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This memorandum i s for reference use only and should nor b e quoted I.S.V.R. Meraorandum N o . . 283 HELICOPTER ROTOR NOISE FINAL RE,PORT: PART I THEORETICAL INVESTIGATION OF ROTATIONAL NOISE by H. K. Tsnna March 1969 HELICOPTER ROTOR NOISE 1st December 1965 t o 30th November 1968 Research Sponsor: National Aeronautics and Space Administration,
Washington D . C
N.A.S.A. Grant N.G.R. -52-025-002 Research Contractor: I n s t i t u t e of Sound and Vibration Research, University of Southampton.
Contract No. 9634 /32 Research Personnel: Research s t a f f : J .W. Lcverton ( E x p e r k e n t a l ) Until 31st August 1968 H.K. Tanna (Theoretical) From 23rd October 1967 Professor E . J . Richards Supervisor: u n t i l 3rd September 1967 C.L. Morfey From 4th September 1967 Associate: Professor J .P. Jones PREFACE This report describes t h e t h e o r e t i c a l work on r o t a t i o n a l noise c a r r i e d out by the author between 23rd October 1967 and 30th November 1968. The e x p e r b c n t a l work on t h e contract has been? c a r r i e d out by M r . J.W. Leverton and a report on t h e findings is being issued s eparat e l y as Part I1 e is concerned with an The major p x t i o n of t h e present report extensive computational study of r o t a t i o n a l noise, and foms p a r t of a l a r g e r programme on r o t o r noise theory conducted a t Southmptsn w i t h t h e j o i n t resources of N e A n S . A . and EinisLryof TechhoPogy grants ACKNOWLEDGEMENTS The author wishes t o express h i s sincere acknowledgements t o h i s supervisor, M r . C.L. Morfey, f o r h i s help and guidance throughout t h e investigationr.
(iii) LIST OF SYMBOLS a blade chord width speed of sound i n air aO r o t o r d i s c a r e a A blade number B dl3 decibel, r e l a t i v e t o 0.0002 dynes per c m D distance from source point on r o t o r disc t o f i e l d point
t o t a l torque force on r o t o r (4 sin e >
FT Bessel function of order- x and- argument p JJP) K constant f a c t o r defining- spectrum l e v e l a t any f i e l d point (Gutin) FT?
torque force eonstant -I
5?
Pao “,J
.,-
I\]
t h r u s t constant (- T s i n 0 1
KT
R a o T term defining spectram’ l e v e l a% my. fie3-d- point (Wright) K 9, t o t a l blade1 section loading at point ( r , $ > on the r o t o r disc
L ( r, $1
steady blade- sectfori .loading LO sth harrnontrc blade loading amp4i%m%e- (Wright ] L S cosine component of SLh harmonic of blade section loadin4 (Sikorsky) LS t o t a l l i f t - o n r o t o r
k
m harmonic ~UrdbeY
e f f e c t i v e Mach nmber. ( a t 0 ; 8 r 1
e 3 M s i n e component- of- Sth- harmonic o f blade section loading S t i p Mach number-
%
N r o t o r r o t a t i o n a l , freqaemy; c/s- r e a l component of sound pressure Pre imaginary component of sound pressure Pim’ P s h a f t horse-power (iv) LIST O F SYMBOLS (continued) mode number
(mB - s ) mode number
Q, (mB + s ) mode number q+ distance from centre of r o t o r head t o source point qri r o t o r disc r area of element on r o t o r d i s c rdrd$ e f f e c t i v e r o t o r radius re r o t o r t i p radius rT distance from ceqtre o r r o t o r head t o t h e point on t h e r o t o r rO blade where t w i s t begins distance from centre of r o t o r head t o f i e l d point R S blade loading harmonic number root-mean-square value of sound pressure spmB A peak amplitude of sound pressure t o t a l t h r u s t on r o t o r (LT cos 6) TT d i r e c t i v i t y function f o r steady r o t a t i n g f o r c e (s=O) yrnB g i r e c t i v i t y function f o r q , mode yq_
d i r e c t i v i t y function f o r s, mode
Y q+ blade span oyer which l o a d i n g is assumed t o be acting A r harmonic blade loading c o e f f i c i e n t a S LO t h r u s t t o torque force r a t i o 1 . I r o t o r efficiency or f i g u r e of m e r i t rl rotor angular frequency, radians per second n density of air P blade f o r c e angle B blade p i t c h angle (SikQrslzy) L3 blade steady p i t c h angle $0 cosine compQnent of c y c l i c p i t c h s i n e Fomponent of c y c l i c p i t c h $1 € ! f i e l d point azimuth angle (0' at t a i l , p o s i t i v e i n t h e d i r e c t i o n or r o t a t i o n ) azimuth angle i n r o t o r plane (0' at t a i l , p o s i t i v e i n t h e d i r e c t ion of r o t a t ion) angle between r o t o r plane and field point, p o s i t i v e upwards blade t w i s t r a t e Y
x wavelength of qth mode
CONTENTS 1. INTRODUCTION 1 SURVEY O F ROTATIONAL NOISE THEORIES 2 2.
