1
Applica ion o compu a ional luid dynamics models o ae odynamic
design and op imiza ion o wind u bine ai oils
E. Cas iñei a-Ma ínez, I. Solís-Gallego, J. González, J. Fe nández O o,
K. A güelles Díaz and S. Vela de-Suá ez
Á ea de Mecánica de Fluidos, Depa amen o de Ene gía
Uni e sidad de O iedo
Edi icio Depa amen al Es e, Campus Uni e si a io, 33203 Gijón, España (Spain)
Phone: +0034 985 182101, e-mail: sa[email p o ec ed]
Abs ac
In his wo k, he capabili y o simple nume ical models wi h coa se g ids o p edic pe o mance
coe icien s in wind u bine ai oils is explo ed. A wide ange o simula ions we e pe o med o a ypical
wind u bine p o ile, unde he main c i e ia o design simplici y and low calcula ion ime. The solu ions
we e compu ed o e di e en mesh sizes using a wo-dimensional Reynolds-A e age Na ie -S ockes (2D-
RANS) app oach. Spala -Allma as, k-ε and k-

u bulence models we e un in he simula ions. Li ,
d ag and momen um coe icien s we e compu ed o ou inciden angles, anging om -2.5 o 12.5, o
each mesh size and u bulence model, compa ing hem la e wi h expe imen al da a. Resul s show a
use ul model which gi es a good ag eemen be ween nume ical and expe imen al esul s and can indeed
be used as a i s app oxima ion p e ious o a mo e de ailed and expensi e s udy.
Key wo ds
Wind u bine ai oils, CFD, 2D-RANS
nume ical models, u bulence models.
1. In oduc ion.
The s a e o he a in he de elopmen o wind
ene gy con e sion sys ems s ill poses some
ques ions on he de ailed ae odynamic
phenomena in ol ed in he low a ound he
u bine blades, gene ally go e ned by qui e
a iable low condi ions and a om he design
ones. One o he pa icula e o s being ca ied
ou is based on he use o Compu a ional Fluid
Dynamics (CFD) echniques o handle he low
s udy a ound he blade ai oils, e en in a design
s age, p e ious o he blade cons uc ion. Fo
such kind o app oach, i is essen ial a good
selec ion o he main pa ame e s depending on
he low condi ions such as he spa ial
disc e iza ion o nume ical g id quali y, he
u bulen closu e scheme, he nume ical
unce ain y, he uns eady ea men , e c.
Se e al wo-dimensional Reynolds-A e age
Na ie -S ockes (2D-RANS) nume ical models
ha e been employed in o de o p edic he
ae odynamic pe o mance o wind u bine
ai oils wi h sa is ac o y esul s. Fo ins ance,
Yu e al. [1] ha e been applying his kind o
me hodology o s udy he dynamic s all o an
ai oil unde going sinusoidal pi ch oscilla ions,
inding p omising esul s in p edic ing li , d a
and momen um coe icien s. In he cases o eal
blades a high angles o a ack, 2D simula ions
a e known o o e p edic d ag, due o ip e ec s
in he spanwise dis ibu ion o d ag. These
e ec s appea o be mo e p onounced a high
incidence angles and can be adequa ely
p edic ed by a 3D-RANS model (So ensen e al.
[2]). When a ull de ailed desc ip ion o he
uns eady low is needed, such as he case o
gene a ion and p opaga ion o ai oil noise,
la ge eddy simula ion (LES) schemes mus be
used (Fleig. e al. [3]), wi h he subsequen
highe compu a ional cos s.
In his wo k, he capabili y o simple nume ical
models wi h coa se g ids o p edic li and d ag
In e na ional Con e ence on Renewable Ene gies and Powe Quali y (ICREPQ’14)
Co doba (Spain), 8 h o 10 h Ap il, 2014
Renewable Ene gy and Powe Quali y Jou nal (RE&PQJ)
ISSN 2172-038 X, No.12, Ap il 2014
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RE&PQJ, Vol.1, No.12, Ap il 2014
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in wind u bine ai oils is explo ed. The main
goal is o de elop a simple and as me hod
which could be employed in he design s age
wi h a low compu a ional cos , in o de o selec
he bes al e na i e be ween se e al op ions, and
p e ious o mo e de ailed and e ined
simula ions which will be needed in u he
s ages o he ai oil de elopmen and
cons uc ion.
