Th e v o rte x noi s e i s caus e d b y t h e sh e d d ing o f vo rt ic es, s imila r t o t h e Ka r man v o rte x street , f rom t h e tr ai l ing edge of a p r op el l er blade. Ro t a t ional noi se i s d e v e lop e d f r om t h e ha r mo n ic loads t ha t e xi st on t h e blad e s due t o l he st a t ic p res su r e fi e ld d e v el op e d b y t h e p r o pe l ler . A t hi r d t yp e of noi se , "bla de -slap " i s men t i on e d in r ef ere nc e s 33 t h r ou g h 35 ; bu t i t is r a re l y p rese n t f o r conv e n t ional p r op e l ler ai r craf t ope r a t ing a t subsonic t ip s pee d s.

T he p r o c e du r e d efi ned fo r v orte x n oise is based o n a c om bina t i o n o f the e mp ir ical ap p roa c h e s g i v en in references 33 throu g h 3 8 . Reference 32 g ives a simplified, empirical procedure for predicting the ro t ational noi s e component. That used here is identical to t hat provided in reference 32 with t h e excep t ion that the Doppl e r shift and level change is included per references 3 3 and 3 6.

Vor tex n ois e . - T he e q uati o n for tn e over all soun d p r e ssu r e le ve l, L o , i n dB r e 2 0 / a N / M 2 at a d i s t ance of 152.4 M is give n by refe r ence 35 as Lo = ? 0 Logl o _ 'V TE T / (VRTR) _

lO LO glo o11 o o

i FI GURE 70 , - M E ASURE D D ATA (H. S . 21 2 - 14 PRO PE LLER) V ERSUS PRE DICTIONS !$1 O C I'A _ E PMl 8 BANI _ e_ HEm2

i

ii, ii ii ii

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FREQUENCY IN HERTZ LE GE I _ O: PREDiCTEDMEASURED } D A TASCATTER FORGROUND MEASUREMENTS MADE AT VARIOU S ANGULAR P OS! TION S ONT H E 51 METERP O LAR ARC TE S TCONDITIONS: MICROPHONE _ ISAC O NDITI O N AIRCRAFT WEIGHT - 20 , 000 N ( _ , S00LB F ) B O ELKO W -1 0 5 HELI C OPTER FIGURE 71 .-S AMPLE HELICOPTER PREDICTION wher e VTE = e ff e ctive h e lical tip sp ee d - _ Co _ / MT 2 + (Mo _ os _ ) 2 VR = r e f e r e n ce v e lo c ity = 0. 3 0 5 M / S (1 fps) MT = tip Mach numb e r Mo = aircraft Mactt numb e r a = _ n gle b e tw ee n prop e ll e r axis an d dir e ction of aircraft m o t ion C O - a m bi e nt sp ee d of sound T = tltrust d e v e loped by pro pe ller TR = reference thrust = 4.4 5 N (1 lbf) A B = tot al blad e ar e a on one side of the propell e r AR = re f e r e nc e ar e a = 0.0929 M2 (1 ft 2) q' = dir e ctivity angl e r e inl e t axis of prop e ll e r = angle be t ween flight path and so u nd propagation path H owever, both referenc e s 33 and 35 point out that this formula p e rtains to prop e llers wit h 5 o r 6 blades a nd a corr e ction of + 5 d B should be added for conventional propellers of 2 to 4 blades.

_M so c orrecti ,,, ns f o r atmospheric absorption and ground re flection app e ar not to have b een incl u ded ! n ref e rences 33, 35, a n d 3 8. it i s desired to have the over a ll at free-field index conditions (R = ! I M). Hence, the consta n t -43 dB in the a bove e qu ation is a djusted as fo U_ >ws.

-4 3 .0 f r om origi n al e q u ation + 42 .7 sp h eric a l diver g e n c e between R 1 = 1 52.4 M a nd R 2 = I M +3.0 est;, m ate of a tmosp h eric absorption a t 152.4 M +5.0 nu m ber of blade correction - 3.0 correction to free-field co ndi tion w +5.7 Total The re sul t ing equation for t h e overall SPL o f a single propeller at fr _ ,-field index, conditions is L o = 2( ;" L _ glO[ V TE T / (VR TR)]

A R(0. 1 + ¢os 2_ ) ( 1 - X o co s_i " 1 ]* _ .7 Of )

+ i O LogIO[ _B 0.1 + cos2 70 ° i, Th e c haract e risticStrouhalfrequency ft ) is giv e n by ref e r e nc e 3 7 as fo = 0.28 V / [(t cos 8 + | sin 6 )f! - Mo c os _ )] where(V, t, l , 6 ) are the effectivehelicalvelocity,blade thickness, chord length,and an gl eof attack respe c tively at 0.7 span.T h e basicspectru m s ha p e , SS,whichincludes frequency modulation effects of bladerotationisgiven by the formula: where

sI = f l / fo

s 2 = f 2 / fo

f l' f2 = lo w er and u pper c utoff freque nc ies tot t h e pa s s ba nd be i ng c ons i dered 1_ 4 t l r g(x) = th e normaliz e d, pow e r sp e ct r al d e nsity function l+a 2x 2) (l+b 2x 2 x I 82 b 2 t -, a = 1 + MTE b ffi 1 - MTE • c ffi loge (a / b) MTE = e ffectiv e h e lic al tip M a ch number .

The spectrum shap e formula ha s a s ingularity at MTE eq ual to on e and thu s th _ procedur e fail s as the effective tip spe e d goe s su pe rsonic. The vortex noise pr e diction procedur e is li m it e d to va lu e s of MT £ l e ss than one. in pr a ctical app li cations this range is r e duced further to: 0 < MTE _ < 0. 93 .

The sound pr e ssure l e v e l s pe ctrum is d e f ine d by addin g th e sp e ct ru m s hape result for a seri e s of p ass b an ds to the ove ra ll s ound pres s ure level , Lo.

,b SPL(f) = ko + SS (4 3 ) Rot at ion al n oise . - Th e char a cteri s tic level in dB r e 20 tt N / M 2 at ! 52 . 4 M for th e rotation a l no i s e is given by reference 3 2 a s Lo = 10 LOglo _ O _ / + 3 8 t ¢i. E

]

- 2 .Z B + FI( _ ) + 100.

where !

W = shaft power WR = re ference po_ ver= 745. 7 KW ( 1 000 Hp ) . t D = propeller diameter DR = r e f e r e nc e diam e t e r= 0 .3 0 5 M (1 It) B = numb e r of blad e s F 1 = dire c tivity co rre c ti on (fig . 72) T he expression above is a curve- fi t to the e m pirical fi gure s g i ven in ref erence 32. It is assumed that th is level is r e pre s enta ti veof me asuredground test dat _ at 1 5 2.4 M from th e source. The lowes t freq u ency for de s t r uctive interference due to ground refl e ction would be bet w een 2 and 5 KHz-w e ll above t he first te n har m onic s in th e rotati o nal noise spectru m . Thi s i m plies t hat t h e characteris ti c level Lo is 6 dB a bo ve free- fi eld conditio n s. Ref e rences 33 and 36 report t h a t a Doppler-s hi ft and le v el chang e occu rs for a propeller in t ranslational mo tio n. Th us to meet th e require m ent h ere, th e followi n g formula re sults for the c h aracteristic level a t t he f re e-field, index condition , Lo 10 Log10 W 1.55 0 -2.Z 6 5 = (1 - H o cosj _ )"4 (4 4 ) + 38 HTE - 2. 2 B + F1( _ ) + 137.7 whe re th e t e rm (1 - Mo cos O i s th e Doppl e r factor . Th is l as t expre ss ion assum e s that the air absorption pr e s e nt is n e gligibl e du e to th e fundam e ntal f re qu e ncy for the prop e ll e r ton e s b e ing typically l e ss than 2 5 0 Hz.

Th e l e vels of t h e harmo n ic ton e s are d e t e r m i n ed through u s e of figu r e 7 3 for the function F2 used in the equa t ion be low.

Lk = Lo + FE(HTE, K) , K = 1 , Z , 3 , ... etc. (4 5 ) The funda me ntal fre qu e ncy for the f'trsth _ monic is d efi ned as fo = B g / [60 (1 - M 0 cos _ )] (4 6 ) where 0 is the shaft speedin rp m . Th e dis c rete t ones ar eaddedto the b r oadb an dspectru m in a manner si m il ar to th a tde sc ribed for the fan n oisepro c edures (se c . 5 . 2.4).

5 .2 .5 . 2 Rotor NoiseP rediction A simplified pre di c tion procedu re for estimating rotor / prope ll er noise h a s been developed. The pr o cedurec onsi ders two noise co m ponents tha t arege n er a ted by rot a ti n g bl a des. Th ese components FIGURE 73 .- RE L A TIVE HARMONIC LEVEL S F" 2 (MT E , K) FOR PROPEL L ER ROTATIONAL NOISE !

a re (I)di s crete-tone, rot a tio n al no is e a nd (2)bro a dband, vorte x noi s e . Rot a tion a l n oi s e i s develo p ed from the h a r m o n ic lo a d s t ha t exi s t o n the b l a de s an d th a t f or vorte x n oi s e i s d u e to the s heddi n g of vo rt i c e s from the tr a ili n g edge of the bl a d e s. O ther n oise s our ces a re me n tio n ed i n the re f ere nc e s, b u t they ar e usua ll y n egle c ted . The r eas o ns a re d i s c uss ed a t th e e n d o f thi s s e c tio n.

