Simple Momentum Theory

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University of Massachuses - Amherst

ScholarWorks@UMass Amherst

Wind Energy Center Reports UMass Wind Energy Center

1976

Discussion Of Momentum Teory For WindmillsForrest S. Stoddard

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Stoddard, Forrest S., "Discussion Of Momentum Teory For Windmills" (1976). Wind Energy Center Reports. Paper 20.hp://scholarworks.umass.edu/windenergy_report/20
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U UZSrrV OF MASSACHUSETE/AMHUZSTENERGY ALTERNATIVES PROGRAM

UNIVERSITY OF MASSACHUSETTSIAMHERSTENERGY ALTERNATIVES PROGRAM

DISCUSSION OF MOMENTUM THEORY FOR WINDMILLS

byFo rr es t S . S toddard

U.Mass. Wind FurnaceEnergy A1 t e r n a t i ves ProgramU n i v e r s i t y o f M a s s a c h u s e t t sAmherst Massachusetts 01002

TR/76/Appendix V


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DISCUSSION OF MOMEr4TUM THEORY FOR WINDM ILLS

Molllenturn th e o r y h a s b ee n e x t e n s i v e l y u se d t o p r e d i c t t h e r e l a t i v e p e r -f or ma n ce o f 1i t i n g p r o p e l l e r s a n d . o t o rs . ' 2 y 3 y 4 ) The p e r fo r m a n c e e q u a t i o n sa r e a n a l y t i c a l l y a nd c o n c e p t u a l l y s im p le ; t h i s l e ad s t o q u i c k i d e a l p r e d i c t i o n sa nd c om p ar is on s. O f t e n a p h y s i c a l f e e l i n g o r u n d e r s t a n d in g o f t h e sy st em c anbe g a in e d by e x e r c i s i n g t h i s s i n i p le a p p ro a ch f i r s t , b e f o r e m o re c om ple x b l a d ee le m en t an d s t r i p t h e o r i e s a r e u se d.

T h i s d i s c u s s io n co nc er ns t h e r a m i f i c a t i o n s and i n t e r p r e t a t i o n o f t h emomentum t h e o r y e x p r es s io n s f o r a t h r u s t i n g w i n d m i l l i n th e l i g h t o f o b se rv edw i n d m i l l b e h a v i o r . It s h ou ld be k e p t i n m in d t h a t t h e ( i d e a l i z e d ) a n a l y t i c a lf o r m u l a t i o n d ep en ds o n t h e f o l l o w i n g s t r i c t a ss um p ti on s :

a ) d e f i n i t e s t r e a m l i n e s e x i s t i n t h e f l o w f i e l d ;b ) n o f r i c t i o n a l l os s e s a r e p r e se n t ;c ) t h e i n du ce d v e l o c i t y i m pa r te d t o t h e f r e e s tr ea m i s c o n s ta n t o v e r t h e

a re a o f t h e i d e a l i z e d r o t o r , o r a c tu a t o r .The f o l l o w i n g w e l l- k n o w n e x p r e s s i o n s a r e t h u s d e v e lo p e d f o r t h e a c t u a t o r shown:

T = t h r u s t = 2p A [Vo-v ]v ( 1P pow er = T ( V o - V ) = 211 A [ v 0 - v l v

I n n on - d im e n s io n a l f o rm :t h r u s t Tc o e f f i c i e n t =T 1 2pAV0 2power

p c o e f f i c i e n t = P 31 2 d V 0and a x i a la = i n t e r f e r e n c e =f a c t o r v o

The f l o w f i e l d fo r t h e n orm al w i n d m i l l s t a t e i s :

v p o s i t i v e i nt h e d i r e c t i o nshown


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where :A c t u a t o r _ V o = f r e e s t r e a m v e l o c i t y

D i s c V = f a r wake v e l o c i t yuv = i n d u c e d v e l o c i t yT = t h r u s t dow n w i n d )P = power ou t o f sys tem)

FIGURE 1T h i s i s a l s o c a l l e d th e w i nd m i l l b ra k e s t a t e f o r r o t o r s s in c e th e t h r u s t i s i nt h e same d i r e c t i o n as t h e f r e e stre am ; t hu s, t h i s s t a t e r e p re s e n ts a r o t o r i na u t o r o t a t i o n o r v e r t i c a l d es ce nt . I n w i n d m i l l t e r m i n o l o g y, as shown a bove ,t h r u s t c o e f f i c i e n t , CT, a n d p o w e r c o e f f i c i e n t , Cp, a r e p o s i t i v e , i n d i c a t i n gt h r u s t o r d r a g ) i n t h e d ownwind d i r e c t i o n an d power o u t o f t h e s ys te m.

As shown b y W i l s o n L is sa man , R e fe re n c e 1 , t h e r e a re two o t h e r imp o r t a n tf l o w s t a t e s d e t er m in e d by t h e v a l u e o f i nd u ce d v e l o c i t y , v, w r i t t e n n on -d i n le n s io n a ll y a s a x i a l i n t e r f e r e n c e f a c t o r , a = v/Vo:

v = O

Norma l Work ing S ta teWindmi 11 Brake S ta te )- .:


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F o r a = 1 / 2, t h e de v el o pe d wake v e l o c i t y i s :f a r

V = wake = V o l 2 a ) = 0v e l o c i t yT h i s c o n d i t i o n r e p r e se n t s a p o i n t a t w hi ch s t re a m l in e s no l o n g e r e x i s t .

H ence, t h e momentum t h e o r y a s s u m p t i o n ha s be en v i o l a t e d , a nd t h i s s t a t e c a n n o te x i s t a s a momentum t h e o r y s o l u t i o n .

W r i t i n g CT and Cp i n t erm s o f a:

W i l so n L i ss a m an g et t h e f o l l o w i n g p l o t R e fe r en c e 1 ) :

C~

I

1 .5a = v/V

Momentum theoryd oe s n o t w or k

I

FIGURE 3


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F o r a -1 .0 , t h e f a r wake v e l o c i t y , . i s s t i l l n o t d e f i n ed by 11ionientu111h e o r y ;b u t t h i s s t a t e can a l s o be seen to be t he p r o p e l l e r a c t i n g a s a b ra k e . T h a t i spower i s b e i n g added t o t h e f l o w t o c r e a t e h i g h CT o r h i g h t h r u s t downw ind.Th i s wou ld be t h e ca se o f r e v e r s i n g p r o p e l l e r t h r u s t o n l a n d i n g .

T he se f l o w s t a t e s r e p r e s e n t a s e r i e s o f g r a du a l c ha ng es w h ic h o cc u r ont h e r o t o r as i n du c ed v e l o c i t y i s c hanged u n i f o r m l y . U n f o r t u n a t e l y , b ec au se a

>d e f i n i t e s l i p s t r e a m do es n o t e x i s t f o r a -1 12 , momentum t h e o r y c a n n o t be u se d t op r e d i c t t h e r o t o r p er fo rm a nc e i n t h i s r e g i o n . However, f r o m h e l i c o p t e r a u to -r o t a t i v e d a ta , e m p i r i c a l c u r v e s h av e b ee n dra wn, a nd t h e f l o w s t a t e s h av e b ee nd o c u me n te d . 2 9 6 9 7 ) E x pa n di ng t h e c u r v e f r o m t h e p r e c e d i n g p age, t h e r o t o rb e h a v i o r c an be d e s c r ib e d i n m ore d e t a i 1 :

Windmil 1 B rake S t a t e

Z e r o S l i p

P ro pe l l e r S t a t e Turbu len t Wake S ta te

FIGUR 4


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T h e e l l ~ p i r i c a ls t a t e b ou n da r i es a r e fo un d f r o m t y p i c a l h e l i c o p t e r d e sc e nta u t o r o t a t i v e ) p e r f o r l l l a n c e d t p l o t t e d a s f o l o w s . The a b s c i s s a i s no n-d im en -

s i o n a l r a t e o f c l im b , To, and t h e o r d i n a t e i s n o n -d i m e ns i on a l i n d uc e d v e l o c i t y .v, as de f i n ed be low:w i t h vv = n 7 7 J r ; = J T / L ~ A[N ote : H ere t h e s i g n o f t h e f r e e s tr ea m v e l o c i t y , Vo i s o p p o s i t e t o t h a t used

f o r w i ndm i 11 t h e o r y ]vD a t a f r o m I

[Momentum \l;i \ , , \ + - 5t h e o r y d o e snot - - - - - -

V o r t e x R i n g S t a t e R o t o r o r P r o p e l l e r S t a t e. .

FIGURE 5

,i n d m i l l B r a ke S t a t e h e l i c o p t e r a s c e n d i n g )- J ~ 1 0 1 2T u r b u l e n t Wake S t a t e v o


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The niomentuni equations (shown h e r e i n s o l d 1 n e s ) f o r t h e he1 c o p t e rp e r f o r ~ i i a n c ecase a re : ( 2 8 )

P r o p e l l e r o r R o t or S t a t e

CJindmi 11 Bra ke S ta te :

t i s a l s o s een t h a t any p o i n t o n t h e c u rv e r e p re s e n ts a v a l u e o f a :

Thus, t h e T u r b u l e n t Wake S t a t e l i m i t i n g c as e o c c ur s a t :v 1 . 0 , ( - ) v o = 2 , = 1 / 2

And t h e V o r t e x R i n g S t a t e :.( - ) \ 1.73, v = 1.3 , a -7 5 (Ref. 7 )V = 1 .75, a 1 .0 (Re f. 6 )

The a c t u a l v a l u e s o f t h r u s t c a n n o t be f o un d fr o ni F i g u r e 5, s i n c e t h eo r i g i n a l d a t a w ere l o s t i n t h e n o n -d i m e n s i o n a l i z i n g p r oc e ss . How ever, t h ee x i s t i n g t e s t d a ta c o u l d b e used t o g e ne ra te T and p v s v/V o e m p i r i c a l p l o t st o a pp ea r i n F i g u r e 4 .

The t e s t d a ta r e f e r r e d t o ap pea r i n two d i s t i n c t gr ou pin gs ; one i s a tVo = -1.75 and t h e o t h e r i s j u s t b e lo w h o ve r ( j u s t d e sc e n di n g) . T h e c l u s t e ra ro u nd h ov er i n d i c a t e s t h e p a r t- p ow e r d e s ce n t o f ( r o t a r y w i n g) l g h t v e h i c l es ;t h e l e f t c l u s t e r i s f r o m f r e e - w he e li n g r o t o r s ( i . . , p = 0 n eg le c t i n g p r o f i l ed r a g l o s s e s ) , a nd o c c u r s a t v/V o 1 .0 . T h i s v e r i f i e s t h e m omentum t h e o r yp r e d i c t i o n t h a t p = 0 a t v/Vo = 1 . 0 ( s e e F i g u r e 3 ) .


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I n t h e T u r b u l e n t Wake S t a t e , t h e s l i p s t r e a m e x pa n si on i s v e r y l a r g e , andc o n s i d e ra b l e t u rb u le n c e and r e c i r c u l a t i o n e x i s t R e fe re nc e 2 ) . I n f a c t , t h er o t o r a c t s as a l a r g e d i s c p e r p e n d i cu l a r t o t h e f l o w . Thus, t h e t h r u s tc o e f f i c i e n t i s synonymous w i t h t h e d ra g c o e f f i c i e n t o f a s o l i d d i s c :C, 1.5 - 2 0 As a r e s u l t we w ou ld e x p e c t t h e CT t o g o up s h a r p l y a sa = v/V s yn on ym ou s w i t h p o r o s i t y o f t h e d i s c ) i n c r e a s e s . H en ce , we w o u lde x p e c t h i g h e r v a lu e s o f C T t h a n t h o s e p r e d i c t e d b y m o m e n t u m t h e o r y .

