083 Martin Rotor
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Transcript of 083 Martin Rotor
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Rotor concepts and load estimation
Assoc. Prof. Martin O.L.HansenDTU Wind Energy and CeSOS, NTNU
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InflowWind shearDisturbance
by tower
Atmospheric
turbulenceWave
loads
if
offshore
The external
conditions
for a wind
turbine rotor is highlynon-steady
Further, the structure
respondselasticly
to the time varying
loads
again
changing
the inflow(aeroelasticity
or
Fluid Structure
Interaction
FSI)
-
The aerodynamic
model is called
many
times during
a time simulationof the structural
dynamics
Typical
simulation time T=600 s and timestep t=0.01s, i.ein the order
of 60000 iterations
per load case
Number
of simulations is in the order
of 2000 load cases !!!!(120 mill. calls)
A FAST MODEL IS REQUIRED
Therefore
engineering
models such
as the Blade Element Momentummodel (BEM) still widely
used
-
( ) ( )m A x u x
2 210 12 ( )
kinEP m V ut
The most basic slide understanding a wind turbine:A force is needed (thrust T) to slow down the wind speed in order to extract kinetic energy per time, P, from the flow approaching the rotor
-
2p Vr r
The thrust force can be achieved as a pressure drop created by flow past a wingT=pA
The local
flow on
a HAWT wind
turbine rotorneglecting
induced
wind
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Aerodynamic
loads
on
a 2-D wing section
212
( ,Re)lLCV c
212
( ,Re)dDCV c
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Real flow past
blade including
induced
wind
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We learned that the power comes from removing kinetic energy from the air through creating a force pointing upstream (thrust)
( ) ( )m A x u x
Should we then not increase the thrust until the velocity in the wake u1 =0 ?
2 210 12 ( )
kinEP m V ut
-
The answer is no
If ones
increases
T too
much
then
the flow will
go around
the rotorandif
T=0, then 1 0u V0m
In both
cases the power is 0 and an optimum value
must exist
2 210 12 ( )P m V u
-
It can be shown that u=(Vo
-u1
)
2 210 12
2 2 2 2 21 10 1 0 0 02 2
20
32 10 03 2
( )
( ) ( ( 2 ) ) 2 ( )
/ 2 (2 3 ) 01627opt opt
P m V u
P Au V u Au V V u Au V u
dP du A uV u
u V P A V
-
312
po
PCV A
312
,max 312
161627 60%27
o
po
V AC
V A
Definition power coefficient
Theoretical
maximum
Betz limit
-
How big must T be to obtain this ?
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)()( 10101110 uVAVAAuAVAm cvcvside 2
002
01211 )( VAVmVAAuAT cvsidecv
)()( 101011 uVAuuVuAT
Conservation
of momentum: ( )CV CS
d Volt
V V V dA F
-
0 1
22 1 10 0 0 03 3 2
( )
8( )9opt
T Au V u
T A V V V A V
2102
TTCAV
2102
, 2102
8899T opt
A VC
AV
Definition thrust
coefficient Optimum value
(Betz
limit)
Conservation
of momentum
-
Measured
CT
(a)U=(1-a)VoMomentum theory
not valid for high
CT
-
]/[cossin]/[sincos
mNDLpmNDLp
T
N
Lift and drag projected
relative to rotorplane
-
Lift and drag responsible
for thrust
and torque
!!!
NT p dr R TR
M rp dr
P M
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Worlds largest VAWT in Cap-Chat Quebec(110 m tall, 3.8 MW rated power)
Vertical axis wind turbines
-
rel rot oV V W V
cos sinsin cos
n
t
p L Dp L D
Velocity
triangle
gives size
of relativevelocity
and angle to rotor f
212
212
( )
( )
p
rel l
rel d
L V cC
D V cC
Lift and drag projected
normal to rotor (L
is normal to Vrel
)
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If the tangential load is known the power can be computed as
1
1 13 3 31 1
2 2
( ) ( )
( )( )2 2
B
tot t
B B
t t
po o o
P t M t p hR
p hR pP tC tV h R V h R V
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For both the HAWT and the VAWT wind turbine the angle of attack can be estimated if the induced wind, W, is known
If the angle of attack is known the aerodynamic lift and drag can be estimated from 2-D airfoil data
From the aerodynamic loads the global power and thrust can be calculated
The induced wind can be estimated 1) from the basic conservation of momentum equations (engineering method)
or alternatively 2) the
flow and thus the loads can be computed using CFD
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HAWT
-
21 1( ) 2 ( ) 4 (1 )o o odT V u dm u rdr V u rV a a dr
(1 ) ou a V 1 (1 2 ) ou a V
Classical
Blade Element Momentum method
for HAWTs
Equlibrium
between
load and wake
-
( cos sin )NdT Bp dr B L D dr
-
( cos sin )NdT Bp dr B L D dr 24 (1 )odT rV a a dr
Two
different
equations
for the local
thrust
force
cos sinn l dC C C
2Bc
r
21
4 sin 1n
aF
C
-
Similarly
can
be
derived
for tangential
induction
a=wtan
/r
2Bc
r
( sin cos )TdM Brp dr Br L D dr 34 (1 )odM r V a a dr
sin cost l dC C C
14 sin cos 1
t
a FC
-
For high
CT the momentum theory
not valid (Glauert
correction)
13
1 14 3
4 (1 )4 (1 (5 3 ) )Ta a F a
Ca a a F a
Empirical correlation
-
Comparison between computed and measured electrical power for the 2MW Tjaereborg
machine
The classical BEM gives good results for the steady loads
-
Can
be
used
as a preprocessor
to a WT controller
to estimate
the maximumpower coefficient
and the necessary
pitch
and tip speed ratio
Cp,max
(p
,)and the gains
in a PI controller
-
The classical BEM code only valid for constant inflowand zero yaw.
