An unsteady helicopter rotor: Fuselage interaction analysis

APPENDIX A - A COUPLED MAIN/TAIL ROTOR INTERACTION STUDY

List Of Symbols l i f t c o e f f i c i e n t of t a i l r o t o r under t h e i n f l u e n c e of t h e main r o t o r l i f t c o e f f i c i e n t of i s o l a t e d t a i l r o t o r v e r t i c a l d i s t a n c e above main r o t o r t i p path p l a n e (m) l o n g i t u d i n a l d i s t a n c e from t h e edge of the main r o t o r d i s k (m) main r o t o r r a d i u s (m) t a i l r o t o r r a d i u s (rn) t i p path plane c o o r d i n a t e s y s t e m of r o t o r 1 (m) 2 r e l a t i v e t o t h e hub of r o t o r 1 i n t r a n s l a t i o n of t h e hub of r o t o r t h e t i p p a t h p l a n e c o o r d i n a t e s y s t e m of r o t o r 1 as used by F389SR (m) t i p path plane c o o r d i n a t e system of r o t o r 2 (m) r o t a t i o n of t h e t i p path plane c o o r d i n a t e system of r o t o r 2 as used by F389SR about t h e x-axis of r o t o r 1 (deg) r o t a t i o n of t h e t i p path plane c o o r d i n a t e system of r o t o r 2 about t h e z-axis of r o t o r 1 a f t e r it has been r o t a t e d about t h e x-axis of r o t o r 1 (deg) 1 and r o t o r 2 r e s p e c t i v e l y ( r a d / s e c ) r o t a t i o n a l v e l o c i t i e s of r o t o r s t a r t i n g p o s i t i o n of r o t o r 2 i n r o t o r 2 ' s t i p p a t h p l a n e azimuthal c o o r d i n a t e system r e l a t i v e t o t h e z e r o azimuthal p o s i t i o n , p o s i t i v e i n t h e d i r e c t i o n of r o t a t i o n of r o t o r 2 (deg) r o t o r advance r a t i o ; f l i g h t s p e e d l t i p speed li wake skew a n g l e r e l a t i v e t o t i p p a t h plane (deg) X

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I n t r o d u c t i o n The r o F o r c r a f t o p e r a t e s i n an i n t e r a c t i o n a l aerodynamic environment which s t r o n g l y a f f e c t s t h e r o t o r c r a f t system performance. Major sources of aerodynamic i n t e r a c t i o n are t h e main and t a i l r o t o r s , t h e f u s e l a g e , s t o r e s , and t h e empennage assembly. These i n t e r a c t i o n s a r e a much more c h a l l e n g i n g aerodynamic p r e d i c t i o n problem than t h e i s o l a t e d component p r e d i c t i o n s ( r e f . A-1). The m a i n / t a i l r o t o r i n t e r a c t i o n problem i s a subset of t h e complete i n t e r a c t i o n problem. The a b i l i t y t o p r e d i c t t h e e f f e c t of t h e main r o t o r i n t e r a c t i o n s on t h e t a i l r o t o r performance and t h e s i m i l a r e f f e c t of t h e t a i l r o t o r on t h e main r o t o r performance i s c r i t i c a l t o t h e d e s i g n of advanced r o t o r c r a f t systems.

F o r t u n a t e l y , a n a l y s e s which treat t h e i s o l a t e d r o t o r / t a i l / f u s e l a g e components have been developed t o a l e v e l of s o p h i s t i c a t i o n adequate f o r the p r e d i c t i o n of simple component i n t e r a c t i o n s . An example of f i r s t l e v e l coupling of t h e s e types of c o d e s . t o address some a s p e c t s of t h e dynamic and aerodynamic problems i n terms of r o t o r / a i r f r a m e v i b r a t i o n s is described i n r e f e r e n c e A-2. The coupled a n a l y s i s (SIMVIB) i n t h i s r e f e r e n c e c o n s i s t s of s e v e r a l component codes which treat t h e main r o t o r wake i n f l u e n c e ( r e f . A-3), t h e f u s e l a g e a i r f r a m e i n f l u e n c e ( r e f s . A-4 and A-51, and t h e blade dynamics.

The r o t o r wake and f u s e l a g e codes have r e c e n t l y been coupled i n t o an unsteady main r o t o r / f u s e l a g e i n t e r a c t i o n a n a l y s i s f o r t h e p r e d i c t i o n of t h e e f f e c t s of t h e main r o t o r wake on t h e f u s e l a g e body and t h e unsteady body e f f e c t on t h e main r o t o r ( r e f . A-6). A s a l o g i c a l e x t e n s i o n of t h i s coupling process, t h e r o t o r wake a n a l y s i s was modified t o t r e a t a coupled m a i d t a i l r o t o r i n t e r - a c t i o n problem using t h e same l e v e l of coupling methodology. This treatment i s d e s c r i b e d i n t h e following s e c t i o n s along with p r e l i m i n a r y a p p l i c a t i o n s t o hover and forward f l i g h t c o n d i t i o n s t o demonstrate t h e p r e d i c t i v e c a p a b i l i t i e s of t h e method.