The V o r t e x R i n g S t a t e b o un da ry i s n o t w e l l e s t a b l i s h e d , b u t ha s beeno b s e r v e d f o r a num ber o f d i f f e r e n t NACA r o t o r s s e e R e f e r e n c e 6 ) a nd e a r l e rt e s t s s e e R e fe re n ce 7 ) . T h i s b ou nd ar y a l s o m ar ks t h e c ha ng e fr o m p o s i t i v et o n e g a t i v e power; t h a t i s , t h e v o r t e x r i n g s t a t e r ep re s en ts h e l i c o p t e r r o t o r si n pow ered a u t o r o t a t i o n f o r w h ic h s i g n i f i c a n t t e s t d ata e x i s t ) as w e l l asr e v e r s e t h r u s t i n g p r op e l 1e r s t h e same f l o w f i e l d ) . Momentum theory cannot beb e l i e v e d i n t h e r an ge , 1 /2 < a 1 .0 , b u t t h e po wer e q u a t i o n E q u a t i o n 5 doesp r e d i c t t h e change i n Cp s e e F i g u r e 3 ) .


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References

1. Wilson &Lissaman Applied Aerodynamics of Wind Power Machines, OregonState University, July 1974.2. Gessow Myers, Aerodynamics of the Helicopter, Frederick Ungar Publishing,1952.3. Prandtl Tietjens, Applied Hydro Aeromechanics, Dover Publications, 1934.4. Glauert, Elements of Aerofoil Airscrew Theory, Cambridge University Press,1959.5. Glauert, Windmills and Fans, Aerodynamic Theory, Vol IV Durand, ed.,Dover Pub1 ications, 1963, pp. 324-332.6. Gessow, Flight Investigation of Effects of Rotor Blade Twist on HelicopterPerformance in the High Speed and Vertical-Autorotative Decsent Conditions,NACA T 1666 1948.7. Lock, Bateman, Townend, An Extension of the Vortex Theory of Airscrewswith Applications to Airscrews of Small Pitch and Includivg ExperimentalResults, British Aeronautical Research Comm. Reports Memoranda, No. 10141924.8. Ham, V/STOL Vehicle Aerodynamics and Dynamics, Course 16.50 class notes,MIT, 1963.


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UNIVERSITY OF MASSACHUSETTS AMHERSTENERGY ALTERNATIVES PROGRAM

UNIVERSITY OF MASSACHUSETTS/AMHERSTENERGY ALTERNATIVES PROGRAM

AN APPROACH TO PRELIMINARY SYSTEMS OPTIMIZATIONOF THE NEW ENGLAND WIND FURNACE

F o r r e s t S. S t o d d a r d

U.Mass. Wind Fu rn ac eE n er g y A l t e r n a t i v e s P ro gr amU n i v e r s i t y o f M a s s a c h u s e t t sA m h er s t M a s s a c h u s e t t s 0 1 0 02

T R/76 /3A p p e n d i x


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AN APPROACH TO-,PR_F-~_T_M ~lA~YvS_Y;T_E_M_S-O_PTJfl ZA_TT_ION- _O _ T 1.r r\rLw. JNGLAND. dI gn 11 N c r1. Genera 1 Appro ach

T he W ind F u rn a c e s y stem i s r e p re s e n te d i n F ig u re 1 . The d ia g ra mi l l u s t r a t e s t h e t h r e e ind epe nd en t c o n t r o l v a r i a b l e s : p i t c h ( ) i e l de x c i t a t i o n ( Pe Xc ), a nd l o a d r e s i s t a n c e ( R L ). T h a t is, f o r e ach s e t o fi n p u t c o n d i t i o n s (Vo,B,,Pex, R ) t h e r e w i l l be a n o u t p u t e ne rg y , 1 ; ~ ~ .The o p t i m i z a t i o n t as k c o n s i s t s o f f i n d i n g t h e r i g h t c om b in at io ns of t he sev a r i a b l e s w h ic h y i e l d t h e h i g h e s t o u t p u t f o r g i v e n w in d speed, Vo. L a t e r ,t h e a n a l y s i s c an b e r e f i n e d t o g i v e dyn am ic a nd s t a b i l i t y im prov em en tsg i v e n V o ( t ) ( s u b j e c t t o t h e q u a s i - s t a t i c a ss um p ti on s used i n d e r i v i n gt h e a n a l y t i c a l mo de ls f o r t h e p r o p e l l e r and g e n e r a t o r) . T r a n s i e n t b e h a v i o ro f t h e s y st em may be a t t e m p te d f o r c e r t a i n e q u i l i b r i u m c a se s, a s i s donew i t h s t a b i l i t y d e r i v a t i v e s f o r f l i g h t systems.

P r e l i m i n a r y , o r " s t a t i c , " s ys te ms o p t i m i z a t i o n u se s a n a l y t i c a n d/ ors e m i -e mp i r i c a l p e rf o rma n c e c h a r a c te r i s t i c s o f t h e tw o s ub sy stems , a n ds i m p l y m atch es o p e r a t i n g p o i n t s t o d e t er m i ne e q u i l i b r i u m c o n d i t i o n s .P a r a m e t ri c t or q ue - sp e e d p l o t s w i l l be u se d i n t h i s a n a l y s i s ; hence t h ei n t e r p r e t a t i o n of " ma tc hi ng t h e c h a r a c t e r i s t i c s , " i s t o eq ua te t h e o u tp u tt o r qu e o f t h e m echanical ( w i n d m i l l ) s h af t, t o t h e i n p u t t o r q u e o f t h e g e n e ra t or .

T he p a ra m e t r i c p e r fo rma nc e o f t h e g e n e ra to r h as be en me as ured i nl a b o r a t o r y t e ~ t s ( ~ ) ( ~ i g u r e) . F o r ea ch p o i n t on t h i s p l o t an o u t p u t l o a d

2c u r r e n t , cyi l l d e t e r m i n e t h e o u t p u t pow er, I o R L Work i s c o n t i n u i n g , t od e v e l op a n a n a l y t i c a l m odel f o r t h e g e n e r a t o r an d f o r o t h e r t y p e s o fg e n e r a t o r s . t i s un de rs to od t h a t l a b o r a t o r y t e s t s a r e i m p o r ta n t f o r t h ec om pr eh en si on a nd v e r i f i c a t i o n o f t h e g e n e r al a n a l y t i c a l t h e o r y .


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eatnergy

genera to r

FIGURE 1

e x c i t a t i o n

N RPFIGURE 2


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Uo chang ing

Input TorqueWindmill)

Torque

N RPM of wi ndmi 1

FIGURE

R PMFIGURE 4

input windmill)

R PMFIGURE 5


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The t a s k r e m ai n in g i s t o d e r i v e a r e p r e s e n t a t i o n o f t h e p r o p e l l e rt o rq u e /s p ee d c h a r a c t e r i s t i c f o r v a r i o u s w in d s pe eds (v,) and p i t c h a ll q le s I:,)( F i g u r e 3 ) . T he c h a r a c t e r i s t i c s ca n th e n b e s up e rp o se d , e Lj l s h f tT and i n t e r s e c t i o n p o i n t s w i l l d e t e rm i n e t h e p a r a m e t r i c o p e r a t i n gg e n e r a t o r 'p o i n t s o f t h e sy ste m. [ A ot e t h a t t h e s h a f t to r qu e , T ~ ~ ~ ~u st i n c l u d e ap e n a l t y d ue t o m e c h an i ca l l o s s e s i n t h e s t e p u p g e a r i n g and b e a r i n g s ,t y p i c a l l y 2 5 % . ]

The system per fo rmance com puta t ion w i l l e s t a b l i s h o u t p u t p ow er ( o re n er gy ) f o r v a r i o u s p o i n t s a l on g t h e i n t e r s e c t i o n l o cu s o f t he se t o r q u ec h a r a c t e r i s t i c s . T h i s w i l l y i e l d t h e c o m bi n at io n o f v a r i a b l e s w h i ch g i v e sh i g h e s t o u t p u t ; e .g . w h i c h c o m b i n a t i o n o f RL Pexc and ro gives (I,RL)maximum. T he se ( q u a s i s t a t i c ) s o l u t i o n s a r e f o r e q u i l i b r i u m c o n d i t i o n s andf o r c o n s t a n t w i nd s p ee d. t i s u n d e rs t o o d t h a t d yn am ic f a c t o r s s uc h a sg u s t a m p l it u d e and fr eq u en cy may d i c t a t e o t h e r o p e r a t i n g c o n d i t i o n s t h a nt h e h i g h e s t o u t p u t d e te r mi n ed by t h i s s i l ~ ~ p l eode l .

I S t a b i l i t y C o n s i d e r a t i o n sThe super imposed curves w i l l g i v e a q u a l i t a t i v e i n d i c a t i o n o f t he

f i r s t o r de r t i g h tn e s s o r s e n s i t i v i t y o f t h e system t o s ma l l p e r t u r b a t i o n sf ro m e q u i l i b r i u m . As an e xa mp le c o n s i d e r t h e p l o t i n F i g u r e 4.

F o r t h i s exam ple assume t h e g e n er a to r t o r q u e c h a r a c t e r i s t i c i s f l a t( i n s e n s i t i v e t o R W ) . If h e o p e r a t i n g e q u i 1i r i u m p o i n t ( i n t e r s e c t i o n w i t hg e n er at o r c h a r a c t e r i s t i c ) o c c u rs a t @ , i t c a n be se en t h a t o u t p u t w i 11 bei n s e n s i t i v e t o a w ide v a r i a t i o n i n RPM. T h a t i s , t h e f i r s t o r d e r systemi s n e u t r a l l y s ta b le , and w i l l e s t a b l i s h e q u i l i b r i u m f o r any RPM s e t t i n gi n t h e f l a t ran ge . A ~ Qs w i n d m i l l RPM d e cr ea se s ( du e t o o v e r l o a d i n g o r


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g u s t s ) t h e g e n e ra t o r c h a r a c t e r i s t i c m us t be ch ange d t o k eep fr o m s t a l l i n gth e s ys te m; l i k e w i s e , a n i n c re a s e i n i n p u t RPM w i l l c a u s e t h e s y s t e m t od i ve r g e. T h is c o n d i t i o n i s s t a t i c a l l y u n st ab le . I n r e gi on @ t h e syste mi s s t a t i c a l l y s t a b le , s i nc e a p e r t u r b a t i o n i n w i n d m i l l RPM w i l l cause ano p p o s i t e c ha ng e i n e xc e ss t o r q u e . The sl o pe of t h e c h a r a c t e r i s t i c i sa na lo go us t o s p r i n g r a t e , and i f o th e r d y n a m i c ( h i g h e r o r d e r ) i n f l u e n c e sa r e i m p o r t an t , t h e s l o p e w i l l be an al og ou s t o t h e n a t u r a l f re q ue n cy o fv i b r a t i o n i n t h a t mode.

Now r e ex a m in e t h e a s su m p t io n of f l a t g e n e r a t o r t o r q u e ; c o n s i d e r F i g u r e5 We have e s ta b l i sh e d t h a t c o n d i t i o n a i s s t ab le ; i f i n p u t RPM decreasest h e t o r q u e i n c r e m e n t T i s p o s i t i v e , and r e a c ce l e r a t e s t h e sy ste m t oe q u i l i b r i u m . t i s e v i d e n t t h a t t h i s t o r q u e i nc r em e n t a l s o depends ont he s lo pe of t h e g en er at or c h a r a c t e r i s t i c : v i z . , f o r l i n e a t h e T i sl a r g e r a nd t h e s ys te m t h a t much t i g h t e r ; and f o r l i n e @ t h e T hasd ec re as ed t o a s m a ll r e s t o r a t i v e q u a n t i t y . Thus, f o r l i n e 4, t h e s y s te mi s s t a t i c a l l y u n sta ble ; i . e . t h e s l o pe o f t h e o u tp u t c h a r a c t e r i s t i c i sl a r g e r t ha n t h e s l op e of t h e i n p u t c h a r a c t e r i s t i c .