Can be used to calculate power curves
but not for unsteadycalculation of the loads during operation
This can be cured adding some engineering models
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Unsteady
BEM (Vo
(t), Vrel
(t), (t)) L(t) and D(t)
(t)
(t)
-
cos4 )n g
BLWrF f
o nV Wsin
4 )t g
BLWrF f
o nV W
Quasi steady induced velocities calculated as:
The equations
for the induced
velocity
consistent
withmomentum theory
for zero
yaw
The equations are also valid for 90 degrees yaw (basic helicopter theory)
And it is therefore assumed they are valid for any yaw angle !!!
-
Unsteady effects
intint 1 1
qsqs
dWdWW W kdt dt
2 intdWW Wdt
Dynamic inflow/wakeDynamic inflow/wake
Dynamic stall
-
These
and similar
equations
are
the basis for the assesment
of the aerodynamic
loads
in most servo-,hydro,-aeroelastic
codes
such
as e.g.
HAWC2FLEX5BLADEDFAST
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VAWTsAlso
for vertical
axis
wind
turbines the momentum based
method
are
popular
Single discDouble disc
-
Single disc theory
Relationship
between
the local
thrust
in a streamtube
and thedecreased
local
velocity
u that
includes
the induced
velocity
-
Step 1: Calculate
aerodynamic
loadsfrom assumed
value
of induced
wind
,
,
2 2 2, ,
rel x o x
rel y
rel rel x rel y
V V y WV x
V V V
, ,
, ,
sin cos
cos sin
atan( / )
t rel y rel x
r rel y rel x
r t
p
V V VV V V
V V
212
212
( )
( )rel l
rel d
L V cC
D V cC
, ,
,,
rel y rel xx
rel rel
rel yrel xy
rel rel
V Vp L D
V VVV
p L DV V
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Step 2: Estimate
mean
axial
load
2
2x x
x
N
B p B ppN
-
Step 3: Calculate
thrust
coefficient
212
xT
o
pCV h
Step 4: Update
induced
velocity
(induction
factor a)
13
1 14 3
(1 )
4 (1 )4 (1 (5 3 ) )
x
o
o
T
WaV
u a V
a a aC
a a a a
Solve
for a new a
and thus
Wx
then
goto
step 1
-
Double disc to simulate
also
the downstream
part of the rotor
Free wind speed approaching rotor(1 ) wind speed at upstream disc(1 2 ) Inflow to downstream disc(1 ) wind speed at downstream disc
u u
e u
d d e
UU a UU a UU a U
au and ad found
similarly
as in single disc from CT
(a) relation
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CFD
0
ij
jiij
j i
D pDt
uux x
V
V g
Numerical solution of the Navier-Stokes equations
Incompressible N-S equations
From ICEM CFD Engineering
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-Preprocessor (where a lot of time is spent)Geometry (CAD or similar)Grid generatorSpecifying boundary conditions (inflow, outflow, wall, symmetry etc.)
-SolverSteady/unsteadyDiscretization (Upwind schemes)Turbulence modelTransition model
-Postprocessorextract specific datavisualization
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Turbulence
-
the great
challengeTurbulent flows are
highly
unsteady
and 3-D contains
eddies
of many
scales.
Sir Horace Lamb
(1932):I am an old
man now, and when
I die and go to heaven
thereare
two
matters
on
which
I hope
for enlightment. One is quantumelectrodynamics
and the other
is turbulent motion of fluids. And about
the former I am rather
optimistic.