Technical Approach Basic Analysis Descriptions.-The P r e s c r i b e d Wake Rotor Inflow Analysis, F389SR, ( r e f . A-3) i s a P r a n d t l l i f t i n g - l i n e l w a k e v o r t e x l a t t i c e method which u s e s a p r e s c r i b e d wake geometry c a l c u l a t e d i n t e r n a l l y i n t h e code o r obtained from an e x t e r n a l source as input t o t h e a n a l y s i s . It can b e run i n two d i f f e r e n t modes of o p e r a t i o n ; t o c a l c u l a t e t h e b l a d e and wake c i r c u l a t i o n and induced v e l o c i t y a t t h e r o t o r blades o r t o c a l c u l a t e t h e induced v e l o c i t y a t a r b i t r a r y f i e l d p o i n t s about t h e r o t o r f o r a s p e c i f i e d wake c i r c u l a t i o n . The a n a l y s i s assumes s t e a d y f l i g h t , p e r i o d i c b l a d e c o n t r o l s and motions, and n e g l e c t s t h e shed wake c i r c u l a t i o n . The e f f e c t o f t h e t r a i l i n g wake c i r c u l a - t i o n is included i n t h e p e r i o d i c l i n e a r i z e d b l a d e c i r c u l a t i o n s o l u t i o n , along with t h e a b i l i t y t o input a d d i t i o n a l sources of inflow a t t h e r o t o r b l a d e s .

This inflow can be obtained from any source, b u t must be p e r i o d i c over t h e r o t o r d i s k . F u r t h e r d e t a i l s of t h e a n a l y s i s and its c a p a b i l i t i e s a r e a v a i l a b l e i n r e f e r e n c e A-3.

The a p p l i c a t i o n of t h i s a n a l y s i s t o t h e m a i n / t a i l r o t o r i n t e r a c t i o n problem on a f i r s t l e v e l b a s i s r e q u i r e s no c a p a b i l i t i e s t o be added t o t h e e x i s t i n g code. The fundamental i n t e r a c t i o n p r e d i c t i o n c a p a b i l i t y a l r e a d y e x i s t s by t h e a p p r o p r i a t e coupling of t h e two d i f f e r e n t modes o f o p e r a t i o n noted above. However, t h e r e a r e some i n h e r e n t l i m i t a t i o n s of t h e a p p l i c a t i o n of t h e a n a l y s i s t o t h e m a i n / t a i l r o t o r problem due t o t h e assumption of a p e r i o d i c r o t o r s o l u t i o n and t h e p r e s c r i b e d wake models a v a i l a b l e . S p e c i f i c a l l y , t h e f a c t t h a t t h e r o t a t i o n a l speeds of t h e main and t a i l r o t o r are not n e c e s s a r i l y i n t e g e r m u l t i p l e s of each o t h e r r e s t r i c t s the s o l u t i o n process. Also t h e l a c k of a p r e s c r i b e d m a i n / t a i l wake i n t e r a c t i o n model may not provide t h e c o r r e c t wake i n f l u e n c e under some c o n d i t i o n s . A s such, t h e following two assumptions f o r t h e i n t e r a c t i o n process of t h i s study a r e made: 1) The wake geometries a r e assumed t o be u n a f f e c t e d by t h e i r mutual i n f l u e n c e .

2 ) When t h e r o t a t i o n a l speeds of t h e two r o t o r s are unequal, t h e y a r e modified f o r f i e l d point c a l c u l a t i o n purposes t o be s e t t o have a r a t i o equal t o t h e n e a r e s t i n t e g e r m u l t i p l e .