Vort ex noise .-The previous se ction 5.2 . 5 . 1 provides a s i mplified , empiric a l p rocedure for estimating t hi s component. Th e met h od used here is identical to that described in that section. An error a n a lysis was made on some of the d a ta given in references 37 and 3 8. The re s ults indicate that the e m piri cal m ethod provide s re as onable prediction s for c ommunity noise estimates and it is " che a p " in co m parison t o refined integration and boundary-value problem a pproaches. Also, t hey require more information than is read i ly available, e.g., the complete blade geo me try , etc.

Rot adonal n ois e .- Th e pro c edure for rotational noise i s b as ed on a theo re ti c al math model (ref. 33) t ha t is s i mplified by a "loa di ng-law " c oncept ( re f _ . 35, 3 7, a n d 38). For the purpose of no is e c al c ul a tions, the h a rmoni c lo a ds ar e considered random in phase and applied at a si ngle point on a blade. The position of t' , .fi sequiv a lent point load is b a sed on a ce ntroid c alc ulation for the me an-squar e pres s ure distribution on the blades. Experimental data (refs. 3 5 , 3 7, an d 38) have shown that the load harmoni c s can be e s timated from a simple formula. This form u la c ontains only t hre e em piri cal p ar am ete r s w hic h can b e de t e r m in e d fro m ac ou s tic dat a .

Reference 35 gives d ata w hich show that the h a rmonic loads ar e different for a ro t or wi t h tran s l a tional mo t ion. Hence, the loading-law p ara me t e rs will h a ve to be ob ta ined from wi n d tunnel tests in order to predict the rot a tiona l noi se for fi i gh ¢ conditions. F rom wh a t little d a ta th a t is a vail a ble , the d is c r e t e-to n es for flight could b e sign ifi c a ntly less t han that fro m a s t a t ic aircraft (ref. 37).

On e m a y a sk , " Why don't y ou a ss u me some f or m of a time-v a rying press u re distribution on a b!a de; compute the F ourier se rie s ; and use the coefficients t h u s ob ta ined for the loading h a rmonic s ? " T h e an s wer i s -it w as tried a n d w a sn ' t succ e ssful ! (re L 33). Furthe rm ore , it is rather co m putati o nall y e x pen s ive an d each rotor de s i gn requires a diffe re nt pre s sure distributio n .

On-the-other-hand, the lo a ding-law concept s implifies a r a ther formid a ble m athem a tical problem a nd provides reali s tic noi s e esti m ates. At the sa m e t im e, it lumps together man y effects th a t are dif fic ult to predict into only t hr ee e m piric al par am eter s . Some of the effect s ar e bl a de fla pping, fl ight, vo r t e x in t e r a ctio n , an d c ha n ge s i n bl a d e de s ig n. Of the v a riou s m e an s a v ai l a bl e to m ea su re th e ha r m oni c lo a d s, the a cou s tic m et h od ( ref s. 37 a n d 3 8 ) see ms to be the be s t . Thi s i s b ecaus e ot h er t e c hn i ques (ref . 33 ) a r e p r esen tly u na bl e t o d e t e r mine th e ha r m o n ic lo a d s to th e hi g h -ord er r equ i r e d for n oi se p redi c tio n.

1 5 9 i | Rotational noise for he lico p ters and tilt roto rs is composed of discrete-tones that occur at harmoni c multipl e s of th e fundam en tal blad e passag e frequ e n c y, fo" t fo = B 0/ (60 SF) in Hz B = Numberof ro t or blades - Rot a tional speed in rpm SF = Doppl e r-shi f tfactor (1 - Mo c o s _ ) !

Mo = AircraftM a chnu mbe r = Angl e be t w e en flight path and lin e to th e obs e rverat " r e tarded time " -th e time th e sound is generated,not th e tim e when th e sound is h e ard.

Th e har m onic levels, dB re 20 A t N / M2, for th e rotational noise are given by

I<. 1

with t _ Po = 20 P N / M 2 = 4.177 x 10" ? p sf P R = 47 . 88 N / M2 = 1 ps f I Re fe ren ce 33 provides a t he o re tical app r oac h for es ti m a t i n g th e f ar -fi eld, a c o u sti c pres sure pro duce d b y h a rm o n ic loads o n a rotor . T he re su lt, eq u ation (3 4 ) in ref e re n c e 33 , g ives a n expressio n for t h e discrete to ne p h asor, CN , a b ov e in t e r ms o f t he se loads .

P N = CTN + CDN+ CRN (4 7) q 1 6 0 i l i with

X'-= 2. Co ' r _ _ r 1

= Thrus t component P = Dr a 9 or t orque component

ca ;; : . i _ , Z . CorzZ ) AR _ J n-). \ ['1 /

= Radial co m ponen t I where n = NB rI = r SF ! r = Di s t a nce from ob s erve r to rotor hub a t retardedtime M = Rot ational Machnumber of a point on the rotor f l = Rotational speed (ra d! s ec ) R = Radius of a point on the rotor co = Loca lspeed of soun d b I X Y- = sine r ¢ = Direc t ivity a ngl e b et w ee n t h e roto r inl e t a xis and a l in e t o the o bs e rv er a t ret a rd e d ti me i = I m aginary n u mber, V'i- an d (AT ? ,, AD ? , , ARX) represent the complex Fouriercoefficients for the har m onic loads appearing on a rotor b l ade , i.e. , A) : fill exp (-i) , _ T) d T

i n

f (l ") = _ Ax e x p (I _A I " ) jL+ - oo However, re ference 3 5 po i nts out that an " ef f ect i ve " he l ical Machnu m ber, ME, is to be used in lieu of M above to accoun t for m o t ion relative t o a s ta tionary ob se rver.

ME2 _ M2 + (Mo cos a )2 In this e xp re ssion, a is the an gl e betw e en the rotor axis and th e directi o n of t he aircraft's motion. Combining ter m s in t o equa t ion ( 4 7) gi ves lnM E c o s _ -(n- _ ) [ nM E sln _ | / CT p + = _ _ i AT), _ n - _

_ =.® \ SF /

.inM E _ = (n=' _ ) F SF' ( n _'_l ( nMF sinl _

+ X,++_ " E ra, = n - x \ S F ]

c m = z. _ , s F _ _ i %) -- _ " / J z

1 62 Chan gi n g t he ord e r of s m nmation fr o m (- _ ) to (I, _ ) and noting that A.x = A ; , co m pl e x conju g at e , yields CN = CTN + CDN + CRN (48) with i MECOS._ [i -n CTN = 2 1 RrSF 'z t AT° 3 n ' " + E i AT) , " Tn-) , +C-Z)) " AT) , 3 n+) ,

. . ]}

.! = i 3n

" [ }

L. ME \ n / J AD _ ' " n - :>, nME sin _ I i-n " - - AR o J _ n

CRN- 2 r r Rr $F2 t

), =1

wher e th e argument i n the Bessel functior,, s above is (n ME sin q # SF)and the following ide n t i tie s are t o be u sed in evalu at in g the n egative o r de r B essel f u nctions and their deriva t ives.

!

3 n - ,_ = X - -l+l ' = 0 ' 5 [ J ' n l ' ' n ] J 'n ,l =0 o 5 J n + _ , .=. l_ ' _ ' n 4.) , + !

3 ' . o _ , -.-- (o i ) " -a3 . 1.. o _, I

16 3 Loading laws . -Up to this point, it has be e n assum e d that t he harmonic loads (AT } , , AD } , , AR } , ) a r e kno w n ; in r e ality t he y a re not . R efe r e nc e s 33 , 3 5 , and 3 6 ar g ue t h at the h ar m onic loads are to be considered random in p h ase wit h respect to h armonic order, }`, and position , R, across t h e rotor. For t he purpos e of nois e cal c ul at ions , an e quivaJ e nt load is a ssu med t o be applied so me w he r e b e tw e en 0 . 5 a nd 0 . 8 s p a n . T h e p o s ition i s b ase d on a c entroid ca l cu l a tion for t he mea n - s quar e - p r essu r e d i st rib u tio n o n a b l ade.

T h is po in t load concept permit s a simplif .ca t i on of eq ua tion (48), i . e. , t h e v a lue s of M E and R at t h e centroid can be used, to relate noise to t h e ste a dy fo r ces on a rotor . T h e h armonic loads are in turn related to t h e steady force by t h e following appro x imate loading law.

