performances of vertical axis wind turbines with

8/14/2019 Performances of Vertical Axis Wind Turbines With

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Journ al of W ind Enginee ring and Industrial Aerodynamics, 39 ( 1992 ) 83-93Elsevier Science Publishers B.V., Amsterdam - - Prin ted in The Netherlands 83

e r f o r m a n c e s o f v e r t ic a l a x is w i n d tu r b i n e s w i t hd i ff e r en t s h a p e sM a r t i n o M a r in i A r i s ti d e M a s s a r d o a n d A n t o n i o S a t taDipartimento di Ingegneria E nergetica, V ia Montallegro 1, 16145 Genoa, Italy

S u m m a r yDifferent types of vertical axis wind turbines (VAWT) are presented and compared as regardsthe ir aerodynamic performances. A blade with a given airfoil section and length can be fastenedto spokes in several ways giving rise to many configurations. Two models are used in the analysisof Darrieus turbines: t he single streamtube momentum model and the free wake vortex model.The former is more suitable to carry out an extensive study because of its short CPU time, thelatter, which guarantees the best accuracy, can be used to verify the most significant results. Thediagrams of the average coefficient of power and of the power for a given speed of the attackingwind are shown. The work-exchange between the wind flow and the machine is investigated bydefining an internal efficiencyof the wind turbine.

N o m e n c l a t u r eA - s w e p t a r e a o f t h e r o t o r ;c l - f r e e s t r e a m w i n d s p e e d ;C D = b l a d e d r a g c o e f f i c i e n t ;C L ffi b l a d e l i f t c o e f f i c i e n t ;- - - P / ~Qc l ,p p o w e r c o e f f i c i e n t : ~ 3 .H = D a r r i e u s r o t o r h e i g h t ;i - - a n g l e o f i n c i d e n c e ;

- b l a d e c h o r d ;L = b l a d e l e n g t h ;N = n u m b e r o f r o t o r b l a d e s;P = p o w e r ;R m .x - D a r r i e u s r o t o r m a x i m u m r a d i u s ;R o = r e f e r e n c e r a d i u s ;R e = R e y n o l d s n u m b e r : Owl / ;w - r e l a t i v e s p e e d ;

- - t i p s p e e d r a t i o : ~ 2Rm ax/Cl;~ ' = t i p s p e e d r a t i o : ~ R o / c l ;~/ - e f f i c i en cy ;/z - - a i r d y n a m i c v i s c o s i ty ;

0167-6105/92/ 05.00 1992 Elsevier Science Publishers B.V. All rights reserved.


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84

0a2

= a i r d e n s i t y ;= ro tor sol id i ty : Nl Rmax;= b lade angu la r ve loci ty .1 I n t r o d u c t i o n

T h e p e r f o r m a n c e o f a w i n d t u r b i n e is u s u a l ly e v a l u a t e d t h r o u g h t h e a v e r a g ecoef fic ien t o f pow er Cp, by re fe r r in g the ob ta in ab le pow er to the w ind k ine t i ce n e rg y fl u x a n d t o i ts n o r m a l s e c t i o n s w e p t b y t h e w i n d . S u c h a p a r a m e t e r i ss i g n i f i c a n t b e c a u s e i t c h a r a c t e r i z e s a m a c h i n e w i t h a g i v e n g e o m e t r y a p a r tf rom it s ac tua l d ime ns ions ( sca le fac to r ) an d f rom the w ind speed c l. However ,i t is u s e fu l t o i n t r o d u c e t w o o t h e r p a r a m e t e r s i n o r d e r t o s p e c if y t h e t e r m s o ft h e c o m p a r i s o n a m o n g t u r b i n e s w i t h d i f fe r e n t sh a p e s . A f i rs t p a r a m e t e r i s t h ep r o d u c t C p A o r i t s n o n d i m e n s i o n a l f o r m ( P s ) , o b t a i n e d b y d i v i d i n g b y t h es q u a r e o f t h e b l a d e l e n g t h L Ps=CpA/L2). P r o b a b l y t h e b l a d e l e n g t h i s o n eo f t h e m a i n d a t a t h a t c o n t r i b u t e t o t h e c o s t o f t h e b l a d e i t s e lf a n d o f t h e w h o lem a c h i n e .T h e s e c o n d p a r a m e t e r i s t h e i n t e r n a l e f f i c i e n c y w h i c h c o r r e s p o n d s t o t h er a ti o b e t w e e n t h e Cp o f a r e a l t u r b i n e a n d t h e C p o f t h e s a m e t u r b i n e t h a topera tes wi th ou t any f r ic t ion .T h e o b j e ct o f t h e p r e s e n t w o r k i s t h e a n a l y s i s o f d i f fe r e n t c o n f i g u r a ti o n s o ft h e V A WT . T h e c o n d i t i o n s f o r t h e c o m p a r i s o n a r e t h e w i n d s p e e d a n d t h eb l a de l e n g t h , t h e l a t t e r b e i n g o n e o f t h e m o s t s i g n i f i c an t c o s t i t e m s i n t h ep r o je c t o f t h e m a c h i n e r o to r . T h e s t u d y o f t h e p e r f o r m a n c e s o f t u r b i n e s w i t hvar ious geomet r ica l shapes p rov ides no t on ly use fu l sugges t ions dur ing thep r o je c t d r a f t i n g b u t a ls o e n a b l e s u s t o c o n c ei v e v a r ia b l e g e o m e t r y m a c h i n e st h a t s a ti s fy t h e r e q u i r e m e n t s o f u s e rs .2 C a l c u l a t io n p r o c e d u r e s