111 . A pp ro ac h t o P r o p e l l e r S o l u t i o nThe ap pr oa ch f o r s o l u t i o n s o f t h e p r o p e l l e r p r ob le m i s t o d ev e lo p po we r-

s pe ed a nd t o rq u e- s pe e d c h a r a c t e r i s t i c s u s i n g n on d im e n si on a l q u a n t i t i e s t o r q u eand p ow er c o e f f i c i e n t s a nd t i p sp eed r a t i o ; t h i s e l i m i n a t e s t h e depe ndenc eon V o o r on RPM. The n o n d im e n s io n a l p l o t c a n t h e n be u se d t o d e v e l o p an yd e s ir e d c r o s s - p l o t a t a ny d e s i r ed V o t o be u se d i n ma tc h i n g t h e s y s te m.

One o f t h e e x i s t i n g c o m p u ta t io n al r e s u l t s i s a p l o t of t h e p owerc o e f f i c i e n t maxima, f o r v a r i o u s t i p speed r a t i o s , f o r t h e m achine, see F i g u r e6. T h i s c u r v e r e p r e s e n t s t h e l o c u s o f a l l maxima o f i n d i v i d u a l C c u r v e s


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f o r v a r i ou s va lu es o f ro, as shown. F or a f i x e d p i t c h a ac hi ne , t h ep e rf o rm a n ce c h a r a c t e r i s t i c w o ul d be a s shown on t h e d o t t e d l i n e . F o r

synchronous co ns ta n t speed) w i n d m i l l system s, t h e power c o a f f c i e n t v a r i a t i o nw i t h i n c r e a s i n g win d s peed i s d et er m in ed f r o m t h i s p l o t 2 ) .

The t o r q u e c an b e d e r i v e d f r o m t h i s c u r v e u s i n g t h e f o l l o w i n g a pp ro ac h.The d e f i n i t i o n s a r e :

power - Pp = c o e f f i c i e n t 1 3?PA ,

p = d e n s i ty o f a i rs e a l e v e lA = p r o p e l l e r d i s c a r e a

Vo = wind speedt o r q u e r

= c o e f f i c i e n t = 1 2p A V ow i t h :

t i p speed szRr a t i o 0n = r o t a t i o n a l s p e e dR = r a d iu s o f p r o p e l l e r

A1 so :

Thus t h e t o r q u e c o e f f i c i e n t ca n be found d i r e c t l y f r om t h e s i m u l a t i o nPr e s u l t s . T h e T dependence on p i t c h w i l l l i k e w i s e be shown F i g u r e 7 )

When t h i s r e l a t i o n s h i p i s found, a map of p o i n t s p a r a m e t r i c p l o t )w i l l be c a l c u l a t e d f o r e ac h w in d speed o f i n t e r e s t , and a c t u a l t o r q u e vs . RPMc u rv e s ca n b e g e n e ra te d s e e F i g u re 8 ) . There w i l l b e re g io n s o n t h e s ep l o t s w hi ch w i l l i n d ic a te ae rodynamic n on - - l in ea r phenomena , and w i l l p r o b a b l yn o t be i m p o r t a n t e q u i l i b r i u m c o n d i t i o n s :

s t a l l - o c c u r s w he re a n g l e o f a t t a c k i s h i g h e r t h a n t h e maximuma )v a lu e f o r m a i n ta i n i n g s t r e am l in e s f o r t h e p a r t i c u l a r a i r f o i l o f


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= t o r q u e

ocu s of axnlulr~v u s

F I G U R E 7

N RPMF I G U R E 8


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i n t e r e s t ; p e rf o rm a n ce i s s h a r p l y de gr ad ed .b ) r e v e r s e f l o w - w here l o c a l v e l o c i t y o ve r bl ad e i s from t h e

t r a i l i n g edge fo r wa r d; t hu s w i l l p r o b a b l y n o t occl;r e x c e p t i ns m a ll p o r t i o n s o f t h e b la d e and f o r un us ua l c o n d i t io n s ; t h i sc o n d i t i o n w i l l n o t show up e x c e p t as a r a p i d d e cr e as e i n C w i t h 11P

c ) n e g a t i v e l i t- - t h e w i n d m i l l a c t s a s a p r o p e l l e r as an g le s o fa t t a c k , 1 f t and tor que , become ne ga t iv e.

I V . R e s u lt s o f P r o p e l l e r S i m u l a t io nThe co m p u t at io n a l r e s u l t s o f t h e p e rf or m a nc e ( s t r i p ) t h e o r y a r e s hown

i n F i g u r e s 9 and 10. I n F ig u re 9 c an b e see n t h e c o n s t a n t p i t c h c u r v e su se d t o g en e r a te t h e l o c u s o f C maxima shown i n F i gu re 6 . As p i t c h a n g l eP(B,) i s d e c rea s e d (e .g . a n g l e o f a t t a c k o f b l a d e e l e me n ts i n c re a s e d a s show ni n t h e i n s e t ) , t h e r o t o r i s lo a d e d m or e a nd m o re . As t h e a n g l e ch an ge s,t h e t i p s peed r a t i o f o r h i g h e s t power i n c re a s e s t o a bo ut 9 (B eo = -2 )and t h e n de cr ea se s t o t h e d e s i gn t i p s peed r a t i o o f 7 . T he d e c rea s e i npower w i t h i n cr e a s ed p i t c h a n g le r e p r e s e n t s t h e c o n t r o l p h i lo s o p h y a dva nc edfor r a t e d ( 2 6 . 1 MPH); t h a t i s , s h a f t spee d i s k e p t c o n s t a n t an d C Pd ec re as es w i t h i n c r e a s i n g f re e s tr ea m v e l o c i t y . T h i s p h il o so p h y i s a l s od i s c u s s e d b y utter, ) ~ o l d i n g , ( ' ) ~ o h r b a c k , ' ~ ) nd ~ e u t s c h , ' ~ ) mong o th e rs .A s i m i l a r c u r v e i n t e rms o f p ow er ( w a t t s ) v s . RPM, i s shown i 1 1 F i g u re 1 1 .T he se re s u l t s w ere o b ta i n e d f r o m w in d t u n n e l t e s t s of a f i x e d p i t c h , c o n s ta n tchord b lade (Re fe rence 7 . The c o rr e s po n d in g power c o e f f i c i e n t c h a r a c t e r i s t i ci s i nc lu de d i n F i gu re 9 .

I n F ig u re 9, a s p i t c h a n g le i s de cr ea se d, t h e p ower c h a r a c t e r i s t i cbecomes more and more sens i t i ve . The l e f t m a r gi n o f ea ch c l l rv e i s a s t a l lb ou nd ary ; a phenomenon w h ic h oc c u rs f i r s t a t t h e t i p o f t h e b l ad e , s i n c e t h eNEWF d e s i g n i s c l o s e t o o p tirn um t w i s t a n d t a p e r . The i n d uc e d v e l o c i t y


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0 30i 4 U 500 OO 00 800 900 1000 R I .I FT IIRF 1 1 \


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(do wn wa sh ) d i s t r i b u t i o n a lo n g t h e b l ad e i s c h a r a c t e r i s t i c o f o ptim umdes ign s (see F i gu re 12). Un tw i s ted , and co ns ta n t cho rd , b l ades show a muchl e s s s e n s i t i v e s t a l l t h a t s t a r t s a t th e r o o t a t much sr l ia ller p i t c h a ng le s

(5,6).t hu s , t h e pow er c h a r a c t e r i s t i c o f an o f f - d e s i q n b la d e w i l l be f l a t t e r a ndh a v e s m a l l e r C t h a n t h e NEWF b l a d e ( s e e F i g u r e s 9 and 1 1 ) . T h i s p o i n t sPo u t t h e n eed f o r t h or o ug h s t a b i l i t y a n a l y s i s o f t h e op tim um momentumexchanger sys tem ph i1o so ph y a do p te d f o r t h e NEWF d e s i g n .

A l s o , f r o m F i g u r e 9, t h e pow er c h a r a c t e r i s t i c i s seen t o becomeh i g h er o r de r as s t a l l i s ap pro ach ed ; t h a t i s , a t p i t c h a n gl es l e s s t ha n0 t h e d ro p i n power w i t h i n c re a s in g t i p speed r a t i o ( o r RPCl f o r c o n s ta n t

i s much m ore s ev er e. T h i s i s a l s o b e l i e v e d t o be a f u n c t i o n o fb l a d e d e si gn , c h a r a c t e r i z e d b y i n cr e a s e d d r a g and h i g h l y t w i s t e d s e c t i o n sbecoming nega t i ve l i f t

I n F i g u r e l o i s p l o t t e d t h e c o rr es po nd in g t o r qu e c h a r a c t e r i s t i c ,d is cu s se d e a r l i e r . The n o n - l i n e a r b e h a v io r a t p i t c h a n g le s l e s s t h a n 0i s a l s o seen. B ut t h e s t r i k i n g c h a r a c t e r i s t i c i s t h e l i n e a r i t y o f t het o r q ue c u rv es o v e r t h e u n s t a l l e d r e g i o n . T h i s r e p r e s e n t s s y s t e m s t a t i cs t a b i l i t y f o r each c on s t an t p i t c h s e t t i n q ( i n t h e 1 n e a r r a n g e ) .

Near maximum to rque , th e cu rves a re ve r y peaky, and may c o n s t i t u t e ac a t a s t r o p h i c s t a l l f o r s ma ll RPM p e r t u r b a t i o n s . T y p i c a l l y , t h es e RPMv a r i a t i o n s w i l l be c au se d b y g u s t s ; a n i n c r e a s e i n w i n d s pe ed m o m e n ta r i l yd e c r e a s i n g t i p sp ee d r a t i o , a nd v i c e - v e r s a . However, when ~ i s d ec re as ed f a renough t o p ush t h e p r o p e l l e r i n t o s t a l l , t h e r e i s a l s o a b a la n c i n g e f f e c tc au se d by t h e i n c r e a s e i n t o r q u e a v a i l a b l ~ n t h e f r e e s t re am ( e .g . due t oi n c r e a s e d w i n d v e l o c i t y ) . T h e re f or e , t h e d yn am ic b e h a v i o r i s i m p o r t a n t , andm ust be c on sid ere d f o r a r e a l i s t i c s t a b i l i t y and ~ o n t r o l o l u t i o n .


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M ore a n a l y t i c a l and e x p e ri m e n t a l d a t a a r e needed t o e s t a b l i s h thcs lo p es o f t h e t o r q u e c u rv e s a t t h e ab s ci s sa i n t e r s e c t i o n ( e .g . r o t o r u n lo a d edT h i s i s t h e c o n d i t i o n wh ic h w ou ld be re ac he d i n t h e e v e nt o f a s h a f t o rg en er a t or f a i l u r e . The w ind genera to r w i l l speed u p t o t h e p o i n t a t w hic hs h a f t t o r q ue i n p u t j u s t ba la nc es f r i c t i o n t or qu e, and c l a s s i c a l w i n d m i l l i n gi s a ch ie ve d. ( 7 ) [ T h i s i s n o t t h e same as f e a t h e r i n g , w h ic h i s r e p r es e n t e db y t h e o r i g i n , o r z e ro RPM.]V R o t o r F l o w S t a t e s

