Ae odynamic Design and Pe o mance Analysis o a Mic o-Scale
Ho izon al Axis Wind Tu bine Blades along wi h endpla e addi ion
h ough mul i- ideli y compu a ional luid dynamics ools
Nés o Alcañiza,Pau Va elaa,∗,Ped o Quin e oaand Robe o Na a oa
aCMT - Clean Mobili y & The mo luids. Uni e si a Poli ècnica de València, Camino de Ve a, s/n, Valencia, E-46022, Spain
ARTICLE INFO
Keywo ds:
Ae odynamics
Mic o-scale Wind Tu bine
Compu a ional Fluid Dynamics
Blade Elemen Momen um Theo y
QBlade
Endpla e
ABSTRACT
The ansi ion owa d enewable ene gy sou ces has posi ioned wind ene gy as a c i ical echnology
o achie ing global ca bon neu ali y a ge s. While la ge-scale wind a ms domina e cu en ins al-
la ions, mic o-scale ho izon al-axis wind u bines p esen signi ican po en ial o dis ibu ed ene gy
gene a ion in emo e and u al a eas. This s udy p esen s a comp ehensi e me hodology o designing
mic o-scale wind u bine blades h ough compa a i e analysis o h ee compu a ional app oaches:
classical Blade Elemen Momen um Theo y (BEMT), QBlade so wa e, and Compu a ional Fluid
Dynamics (CFD) simula ions, selec ing he designing me hodology based on a ade - o be ween ac-
cu acy and compu a ional cos . A nume ical campaign on ai oil assessmen was conduc ed o iden i y
op imal blade geome ies, wi h pe o mance e alua ed based on powe coe icien dis ibu ion, peak
powe ou pu , and cu -in wind speed. The in es iga ion e eals ha CFD simula ions p edic 23.34%
highe powe coe icien s a peak compa ed o BEMT and 22.46% compa ed o QBlade due o h ee-
dimensional e ec s including o a ional s all delay. The addi ion o endpla es o he op imized blade
design demons a es signi ican imp o emen s in pe o mance. This mul i- ideli y app oach p o ides
a obus amewo k o mic o-scale wind u bine design, balancing compu a ional e iciency wi h
accu acy equi emen s, and s udies he impac o adding endpla es.
1. In oduc ion1
The global impe a i e o ca bon emission educ ion2
has accele a ed he deploymen o enewable ene gy ech-3
nologies. In his global con ex wind ene gy p esen s i sel 4
as a key ac o o achie ing in e na ional clima e a ge s.5
The Pa is Ag eemen o 2015 es ablished he goal o lim-6
i ing global empe a u e inc ease o well below 2°C abo e7
p e-indus ial le els [1], subsequen ly s eng hened by he8
Glasgow Clima e Pac in 2021, which aims o a 1.5°C9
limi [2]. To mee hese a ge s, coun ies wo ldwide ha e10
commi ed o a deca boniza ion goal, wi h China a ge ing11
ca bon neu ali y by 2060 [3] and he Eu opean Union by12
2050 [4] among o he s.13
Wind ene gy capaci y has ecen ly expe ienced a con in-14
uous g ow h, wi h global ins alla ions con inuing o expand15
bo h onsho e and o sho e [5]. Howe e , he bene i s o 16
wind ene gy mus ex end beyond la ge-scale cen alized17
wind a ms in o de o encompass dis ibu ed gene a ion18
sys ems ha can se e emo e and u al communi ies wi h19
a lack o access o he cen alized elec ical g id o ade-20
qua e in as uc u e o la ge-scale ins alla ions. Mic o-scale21
ho izon al-axis wind u bines (HAWT), commonly de ined22
by a a ed powe ou pu below 1.5 kW [6], ep esen a c i ical23
componen o his dis ibu ed ene gy s a egy, e en being24
able o be combined wi h o he enewable ene gy sou ces25
such as sola panels [7].26
∗Co esponding au ho
[email p o ec ed] (N. Alcañiz); [email p o ec ed] (P. Va ela);
[email p o ec ed] (P. Quin e o); [email p o ec ed] (R. Na a o)
ORCID(s): 0009-0002-3285-8055 (N. Alcañiz); 0000-0002-7909-4569 (P.
Va ela); 0000-0003-4373-2079 (P. Quin e o); 0000-0003-2587-4954 (R.