Because o f t h e l a r g e number of input d a t a r e q u i r e d t o d e s c r i b e t h e f i e l d p o i n t c o o r d i n a t e s o f t h e b l a d e s of a r o t o r o p e r a t i n g w i t h i n a r e g i o n of i n t e r a c t i o n of another r o t o r , t h e F389SR a n a l y s i s was modified t o i n c o r p o r a t e t h e f e a t u r e of i n t e r n a l l y c a l c u l a t i n g t h e f i e l d p o i n t s of another r o t o r . I n t h e f i e l d p o i n t mode, t h e u s e r s p e c i f i e s t h e hub p o s i t i o n r e l a t i v e t o t h e i n f l u e n c i n g hub, harmonics of f l a p p i n g motion and f l a p p i n g hinge, azimuthal phase a n g l e , number of b l a d e s , b l a d e r a d i u s , inflow s t a t i o n s , and r o t o r t i p w i l l i n t e r n a l l y c a l c u l a t e t h e speed. From t h i s information, t h e a n a l y s i s p o s i t i o n s of t h e influenced r o t o r b l a d e s r e l a t i v e t o t h e i n f l u e n c i n g r o t o r f o r t h e f i e l d p o i n t c a l c u l a t i o n process. The geometry of a main r o t o r and t a i l r o t o r c o n f i g u r a t i o n i s shown i n f i g u r e A - l which u s e s t h e above information t o w a s a l s o modified t o output t h e d e f i n e t h e r e l a t i v e p o s i t i o n s . The a n a l y s i s induced v e l o c i t y , i n harmonic form, a t t h e s e f i e l d p o i n t s a t t h e a p p r o p r i a t e t i m e when t h e b l a d e of t h e influenced r o t o r i s a t t h e f i e l d point l o c a t i o n .

I f t h e influenced r o t o r b l a d e i s r o t a t i n g f a s t e r t h a n t h e i n f l u e n c i n g r o t o r , t h e n t h e induced v e l o c i t i e s r e p r e s e n t an averaging over t h e i n t e g e r m u l t i p l e of t h e period of t h e influenced r o t o r . This process f i l t e r s out sub-harmonic induced i n f l u e n c e . I f t h e influeneed r o t o r b l a d e i s r o t a t i n g slower than t h e i n f l u e n c i n g r o t o r , then t h e induced v e l o c i t i e s r e p r e s e n t a t i m e period e q u a l t o the i n t e g e r m u l t i p l e of t h e period of t h e i n f l u e n c i n g r o t o r . The output of t h e r e s u l t i n g induced v e l o c i t y f i e l d i s i n t h e form o f harmonic c o e f f i c i e n t s c o n s i s t e n t with t h e input requirements of t h e o r i g i n a l code f o r t h e input of e x t e r n a l inflows noted above. These f e a t u r e s allow t h e u s e r t o minimize t h e input of d a t a f o r t h e m a i n / t a i l r o t o r coupling d e s c r i b e d i n t h e next s e c t i o n .

Coupling Procedure.-The coupling of t h e main r o t o r and t a i l r o t o r i s performed by u s i n g t h e e x i s t i n g f e a t u r e s of t h e code with t h e m o d i f i c a t i o n s noted above t o minimize t h e amount of input d a t a t h e t h e u s e r mast provide.

A l l c o u p l i n g i s done u s i n g e x t e r n a l l y d e f i n e d d a t a f i l e s and the a p p r o p r i a t e system commands ( j o b c o n t r o l language, JCL). The sequence of program execu- t i o n i s d e s c r i b e d below along w i t h t h e key d a t a t h a t must be s t o r e d as i n p u t are used, f o r subsequent e x e c u t i o n s f o r t h e code. The following a b b r e v i a t i o n s MR f o r main r o t o r , TR f o r t a i l r o t o r , GC f o r geometric i n f l u e n c e c o e f f i c i e n t s .

1 ) C a l c u l a t e I s o l a t e d MR C i r c u l a t i o n S o l u t i o n Save MR C i r c u l a t i o n S o l u t i o n GC Save MR C i r c u l a t i o n S o l u t i o n 2 ) C a l c u l a t e Induced V e l o c i t y Of MR on TR F i e l d P o i n t s Read MR C i r c u l a t i o n S o l u t i o n Save MR on TR F i e l d Point GC Save Harmonics of MR Induced V e l o c i t y A t TR 3 ) C a l c u l a t e I s o l a t e d TR C i r c u l a t i o n S o l u t i o n Save TR C i r c u l a t i o n S o l u t i o n GC 4 ) C a l c u l a t e TR C i r c u l a t i o n with MR I n f l u e n c e Read Harmonics of MR Induced V e l o c i t y A t TR Read TR C i r c u l a t i o n S o l u t i o n GC Save TR C i r c u l a t i o n S o l u t i o n 5) C a l c u l a t e Induced V e l o c i t y Of TR on MR F i e l d P o i n t s Read TR C i r c u l a t i o n S o l u t i o n Save TR on MR F i e l d Point GC Save Harmonics of TR Induced V e l o c i t y A t MR 6) C a l c u l a t e MR C i r c u l a t i o n w i t h TR I n f l u e n c e Read Harmonics of TR Induced V e l o c i t y A t MR Read MR C i r c u l a t i o n S o l u t i o n GC Save MR C i r c u l a t i o n S o l u t i o n MR on TR F i e l d P o i n t s 7 ) C a l c u l a t e Induced V e l o c i t y Of MR C i r c u l a t i o n S o l u t i o n Read Read MR on TR F i e l d Point GC Save Harmonics o f MR Induced V e l o c i t y A t TR 8) C a l c u l a t e TR C i r c u l a t i o n with MR I n f l u e n c e Read Harmonics of MR Induced V e l o c i t y A t TR Read TR C i r c u l a t i o n S o l u t i o n GC Save TR C i r c u l a t i o n S o l u t i o n 9) Repeat Steps 5 t o 8 u n t i l convergence i s obtained This process r e q u i r e s t h a t t h e u s e r i s f a m i l i a r with t h e i n p u t l o c a t i o n s i n t h e F 3 8 9 S R code which t u r n on ( o r o f f ) t h e a p p r o p r i a t e o p t i o n s needed t o s a v e o r u s e t h e information c a l c u l a t e d d u r i n g previous s t e p s of t h e process.