2 { / _ - [ / AO = g( _ ) (49) i, / w h er e _ a nd m an d c are determi n ed by ph ysi c al a rgumen t and / or e xperi m ent .

itli_ Th ese loading laws imply th a t a n e ff e c ti v e p h as e for th e Fouri e r co e ffi c i en ts, A},, is 45 ° for _ _ ,>0. A lso , t he s u m m a tion i n eq u a t i on ( 48 ) wit h r es p e ct to } , is t o b e do ne on an R -M- S b as i s a f te r t he a lg e br a i c sum of t he lo a d c om p o nen t s. F r ee -fi e l d , ac ou s ti c m easu r e m ents o n t he in l et ax i s of the ro t or , the or e ti ca ll y , p rovid e an es ti m ate for IA T } ,[ w i th l r > 10 maX [ C o / (Nf o ), RT} at: ! }, = N B ).

T ha t i s: [ A T _. I 2 _8( " R r SF2p° _2 ) ,M E ] 1 0 "l L N Si mil a rly , measu r eme nt s in t ile p la_e of t he r ,_ tor c a n p rovid e an es timat e of IAD ) _I 2 i f lhe r a d ial l or ccs a re smal l in c o m p a ri s o n to t he dr a g for ces d ue to tor que- i .e., S ee references 3 7 a nd 3 8 for furt ht . % t a ils .

Refe r ence s 33 and 3 7 sa y that c = ! a nd • _ 2 t br h ov e r in g he licopt ers. T h us _2. 5 {50A ) 164 r On the o t her ha n d, reference 35 gives a physical argumen t and data ( fi g. 74) which s h ow t ha t equation (49) applies with c =l and t he exponent term, m , determined by a formula whic h includes effects of rotor o rientation and aircraft speed. Theref, _ ,' o f o r h elicopters and til t rotors:

- (m +0 .5)

m |

9c ) - - , s o B )

wh_ , re 16t r( V o co_ a + v) '_ m " 0. 0 485 - J + 1 . 3 6 u S f _ R T [ : - ' : " !.3 + 0 .48 7 6 [VISo / ( S O'VT)!

i , Vo = Ai r c raft velo c it y i'I - v = I nduc e d v el oc it y of the a ir - - 0 .5 - (V o cos ) + I V o c o scx) 2 "_ g c T) / ( O o RT 2 ) ] . 5 r VI = N o rma l i n flo w v el o ci t y - - 0 . 5 { (V o c os ) + [(V o co s ) 2 + a Ts _ °T- - 1 "5 PsoDT 2 - 1 J VT - Tip speed T = Total gross thrust for rotor P o = Density of th e ai r = Pso / fR c T s o) Ps o = ,_ tati c pr es s u r e o f am bie n t a ir ( abs olute unit s) T s o = St a ti c te m p e rature o f am bient air ( a b solu te unit s ) I R T = Tip r adiu s D 1 - = T ip d i a me t e r 4 i :

: :3 , ,.- " .... _ • • •

_o_i 1 ......

1 ® SCHEIMAN'S DATA • BOEING - VERTO L WIND TUNNEL M ODELROTOR DATA 0 , I , ;,, I ...... _ ........ , I 0 10 20 30 40 50 XP E£ 16It (Vo C OSc_+ v) XPEE ,.

- o S,9, RT FIGURE 74 .- LOADING LA WPARAM ET ER "m" FOR HELICOPTERSAND TIL T ROTOBS i I ¢T - Blade ar e a / disc are a S - Lift-curv e slop e of on e rotor blad e SO = R e fer e nc e lift- c u rve slop e = 5 for data in figur e 74 a = 7 3 0.97 (M / S) 2 p e r ( _ ) = 7 . 2141 x 10 . 3 ATM (M / S ) 2 pe r ( OK )

N / M 2

= 43 71 . 0 3 (fp s ) 2 pe r ( O R) KG-M _ lbm-ft gc = !.0 _ - 3 2.17 4 0 5 N-M _ ATM-M3 _ , R c _ 2 8 7 . 0 5 K _ - 2 .833 x 10- 3 _ - = _ __045 ft'l b f

_'_ Ib "b_ Y '- R

_ For low-sp e ed , MT < 0. 3 , propeller nois e estim a te s , r e f e r e nce 3 7 give s th e e mpirical lo a ding

l aw -1. 4 3

gcx ) = o. e 6 l x l

(50C)

!

and r e feren c e 3 6 says; for th e sa m e tip speed r a nge g(X. ) -" 0.04 IX 2 (] °0" 5 T h e r e se e msto b e a typo vaphi cal e rror h e r e, be caus e t h is f ormul a do e s n't match t h e e m piric a l d a t a in r e f e r e n ce 3 ' 7 . Th e corr ect f orm u l a s hould be

e ( x ) = ) oz2[I x l 3 l .(x / 36 )z ( 5 0D)

0 . 5

= 44. 0

. i Although t h e two equations, ( 5 0C) and ( 5 0D), app e ar quit e diff e r e nt, they matc h t h e sa m e pro pe ll e r harmonic loads are typically highe r.

Mor e r e c e nt data (r e f. 3 8) at th e pro pe ll e r conditions, 0. 5 < MT < 0.7, yi e ld y e t anoth e r data (fig. 7 5 a) and hav e on e thing in common wh e n compar e d to the e q u ations for h e licopt e rs - th e loa di ng law g() ,) " - 24. 0, IXJ"2"5 / [1 + (30 / X)2] 0"5 •., ( 50 E) This formula is de riv e d from th e data giv e n in r e f e r e nc e 3 8. Th e spr e ad in th e data b e tw ee n that f or th e thrust an d torqu e harmonics is probably du e to-th e e quival e nt point loads for thrust and d r ag act at diff e r e nt c e ntroids. Thus, the use of a single po in t load for calculating the h a rm onic t ones , - i! res u lt s in a tolera n c e of about +8.0 dB. A plot of e q u at ion ( 5 0E) is shown in fi gu re 7 5 b. In view of ' _i t he d ata a nd form u lae p rese n ted , one would expect that th e general form of th e loading law is (5 1 )

{ ,, ' 1 ]

g(x ) - c _ 'LI _ I z _ +l _ 1 , x) 2 '

with the parameters ( c, __ , _ ,c ) dete rmin e d by ex pe riment. In actual practice , the fo rm of equa t io n (49) should suf fi ce for determining the s ound h ar monics of order s ; 1 < N < 30 / B o For more accurate e s timation of s ound har m onic s out s ide t his r ange, equation ( 5 1) s h, ' mld be used.

Simpl ificat ion . - In order to p u t equatio n (48) i n more usea bl e form , t he following n ot a t i o n i s used.

AT O = T / B ADO = h D ATO ARO = hR A T O

[AT _ I = 0.5 A TO g ( A ) forl ^ l >0

I ADA] = hDIATA I forl _ -I > o

IAR I = h RJAT _ I f or l, x l >0

| 1 6 9 _ _ . _ ......... _ ....... _ ' -_ '_--I I I I II IIIIIII .... I i I l l .... i ii ii I ........... I ............ I .... | with th e function f l (X) giv e n by o ne of th e variou s loading laws, equations ( 4 9), ( 5 0A) through ( 5 0E), and ( 5 1). As,, mm ing r ando m phas e , as was don e in r e f e r e n c e s 33 and 35 , w e put A_ , = _ ( 1 + i), x>O for each load compone nt. In se rtion into th e random phas e f o r m of e quation 48 yi e lds

: : ICNI 2 -

i . ]

; t i where _n ) , R s i n_ - + co s, [ , hD S F n+), i x

[ ( - ) ]

B nX = [ cosq , -hD _ ME / (n ME sin # / SF) = argum e nt i n th e B e ss e l functions n = NB M E = Hefic al Ma c h numb e r at radius R R = Radial c e ntroid for e quival e nt point load.

Equ x tion ( 5 2) abov e provid e s an e stimat e of th e far- fie ld discr e t e ton e s at a distance, r, fro m ti' _e rotor h ub. This e stimat e also corr e sponds to fr ee -fi e ld conditions.

in th e application of e quation ( 5 2), limitations must b e e mployed to c omput e riz e t he proc e dur e . Obviously, th e summation with r e sp e ct to X must b e trun c at e d wh e n th e t e rm s c e as e to a dd to th e noise. Refer e nc e s 33 , 3 7, and 3 8 show that th e e ff e ctiv e rang e for X is n (1 - q) " - _ , - _ n ( I + q) with

q = I"E t . / s e I

: i

P | and the ter m s containing Jn+) , and Jn+ ) , canb e n e glected.

it also c an be shown that the radial load componentscan be neglec t edin equation 52 because their amplitude is much less tha n t hat due to thrust or torque. This results in a less complex equation •

Ic.I-- ,, e r co---, 0

_ : K2 2]

where _ K ! = M a x[n (i - q )-0 .5, ! i (in t eger re s ul t ) K2 = n(! + q )+0 . 5 (integerre s uit) : _ q = [M E s in q_ / sF[ n = N B M E = H e li c a l Ma c h n umber at radi us R R = Radi a l ce n tro id for e qui valent po i nt load g O , ) = Represent s the loading-l a w function , e q u a tions (4 9 ) t h roug h (51 ) T = Tota l t h r us t for rotor h D = Dr a g / t h r us t r a tio | __ ( Q / R) / T whe r e Q i s t h e t o t a l tor q ue on t h e rotor r = Di sta nc e f ro n t roto r hu b at retar d ed t im e = Dire c ti vi ty angl e re . rot o r i n let a xi s a t ret a r d ed t im e t SF = Dopp l e r - s h ift fa c t o r , 1 - Mo co s 1 71 T h e u se of equation ( 5 3) to calcul a t e a/I the sound harmonics required in t he audio frequency r an g e would be quite exp e nsive - eve n on hig h -speed computers. Reference 33 h as s h own t h at t h e r e sulting valu e s of LN v ary in a smoot h fas h ion w h en plotted against log(N). Suppose t h at a data c urv e as shown in figur e 76 c a n b e d e velop e d throu gh use of e quation ( 53 ) for a s e l e ct e d set of !