The v a r io u s r o t o r f l o w s t a t e s can be i d e n t i f i e d on t h i s c h a r a c t e r i s t i c . ( 5T he Z e r o S l i p Case i s r e p r e s e n t e d b y T 0 j u s t d is c us se d ; and t h e P r o p e l l e rS t a t e i s b el ow t h e a b s c i s sa , w he re T i s n e g a t i v e ( po we r goes i n t o t h e s y st e mAs t h e c o n s t a n t p i t c h p r o p e l l e r i s l o a d e d m o re an d m ore , t h e o u t p u t po we r ( ant h r u s t ) i n c r ea s e s t o t h e p o i n t whe re ( t o r q u e x RPM) = power i s a maximum( t o r q u e a l o n e i s n o t a m axim um). T h i s p o i n t o c c u r s , a c c o r d i n g t o momentumt h e o ry , w he re t h e av er ag e i n f l o w i s 1 /3 ; and t h e i d e a l = . 5 9 2 6 . (2 ) fl o a d in g i s i n c re a se d beyond t h i s , t h e i n f l o w i n c re a s e s on t h e b l a d e u n t i l t h ea i r f o i l s t a l l s ; power f a l l s o ff and t h r u s t ( n o t shown) i nc re a se s, a s v e r i f i e dby h e1 c o p t e r a u t o r o t a t i v e t e s t s . ( 6 ) T h i s i s c a l l e d t h e T u r b u l e n t Wake S t a tea nd i s c h a r a c t e r i z e d b y t h e a bs en ce o f s t r e a m l i n e s , s e v er e b u f f e t i n g , and t h eq u i c k f a l l - o f f i n d ev e lo p ed pow er. The t a s k o f t h e c o n t r o l s y st em w i 11 be t op r e v en t e n tr a nc e i n t o t h i s o p e r a t i n g s t a te , eve n f o r t r a n s i e n t c o n d i t i o n s .s h o u l d be u n d e r st o o d t h a t f o r h i g h v a l u e s o f ro ( e .g . 12O) t h e a n g le s o fa t t a c k a r e s m al l t o b e g i n w i t h , and t i s u n l i k e l y t h a t a s i g n i f i c a n t p o r t i o no f t h e ( h i g h l y t w i s t e d ) b l a d e c o u l d e v e r be s t a l l e d . And t h e b la d e may n ev er e a l l y e n t e r T u r b u l e n t Wake S t a t e . Hence a p o s i t i v e o u t p u t t o r q u e c o u l d b eexpec ted fo r ex t rem e ly lo w RPM (o r u . However, o u r d i s c u s s i o n w i l l f o c u s


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v i b r a t i o n and b u f f e t t i n g can o cc u r , a s w i t h h e l i c o p t e r r o t o r s .t i s i n t e r e s t i n g t o a l s o c o ns id e r t h e l ow RPM b e ha v io r o f h i g h

s o l i d i t y p r o p e l l e r s , s uc h a s t h e A me ric an f a n n i i l l . A s RPM i s d ec re as e d,t h e c o r r e s p o n d i n g c h an g e i n downwash an d a n g l e o f a t t a c k i s much s m a l l e rf o r t h e se m ach ine s; hence, l a r g e p o s i t i v e to r q u e i s s t i 11 p r od u c ed a tv e r y l o w RPM and t h e ma ch in es ca n 1 t e r a l l y n e ve r be s t a l l e d b yc o n v e n t i o n a l l o a d s. A l s o , i t p o i n t s o u t t h e n o n -n e c es s it y o f v a r i a b l e p i t c h ont h e s e m a ch in es ( s t a t i c t o r q u e i s a l r e a d y h i g h ) . H ow ev er, t h e s e m a ch in e sa r e g e ne ra l l y n o t i m po r t a nt f o r e l e c t r i c i t y g e n e r a t io n s i n ce t h e o v e r a l lp ow er c o e f f i c i e n t s a r e s m a ll , and o ptim um t i p s peed r a t i o s a r e c l o s e t ou n i t y . ( 2 )

A r o u g h i d e a of t h e T u r b u l e n t Wake S t a t e b ou n da ry ( f o r l o w s o l i d i t y ,h i g h sp ee d w i nd g e n e r a t o r p r o p e l l e r s ) c a n be g a in e d f ro m s i m p l e t h e o r y .

From b la d e e le me nt t h e o ry ( n e g le c t in g s l p s t r ea m r o t a t i o n ) t h e t i ps e c t i o n i s :

where4 = b l a d e e l e m e n t a n g l e

The T u r b u l e n t Wake S t a t e b o u n da ry i s t h e p o i n t a t w h i c h s tr ea m 1 n e s a r e n ol o n g e r w e l l -d e f i ne d ; t h i s o cc u rs a t v a l u es o f a v /V o = 1 / 2 . ( ~ ~ ~ ) ence:

V ( 1 - a )-1 0t a n -1 1-a1 = t a n [ I = t a n 1 140 nR u [ IT u r b u l e n tWake StateBoundary

Thus, t h e b l ad e e le me nt a n g l e ( o r i n f l o w an g le ) a t t h e t i p f o r T u rb u l e ntWake S t a t e t o o c c u r de pe nd s on t i p s pe ed r a t i o :


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Tip Speed Ra t io T u rb ul en t Wake BoundaryR V o $o a t b la de t i p

TABLE 1Most a i r f o i l s ap pr oa ch s t a l l a t a n g l e s of a t t a c k ab o u t 1 2 . T h us , thea pp r ox im a te p i t c h a n g l e t o p ro du ce t u r b u l e n t wake s t a t e i s s im p ly :

O m o a t a l lT ur bu le nt TWSWake Sta tewhere I is g i v e n i n T a b l e 1 a b o v e , a nd a s t a l l 1 2 .-rws


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R e f e r e n c e s1 . H u t t e r , O p e r a t i n g E x p e r i e n c e O b t a i n e d w i t h a 100-kW W ind P ow erP la n t, NASA TTF-15, 063, Au gus t 1973 .2. G o l d i n g , T he G e n e r a t i o n. f E l e c t r i c i t y .y Wind Power,.. P h i l o s o p h i c a lL i b r a r y , 1 9 5 5 .3 . Rohrback and Worobel , P e rf or m an c e C h a r a c t e r i s i c s o f A er od yn am ic al l yO ptim um T u r b i n e s f o r W in d E n e r g y G e n e r a t o r s , 3 1 s t A n n u al N a t i o n a lFo rum , A m e r ic a n H e l i c o p t e r s o c i e t y , May 19 75 .4 . Deu tsch , L . Grunlman Ae rospace Co rpo ra t i on , pe rson a l comnuni ca t i on ,19 March 1976.5. i so n and L issn lan , Ap p l i e d Aerodynamics o f Wind Power Mach ines ,O re go n S t a t e U n i v e r s i t y , J u l y 1 97 4.6. Gessow and Myers , Aerod ynam ics~ -- o f t h e H e l i c o p t e r ,. F r e d e r i c k U ng arP u b l i s h e r s , 1 9 5 2 .7 . S todd a rd , Edds , F in a l Re po r t on Wind Tunne l Te s t Program o f Mode lB l a de s o n a 2 00 w a t t , 1 2 v o l t W ind G e n e ra t or , U n i v e r s i t y o f M a s s a c h u s et t sC i v i l E n g i n e e r i n g D e p a r tm e n t In - H ou s e R e p o r t , May 19 74 .8. S t od d ar d, D i s c u s s i o n o f Monientum T h e or y f o r W i n d m i l l s , ( t h i s r e p o r t ) .9. Edds, M. O p t i m i z a t i o n of O u t p u t Power o f an AC Synchronous Mach ineby V a r y i n g E x c i t a t i o n a nd L oa d, M.S . O cean E n g i n e e r i n g T h e s i s , t o b epub l i shed , June 1976 .

10. B l a c k w e l l , T h e V e r t i c a l A x i s W ind T u r b i n e ; How i t Works, SandiaLa bo ra to r i e s , A lbuqu e rque , New Mex ic o , SLA-74-0160 , A p r i l 1974.


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UN TTY OF MASSACi 3SElTWAhllHERSTENERGY ALTERNATIVES PROGRAM A


P r e l ~ n ia r y R e p o r t o nOPTIMIZING THE WINDMILL ROTOR

P a u l L e f e b v r eand

Duane E Cromack

U.Mass Wind FurnaceEnergy A 1 t e r n a t i v es P ro gr amU n i v e r s i t y o f M a ss ac hu se tt sAmhers t Massachuse t t s 01002

TR/76/4Append ix V I


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OPTIMIZING THE WINDMILL ROTOR

a b s t r a c tT we lv e h o r i z o n t a l a x i s w i n d r o t o r sy st em s a r e a n a l y z e d b y means o f c o m pu t er

s i m u l a t i o n . The p u rp os e o f t h i s a n a l y s i s i s t o d e v e lo p a m eth od o f d e s i g n i n go p t i m iz e d b la de s o f d i f f e r e n t r o t o r c o n f i g u r a t i o n s . The r e s u l t s o f t h e s i m u la -t i o n a r e t h e n com pa red w i t h w i n d t u n n e l t e s t r e s u l t s .

i n t r o d u c t i o nOne o f t h e p r i n c i p a l omponents o f a n y w i n d m i l l i s t h e m omentum e xc ha n ge

d e vi ce , o r r o t o r . T h i s de v i c e c o n v e r t s t h e k i n e t i c en er gy o f a m ov in g a i rs t r e am t o a more us a b le fo r m o f p owe r. T h er e a r e two b a s i c c l a s s i f i c a t i o n sf o r w i n d m i l l s : v e r t i c a l a x i s m ac hin es a nd h o r i z o n t a l a x i s m ach in es . T h i sr e p o r t d e a ls o n l y w i t h h o r i z o n t a l a x i s r o t o r s . W i t h i n t h i s c a te g o r y a l l r o t o r st a k e t h e f o rm o f a n a i r s c re w w i t h t h e d i f f e r e n c e b etw e en d es ig n s b e i ng i n t h ec h o r d a nd t w i s t d i s t r i b u t i o n o f e ac h bl a d e , a nd t h e n um ber o f b l a d e s er r~ pl oy edf o r a ny g i v e n r o t o r . The fu n c t i o n a l r e l a t i o n s h i p o f t he s e v a r i a b l e s d e te r mi n eshow e f f i c i e n t l y a r o t o r p e r f o r n ~ s . F ou r d i f f e r e n t r o t o r s ys tems a r e s t u d i e da nd t h e i r p e r fo rm a nc e c a p a b i l i t i e s o p t im i z e d. The r o t o r t yp e s c o n s id e r e d a r e :

1 ) c o n s t a n t c ho rd , z e r o t w i s t CCZT); 2 ) l i n e a r t a p e r e d c h or d , z e r o t w i s tLCZT); 3 ) l i n e a r t ap e re d c h or d , l i n e a r t w i s t LCLT); a nd 4 ) a e r o d y n a m i c a l l y

o p t im u m c h o r d an d t a p e r O P T) . The op tim um b l a de i s t a k en t o be t h a t a i rs c re w c o n f i g u r a t i o n w h i c h w i l l e x t r a c t t h e h i g h e s t p e rc en ta g e o f t h e p ow era v a i l a b l e . t h a s b ee n shown t h a t t h e maximum p ow er c o e f f i c i e n t o b t a i n a b l ei s .5926 and i n p r a c t i c e w i l l i n v a r i a b l y be l e s s t h a n t h i s v a lu e . ToP


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d e t e r m in e t h e m os t a dv an ta ge ou s c h o r d a nd t w i s t d i s t r i b u t i o n , t i s n e ce s sa r y2t o comb ine momentum and an nu lu s th eo ry . The f o l l o w i n g e q u a t i m s a r e o b t a in e d

a n d t h e o p ti mu m b l a d e c a n be d e s i g n e d a c c o r d i n g l y .X = s i n + (2 c os - 1 ) / ( ( 1 + 2 c o s + ) ( l -c o s + ) )BcCL ~ / 2 n o=4 s i n ( 2c o s - 1 ) /( 1 + 2 c os )

A s im p l e co mp ute r pro gra m was w r i t t e n t o f a c i l i t a t e t h i s d e s ig n s p e c i f i c a t i o np ro ce ss and i s l i s t e d i n A pp en dix A. The p ro gra m i s w r i t t e n i n F o r t r a n f o r u seo n t h e K ro no s t i m e s h a r i n g s y st em i n us e a t t h e U n i v e r s i t y o f M as sa c hu se t ts ,and s h o u l d be r e a d i l y a d a p ta b l e t o a ny o t h e r syste m. The i n p u t i s l i m i t e d t of i v e l i n e s c o n t a i n i n g t h e r o t o r r a d i u s , t h e number o f b la de s, t h e t i p speedr a t i o a nd t h e CL and t h a t c o rr e sp o n d t o CL /CD maximum f o r t h e a i r f o i l d a t ab e i n g u se d . Th e f o r m a t i n e a ch c a se i s F7 .3 .

