Nwtc turb sim workshop september 22 24, 2008- boundary layer dynamics and wind turbines

National Wind
Technology Center
Neil Kelley
Bonnie Jonkman
September 22-24, 2008
TurbSim Workshop

National Renewable Energy Laboratory Innovation for Our Energy Future2
Meeting Purpose
• To give the wind turbine design community an
opportunity to hear about the latest improvements we
have made in the NREL TurbSim Stochastic
Turbulence Simulator Code
• To give the community an opportunity to learn in more
detail about the development of the code, its physical
basis, and how to use it.
• To have the opportunity to share ideas and questions
on how best to use the features of the code.

National Wind
Technology Center
Neil Kelley
September 22-24, 2008
TurbSim Workshop: Boundary Layer Dynamics and
Wind Turbines

Wind Turbines and Boundary Layer Turbulence
• Wind turbines must operate in a wide range of
turbulent flow conditions associated with the
Atmospheric Boundary Layer (ABL)
• The ABL occupies the lowest 1-2 km of the
atmosphere where surface frictional drag has an
influence on the movement of the wind
• Wind turbines occupy the lowest layers of the ABL
and may eventually reach heights of 200 m or more
• The vertical structure and the turbulence
characteristics of the ABL vary diurnally due to the
heating and cooling of the solar cycle

Wind Turbines and Boundary Layer Turbulence – cont’d
• It is this change in turbulence characteristics that has
a significant impact on the operations of wind
turbines
• Turbulence induces structural load responses in
operating turbines which in turn creates wear in
components from fatigue
• The purpose of the TurbSim Code is to provide the
turbine designer with the ability to expose new
designs to flow conditions that induce random or
stochastic load responses for a range operating
environments

Some real world examples
• The best way to understand the role of turbulence on
the operations of wind turbine is to discuss examples
who operating experiences are similar in key
respects
• The greatest operating challenges were found to
occur during the late afternoon and nighttime hours
with the period between local sunset and midnight
often the most challenging

Hawaii
• 15 Westinghouse 600 kW Turbines (now
NWTC CARTS 2 & 3) 1985-1996
• DOE/NASA 3.2 MW Boeing MOD-5B
Prototype 1987-1993
• Installed on uphill terrain at Kuhuku Point
with predominantly upslope, onshore flow
but occasionally experienced downslope
flows (Kona Winds)
• Chronic underproduction relative to
projections for both turbine designs
• Significant numbers of faults and failures
occurred during the nighttime hours
particularly on Westinghouse turbines.
Serious loading issues with MOD-5B
during Kona Winds required lock out
Oahu

Hawaii – cont’d
• 81 Jacobs 17.5 and 20 kW
turbines installed in
mountain pass on the
Kahua Ranch 1985-
• Wind technicians reported
in 1986 a significant
number of failures that
occurred exclusively at
night
• At some locations turbines
could not be successfully
maintained downwind of
local terrain features and
were abandoned
Hawaii

2.5 MW MOD-2
• Post analysis showed
loads much greater than
had been predicted
• Highest loads generally
to occurred during
nighttime hours
• Terrain induced low-
level jet structure
developed during
nighttime hours

Uhub = 7.8 m/s
Ri = − 0.12
Uhub = 9.0 m/s
Ri = + 0.13
Uhub = 9.8 m/s
Ri = + 0.26
Uhub = 12.8 m/s
Ri = + 0.72
Uhub = 13.1 m/s
Ri = + 6.68
Uhub = 6.5 m/s
Ri = + 11.7
30-minute smoothed profiles from PNL Met Tower MOD-2 Site Goldendale, Washington
MOD-2 Hub Height 61 m
Wind speeds normalized by hub-height value - Stability measured between 2 and 107 m
)
Time (LST)16:00 02:00
Turbine Layer Vertical Wind Profile Evolution
wind speed
turbulence intensity
height

San Gorgonio Pass California
• Large, 41-row wind farm located downwind of the
San Gorgonio Pass near Palm Springs
• Wind farm had good production on the upwind (west)
side and along the boundaries but degraded steadily
with each increasing row downstream as the cost of
turbine maintenance increased
• Frequent turbine faults occurred during period from
near local sunset to midnight

Pacific Ocean
Salton
Sea
wind farms
(152 m, 500 ft)
(−65 m, −220 ft)
(793 m, 2600 ft)
San Gorgonio Regional Terrain

Palm Springs
Mt. Jacinto
(
downwind
tower
(76 m, 200 ft)
upwind
tower
(107 m, 250 ft)
row 37
San Gorgonio Pass
nocturnal
canyon flow
(3166 m, 10834 ft)
Wind Farm Nearby Topography

SeaWest Wind Farm San Gorgonio Pass
• 1000 unit wind farm of 44, 65, 108 kW wind turbines (1989-90)
• Significant turbine faulting occurred during late evening hours
• Yaw drive slew rings required repositioning every 3 months and
replacement once a year

Schematic of SeaWest San Gorgonio Wind Park
N
Additional
Operating
Wind Parks

Park Energy Production and Maintenance &
Operations Costs
Highest
M&O Costs
Energy
M&O
High
Low
Low
High

