Post on 16-Sep-2018
transcript
Inflow•Wind shear•Disturbance
by tower
•Atmospheric
turbulence•Wave
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 Δt=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 u
t
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=p·A
The local
flow on
a HAWT wind
turbine rotorneglecting
”induced
wind”
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 u
t
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=½(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
)()( 10101110 uVAVAAuAVAm cvcvside
200
201
211 )( 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
21
02
, 2102
8899T opt
A VC
AV
Definition thrust
coefficient Optimum value
(Betz
limit)
Conservation
of momentum
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
)
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
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
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
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
/ωr
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 ) )T
a a F aC
a 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
(θp
,)
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
cos4 )n
g
BLWrF f
o nV W
sin4 )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
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 V
V 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
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
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
-Preprocessor (where a lot of time is spent)•Geometry (CAD or similar)•Grid generator•Specifying boundary conditions (inflow, outflow, wall, symmetry etc.)
-Solver•Steady/unsteady•Discretization (Upwind schemes)•Turbulence model•Transition model
-Postprocessor•extract specific data•visualization
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=1.8·1011
Re=106
N=3.2·1013
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 theReynold’s
stresses through
an eddy
viscosity
t
23 ijkIf the term is added
to the pressure
the 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)
Low
-Spe
ed S
haft
Torq
ue (N
m)
Risø comp.
measurements
∎
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… ?