2.1 On t h e Sound F i e l d of a Rotating Propeller (Gutin,l) 3 2.2 Helicopter Rotor Noise Generation and Propagation Qchlegel, King and Mul1,2) 6 Sound Radiation from a L i f t i n g Rotor Generated by 2.3 Asymmetric Disc Loading (Wright , 3 ) A Theoretical Study of Helicopter Rotor Noise 2.4 (Lowson and Ollerhead,k) 12 2.5 Conclusion 12
3. DESCRIBION AND INTERPRETATION OF COMPUTED RESULTS 1 4
Properties o f Blade Loading Harmonic Radiation i n 3.1 t h e Far F i e l d 1 4 3.1.1 Steady blade loading radiation properties 1 4 3.1.2. Fluctuating blade loading radiation properties 19 4. C O M M E N T S AND CONCLUSION 24 FUTURE INVESTIGATION 25 5.
6.
REFERENCES 27 ( v i i ) 1. INTRODUCTION Several investigators have t r i e d t o study helicopter roto$ noise, both t h e o r e t i c a l l y and e x p e r k e n t a l l y , and many investigators including t h e author are of t h e opinion t h a t r o t a t i o n a l or d i s c r e t e frequency noise i s t h e dominant noise source f r o m t h e rotor. A s a r e s u l t , it w a s decided t o persue a t h e o r e t i c a l study of r o t a t i o n a l noise i n order t o understand it thoroughly. Means of predicting such noise and methods of reducing it can be obtained only after having a thorough understanding of t h e generating mechanisms involved The first s t e p i n t h e study t h e r e f o r e w a s t o conduct a survey on existing r o t a t i o n a l noise t h e o r i e s and t o evaluate t h e i r usefulness.
FOW reports (references 1, 2 , 3 and h ) were found t o be most appropriate f ~ r The r e s u l t s a r e summarized t h e survey and they were studied i n detail.
i n Section 2 , The survey revealed t h a t t h e most .&portant f a c t o r i n t h e generation of r o t a t i o n a l noise is t h e presence of f l u c t u a t i n g forces on r o t o r blades due t o non-uniform inflow. A s a r e s u l t , e f f o r t w a s concentrated on studying t h e r a d i a t i o n due t o t h e s e f l u c t u a t i n g forces and t h i s l e d t o an extensive computational study of r o t a t i o n a l noise., The computer program used i n t h e study is described in I.S.VnR. Technical Report No- l 3 (reference 5) and t h e computed results a r e given i n I.S.VQR. Technical Report No. 15 (reference 69.
A s m a l l portion of these results is d e s c r i b d a n d i n t e r p r e t e d i n Section Further i n t e r p r e t i v e studies are i n progress as part of a continuing 3.
prograrmne on r o t o r noise at Southampton.
- 1 - $XRvEY OF ROTATIONAL NOISE THEORIES 2 * The four t h e o r i e s found most useful f o r t h e survey a r e listed below.
"On t h e Sound F i e l d of a Rotating Propeller" by L. Gutin (reference 1) 'tHelieopter Rotor Noise Generat ion and Propagat ion!'
by R. Schlegel, R. King and H. Mull (reference 2 ) "Sound Radiation from a L i f t i n g Rotor Generated by Asymetrie Disc Loading" by S .Wright (reference 3) "A Theoretical Study of Helicopter Rotor Noise" by M. Lowson and J. Ollerhead (reference b ) A l l t h e authors have made t h r e e basic ass.umptions and they a r e : The ra'c.qr ( o r p r o p e l l e r ) system i s assumed t o be stationary. A s s resul%, t h e s o l u t i o n ' s accuracy decreases as t h e r o t o r system t r a n s l a t i o n a l speed increaseso Steady conditions a r e assumed. That is, what happens in one revolution happens i n every other revolution, and i n f a c t , what happens t o one blade at a par6icular azimuth is repeated on every other blade when it is a t t h a t azku$h.
The chordwise pressure p r o f i l e is etsswned t o be rectangwlar. That is, t h e aotual pressure p r o f i l e across t h e chord is approxhated by an equivalent rectangular d i s t r i b u t i o n f o r e a s i e r harmonic analysis, It is i n t e r e s t i n g t o note t h a t t h e Gutin thetory foms t h e foundation a l l t h e l a t e r t h e o r i e s t o date.
A l l authors s t a r t off by f o m u l a t i n g t h e r a d i a t i o n from an elemen% and obtaining t h e t o t a l r a d i a t i o n by r a d i a l r dr dJ, on t h e r o t o r d i m , (r) and a z b u t h t t l ( $ 1 integrations.
- 2 - 2.1 , O n the Sound F i e l d of a Rotating Propeller by Gutin The theory is based on t h e assumption t h a t t h e axial inflow throughout t h e r o t o r disc is uniform. This is more true i n t h e case of propellers than i n t h e case of helicopter r o t o r s .
2.1.1 camm%$s,oe,zlzeory
Since uniform inflow is assumed, there a r e no f l u c t u a t i n g forces ( a > acting on t h e blades, if t h e e f f e c t s of turbulent boundary l a y e r s on t h e blades a r d neglected("vortex Pioise") e The sound r a d i a t i o n i s therefore caused by steady r o t a t i n g forces only and as such i% is symmetricalabout t h e r o t o r axis.
