Presentation of the scaling-up method.

F our re fe re n c e conventional tu rb in es were u sed. Th ey are:

•1 . Polenko W P S 8 (15 kW )

•2 . Aiolos 33 (55 kW )

•3 . Aiolos 100 (1 0 0 k W )

•4. W EG M S -3 (3 0 0 kW )

T h e characteristics o f th e s e turbines are sho w n in tables 1. 2 , 3 and 4 respectively, tog eth er with th e sy stem sca lin g -u p results fo r com parison.

It is ev id e n t that the rated ele ctrica l pow er (P e) o f the system an d the conventional turbine w ith w hich it is being co m p a red m ust be th e sam e. W ith the pow er o u tp u t given, the d im e n s io n s o f the delta w ing an d the turb in es can be calcu lated o n the b asis o f the d esig n re s u lts presented in the p revio us section a n d com parisons c a n follow . T h e rated electrical p o w e r o f the system is g iv en by:

p.

In the above form ula, Pe is equal to tw ice th e pow er p ro du ced by one turbine (see equatio n 4.2.2) since th e s y stem w as assum ed to have tw o tu rbin es, o n e fo r each vortex. A lso , q , and q g are th e g e a rb o x (transm ission) and g enerator efficiencies respectively. U se o f gearboxes w as a s s u m e d because, alth o u g h the vortex turbine tip speed ra tio is h igh enough to o b tain d ire c t coupling to a g en e rato r for sm all turbine d iam ete rs (low er than 2m ), fo r large tu rb in e d iam eters w hich re s u lt from the sy stem scaling-up, th e turbine rotational speed d e c re a se s an d direct connection to a g enerator is not an y m ore possible. In equatio n 4.3 .1 , the fo llo w in g param eters m u st be determ ined:

a) Cp gyMem. A s w ill be seen later, the d elta w in g will be a larg e structure, an d its apex m ay b e at a height g ra te r than 20m . T h erefore, w in d shear effe c ts are co nsiderable. T h e fa c t th at along the w ing 's leading edges the u nd isturb ed wind v elo c ity varies d u e to w ind s h e a r effects is e x p e cted to influence the vortices. W ind shear effec ts on the d elta w ing v o rtice s were experim entally investigated in [45] by testing a d elta wing m od el (w ith sw e ep b ac k angle eq u a l to 79°) in a wind tun nel. T h e result from th at study w as that alth oug h prox im ity o f the delta w ing to the g ro u n d (w ithout a w in d shear p re sen t) in cre ase d th e wind v elo c ity within the vortices, w h en a wind s h e a r was added the b en eficial g ro u n d plane effec t w as counterbalanced b y the wind s h ea r effect, leaving the w in d v e lo c ity within the vortices nearly the sam e a s th at shown in fig u re 4.3. T herefore, the tu rbine C p is not ex p e cted to change considerably w hen a wind s h e a r is present. T h e value o f 1.4 0 6 was used fo r the pow er coefficient, d e riv e d from the d esig n work o f [4 3 ].

b) t\, a n d tis. T y p ical values o f T|t = 0.8 and T)g * 0.8 were c h o se n . Hence, 64% o f

the m ec h an ical pow er p ro duced by the turbine is co n v e rted to ele ctrica l. This is a fa ir assu m p tio n , since m ost conventio nal turbines have o v erall efficien cies o f 25% to 30% , ie C p t |, T)g = 0 .2 5 to 0 .3 0 an d with Cp - 0.4, this im plies that rj, q g = 0 .6 2 5 to 0.750.

c ) V R. D eterm ining a reasonable value fo r the rated w in d sp ee d (VR) is v ery im p ortan t, sin ce Pe ~ V R3. The w ind regim e at w h ich the delta w ing-turbine system o perates m u s t be related to that o f the reference tu rb in e, for a fa ir com parison. T h e system 's tu rb in es are ex p ected to operate at a lo w e r rated w in d sp eed than that o f the c o n v e n tio n a l turbine w ith w hich they are being c o m p a red because th e form er are c lo s e r to the g ro u n d . Since the d elta wing is tilted in pitch h ow ev er, it "catch es" fast-m oving air from h ig h e r altitudes an d d irects it dow n w ard s, to w ard s the turbines. W ind shear effec ts w ere tak e n in to account w hen determ ining the rated w indspeed for th e system . T h is w as done as fo llo w s: The V R valu e for the reference tu rb in e (ie the un d istu rb ed w indspeed at

case 4 with Pe = 300kW . In each ca se the system VR is d iffe ren t, calcu lated from (4.3 .3) in o rd e r to m atch the flow the reference turbin e is ex p erien cing. From tab les 1', 2, 3 an d 4 it is ev id e n t that w ith Pe increasing, the system 's turbine ra d iu s in creases. C om parison

TABLE 1 CASE 1

Pe = 15 kW

D ella w ing-turbine system Reference turbine: Polenko W PS8

v . 10.5 m/s 12 m /s R 1.9 m 4.25 m D 3.8 m 8.5 m c 24.32 m s 9.45 m h 13.28 m 16 m n 430.22 rpm Not known B _{__________ 12_______________ ______________ ____________________} - 6 6 1 .3 W/m2 2*R2 P. * 264.3 W/m2 n R ^ “* - 1 .4 .9 m1 Area * r - ,o , 9 "■ TABLE 2 C A SE 2 Pe = 55 kW