T h e r e a r e s e v e r a l m e t h o d s t o e s t i m a t e V A W T p e r fo r m a n c e s , a c l a ss i fi c a ti o nof the m i s repo r ted in [ 1 ,2 ] .T h e m o m e n t u m m o d e ls , b y a v a i li n g t h e m s e l v e s o f th e a c t u a t o r d i s k t h eo r y ,can p red ic t overa l l VAWT per fo rmances in a s imple and fa i r ly accura te way .Th e accuracy inc reases i f the s ing le s tream tube s ing le ac tua to r d i sk bas ic mode lis r ep l a ce d w i t h m o r e c o m p l e x m o d e l s w i t h s e v e r a l s t re a m t u b e s , e ~c h o f t h e minc lud ing two or mo re ac tua to r d i sks .A d e t a i le d s t u d y o f t h e f lo w f ie ld n e a r t h e t u r b i n e c a n b e c a r r i e d o u t o n l y b ym a k i n g u s e o f m o r e s o p h i s t i c a t e d m e t h o d s , e s p e c i a l l y t h e f r e e w a k e v o r t e xm o d e l [ 3 ]. T h e c o m p u t a ti o n a l ti m e r e q ui re d b y th e l a st m e t h o d m e n t i o n e d( V D A R T ) c a n b e c o m e v e r y l o ng , b e c a u s e th e c a l c u l a t i o n m u s t b e r e p e a t e d f o rsevera l comple te revo lu t ions o f the ro to r un t i l the s teady f low cond i t ion i sreached.


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85T h e mo d e l s u s u a l ly u ti l iz e d i n t h e s tu d y o f VA W Ts a r e i n v is c id . On e n e e d sto k n o w th e e x p e r im e n ta l v a lu e s o f t h e a e ro d y n a mic c o e f fi c ie n t s CL a n d CD fo rth e a c tu a l a i r fo i l se c t io n t o t a k e i n to a c c o u n t f r i c ti o n e f f e c ts i n t h e wo rk -e x -c h a n g e b e twe e n b l a d e a n d win d f l o w . T h e l i ft a n d d r a g c o e f fi c ie n t s a r e i n flu -

e n c e d , a s we k n o w, b y t h e Re y n o ld s n u m b e r (Re ) a s we l l a s b y t h e i n c id e n c ea n g le ( i ) . Th e a b o v e m e n t io n e d c a l c u l a t i o n p ro c e d u re s n e g l e c t t h e a c tu a l v a r i-a t i o n s o f R e e v e n t h o u g h i t w o u l d b e p o s si b le t o i n s e r t s u c h a p a r a m e t e r w i t h i nt h e s e m i e m p i r i c al p r o ce d u re s , m a k i n g t h e m v e r y c o m p l ex .