Na a o)
The design philosophy o mic o-scale wind u bines 27
undamen ally di e s om hei la ge-scale coun e pa s, 28
emphasizing modula i y, simplici y, and educed main e- 29
nance equi emen s. T adi ional pi ch con ol sys ems, while 30
e ec i e o la ge u bines, in oduce complexi y and cos s 31
ha a e o en p ohibi i e o small ins alla ions. Conse- 32
quen ly, passi e op imiza ion s a egies ocusing on ae ody- 33
namic blade design combined wi h elec ical con ol sys- 34
ems such as Maximum Powe Poin T acking (MPPT) ha e 35
become he p e e ed app oach [8]. The implemen a ion o 36
his con ol me hod mus be coupled wi h a su icien ly wide 37
ope a ional ange o maximum o nea -maximum e iciency 38
o a oid losses associa ed wi h educed e iciency [9]. These 39
sys ems maximize powe ex ac ion by egula ing he wo k- 40
ing ip speed a io h ough gene a o con ol, elimina ing he 41
need o complex mechanical pi ch mechanisms. 42
The ae odynamic design o mic o-scale wind u bine 43
blades p esen s unique challenges ha equi e ca e ul con- 44
side a ion o compu a ional me hods and hei inhe en lim- 45
i a ions. The classical Blade Elemen Momen um Theo y 46
(BEMT)hasbeen he co ne s oneo wind u binedesigndue 47
o i s compu a ional e iciency and easonable accu acy, be- 48
ing ex ensi ely used in he li e a u e whe e se e al di e en 49
au ho s use his me hod in o de o op imize he cho d and 50
wis dis ibu ion along he blade [10,11], since i has been 51
p o en o imp o e he wind u bine pe o mance espec a 52
non-op imized blade [12]. Howe e , BEMT undamen al as- 53
sump iono wo-dimensional lowneglec ssigni ican h ee- 54
dimensional e ec s ha can impac he wind u bine pe o - 55
mance. Recen ad ances in compu a ional ools ha e p o- 56
ided al e na i es o adi ional BEMT app oaches aiming 57
o inc ease he s udying ideli y o hose h ee-dimensional 58
N.Alcañiz e al.: P ep in submi ed o Else ie Page 1 o 12
Mic o-scale HAWT Blade Design
e ec s. Fo ins ance, he open-sou ce wind u bine design59
so wa e QBlade [13] inco po a es co ec ions o h ee-60
dimensional e ec s while main aining compu a ional e i-61
ciency. Fo ha eason, QBlade has ecen ly s a ed o be62
used in he li e a u e as a design ool [14,15] and ali-63
da ed compa ing he esul s ob ained espec o he classical64
BEMT and expe imen al da a [16,17]. The co ec ions65
included by his so wa e add ess some o he limi a ions66
o classical BEMT by inco po a ing bounda y laye analysis67
and o a ional e ec s in o he momen um heo y amewo k68
[18]. Fo cases equi ing highe ideli y, h ee-dimensional69
Compu a ional Fluid Dynamics (CFD) simula ions can be70
used in o de o cap u e complex phenomena such as o-71
a ional s all delay, ip o ex o ma ion, and blade-wake72
in e ac ions[12,19,20].Theseme hodologiesa eo enused73
in he design p ocess [21,22], allowing o c ea e an op imum74
design.75
The educed scale o he mic o-scale wind u bines al-76
lows di e en me hods o imp o ing ae odynamic pe o -77
mance o be p oposed, such as su ace ea men s [23],78
combining wind u bines in andem con igu a ion [24] o 79
di e en blade ip designs ela i e o he bigge -scale op ions80
such as backwa ds o o wa ds swep blades [25] and he81
design o di e en kind o wingle s [26,27]. Pa icula ly,82
endpla es ( he simples e sion o a wingle ) ha e been also83
s udied in he case o e ical-axis wind u bines [28].84
Ye , o he au ho ’s knowledge, he li e a u e does no 85
add ess he endpla es impac in he case o a ho izon al-86
axis wind u bine, being he endpla es a ea u e ha could87
inc ease he ae odynamic pe o mance o HAWTs wi hou 88
inc easing signi ican ly hei manu ac u ing o design cos s.89
While he li e a u e examines he di e ences be ween90
he analysis me hods p esen ed [29,30], i is necessa y o91
de e mine a ade-o be ween hei ideli y and compu a-92
ional cos in o de o es ablish an e icien ye unc ional de-93
sign me hodology, aiming o cap u e he h ee-dimensional94
e ec s. The p esen s udy add esses he c i ical need o 95
a comp ehensi e design me hodology ha sys ema ically96
compa es hese compu a ional app oaches while op imizing97
blade geome y o mic o-scale HAWTs.98
This wo k de elops a mul i- ideli y design amewo k99
compa ing BEMT,QBlade,and CFD me hodologies.Wi hin100
his amewo k, a sys ema ic op imiza ion o blade geome y101