I n order t o e l b i n a t e r a d i a l integration, t h e loading p r o f i l e ac3loss ( b ) t h e blade span is neglected and t h e t o t a l loading on a blade is supposed t~ be acting over a small span A r (point loading) at an e f f e c t i v e radius
, usually taken t o be 0 , 8 of t h e t i p radius r e
r e T ( c ) The analysis is simplified by considering r d i a t i o n in t h e far f i e l d can be negleeked eon- only, i n which case r a d i a t i o n due t o terms in & ' - 1
pared t o t h e radiation due t o terns in i i l
The s o l i d i t y of t h e r o t o r is assermed to be low ( T e e n s m a l l blade
( a >
chord a> and s o at l e a s t f o r lower harmonics, The azimuthal integration is perfomned a n a l y t i c a l l y by introducing ( e > The peak amplitude of lp$@ hambnic of sound p r e s s w e due -bo a B-bladed - 3 - r o t o r r o t a t i n g at N cycles per second is given by K where J = Bessel M c t i o n of order mB, m J 3
= $ 60s B and FT = LT s i n B e
TT Other symbols are e m l a i n e d i n t h e list of symbolso Properties of K f a c t o r : Depending on t h e r a t i o of t h r u s t t o torque fo.rces, t h i s facqor deternines t h e shape of t h e polar diagram f o r given mB.
L cos B s i n C I M . M sin CT thrus.t t e r n = T .e :e 1 - I = Let torque t e r m L s i n B t a n B T Then, f o r 1-1 >> I, t h e polar diagram is t h r u s t dominated and f o r p .c< 1, t h e
polar diagranp is torque dominated ( s e e f i g u e s ( a > and ( e ) 1
When t h e t h r u s t t e r n and t h e torque t e r n a r e of s h i l a r order, t h e shape of t h e polar diagran is as shown i n f i g u r e ( b ) belowo
- 4 , -
PrQperties of y f a c t o r : mB Effects of mB are contained i n t h e d i r e c t i v i t y function y It nlB' hgs a value zero on t h e r o t o r axis and so t h e theory predicts zero r a d i a t i o n on t h e r o t o r axis.
The same f a c t o r provides a r a p i d harmonic f a l l o f f at any f i e l d point The and s o t h e theory is useful f o r predicting t h e first harmonic only.
spectrum l e v e l can be reduced by reducing and from t h e figures below, y mB it is c l e a r t h a t t h i s can be done by having l a r g e B and s m a l l M .
e If t h e shaft horse-power P and t h e r o t o r efficiency ( o r f i g u r e of m e r i t h are knom,then an estimate of t h e t h r u s t and torque forces cap? be obtained from t h e momeleum theory; and D where A = r o t o r d i s c area, p = density of air, and R = angular v e l o c i t y i n radians per second.
- 5 - The theory is more usefyl f o r propellers where t h e fundamental l i e s w e l l i n t h e audio region, Q p f p recornendat ions 2 1 3 The theory predicts that % r a given thrust, a r o t o r must have l o w - r . p . ~ ? ~ , l a r g e number of blades and l a r g e radius i n order t o reduce t h e noise.
2 , 2 Helicopter Rotor N0is.e GeneratiQn and Propagation by SchleEeJ., Bing and Mull. ' $he helicopter r o t o r has a l a r g e diameter (compared t o fans or propellers) and nonaxial t r a n s l a t i o n a l motion, and so t h e inflow across t h e r o t o r d i s c i s nonunifom, Also because t h e r o t o r has a l o w number of blades and Sow r,pom., t h e fundamental generally l i e s below audible frequency and i s Gutin's theory f o r propellers, t h e r e f o r e , is subjectively unimportante not adequate f o r helicopter ro%oYswhere higher harmonics are requiredn Although t h e importance of f l u c t u a t i n g forces on r o t o r blades in t h e r a d i a t i o n of sound had been s t r e s s e d by several investigators, t h e first mathematical treatment of t h i s mechanism, which r e s u l t e d in an is given in t h i s reference" extension of Gutinls work, 2 . 2 c l Comments on theory
----------_------
Most of t h e approximations involved i n Gutinss work are eliminated here. The result is not r e s t r i c t e d t o low s o l i d i t y rotors and t h e sound pressure s p e c t r a can be evaluated at any point i n t h e far f i e l d o r i n t h e near f i e l d .
The spbnwise loading p r o f i l e is not neglected and t h e steady loading i s replaced by fluqtuating loading, which is harmonically analysed i n t o D.C. and harmonic components of blade loading at several r a d i a l s t a t i o n s .
This accounts f o r t h e nonunifom infJow across t h e r o t o r d i s c , - 6 - The method b a s i c a l l y evaluates t h e t o t a l r a d i a t i o n , from a l l elements r d,r d$ of t h e r o t o r disc,by azimuthal ($) and r a d i a l (r) integrations.
These integratidns are c a r r i e d out by numerical methods with t h e help of a computer program.
The work a l s o includes t h e v a r i a t i o n of f o r c e angle with radius and azimuth, by introducing blade t w i s t and c y c l i c cordponents of p i t c h respectively i n addition t o steady pitch.
It i s i n t e r e s t i n g t o note t h a t f o r steady loading, concentrated at e f f e c t i v e radius r t h e predicted spectrum would be i d e n t i c a l t o t h a t e' due t o Gutin's work f o r i d e n t i c a l input parameters.