The p e rf or ma nc e c h a r a c t e r i s t i c s o f e ac h o f t h e se f o u r a i r s c r e w c o n f i g u r a -t i o n s a r e d e t e r m i n e d f o r t w o , t h r e e , a n d f o u r b l a d e d s ys te m s. T he p ow erc o e f f i c i e n t s c i t e d w ere o b t a i n e d u s i n g a NACA 441 5 s t a n d a r d r ou gh ne ss a i r f o i lp r o f i l e a nd a d e s ig n t i p s peed r a t i o of 7. Each v a lu e r e p r e s e n t s t h e maximumpower o b t a i n a b l e f o r t h a t g i v e n r o t o r t yp e u n de r t he s e co n d i t i o n s .

C om pu te r S i m u l a t i o n : The c o mp u te r m od el us ed t o p r e d i c t p e rf or m an c e c a p a b i l i t i e si s o ne d e ve l op e d b y W i l s o n a nd L i s s a m a n Y 3 a nd m o d i f i e d f o r o u r p u r po s e s. T h i smodel uses b l ad e e le me nt t h e o ry t o c a l c u l a t e t h e o p e r a t i n g c h a r a c r e r i s t i c s a te ach r a d i a l s t a t i o n . These c h a r a c t e r i s t i c s a r e t h e n n u m e r i c a l l y i n t e g r a t e da l o ng t h e b l ad e t o o o b t a i n t h e c a l c u l a t e d r o t o r p e rfo rm an ce . R e f er in g t oF i g u r e 1, t h e f o l l o w i n g e q u a t i o n s may be o b t a i n e d :


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LY = - I)t a n = ( 1 a ) ( V o / ( ( l + a l ) ; r )Cy=CL cos @ +CD s i n 4c X = cL s i n + cD C O S ~ 6

From a er od yn am ic s t r i p t h e o ry , t h e t h r u s t an d t o r q u e o n a d i f f e r e n t i a l b l a d ee le m e nt a r e g i v e n a s

dT, = .5Bc p v r 2 C y d r

F rom momentum th eo ry , t h e t h r u s t and t o rq ue become

dTm = ( 2 n r d r ) , ~ ~ ( V o - u ~ ) ( 9 )

D e f i n i n g t h e d ow ns t re am a x i a l i n t e r f e r e n c e fa c t o r , aw, a s t w i c e t h e a x i a l i n t e r -f e r en c e f a c t o r a t t h e r o t o r , e q u a t i o n s ( 7 ) and ( 9 ) may t h e n b e e q ua te d t o y i e l da r e l a t i o n b etw ee n a a nd o t h e r known r o t o r p a r a m e te r s su ch t h a t

a = ( ~ c ~ ~ / ~ n r ) / ( s i n ~ ;(Bc Cy /8 . r ) ) ( 1 1 )I n a s i m i l a r m anner, i f t h e a n g u l a r v e l o c i t y d ow ns tr ea m i s assumed t o b e t w i c et h a t f oun d a t t h e r o t o r , e q u at io n s 8) n d ( 1 0 ) may be eq u a te d t o o b t a i n t h ea n g u l a r i n t e r f e r e n c e f a c t o r i n te rm s o f known v a r i a b l e s . Th us :

a ' = ( B c C X / 4 n r ) / ( s i n 2 j - ( B c C X / 4 n r ) ) ( 1 2 )Enough i n f o r m a t i o n i s now a v a i l a b l e s o t h a t t h e f l ow c h a r a c t e r i s t i c s f o r

a n y g i v e n b l a d e e l e m e n t c a n b e f o u n d . f i n i t i a l v a l u es f o r a an d a ' a r ea s s u m e d ( a = . 0 5 a n d a l = O ) e q u a t i o n ( 4 ) c a n be u sed t o c a l c u l a t e 4 Once i s


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C om p ute r S i n l u l a t i o n R e s u l t s : The po we r c o e f f i c i e n t s o btc tin t.d w i t h o p t ~IIIUIIIr o t o r s o f two t h r e e and f o u r b la de s a r e l i s t e d i n T ab le 1 T h e s e r o t o r sw ere d es ig ne d f o r a t i p s peed r a t i o o f 7 a CL o f -9 1 4 a t an an g l e o f a t t a c ko f 5 . 5 7 d eg re es . The l a s t tw o f i g u r e s r e p r e s e n t t h e p o i n t a t w h i c h CL /CD i smax imum f o r an NACA 4415 s ta nd a rd roughness p r o f i l e .

The n e x t tw o b l a d e ty p e s t o be c o n si d e r e d a r e l i n e a r c h o rd z e ro t w i s tand l i n e a r c ho rd l i n e a r t w i s t . I n b o th c as es t h e f i n a l d e s ig n c o n f i g u r a t i o n wasf o u nd b y m a ki ng a s e r i e s o f c o rr ~p u te r u n s i n w h ic h c h o r d and t w i s t w eres y s t e m a t i c a l l y c hange d i n a s e r i e s o f a p pr o x im a t io n s a s w ere f i and X u n t i l0a maximum power o u t p u t a t a t i p speed r a t i o o f 7 was reac hed . The ch or d andt w i s t a p p r ox im a t i on s t h a t w ere t r i e d a r e shown i n F i g u r e 3. I n o r d e r t o o b t a i na c o n s i s t e n t m ethod o f d e s i g n in g b la de s o f t h i s t yp e t h e i r c h o rd and t w i s t d i s -t r i b u t i o n s a r e l i s t e d i n Ta bl e 2 i n t erm s o f t h e o pt in lum bl a d e o f s i m i l a r d e s ig nc o n s t r a i n t s .

For example i f a n LCZT 3 -b la de d r o t o r w i t h a r a d i u s o f 1 0 f e e t a nd a t i pspeed r a t i o o f 7 i s d e s i r e d t h e b l ad e c o n f i g u r a t i o n i s f ou nd as f o l l o w s . Theo pt im um b l a d e f o r t h e se c o n d i t i o n s i s l a i d o u t . The ch o r d o f t h e LCZT b l a d e a t100 p e r ce n t o f t h e r a d i u s i s t a k en as 90 p e r c en t o f t h e c h o rd o f t h e o pt im umb l a de a t t h a t p o i n t . The c h or d o f t h e LCZT b la d e a t 10 p e r c e n t o f t h e r a d i u si s t ak e n as 67 p e r c e n t o f t h e c ho r d o f t h e op tim um b la d e a t t h a t p o i n t . Ast h e ch o rd d i s t r i b u t i o n i s l i n e a r t h e d im en sio ns o f t h e b l ad e a r e now f i x e d .A l l t h a t re m ain s i s t o s e t t he -o t o t h a t s p e c i f i e d i n Ta b le 2 .

T he p ow er c o e f f i c i e n t s o b t a i n e d f o r LCZT a nd LCLT r o t o r s o f tw o t h r e ea nd f o u r b l a d e s a r e shown i n T a b le 1 .

The f i n a l b l a d e t y p e t o be c o ns id e re d i s co n s ta n t c ho rd z er o t w i s t . F orr o t o r s o f t h i s t y p e t h e r e a re t h r ee v a r i a b l e s t h a t w i l l a f f e c t p er fo rm a nc e:


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F o r e ac h r o t o r t y pe a s e r i e s o f t e s t s w ere f i r s t c on du cte d t o a s c e r t a i nt h e po s e t t i n g f o r maximum p ow er. T h a t s e t t i n g was t h e n u se d f o r a s e r i e s o fr u n s a t i n c r e a s i n g w i n d s p ee ds . T he i n c r e as e i n maximum pow er w i t h w i nd s peedp a r a l l e l e d c l o s e l y t h e e x pe ct ed cu b i c r e l a t i o n s h i p and i s shown i n F i g u r e 6.A l s o shown i s t h e r e l a t i o n s h i p b et we en pow er a nd RPM a s a f u n c t i o n o f a p p l i e dl oa d . T a b le 3 c o n t a i n s t h e power c o e f f i c i e n t s o f t h r e e r o t o r syste ms f o rc o mp a ri so n w i t h t h e po we r c o e f f i c i e n t s p r e d i c t e d b y t h e c om p ut er s i m u l a t i o n .

c o n c l u s i o nE x p e r im e n t a l v e r i f i c a t i o n o f t h e c om p ut er s i m u l a t i o n h as n o t be en c om p le te d .

The d i f fe r e n c e s i n power c o e f f i c i e n t s l i s t e d i n T ab le 3 a r e q u i t e l a r g e w i t hn o c o n s i s t e n t p a t t e r n d i s c e r n a b l e . A d d i t i o n a l w i n d t u n n e l t e s t s a r e p l an n e di n o r d e r t o o b t a i n a b e t t e r c o r r e l a t i o n b etwe en t h e o r e t i c a l and e x pe r i me n ta lr e s u l t s . S i n c e t h e c o mp u te r m od el i s b as ed o n w e l l - e s t a b l i s h e d a e ro d yn a m ict h eo r y t h e r e s u l t s f o r co m pa ra ti ve p urp ose s a r e c e r t a i n l y v a l i d .

T he s e l e c t i o n o f t h e r o t o r t y pe e . opt im um LCLT CCZT e t c . dependso n t h e p a r t i c u l a r a p p l i c a t i o n b u t m ore i m p o rt a n t depends o n t h e metho d o fb l a d e m a nu fa c tu re an d t h e m a t e r i a l t o be used. T h i s i s a pr o bl em o f c o s te f f e c t i v e n e s s a nd n o t o f j u s t r o t o r p e rfo rm an ce .

The p ro b le m o f o p t i m i z i n g may b e v ie we d d i f f e r e n t l y b y s t a n d a r d i z i n g t h epower o f e ac h r o t o r s ys te m i n t er ms o f t h e r e q u i r e d r o t o r d i am e t e r. T hi s i sdone i n t h e f o l l o w i n g manner. F o r a ny p r o p o se d w i n d g e n e r a t i n g s y st em t h e r ew i l l b e a r e q u i r e d p ow er f o r a p a r t i c u l a r d e s i g n w i n d sp ee d. F or t h e d e s i g np ow er and r a t e d w i n d spe ed t h e r e q u i r e d r o t o r di a m e t e r ca n b e c a l c u l a t e df r o m t h e s t a n d a r d p o w er e q u a t i o n a s = [8P/nC The r e s u l t i s t h a tP


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a t w o - b la d e d CCZT r o t o r w i t h a d i a m e t e r 5 . 2 7 p e r c e n t g r e a t e r t h an a t e n - f o o td i a m e te r tw o b l ad e d o pt im um r o t o r w i l l y i e l d e q ua l po wer. T h e re f or e t h ec h o i c e t o b e made i s b e t w ee n a t e n - f o o t o p ti m um b l a d e an d a 1 0 .5 3 f o o t CCZTb l a d e . The d e c i s i o n a s t o w h ic h b l a d e t o u s e i s b a se d on w h i ch b l a d e t y p ew o ul d h ave t h e l o w e s t u n i t p r o d u c t i o n c o s t f o r t h e number o f b l a d e s r e q u i r e d .T a b l e 4 i n d i c a t e s t h e p e r c e n t i n c r e a s e i n b l a d e d i a m e te r needed f o r e q u alp ow er o u t p u t s t a n d a r d i z e d t o t h e o ptim um b l a d e shape.

t s h o u ld be s t r e s s e d t h a t t h e r e s u l t s c i t e d a p p l y r e a l l y o n l y t o NACA 4415a i r f o i l p r o f i l e s a l t h o u g h t h e r e s u l t s o b t a i n e d u s i n g a NACA 4418 p r o f i l e w e req u i t e s i m i l a r . O t h e r b l a d e s e c t i o n s need t o b e a na l yz e d b e f o r e t h i s p r oc e du r ec a n b e g e n e r a l i z e d .

t s ho u ld a l s o be k e p t i n m in d t h a t t h e p ower c o e f f i c i e n t s f ou n d a r e f o rp e r f e c t l y c o n s t r u c t e d b la d es . f l i m i t e d num ber o f o pt im u m b l a d e s w er e t obe p roduced i t w ou ld be d i f f i c u l t t o o b ta i n t h e e x ac t ch or d and t w i s t d i s t r i -b u t i o n n ee ded . On t h e o t h e r hand b e t t e r q u a l i t y c o n t r o l m i g h t b e e x p ec t ed f o rCCZT b l a d e s be ca us e o f t h e s i m p l e r c o n s t r u c t i o n .