2 1 Reynolds num ber influenceTh e in f lu e n c e o f Re u p o n b o th t h e a e ro d y n a m ic a c t i o n c o e ff ic i en t s i s r e -m a rk a b le , a s w e k n o w, fo r h ig h in c id e n c e a n g le s ( i = 8 -2 0 ) i n t h e s t a l l z o n e(F ig . 1 ) . Th e e f f e c ts o f Re o n V AW T p e r fo rm a n c e s a r e p o in t e d o u t i n F ig. 2w h e r e t w o c u r v es o f Cp f o r t h e s a m e t u r b in e , o b t a i n e d f r o m t h e m o m e n t u mm o d e l b y a s s u m i n g t w o d i f fe r e n t R e n u m b e r s , a r e d r a w n .T h e r a n ge w i t h i n w h i c h R e v a r i e s f o r lo w a n d m e d i u m s iz e a n d p o w e r t u r -b in e s ( 5 < R < 2 0 m ) i s q u i t e w ide : f ro m 0 . 2 8 1 06 to 6 . 6 106 fo r l ow s o lid i tyt u r b in e s ( ~ = 0 . 1 5 ) , f r om 0 .5 4 10e t o 1 . 1 107 fo r h i g h s o l i d i t y ( ~ = 0 . 4 ) t u r -b in e s . Th e c a l c u l a t i o n fo r t h e h ig h e s t v a lu e s o f t h e t i p t o w in d s p e e d ra t i o (A)shou ld be re fe r red to th e coef f ic ien ts o f Re = 1 .8 106 , whi le the lowes t va luesof Yt shou ld be re fe r red to th e lower va lue o f Re . Bes ides , in d raw ing up a p ro jec tu n d e re s t ima te d s o lu t i o n s a r e p r e f e r a b l e . Th e re fo re , b e a r in g i n min d a l s o t h es u g g es t io n s o f o t h e r a u t h o r s [ 5 ] a n d t h a t t h e m a i n i n t e r e s t o f t h e p r e s e n t w o r k

1.5A - - - R e : 1 .8 1 0'1

' I . . . . . : ; i l l . . . . . . . . . . . . 1

0.5

O. o. lo. ~o. i( )

Fig. 1. Reynolds number influence on CL and CD coefficients for NACA 0012 airfoil.


4/11

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0 . 20 . 1O .

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0 3 l O ~ l

2. 3 . 4 . 5 . 6 . 7 . ~ .

F i g 2 . R e y n o l d s n u m b e r in f l u e n c e o n c y l i n d r i c a l V A W T c h a r a c t e r i s ti c .

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F i g 3 C h a r a c t e r i s t i c c u r v e s f o r d i f f e r e n t o l i d i t y y l i n d r i c a l u r b i n e s a c c o r d i n g t o m o m e n t u m a n dv o r t e x m o d e l

l ie s i n t h e c o m p a r i s o n o f d i f f e r e n t c o n f i g u r a t i o n s o f w i n d t u r b i n e s , o n l y t h el o w e r v a l u e o f R e h a s b e e n r e fe r r e d t o t h r o u g h o u t t h e s t u d y r e l a t e d h e re .2.2. Compar i son of VA T computat ional methodsT h e s i m p l i f ie d m o m e n t u m m o d e l , a s sh o w n b y th e a u t h o r s i n [ 2 ] , g i v e sr e li a b le r e s u lt s a s l o n g a s t h e V A W T s o l id i t y ~ a n d ~ p a r a m e t e r a re l o w . T h er e su l ts o f th e c o m p u t a t i o n a l m e t h o d s b a s e d o n m o m e n t u m a x id v o r t e x m o d e l sconcern ing a cy l indr ica l turb ine are near ly co in c iden t F ig . 3 ) for a = 0 .15 w i th int h e w h o l e /~ r a n g e , a n d , f o r ~ = 0 . 4 u n t i l 2 < 3 ; w h i l e t h e y d r a w a w a y f o r h i g h e rv a l u es o f ~ i n t h e l a st c as e. W h e n t h e b l o c k a g e in d u c e d b y t h e V A W T i s s os tr o n g , a c c o rd i n g t o t h e m o m e n t u m m o d e l, t h a t t h e d o w n s t r e a m v e l o c it y b e -c o m e s n e g a t iv e , t h e p r e d i c t io n o f t h e s i m p l e m o d e l i s m e a n i n g l e s s . T h i s s i tu -a t i o n t a k e s p l a c e o n t h e r i g h t o f t h e a s t e r i s k o n t h e c o n t i n u o u s c u r v e j u s t w h e r et h e p r e d i c t i o n s o f th e m e t h o d s d o n o t a g r e e d e f i n i te l y .