* values for N. The n by m e ans of int e rpolation / ex trapolation with r e spect to log(N ) , all t he n e c e ssary sound har m oni c l e v e ls, LN , c an b e obtain e d at a tr e m e ndous sa vin g in c omput e r s torag e and tim e .

: Additi o nal limitations must b e e mploy e d in ord e r to r e du ce comput e r storag e and tim e . The _l p r a ctical l imitations for rotors and prop e ll ers ar e i! 2 _ gB _ g 6 i. : _ ME

0<g- < l

As was mentioned previously, the values of N will b e li m ited to l_ gN _ 21 Also, symme try impli e s t h at th e v a lu e s for sin q , are contain e d in O _ sin , I , _ 1 Th us th e m a xim u m ra ng e for X in e qu a tion ( 53 ) is giv e n by l_ g _, _ g2n w he re n = N B a nd th e orders of t he B e ssel function s , JK, w h ich could h av e to be c a lcul a t e d a nd stor e_i are 0 _ gK q gn In s ertin g t he po ss ibl e valu es giv e 0 g K 4 42 forB=2 0 E gK ,g 63 f o rB= 3 0 _ g K _ g 12 6 for B =6 17 2 FIGURE 76. - TYPICAL DISCRET E - TONE LEVELS VERSUS HARM ONIC NUMBER 17 3 l or in g e n e ral, I O _ K _ NB with N being the harmonic number for th e discrete- t one occurring at the frequency, N fo' Other h armonic noise s our ces .- There are three o t her noise sources present for rotating prop e llers _ and / or rotors. The s e sources ar e (!) " thickness-nois e" (dipole character), (2)Reynolds i stress noise (quadrupol e c haracter) , and ( 3 )blad e -slap. In practic e , th e se nois e sources are usO al ly i_ n e gl e ct e d. The reasonsare discu sse d b e low.

,t

!_ In addition to th e thrust and drag loading nois e alr e ady di scuss e d, an oth e r dipol e sol_ rc e is pr ese nt (r e fs. 36 t hr ough 3 8). This sourc e has b ee n giv e n th e t e rm " t hi ckn ess nois e" du e to its str e ngth b e ing proportional to th e blad e volume and th e local blad e acc e l e ration (r e f. 36 ). For roto rs operating at constant sp ee d ( 0 and Mo constant), th e only acc e l e ration pr ese nt is t ha t in th e radial di re ction. (Not e that th e blad e s are consid e r e d r ig id.) Thus t hi s source corresponds to th e ra di al loads t ha t app e aro _ : th e blad e s. In ord e r to e v a luat e t hi s sourc e, knowl e d ge of th e compl e t e blad e g e o me try is r e quir e d to r, erform th e n e c e_q x y int e gration ov e r th e blad e s. Both Hamilton Standardr e ports (r e fs. 3 7 _ n _ 3 8) hav e includ e d this sourc e in th e ir calculations. Th e y r e port th at t hi s sourc e c an domin a t e ov e r th e loading nois e du e to thrust and drag i f th e prop e ller is li gh tly load e d or if th e b la d e s ar e rath e rt hi ck. R e f e r e nc e 36 argu e sthat this sourc e will only b e signi fi cant , r e lativ e to the thrust an d d r ag t e rms, for u ery thick blad e s at low loading conditions. Although th ese thr ee r e portsa gree in conc e pt; th e em p ha sis of ref e r en c e 36 diff ers . This latt e r em phasis l e ads to th e assumption: "The t hi ckn e ss-noi se contribution t o t h e discr e t e -ton e l e v e ls produc e d by prop e ll e rs / roto rs can b e n egle ct e d, if t h e blad e s ar e not t hi ck and / or li gh tly load e d. " Th e r e lativ e ma gn itud e of th e qu a dmpol e sourc e s wh e n co m p are d t o that for dipol e sourc e s is giv e n by r e fer e nc e 36 as Q uadru- D|pole pole This re lation shows that the dipo l e (force) noise components dominate in most practical applications. Howev e r, a s M cos / _ approaches unity and n gets grea ter than 100, th e qu a drupole s ources becom e do m inant. " In assessin g these results, it is of course imp o rtant to remember that these results apply only to th e specifi c ca s e exami u ed .... Despite these li m itations, it m ay be concluded that for quiet prop e llers operating at tip s peed s of less than about M = 0. 5 , the quadrupol e noise should not be expected to n _ akesi g ni fi cant contribution s to th e harm o nic noise t I [ for n < 200, even on the propeller axis " (ref. 36 ). For furth e r d e tails see pages ; , 9, 6 8 of r e f e r e nc e 36 .

Under the various h e l icopt e r op e rations (for instance, during l ow-pow e r descent), t he rotor produc e s a loud impulsiv e nois e . Th e e n e rgy for this nois e consists of har m onic tones that occ u r at [ multipl e s of th e f u ndamental blad e -passag e fr e qu e ncy, but th e distribution do e s not fall-off rapidly with incr e asing harmonic numb e r-h e nc e , th e impulsiv e charact e r. Th is nois e has b ee n giv e n th e t e rm " blad e -slap. " Wh e n e v e r t hi s " impulsiv e" nois e occurs , it is particul ar ly s e v e r e , but it also has a hi ghly dir e ctio n a l radiation patt e rn. Thus blad e -slap is ne t always h e ard, e v e n though it may e xist | (r e f. 33 ).

Th is ph e nom e na occurs at pr e cis e ly thos e conditions wh e n a vort e x wak e can b e e xp e ct e d to p a ss v e ry clos e to th e rotor. Blad e -slap can also occur wh e n th e rotors ar e op e rat e d at hi gh sp ee d.

The n, it is ass ociat e d with transonic flow ov e r th e rotor blad e s. Th us, th e r e are two po s sibl e sourc e s of blad e -slap-vort e x interaction and / or transonic flow. These p h enomena can b e predicted.

" However, it see m inapprop ri ate to con si der blade-slap as a separate phenomenon. Th e helicop t er rotor i s always undergoing some for m of vortex in t eraction, a nd blade-slap is simply a severe for m .

Perhaps it is more realistic to suppose that, at least from the acoustic point of view, the helicopter is always flying under som e degree of b |a d e -slap " (ref. 3 3).

The loading-law, e quation ( 5 0 _ ), includ e s som e of th e s e vort e x interaction e ff e cts and its us e is re co mme nd e d. Hop e fully , t his e quation approximat e s th e low.d egree , blade-slap m e ntion e d above , No additional e ffort was mad e , how e v e r, to try and pr e dict th e sp e cial s e ver e cas e .

5. 3 NOI S E CONTOUR ESTIMATION A noise contour is the l oc u s of points on the gr ou n d i n whic h the noise is at a constan t acoustic l e v e l. Th e c _ culation of a nois e contour r e quires the e stablishm e nt of the r e lationship betw e en th e aircra f t's nois e p e rfo rm anc e and the aero / propulsion p ar a me ters during tak e off a nd landing. Th e following optimiz e d m e thod is pres e nted w hi ch wi l l fi t within th e comput e r tim e and storag e consh'aints of th e Ames flight simul _-t or.

Th e re l ationships m entioned abo v e are e stablished when data points are g i v en for noise lev e l (NL), en gi n e perfor m tmce (EPP), range at closest _ oint of approach (R), a nd elev at ion angle ( o0 , for a , _ ai rcraft dur i n g level fl i g ht ( s ee fi g. 1 5 and t a ble ! I ). Thi s data can then be for m e d in t o t abular t u nction s : NL versu s (E P P, lo g R, _ ) , or lo g R ver s u s (a , EPP) for each noi se contour. When the airplane coordinates and E PP are give n , interpolation u s in g these f unction s at the g eo m et ry shown in fi gure 7 7 provides t w o points (one for eac h sicle of the fli gh t track) o n th e gro u nd for a s peci fi c 17 5 TABLE 11 .- SAMPEL N _ I, , _ <' c D ATA GRID FOR NOISE CONTOUR COM PUTER PROGRAM _ I N DEP E NDE N TVA R IAB L ES R ANG E i . 1 1 E PP L , Eppl , E PP2 , . . . , Ep p I ! 2 1R • RI, R2,...RI .0 5 < R <12.8 Ku )) G m al , Q 2 '""a k 0" < Q < 90 "

-1

I L I NOISECONTOU R S (U . V) U II -- Ir ...... _ ---. , NOISEDATA GRID: 54 OBSERVERPOSITIONS , : _2 ALTITUDES ' ' " ..'.. II III R II VARIAB L E DISTANCES(KM) I j li I i R .05 .2 .4 .8 1.6 3-_ 6.4 12. 8 ...... • I |1 I _ I i i III I Q = 0" S I NI3I = 0 L ii U = .05 .1 .2 .4 . 8 1.6 5 .2 6.4 12.8 Z-- 0 0 0 0 0 9 0 0 0 (I -- 7.18" SINQ = o 125 -_ , _ .,.