The s udy s a s wi h he CFD nume ical s udy
o a ypical ai oil geome y used in wind
u bines, in o de o de e mine he main c i e ia
o choose he op imum model and nume ical
pa ame e s, depending on he low condi ions.
The s udy co e s he ollowing wo main
aspec s: sensi i i y s udy o he de eloped
compu a ional g id and e i ica ion o he be e
u bulence model o cap u e he main physical
phenomena. In o de o con as he ob ained
nume ical esul s, he expe imen al public
da abase o he Na ional Renewable Ene gy
Labo a o y (NREL) a Golden, Colo ado, USA
(Selig e al. [4]) has been conside ed.
2. Me hodology
The esea ch begins wi h he nume ical s udy o
a ypical ai oil geome y used in wind u bines.
Fo all he cases p esen ed in his s udy, a FX
63-137 ai oil model was used. Simula ions
we e un combining di e en pa ame e s, while
some o hem ha e been main ained cons an
such as he inciden eloci y, compu ed o a
Reynolds numbe o 350,000 based on he
ai oil cho d leng h.
Th ee pa ame e s we e modi ied: he numbe o
mesh cells, he inciden angle o he low and
he u bulence model employed in he
simula ion. Fo he sake o compa ison, he
nume ical esul s achie ed we e alida ed wi h
he expe imen al public da abase o he NREL
(Na ional Renewable Ene gy Labo a o y) a
Golden, Colo ado, USA (Seling e al. [4]).
2.1. Geome y and mesh gene a ion.
GAMBIT meshing so wa e was used o
geome y and mesh gene a ion. This so wa e is
associa ed wi h Fluen , whe e la e simula ions
we e made. Fou mesh densi ies we e c ea ed o
a oid high skewed elemen s: a coa se mesh wi h
2,992 cells, a middle densi y mesh wi h 12,451
cells, a high-densi y mesh wi h 48,780 cells and
one ex a mesh o he k- SST case wi h
111,105 cells. In he ollowing, a simple
nomencla u e is used o e e he di e en
meshes, named G1, G2, G3 and G4,
espec i ely. The pu pose o he chosen shape is
o c ea e a meshing ha is adap ed o he
geome y om a simple and e ec i e way as
shown in Fig.1. Howe e , o he ines meshes
i was necessa y o make some changes in he
geome y o he mesh o keep he s abili y in he
simula ions.
.
Fig. 1. Simple scheme o he geome y o he mesh
o coa se and middle mesh.
In Fig. 2, a de ail o he middle densi y mesh is
shown, allowing a be e app ecia ion o he
ai oil and he geome y o he mesh a ound i .
Fig. 2. De ail o middle mesh (G2).
2.2. Inciden angles.
In his pape , ou di e en inciden angles we e
conside ed o he simula ions: -2.5°, 2.5°, 7.5°
and 12.5°, as ep esen a i e o nega i e, low,
medium and high angles. These ha e been
selec ed owing o i s dis ibu ion along he
expe imen al cu e, enabling a wide ange o
esul s, wi hou excessi ely inc easing he
calcula ion ime, which is e y impo an in his
s udy.
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2.3 Tu bulence models.
Simula ions we e ca ied ou o h ee di e en
u bulence models: Spala -Allma as, k-ε and
k- using he comme cial CFD code, ANSYS
FLUENT.
De aul cons an s p o ided by he p og am we e
used o he k-ε and he Spala -Allma as
models. In pa icula , he k-ε model employed
he e is he ReNo maliza ion G oup (RNG), a
a ian o he s anda d. Va ia ions in he wall
unc ions ha e been also conduc ed, unning
simula ions wi h S anda d Wall Func ions
(SWF) and Enhanded Wall T ea men (EWT).
Finally, ini ials pa ame e s (k and ) calcula ed
as exposed by So ensen e al. [2] and using
NREL expe imen al alues we e used o he k-
 model. Fo his model, wo a ia ions we e
conduc ed. Fi s ly, he simula ions we e un
wi h he s anda d model and la e he k- SST
model o Men e was used, included in his
la e he op ion o ansien lows.