T h i s s t u dy a tt em p te d t o o p t i m i z e t h e c h or d and t w i s t d i s t r i b u t i o n o f f o u rr o t o r t yp e s. t h as b een s ug ge st ed t h a t f u r t h e r i n c re a s e s i n t h e p ow er c o e f f i -c i e n t s m i g h t be o b t a in e d b y su ch m ethods as v a r y i n g t h e a i r f o i l p r o f i l e a l o n gt h e bl ad e o r by d e s i g n in g t h e b l ad e i n s uc h a way t h a t t h e C L C D r a t i o was af u n c t i o n o f t h e r a d i a l s t a t i o n i n s te a d o f h o l d i n g t a t a c o n s t a n t C L C D maximum.


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TAGLEPOWER COEFFICIENTS O TWELVE SIMULATED ROTORS

L i s t e d i n o r d e r o f m a g n it u de )

T yp e o f R o t o r No. o f B l ad e s B o Power C o e f f i c i e n tOptimumOpt imumOpt imumLCLTLCLTLCLTLCZT

CZTLCZTCCZTCCZTCCZTCCZT


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TABLE 4

INCREASE OF BLADE DIAMETER NEEDED TO OFFSET LOSS OFEFFICIENCY DUE TO USE OF NON OPTIMUM BLADE

I nc re as e i nN a B l a d es R o t o r T yp e Power C o e f f i c i e n t D i a m e te r@ o

2 Opt imum 0.0 .439 0.002 LCLT 2.0 .428 1.2 82 LCZT2 CCZT

3 Optimum 0.0 .4633 LCLT 1.5 .4493 LCZT 4.5 .423 4 .623 CCZT 6.1 .41 5 5.6 2

4 Opt imum 0.0 .474 0.004 LCLT 1.5 .460 1.514 LCZT 4.5 43 0 4.994 CCZT 6.1 .425 5. 61


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F I G U R E

I 4 ar5 6 7L O C A L S P E E D R A T I O V o

A X I A L A N D A N G U L A R I N T E R F E R E N C EF A C T O R S v s L O C A L S P E E D R A T I O


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FIGUREAPPROXIMATIONS USED FOR THE COMPUTERSIMULATION OF THE LCZT AND LCLT BLADES

LINEAR TWISAPPROXIMATION

CHORD TWIST


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F I G U R E 4SOLID ITY vs P I T C H A N G L E AND T I PS PE ED R A T IO F O R C O N S T AN T C H O R DZ E R O T W I S T B LA DE S

/ N A C A 44 5o

STD ROUGHNESSN A C A 44 8

V

O 3 0 O9 I 2S O L I D I T Y 0


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F I G U R EP OWE R vs R.F M. F O R2 B L A D E D O P TIM U MR O T 0 R

300 4 00 500 6 7 8 900R O T O R R.P.M.


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Nomencl a u reA x i a l i n t e r fe r e n c e f a c t o rA ng ula r i n t e r f e r e n c e f a c t o rWake a x i a l i n t e r f e r e n c e f a c t o rNumber o f b la d es i n a g i v e n r o t o rL o ca l c h o rd f o r a g i v e n b l a d eD r a g c o e f f i c i e n tL i f t c o e f f i c i e n tP o w e r c o e f f i c i e n tC o e f f i c ie n t o f f o r c e i n t h e d i r e c t i o n o f r o t a t i o nC o e f f i c i e n t o f f o r c e normal t o t h e p l an e o f r o t a t i o nR a d i u s o f t h e r o t o rR adius o f a g i v e n lo c a l s t a t i o nA x ia l f l o r v e l o c i t y t t he r o t o rA x i a l f l o w v e l o c i t y i n t h e wakeTorque as g i ve n by aerodynamic th eo ryTorque as given by momentum theoryTh r us t as g i v en by ae rodynam ic t h eo r yThrust as g iven by momentum theoryF re e s tr ea m v e l o c i t yThe r e l a t i v e v e l o c i t y a s seen by a moving b la de e lementThe t i p speed r a t i o o f t h e r o t o r d e vin ed a s nR/VoThe ang l e be tween t he cho r d o f t h e b lade e lem en t and t he r e l a t i v ev e l o c i t yAn equa l angu l a r de f l e c t i o n i n a d d i t i o n t o b la de t w i s t g i ve n t oeach b lade e lement


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n A ng ula r v e l o c i t y o f t h e r o t o rD e n s i t y o f t h e f l u i d mediumA ng le b etween t h e p l a ne o f r o t a t i o n and t h e r e l a t i v e v e l o c i t yA n gle b etw ee n t h e p l a ne o f r o t a t i o n and t h e c ho r d o f t h e b l a d eelement


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r e f e r e n c e s

1 . G l ave r t , H., Aerodyn an~ics Theory IJ. F. Durand , Ed i t o r - i n - C h i e f ) Vo l I V ,D i v i s i o n L , J u l i u s S p ri ng e r , B e r l i n , 1935.

2. i b i d3. Wils on and L issaman, A pp l ie d Aerodynamics o f Wind Power Machines, OregonS t a t e U n i v e r s i t y , J u l y 1 974.4. Putnam, P. C., Power from t h e Wind, Van No str an d Company, I n c . , New York,1948.


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P P E N D I X PL N H0 0 1 0 0 P??OG??AI.1 O?T IPJP 'JT O T? T0 0 1 0 5 D I M E ? I .S IC ? IC E ( 1 5 )0 0 1 1 8 ?EAD l r ?0 0 1 2 0 ?EAD l r B0 0 1 3 8 ? E A 9 l r X0 0 1 4 3 FZAD l r C L0 0 1 5 8 ?EAD l r A0 0 1 6 0 1 F O ? A A ( F 7 * )@ 0 1 7 E ? ?I N? 20 0 1 68 2 FC ? M A T 0 0 2 4 5 v = ? ./ i e0 0 2 5 0 DO 3 2 L -1 1 00 0 2 6 0 Y L = Y L + ( Y / l B m >0 0 2 7 0 P = ? * P I / l E B *E 0 2 8 8 ? L = ? L + ( ? / l a * )0 8 2 9 3 ? E ? = ? E " + * l0 0 3 0 0 DO I = 1 ~ 6 0 0 C0 0 3 1 0 P = ? - < * C l * ? I / 1 8 3 * >0 0 3 2 0 XE= SI?I ?>* 2**CCC ?>-l*>)/< l * + 2 e * C O ~ ( ? > > * ( l - C G S ( P ) ) )00330 I F ( A S Z ( : < L - X E > * L T * 2 5 > O T O 60 0 3 3 2 5 COM?IP E0 0 3 3 4 6 DO 7 J - l r 4 D 2 20 0 3 3 6 ? = ? - < .C O l* ? I / lE ? ~ >00338 Y E = < S I ~ l < ? ? * 2 ~ * C @ S < ? > - l e> / ( ( I * + ~ * * C O S ( Q ) ) * ( I - C O S ( ? ) ) )0 3 3 4 8 I F< A SC . Y L -X E ) e L T * e Z C 5 O T O I O0 6 3 4 2 7 COP TIN'JE00358 l e 9CCL=


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UNIVERSITY O MASSACr:;JSETTS/ AMHWENERGY ALTERNATNES PROGRAM

UN IVERSITY OF F1ASSACHUSETTS/AMHERSTENERGY ALTERNATIVES PROGRAM

FIELD COtiTROLLER FOR THE UMASS W IN FURNACE

byDaniel Handmann

U.Mass Ui nd Furna ceE n e rg y A l t e r n a t i v e s P ro g ra mU n i v e r s i t y o f M a s s a c h u s e t t sAmhers t Massa chuse t t s 01002

TR/ 7 6 5Append ix V I I


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FIELD CONTROLLER FOR THE UMASS WIND FURNACEt has been de te r rn i ned exper i l nen ta l l y t h a t I I I~X~I I~UI I I power o u t p u t o f t h e

Lim a E l e c t r i c G e n e r a to r c a n be a c h ie v e d i t h e f i e l d c u r r e n t su p pl ie d t o t h eg e n e r a t o r f o r a g i v e n g e n e r a t o r s peed f o l l o w s t h e c u r v e shown i n F i g u r e 1 .The fu n ct io n o f t h e f i e l d c o n t r o l l e r i s t o s up ply f i e l d c u r r en t alo ng t h i s fvs. RP c u r v e . To a cc om p lis h t h i s t a s k t he f i e l d c o n t r o l l e r has f i v e b a s icc om po ne nts ; ( r e f e r t o d r a w i n g # SH -I, 0 3.0 1.0 1 F i e l d C o n t r o l l e r , B l o c k D i ag r am )a ta ch om ete r, a 6 b i t an a lo g t o d i g i t a l c o n v e r t e r , a 64 w ord b y 8 b i t sem i-c o nd u ct or memory, an b i t d i g i t a l t o a n al og c o n v e r t e r, and a p u l s e w i d t hm od ula te d t r a n s i s t o r s w i t c h i n g amp1 i f i e r .

The o p e r a t i o n o f t h e s ys te m i s a s f o l l o w s : The t ac h om e t er i s g ea r ed t ot h e g e n e r a t o r and has a d .c . v o l t a g e o u t p u t t h a t i s l i n e a r w i t h rpm. Theo u t p u t of t h e ta ch om ete r i s c on v e rt e d f r o m a v o l t a g e l e v e l t o a 6 b i t b i n a r ynum ber by t h e a n al o g t o d i g i t a l c o n v e r t e r . The 6 b i t b i n a r y num ber c an t a k eo n i n t e g e r v a l u e s b e tw ee n 0 a nd 63 ( ba s e 1 0 ) w h ic h h as t h e e f f e c t o f b r e a k -i n g down t h e o p e r a t i n g s peed r a n g e o f t h e g e n e r a t o r i n t o i n c r e m e n ts o f 28.5 rpm.The o u t p u t o f t h e a n a lo g t o d i g i t a l c o n v e r t e r i s used t o ad dr es s one o f t h e 6 4words i n memory. The c o n t e n t s o f t h e a d d re ss ed 8 b i n a r y b i t w or d a pp ea r a t t h eo u t p u t o f t h e memory. The d i g i t a l t o an a l og c o n v e r t e r c o n v e r t s t h e w ord f r ommemory i n t o a c u r r e n t l e v e l b et we en 0 and 2.6 m i 11 -amps. T h i s c u r r e n t 1eve1 i st h e c o n t r o l s i g n a l f o r t h e p u ls e w i d t h mo du la te d t r a n s i s t o r s w i t c h in g a m p l i f i e r .The s w i t c h i n g a m p l i f i e r s w i tc h e s a 50 v o l t d. c. power s u p p l y on an d o f f a t af i xed f requency (10kHz) . The w i d t h o f t h e p u ls e v a r i e s l i n e a r l y w i t h t h e c o n t r o ls i g n a l f ro m t h e d i g i t a l t o a n al og c on v er te r. T h e w i d e r t h e w i d t h o f t h e p u l s e s ,t h e h i g h e r t h e av er ag e c u r r e n t s u p p l i e d t o t h e g e n e ra t o r f i e l d . T h e s w i t c h i n g


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a m p l i f i e r a l s o m o n i to r s t h e am ount o f c u r r e n t b e i ng d e l i v e r e d t o t h e g e n e r a to rf i e l d by means o f a feedback l oop . The feedback s i gna l i s sumed i n t o t hec o n t r o l s i g n a l t o p r o v id e c u r r e n t re g u l a t i o n n e c es s it a te d by t h e f l u c t u a t i o no f t h e g e ne ra to r f i e l d s r e s i s t a n c e w i t h c hanges o f f i e l d t em p er at ur e.