T h e d i f fe r e n c e b e t w e e n t h e m o d e l s r e s u l ts i s m o r e e v i d e n t fo r c u r v e d b l a d e


5/11

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~ '5 K \ , iI i I ' / " // \ ,0 .1~__ .C_~L-,4-- _ ~ _ ~

o . . . . . . . . . 11 O = 0 . 2 7- - 0 , 1 ~ L _1. 2. 3. 4. 5.

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Fig . 4. Charac te r is t ic curves for d i f fe rent so l id i ty parabol ic turb in es accord ing to m om en tu m andvor tex model .v e r t i c a l a x is t u r b i n e s . T h e s p e e d o f t h e w i n d t h a t i s a t t a c k i n g t h e t u r b i n e b l a d echang es n o t o n ly in a s t ream wise d i rec t ion [ 2 ] , bu t a l so in a ve r t i ca l d i rec t ionf r o m t h e c e n t r a l p a r t o f t h e b l a d e w i t h t h e l o n g e s t r a d i u s a n d a h i g h p e r i p h e r a ls p e e d t o t h e e x t r e m e p a r t s w i t h v e r y s h o r t r a d i i a n d v e r y lo w p e r i p h e r a l s p ee d .T h e m o m e n t u m m o d e l d r a w s a n a v e r a g e s pe e d, t o b e a t tr i b u t e d t o t h e e n t i r erotor , th a t i s even v ery di f feren t f ro m the local value s of speed, i f i t i,s h ighlyv a r y i n g n e a r t h e V A W T .In F i g. 4 t h e C p -~ c u r v es o b t a i n e d b y a p p l y in g b o t h t h e m e t h o d s t o a p a r a -b o l i c V A WT H / R m a x = 2 ) a r e c o m p a re d . T h e s in g le s tr e a m t u b e m o m e n t u mmo de l p roduces re l iab le resu l t s fo r low so l id ity m ach ines fo r any va lue o f ;t,tho ug h i t t en ds to overe s t ima te Cp, whi le i t i s unre l iab le i f so l id i ty i s h igh . T hemo de l i s accura te fo r m edium and h igh va lues o f ap rov ide d th a t ~ is low (/~ < 3 -3 .5) .I f A > 3 . 5 fo r a m e d i u m ( a = 0 . 2 7 ) o r h ig h ( a = 0 . 4 ) s o li di ty t h e m e t h o d isi n a c c u r a t e a n d e v e n i n c o n s i s t e n t ( se e t h e a s t e r i s k s ) . S i n c e t h e c o m p u t a t i o n a lt i m e r e q u i re d b y t h e s i m p l e m o m e n t u m m o d e l is v e ry s m a l l i f c o m p a r e d t o t h evor tex mode l , i t w i l l be ch ie fly em ployed to d raw the charac te r i s t i c cu rves o ft h e w i n d t u r b i n e s c o n s i d e re d b e lo w a l so t a k i n g i n t o a c c o u n t t h e f a c t t h a t c a l-c u l a t io n s r e g a r d c o m p a r i s o n s a m o n g d i f fe r e n tl y s h a p e d V A W T s . H o w e v e r, f ol-l o w in g w h a t h a s b e e n d e d u c ed f r o m t h e c o m p a r i s o n o f t h e a v a il a b le m e t h o d s ,some imu or tan t po in t s wi l l be rep ea ted by us ing the h igh ly re li ab le vor tex m ode lwh ich a l lows the overa l l ca lcu la t ions co ncerned he re to be ve r if ied .3 I n t e r n a l e f f i c i e n c y

T h e c y l in d r ic a l a n d t h e D a r r ie u s ( w i t h a p p r o x i m a t e l y p a r a b o li c b l a d e s ) t u r -b i n e s t o g e t h e r w i t h t h e c o n i c a l o n e s a r e f u n d a m e n t a l V A WT c o n f i g u r a t i o n st h a t h a v e b e e n c o n v e r t e d f r o m p r o je c t s i n t o p o w e r p l a n t s s o fa r. O t h e r p o s s ib l ec o n f i g u r a ti o n s c a n b e c o n c e i ve d a n d t h e a e r o d y n a m i c a d v a n t a g e s c a n b e i n -


6/11

88

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vor te x rood - Q - - -m o m e n t u m m o d. - - -r 1

2 , 3 . 4 .