References A-3 i n c l u d e s a u s e r s manual f o r t h e o r i g i n a l F389SR code and r e f e r e n c e A-7 i n c l u d e s an addendum t o r e f e r e n c e A-3 f o r t h e use of t h e l a t e s t v e r s i o n of F389SR.

P r e l i m i n a r y A p p l i c a t i o n I n o r d e r t o determine i f t h e coupled m a i n / t a i l r o t o r a n a l y s i s i s capable o f p r e d i c t i n g t h e mutual i n t e r f e r e n c e o f t h e two r o t o r s on each o t h e r , some p r e l i m i n a r y a p p l i c a t i o n s were performed i n both hover and forward f l i g h t .

These i n i t i a l a p p l i c a t i o n s were not intended t o v a l i d a t e t h e methodology, but were performed as a demonstration of t h e method.

Rotor Geometries.-The r o t o r geometries were both two bladed, c o n s t a n t chord blade d e s i g n s . The main r o t o r blade had a r a d i u s of 36.11 f e e t , a chord of 2.167 f e e t , and a t w i s t rate o f -10.0 degrees w i t h a c o l l e c t i v e of 10.0 degrees. The t a i l r o t o r blade had a r a d i u s of 6 f e e t , a chord of 1.167 f e e t , and t h e same t w i s t r a t e and c o l l e c t i v e p i t c h as t h e main r o t o r . No b l a d e p i t c h i n g o r f l a p p i n g motions were used. Thus c o n c l u s i o n s drawn from t h e s e p r e l i m i n a r y a p p l i c a t i o n s should be i n t e r p r e t e d with some degree of c a u t i o n i n terms of t h e r e p r e s e n t a t i o n of a c t u a l r o t o r c r a f t o p e r a t i n g geometries.

I n t e r f e r e n c e Measure.-The F389SR a n a l y s i s does not p r e d i c t r o t o r performance, however i t does c a l c u l a t e a r o t o r l i f t c o e f f i c i e n t based on t h e bound c i r c u l a t i o n . This c a l c u l a t i o n was o r i g i n a l l y intended as an informal check t o compare with o t h e r p r e d i c t i o n codes and does not account f o r t h e t r u e o r i e n t a t i o n of t h e b l a d e o r t h e inflow angle. This r o t o r l i f t c o e f f i c i e n t normalized by t h e i s o l a t e d r o t o r l i f t c o e f f i c i e n t was used i n t h i s study as t h e measure of t h e i n f l u e n c e of t h e i n t e r a c t i n g r o t o r s .

Hover Application.-The firs,t set of c a s e s run were focused on a s i n g l e hover c o n d i t i o n with using v a r i o u s t a i l r o t o r hub p o s i t i o n s r e l a t i v e t o t h e main r o t o r . The t a i l r o t o r w a s p o s i t i o n e d at a r i g h t a n g l e t o t h e main r o t o r b l a d e f o r a l l b u t t h e l a s t c a s e where i t w a s set a t 70.0 degrees. The t a i l r o t o r hub p o s i t i o n was v a r i e d i n both t h e v e r t i c a l and l o n g i t u d i n a l p o s i t i o n r e l a t i v e t o t h e main r o t o r . For t h e i n i t i a l seven c a s e s , t h e main and t a i l r o t o r s were run using a azimuth increments of 15 degrees. The main r o t o r used n i n e inflow s t a t i o n s and t h e t a i l r o t o r used f o u r . For t h e second set of hover c o n d i t i o n s ( c a s e s 8-11), t h e t a i l r o t o r used n i n e inflow s t a t i o n s . The r o t o r inflow s t a t i o n s used are shown i n Table A-I. The h o r i z o n t a l and v e r t i c a l p o s i t i o n s are shown g r a p h i c a l l y in f i g u r e A-2 f o r t h e hover c a s e s .