is conduc ed h ough a nume ical campaign. The s udy102
also ocuses on he quan i ica ion o he h ee-dimensional103
e ec s on pe o mance p edic ions. Finally, e ec i eness o 104
endpla es will be in es iga ed as a s a egy o ae odynamic105
pe o mance enhancemen .106
This a icle i s desc ibes he implemen a ion o he107
BEMT me hodology and i s h ee-dimensional co ec ions108
in subsec ion 2.1. Nex , he CFD model se up and i s mesh-109
ing and alida ion a e add essed in subsec ion 2.2. Then,110
he ollowed design p ocedu e, s a ing wi h he compa ison111
o he di e en compu a ional me hods used and inally112
he e ec s o he endpla es on he blade pe o mance a e113
p esen ed in sec ion 3. Finally, some concluding ema ks a e114
p o ided in sec ion 4.115
2. Me hodology 116
The design and analysis p ocedu es ou lined in his s udy 117
employ a ious nume ical me hodologies whose p ope con- 118
igu a ion and implemen a ion a e c i ical o ensu ing e- 119
liable esul s. This sec ion p esen s he de ailed se up and 120
p ocedu es employed o each compu a ional app oach. 121
As i is obse ed in Figu e 1, he design p ocess is 122
di ided in di e en s eps. The design and analysis me hod- 123
ologies a e desc ibed in subsec ion 2.1 and subsec ion 2.2.124
Then, he me hods a e compa ed in subsec ion 3.1 and a 125
me hod is selec ed in o de o compu e he ai oil assessmen 126
s udy, which is done in subsec ion 2.3. Finally, a geome y 127
is selec ed and he e ec s o adding an endpla e a e s udied 128
in subsec ion 3.3.129
2.1. Blade Elemen Momen um Theo y 130
Implemen a ion 131
Thisme hod disc e izes he o o blades in oindependen 132
sec ions, each assumed o gene a e cons an o ce on he 133
low ield. The heo y employs wo undamen al induc ion 134
ac o s: he axial induc ion ac o (𝑎) and he o a ional 135
induc ion ac o (𝑎′), which, oge he wi h he ai eloci y 136
𝑈∞and he o a ional speed, 𝜔𝑟, de ine he eloci y iangle 137
expe ienced by each blade sec ion, as obse ed in Fig- 138
u e 2, c ea ing he ela i e eloci y 𝑈𝑟𝑒𝑙. These pa ame e s 139
a e essen ial o de e mining he esul an angle o a ack, 140
ollowing es ablished me hodologies [31]. This app oach 141
inhe en ly neglec s h ee-dimensional low e ec s. Addi- 142
ionally, he implemen a ion equi es li and d ag coe icien 143
da abases as unc ions o angle o a ack o each o he blade 144
sec ion s udied. The angle o a ack has been ob ained o 145
his pape h ough XFoil [32], which calcula es li by means 146
o an in iscid linea - o ici y panel me hod, whe eas d ag 147
conside s he iscous e ec s h ough a dis ibu ed sou ce 148
model supe imposed on he ai oil and wake geome y. 149
These da abases allow o calcula e he loads a each sec ion. 150
To enhance accu acy, P and l ip loss and Glaue co ec- 151
ions we e implemen ed, aiming o accoun o ini e blade 152
numbe e ec s and induc ion ac o s exceeding he c i ical 153
alue 𝑎𝑐(usually de ined as 1/3), espec i ely [31]. 154
Fu he mo e, o he co ec ions aiming o model h ee- 155
dimensional e ec s can be added. QBlade [13], an open- 156
sou ce wind u bine design and analysis pla o m, inco - 157
po a es a h ee-dimensional co ec ion o classical BEMT. 158
This co ec ion employs bounda y laye equa ion magni ude 159
analysis o high aspec a io o a ing blades unde bo h 160
a ached and sepa a ed low condi ions, yielding simpli- 161
ied equa ions ha a e in eg a ed in o BEMT compu a ions 162
wi hou signi ican compu a ional cos inc ease [18]. This 163
so wa e also allows o c ea e 3D models o blades op imiz- 164
ing he cho d and wis dis ibu ions based on he BEMT 165
me hod. 166
The classical BEMT and he QBlade implemen a ion 167
bo h allow o asses he wind u bine pe o mance by cal- 168
cula ing he powe and o que coe icien s, which a e di- 169
mensionless alues o powe and o que, as a unc ion o 170
ip speed a io, a ela ion be ween he o a ional and lineal 171
N.Alcañiz e al.: P ep in submi ed o Else ie Page 2 o 12
Mic o-scale HAWT Blade Design
Figu e 1: Schema ic ep esen a ion o he ollowed wo k low.
Figu e 2: Veloci y iangle con igu a ion es ablished by BEMT
me hodology.
speeds pe cei ed by he blade ip. These coe icien s a e172
de ined, espec i ely, in Equa ion 1 and Equa ion 2 and he173
ip speed a io in Equa ion 3.174
𝐶𝑃=𝑊
1
2𝜌𝐴𝑈3
∞
, 𝐶𝑄=𝑄
1
2𝜌𝐴𝑈2
∞𝑟
, 𝜆 =𝜔𝑅
𝑈∞
.