1 cy l . tu r b .[ ] 2 Dar . tu rb .

5 6 7

F i g . 5 . I n t e r n a l e f f i c e n c y o f c y l i n d r i c a l a n d p a r a b o l i c t u r b i n e s .

vest igated by ca lcu la t ing thei r coeff ic ien ts Cp an d P~ and the i r in te rna l eff i-c iency r/i. T he m ean ing of Po, wh ich take s in to acc oun t the tu rb ine d im ensions ,i s re la ted to th e tu rb in e cos t as s ta te d above.Th e VA W T eff ic ien cy i s a p a ram ete r t h a t i s se ld o m tak en in to co n s id e ra t io ns ince the w ind energy i s free and i t i s be t ter to re fer to a n ondim ensio nal coef-f ic i ent p ro p o r t io n a l to th e ex ch an g ed p o wer th a t a l lo ws th e u se r to e s t im a te i td i rec t ly . Nev er theless i t i s im po r ta n t to in t roduc e th e ef f ic iency of a wind tu r-b in e to t r ea t i t a s an y o th e r tu rb o mach in e .Th e in te rn a l e f fi ci en cy o f a V AW T [2 ] , co n s i s t s o f th e ra t io b e tw een th ep o wer y ie ld ed b y th e rea l m ach in e (P ) an d th e p o w er (P i ) y i e ld ed b y an id ea lma chine (CD = 0) w i th the sam e geom etry and wo rk condi t ions (~) ,~h-P/P~ (1)

Th e in te rn a l e f fi ci en cy o f th e two ex amp les o f a cy l in d r ica l tu rb in e (a -0 .4 ,a = 0 .1 5) an d o f two o f th e th ree ex amp les o f Da r r i eu s tu rb in es ( a -0 .1 5 ; 0 .4 )d ea l t w i th in th e p rev io u s p a rag rap h w as ca lcu la ted . Th e co n t in u o u s cu rv es o fF ig . 5 were o b ta in ed wi th th e mo men tu m mo d e l r ep ea t in g th e ca lcu la t io nth ro u g h th e v o r t ex mo d e l n ea r th e m ax imu m ef f i ci ency p o in t s ( cy l in d r i ca lan d [ ] Dar r i eu s tu rb in es ) .4 T a r b i n e s w i t h d i f f e r e n t c o n f i g u r a t i o n

Let u s su p p o se th a t two b lad es w i th f ix ed l en g th a re av a i l ab le an d th a t th eyare so f lex ible tha t , i f fas tened to th e th res t le in d i f feren t p o in ts , they g ive r i seto parabo las wi th var iab le fo rm. The 12 tu rb ines ob ta ined by curv ing the sam eblade ( L = 2 .96Ro) are show n in F ig . 6a , the so l id i ty o f the bas ic conf igura-t io n (8 ) b e in g eq u a l to 0 .1 5 (as = 0 .1 5 ) . Th e i r ch a rac te r i s t i c cu rv es (F ig . 7 )over lap as they concern d i f feren t so l id i ty tu rb ines . So l id i ty changes , as thec h o r d le n g th is o b v io u sl y t h e s a m e , b ec a u s e t h e m a x i m u m ( a n d m e d i u m )


7/11

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Fig . 6 . Conf igura t ion of ana lyzed ver t ica l ax is wi nd turb ines .


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F i g . 7 , C h a r a c t e r i s t i c c u r v e s o f p a r a b o l i c t u r b i n e s w i t h c o n s t a n t b l a d e l e n g t h ,

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F i ~. 8 , C ~ 4 c h a r a c t e r i s t i c c ~ J e s o f p a r a b o l i c t u r b i n e s w i t h c o n s t a n t b l a d e l e n g t h ,

rad ius va r ie s . The bes t conf igura t ion , a s rega rds Cp i s conf igura t ion 5 ra the rth a n c o n f ig u ra t i o n 8 : i t i s p r e f e r a b l e t o f a s t e n t h e b l a d e s o t h a t a n "o p e n "p a ra b o la i s f o rme d .