2.2.2 Comments on f i n a l result -------------------u---- The root-mean-square value of mth harmonic of sound pressure due t o a B-bladed r o t o r r o t a t i n g at 52 radians per second is given by where 're O J 0 and
{sin B cos 0' s i n ( $ - 0 ) + cos 6 s i n a ) r d r d$
- 7 - f o r which and
L ( r , I ) > = Lo + L cos SI) +M. s i n s $ -
s S Other symbols a r e explained i n t h e l i s t of symbolsp Measured blade loading data from reference 7 w a s used t o compute sound pressure spectra, and t h e c o r r e l a t i o n between computed values and measured values w a s found to be good at l e a s t f o r t h e first four harmonics+ Also, i n contrast t o t h e Gutin prediction, t h e r e was f i n i t e r a d i a t i o n on t h e r o t o r axis. This agreement wi%.hmeasured acoustic data showed t h e importance of fluctuating forces i n higher harmonic noise generationc A t t h a t t i m e , only 10 harmonics of blade loading were available and it w a s shown t h a t prediction of higher harmonics in. t h e acoustic spectrum depended on having higher harmonics of" blade loading available.
Design ---- ----------------- reeomendat ions (Sikorsky Aircraft 1
2 2 3 Although Gutin's prediction mderesZimates t h e l e v e l of t h e fundmental, it is adequate f o r estimating t h e r e l a t i v e effect, o f desigm p a r m e t e r s - f o r a given t h r u s t , have low r - p c m e , Parge B and l a r g e r t o reduce so T noise Since nonuniform loading is t h e major f a c t o r i n t h e generation of higher hamonic noise, it is necessary t o conLro1 t h e harmonics of blade loadingc The authors suggest t h a t the nost important consideratlion which - 8 - contribues t o t h e nonuniform inflow pat%em is t h e presence o r absence of wake i n t e r a c t i o n from other blades o r r o t o r systems. High harmonic r o t a t i o n a l noise may be reduced by reducing t h e l o c a l s t a l l and drag vergence tendencies of blades and by a l t e r i n g a e r o e l a s t i c c h a r a c t e r i s t i c s t o m i n i ~ z e harmonic airloads.
Sound Radiation from a L i f t i n g Rotor due t o A s m e t r i c Disc 2,3 Loading by Wright 2 0 3 a l Comments on theory
------------------
Unlike t h e Sikorsky theory, a l l Gu-Gin approxima-kions except one are retained here. The Gutin steady loading at e f f e c t i v e radius,
r , is replaced by f l u c t u a t i n g loading, which i s introduced i n t h e form
e of D O C o and harmonic components of blade loading, This makes Gutin's theory t o be a s p e c i a l case of t h i s mcdification.
The mathematical r e s d t s are interpreted by using t h e concept of r o t a t i n g modes, a mode being defined as a r o t a t i n g sinusoidal loading p a t t e r n which results from r o t a t i n g forces within t h e r o t o r disc. The theory predicts tha%,sthazimuthal harmonic o f bY&de loading produces two ail m S . 2
and - such r o t a t i n g modes, r o t a t i n g at angular v e l o c i t i e s -
a + s e nriB-s For s > 0 , t h e first mode r o t a t e s at higher angular velocity thw- t h e second mode and s o t h e second mode can be neglectedfk-om t h e radiation point of view. A t mB = s , t h e first made r o t a t e s & an i n f i ~ t e speed and sa a given loading harmonic produces n a x ~ r m ~ rad-iation i n t h i s region of t h e spectrum (corresponding t o acoustic frequencies around t h e f l u c t u a t i n g frequency of t h e blade load:).
This shows t h e importance of f l u c t u a t i n g blade loading in predicting higher harmonics of" t h e sound pressure spectmxnp 2-3.2 Comments on f i n a l r e s u l t .
--------3-----------__c_ The radiation from t h e 4th mode is- given by - 9 - y = m B J ( @ M cos a) , d i r e c t i v i t y function of qth mode, where 9 g e
-
LS a = - (harmonic blade loading c o e f f i c i e n t ) , S LO q, = mB * s, = m B - s , q- - - - T s i n ( t h r u s t constant), KT R a o T (TT = LT cos 6 ) N FT
(torque force constant 1
and K F = q M e
Other symb0.p are explained in t h e l i s t of symbols.
For s = 0 , i , e . f o r steady loading, q = mB and as 1.
Therefore t h e r e s u l t becomes h
spa - - ‘KT - $ 3 ym
This r e s u l t is i d e n t i c a l t o t h a t predietedby Gutin for &ea,@ loading.
For s 0 ,
- 10 -
and so t h e second tern of t h e result can be neglected. The r e s u l t then becomes ~ The above result can predict t h e h d i a t i o n due t.o a s i n g l e blade loading harmonic, s , and so t h e theory is very useful i n predicting t h e properties of blade loading harmonics, within t h e l i m i t a t i o n s of t h e point loading model a It should be noted t h a t t h e Sikorsky theory can a l s o be used t o predict these properties and t h e two t h e o r i e s would give i d e n t i c a l answers f o r i d e n t i c a l input parameters. However, Wright's theory gives an e x p l i c i t a n a l y t i c a l r e s u l t f o r t h e simple model considered.
Gutin's theory, t h e d i r e c t i v i t y function, y
i n , has
Unlike ym.B 9 , resonance-like properties. That i s , t h e spectrum has a maximum value The polar diagram in t h i s case is t h a t of around mB = s. (q = 0 qode).
a dipole noma1 t o r o t o r axis - contrary t o Gutin's prediction f o r steady
For any other value of mB, t h e polar diagram will be of t h e Gutin loading.
type f o r steady loading.
From t h e measured blade loading data available (reference 7 ) , it w a s found t h a t i r r e s p e c t i v e of f l i g h t condition, t h e spectrum of blade loading harmonics f a l l s off approximately at 6 dB per octave. The present theory predicts a sound pressure spectrum f a l l i n g at 3 dB per octave i n t h i s case.