U _ - . _ % . 1 )9q2 .lq8 . 3 97 .7q4 1 . 5q 3 . 17 6 . 35 12 . 7 Z = .00t,25 .0125 .025 ° 05 . 1 .2 .4 .8 1.6 ( 1 = 14.46" S ING = .25 U =: ,0484 .0968 .1 _ 4 .3 8 7 .774 1 . 55 3.10 6 .2 Q 12 , , 4 Z -" . 0125 .025 .05 .1 .2 .4 .8 1 .6 7.2 (1-'- 30* SIN• = .S _ J i !1 -- U _ .0433 .08bb .173 .34b .693 1 .38 2.77 5.54 11 . 1 Z "= . 025 .05 . 1 .2 0 4 .8 1.6 3.2 6.4 (_ _ 45" SIN ¢i " .707107 U -_ . 03_ . .0707 .141 .28 3 .566 1.13 2. 2 6 4.5 2 9.05 Z m .0354 .07 0 7 .14 1 .203 .%6 1 . 13 2. 2 6 4.52 9. 0 5 ¢L m _" SI N a m 1+0 Um 0 0 0 0 0 0 0 0 0 Z m .0 5 .1 .2 4 _ l.b 3.2 6 . 4 1 2 . 8 I "/ 6 |

t

7J "I n oi se l e ve l. If a serie s of thes e po in ts are ca l culated d ur i n g an aircr a f t's t ake o f f or l a nd in g , a noise c o n tour i s determi n ed . T he a re a e nc lo s ed b y t h i s c o n to u r can be c a l cu lated .

A lt h o u g h t h e r e exi s t m ore refi n ed met h o ds for cz_i c u lati n g n oi s e co n to u r s, t h e y re qu ir e r a t h er le n gt hy ca lc u l a tio ns, an d re s ult i n i nc re as ed c om pu ter t ime an d s tor a ge . T h i s ma ke s t he m un de s ir ab le can did at e s for fli g h t s i m ul a tor us e . T h e app ro ach pr e s ent e d h ere has t h e a d v an t a ge of m i n i m i z i ng c om p u tat io ns an d r ed uc i n g st or a ge re qui re me nt s. De sp it e t h e f ac t t ha t t h i s m et h od uses app ro x im at io ns, wh en su ffi c i e n t d a t a p oi nts a re p ro v id e d b y me asu re m e nt or by p redi c tio n , th e pro ce d u r e p rovide s re as onably accu r a te noi s e c onto u r s .

5. 3.1 Acoustic Da t a The ac o us t ic da t a re q u i r e d fo r noi se c o n to ur e sti m a t ion c on s i sts o f a dir ectiv it y angle fo r p eak noise radia , ion and a tabulated function of three va ri able s -noi s e le v el v ersus EP P , R, and _ ( see fig. 15). I t is of p articular importance, when constructing this function, that the data is for level ._: fli gh t an d t h at it i s s am p le d in the ma n n e r in d ica t e d in t a b l e 11 ; i.e. , i n e q ual s t e p s o f lo g R for i'!_ : _i an g ular i ncremen t s o f s i n c _ = O, 0. 12 5, 0.25, 0.5, 0. 7 0 71 07, and 1 .0. The n o ise c o nt o u r com p uter p rog ram h a s been o ptimized f o r d _ta gi v en in this f orm and pr o v id es the gr eates t accu r acy for a - _i_!_° minimum am o unt o f d , _ta. A ls o t he noise levels are t o be str i c tl y m o n o t oni c; a ec r easin g noise wi t h -fill res p ect to i n creas i n g valu e s o f l og R. If this c o nstra i n t is n o t a d hered to, t h e whole p r o ce d ure fa i ls.

This constraint poses no restriction to observed aircraft noise or t o that p rovided by the noise source estimatic.l procedure.

" 5 . 3 .2 A e ro / P r opu is ion Data The a e ro-pr opu isi o n d a t a re qui re d for n o is e con to u r e s t ima tio n c on sists o f a s e r i es of poi n t s a l ong the aircraf t 's t akeoff or l a ndin g flight path which de fi ne the airplane posi t ion ( x, y , z ) , the o ri e n tation a ngle (fie ) t or the ref e rence axis of the dominant noise source and the engine p erf o rm_uacc ( EPD ) . D u ri ng the Phase A portion of the con t ract, the key engine performance par a meter w a s engine pressure ra t io ( EPR ) due t o its relationship to other j et engine cycle par a meters , i.e. . there is one - to- o ne correspondence between EPR a nd all other engine cycle p a r a _ , n et e rs a nd t his c o rr e spondence is constant wi t h a ltitude for a fixed aircraft velocity. Since the noise p_ o d u c ed by je t en g i nes i s d irec tly r el at e d t o t he e n g i ne c y c l e , it w i l l also f o llow t h i s c o rrespondence wi t h E P R at a refere n ce off a xis dist a nce. Howe v er, jet e:_gine s are not the on ly po wctplant_ co n sidered in the Phase B effort. The choice of what the engine perfo r mance p aramete r rc p rcsen t s is I clt up to the u ser.

5 .3.3 Nois e Contour Calculation T h e no i se co n to u r c a lcul a tion can be brok e n down i n to four basi c steps . T h e fir s t is t h e form a tio n of t h e a co ust ic d a t a f unct io n s : NL = fI(EPP, log R, t _ ) and Log R = f2( a , E P P) for e a ch nois e c ontour fro m t h e giv e n d a t a point s ( N L k, EPPk, Rk, a k). Thi s st e p i s don e only on c e.

_ , The re a fter , t he cal c ul a tion requir e s interpol a tion for log R at a desired contour nois e l e vel ( C NL) a nd g eo m e t ry sh o wn in fig ur e 7 7 . T h e ne xt s t eps are t h e geo m etri c s ol u tions for the c on t o u r poin t s (U, V) i n a m o ving reference f r ame and £ , na Hy, t he t ransforma t ion of con t our coordina t es (U , V) t o !t t h e fi x ed ( X, Y , Z ) coo rdin a te s y s tem ( s ee fig . 77) . Th e detail s are o u tlined b e low .

t _t_ a ) Form a tion of t h e acousti c d ata function s, fl a n d f 2 : i D at a points (NL k, EPPk , Rk _ a k) a _ assum e d t o be given from th e use of t h e noi s e sour c e estimation comp ut er progra m or from measureme nt s (table 11). S o rt t he gi ven _ d a t a wit h respe c t to incre a si n g v alu es o f EPP k, R k, u k as t h e s e v ar iable s w il l b e tre at ed as independent for the functi o n fl" Next, d etermine the distin c t values for the given arrays (EPPk, Rk , t _ k) and use the results for the independent variab l e data arra y s specif y ing whe r e noise l eve l s are d e fi raed.

NOTE: The t hree - dimensional fun ct ion NL = fl (EPP, log R, t _) is n ow formed.

S pe c ifyi ng t il e desired contour no i se level s ( CNLj ) per m i t s the t ra n sform a t io n of t h e functio n fl t o a f unction logR = f2( t _ , EPP ) for each CN L j. This is done b y _ o n e-di m e ns ional inte rp ola t ion on fl a t NL = C N L j fo r j = ! , 2 , e t c .

N O T E: Th e t rans f or ma tion as sumes th a t t h e functi on f l is mon oton i c: de cr e a s i ng w ith re sp e c t to incre a sin g v alu es o f l o g R .

b) C al culat i on o f l og R for a s p ec i f i c c on t o u r CNL j: A t each po int a l o n g the a ircr a ft's flight p ath th e foli o ri ng da ta is req u i re d .

_-_ zi aircr a ft he ig h t a b ov e the gr o und 6i cl im b angle , i , : . , c o mp u te d a s the a r c t a n g ent c,f t he cl i mb _y_ 'a die n t , 179 | |, 6Ei Ori e ntation angle of t h e dominant noise source reference axis-usually the a n gle bet w een the gross thrust vector and the horizon EPPi eng in e perfor m ance parameter Calc ulat ion : let ZE = aircraft-to- gr ound distance perpendicular to the flig h t path = zi cos 6i Iterate t h e calculations below until [¢ _ -¢ _ ol _ , _ [¢ a I. In this iteration , o t o is set initially to t h e v _ lue 45 ° for eac h noise contour and is updated at eac h aircraft position al ong the flight pat h . l ' h e v al ue , c , is a tole r ance constant for t he iteration; a reasona b le value is 1.2 x 10"3.

lo g R = interpolation on f2 at ( a o, EPPi ) ¢ _ = arcsin (ZE / R) T est ¢ _ for convergence wit h °t o and update _ o i f anot h er ite ra tion is required.