(1) (2) (3)
175
2.2. Compu a ional Fluid Dynamics176
WhileCFD p o ides enhanced ideli yin h ee-dimensional177
low modeling compa ed o BEMT, his ad an age comes178
a inc eased compu a ional expense. Fo achie ing his179
inc ease in ideli y, he ull geome y mus be sol ed in a180
h ee-dimensional manne , omi ing hyb id models such as181
he ac ua o disk.The model se up and meshing s a egy will182
be discussed and alida ed using a NREL e e ence case.183
2.2.1. CFD Simula ion Se up184
Thecompu a ional luid simula ions a epe o med using185
he so wa e S a CCM+. Mul iple con ol olumes we e186
es ablished o ensu e well-de ined compu a ional domains,187
as illus a ed in Figu e 3 and Figu e 4. The con igu a ion188
o a h ee-bladed HAWT employs a hi d o a cylinde as189
he domain imposing pe iodic bounda y condi ions phased190
a 120◦, neglec ing owe e ec s o compu a ional simpli i- 191
ca ion. The luid is modeled as d y ai a sea le el condi ions. 192
The main ac o s a ec ing he u bine pe o mance a e 193
he wind speed and he u bine o a ional speed. The desi ed 194
low eloci y is imposed as no mal o he domain inle , while 195
a mosphe ic p essu e a sea le el is imposed a he ou le , as 196
seen in Figu e 4. The cu ed sides o he domain a e es ab- 197
lished as symme y planes. This symme y condi ion, while 198
no physically ep esen a i e, is commonly employed o 199
simula e ex ended domains while a oiding wall in e ac ion 200
e ec s [33]. Simula ions a e un conside ing a s eady-s a e 201
app oach, modeling he o a ion o he wind u bine h ough 202
Mo ing Re e ence F ame (MRF) me hodology, applied o 203
he inne mos olume obse ed in Figu e 3 and Figu e 4.204
Domain dimensions we e es ablished o ensu e con e gence 205
by minimizing bounda y condi ion in luence on he egion 206
o in e es . 207
A seg ega ed sol e was employed gi en Mach num- 208
be s below 0.3, enabling incomp essible low assump ions. 209
Flow modeling u ilized Reynolds-A e aged Na ie -S okes 210
(RANS) equa ions unde s eady-s a e condi ions. The 𝑘−𝜔211
𝑆𝑆𝑇 u bulence model was selec ed based on he li e a u e 212
[34,19]. The desc ibed me hodology is consis en wi h 213
es ablished p ac ices [35]. 214
2.2.2. Mesh Gene a ion 215
The domain is disc e ized using polyhed al cells. The 216
mesh includes a 1.4 mm global hickness p ism laye mesh 217
consis ing on se en laye s as well as local e inemen s a 218
he blade su ace and i s su oundings, including he o a - 219
ing egion. The su ace e inemen consis s on inc easing 220
he maximum cu a u e allowed o he cells on he blade 221
su ace o a alue o 168 and imposing i s cell size o be 222
a 1% espec o he cell size imposed on he global domain. 223
The olume ic con ols can be seen in Figu e 3 and Figu e 4 224
and consis on educing he cell size o a 15% o he global 225
N.Alcañiz e al.: P ep in submi ed o Else ie Page 3 o 12
Mic o-scale HAWT Blade Design
Figu e 3: CFD simula ion domain and e inemen olumes (no
scale) side iew
Figu e 4: CFD simula ion domain and e inemen olumes (no
scale) pe spec i e iew
Mesh 1 Mesh 2 Mesh 3
Base Size [ m ] 0.24375 0.1875 0.15
𝐶𝑃[ - ] 0.3638 0.3681 0.3798
E o - 1.19 % 3.18 %
Numbe o elemen s 2 × 1064 × 1068 × 106
Di e ence - 170.47 % 176.13 %
Table 1
𝐺𝐶𝐼 s udy esul s.