2.3.3 Design Recomendatiogg The author mentions t h a t removal of fluctuating forces from t h e blades both l o c a l and n e t , i s t h e most important f a c t o r i n reducing t h e r o t a t i o n a l noise. Here, he suggests t h e use of r e a c t i v e techniques r a t h e r than r e s i s t i v e 6echniques.
- 11 -
2.4 A Theoretical Study of Helicopter Rotor Noise by Lowson and Ollerhead The work is very similar t o t h a t of Wrightc That i s , steady blade loading is replaced by fluctuating loading and a l l t h e other Gutin approx- imations a r e retained" I n addition t o t h e t h r u s t (axial) and torque I) t B e authors a l s o include t h e r a d i a l forces acting (circumferential) forces on t h e blades. The f i n a l result t h e r e f o r e has an esdra t e r n involving differenkials of Bessel functionso The f i n a l result is used t o i n v e s t i g a t e power Paws f o r blade loadfing harmonics as a function of speed and ft w a s found t h a t a -2,5 power l a w gives good agreement with experiment.
The authors conclude t h a t f o r clean flow cases, t h e theory is useful f o r investigating trends I) but f o r rough running cases agreement was not good because of lack of information on loading harmonics.
2.5 Conclusion The most important outcome of t h e survey w a s t h e f a c t t h a t f l u c t u a t i n g blade loadings produce acoustic s p e c t r a which a r e r i c h i n higher harmonic content. A s far as predicting t h e sound pressure spectrum with great accumcy is concerned t h e problem is Rar from solvedo Measurement of f l u c t u a t i n g airloads on r o t o r blades i s a very difficeil% and expensive instrumentation problem where t h e results depend c r i t i c a l l y upon t h e e accuracy of t h e measuring i n s t r m e n t ~ s The t h e o r i e s a l s o involve some approximations, which may be v a l i d f o r many>flight regimes but could introduce l a r g e e r r o r s i n predicting acoustic spectra f o r other f l i g h t regimes, One of t h e most important i n t h i s context could be t h e imporbance of chordwise loading factors p r o f i l e . This is discussed in section 5.
- 12 -
Howeverofor design purposes, a knowledge of t r e n d s i s e s s e n t i a l i n designing a quieter r o t o r . Thus it w a s decided t o carry out an extensive computational study of r o t a t i o n a l noise, i n order t o under- stand t h e properties of a single blade loading harmonic and t o obtain trends of r a d i a t i o n due t o various composite blade loading spectra.
The computer program f o r t h i s investigation i s described i n reference 5 and t h e computed r e s u l t s are presented i n reference 6.
- 13 -
3. DESCRIPTION ,AND IP1JTERPRETATI0NNOF COWUTED RESULTS A n attempt t o describe and t o give physical i n t e r p r e t a t i o n s of a portion of t h e compuf;.ed results is made i n t h i s section, results The are reported i n I.S.V.R. Technical Report No. 1 5 (reference 6),and t h e figures referred t o throughout t h i s section are those of t h a t report.
Proaerties of Blade Loading Hamonic Aadiation i n t h e Far 3.1 F i e l d (figures 1 . 1 . 1 t o 1.i.42) Properties of steady blade loading radiat.ion a r e given by s = 0 computations, and properties of fluctuating loading radiation are given by t y h i c a l (s = 12 and B = 48) blade loading harmonic computations.
3.1.1 SteaQ blade loading r a d i a t i o n r o p e r t i e s
---+ ------------- ---".------_- ---------
T? = 0 , yiaures 1.1.1 t o 1.1.14P Sound pressure spectra (mB p l o t s ) ( a ) The c h a r a c t e r i s t i c feature i s t h e Gutin type sharp by steady f a l l o f f , which a r i s e s from t h e f a c t t h a t f o r s = 0 , t h e Bessel functions encountered a r e of p o s i t i v e i n t e g r a l order, and so y falls off s t e a d i l y mB with mB at any f i e l d point.
Effect of Mach number Me, Figure 1.1.11 (i) ----------------Y---________________I__ The spectrum l e v e l at any f i e l d point is b a s i c a l l y determined a s W FT
- -
(TT s i n G - -
Me which can be rearranged as Thus, below t h e r o t o r d i s c ( a negative), t h e spectrum l e v e l increases with increasing M .
e The spectrum shape is coslpletely determined by t h e y term.
mB The mB fall-off decreases with increasing M T h i s is because of e t h e f a c t t h a t f o r Me < 1.0 t h e l e v e l s o f t h e sidebands f a l l off s t e a d i l y above t h e centre frequency. A s M is increased, t h i s fall- e off decreases and when M reaches 1.0, t h e r e are an i n f i n i t e number of e wavefronts which coincide i n front of t h e source, thus giving rise t o an i n f i n i t e number of sidebands a l l having equal i n t e n s i t i e s , There i s very l i t t l e difference between t h e r a d i a t i o n due t o t h e f i v e d i f f e r e n t span d i s t r i b u t i o n p r o f i l k s considered, which shows t h a t t h e e f f e c t i v e radius approximation is v a l i d for steady loading. It should, however, be noticed t h a t as t h e concentrated loading becomes more d i s t r i b u t i v e , t h e mB f a l l off decreases, t h u s showing t h e importance of loading a% l a r g e r i n t h e higher harmonic radiation.