I is wo h no ing ha a con e gence s anda d o
10-6 o he esidual pa ame e s was employed.
A Semi Implici Me hod o P essu e Linked
Equa ions (SIMPLE) algo i hm was applied o
en o ce he p essu e- eloci y coupling o he
h ee models and he spa ial de i a i es a e
disc e ized using a second o de upwind
app oach.
In Table 1 he p essu e in e pola ion schemes
employed a e summa ized.
Table 1. P essu e in e pola ion schemes used o
each mesh and model.
2.4 Es ima ion o e o s
Dimensionless coe icien s ob ained
nume ically a e compa ed o he expe imen al
da a p o ided by he bibliog aphy, calcula ing
he a e age e o o he whole ange o inciden
angles conside ed. As only he simula ion o
ou angles has been pe o med, he mos
a ional p ocedu e o ob ain an es ima ion o he
e o is o ob ain om he expe imen al
dis ibu ion he exac alues o each o he
simula ed angles h ough a polynomic equa ion
o he endency line. A e wa ds, he global
a e age e o is ound wi h equa ion [1] .
∑|
|
|
|
[1]
whe e Rglobal is he a e age e o o a
speci ic mesh size and u bulence model, N is
he o al numbe o inciden angles o which
his calcula ion is made, Ciexp is he app op ia e
coe icien (li , d ag o momen um) ob ained o
he expe imen al s udy and Cinum is he
coe icien ob ained by nume ical simula ion.
3. Resul s and discussion
3.1 Spala -Allma as u bulence model.
The g aphs shown in Fig. 3 co espond o his
one-equa ion u bulence model. The e olu ion
o he li coe icien p esen s a no able
ag eemen wi h he expe imen al da a, e en in
he case o coa se meshes. As can be seen,
esul s wi h G2 appea o be he closes o he
e e ence da a, while G3, supposed o be close
o he e e ence alues, has a simila beha iou
o G1. Tha could be because he hi d g id
in ol es an excessi e amoun o nea wall cells
o a Spala -Allma as u bulence model, as his
model does no include any wall ea men .
On he o he hand, an accu a e es ima ion o he
d ag coe icen is mo e di icul o ob ain by
nume ical simula ion, and esul ing alues a e
usually o e p edic ed ega ding o expe imen al
da a. O e all esul s appea o imp o e wi h he
inc ease o numbe o cells.
The momen um coe icien is in pe ec
co espondence wi h he expe imen al cu e o
low angles o a ack, de ia ing g adually wi h
an inc easing o he angle o a ack.
3.2. k-ε u bulence model.
Fo his model, he g aphs a e plo ed in Fig. 4.
The li coe icien shows an accu a e p edic ion
o he alues and he endencies, especially
using medium and e ined g ids, epo ing he
bes alues wi h high inciden angles wi h he
S-A
k-ε
k-
G1,G2
G3
G1,G2
G3
G1,G2,
G3,G4
PRESTO!
Second
O de
Second
O de
S anda d
S anda d
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enhanced wall ea men (EWT) model. Fo his
u bulence model, he d ag coe icien alues
a e excessi ely away om he expe imen al
cu e in all ype o meshes and condi ions, hus
poin ing ou ha his is no a good model o
p edic he d ag coe icien .
Fig. 3. Li , d ag and momen um coe icien s o
Spala -Allma as model.
Fo he momen um coe icien , a good accu a e
p edic ion o he alues is shown, especially a
low angles o a ack .
Fig. 4. Li ,d ag and momen um coe icien s o k-ε
model.