According to an apocryphal story, Heisenberg was asked what he would ask God, given the opportunity. His reply was: "When I meet God, I am going to askhim two questions: Why relativity? And why turbulence? I really believe hewill have an answer for the first."
-
Scales
in turbulent fluid flow
Largest
scales
similar
to the physical
dimension of the problem
Smallest scales: Kolmogorov
length
scaleTypically
fractions
of mm
is the energy
dissipation
rate per unit mass
[m2/s3]
is the kinematic
viscosity
[m2/s]
1/ 43
-
Number
of gridpoints
required
for a Direct
Numerical
Simulation (DNS)
Re9/4
Example
:
Re=105 N=1.81011Re=106
N=3.21013
-
Modeling the turbulence therefore necessary
-
Reynolds averaging
of the equations
RANS
0
1 ( )
0
T
f f f g g g
f f t dtT
f ff f g f gs s
gf gf
-
u u u v v v w w w p p p Following
is set into
the NS equations
Afterwards
the NS equations
are
timeaveraged
usingthe formulaes
from previous
slide as:
ij
jiij
j i
D pDt
uux x
V g
-
The result
becomes
' '( )ij i jD p u uDt
V g
This
is the standard NS equations
with
an addedterm denoted
the Reynolds stresses (stress tensor)
' 'turbij i ju u
-
Transport equations
can
be
derived
for the Reynoldsstresses, but this
introduces
terms of third
order
products
of the fluctuating
velocities.
This
is known
as the closure
problem.
-
' ' 23
jturb iij i j t ij
j i
uuu u kx x
Boussinesq
approximation
therefore
models theReynolds
stresses through
an eddy
viscosity
t
-
23 ij
kIf the term is added
to the pressurethe equations
becomes
similar
to the normal NS equations
*
*
( )
23
ij
jiij t
j i
D pDt
uux x
p p k
V g
-
Turbulence
is modeled
as an extra
diffusionand the role
of the turbulence
model is to calculate
the size
of this
diffusion
-
Different
catogories
of turbulence
models:
Algebraic
One-equation
models
Two
equations
models
RNG (ReNormalization
Group)
Reynolds stress models
LES (Large Eddy
Simulation)
DES (Deatached
Eddy
Simulation)
DNS (Direct
Numerical
Simulation)
-
Despite the many challenges CFD is routinely used also in WT industry
2-D aerodynamics (airfoil data)
Full rotor computations
Aerodynamic accessories
Flow in landscape (siting)
?
-
NREL Wind tunnel measurement
NASA Ames Tunnel (24.4x36.6 m)NREL Phase-VI Wind Turbine
Breaktrough of CFD for wind turbine rotors
-
Blind test comparisonUpwind Configuration, Zero Yaw
0
500
1000
1500
2000
2500
3000
3500
4000
5 10 15 20 25
Wind Speed (m/s)
L
o
w
-
S
p
e
e
d
S
h
a
f
t
T
o
r
q
u
e
(
N
m
)
Ris comp.
measurements
-
Pressure distributions at 7 m/s
-
Pressure distributions at 10 m/s
-
CFD for wind turbine rotors
AdvantagesFull control over input parametersCheap compared to measurementsParametric variations can easily be madeProvides detailed information of the very complex flow everywhere in the field Input to faster empirical engineering type modelsGain knowledge of complex flow physics
DisadvantagesLarge computer resourcesPrediction of separation,
turbulence and transition modellingSlow compared to BEM, not suited for realistic aeroelastic
simulationsGrid generation ?
Slide Number 1Slide Number 2Slide Number 3Slide Number 4Slide Number 5Slide Number 6Slide Number 7Slide Number 8Slide Number 9Slide Number 10Slide Number 11Slide Number 12Slide Number 13Slide Number 14Slide Number 15Slide Number 16Slide Number 17Slide Number 18Slide Number 19Slide Number 20Slide Number 21HAWTSlide Number 23Slide Number 24Slide Number 25Slide Number 26Slide Number 27Slide Number 28Slide Number 29Slide Number 30Slide Number 31Slide Number 32Slide Number 33Slide Number 34VAWTsSlide Number 36Slide Number 37Slide Number 38Slide Number 39Slide Number 40CFDSlide Number 42Turbulence - the great challengeSlide Number 44Slide Number 45Slide Number 46Slide Number 47Slide Number 48Slide Number 49Slide Number 50Slide Number 51Slide Number 52Slide Number 53Slide Number 54Slide Number 55NREL Wind tunnel measurementBlind test comparisonPressure distributions at 7 m/sPressure distributions at 10 m/sSlide Number 60