A n i n t e r e s t i n g case is t h e 'zero lift' case where Gutin's theory would predict zero radiation because t h e r e is no net force acting over is no net force over t h e t h e blade span. Physically, although t h e r e blade, t h e r e are l o c a l forces over t h e span and one would expect radiation from these l o c a l forces. Computationally, t h i s is found t o be t r u e and, i n f a c t , t h e r e i s hardly any difference between t h e radiations due t o 'zero lift' d i s t r i b u t i o n and 'constant ' d i s t r i b u t i o n .
Thus, spanyise loading p r o f i l e cannot be neglected when t h e r e is l o c a l lift on t h e blade span.
negative
- 1 5 -
unaffected. The spectrum l e v e l i s determined by
$ s i n $
ts B s i n ff - 1 4
Me As $ increases, t h e torque term increases and since t h r u s t and torque terms a r e a d d i t i v e below t h e r o t o r d i s c , t h e r e is a general rise i n t h e spectrum l e v e l as shown i n t h e figure. Clearly, if t h e r a d i a t i o n was computed above t h e r o t o r d i s c , an opposite e f f e c t would be ob4erved; t h a t i s , t h e spectrum l e v e l decreases with increasing 8 .
Physically, t h e s e e f f e c t s can be explained by t h e f a c t t h a t t h e radiatiolrsdue t o t h r u s t and torque are of t h e same p o l a r i t y below t h e r o t o r disc and a r e of opposite p o l a r i t y above t h e r o t o r d i s c .
Effect of Chord,Width a . Figure 1.1.7 ( i v ) --_-----------1-----y_I____ --I--_---
The e f f e c t a r i s e s from t h e spectrum function x. For a
rectangular pulse, t h e Epectrum function is 2r e N o w for very small a,X 13 1 a t l e a s t f o r low mB nwribers and as a increases, zeros; begin t o appear i n t h e spectrum function, as shown i n t h e f i g u r e below
x
7 16 -
Thus, as t h e chord width is increased, t h e sound pressure spectrum begins t o show zeros which occur when when i.e.
m a B = 7r
2re For t h e dhord widths considered, taking r = 24 f t , t h e zeros a r e given at: e a
-
mB
1" 1808 16" 6 4 ' ' Physically, one would expect higher radiation when t h e pulse is sharper (small a ) , t h e e f f e c t being more pronounced at t h e higher' Frequencies.
(b) D i r e c t i v i t y (polar e1evatio.n p l o t s ) For s 0, the g , = 0 mode does not e x i s t and so Gutin type polar p l o t $
are observed for a l l & numbers - no r a d i a t i o n along t h e r o t o r mise
Another zero appears when t h e radiations due to t h r u s t and torque cancel each other. This happens when 01 N I+, cos B s i n (T
a s N k s i n B
S
-
- c _ _ r _ l M e RaO RaO t a n f3
i.e. when s i n d i=: -
M e The computed P l a t s do not show i d e a l zeros because t h e span loading i s
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d i s t r i b u t e d over 10% of t h e span and is not concentrated.
s i n (T = t a n 6 ' . Thus, f o r M = 0.25 zero occurs at u = 24.0°
e Me 0.50 12J0 8.0' 0.7'5 1.25 Ec.80 The zero approaches t h e r o t o r plane and tends t o be sharper as M increases. Physically, as M increases, t h e t h r u s t t o torque r a t i o e e M s i n 0 e ) becomes l a r g e r and so t h e rqdiation tends t o be of t h e v ( = t a n 8 t h r u s t dominated, dipole type.
For a fixed value of M t h e shapes of t h e polar elevation p l o t s e' do not a l t e r much with JnB number.
-EZffect of Span Distribut,ion. --s&Lures 1.1-2 t o 1.1.6 (ii)
...---r--------'=.P--- -------------------
Here again, t h e r e i s not much difference between t h e radiations due t o t h e f i v e d i f f e r e n t span loading p r o f i l e s considered, proving t h e v a l i d i t y of t h e effective radius approximation within t h e range of d i s t r i b u t i o n s tested here. An i n t e r e s t i n g point t o be noted here i s t h a t t h e r e i s no difference at a l l between t h e radiations due t o 'rectangular 10%' loading and 'rectangular 0.3%' loading which shows t h a t f o r a c e r t a i n value of effective radius r t h e polar p l o t f o r r a d i a t i o n due t o concentrated loading e' at re is unaffected i f t h e loading i s spread over a f i n i t e span about r .
e The zeros f o r ' t r i a n g u l a r ' and 'constant d i s t r i b u t i o n s are found t o occur at l a r g e r elevations ( 0 ) than t h e zeros due t o other d i s t r i b u t i o n s .
N o w since a zero occurs at s i n 0 = t a n 8 , it would suggest t h a t M f o r
-
e ' e
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'triangular' and 'constant' d i s t r i b u t i o n s i s smaller than M f o r other e d i s t r i b u t i o n s . Looking at t h e s e d i s t r i b u t i o n s , it is easy t o see t h a t t h i s may be q u i t e true.