domain cell size o he ou e mos olume and o a 5% o 226
he inne mos one.227
G id Con e gence Index (𝐺𝐶𝐼) analysis was conduc ed228
o quan i y he e o ela i e o he asymp o ic solu ion. This229
me hodology in ol es mul iple simula ions wi h a ying230
mesh densi ies in o de o de e mine he o de o app oxi-231
ma ion o he solu ion and o es ablish app op ia e base size232
o main aining he desi ed e o ole ance [36]. The esul s233
o hese simula ions can be seen in Table 1, he e inemen 234
a e chosen is 1.25. Bo h he e o in powe coe icien and235
he di e ence in numbe o elemen s a e de ined espec o236
he p e ious mesh.237
Asymp o ic ange alida ion o he ob ained esul s can 238
be con i med h ough he exp ession shown in Equa ion 4 239
[37], con i ming he aba emen o disc e iza ion e o . 240
𝐺𝐶𝐼23
𝑟𝑟𝑝𝐺𝐶𝐼12
= 0.998 ∼ 1.(4)
Based on he simula ions esul s, he o de o app oxima- 241
ion o he solu ion can be calcula ed. Nex , a desi ed e o 242
o 5% is imposed. The equi ed base cell size o keeping he 243
e o wi hin he desi ed ange can be calcula ed, as desc ibed 244
in he li e a u e [36], o be 0.178 me e s. The inal mesh, 245
consis ing on 6 × 106cells, can be seen in Figu e 5.246
While his analysis was pe o med o a ep esen a i e 247
geome y, he calcula ed base size was applied o all simu- 248
la ions due o he equi alen na u e o he low phenomena 249
ac oss con igu a ions. 250
In o de o ensu e p ope wall esolu ion and mesh qual- 251
i y, a Wall Y+ and cell aspec a io analysis is pe o med. 252
The dis ibu ion demons a es alues o Wall Y+ below 5 o 253
all cells and below 1 o he 57.42% o he cells, con i ming 254
mesh adequacy acco ding o es ablished c i e ia [38]. In case 255
o he cell aspec a io, all he cells ha e a alue o e 0.05, 256
ha ing he 75.53% o he cells a alue abo e 0.95. 257
2.2.3. CFD Model Valida ion 258
The alida ion o he CFD model was conduc ed us- 259
ing he NREL Phase VI o o geome y. Scaled compu a- 260
ional domains we e de ined o p ese e consis en blade- 261
o- olume a ios, and p ism-laye emeshing was applied 262
o ensu e ha he Wall Y+ alues emained wi hin he 263
ecommended ange. The selec ed expe imen al da ase co - 264
esponds o Sequence I, cha ac e ized by a se ies o wind 265
speeds anging om 5 m/s o 24 m/s, a cons an o a ional 266
speed o 72 pm, and ze o yaw angle. This sequence was 267
selec ed since i ep esen s he condi ions s udied in his 268
pape . Nume ical calcula ions o he p essu e coe icien 269
dis ibu ion along he blade cho d a selec ed spanwise po- 270
si ions we e compa ed agains a ailable expe imen al mea- 271
su emen s [39] a h ee di e en wo king ip speed a ios. 272
De ining he p essu e coe icien as seen in Equa ion 5, he 273
compa isons a e p esen ed in Figu e 6. The p essu e coe - 274
icien dis ibu ions along he cho d calcula ed by he CFD 275
show he same endencies o hose measu ed expe imen ally, 276
demons a ing he capabili y o he CFD o p ope ly es ima e 277
he expe imen al da a and endencies a di e en wo king 278
condi ions. 279
𝑐𝑃 𝑟𝑒𝑠𝑠𝑅𝑜𝑡 =𝑃−𝑃0
1
2𝜌[𝑈2
∞+ (𝜔𝑟)2]
.(5)
In addi ion o he p essu e coe icien dis ibu ions, he 280
powe coe icien s ip speed a io cu e was calcula ed 281
om he compu a ional p essu e coe icien da a ollowing 282
he p ocedu e es ablished in he expe imen al epo [39]. 283
The esul s, which can be seen in Figu e 7, show a simila 284
powe coe icien dis ibu ion o he di e en calcula ion 285
N.Alcañiz e al.: P ep in submi ed o Else ie Page 4 o 12
Mic o-scale HAWT Blade Design
Figu e 5: CFD mesh side iew close-up o he in e es zone. Addi ional close-ups o he blade e inemen olume and p ism laye
(a) P essu e coe icien dis ibu ion along cho d o 46.6% span (b) P essu e coe icien dis ibu ion along cho d o 80% span
Figu e 6: P essu e Coe icien dis ibu ion along he cho d o CFD and expe imen al calcula ions a di e en span % a 𝜆= 1.67,
𝜆= 4.02 and 𝜆= 8.04
me hods. The mos no iceable disc epancies appea in 𝜆=286
5.02 and 𝜆= 5.74, which a e a 10.03% lowe and a 9.45%287
highe espec i ely when calcula ed om he CFD ex ac ed288
da a.289
2.3. Nume ical Campaign290
A nume ical campaign was o mula ed o sys ema ically291
e alua e all easible design con igu a ions. The campaign292
amewo k was s uc u ed o assess h ee p ima y pe o -293
mance c i e ia:294
•Peak powe coe icien maximiza ion.295
•Powe coe icien dis ibu ion as a unc ion o ip296
speed a io, a ge ing low s all ip speed a ios, mean-297
ing a lowe maximum o a ional speed o a gi en298
wind speed, hus inc easing o e all secu i y, while299
main aining an adequa e op imum ope a ional ange 300
o mi iga e e iciency losses associa ed wi h Maxi- 301
mum Powe Poin T acke (MPPT) sys em impe ec- 302
ions [9]. 303
•To que coe icien a a ip speed a io o ze o, se ing 304
as an indica o o cu -in wind speed. 305
The cu -in wind speed is calcula ed as shown in Equa- 306
ion 6 307
𝑉𝑐𝑖 =√2𝑄𝑐𝑖
𝜌𝐴𝑐𝑄𝑅,(6)
N.Alcañiz e al.: P ep in submi ed o Else ie Page 5 o 12
Mic o-scale HAWT Blade Design
Figu e 7: Powe coe icien e sus ip speed a io cu es o
he NREL Phase VI blade geome y ob ained using di e en
calcula ion me hods.