Delta wing-turbine system Reference turbine: A lO LO S 55

v , 12 m/s 14 m /s R 3.1 m 7.75 m D 6.2 m 15.5 m c 39.7 m s 15.4 m h 19.78 m 24 m a 295.7 rpm 56 rpm B 15 - ^ 5 -910.9 W/m2 - A - - 291.5 W/nf 2*R | nR^, - J , i : 305.7 n/ T™ ' : 27. 7 m2 Pag. 86

betw een tab les 1 and 5 re v eals that the system 's tu rb in e rad iu s decreases fo r th e sam e Pe a n d with V R increasing. F o r each case, the ratio [rated pow er]:[tu rbine sw ep t area] was ca lcu lated a s an indication o f the system 's perfo rm an ce and it w as com pared w ith that o f th e reference turbines. F o r the system , P ^ t t R 2 w as ca lcu lated , since tw o tu rb ines are used . It was fo u n d that P J l n K 2 increases with V R in creasin g (since Pe ~ V R3). F o r the referen ce turb ines, P ^ j t R ^ w as calculated. It w as also fo u n d to increase with VR increasing fo r the turbines o f cases 1, 2 and 3. C o m p a rin g cases 1 and 4 re v eals that the W E G M S -3 turbine has a h ig h er P ^ jiR ^ f2 than the P o le n k o turbine. T his is d u e to the technology im provem ent in turbine design and co n stru c tio n th at has taken p lac e in the re cen t years. P olenko W P S 8 is a ra th e r old turbine, w h ile W E G M S-3 is a re c e n t state- o f-the-art turbine with b etter blade quality and generator-tran sm ission efficien cies than th e form er.

TABLE 3 CASE 3 Pe = 100 kW

Delta w ing-turbine system Reference turbine: AIOLOS 100

v . 12.9 m /s 15 m/s R 3.7 m 9.5 m D 7 .4 m 19 m c 47.36 m s 18.41 m h 23.0 m 30.0 m a 266.35 rpm 52 rpm B 15 3 -1162.6 W/ffl2 P, kr; - 3S2.7 W/m2 iiR2, — % = 3.3 2*R2 Dd" *” * : m , m* To- “ : 4,7.9 Area

C om parison o f the d elta w ing system a n d the reference tu rbines reveals th a t the system requires less turbine sw ept area than the conven tion al turbines (fo r the sam e pow er output). As a co m parative indicator, the ra tio t c R ^ ^ n R 2 was c a lcu lated for

all cases. T h e ra tio is alw ays larger than 1.0 a n d its highest value is that fo r ca se 3. Its lo w est value is 1.36 fo r ca se 4 show ing o n c e m o re the im pro ved perfo rm ance o f the W E G M S-3 tu rb in e. A n o ther very im p o rtan t p a ram eter is the o v erall size o f the system .

TABLE 4 C A SE 4

I f the system is p h ysically larger than th e eq u iv a le n t conventional turbine, it is not ex p e cted to b e co st-effective, as m ore m ateria l w ill be needed fo r its constru ction . T o d ete rm in e this, the overall dim ensions o f th e system w ere co m p a red with those o f the reference tu rb in es. Figures 4 .5 , 4.6 and 4.7 sh o w sketches o f the system s and equivalen t tu rb in es fo r ca ses 1, 3 and 4 respectively. F ig u re s 4 .5 and 4.6 sh ow th at the system s co m p a re favo u rab ly with the reference tu rb in e s . T h e ir turbines are sm aller an d clo ser to the g ro u n d w hich m akes installation an d m a in ten a n ce easier. T h e d e lta w in g ce n te r o f m ass is low er, w h ich is an advantage. H o w e v er, large d elta w ings are needed. T h e ir centrelin e lengths are: 24.3m fo r case 1 a n d 4 7 .4 m fo r case 3. T h e v ertical heig h t (h ) o f th e d elta w ing ap e x is 13.3m an d 23.0m fo r c a s e s 1 an d 3 respectively. T h ese h eigh ts are sm aller than th e to w er heights o f the e q u iv a le n t reference turb ines, as show n in fig ures 1

and 2. A lso, the delta w in g spans f o r cases 1, 2 and 3 are ab o ut the sam e as the equ iv alen t referen ce turbines' rotor diam ete rs. A s an indication o f the m aterial required fo r co n stru c tio n , the d elta w ing area w as com pared with th e reference turbine to w er surface area. F o r cases 1, 2 and 3 the tw o areas are ab ou t the sam e. T herefore, it c a n be concluded th at th e d elta w ing system is o f com parable size w ith a co nventional turbine producin g the sam e po w er up to lOOkW.

H ow ever, com parison b etw een the system an d the W EG M S-3 turbine (see figure 4 .7 and table 4 ) is in fa v o u r o f the latter. T h is is d u e to the enorm ous size o f the delta w in g required. A lthough the d e lta wing turbines are sm aller in diam eter than the W EG M S -3 ro to r, the d elta wing ce n trelin e is 128m long an d the w ing apex heig h t is about 57m ab o ve the ground, w hile the W EG M S-3 turbine to w er height is o n ly 25m . T h e increase o f the delta w ing re la tiv e size com pared to the referen ce turbine for ca se 4 is cau sed by the decrease in the (to w e r heig ht]:[ro tor diam eter] ratio with Pe increasing fo r the co n v en tio n al turbines. As show n below:

P olenk o W P S 8 : h/D = 1.88 A iolos 100: h/D = 1.57 W EG M S -3: h/D = 0.7 6

U nlike con v entio n al turbines, the ra tio o f (delta w ing centrelin e]:(roto r diam eter] rem ains co n stan t (c/D =6.4) and this c a u ses the increase in the d elta w ing relative size.

4.3.3. Changes In the system's design for increasing the turbine rotational