( iii 1 . ~ f r e c t , o f - F _ o r c ~ - ~ ~ ~ ~ ~ - ~ - ~ -
When B = 0 t h e r e i s no torque r a d i a t i o n and so t h e polar
a. dipole noma1 t o t h e r o t o r
diagram i s completely t h r u s t doininated; There is no r a d i a t i o n on t h e r o t o r axis because of perfect cancellation axis3 ( a r i s i n g from y t e r m ) .
mB For medium B ( = 6'1, t h e r a d i a t i o n is t r a d i t i o n a l Gutin type, w i t h t h e zero occurring at CJ = 12.1 .
m e n f3 i s large ( = 24'9, t h e t h r u s t t o torque r a t i o II < < 1 and so ,he h e , s p h e r i c a l b u t modified by y radiation teqds t o be torque dominated; mB term t o give zero radiation on r o t o r a x i s .
Fluctuating Blade Loading Radiation PProEert i e s 3.1.2 --y---c--c"-.--- c--3--------- --u--
7; ,= -E, Figures 1.1.15 t o 5.1..28; s = 48, Figures 1.1.29
t o 1 . 1 . 4 2 ) A s mentioned i n reference 3, f o r point loading, t h e sound pressure spectrum due t o a s i n g l e blade loading harmonic, s, i s given by h a NLT
= - S {COS B s i n CJ - - s i n B ( ~ B - S ) ~ ~ ~ -
(mBM cos 01
e spmE, 2Ra0 M e IllB mB-s K 4, Sound Dressure spectra ( m ~ PIO$E;) (a) HePe again, t h e spectrum level for any s i s determined by t h e K term 4- $ern, and t h e spectrum shape at any f i e l d point i s determined by t h e y
e
shows resonances Unlike t h e sharp mB f a l l o f f observed f o r steady loading, y q- l i k e properties have maximum values about mB = s ( i . e e q = 0 rnode).
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Effect of Mach Number M
. Figures 1.1.25 and 1.1.39 (i>
e ....................................................
' The sound pressure spectrum has a plateau whose height and width increase with Me" The width of t h e plateau i s determined by t h e Doppler e f f e c t and i s given by Physically, t h i s can be explained by t h e f a e t t h a t f o r a f l u c t u a t i n g
r o t a t i n g force , sideband tones are generated. N o w as M increases, t h e
e i n t e n s i t y of these tones and t h e band spreading increases u n t i l M COS (T = 1 e is reached. A t t h i s stage, t h e r e is an i n f i n i t e nupber of sidepandg a l l having equal i n t e n s i t y , r e s u l t i n g i n t o a f l a t mB spectrum above mB = s e A t higher Me, one observes dips i n t h e spectrum especially i f each
mB value is computed. This i s because of cancellation - t h e Bessel function
reaching t h e o s c i l l a t o r y region of Bessel h i l l s .
Effect of s2an d i s t r i b u t i o n . F i g x y s l * l * l zand 1.1.22 (ii)
--------I-- --_----------c----s -------- ----------
The e f f e c t is similar t o t h e one observed f o r steady loading radiation. For t h e f i v e d i f f e r e n t span loading profiles considered, t h e r e is no difference i n r a d i a t i o n at low mB n w b e r s ; but at high mB numbers, t h e sound pressure l e v e l due t o d i s t r i b u t i v e loading i s higher than t h a t due t o point loading, t h e l e v e l s increasing as t h e loading becomes more distributive.
This shows t h e importance of loading at l a r g e r i n t h e radiation from higher order modes.
(iii) Effect of Force angle 8. Figures 1,1.22 and 1.1.36
------------------
t e r m , which i s given as Force angle B appears i n t h e K q_
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a NLT
s i n B ( m ~ - s ) . S
K = -
{cos B s i n CT -
mB M q- 2Ra0 e m e n B = O o , t h e spectrum is thru&dominated. wen B 0 t h r e e s i t u a t i o n s arise :
( a ) mI3 = s. Irrespective of , t h e r e f s no torque radiation afid
so t h e spectrum 1 s completely t h r u s t domina3.ed.
Thrust an4 torque radiqtions are of ppBsite p o l a r i t y ( b ) mB < s.
below t h e r o t o r disc ( C T negative) and so t h e spectrum l e v e l decreases with increasing B.
( c ) mB < s. Thrust and torque radiations are of t h e same p o l a r i t y below t h e r o t o r d i s c and so t h e spectrum l e v e l increases with increasing For f i e l d points located above the r o t o r disc ( a p o s i t i v e ) , t h e trends i n ( b ) and (c9 above would be reversed- steady loading, and t h e computed s p e c t r a f o r a = 64" show t h e dips a t m E 3 = 28,56,84 which coincide with t h e zeros i n t h e spectrum function,
D i r e c t i v i t y (Polar e&vation p l o t s 1
( b ) When mJ3 = s, t h e q = 0 mode is r o t a t i n g at i n f i n i t e speed and so t h e radiation is maximum.
Also, t h e r e i s no torque force radiation, i r r e s p e c t i v e o f force angle B. Thus t h e polar diagram is completely t h r u s t dominated, dipole type.
For any &her value of mB, i t s shape is similar t o t h a t due t o steady loading, although f o r f l u c t u a t i n g loading, lcbes begin t o appear because of cancellation. For point loading, a zero appears when
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For a l l modes eccept q ' 0 , as w i t h steady loading, t h e r e i s not much difference between t h e polar p l o t s due t o t h e d i f f e r e n t span loading p r o f i l e s considered.