whe e 𝑄𝑐𝑖 ep esen s he gene a o s a ing o que, assumed308
o be 0.5 Nm o his analysis. The o que coe icien 𝑐𝑄is309
de e mined a ze o ip speed a io acco ding o Equa ion 7.310
𝑐𝑄=𝑄|𝜆=0
1
2𝜌𝐴𝑈2
∞𝑅
.(7)
The design a iable will be he ai oil used along he311
span. The same ai oil will be used along he whole span, as312
commonly used in he design o mic o-scale wind u bines313
[35,40]. The di e en ai oils a e ob ained om an ai oil314
da abase [41], il e ing o ob ain hose designed speci ically315
o wind u bines and a NACA0015, making a o al o 33316
di e en ai oils. The selec ed amilies a e he Be gey, Selig,317
Al haus, Ma in-Heppe le, Jacobs, and Wo mann [42,43].318
The ollowing design cons ain s we e imposed o ensu e319
p ac ical easibili y:320
•Ro o adius o 0.8 m, ep esen ing a balance be ween321
compac ness and powe ou pu capabili y (es ima ed322
maximum o 1 kW) [44].323
•Blade numbe as h ee, p o iding a comp omise be-324
ween powe ex ac ion, ope a ional s abili y, and325
manu ac u ing cos s [45].326
•Design ip speed a io as 3.0, selec ed o enhance low327
wind speed pe o mance while educing s uc u al328
loading equi emen s [46].329
•Solidi y a he oo lowe han one, es ablished o330
p e en in e -blade in e e ence gi en he endency o 331
cho d inc ease a he oo du ing op imiza ion and332
achie ed by imposing a cho d a he oo o 0.2 m.333
The cho d and wis dis ibu ions along he span o he334
di e en geome ies a e no conside ed a a iable since will335
be op imized based on he BEMT me hod.336
Figu e 8: Powe coe icien e sus ip speed a io cu es o he
Be gey blade geome y ob ained using di e en compu a ional
me hods
3. Resul s 337
This sec ion p esen s he esul s ob ained h ough he 338
di e en me hodologies employed in his s udy. Ini ially, 339
a compa a i e analysis be ween compu a ional me hods is 340
conduc ed o es ablish he mos sui able app oach o he 341
nume ical campaign. Subsequen ly, he campaign esul s 342
and associa ed analyses a e p esen ed and discussed. Finally, 343
endpla es a e implemen ed in he geome y aiming o im- 344
p o e he blade pe o mance. 345
3.1. Compa a i e Analysis o Compu a ional 346
Me hods 347
To e alua e he pe o mance and compu a ional cos o 348
he di e en app oaches, a e e ence blade geome y based 349
on he Be gey BW-3 ai oil was selec ed o compa a i e 350
analysis. The powe coe icien cha ac e is ics o his blade 351
we e calcula ed using he h ee me hodologies desc ibed in 352
he p e ious sec ion. The compa a i e esul s a e p esen ed 353
in Figu e 8.354
The obse ed disc epancies be ween he compu a ional 355
me hods can be a ibu ed o h ee-dimensional low e - 356
ec s, which a e neglec ed by he BEMT and simpli ied by 357
QBlade. These e ec s esul in signi ican di e ences in 358
he p edic ed powe coe icien dis ibu ion and peak alue: 359
23.34% be ween CFD and BEMT, and 22.46% be ween 360
CFD and QBlade, being he CFD he me hod p esen ing a 361
highe peak powe coe icien . The h ee-dimensional low 362
s uc u es esponsible o hese disc epancies a e isualized 363
in Figu e 9.364
The h ee-dimensional e ec s obse ed a e p ima ily 365
associa ed wi h he phenomenon o o a ional s all delay, 366
whe eby he ai oil s all condi ion is pos poned due o cen- 367
i ugal and Co iolis o ces ac ing on he o a ing blade. This 368
mechanism has been demons a ed o be ele an in wind 369
u bine applica ions [47]. Figu e 9, illus a es wall shea 370
s ess s eamlines wi h p essu e coe icien colo map a he 371
design ip speed a io (𝜆= 3.0). I is obse ed ha he low 372
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Mic o-scale HAWT Blade Design
Figu e 9: Wall shea s ess s eamlines wi h p essu e coe icien
colo map on he suc ion side o he Be gey blade a 𝜆= 3
de aches om he blade nea he leading edge on he suc ion373
side, co esponding o he egion o maximum suc ion, and374
ea aches a highe cho d alues. This beha io is associa ed375
wi h he o ma ion o a eci cula ion zone, indica i e o com-376
plex h ee-dimensional low s uc u es. Such low ea u es377
enhance suc ion, leading o highe powe coe icien s han378
hose p edic ed by me hods ha neglec h ee-dimensional379
e ec s, as illus a ed in Figu e 8.380
F om a compu a ional cos pe spec i e, he CFD simu-381
la ions equi ed an a e age o 27 hou s o gene a e comple e382