These p o s i t i o n s are l i s t e d i n Table A - I I along w i t h t h e normalized r o t o r l i f t c o e f f i c i e n t . These r e s u l t s are d i s p l a y e d g r a p h i c a l l y i n f i g u r e A-3 as a f u n c t i o n o f l o n g i t u d i n a l p o s i t i o n from t h e edge o f t h e main r o t o r d i s k . The key f e a t u r e s t o n o t e from t h e s e p r e d i c t i o n s are t h a t the i n t e r f e r e n c e decays as t h e r o t o r s are s e p a r a t e d . The u s e of a f i n e r inflow s t a t i o n d i s t r i b u t i o n changes t h e normalized v a l u e s s l i g h t l y ; however, t h e a b s o l u t e v a l u e of t h e l i f t changed by about 15 p e r c e n t . The c a n t i n g of t h e t a i l r o t o r had a measurable e f f e c t on t h e i n t e r f e r e n c e along w i t h changing t h e v e r t i c a l p o s i t i o n . These r e s u l t s a r e not unreasonable. The e f f e c t o f t h e main r o t o r on t h e t a i l r o t o r performance i n hover i s documented i n a r e c e n t r e p o r t ( r e f .

A-8) and show s i m i l a r l e v e l s of change i n t e r m s of performance, although t h e r e s u l t s r e p o r t e d i n t h a t r e f e r e n c e a l s o include t h e e f f e c t of t h e f u s e l a g e .

The e f f e c t of t h e t a i l r o t o r on t h e m a i n , r o t o r w a s found t o be i n s i g n i f - i c a n t f o r every hover c o n d i t i o n s t u d i e d . This r e s u l t i s not unexpected because t h e c u r r e n t model n e g l e c t s wake d i s t o r t i o n and it is believed t h e t h e major e f f e c t of t h e t a i l r o t o r on t h e main r o t o r i s caused by t h e i n g e s t i o n of t h e t a i l r o t o r wake i n t o t h e wake of t h e main r o t o r , i n t h e v i c i n i t y of t h e main r o t o r d i s k .

Forward Flight.-The a n a l y s i s was a l s o run f o r four forward f l i g h t c o n d i t i o n s r e p r e s e n t i n g a v a r i a t i o n of advance r a t i o . The t a i l p o s i t i o n w a s h e l d f i x e d f o r t h e s e c o n d i t i o n s and t h e r e s u l t s a r e t a b u l a t e d i n Table A-111.

The n i n e inflow s t a t i o n s noted above were used f o r both f o t o r s and t h e same c o l l e c t i v e p i t c h w a s used. The r o t o r s h a f t angle was held fixed a t 0.0 degrees f o r a l l c o n d i t i o n s . Again, conclusions drawn from t h e s e preliminary a p p l i c a t i o n s should be i n t e r p r e t e d with some degree of c a u t i o n i n terms of t h e r e p r e s e n t a t i o n of a c t u a l r o t o r c r a f t o p e r a t i n g geometries and c o n d i t i o n s .

The r e s u l t s are shown i n g r a p h i c a l form i n f i g u r e A-4, p l o t t e d a s a f u n c t i o n of r o t o r advance r a t i o . The corresponding hover p r e d i c t i o n i s included. I n f i g u r e A-5, t h e main r o t o r wake boundary is d e p i c t e d r e l a t i v e t o t h e t a i l r o t o r d i s k . The r e s u l t s i n d i c a t e t h a t t h e main r o t o r wake i n f l u e n c e i n c r e a s e s t h e t a i l r o t o r l i f t w i t h i n c r e a s i n g advance r a t i o . It i s obvious from f i g u r e A-5, t h a t as t h e advance r a t i o i n c r e a s e s , t h e t a i l r o t o r d i s k i s i n c r e a s i n g l y immersed i n more of t h e main r o t o r wake. Again, no s i g n i f i c a n t e f f e c t of t h e t a i l r o t o r presence on t h e main r o t o r l i f t was p r e d i c t e d .

Discussion And Recommendations The u s e of t h e P r e s c r i b e d Wake Rotor Inflow Analysis (F389SR) has been shown t o demonstrate t h a t t h e i n f l u e n c e of t h e main r o t o r wake on the t a i l r o t o r can be p r e d i c t e d . The degree of c o r r e l a t i o n w i t h t e s t d a t a is u n c e r t a i n due t o t h e p r e l i m i n a r y n a t u r e of t h i s study. In hover, t h e e f f e c t of t h e main r o t o r on t h e t a i l r o t o r is of t h e c o r r e c t l e v e l o f change, based on some test d a t a which i n c l u d e s f u s e l a g e i n f l u e n c e . It was a l s o determined t h a t the p r e d i c t e d i n f l u e n c e of t h e t a i l r o t o r on t h e main r o t o r l i f t u s i n g t h e c u r r e n t coupled a n a l y s i s i s i n s i g n i f i c a n t and t h a t t h i s i s b e l i e v e d t o be due t o t h e assumption of n o n - i n t e r a c t i n g wake geometries.