For the 9 = 0 mode, t w o t h i n g s should be noted. The lobes due t o d i s t r i b u t i v e loading do not show perfect zeros l i k e t h o s e due t o point loading and t h e dips i n t h e lobes become shallower as t h e loading becomes more d i s t r i b u t i v e . T h i s would suggest that f o r d i s t r i b u t i v e cancellation i s not perfect, loading, the B = O o , t h e r e i s no t o r q i e force and so t h e r e i s zero When For q = 0 mode, there is maximum radiation radiation along t h e r o t o r plane.
on t h e r o t o r axis wherea$ f o r a l l t h e other modes, t h e r e is zero r a d i a t i o n on t h e axis.
When B > 0 , zero r a d i a t i o n occ'ws at an angle given by
g_ t a n B s i n CT = OT m B M e Thus for negative order modes, t h e zero appears below t h e r o t o r disc and for p o s i t i v e order modes, t h e zero appears above t h e r o t o r d i s c , 4. C O M M E N T S AND CONCLUSION Only a s m a l l portion of t h e computed results i s discussed i n section The rest of t h e results are being studied at I.S.V.R. and a report on 3.
the-findings w i l l be available i n t h e near future.
The study of t h e of a s i n g l e blade loading harmonic has proved very useful properties i n understanding t h e radiation properties of corpposite blade loading spectra.
so far, it i s Although t h e whole cosnputational study has been r a t h e r academic hoped t h a t t h e t r e n d s obtained w i l l be more useful when f u r t h e r data on blade airloads become available.
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5. FUTURE INVESTIGATIONS I n reference 7, measured values of t h e first t e n harmonics of ( a ) are tabzlPat.ed.
blade loadings f o r various f l i g h t conditions For a
t y p i c a l helicopter r o t o r (M p. 5 ) , t h e acoustic speckra computed with
e t h i s data w i l l be t h e o r e t i c a l l y v a l i d upto mB = 7 onlyo I n order t o at obtain improved correlation between t h e o r e t i c a l and measured values higher mB numbers, it i s e s s e n t i a l t o obtain higher harmonics of blade loadings. This is being done at present at Sikorsky Aircraft where fluctuating a i r l o a d s f o r t h e NH-3A ( s - 6 1 ~ ) helicopter a r e being measured up t o a frequency of 2 KHz. A c o r r e l a t i o n study between t h e o r e t i c a l and measured acoustic spectra should be conducted as soon as these airloads are available.
It should a l s o be noted t h a t i n order t o obtain a correct r a t i n g f o r t h e usefulness of e x i s t i n g t h e o r i e s , noise recordings and blade a i r l o a d measurementsshould be conducted simultaneously.
The e f f e c t of forward speed on propeller noise has been investigated ( b ) by Garrick and Watkins (reference 8 ) and t h i s may be e a s i l y applied to a l i f t i n g helicopter r o t o r , but t h e e f f e c t of t h e motion o f a ro%or system i n any other direction (e,.g. forward speed) on t h e radiation of rotzltioaal noise needs investigation.
The importance of chordwise pressure p r o f i l e capnot. be neglected, ( c > as described below: A blade might not have any net force across t h e chord (i> but it can have posit.ive and negative conponents which cancel each other. In p r a c t i c e , such a d i s t r i b u t i o n w i l l radiate sound although t h e e x i s t i n g t h e o r i e s do not. predict s o ,
- 25 -
The chordwise pressure p r o f i l e may a l s o vary with (E) a z b u t h and such a f l u c t u a t i o n (which may be due t o such causes as gusts, presence of fuselage, climb, forward speed, etc,) may produce s i g n i f i c a n t radiation which is not accounted f o r i n t h e present theories.
Thus t h e analysis i n t h e e x i s t i n g theory f o r fluctuating Toads should be extended t o include t h e shape o f t h e chordwise pressure d i s t r i b u t i o n and i t s v a r i a t i o n with azimuth.
6. REFERENCES Gutin, L. "On t h e Sound Field of a Rotating Prapeller", 1 . N .A.C ,A, Technical Memorandum No. 1195. October, 1948, 2. Schlegel, R.G., King, R . J e Mull, H.R. "Helicopter Rotor Noise Sikorsky Aircraft USAA4n;BBS Technical Generat ion and Propagat ion" Report 66-4, October, 1966.
Wright , S .E. "Sound Radiation from a L i f t i n g Rotor Generated by
3.
Asymmetric Disc Loading".
I n s t i t u t e of Sound and Vibration Research, Southampton University, Technical Report No. 5c April, 1968,
Lowson, MeV. , Ollerhead, J O B *
4. "A Theoretical Study of Helicopter qotor
Noise", Wyle Laboratories Huntsville, Alabama. May, 1968.
Tanna, H.K. "Computer Program for t h e Prediction of Rotational 5.
Noise due t o Fluctuating Loading on Rotor Blades".
I n s t i t u t e of fjound and Vibration Research, Southampton University, Technical Report No. 13.
December ,1968 Wright , S.E., Tanna, H,K.
6 . "Computat.ional qtudy of Rotational Noise P a r t I1 - Computed Ou'cput".
I n s t i t u t e of Sound and Vibration Research, Southampton University, Technical Report Noo 1 5 . 1969, Scheiman J a "A Tabulation of Helicogter Rotor Bka3e D i f f e r e n t i a l '1.
Pressures, S t r e s s e s , and Motions as Measured i n Flight". N A S A TM X-952.
March, 1964.
8.
Garrick, I . E . , Watkins, C.E. "A Theoretical Study of t h e Effect of
Forward Speed on t h e Free Space Sound Pressure Field Around Propellers" N.A.C.A. RepQr'c 12-98. 5954,
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