Th e c a l c u l a t io n o f C~A c h a n g e s t h e p i c tu r e j u s t o u t l i n e d . Th e e x t r e m e p a r -a b ol ic tu r b in e s w i th t he m a x i m u m a n d m i n i m u m r a ti o H[Rma ~are to be re -j e c t e d b e c a u s e o f t h e i r r e d u c e d f ro n t a l a r e a A , wh i l e c o n f ig u ra t i o n s 6 , 7, 8supp ly the bes t power . I t i s no use to repea t th e ca lcu la t ion o f a cha ra c te r i s t icb y me a n s o f t h e v o r t e x m o d e l i f i t c o n c e rn s a c a s e t h a t c l e a rly i n v o lv e s a l owv a lu e o f Cp A. Th e c h o ic e o f t h e m o s t p ro f i t a b l e c o n f ig u ra t i o n (F ig. 8 ) wo u ldb e c o n f i rm e d b y th e v o r t e x m o d e l s i n c e t h e a c c o rd a n c e o f t h e two me th o d s i sg o o d fo r l ow a n d m e d i u m s o l id it y tu rb in e s .I t i s t o b e e x p e c t e d t h a t t h e p o we r i s s l i g h t ly o v e re s t ima te d w i th t h e mo -m e n t u m m o d e l .


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91A second comparison among turbines with the same blade length regardedthe conic-cylindrical configuration shown in Fig. 6b. The blade was subdi-vided into three equal parts that were thought as joined to each other and tothe threstle by hinges so that various configurations for various inclinations

of the oblique segments were generated. Four turbines with a chord as long as0.075 times each segment of the subdivided blade were analyzed. The varia-tion of the maximum values of Cp is not marked, the higher is the inclinationangle the worse the oblique segments work, at the same time the turbine solid-ity changes. If we look at CpA (Fig. 9) the extreme configurations are still tobe avoided.A conic-cylindrical VAWT, inclined on the outside rather than on the in-side, was then considered. These turbines, like the cylindrical ones, need sup-port spokes, whose aerodynamic action, as usual, is at first neglected. In thiscase an essential difference between Cp and CpA diagrams does not come outdue to the small variation of A; yet the most open configurations allow us toexploit the lowest values of2' for which the cylindrical turbine is less efficient(Fig. l 0 ). A variable geometry VAWT would avail itself of a wider character-

0 . 8 - , _ ~ / . . _ ~ . . . . ~ mo~ m

. . . .. . . . i \ . . . . .

1. 2. 3. 4, 5. 6. 7.F i g . 9. C pA c h a r a c t e r i s t i c c u r v e s o f c o n i c - c y l i n d r i c a l t u r b i n e s .

m~)l- - - I I I _ . L ~ : _ 2 morn. m /2 / | ,L Z ~- ~': ~' - . v0rtexm. [

\ i

o . V f + , / ~ - _ L . _ . L % - : : ~ . i . iI I I ~ , \ ',, iI I I I I , \ .,

. . . . . t i V ,I 2 3 4 5 6 7 X

F i g . 1 0 . C pA c h a r a c t e r i s t i c c u r v e s o f o u t e r c o n i c - c y l i n d r i c a l t u r b i n e s .