0
0,2
0,4
0,6
0,8
1
1,2
1,4
1,6
1,8
-5 0 5 10 15
CL coe icien
Incidence Angle []
Exp Num(G1)
Num(G2) Num(G3)
0
0,05
0,1
0,15
0,2
-5 0 5 10 15
CD coe icien
Incidence Angle []
Exp Num(G1)
Num(G2) Num(G3)
-0,25
-0,2
-0,15
-0,1
-0,05
0
-5 0 5 10 15
Cm coe icien
Incidence Angle []
Exp Num(G1)
Num(G2) Num(G3)
0
0,2
0,4
0,6
0,8
1
1,2
1,4
1,6
1,8
-5 0 5 10 15
CL coe icien
Incidence Angle []
Exp Num(G1)
Num(G2) Num(G3)
Num(G1)-EWT Num(G2)-EWT
Num(G3)-EWT
0
0,05
0,1
0,15
0,2
-5 0 5 10 15
CD coe icien
Incidence Angle []
Exp Num(G1)
Num(G2) Num(G3)
Num(G1)-EWT Num(G2)-EWT
Num(G3)-EWT
-0,25
-0,2
-0,15
-0,1
-0,05
0
-5 0 5 10 15
Cm coe icien
Incidence Angle []
Exp Num(G1)
Num(G2) Num(G3)
Num(G1)-EWT Num(G2)-EWT
Num(G3)-EWT
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3.3. K-

u bulence model
In his u bulence model only he SST e sion is
shown, because i is he model which has
p esen ed he bes esul s, excep o he middle
mesh (G2), whe e he s anda d model had
sligh ly be e esul s wi h espec o he d ag
coe icien . The s anda d model has shown o
ep oduce he expe imen al cu e wi h a good
accu acy, excep o high angles o a ack in he
ines meshes.
Fig. 5. Li ,d ag and momen um coe icien s o he
k- SST model.
Looking a he li coe icien cha , shown in
Fig. 5, i can be no iced ha in he mos e ined
mesh exis s a la ge accu acy a high angles,
al hough he coe icien is o e p edic ed o he
lowes angles. In his case, he middle mesh
(G2) is he one showing he bes ag eemen wi h
he expe imen al da a.
In he g aph o he d ag coe icien , o he
ines meshes, he nume ical cu e p esen s he
highes accu acy wi h espec o he
expe imen al one o he en i e nume ical
da abase.
Finally, he momen um coe icien has an
accu a e p edic ion o alues and endencies;
qui e simila wi h he expe imen al cu e,
especially o he ines meshing (G4).
3.4 A e age uni a y e o s.
Summa y ables o a e age uni a y e o s o
each u bulence model and o each mesh size
a e p esen ed in his sec ion. The compu a ional
ime o each simula ion is also shown.
These esul s show ha e ined meshes and
complex u bulence models a e no equi ed o
he li coe icien . To ob ain an accu a e
app oxima ion, jus a mesh wi h a ela i ely low
numbe o cells (G2) and wi h a one-equa ion
model as he Spala -Allma as can be used.
Ne e heless, o he d ag coe icien , i is e y
di icul o ob ain accu a e nume ical esul s
conce ning expe imen al ones. A mo e complex
u bulence model, such as k- SST, and high
densi y meshes a e equi ed o achie e an
accep able e o . Resul s o he momen um
coe icien a e be e o k- s anda d model
wi h a ela i ely e ined mesh (G3), al hough
low e o s a e also ob ained o middle meshes
and wi h a one equa ion u bulence model.
Table 2. A e age uni a y e o s o he Spala -
Allma as model.
0
0,2
0,4
0,6
0,8
1
1,2
1,4
1,6
1,8
-5 0 5 10 15
CL coe icien
Incidence Angle []
Exp Num(G1)-SST
Num(G2)-SST Num(G3)-SST
Num(G4)-SST
0
0,05
0,1
0,15
0,2
-5 0 5 10 15
CD coe icien
Incidence Angle []
Exp Num(G1)-SST
Num(G2)-SST Num(G3)-SST
Num(G4)-SST
-0,25
-0,2
-0,15
-0,1
-0,05
0
-5 0 5 10 15
Cm coe icien
Incidence Angle []
Exp Num(G1)-SST
Num(G2)-SST Num(G3)-SST
Num(G4)-SST
Spala -Allma as
Tes ed
G ids
Max.
Compu a ion
imes
A e age uni a y
e o s
CL
CD
Cm
G1
10 seconds
0.08
1.93
0.18
G2
2 minu es
0.03
0.73
0.10
G3
2 hou s
0.08
0.68
0.14
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Table 3. A e age uni a y e o s o he k-ε model
wi h SWT.