In t h e co m p ut e r p rogram, a t e s t fo r co nt ou r c l osu r e is m a d e jus t b e fo r e t h e ca lc ulat ion of ot above. Cl osure o ccurs when R < Z E. The a c tion taken is to set a = 0.5 ( c _ o + 90*). This is done to a v oid prematur e clo s ure estimat e s that have occurred during r a pid cutback operations. If c losure has indeed occurred, the program cont ai ns a "trap" and sets a corr e sponding error c o de.

c) C alculation o f conto ur poin ts (U , V ) : U2 R 2 = , ZE2 P cos_ P V cos S Ei - zi sin 6 Ei

f !

V = Solu t i on of | |

t

p 2 J

= U 2 + V2 + zi2 where R = range at C P A c a lculated for the noise contour i n s t ep (b), = d i rec t ivit y a ng l e f _r pe a k p as sb y no i se prop a g a tion relati v c to the domin a nt noi s e source reference axis.

l ,_ NOTE: Singularities can exist when 6 El =+ - 90 ° , and / or t h e directivity cone does not int e r se ct th e ground at sid e lin e distances-+ U. H efi copt e rs , tilt rotor aircraf t , e t c.

r e quir e sp e cial consid e ration. Th e singu l ariti e s can b e avoid e d by l e tting _ Ei = 6 i a nd q ' = 90 °.

d) Coordin at e tr a nsformations: l e t dx -- xi - xi. 1 L dy = Yi" Yi-!

dsi2 = dx 2 + dy 2 sin 0 = -dx / ds i ; cos 0 = dy / ds i i _ x = Ucos 0 -Vsi n 0 + x i • y = Vcos 0 +Usin 0 +yi

i

w h e r e i ( xi. _ , yi. | ), (x i , y |.) = A ircraft coordinates for t h e pr e vious and e ! presen t po s ition al o ng t h e fligh t p a t h.

f (U , V) = Conto u r points in moving reference fr am e c a l c ul a ted i n (c).

5 .3 . 4 Ar e a C a lculation T he ar e a e nc lo se d b y ea ch noi s e contour is calc u l a t e d af ter t he points , (U , V ), are determined for a i rcraft po s itions ( x i , Yi ' z i) ' i = i ,2 , etc. T h e procedure i s as foll ow s: Aj = _ AA ij 1 8 1

ilt

' _' for eac h contour C NLj whe r e (from s e ction 5 .2 .3 ) _ Aij = (U i + Ui. ! ) (V i - Vi. 1 + dsi) it e ration (i-!) to (i).

iI NOTE : The formula assumes n e gligible error due to c hanges i n the flight track ve c to r fro m 5 . 3 . 5 N ois e Esti m at e on Sid e li n e Multipl e sid e lin e nois e e stimat e s ar e includ e d with th e noise contour comput e r progra m . Th e ob se r v er loc at io ns for these n oi se n um ber s a r e on the s idelin es in the (U , V , Z) coordi na t e s y st e m, | ' !_i as shown i n figur e 77 . Th e s ideline dist a nces can be sp e cifi e d by the us e r; the def au lt v a l ues a re • • 1 . 0 m, 1 5 2 . 4 m ( 5 00 fe e t), 46 3. 3 m. If any or all of th e v a lu e s r,. : ed to be c h anged, they m ay be as a % us e r i n put.

Calc ul a tio n: l e t R i 2 - SD 2+ZE2 i = arc°s(SD / Ri) w h e r e SD is a set of s ideli n e di s t a nce s .

A t h ree- d i mens io nal inter p ol a tio n o n fi at (EPPi , log Ri, o t i) yields t h e spe c ifi e d n o i s e _ .

est i ma te s.

Boei n g Co mm ercial A i rp lane Company P .O. B ox 3 7 07 Sea ttle , W ash i n g Cc m , J ul y ! 97 3 1 82 APPENDIX A THEORETICAL GROUND REFLECTION PREDICTION PROCEDURE BACKGROUND _ PLANE WAVES) An _ .coustic w a ve in the vicinity of a reflecting surface can be tw ated as t he sum of a direc t and reflected wave. The difference in path length for the two signals introduces terms for spherical divergen c e, phase delay, and absorption (grou n d and the air). This latter ter m for air absorption is n e gligible when c o mp ared to t he others and will therefore be ignored. Whe n the pha s e delay approac h es odd multiples of 180°, destructive interference results . A t even m ultiples of 180° constructive interference occurs. T his in t erference complica t es t h e analys i s of acoustic da t a unless efforts are made t o elimina t e th e ano m a fi es it produces in noise spec t ra. If gr ound reflec t ion canno t be elimina t ed, perhaps i ts effect can be es t ima t ed, and measured da t a can be correc t ed to free- fi eld or vi c e-ve rs a. Th e fo ll o wi n g is an an alysis directed at solving this pr o blem.

i Figure A! shows the ge o m e try of the reflec t ion problem. Th e rec e iver (microphone or ear of _i the observer) receives signals from a direc t pa t h and from a reflec t ed pa t h. The distance for the ! reflected pa t h is (P + A p), w h ich c a n be readily computed from equations ( 6 A) or ( 6 B) in section _l 5.1.2. Similarly, t h e an gle of incidence, u O, (w h ich is t h e sa m e as llI in section 5.1.2) can be obtained from equation 7. T h e angle of refraction , u 1, is gi ven by t h e acoustic equivalent of S n ell's la w .

KOcos v O= K ! cos v I wh ere K 0 = 21 rf / C0 ( wa ve n u m ber i n air) K 1 ~ 2 7 rf / Ci (wave number i n ground) i n gene ral, K l i s co mp le x (n on- un ifor m wave) , but it c a n be s h o w n that a unif orm acoustic plane , _ w ave c anno t attenu a t e in t h e Y-direction for bo th m edia ( air an d g rou n d) w h e n a ir a b sorption i s ne g lec t ed .

m .

F|| r th er , t h e im agi na r y p a rt o f K I aff ects o n l y t he t r a ns mitt e d sign a l an d not t h e refl e c te d sig na l . F or this r_ , a so n , o n l y t h e real pa rt of K I w ill be co ns id e red in w h at f ollo ws Sph eri ca l II pr o pa gation will b e t r eat ed l at er .

t 4 v - i iiiiiiii! iiii!_i_l __ ;:i_.iiiiill ii_: _ ::i :ii!!:_ililii!iiiii!i ii! :i::i i!!i;.ii!] ii::i!i_!_] _:_ :: _ : _i:.i!!!ill i_i_i: . i :: iiiiiiii!:iiiiiii_i!i TG R OUN O : K s , C S , Z sl ATTENUATION " 1

\ ii - j - " ANP',,.O E ' L AN E SO'CO"S T AN T

_ P,AN. o _ CONS T AN T PHAS e

PHASF LAG

"<s _lJ _ NON-UN I_ O R " P_AN E . V E

FIGURE A2. - ANGL E OF INCIDENCE LESSTHAN CRITI C AL FIGURE A3 .- PROPAGA TI " I V NEAR A DISSAPA ]r IVE MEDIUM ! 84 Th e r e fore, K1 / K 0 ~ C0 / C1 where COand CI are speeds of sound i n the air and ground respective l y.

Continuing with the solution for sin v ! , yields stn21 _ - ' - 1 - (Ko / K1)2 cos2 , If Ko / K1 is greater t ha n u n ity, a s ismo s tlikely t he case for theground,thereisa c riticalangle, V c, in whichsin2 v l canbecome negative . That is, SIN vl ffi _+}, aI FOR v o< u c (AI ) { a , FOR u ° _ vc } J where = CO S - I (K I / K 0)

" _ =_ = ]l-(Ko / K _ ) = COS Zv oJ°' s

T he c ho ice o f si g n w h en sin v I is i maginarydepends up o n t he conven t ion used to deno t e p h ase del a y in the veloc it y po t en ti als ( ¢ ) and i mped a nce (ZI), and i n th e bound a ry cond iti on-the transmit t ed signal ( _ T) should vanish as X approaches in fi nity.

The convention used h ere is _, _ I = lnc i den t s t gn a l : % exp[-t K o (X s _n u o + Y cOS U o) ] O R = re f lected stgn a l = _ o IP exp[-t K o (-X stn _ , o + ¥ coS J ,o } ] P C T = a ns mi tted s t gn a l

: _ ¢,T ex p[- l K 1 (X s tn / _ * Y c os; U l) ]

r = plane = wav e r eflec t io n coefft ,:A ent

(zl / z o) = (s.l. ,, ] / s in . o)

1 ' = pl a ne-wave t ra nsmission coefficient Z(Zl / Z O)

= 1 , r = (zi zo).- + (s i n. l / s t , o)

when v o i s l e ss t h an v c, wes e eth a t _ T wiP _ vanis h asX approach es infini t y, i f and only if; , stn p 1 = -1 _ 1 a nd cos _ , 1 = _ 1 = ( Ko / K1) cO SP o _l where ( o r I, / ) l ) are positive real nu m bers.