The r e s u l t s of t h i s p r e l i m i n a r y study i n d i c a t e t h a t t h e method has t h e p o t e n t i a l t o p r e d i c t t h e m a i n / t a i l r o t o r i n t e r a c t i o n and t h a t the wake modeling must be improved f o r t h e a c c u r a t e t a i l r o t o r e f f e c t on t h e main r o t o r are recommended; (1) t h e coupled m a i n / t a i l i n hover. Two c o u r s e s of a c t i o n r o t o r a n a l y s i s be a p p l i e d t o r o t o r designs f o r which m a i d t a i l r o t o r i n t e r - action data exists without the presence of a fuselage for correlation purposes and to determine the sensitivity of the method to the number of inflow stations and the wake azimuth (time step) increment and (2), develop main/tail rotor wake interaction models, either (or both) based on experimentally obtained geometries or by prediction methods such as free wake methods.

References

A-1. Sheridan, P.F., and R.P. Smith, Interactional Aerodynamics - A New

Challenge to Helicopter Technology, Journal Of the American Helicopter Society, Volume 25, No. 1 January 1980.

A-2. Sopher, R., R.E. Studwell, S. Gassarino, and S.B.R. Kottapalli,Coupled Rotor/Airframe Vibration Analysis, NASA CR-3582, Nov. 1982.

A-3. Egolf, T. A,, and A. J. Landgrebe, A Prescribed Wake Rotor Inflow and Flow Field Prediction Analysis - User's Manual and Technical Approach, NASA CR-165894, June 1982.

A-4. Sheehy, T. W., A Simplified Approach to Generalized Helicopter Config- uration Modeling and the Predictions of Fuselage Surface Pressures.

Paper presented at the National Symposium on Helicopter Aerodynamic Efficiency, American Helicopter Society - Northeast Region, March 1975.

A-5. Sheehy T. W., A Method For Predicting Helicopter Hub Drag., USAAMRDL-TR- 75-45, 1975.

A-6. Egolf, T. A., and P.F. Lorber, An Unsteady Rotor/Fuselage Interaction Method, Proceedings of the National Specialists' Meeting on Aerodynamics and Aeroacoustics, Arlington Texas, Feb. 25-27, 1987.

A-7. Lorber, P. F . : Program User's Manual for an Unsteady Helicopter Rotor- Fuselage Aerodynamic Analysis. NASA CR-181701, 1988.

A-8. Balch ,D. T., Experimental Study Of Main Rotor/Tail Rotor/Airframe Interaction In Hover, Presented at the 39th Annual Forum of the American Helicopter Society, St. Louis, Missouri, May, 1983.

Table A-I - Rotor Inflow Stations

Station Number Main Rotor Tail Rotor .329 .350 .329 L410 .600 .410 .525 ,800 .525 .650 * 900 .650 .750 ,750 .850 .850 .925 .925 ,965 .965 .990 .990

Table A-11 - Tail Rotor Results i n Hover

Case Vertical Longitudinal Vertical Normalized Number Position Position Tail Angle Lift Coef.

(ft) (ft) (deg) 1 0.0 42.2 90.0 .907 0.0 42.5 90.0 .911 44.5 90.0 ,927 3 0.0 90.0 .939 4 0.0 46.5 48.5 90.0 ,948 5 0.0 .933 6 -6.0 42.2 90.0 .923 7 +6.0 42.2 90.0 .928 8 +6.0 42.2 90.0 .913 9 0.0 42.2 90.0 10 0.0 48.5 90.0 .952 11 0.0 42.2 70.0 .921 in Forward Flight

Table A-111 - Tail Rotor Results

Wake Normalized Case Advance Vertical Longitudinal Vertical Skew Angle Lift Coef.

Number Ratio Position Position Tail Angle (ft) (ft) (deg) (deg) 43.5 1.000 12 0.06 0.0 48.5 90.0 25.4 1.049 13 0.12 0.0 48.5 90.0 90.0 13.4 1.049 1 4 0.24 0.0 48.5 9.0 1.059 15 0.36 0.0 48.5 90.0 Z INFLUENCING ROTOR 8 , ROTATION OF xT ABOUT x AXIS eZ ROTATION OF ~$8,) ABOUT z AXIS X h TRANSLATION OF X T (ex, BZ) IN X Figure A-1. Relative Geometry of Main Rotor-Tail Rotor Configuration TAIL ROTOR DISK Figure A-2. Relative Position of Tail Rotor Disk to Main Rotor Disk 0 H = 0. 90' 4 INFLOW STATIONS 0 H = 0, 9 0 ' 9 INFLOW STATIONS A H = 0, 70' 9 INFLOW STATIONS