Daytime Flow Patterns Affecting the Wind Park
Westerly flow coming
through the Pass
Warm air flows up
towards mountain
top replacing air heated
by sun
Hot Southeasterly
flow from Salton Sea

Nighttime Flow Patterns Affecting the Wind Park
Cooler drainage flows from
canyon to the south
Warmer flow
coming through
the Pass
Strong turbulence
generated where two
streams meet

Micon 65 kW Turbine Inflow/Structural Response Testing
Hub-height
sonic
anemometer
50 m
Outflow
Tower
(Row 41)
AeroStar
Rotor
SERI
S-Series
Rotor
30 m
turbine
inflow
Tower
Row 37

NWTC ART Turbine

NWTC
(1841 m – 6040 ft)
NWTC
Great Plains
Terrain Profile Near NWTC in Direction of Prevailing Wind Direction
Denver
Boulder
NWTC Regional Topography

NWTC
(1841 m – 6040 ft)
Marshall Mesa
(1768 m – 5800 ft)
NWTC Local Topography

Diurnal Variations in High Blade Loads
San Gorgonio Wind Farm Micon 65 Turbines at Row 37
Time-of-Day Distribution of Occurences of High Root Flapwise DEL
Local standard time (h)
2 4 6 8 10 12 14 16 18 20 22 24
Probability(%)
0
2
4
6
8
10
12
14
sunrise sunrset
0 2 4 6 8 10 12 14 16 18 20 22 24
Probability(%)
0
2
4
6
8
OctMay Oct May
NWTC ART Turbine
Time-of-Day Distribution of Occurences of High Root Flapwise DEL

Wind speeds at High Loads
Hub mean wind speed (m/s)
8 10 12 14 16 18
Probability(%)
0
5
10
15
20
25
30
rated wind speed
NWTC ART Distribution of Mean Hub Wind Speeds Associated
with High Values (P95) of Flapwise Root BM DEL
San Gorgonio Micon 65 (SERI Blades) Distribution of Hub-Height
Mean Wind Speeds Associated with High Values (P95)
of Flapwise Root BM DEL
Hub mean wind speed (m/s)
8 10 12 14 16 18
Probability(%)
0
10
20
30
40
rated wind speed

Before we can proceed . . .
• We need to define a range of tools that we can
employ to describe both the motions and
thermodynamics of the ABL, its vertical structures,
and the turbulence characteristics associated with
those structures
• We will then be in a position to interpret the observed
turbine aeroelastic response seen over a diurnal
period
• First some atmospheric thermodynamics . . .

Adiabatic Temperature Changes
• Air parcels moving vertically (lower pressure) in the
atmosphere expand when rising and contract when
descending (higher pressure)
• With this expansion/contraction their temperature
changes in accordance with the 1st Law of
Thermodynamics
• The following discussion assumes that the air we are
tracking is dry and not saturated with water vapor

Adiabatic Lapse Rate
It can be shown that for dry air changing height from z1 (p1) and
temperature T1 to z2 (p2) its temperature will be T2 as a result of an
adiabatic expansion/contraction (assuming no heat is gained or lost in
the process)
And after taking the anti-logs of both sides
This result allows us to define an adiabatic change in air temperature
with a change in height (pressure)
The rate of (heating/cooling) is 1o C per 100 m height change
2 2
1 1
ln ln
d
p
R
c
p T
p T
 
     =   
    
 
2 2
1 1
d
p
R
c
p T
p T
  = 
 

Potential Temperature
/
( )
( )
d pR c
op
T z
p z
θ
 
=  
 
Using the definition of the adiabatic lapse rate we can define
the potential (or thermodynamic) temperature as . . .
where
z is in meters
T is in °K
p and po are in equivalent units of pressure (mb, kPa, etc)
po is a reference pressure = 1000 mb or 100 kPa
Rd /cp = 0.286

Concept of Atmospheric Stability
• Static Stability
• Dynamic Stability

Schematically
cold, dense air
warm,
less
dense
air
IT IS STABLE
But if . . .
IT IS UNSTABLE

Static Stability
z
θ oK
z
θ oK
z
θ oK
Parcel has
positive
buoyancy
and will continue
to rise
Parcel has no net
buoyancy
and will remain at
this height
Parcel has negative
buoyancy
and will return
to its original level
It is Unstable It is Neutral It is Stable
If we vertically displace the air parcels below .. .

Dynamic Stability or Instability
Time
Z
An example of dynamic instability
The right combination of vertical temperature
and wind speed stratification can produce an
oscillatory or resonant response in the wind
field particularly in vertical motions

Stability is Important
• The vertical stability exerts a significant influence
over the nature of turbulence in the atmospheric
boundary layer
• We will show that under certain narrow ranges of
atmospheric stability, wind turbines can experience
significant structural loading and fatigue damage

Next . . .
• Now lets more on to describing atmospheric motions
and their chaotic behavior --- turbulence!
• This is the stuff that wind turbine blades must ride
through 24/7 year and year out
• ABL turbulence, while stochastic in nature, does
exhibit spatial and temporal organizational structures
and that have an impact on wind turbines and we will
see
• First some basic definitions and turbulence scaling
concepts . . .