Table 4. A e age uni a y e o s o he k-ε model
wi h EWT.
Table 5. A e age uni a y e o s o he k- s anda d
model.
Table 6. A e age uni a y e o s o he k-Ω SST
model.
4. Conclusions
2D-RANS nume ical models a e able o p edic
global pe o mance o wind u bine ai oils wi h
easonable accu acy and compu a ion imes o
ew hou s (maximum) unning in a con en ional
desk op pe sonal compu e .
Li and momen um coe icien s a e accu a ely
p edic ed wi h a simple one-equa ion Spala -
Allma as u bulence model using medium
meshes and compu a ional imes o a ew
minu es, o all he incidence angles es ed. In
hese condi ions, he nume ical esul s o d ag
coe icien ep oduce he global endency o he
expe imen al ones, bu uni a y e o s a e
excessi ely high.
D ag coe icien is accu a ely p edic ed o all
he incidence angles es ed using he k- SST
u bulence model wi h an adequa e e ined
mesh, esul ing in compu a ional imes o some
hou s. In hese condi ions, he esul s o li and
momen um coe icien s a e also accu a e.
Global endencies o li , d ag and momen um
coe icien s a e well cap u ed wi h hese
ela i ely simple models, hus allowing he
compa ison o al e na i e ai oil geome ies in
he design s age.
Acknowledgemen
This wo k has been suppo ed by P ojec
“Ca ac e ización y p edicción de la gene ación
ae odinámica de uido en pe iles de u binas
eólicas”, DPI2011-25419. Minis e io de
Economía y Compe i i idad, España.
Re e ences
[1] Yu, G.H.; Zhu, X.C.; Du, Z.H., 2010,
"Nume ical simula ion o a wind u bine ai oil:
dynamic s all and compa ison wi h
expe imen s", P oceedings o he Ins i u ion o
Mechanical Enginee s, Pa A: Jou nal o Powe
and Ene gy, Vol. 224, 657-677.
[2] So ensen, N.N.; Michelsen, J.A., 2004,
"D ag P edic ion o Blades a High Angle o
A ack Using CFD", Jou nal o Sola Ene gy
Enginee ing, Vol. 126, 1011-1016.
[3] Fleig, O.; Iida, M.; A akawa, C., 2004,
"Wind Tu bine Blade Tip Flow and Noise
P edic ion by La ge-eddy Simula ion", Jou nal
o Sola Ene gy Enginee ing, Vol. 126, 1017-
1024.
[4] Selig, M.S.; McG anahan, B.D., 2004,
"Wind Tunnel Ae odynamic Tes s o Six
Ai oils o Use on Small Wind Tu bines",
NREL/SR-500-34515.
K-ε S anda d Wall Func ion
Tes ed
G ids
Max.
Compu a ion
imes
A e age uni a y
e o s
CL
CD
Cm
G1
10 seconds
0.19
3.92
0.16
G2
1.5 minu es
0.02
3.01
0.14
G3
2.5 hou s
0.03
3.28
0.15
K-ε Enhanced Wall T ea men
Tes ed
G ids
Max.
Compu a ion
imes
A e age uni a y
e o s
CL
CD
Cm
G1
10 seconds
0.19
3.93
0.16
G2
1.5 minu es
0.03
3.07
0.12
G3
2.5 hou s
0.06
2.96
0.22
K- S anda d
Tes ed
G ids
Max.
Compu a ion
imes
A e age uni a y
e o s
CL
CD
Cm
G1
45 seconds
0.22
2.50
0.17
G2
5 minu es
0.07
0.95
0.08
G3
2.5 hou s
0.09
0.53
0.07
G4
2.75 hou s
0.06
0.55
0.06
K- SST
Tes ed
G ids
Max.
Compu a ion
imes
A e age uni a y
e o s
CL
CD
Cm
G1
45 seconds
0.23
2.27
0.15
G2
5 minu es
0.08
1.08
0.11
G3
2 hou s
0.12
0.27
0.16
G4
4 hou s
0.09
0.19
0.14
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