0 H = + 6.0, 9 0 ' . 4

ft H = +6.0, 90°, 9 0.95

v H = -6.0, 9 0 ' . 4

MAIN ROTOR DISK PLANE 0.90 LONGITUDINAL POSITION OF TAIL ROTOR Figure A-3. Effect of Main Rotor on Tail Rotor Lift In Hover 3 H = 0, LIRT = 0.015, 90° 9 INFLOW STATIONS

1 .o

i

I

0.9 1 I I

0 . 0.1 0.2 0.3 0.4 0.5 ROTOR ADVANCE RATIO, I.( Figure A-4. Effect of Main Rotor on Tail Rotor Lifting in Forward Flight X W -4

a

& h & c , a Q

a

c rl -4 m H Q, X I a Lc U

a

c c ,

a

APPENDIX B TWO-DIMENSXONW HODELLING OF VORTEX-INDUCED UNSTEADY PRESSURES This appendix will present several analytical model problems that illustrate various aspects of the unsteady interaction between a vortex and a surface, in order to demonstrate the importance of various terms that are present in the calculation of rotor-fuselage interactions. Two-dimensional, incompressible potential flow aerodynamics are used for the analysis.

Fundamentals The first series of problems are concerned with a constant strength vortex that moves parallel to a flat plate, as shown in this sketch:

-I + x

The velocity potential associated with the vortex is given by:

r t a n - ’ ( Y-Yv ]

+(X,Y) = -

2n x-x The Cartesian velocity components are:

a+ r 4Y-h)

v = - - -

- X ax 2n (x-Vt)2 +(y-h) a+ r (x-Vt)

v = - - -

- 2 2 aY 2n (x-Vt) +(y-h) The time derivative of the potential is:

a+ r v (Y-h)

- - -

- at 2n (x-Vt)2 + ( y - h ) I The unsteady Bernoulli equation for the pressure coefficient is: P - POD U2 2 a + = I - - - - - CP(X,Y,t) = 2 2

u,2 at

0 . 5 p U , u m

Wake - Fuselage Interaction A simple model for a helicopter wake tip vortex that is convected past a section of a fuselage includes a vortex, a flat plate, and an image vortex to satisfy the surface boundary condition:

- > urn - rC ->v

f h The combined velocity potential is therefore:

+(x,y,t) = urnx + - r t a n - ' [ -1 - - t a n - ' [ -1

Y-h r Y+h

2n x-v t 2n x-v t A t the surface (y=O)'the pressure coefficient is:

2 r 2hV

Cp(x,O,t) = 1 - 7 1 I urn + - r

2 1 2 - $ [--

U r n 2n (x-Vt)2 + h 2n (x-Vt)2 + h2 The peak pressure (at x=Vt) is: CpPeak 2r For the tip vortex - fuselage interactions used in this report, typical values of the constants are:

urn = 100 ft4sec (+0.15)

r = 400 ft /sec

h = 1 ft

v = urn

Using these values the peak Cp is about -4.2 if the effect of the a+/at This implies that term is ignored, and about -1.6 if all terms are included.

the &#/at term is quite important, and that it acts to reduce the intensity of the wake-fuselage interaction.

Blade - Fuselage Interaction The blade-fuselage interaction may be modelled in a similar fashion, with the freestream velocity vector now perpendicular to the vortex motion velocity The velocity vector (in the sketch, the freestream points up out of the p a g e ) .

potential is therefore:

r r

2K x-v t 2K x-v t The surface pressure coefficient is: 1 2h 2

Cp(x,O,t) = 1 - -

2 2

u m 2 [ '' + [ : r [ ( x - V t ) 2 + h 2 ) 2 1 - (x-Vt) +h

The peak value (at x=Vt) is: If V is set equal to a typical tip speed (700 ft/sec), and with the other parameters defined as above, the steady terms contribute a Cp of -1.6, while the While three-dimensional effects are a+/at term contributes a Cp of +17.8.

likely to reduce these values, this model problem has clearly demonstrated both the importance of the a+/at term in calculating close blade-fuselage interactions, and the dominance of the blade-fuselage interaction, when the tip passes close to the surface.

geometry is such that the blade Time-Dependent Vortex Strength Since the bound circulation of the rotor blade varies with azimuth, the effect of this variation on the a+/at must be examined. The velocity potential associated with the vortex may be expressed as:

a+ v (Y-h) 1 dT

-

+ - - t a n - ' [

1 2K dt

at (x-Vt)2 + (y-h) For the typical qelicopter case at 1 . 1 = 0.15, as defined above, dr/dt is approximately 1300 ft /sec/sec at the position of maximum interaction near the fuselage nose (Jr-0), so that the increment that would be added to the surface pressure coefficient is: 1 d r -h

Acp(x=Vt,y=O) = - - -

' C U W dt (1300 ft2/sec2) ( n / 2 ) ACp(x=Vt,y=O) = - K( 115 ft/sec) = 0.05 The contribution of this term is obviously much smaller that the contributions of the constant vortex strength a+/at term or the steady-state term. Therefore i t is neglected in the current analysis.