By b u i l d i n g t h e s ys te m a ro u nd a memory, a c e r t a i n am ount o f f l e x i b i l i t yi s i n tr o d u c e d i n t o t h e s yste m. I f for example, t s d e te rm in ed d u r i n g t e s t so f t h e wind g e n er at or t h a t a d i f f e r e n t f s. RP curve should be used, theo ld memory can be unplugged and rep laced by a d i f f e r e n t l y programe d one. Fort h e f i r s t model o f t h e f i e l d c o n t r o l l e r , two 32 word memories were usedi ns t ead o f one 64 word memory. Th i s p rov i des t he op t i o n o f chang ing pa r t o ft h e f s. RP c u r ve a t o n e -h a l f t h e c o s t . The f s. RP cu rve can a l so bes h i f t e d h o r i z o n t a l l y and v e r t i c a l l y by a d j u s t i n g t ri m n e r p o te n ti om e te rs i n -c lu d ed i n t h e c i r c u i t . The a c tu a l o u t pu t o f t h e f i e l d c o n t r o l l e r i s shownsuper imposed over the ideal f s. RP c urv e i n F i g u r e 2.


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.-.- . . .--- - -.- . .-.- - -, .

..

.- - - --- ----III

-- ... -

I ---.. ..-- ,. Tg - ... . -- . . . - - j7 -L ,.--.., 1I." ?< r - , y.. -I-:.; c;, -.-. kcr 0 I....--- L-C . : j 7 I

\ LJ;_. I -... ; --LLJ clj i .A 2 : I I.\ / W c ; Z ,g a t I c .< A t ic i Ioi u 4 f f c * Ii. i IjIi

I I ...j


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APPENDIX I : Determination of the Memory Bit Structure

In order t o determine the proper b i t pa tt ern t o be programmed int o thememory to match the If vs. RPM curve, i t was necessary t o f irs t determinethe output current of the field controller circuit for every possible value ofa memory word. Since each word con ta ins 8 b i t s of information, each word canhave 256 different values. To find the output curr ent t ha t would re s ul t fo reach of the 256 possible combinations of bits in a word, the following testswere run. ( r e fe r to drawing kSH-1-03.01.03, Fie ld Control er , Memory Simula-t io n Te st ) The memories were simulated with s p t switches that connectedeach input of the di gi ta l t o analog converter t o ei th er +5 volts ( logical 1)or ground (lobical 0). Then the swi tches were s e t fo r a l l of the 256 possiblecombinations of the b i t s , and with an ammeter, th e re su lt in g cur rent deliveredto the generator field for each combination was recorded. Cornb-ining ther es ul ts of the memory simulation t e s t with a li st i ng of the rpm range that eachmemory word would cover, and the ideal If vs. RPM curve, the proper memorycontents t o generate the desired shape for the I f vs. rpm curve were determined.A copy of the b i t s tr uc tu re i s shown in Table 1. The memories were programmedusing the Signetics 8223 Programming Procedure A a copy of which i s provided.


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RPV RP :E MLMrJhY PIrhESS 89 MFMGhY CCvPJ IFN------- . m 53 L rl0 - 29 0 . .0 0 3 0 . .---- . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

29 5 7 i : - ;>. c . .

5 7 86 0---------------.-.----. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .86 4 3 a G i .I> 3 . J ~I...-....---------------.---.----.---


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-S l G NE T l CS D I G I T AL 8 S E RI ES T T L / MS I -8 2 2 3

~- ~-

8 2 2 3 P RO G RAM MI NG P RO CE DURETl~cs ; :3 I ~ I I ~ ~ r1o(ll;1n1rr11~0l y 11511111 ( : t ~ r t ~


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UNNERSlTY OF M A S S A C i : ; I S m / M H mENERGY MTERNAtlVES PROGRAM


A GENERAL DESCRIPTION OF THE BLADE-PITCH CONTROLLER

yBruce A Caccamo

U M ass. i nd FurnaceE n e r g y A l t e r n a t i v e s P r o g r a mU n i v e r s i t y o f M a s s a c h u s e t t sAmherst Massa chuset ts 01002

TR/76/ 6Appendix V I I I


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GENERAL DESCRIPTION OF THE BLADE-PITCH CONTROLLER

A b s t r a c tThe b l a d e - p i t c h c o n t r o l l e r p r o v i d e s f o r maximum e n e rg y t r a n s f e r b etw ee n

t h e w in d and t h e w i n d m i l l u n d e r v a r y i n g w in d c o n d i t i o n s . The p u rp o se o f t h i sp a pe r i s t o d e f i n e t h e n e ce ss ar y r e g i o n s o f c o n t r o l an d t h e method s w h i chp e r m i t s t a b l e o p e r a t i o n t h ro u g h b l a d e - p i t c h c o n t r o l .

The b l a d e - p i t c h c o n t r o l l e r p r o v i d e s f o r maximum e n e rg y t r a n s f e r b etw ee nt h e wi nd and t h e w i n d m i l l u n de r v a r y i n g w in d c o n d i t i o n s . I n o r d e r t o u nd er -s ta n d how t h e c o n t r o l l e r does t h i s , we m us t f i r s t l o o k a t t h e o v e r a l l s t r u c t u r e .

The w in d m i l l i s f r e e t o r o t a t e i n yaw o n a p l a t f o r m so t h a t t h e b la de sa r e a lw a ys f a c i n g i n t o t h e w in d. T h re a r e t h r e e b la d es , w h ic h a r e c o n t r o l l a b l ei n p i t c h . The r o t o r i s c on ne cte d th r o ug h a speed-up d r i v e t o a 25 kW gene r a t o r .

R e l a t i v e t o wind speed t h e r e a r e f o u r d i s t i n c t r eg i on s o f p i t c h c o n t r o l . I nr e g i o n 1 0 -5 mph) t h e p i t c h c o n t r o l l e r w l l be c a l l e d upon t o p o s i t i o n t h eb la de s a t an a n g le o f a t t a c k w h ic h w i l l p r o v id e t h e g r e a t e s t s t a r t i n g t o rq u e.F o r th e s e w in d s pee ds, t h e p i t c h a n g l e i s s e t a t m in u s e i g h t de gre es . I nr e g i o n 2, 5 -2 6 mph) t h e c o n t r o l l e r w l l m a i n t a i n t h e p i t c h a n g le a t m in use i g h t de gre es . T h i s w i l l b r i n g t h e ge n e ra t or up t o speed i n t h e s h o r t e s tp o s s i b l e t i m e a n d w l l d e l i v e r t h e maxim um power a t any g i ven w i nd speed. I nr e g i o n 3 26 - 45 m ph) t h e c on t r o l l e r m a i n t a i ns t h e g ene r a t o r speed a t 1800 RPM.W i th o u t t h e c o n t r o l l e r , t h e g e n e ra t or wo uld ov ers pe ed a nd t r i p o f f t h e l i n e .I n r e g i o n 4 above 45 mph) t h e c o n t r o l l e r h as t o f e a t h e r t h e w i n d m i l l b l a d e s .T h i s a mounts t o s h u t t i n g down t h e s ys te m t o p r e v e n t d e s t r u c t i o n u nd e r h i g h w in d s .


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Thr ough com pu t e r ana l ys i s , t h e p ow er o u t p u t c u r v e h as b een r e l a t e d t op i t c h a n g l e t h ro u g h t h e t i p speed r a t i o s ee b l a d e - p i t c h s c h ed u le , F i g u r e 1 ) .The t i p speed r a t i o nR /V ) i s t h e a c t u a l c o n t r o l s i g n a l u sed i n t h e p i t c h -c o n t r o l c i r c u i t r y t o r e pr e se n t th e d e si re d p i t c h a ng le .

As t h e f o u r c o n t r o l r e g io n s a r e t ra n s v er s ed , t h e t i p speed r a t i o w i l li n c r e a s e f r o m 0 t o 7 and the n decrease t o 0 . As w ind speed i nc r eas es f r om0 -5 mph, t h e t i p speed r a t i o i n cr e a s e s u n t i l t r eaches 7 . T h i s p o i n tr e p r e s e n t s t h e b e g i n n in g o f r e g i o n 2 wh ere g e n e r a t o r RPM w i l l i n cr e as e w i t hi n c r e a s i n g w in ds pe ed . T h ro ug ho ut t h i s r e g i o n t h e b l a d e p i t c h w i l l be m a i n t a i neda t ~ i l in u s i g h t deg ree s w h ic h i s e q u i v a l e n t t o Q R / V = 7 A t 26 n lph the generatorw i l l re ac h ra t e d RPM, and i i R / V w i l l s t a r t t o d e cr ea s e as w i n d sp ee d i n c r e a s e s .T h i s o cc u r s be ca us e t h e t a c h om e t e r o u t p u t i s cla mp ed a t 20 v o l t s . Thus, asw ind speed i nc reases , nR/V w i l l dec r ease and b l ade - p i t ch w i l l i n cre as e u n t i lr e a c h i n g t h e f e a t h e r e d p o s i t i o n a t a w in ds pe ed o f 4 5 mph. t shou ld be no tedt h a t t h e c o n t ro l 1er can be commanded t o f e a th e r sooner i f d e si re d see Dwg.03.02.01 ) .

The p i t c h c o n t r o l l e r i s a c t u a l l y a p ul s e -w i d th m od ula te d P W ) t r a n s i s t o rsw i t c h i ng am p l i f i e r . see Dwg. 03. 02 .01 ) t uses a DC power s upp ly wh icht h e a m p l i f i e r s w it ch e s on and o f f a t a f i x e d f re q ue n cy . The w i d e r t h e w i d t hof t h e d r i v i n g p u ls e ; t h e h i g h e r w i l l be t h e a ve ra ge c u r r e n t d e l i v e r e d t o t h em o t o r; and t h e f a s t e r t he m o t o r w i l l t u r n . PWM p r o vi d es a c o n t in u o u s f i n ec o n t r o l o f t h e p i t c h an gle .

P ul s e - w i d th m o d u l a t io n i s o b t a i n e d b y c om p ar in g t h e d e s i r e d p i t c h a n g l es i g n a l n R/V ) w i t h a t r i a n g l e wave. The t r i a n g l e wave i s o b t a in e d by i n t e -g r a t i ng a squa r e w ave . The l e n g t h of t im e i n w h ic h t h e v o l t a g e l e v e l o f t h e


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t r i a n g l e wave i s g r e a t e r t h a n t h a t of R V d ete rm in es t h e w i d t h o f t h e d r i v i r ~ gp u l s e s e e F i g u r e 2 ) . s i m i l a r c o m p a ri so n i s made be tw ee n t h i s same t r i a n g l ewave an d a fe ed ba ck s i g n a l w h ic h r e p r e s e n t s t h e a c t u a l p o s i t i o n o f t h e b l a d e s .These tw o pu l s e - w i d t h m odu la t ed s i gn a l s a r e t hen compared t he y a r e 180 deg reeso u t o f p hase w i t h each o t h e r ) ; th us , p r o v i d i n g t h e d r i v i n g s i g n a l f o r t h emotor . The moto r w i l l t u r n i n t h e d i r e c t i o n w h ic h w i l l e q u a t e t h e a c t u a la n g l e w i t h t h e d e s i r e d a n gl e.