powe coe icien cu es when un on a 15-co e clus e ,383
ep esen ing a compu a ional cos app oxima ely 810 imes384
highe han ha o BEMT o QBlade, which comple ed he385
same calcula ions in app oxima ely 2 minu es on a e age386
using an 8-co e lap op.387
Conside ing he ade-o be ween compu a ional accu-388
acy and cos , and acknowledging ha he signi icance o 389
h ee-dimensional e ec s has been es ablished, QBlade was390
selec ed as he p ima y compu a ional ool o he nume ical391
campaign on u bine blade ai oil assessmen . This decision392
was based on i s subs an ially lowe compu a ional cos 393
compa ed o CFD, while s ill conside ing h ee-dimensional394
e ec s, albei in a simpli ied o m.395
3.2. Nume ical Campaign Resul s and Analysis396
A nume ical campaign o e alua e he sui abili y o 397
33 di e en ai oils o he design o u bine blades was398
conduc ed using QBlade, acco ding o he me hodology399
desc ibed in sec ion 2.400
Based on he selec ion c i e ia es ablished in he me hod-401
ology sec ion, he h ee highes -pe o ming geome ies we e402
iden i ied om he campaign esul s. These candida e con-403
igu a ions demons a e supe io ae odynamic pe o mance404
cha ac e is ics based on he c i e ia p e iously es ablished,405
as illus a ed in Figu e 10.406
The ai oil p o iles co esponding o each candida e ge-407
ome y a e p esen ed in Figu e 11. I should be no ed ha 408
he blade nomencla u e e e s o he ai oil amily employed409
in each design con igu a ion.410
Figu e 10: Powe coe icien e sus ip speed a io cu es o
he h ee selec ed candida e geome ies
Figu e 11: Ai oil p o iles o he h ee nume ical campaign
candida e geome ies
3.2.1. Cu -in Wind Speed Analysis 411
The emaining pe o mance c i e ion e alua ed o he 412
candida e geome ies is he cu -in wind speed, wi h p e e - 413
ence gi en o con igu a ions exhibi ing he lowes alues. 414
The lowes cu -in speed was achie ed by he Jacobs 415
blade, ea u ing a USNPS4 ai oil, wi h 3.10 m/s. The high- 416
es cu -in speed was he Selig blade, ea u ing a SG6041 417
ai oil and a alue o 3.59 m/s. The Be gey blade, consis ing 418
o he BW-3 ai oil, achie ed a cu -in speed o 3.12 m/s. 419
3.2.2. Final Geome y Selec ion 420
Followingcomp ehensi ee alua iono he ae odynamic 421
pe o mance me ics and cu -in wind speed cha ac e is ics, 422
he Be gey blade con igu a ion eme ges as he selec ed de- 423
sign candida e. This selec ion is jus i ied by i s pe o mance 424
cha ac e is ics, including he lowes s all ip speed a io, a 425
simila peak powe coe icien espec o he o he candi- 426
da es, and compe i i e cu -in wind speed pe o mance. 427
N.Alcañiz e al.: P ep in submi ed o Else ie Page 7 o 12
Mic o-scale HAWT Blade Design
Figu e 12: Cho d and wis dis ibu ions along he span o he
Be gey blade
Figu e 13: Endpla e geome ic speci ica ions
The op imized cho d and wis dis ibu ions along he428
blade span, ob ained h ough QBlade BEMT-based op i-429
miza ion algo i hm, a e p esen ed in Figu e 12. These dis-430
ibu ions ep esen he geome ic pa ame e s ha maxi-431
mize ae odynamic e iciency while sa is ying he design432
cons ain s imposed du ing he op imiza ion p ocess.433
3.3. E ec s on Pe o mance due o Endpla e434
Addi ion435
Endpla es a e la su aces a ached o he blade ip. Thei 436
main objec i e is o p e en he o ma ion o eci cula ion437
o exes a he blade ip, he eby inc easing he o que gen-438
e a ion and consequen ly imp o ing he powe coe icien .439
To enhance he ideli y o he compu a ional simula ions,440
addi ionalgeome ic ea u esincludingahemisphe icalnose441
and a cylind ical nacelle we e inco po a ed in o he model.442
P elimina y analysis con i med ha hese ea u es ha e neg-443
ligible impac on he calcula ed powe coe icien cu es,444
while p o iding a mo e ealis ic ep esen a ion o he com-445
ple e u bine geome y.446
The chosen endpla e is illus a ed in Figu e 13.447
The ae odynamic impac o he endpla e implemen a ion448
on he powe coe icien cha ac e is ics is p esen ed in Fig-449
u e 14. The esul s demons a e signi ican modi ica ions in450
Figu e 14: Powe coe icien e sus ip speed a io cu es o
Be gey blade wi h di e en wing ip con igu a ions
he u bine ope a ional beha io ac oss di e en ip speed 451
a ios. 452
The mos no able e ec obse ed is he inc ease o he 453
nega i e slope in he powe coe icien cu e o ip speed 454
