ECN-L--07-068 A short history of wind turbine aerodynamics, or: From Betz to Better Herman Snel Invited presentation for the Conference: The second conference on the Science of Making Torque from Wind Lyngby, Denmark, August 28-31, 2007
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ECN-L--07-068
A short history of wind turbine aerodynamics, or: From Betz to Better
Herman Snel
Invited presentation for the Conference:The second conference on the Science of Making Torque from Wind
Lyngby, Denmark, August 28-31, 2007
A s
hort
his
tory
of w
ind
turb
ine
aero
dyna
mic
s, o
r:Fr
om B
etz
to B
ette
r
Her
man
Sne
l, EC
N W
ind
Ener
gy
2
Con
tent
s
•Fr
om th
e st
art t
ill 1
973
•Fi
rst a
dvan
ces
in th
e ne
w w
ind
age
•P
uttin
g dy
nam
ics
into
aer
o•
The
big
expe
rimen
ts•
The
daw
n of
CFD
•W
here
to fr
om h
ere?
To
Bez
t?
Pho
togr
aph
from
: E. H
au,
Win
dkra
ftanl
agen
3
From
the
star
t till
197
3
Win
d po
wer
(mec
hani
cal)
has
been
in u
sed
at le
ast s
ince
the
early
mid
dle
ages
and
perh
aps
alre
ady
for t
wo
mill
enni
aW
ith s
tart
, we
refe
r to
the
star
t of
hydr
odyn
amic
or a
erod
ynam
ic th
eory
ap
plic
able
to w
ind
pow
er. F
irst s
teps
w
ere
appl
ied
to s
hip
prop
elle
rs.
oFi
rst s
tep
is W
.J.M
.Ran
kine
, who
firs
t de
scrib
ed th
e m
omen
tum
theo
ry fo
r an
actu
ator
dis
k (1
865)
oS
econ
d W
.Fro
ude,
who
dev
elop
ed
blad
e el
emen
t the
ory
(189
8) a
nd m
ade
the
first
com
bina
tion
(BE
M w
as b
orn)
Ran
kine
:
Pho
togr
aph
from
: Wik
iped
ia
4
The
so-c
alle
d B
etz
max
imum
The
dete
rmin
atio
n of
the
max
imum
am
ount
of
pow
er th
at c
an b
e ex
tract
ed fr
om a
free
st
ream
for
ms
a de
finite
app
licat
ion
to w
ind
ener
gy. A
ccor
ding
to a
rece
nt a
rticl
e by
van
K
uik,
thre
e na
mes
are
rela
ted
to th
is:
Lanc
hest
er19
15B
etz
1920
Zhuk
ovsk
y(J
ouko
wsk
y)19
20
All
base
d on
act
uato
r dis
k m
omen
tum
theo
ry
(Ran
kine
)La
nche
ster
’spa
per i
s pr
imar
ily d
irect
ed
tow
ards
pro
pelle
rs, p
erha
ps b
ecau
se o
f tha
t no
t not
iced
by
Bet
z
Jouk
owsk
y:
Pho
togr
aph
from
: Wik
iped
ia
5
Bla
de E
lem
ent M
omen
tum
The
ory
Her
man
n G
laue
rtfir
st d
escr
ibed
a fu
ll fle
dged
Bla
de E
lem
ent M
omen
tum
(BE
M)
Theo
ry, i
n D
uran
d (e
d): A
erod
ynam
ic T
heor
y di
v L,
Ch.
X, p
ublis
hed
in 1
935,
one
yea
r afte
r hi
s ac
cide
ntal
dea
th. T
his
theo
ry in
clud
ed
som
e as
pect
s of
wak
e sw
irl, b
ut n
ot th
e ef
fect
on
the
radi
al p
ress
ure
grad
ient
Ludw
ig P
rand
tl(1
926)
con
tribu
ted
the
so-
calle
d tip
cor
rect
ion,
whi
ch in
real
ity is
a
corre
ctio
n fo
r the
non
-uni
form
ity o
f the
flow
be
twee
n bl
ades
.
Pra
ndtl:
Pho
togr
aph
from
: Wik
iped
ia
6
Early
vor
tex
theo
ry, G
olds
tein
Alre
ady
at a
n ea
rlier
sta
ge, a
vor
tex
wak
e de
scrip
tion
for i
nduc
tion
calc
ulat
ion
had
beco
me
avai
labl
e, fr
om S
ydne
y G
olds
tein
(1
929)
, but
bas
ed o
n so
lely
tip
vorti
ces
of a
fix
ed h
elic
al fo
rm.