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> :n l . l

ENERGY LTERN TIVE PROGR MUNIV ERSITY OF M SS CHUSETTS


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UNN RSITY OF MASACHUSElTS AMHERSTENERGY ALTERNATIVES PROGRAM

UNIVERSITY O MASSACHUSETTS/AMHERSTENERGY ALTERNATIVES PROGRAM

PRELIMINARY REPORTTHERMAL SYSTEMS

W I N FURNACE PROJECT

Jon G. McGowanandG h a z i D a r k a z a l l

U.Mass. Wind FurnaceE n er gy A l t e r n a t i v e s P ro gr amU n i v e r s i t y o f M as sa ch us et tsAmhers t Massa chuse t ts 01 002

A p r i l 1 9 7 5

TR/76/ 7Append ix


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Work in the area of thermal systems can be divided into two categories:analytical model ing work and experimental work. The analytical modeling hasformed the basis for the experimental design a n d a summary of i t s keypoints follows. With the completion of the economic p a r t of t h i s work,a more detail ed technical rep ort on th i s subjec t will be iss ued. )1. N L Y T I C L MODEL

A. Description of the Overall System ConfigurationThe an al yt ic al model i s based on a mathematical simulation using

a d ig i ta l computer t o determine the feasibility and performance ofusing w-ind heating systems fo r home heating a n d domestic hot waterdemands. Also, the poss ibi l ity of combining the wind systems with afl at -p la te s ola r col lec tor sub-system i s investig ated. The basic windenergy input component for a l l systems i s a horizonta l ax is wind machine.

The performance of the heating systems, for a given s i t e andweather condi tions , i s studied as a function of the following keysystem parameters: 1 the wind genera tor blade diameter, 2 the windgenerator tower height, 3 the s iz e of the res ide nti al heating del iverysystem, 4 the siz e of the sol ar co lle ct or , and 5 the s iz e of the thermalstorage water tank. det ail ed economical ana lys is of the to ta l co st ,for each of the systems studied wil l be based on the assumption of massproduced unit manufacturing. The description of the different systemmodel s fo l 1ows.

Model I i s the simples t windpower system Fig. 4 . 1 . I t has no energystorage and el ec tr ic al energy i s delivered t o the house directly from the


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s t o r a g e t a n k t o t h e h ou se . When th e t e mp e ra tu re o f t h e s o la r s t o ra g ei s l e s s t h an t h e d e s i r e d l o we r l i m i t t h e n t h e s y s t e m w i l l d e l i v e r e n e r g yf r o m t h e w i n d s t o r a g e t a n k . The t wo s t o r a g e t a n k s a r e c o n ne c te d t oe ac h o t h e r v i a a m i x i n g pump w hi c h i s u s ed when t h e t e m p e r a t u r e o f o n eo f t h e s t o r a g e ta n ks i s h i g h e r t h a n t h e u pp e r l i m i t .

5 ) Domes t ic Ho t Wate r Node l .T h i s model i s used, i n c o n j u n c t i o n w i t h t h e p r e v i o u s m ode ls , t o

i n v e s t i g a t e t h e p o s s i b i l i t y o f u s i n g t h e w in d and s o l a r sys tem s t op r o v i d e t h e d om e st ic h o t wa te r r e q u ir e m en t o f a r e s i d e n t i a l home.

B. Sys tem Componen ts Desc r lp t ionS i nc e t h e o v e r a l l sy stem p er fo rm an ce i s a f u n c t i o n o f ea ch i n d i v i d u a l

c ompo ne nt , a d e ta i l e d p h y s i c a l mo de l and ma th e ma t i c a l a n a l y s i s h as b ee nd ev e lo p ed f o r t h e f o l l o w i n g b a s i c co mp on ents: t h e e l e c t r i c w i n d g e n e r a t o r ,t h e f l a t - p l a t e s o l a r c o l l e c t o r , t h e th er m al wa te r s to r ag e t an k, t h ehouse, and th e baseboard he at exchangers . A lso, t i n c l u de s a d e r i v a t i o no f t h e maximum w in d po w er d e l i v e re d b y a w in d g e n e ra to r a s a f u n c t i o n o ft h e w in d v e l o c i t y , g e n e r a t o r b l a d e d i am e t e r, and g e n e r a t o r e f f i c i e n c y .I n a d d i t i o n , based on a v a i l a b l e da ta , t h e u s e f u l s o l a r e n er gy i s de te rm i ne d .A l s o , a n e n er gy b al a nc e e q u a t i o n f o r t h e c o n t r o l v o lu me a ro u n d a s to ra g et a n k i s d e r i v e d . The h o u r l y h e a t i n g demands a r e c a l c u l a t e d u s i n g b a s i cp r in c ip l e s o f thermodynamics and hea t t r an s f e r , and s tan dar d ASHRAEp r a c t i c e . The am ount of h e a t t r a n s f e r r e d t o t h e house b y t h e h e a t d e l i v e r ysys te m i s c a l c u l a t e d a s a f u n c t i o n of t h e s i z e and c h a r a c t e r i s t i c s o f t h ei n t e r n a l h e a t ex c ha n ge rs .


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C D i g i t a l C om puter A n a l y t i c a l M o de lsBecause o f t h e v a r i e t y o f m od els t e s t e d and t h e number o f d i f f e r e n t

com ponent c o n f i g u r a t i o n s t h e c om p ut er m o de ls i n c l u d e s t h e f o l l o w i n gprogram and sub-programs: 1 ) a m ai n p ro g ra m w h i ch s p e c i f i e s t h e m o de l,t h e system c o n f i g u r a t i o n , and t h e i n i t i a l c o n d i t io n s o f t h e v a r i o u scomponents. A l s o , t h e p ro gra m c o mbine s t h e o th e r s u b -pro gra ms t o d e te rm in eth e s y ste m p e r fo rma n c e F ig . 4.5) , 2 ) a d a ta s u b -p ro g ra m w h i c h i n c l u d e st h e we at he r a nd s o l a r d a t a f o r a g i v e n s i t e , 3 ) a w in d su b -p ro g ra m t h a tc a l c u l a t e s t h e w in dp ow er a v a i l a b l e , 4 a s o l a r s ub -pro gra m t h a t c a l c u l a t e st h e u s e f u l s o l a r en e r gy a v a i l a b l e t o t h e house, 5 ) a l o a d su b- pr og ra m wh i chc a l c u l a t e s t h e h ou se h e a t i n g l o a d , 6 ) a hea t exchanger sub-program wh ichc a l c u l a t e s t h e e n e r g y d e l i v e r e d by t h e b as eb oa rd h e a t e r s , a nd 7 ) a h o tw a te r s u b - ro u t i ne t h a t d e te rm i ne s t h e e n er gy d e l i v e r e d b y t h e sys te m i na f o rm o f d o me s t i c h o t w a te r . T he u s e o f a s p e c i f i c s u b -p rog ram d e pe nd so n t h e s y st em c o n f i g u r a t i o n o f t h e m od el t e s t e d .

D S ys te m P e r forma n ce a nd A na l t y i c a l R e s u l t sA summary o f t h e m o st i m p o r t a n t a n a l y t i c a l r e s u l t s f o r t h e v a r io u s

m o d e l s p r e v i o u s l y d i s c u s s e d f o l l o w s . The r e s u l t s a r e b ased o n m a i n t a i n i n gt h e house i n s i d e t e m pe r at u re a t 68OF. A l l sys tem s a r e t e s t e d f o r b o t h t h eavera ge and model homes by va r y in g key sys tem param eters suc h as:

1 ) w i n d g e n e r a t o r b l a d e d ar n e te r2 ) w i n d g e n e r a t o r t o w e r h e i g h t3 ) w a t e r s t o r a g e t a n k s i z e4 t h e h e a t d e 1 iv e r .y s ys te m s i z e5 s o l a r c o l l e c t o r s i z e


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T a b l e 4. 1 r e p r e s e n t s a m o n t h l y sum nary o f t h e h e a t i n g l o a d o f b o t hthe average and model hal ies based on the weather data f ro111 art fordConn. F igure 4.6 r e p r e s e n ts t y p i c a l m o n th l y v a lu e s o f th e a ve ra g ehome ene rgy r equ i r em en t s and t he i n p u t o f t h e w i nd and so l a r sys tem s.The r e p r e s e n t a t i v e w in dp ow er o u t p u t shown i n t h e f i g u r e i s b ase d on a3 2.5 f o o t b l a d e d ia m e t e r w i n d g e n e r a t o r p l a c e d on an 80 f o o t h i g h t o w e r .The s o l a r e ne rg y i n p u t i s g i ve n f o r a 200 s qu are f o o t f l a t p l a t e s o l a rc o l l e c t o r , m oun te d v e r t i c a l l y o n t h e s o u t h w a l l o f t h e h ou se. Due t ot he i n t e r a c t i o n be tween t h e sys tem com ponen ts , and o t h e r l oss es , t heamount o f s o l a r a nd w i nd e n erg y t h e s ys te m d e l i v e r s t o t h e h ouse i sl e s s t h a n t h e e n er gy i n p u t s shown i n t h e f i g u r e . To d e te r m in e t h e e x a c tam ount o f u s e f u l e n e rg y d e l i v e r e d b y t h e s y st em an h o ur -b y -h o ur a n a l y s i si s p e rf orm e d u s in g t h e a n a l y t i c a l m odel d e s c r ib e d p r e v i o u s l y .

To de t e r m i ne and compare t h e per fo rm ance o f t he p r ev i o us l y desc r i bedmo dels , a par am et er (Qaux/Qtotal ) i s d ef in ed a s th e r a t i o o f t h e en erg yd e l i v e r e d t o t h e house from a n a u x i l i a r y s ou rc e t o t h e t o t a l house h e a t i n gene rgy r equ i r em en t s . Th r oughou t t he pas t yea r , a l a r ge num ber o fc a n p u t e r ru n s f o r t h e H a r t f o r d w i n d d a t a an d B l u e H i l l s , M ass. s o l a rdata were per formed. Th i s pa r am e t e r se r ves t o m easure t h e ene r gy pe r f or m anceof t h e va r io us sys tems, and a s a m a j o r i n p u t t o f u t u r e s ys te m ec on om ics t u d i e s . F i gu re 4 .7 shows per fo rmance f o r t he w ind ge ne ra t or sys temw i t h o u t s t o r a g e ( Y o de l 1 ) as a f u n c t i o n o f w in d g e n e r a t o r b l a d e d i a m e t e rand t ower he i gh t ( l ow e r 1 nes o f each band r ep r es en t 100 f t t o w e r h e i g h t s ) .The p e rfo rm a nc e o f t h e win dp ow er h e a t i n g s ys te m w i t h w a t e r t h er m a l s t o r a g e i ss um m ariz ed f o r v a r y i n g s t o r a g e s i z e s a nd b l a d e d i a m e t e rs i n F i g u r e s 4 .8and 4.9.


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otal0.6

NO ENERGY STORAGESYSTEM

TOWER HEIGHTS 60 to I f t .

AVERAGE RESIDENCE

MODEL HOME)

BL DE DI M ETER FT


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Th e mo d e l l i n g o f t h e c o mb i n e d w i n d a n d s o l a r h e a t i n g s y s t e m o b v i o u s l yopens up th e poss i b i 1 y o f v a r y i n g mo re sy s te m p ar a me te r s, t h u s t t a k e smore g raphs t o show t h i s sys tem s pe rformance. F i g u r e s 4.10 t o 4 .1 7s ummariz e a s e r i e s o f r u n s f o r t h i s s ys te m. F i g u r e 4.10 g i v e s r e s u l t sf o r t h r e e h ouse h e a t in g l oa d s and v a ry i n g c o l l e c t o r s i z e , w i t h t h es y s t e m a l s o s u p p l y i n g 50 g a l l o n s o f h o t w a t e r p e r day . Figure 4 .11shows t h e e f f e c t o f s t o r a g e s i z e a nd b l a d e d i a me t e r o n s ys te m pe rf o rma n c e.F i g u r e s 4.12 t o 4.14 p r e s e n t r e s u l t s f o r 3 d i f f e r e n t to we r h e i g h t s v a r y in gb l a d e d i a me t e r a nd c o l l e c t o r a r e a . F i g u r e s 4.15 t o 4.1 7 r e p r e s e n t a n o t h e rway o f s h ow in g th e s e r e s u l t s .

The two tank storage system (Model 3B p e rf or m an c e i s s

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