:!ii

_ T hat is: _ T = _ ol ' exp['t K 1 (-1 a 1 X + _ 1 Y)] = _ o T exp ( -K] o _ 1 X) exp(- t K] _ 1 Y) x - _ oo" m 0 T = x- _ o _ "m exp('K1 _ 1 X) [ _ o ' _ exp (-i K1 / ) 1 Y)] = 0 These rel atio n ships where 0 T r epre s ents a non . u niform , plane wave ar e s ho w n i n fi gure A2. It is worth noti n g that there is n o flow c of real ac ous t i c power in the X d ir ec t io n , bu t t h e r e is real p o wer flow in the Y directio n for both m edia (air and groun d ). No t e t ha t g I is co nsi dered real, i.e. , a lossles s m ed i u m . If ZI / Z0 i s a positive r e a l number, t hen t he re fl ection coeffi c ient r is e x p(i 0 ); and the re fl ec t ed . _i gnal O R is eq u al in _n agnit ud et o the inciden t signal 0 I , b u t suffe r s a phases h ift g i ven by 0 _ - Z tan' l[ a I Zo I ( Z 1 s in_ o)] Thi s e xplains h ow t he refle c tion co e f ficie n t ca n h ave a p h ase ter m diffe r ent than z e r o w h en th e gr o u nd impeda n ce is real - an appar e nt con t radiction of p h ysics ; t h oug h no t really so , w h£ :nt h e critical angle is included in t h e a na l_ j si s .

T he c o m p o sit e signal of t h e d i rect and refle c ted s o und i s t h en giv en by t h e veloc i ty potential so luti o n f o r r lan e wave s a s

¢ 'c ° %+ - -

_D [l + P e xp(ol K° LkP)] (A 3 ) i w h er e O D is the signal for t h e direct path and F is t h e reflection coefficient given in equa t ion (A2).

For acoustically h ard surfaces like w ater or concr e te, [Z i / Z0 1m ay be as l ar ge as 3 x 103 ; so t h at t h e reflection coefficient is approximately unity, except for very s m all angles of t o. W h en v o approac h es zero (grazing incidence), t h e r' _,pproachesminus one regardlessof t h e impedance values. Since t h e di f ference in pat h l e ngt h , Ap, also approac h es z e ro v nd e r t h ese conditions, t h e e rron e ous c o nclusion gi v e n by e quation (A 3 ) is that th e obs e rv e_ signal, ¢C , vanishes Th e contradiction k s solv e d by noting thatuniform acoust i c plan e wav e s just do not e xist. A m , _re tt _ tt _ d e tail e d analysis in _e f e r e n ce s 5 and _ shows that th e wav e fronts are _e nt in th e vicinity of th e ground for a " dissipativ e" r e fl e cting plan e (s ee figu re A 3 ).

Sinc e w e ar e int e r e st e d in th e r e fl e ct e d signal, not th e transmitt e d signal, furth e r analysis of th i s bound ar y lay e r ph e nom e non c an s e w e only acad e mic int e r e st. Its pr e s e ntation was to point out on e r e ason why e quation (A 3 ) fail s for propagationat gr azing incid e nc e . Anoth e r approachf oUo ws w hic h considers acoust i c w aveswith sph e ricalpropa ga tion. It does not h a ve t hi s s ingul ar ity.

SPHERICALPROPAGATION Rudnick (re f. i6 ) s h o we d that eq uati o n (A 3 ) c an be repl a ced by ¢_ C = ¢ _ D i I + r " exp('i Ko _ P) 1 (A4) wh ere l" = e ffec ti v e refle cti on c oeff i c ie n t for s p h eri c a l p rop agati o n

j r + (I -r ) r ( w ) ] I (l I" = plane - waver e f l ectlonco e fflclent

F(_i) = the "boundaryloss factor" Equation (A4) appli e s to _ point source, h omog e n e ous m e dia (air and ground) and a sm ooth / infinit e / r e fl e cting plan e with compl e x acoustic wav e imp e danc e . Wh e n t he obs e rv e r g e ts suffici e ntly far a way from th e s ound sourc e , L ,P / P approach e s z e ro. if th e angl e of in cid ence , v o, approach e s 90 ° und e r t he s e conditions, th e n e quation (A 4 ) b e com e id e ntical to e quation (A 3 ). In this c as e, th e plan e wav e appro x imation is as g ood as that for spherical pr o pa g ation. How e v e r, aircraft / obs erve r ge om e try, ca n not b e re s tri c t e d to just t hi s case and e quation (A4) is a b e tt e r for m ulation for d e s crib ing th e gr o und r e fl ec tion ph e nom e non and it has ther e for e b ee n in c orpo ra t e d into th e e xtrapolation m e thods us e d in th e comput e r pro gr a m .

i For th e purpos e of e valuating th e " boundary lo s s fa c tor, " th e fo l lowing e xpansions ar e giv e n.

, ] !_ Whe _ W is l e ss t ha n t e n, th e n

K, - t

K - O (AS.1) o I I Wh e n [W] is gre at e r than or eq ual to t e n, th e n

F(W ) = g( W ) / [ w +

wit h g ( kl ) = - [ 0 .5 + 0.5

w - z . s 3 (A S . 2)

W i 1 4 . 5, . "7 ' . 5

- 6.s ] o .8o $

D ue to trun c ation e rror by th e c. omput e r ( n ot en ou g h signifi c a n t digits), eq uation (A5. ! ) is not B E c o m putatio, , tally stable for valu e s of IW[ gre at e r = =thant e n, altho ugh , in th e ory, t he s e ri e s c onv e rg e s for all W. Equation (A5.2) is _ tabl e for valu e s of IW] gre at e r t han 10. It was form e d by transfor m ing .

th e Tay i or s e ri es of Erf c (Z) into Gaussian c ontinu ed fra c tion (r e f. 19) and trun c ati ng aft e r fiv e terms , T he m aximu m absolut e e rr or of this approximation is ( I. I x 1 0"9).

BA NDWIDTH EFFECW $ _0' - _1 " I p 'm ' So t' _J r t he a na ly s is h as c on s id e r e d + re ly a simple h armoni c sour ce . What a c ousti c a; e n g i . ee f _ ar e r ea l l y i n t e r e st e d in i s h o w gro u nd refl ec tion _ : ffec ts Sound Pr es sur e r e v e l S pec tr a {SP L S ). as m e a s ur e d w ith f i n it e b a n d w idt h equ , pmen t . S i nt : e d e t ecti o n equ i p r, len t s ums t he si g na l s wit h t I frequencies contained in t he bandwidt h of t i l e fi lters, it i s necessary t o int e grate equation ( A4) to determine t h e band w idt h effect .

A SPL = 10 Log10 f- _ f-fL df where (*) denotes com plex conj ug ate and ( fL, fu) denote th e cuto f f frequencies for t h e fil t ers .

If t h e values for ZI / Z 0 and K I / K 0 do not va ry erratically over th e frequency limits of integra t ion, t h is integral can b e appro x i m ated b y ASPL -" 10 Log10 + A2 + 2 A c os ( Sz - g) [1 s tn ($ 1)] ( A6, wh ere

_ A = l r ' l and O = arg (r' )

; SI = _ _ p f fU'fL) / CO '_: ' _ $ 2 = _ / ' _ P ( f u + fL) / C o i t a nd t he v al u es f or F ' ar e eva l uat e d a t t he g e om et ric-m ea n-fr eq u e ncie s f or th e fil t er s.

OTHER E F FECTS t The r e a r e ot her e tf ec t s w hich a ff ec t noise mea s urements i n t i le vicin i ty of a r efl e cting g ro un d p l ane: wind and tempe r ature g r a d ients: n o ise so u rce dis_fibution, and s cattering of t he s o und b y an acou st icall y rough ground p la n e, etc. The s e o t he r effec t s have _ :ot been adeq u atel y quanti fi ed at t th is U m e f or i n c o rpor a ti o n into math em a tic a l te r m s .

i I

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J, " , , A PP ENDIX B , ' THEORETICAL EJECTOR PERFORMANCE 19!

C OOR DI N AT I O N S HEET

TO tIC R FP-6-8462-30-59 W. C. S: _ r o y IT r t . _ NI 1 9 71 t CC J.R. Ande rso_ W.R. J o h mon bait October 7, mu._E ; l 7 27 -_ W.K. B o ue rme ; : t or R. B. Tara ,_ii GROUP INDEX 72 7 Retrofit Feas ibil ity Progra m - . i , _'_ SUBJECT Th e oretical E l ec t or Pe rf o r m ance P ara m e t e rs ;:, U t i li z i ng S i m u la t ed J T BD-9 Engine Cond i tion s o + i i,I _1' _ in order to m , l ke c ertain ejector d es i gn d ec | s i am, the f l ow propert i es at the en t rance and exi t of t he e j ec t or shro u d we r e r e que s t ed verbally by Aco u stic s Staff personnel. Pr es ented here are t h ese flow proper t ios m d e ter mi ned by a Pr opul s io n R es earch-developed ejector c o m p u t e r progr am f o r mi xed=to-pri m ary area ratios ( ; - t. /W/ Ap) of 1. 6 , 1.8, 2.0, and 2.2.