a ios exceeding he design alue. This cha ac e is ic is 455
ad an ageous om a sa e y pe spec i e, as i educes he 456
maximum achie able o a ional eloci y. Addi ionally, he 457
endpla e con igu a ion esul s in an inc ease in he peak 458
powe coe icien o a 2.3%. The inc ease in peak powe 459
coe icien p o ided by he endpla e is o he same o de 460
o magni ude as o he ip ea men s epo ed in he li e a- 461
u e [25,26]. Howe e , he e ec s on he powe coe icien 462
dis ibu ion a e no obse ed wi h o he ypes o wing ip 463
con igu a ions. Rega ding he cu -in speed he e a e no 464
ele an changes. I is impo an o conside ha adding an 465
endpla e would mean an inc ease o ine ia, so he cu -in 466
speeds could be inc eased. 467
In o de o de e mine he easons behind he inc ease in 468
peak powe coe icien , se e al low analysis a e pe o med. 469
Fi s ly, he o que coe icien along he adius is shown in 470
Figu e 15, indica ing an inc ease in he o que gene a ed 471
owa ds he ip when adding he endpla e. 472
The enhanced o que gene a ion is u he co obo a ed 473
by he p essu e coe icien dis ibu ion analysis on he blade 474
suc ion su ace, as shown in Figu e 16, whe e an inc ease in 475
suc ion can be obse ed. 476
The obse ed imp o emen s in bo h p essu e coe icien 477
and ip o quegene a iona e a ibu ed o heendpla e abili y 478
o supp ess ip o ex o ma ion a he blade ip, e ec i ely 479
eloca ing he o ical s uc u es o he uppe egion o he 480
endpla e. This phenomenon can be isualized h ough wall 481
shea s ess s eamlines supe posed o he p essu e coe i- 482
cien dis ibu ion al eady shown, as p esen ed in Figu e 17,483
whe e i is shown how he low is a ach o he whole blade 484
when adding an endpla e. 485
These isualiza ionsdemons a e ha he endpla e size is 486
a c i ical ac o in i s pe o mance. Unde sizing he endpla e 487
could esul in dec eased e iciency due o he p oximi y 488
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Mic o-scale HAWT Blade Design
Figu e 15: Spanwise dis ibu ion o o que coe icien o
di e en wing ip con igu a ions a 𝜆= 3
Figu e 16: P essu e coe icien dis ibu ion a he ip o he
blade suc ion side wi h (le ) and wi hou ( igh ) endpla e a
𝜆= 3
o ip o ices o he blade su ace, nega i ely impac ing489
ae odynamic pe o mance. Con e sely, o e sizing he end-490
pla e could in oduce unnecessa y s uc u al loads due o491
inc eased weigh wi hou p o iding addi ional ae odynamic492
bene i s, as he ip o ex e ec s on he blade would emain493
unchanged.494
The modi ica ion in powe coe icien s. ip speed a io495
dis ibu ion can be explained h ough low physics analysis.496
In he baseline con igu a ion wi hou endpla es, low eci -497
cula ion a ound he blade ip enhances he adial eloci y498
componen . The endpla e implemen a ion supp esses his499
eci cula ion, consequen ly educing he adial low com-500
ponen . A ele a ed ip speed a ios, low sepa a ion occu s501
a he nose egion, gene a ing o ical s uc u es. The e-502
duced adial low componen allows he o ical s uc u es503
o de elop and ex end un il eaching he blade p essu e side,504
nega i ely a ec ing he blade pe o mance, as illus a ed in505
Figu e 18.506
Figu e 17: Wall shea s ess s eamlines wi h p essu e coe i-
cien colo map a he ip o he blade suc ion side wi h (le )
and wi hou ( igh ) endpla e a 𝜆= 3
Figu e 18: Veloci y magni ude colo map wi h s eamlines in
spanwise iew a 𝜆= 7 o con igu a ions wi hou ( op) and
wi h (bo om) endpla e
4. Concluding Rema ks 507
This s udy p esen s an o iginal comp ehensi e me hod- 508
ology o he design and analysis o mic o-scale ho izon al- 509
axis wind u bines blades, demons a ing he c i ical im- 510
po ance o compu a ional me hod selec ion and h ee- 511
dimensional e ec s conside a ion in achie ing op imal ae o- 512
dynamic pe o mance. 513
The sys ema ic compa ison o he adi ional BEMT 514
o mula ion, QBlade, and CFD me hodologies e eals sig- 515
ni ican pe o mance p edic ion di e ences, wi h CFD sim- 516
ula ions indica ing 23.34% highe powe coe icien s com- 517
pa ed o classical BEMT and 22.46% compa ed o QBlade. 518
This dispa i y s ems om h ee-dimensional e ec s, pa ic- 519
ula ly o a ional s all delay, which a e inadequa ely cap u ed 520
by wo-dimensional assump ions inhe en in BEMT. The 521
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