Gol
dste
in:
Pho
togr
aph
from
: Wik
iped
ia
7
Firs
t adv
ance
s in
the
new
win
d ag
e
The
oil c
risis
of 1
973
star
ted
the
sust
aine
d m
oder
n de
velo
pmen
t of
win
d en
ergy
, inc
ludi
ng a
dev
elop
men
t of a
erod
ynam
ic th
eory
The
stat
e of
the
art o
f aro
und
that
tim
e is
pre
sent
in th
e cl
assi
c W
ilson
and
Lis
sam
anpu
blic
atio
n of
197
41)w
hich
intro
duce
d op
timiz
atio
n, a
nd in
the
(Aga
rdog
raph
) rev
iew
by
Otto
de
Vrie
sof
19
792)
.
1)A
pplie
d A
erod
ynam
ics
of W
ind
Pow
er M
achi
nes
2)Fl
uid
Dyn
amic
Asp
ects
of W
ind
Ene
rgy
Con
vers
ion
8
Stat
e of
affa
irs b
y th
e en
d of
the
70’s
Ass
umpt
ions
in B
EM, a
s de
scrib
ed a
t the
end
of t
he ’7
0’s:
Ste
ady
flow
Axi
ally
sym
met
ric c
ondi
tions
App
roxi
mat
ely
2D s
ectio
nal f
low
be
caus
e of
sle
nder
bla
des,
co
mpa
rabl
e to
sle
nder
win
gs
No
radi
al in
terd
epen
denc
e
Rea
lity
Uns
tead
y flo
w: T
urbu
lent
win
d,
Con
trol a
ctio
ns, s
yste
m v
ibra
tions
Alw
ays
yaw
ed fl
ow, g
ivin
g ris
e to
un
stea
dine
ss a
nd n
on u
nifo
rm
indu
ctio
n
Rot
atin
g bl
ades
cau
se la
rge
3D
effe
cts
espe
cial
ly in
sta
ll
Esp
ecia
lly in
yaw
ed fl
ow ri
dicu
lous
9
Dev
elop
men
ts in
the
80’s
and
90’
s
The
last
two
deca
des
of th
e X
X-th
cent
ury
show
ed a
n im
porta
nt
num
ber o
f Eur
opea
n an
d N
atio
nal p
roje
cts,
lead
ing
to s
o-ca
lled
‘Eng
inee
ring
Met
hods
’, to
rem
ove
part
of t
he li
mita
tions
of B
EM
and,
the
deve
lopm
ent o
f so
calle
d ae
ro-e
last
ic d
esig
n co
des
at th
e m
ayor
Eur
opea
n an
d A
mer
ican
Res
earc
h C
ente
rs, i
nclu
ding
tu
rbul
ent w
ind
gene
rato
rs.
Apa
rt fro
m u
nste
ady
aero
dyna
mic
form
ulat
ions
, the
se p
rogr
ams
incl
ude
time
depe
nden
t str
uctu
ral d
efor
mat
ions
and
def
orm
atio
n ra
tes,
and
thei
r effe
ct o
n ae
rody
nam
ic fo
rces
10
Dyn
amic
pro
file
char
acte
ristic
s
Ste
ady
prof
ile c
hara
cter
istic
s de
pend
on
αon
ly:
Dyn
amic
pro
file
char
acte
ristic
s,
espe
cial
ly b
ut n
ot e
xclu
sive
ly d
ynam
ic
stal
l: M
odel
s de
scrib
ing
hyst
eres
islo
ops,
in th
e fo
rm o
f firs
t or s
econ
d or
der O
DE
’sin
tim
e:
()
()
()
αα
αm
dl
cc
c,
,
0,..