T he P &WA J T 8D-9 tu rbofan engine co n d it ions wer e s l m u la t _ d a n d are t a bu la t ed along w i th the ejector g eo m etry and los s i n pu t s. Figure 1 t h roug h 3 2 present _ he eje c t or performance para m© ter versus air s p e ed f or li n es o f constant E PR. T he following table i s a n inde x to t h e f | gures: P erformance AM / A F Pa r ameter 1. 6 1 . B 2 . 0 2 . 2 F ig . 1 Fig 9 F i g. 1 7 F i g. 25 M E Fi g 2 Fig. 10 . : i9 . I _ F ig. 2 t ME), Fi g . 3 Fig, il Fi g . 19 Fig. -2_'" . _ / _ A S F;g. 4 Fi q . 1 2 Fi g . ? 0 Fig. 2B WS / W P Fig. 5 Fig. 13 Fi _. 2 1 _ q . 29 T T E / _ T _ F ig 6 F i 3 . 14 Fig. 2 2 F i g _ 30 Ps / P , _ F ig. 7 F i g. 15 F _g . 2 3 F i_ . 31 p / p _ Fig 8 Fi g . 16 F ig. 24 Fi g . 32 W her e : AM / A p : Ej e c t or Mi x irm j to Pri m ury Area Ratio - " E j e ctor N e t Thr ust R , ,tio (Fn e j / F .p ) Ej e c t or E _i t M c+ ch No. , _t St a tion Q M E Mp P ri m arv F l o w M u,_ h N o. , , t _ tat;, _n_ M S Secondary F l ow M_jc h N o. _ t Stat l o r_ _ l j |_ ws / _ / p - Se co P d _ ry A i r f lo _ to P ri , l ary Airflo _ Ra ,io TT E / TT + . , _ E je ct o r E x i _ T ottll Tem p e r _J t. r e r: tl tio I _ / P c _ "" S ec o n d a r y St _ t l c P r e s su r e R a t io " _Jt St u t io .. _,_ l _ P , "P oe - P ri ma ry St ot l c Pre_ , J r o R a t io u t St , t ior ,_J ' Page 2 RFP-6-8462-30-59 *j T h ese c urves are t o prov i de t rend d ata only and ore not to be ut l l iz e d for _tim a t ing the performance of a speci f i c ejecto r , suppressorco n figuration.

It s hou l d be no t ed t hat the primary fl ow Mo c h N u mb er a t S t a t i o n 0 i s not the f u l l y expan d ed Mo t h N u m ber ° Unfort u nately, t his ejector progra m ass u m e s c o,,t _!_ e mix i n g a n d _ Joes n o t provide t h e ejec t or flow pro p er t i es be t wee n the en t ran c e m, J 4_i t of the shroud . A mi x i n g progra m is be i ng formula t ed by the Propulsio n Resear ch group to provide flow prop e r t i es as a f u nctio n of a x ial displacement . T he m | x i ng prog r am w ill pro b ably be ready for checko ut i n De c e m ber 197 1 .

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| I t i | i 22 5 | I 22 6 l |i REFERENCES !. K.C. Crowley, e t al , " Aircraft Noise Source and Contour Computer Progra m s-User's Guide, " NASA CR114 65 0 , July 1973.

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2. DOT / FAA , " Federal Aviation Regula t ions, " Vol. Ill-Part 36, Appendix B, December 1969.

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1 2 . P .M. Mors e a nd K . U. lng a rd, Theoretic a l Acoust i cs . M c GrawHill Boo k Co., 196 8 .

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2 2 7 i 1 13. S. P. Fao and M. V . Lowson, "S pect r al Techniques in Jet Noise 'theory, " W y le Labs Report WR68-2 I, April 19 6 9.

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1 5 . P. B. Oncl e y, " Propagation of J e t Engin e Nois e N e ar a Porous Surface, " Journal of Sound and Vibr _ ,tion, Vol. i 3 , C 1970, pp. 27- 35 .

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_ 17. U. lngard, " On th e Reflec ti on of a Sph e rical Sound Wav e from an In fi nit e Plane , " Journ al of Acou s tical Socie ty of A m erica, Vol. 23, C19 5 1, p. 329.

18. R. B. Adl e r / L. J . C hu / R. M. Far.o, Electromagnetic EnerB y Transmission and Radiation , John Wil e y and Sons, Inc., C 19 6 0, pp. 35 1- 36 9 , 442- 44 8.

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20. W. Bhat / C. Jaeck, " A Study of the Effect of Density Varia ti on s on Cle an Jet Noise, " Boeing Document D6- 4 0604 , 21 S e ptember 1972. ( Pr oprietary) 21. R.J. Kcenig / P. R. Schorr, " Procedures for Estimating the Magnitude and Directivity Pa t terns of Jet N oise, " Boeing D oc ument D 6 -2 5 490, 2 6 March 1971 ( P rop ri eta ry ) 22. G. g. B ie l ak, " Coaxi al Flo w Jet No is e, " B oeing / Ae ri talia Docu m ent D6E-10041-1 , 18 April 1972 ( Pr op rie tary) 2 3 . E. J. Richards / D. J . Mead, Noise and Acoustic Fatigue in Aero nau tics , Chapter ! i , John Wiley and Sons, Ltd., N e w York , 19 6 8.

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24. J. C . Laur e nce / J. M. Ben n inghoff, " Turbu l enc e M e as u re m ents in M ultipl e Interfacing Air J e ts, " NA C A T N 4 029.

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228 !

2 6 . Th e Boein g Company, "D :si g n In teg ra ti on and N oise St u dies f or .let STOL A irc raft Task V II A , Augm entor W i n g C rui se Blowing Val v e less Sy st em , Vo l. il - Desi gn Explo r atio n," N A S A CR - 11 4 5 7 0 , A pr i l 1 9 73.

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i 30. D . L . Sti mp ert , " Effect of VTO L A ircr a ft F li gh t S peed o n Lift Fa n N oise Generation, " i G eneral Electri c al Comp a ny , TM N o . 72 -15 ! , ! 5 Ma y 1972 .

$ 3 1. S. B . Kaz i n / L . J . Volk, " L F 33 6 Lift Fa n Modi fica tio n an d Ac o us ti c Te s t Pro gram," N AS A C R-1 9 3 4 , D e cem b er ! 9 7 I .

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33 . M .V. Lo w so n / J. B . Olle rh e a d , " St u die s of Helicopter Rotor N oi s e, " USAAVLAB S TR 68 - 6 0 , J an u a r y I969.

34 . J . B . O ll er h e ad / R. B . T a y l or , " D es cription of a He l ic o pter Rot o r N oi s e C omputer Progr a m, " U S AA VL A B S TR 68 - 6 1 , J a n ua ry ! 969.

3 5. F. I t . S, : hm itz / W . Z. S tepnie ws ki / J . G ib s / E . Hinterke use r , "A Co m pa r i s on of O pti m al a nd Noi s e-Abatement T rajecto r ies of a Tilt-Rotor A ircraft, " NA S A CR-2034 , Ma y i 972.

36. D . Bro w n / J . B . Oll e rhe ad , " P r ope ll e r N oi se a t L ow Tip Spee d s , " AFA PL- T R-71-5 5 , Sep te m b e r 1 9 7 ! .

37. F. W. Barry / B . Maglio zz i (Ha mi lton Standard), "N ois e D e tectability P r ediction Method for Lo w S p e ed Pro pe ller s," AFA PL-TR -7 1- 37, J une 1 97t.

38. T . G. G ran g e r / B. M a g l io zz i ( Ham ilt on St an d a rd), " Adv a nced V / STOL P r ope ller Tech - no l ogy F a r [' i cld ln v e st le at t on , AF F D DT R - TI-8 8 , V ol . XI I , M _rch 19 7 2 .

fi

3 9. John Lauf e r, e t a l, "A coustic Mod e ling of the Jet Noise Abatem e nt Proble m , " i n teragency Sympo s iu m on Univ e rsity R e s e arch in Trans po rt a tion Nois e , Pr o cee dings Vol. !, Stanford Univ e rsity, Stanford, C alifornia, March 28- 3 0, 197 3 .

4 0. G. R. MacGr e gor, " Th e Lo c ation of Acoustic Sourc e s in J e t Flows by M e an s of th e Wall Isolation T e chniqu e , " Bo e ing Do c u m ent D 6 - 4 01 ! 6 , F e bruary 1 5 , _, 972 ( Pr opri e ta r y) i - !_ 41 . W. V. Morgan / L. C. Suth er land / K. J. Young, " Th e Us e of Aco u stic Scale Mod e ls for .:ii I_': I nv es tigating N e ar Fi el d Nois e of J e t and Rock e t Engin e s, " WADD T e chnical R e port _ : i 61 - 1 _ 8 , 1 9 6 1 .

23 0

Overview

Key points