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9 2

l i h i u t s p 0 k, .o.2i. i ' i J i

O. 1 [ c0n~igurati0nI , ' ~ t i . . . . o 1i # ~ , ' i e' i u : : 3 4o . i # i , , - I

t Ii i I J ',0 . 1 [ . ; . . . . . . . . . . . t J

2 . : 3 . , I . 5 . . ~

F i g . 11 . I n f l u e n c e s o f s p o k e s o n c y l i n d r i c a l t u r b i n e p e r f o r m a n c e s .i st ic cu rve : wh en th e tu rb in e an g u la r sp eed is lo w th e o b l iq u e seg m en ts sh o u ldbe very incl ined , whi le they shou ld ten d to the ver t ica l pos i t ion fo r h igh pe-r iphera l speeds .Th e s tu d y o f co n ic -cy l in d r i ca l co n fig u ra t io n s can b e u t i l ized to t ak e in toacco u n t th e in flu en ce o f sp o k es o n th e ae ro d y n am ic p e r fo rman c e o f a s t r a ig h tv e r ti ca l b l ad e VAWT, assu m in g th a t th e ae ro d y n am ic p ro fi le o f b lad es a n dsp o kes i s th e same . T h e ch arac te r i s t i c o f a cy l in d r ica l tu rb in e w i th o u t sp o k eswas tak en as r e fe ren ce an d rep resen ted b y a co n t in u o u s l in e in F ig . 1 1, wh erea ll t h e d a ta a re o b ta in ed u s in g th e v o r tex m eth o d . Ho r izo n ta l sp o k es h in d erthe ro to r m ovem ent , as Cp is s l igh t ly lower than fo r the tu rb in e w i thou t spokes .On th e co n t ra ry i f sp o k es a rc in c l in ed th ey p ro v id e a p o s i tiv e co n t r ib u t io nth a t is ev id en t a lo n g th e p a r t o f cu rv es ex am in ed , in p a r t i cu la r fo r co n f ig u ra -t ion ( 3 ) (F ig . 11 ) . Clearly us ing the vor tex m eth od the f lu id dynam ics in ter -fe ren ces b e tween b lad es an d sp o k es a re t ak en in to acco u n t .5 . C l o s u r e

Th e main o b jec t iv e o f th i s p ap er was th e an a ly s i s an d th e co mp ar i so n o fposs ib le d i f feren t conf igura t ions o f VAW T. Th e fo llowing conclus ions can bedrawn:- Tak in g in to acco u n t th e co m p ara t iv e ch arac te r o f th e an a ly s is , t h e mo m en -tu m mo d e l p red ic t s in a s imp le an d fa ir ly acc u ra te way VAW T o v era l l p e r -fo rman ces , p ro v id ed th a t 2 an d a assu me su i t ab le v a lu es , a s p o in ted o u t inthe paper .

F ro m th e m ax im u m tu rb in e p o wer p o in t o f v iew , assu m in g a co n s tan t b lad elen g th , th e b e t t e r co n f ig u ra t io n i s o b ta in ed f ro m th e p a ram ete r CpA in s teado f C p

- Th e s tu d y o f ae ro d y n amic sp o k es in f luen ce o n th e VAW T p er fo rman ce , ca r -


11/11

9 3

r i e d o u t w i t h t h e v o r t e x m e t h o d h a s s h o w n t h a t t u r b i n e p o w e r c a n b e i n -c r e a s e d p r o v i d e d t h a t t h e s p o k e s a r e n o t h or i z on t a l.c k n ow l e d g em e n t sThis works was supported by the Ministry of University and Scientific Re-search of I ta ly M U R ST ) and by Na t ional Research Council C N R ).

Re f e r e n c e s1 J . H . S t ri c kl a nd , r e v i e w o f A e r o d y n a m i c A n a l y s i s M e t h o d s f o r V . A . W . T u r b i n e s , P r o c . 5 t h

A s m e W i n d E n e r g y S y m p o s i u m , 1 9 8 6 .2 M . M a r i n i , A . M a s s a r d o , A . S a t t a a n d G . Z a m p a r o , P e r f o r m a n c e s o f a n g e n t i a l W i n d T u r b i n e s

i n I ta li a n ), n: D e v e l o p m e n t o f W i n d T e c h n o l o g y i n I ta ly , N E A P u b l i s h e r , 9 8 9 .3 J . H . S t ri c kl a nd , . T . W e b s t e r a n d T . N g u y e n , A V o r t e x M o d e l f o r t h e D a r r i e u s T u r b i n e : a nA n a l y t i c a l a n d E x p e r i m e n t a l S t u d y , S A N D 7 9 - 7 0 5 8 , 1 9 8 0 .

4 M . M a r i n i , A . M a s s a r d o , A . S a t t a a n d G . Z a m p a r o , T h e o r e t i c a l A e r o d y n a m i c M e t h o d s f o rV . A . W . T . A n a l y s i s , r o c . 2 4 t h I E C E C C o n f e r e n c e , 1 9 8 9 .

5 R . J . T e m p l i n , A e r o d y n a m i c P e r f o r m a n c e T h e o r y f o r t h e N C R V er t i c a l - a x i s u r b i n e , L T R -L A - 1 6 0 , 1 9 7 4 .

performances of vertical axis wind turbines with

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