.,
,2
2
= ⎟ ⎠⎞⎜ ⎝⎛
++
dtdc
fdtdc
Bdt
cd
Al
ll
αα
11
Dyn
amic
Inflo
w
Ste
ady
inflo
w e
quat
ion:
Uns
tead
y (d
ynam
ic) i
nflo
w
Bas
ed o
n si
mpl
e vo
rtex
cylin
der a
naly
sis
and
mea
sure
men
ts o
n th
e ‘o
ld’
Tjae
rebo
rg2M
W tu
rbin
e
Effe
ct o
f a s
tep
in p
itch
angl
e on
load
s
()
()
() i
iax
Di
axD
ii
uU
uU
Cdtdu
Rr
C
UC
uU
u
−−
=
=−
∞∞
∞∞
4
4
2,
2,
0
0.51
1.52
2.53
3.54 0
1020
3040
5060
blade pitch setting [deg]
time
[s]'T
j_II
4.da
t' us
ing
1:2
100
200
300
400
500
600
700
800 0
1020
3040
5060
loads and power
time
[s]
12
3D ro
tatio
nal a
ugm
enta
tion
Out
war
d R
adia
l flo
w c
ause
d by
radi
al p
ress
ure
grad
ient
an
d ‘c
entri
fuga
l’ fo
rces
, whe
n ‘re
side
nce
time’
of f
luid
is
long
eno
ugh
(sta
ll)
Rad
ial f
low
toge
ther
with
ro
tatio
n gi
ves
virtu
al C
orio
lisfo
rces
whi
ch a
ct a
s a
chor
d w
ise,
favo
rabl
e pr
essu
re
grad
ient
and
cha
nge
the
char
acte
r of s
tall
(less
de
cam
berin
g)-0,5
0
-0,25
0,00
0,25
0,50
0,75
1,00
1,25
1,50
1,75
2,00
-5,00,0
5,010,
015,
020,
025,
030,
0
Res
ults
from
RFO
IL c
alcu
latio
ns
13
Yaw
ed fl
ow in
duct
ion
mod
els
For y
awed
flow
, the
indu
ctio
n di
strib
utio
n is
far f
rom
uni
form
, gi
ving
uns
tead
y flo
w c
ondi
tions
for
the
blad
es a
nd c
ontri
butin
g to
fa
tigue
load
s. B
ecau
se o
f tu
rbul
ence
, a c
erta
in a
mou
nt o
f m
isal
ignm
ent i
s al
way
s pr
esen
t.
Mod
els
base
d on
hel
icop
ter
prac
tice,
on
pres
crib
ed w
ake
resu
lts a
nd/o
r on
win
d tu
nnel
m
easu
rem
ents
: firs
t and
sec
ond
ha
rmon
ic d
istri
butio
ns:
()
()
()
{}
2,1si
n,
=Ξ
+Φ
Ψ=
ir
ir
Af
ui
azya
wi
i
3
3.1
3.2
3.3
3.4
3.5
3.6
3.7
3.8 0
5010
015
020
025
030
035
0axial velocity [m/s]
azim
uth
Incr
easi
ngr/R
14
Free
vor
tex
wak
e m
odel
s
Ano
ther
dev
elop
men
t for
in
duct
ion
dete
rmin
atio
n w
as
free
vorte
x w
ake
mod
ellin
g(e
.g.
NTU
A, U
niS
tuttg
art,
EC
N).
Rot
or p
lane
indu
ctio
n is
ca
lcul
ated
on
basi
s of
all
traile
d an
d sh
ed v
ortic
ity p
rese
nt in
the
wak
e. V
ortic
ity is
tran
spor
ted
with
the
tota
l loc
al c
onve
ctio
n ve
loci
ty in
the
wak
e, p
artly
in
duce
d by
wak
e vo
rtici
ty it
self.
This
mod
el c
an h
andl
e ya
wed
in
flow
and
uns
tead
ines
s in
an
acce
ptab
le w
ay, b
ut m
uch
mor
e tim
e co
nsum
ing
than
B
EM
15
The
big
expe
rimen
ts
16
NR
EL N
ASA
Am
es a
nd M
EXIC
O
Two
larg
e sc
ale
aero
dyna
mic
ex
perim
ents
wer
e he
ld in
the
first
de
cade
of t
he X
XI-s
tcen
tury
•20
00: N
REL
NA
SA A
mes
, 10
m
diam
eter
, 2 b
lade
d m
odel
: S
urfa
ce p
ress
ure
dist
ribut
ions
bl
ade
load
s an
d to
tal l
oads
. M
uch
anal
ysis
alre
ady
done
•20
06: E
urop
ean
‘MEX
ICO
’ pr
ojec
t. 4.