Time - Dependent Source Strength The final example will study the remaining contribution to a+/at for the rotor-fuselage interaction: the unsteady variation in the strength of the source panels that represent the fuselage.

(The source strength must be time-variant to maintain the flow tangency condition on the surface, given the unsteady velocities induced by the rotor and wake).

The model used in this Appendix will be a simple point source. In a uniform flow, a point source represents a semi-infinite half-body:

s

U W The velocity potential is: The velocity components and the time derivative are:

a+ R ( t )Umx

vx = - = u r n +

ax x + Y The surface velocity is: 2x + R 2 + V 2 = U r n 2 + U : R vx Y x + Y The surface pressure coefficient evaluated directly above the source point is: dR 2

CP(0,nR/2) = 1 - (1 + ( 2 / n ) 2 ) - - - In (nR/2)

dt Uo, For the ellipsoid used in this report, a typical value of R is 4 ft, and with a maximum change in source strength of 5% over a rotor half-period of 0.125 see, the pressure coefficient becomes:

Cp(0,nR/2) ,c 1 - (1.4) - (.2ft/.125sec) 2/(115ft/sec) ln(6.3)

c - (0.4) - (0.05) For this example the contribution of &#/at is relatively small in comparison with the steady source contribution, and quite small in comparison with the steady and unsteady pressures induced by the wake and rotor. Therefore the neglect of the unsteady source tyerms in the current analysis appears reasonable.

Report Documentation Page % t o w cpcrarcs aw 5rxe m c w a t r y 2. Government Accession No. 3. Recipient's Catalog No.

1. ReDOrt No.

NASA CR-4178 4. Title and Subtitle 5. Report Date September 1988 An Unsteady Helicopter Rotor-Fuselage Interaction Analysis 6. Performing Organization Code 8. Performing Organization Report No.

7. Authork)

- 6977- 1 5

Peter F. Lorber and T. Alan Egolf 10. Work Unit No.

- 505-61-51

9. Performing Organization Name and Address United Technologies Research Center 11. Contract or Grant No.

400 Main St East Hartford, CT 06108 NASI- 1 7 4 6 9

1 13. Tvoe of Reoort and Period Covered

- ,.

12. Sponsoring Agency Name and Address Contractor Report National Aeronautics and Space Administration 14. Sponsoring Agency Code Langley Research Center 23665-5225 Hampton, VA 15. Supplementary Notes Langley Technical Monitor: John C. Wilson Final Report 16. Abstract A computational method has been developed t o t r e a t unsteady aerodynamic i n t e r a c t i o n s between 8 A n e x i s t i n g l i f t i n g helicopter r o t o r , wake, and fuselage and between the main and t a i l rotors.

line-prescribed wake rotor analysis and a source panel fuselage analysis were coupled and modified A prescribed displacement technique t o predict unsteady fuselage surface pressures and airloads.

is used t o position t h e rotor wake about t h e fuselage. Either a r i g i d blade or an a e r o e l a s t i c S e n s i t i v i t y s t u d i e s were blade analysis may be used t o e s t a b l i s h rotor operating conditions.

performed t o determine t h e influence o f t h e wake and fuselage geometry on t h e computation. R e s u l t s a r e presented t h a t describe t h e induced v e l o c i t i e s , pressures, and a i r l o a d s on the fuselage and on t h e rotor. The a b i l i t y t o t r e a t a r b i t r a r y geometries is demonstrated using a simulated helicopter fuselage. I n i t i a l computations were made t o simulate an experimental atudy performed a t the Georgia I n s t i t u t e of Technology. The computational r e s u l t s are compared with fuselage surface pressure measurements a t s e v e r a l locations. No experimental d a t a w a s available t o v a l i d a t e t h e A main r o t o r - t a i l primary product o f t h e analysis: the vibratory a i r l o a d s on t h e e n t i r e fuselage.

rotor i n t e r a c t i o n analysis is also described, along with some preliminary hover and forward f l i g h t results .

17. K e y Words Zuggestsd by Authods)) 18. Distribution Statement Helicopter Interactional Aerodynamics

Aerodynamics Computational Aerodynamics Unclassified - Unlimited

Unsteady F l o w Subject Category 01 19. Security Classif. (of this report) 20. Security Classif. (of this page) 21. No. of pages 22. Price 128 A0 7 Unclassified Unclassified NASA FORM 1626 OCT 86 NASA-Langley, 19 For sale by the National Technical Information Service, Springfield, Virginia 22161-2171