5 m
dia
met
er, 3
bla
ded
mod
el: S
urfa
ce p
ress
ure
dist
ribut
ions
, bla
de lo
ads,
tota
l lo
ads,
flow
fiel
d by
PIV
. Ana
lysi
s ju
st s
tarti
ngTh
e ex
perim
ents
mak
e re
al
valid
atio
n an
d im
prov
emen
ts
poss
ible
for b
oth
BEM
and
C
FD
17
Exam
ples
of v
alid
atio
n ef
fort
s
-300
-200
-1000
100
200
300
400
500
600
-50
510
Tim
e [s
]
Normal force [N]
mea
s. 8
0%A
WS
M 8
0%
-100-5
0050100
150
200
250
-50
510
Tim
e [s
]
Normal force [N]
mea
s. 4
7%A
WS
M 4
7%
-60
-40
-20020406080100
-50
510
Tim
e [s
]
Normal force [N]
mea
s. 3
0%A
WS
M 3
0%
-200
-1000
100
200
300
400
-50
510
Tim
e [s
]
Normal force [N]
mea
s. 6
3%A
WS
M 6
3%
Free
wak
e pr
ogra
m A
WS
M c
ompa
red
to N
RE
L N
AS
A A
mes
mea
sure
men
ts
for p
itch
step
s, a
t 4 ra
dial
sta
tions
18
Exam
ple
of M
EXIC
O R
esul
ts
0° a
zim
uth:
α~1
9°18
0° a
zim
uth:
α~
10°
-0.20
0.2
0.4
0.6
0.81
1.2
1.4 -5
05
1015
2025
30
cl, cd [-]
alfa
[deg
]
‘Adv
anci
ng a
nd
retre
atin
g bl
ade’
ef
fect
s
Dyn
amic
Sta
ll in
45
degr
ees
yaw
mea
sure
men
ts
19
Mex
ico
PIV
resu
lts
The
PIV
resu
lts p
erm
it a
valid
atio
n of
vor
tex
path
s an
d tra
ject
orie
s
20
The
daw
n of
CFD
CFD
in th
e fo
rm o
f the
num
eric
al
solu
tion
of th
e R
eyno
lds
Ave
rage
d N
avie
rSto
kes
equa
tion,
or L
ES
/DE
S
type
of s
olut
ions
, hol
d a
larg
e pr
omis
e. F
or m
uch
time
to c
ome
this
w
ill n
ot b
e th
e so
lutio
n fo
r des
ign
or
certi
ficat
ion
calc
ulat
ions
(exc
ept
spec
ial c
ases
) but
to im
prov
e:•
Aer
o-el
astic
cod
es b
ased
on
‘impr
oved
’ BE
M•
Free
or p
resc
ribed
wak
e ty
pe c
odes
•M
ost i
mpo
rtan
t: an
impr
oved
fu
ndam
enta
l und
erst
andi
ng o
f the
ae
rody
nam
ics
of w
ind
turb
ines
an
d fa
rm in
tera
ctio
n
Exa
mpl
e of
DE
S c
alcu
latio
ns fo
r the
N
RE
L N
AS
A-A
mes
turb
ine
in s
tall
by
Elli
pSys
3D (D
TU/R
ISO
E)
21
The
daw
n of
CFD
-2-
Mai
n ac
tors
:C
RE
S/N
TUA
DTU
/RIS
OE
(Elly
psis
3D, i
nclu
ding
DE
S p
ossi
bilit
ies)
Pre
sent
lim
iting
fact
ors
for C
FD•
Com
pute
r tim
e ne
eded
, bec
ause
of l
arge
Re
num
bers
and
as
soci
ated
grid
requ
irem
ents
nea
r the
bla
de s
urfa
ces
•La
min
ar-tu
rbul
ent t
rans
ition
issu
es, i
nclu
ding
roug
hnes
s ef
fect
s an
d by
pas
s tra
nsiti
on d
ue to
free
flow
turb
ulen
ce•
In g
ener
al tu
rbul
ence
mod
ellin
g, s
peci
fical
ly fo
r RA
NS
•C
ompr
essi
bilit
y ef
fect
s fo
r hig
her t
ip s
peed
off-
shor
e tu
rbin
es?
22
From
Bet
z to
Bet
ter t
o B
ezt?
Poss
ible
road
s to
mor
e re
liabl
e de
sign
tool
s, n
eede
d to
lim
it ris
ks a
nd o
ptim
ize
mul
ti M
W w
ind
turb
ines
:
•Fa
ster
, muc
h fa
ster
CFD
•Te
mpo
rary
use
of ‘
inte
rmed
iate
’ met
hods
, pot
entia
l flo
w +
bo
unda
ry la
yer c
ombi
ned
with
free
vor
tex
wak
e.•
Valid
atio
nus
ing
the
big
expe
rimen
ts.
•B
ette
r fre
e w
ind
desc
riptio
n is
impo
rtant
for l
oads
, esp
ecia
lly
stro
ng g
usts
•C
FD fo
r wak
e in
tera
ctio
n pr
oble
ms
•E
tc, e
tc, m
any
year
s of
wor
k
23
Con
clus
ion
and
ques
tions
•W
hom
or w
hat d
id I
forg
et?
•W
e ha
ve c
ome
a lo
ng w
ay, b
ut
ther
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