Flow Coordinate Systems
+UE
+VN
+Wup Meteorological Coordinates
U = E-W flow component
V = N-S flow component
W = vertical component
+u
+v
+w Aligned with the local flow vector
±u = streamwise component (parallel
to the mean streamline)
±v = lateral or cross-wind component
±w = vertical component

Definition of Turbulent Wind Components
This image cannot currently be displayed.
0where
u u u
v v v
w w w
u v w
θ θ θ
θ
′= +
′= +
′= +
′= +
′ ′ ′ ′= = = =
Decompose orthogonal flow velocity components and temperature
into mean and fluctuating (eddy) components( ) ( )′

The Role of Friction -- Vertical Shearing Stress
x (+u’)
z
(+w’)
(-u’w’)1/2
≡ u
*
Downward flux
or transport of
horizontal
momentum
friction or
shear velocity

Shearing Stress  The Log Wind Profile
• Has a physical basis
• Assumes that the shearing stress in the wind is
constant with height and that the influence of the
earth’s rotation can be ignored
• The height of this “constant stress” layer can
extend up to 200 m under neutral stability
conditions
• This is called the “surface layer” of the
atmospheric boundary layer

The Log Wind Profile
Under these assumptions for a statically neutral
boundary layer . . .
*
( ) ln
o
u z
U z
k z
 
=  
 
The “log” wind speed profile can be written
where zo is the surface aerodynamic roughness length
u* = 0.695 m/s
zo = 0.1 m
k = 0.4
U(z) (m/s)
0 2 4 6 8 10 12 14
Height(z),m
0
20
40
60
80
100
120
140
160
180
200
u* = 0.695 m/s
zo = 0.1 m
k = 0.4
U(z) (m/s)
0 2 4 6 8 10 12 14
0.1
1
10
100
u* = slope*0.4
linearheight
logheight
U(z)  U(z) 
zo

Surface Layer (SL) Characteristics
• Assumes horizontal homogeneity
• The value of u* is approximately constant (>
±10%) throughout its depth ≅ constant shear
stress
• The logarithmic wind profile applies
• The effect of the earth’s rotation can be ignored
(insensitive to Coriolis accelerations)

How Turbulence Scales in the Surface Layer
Monin & Obukhov developed Similarity Theory using advanced
dimensional analysis techniques
If the vertical fluxes of heat, moisture, and momentum are “constant”
with height (everything is in a more or less steady state or balance),
then the following velocity, temperature, and length scales can be
used to scale turbulence in the surface layer:
Velocity: * /ou τ ρ= where τo is the shear stress at the surface
and ρ is the air density
Temperature: * */oHT F u= −
Length:
3
*
oH
u
L
kgF
θ
= −
where FHo is the vertical heat flux at the earth’s surface
Often referred to
as the M-O or
Obukhov length

Measures of SL Dynamic Stability
( )owθ′ ′ =
( )( )
( )
2
/ /
/
g z
Ri
u z
θ θ∂ ∂
=
∂ ∂
3
*
( / )( )
/
og wz
L u kz
θ θ′ ′
= −
Gradient Richardson number, Ri
Monin-Obukhov (M-O) stability parameter, z/L
turbulence generation by buoyancy
turbulence generation by shear
=
where
temperature flux
at ground surface
k = 0.4
g = gravity acceleration
Ri, z/L < 0 = unstable; Ri, z/L = 0, neutral; Ri, z/L > 0, stable

2 2 2
2 2 2
2
' ' ' ' ' '
' ' ' ' ' '
' ' ' ' ' '
, ,
, ,
1/ 2( )
1/ 2[( ) (
u v w
u u u v u w
v u v v v w
w u w v w w
u w w u u v v u v w w v
u u v v w w
u v w
u w u
σ σ σ
′ ′ ′ ′ ′ ′ ′ ′ ′ ′ ′= = =
′ ′ ′ ′ ′ ′= = =
′ ′ ′+ +
′ ′ ′ ′+
assume
Turbulent Kinetic Energy (TKE) =
Coherent Turbulent Kinetic Energy (CTKE) = 2 2 1/2
) ( ) )]v v w′ ′+
Reynolds stress tensor
Reynolds stress components
(turbulence component
covariances)
1/2
* 0( )o
u u w ′ ′= − 
= momentum flux at ground surface
Turbulent Reynolds Stresses, Fluxes, & Kinetic Energy
Important Turbulence Fluid Dynamics Parameters
Need to be reasonably matched for proper modeling

Surface Layer Turbulence Spectra
Scales with Height Above Ground
v-component
f (Hz)
0.001 0.01 0.1 1 10
f Sv(f)
(m/s)
2
0.01
0.1
1
λ (m)
10-1100101102103104105
w-component
f (Hz)
0.001 0.01 0.1 1 10
f Sw(f)
(m/s)2
0.001
0.01
0.1
10-1
100
101
102
103
104
105
u-component
f (Hz)
0.001 0.01 0.1 1 10
f Su(f)
(m/s)
2
0.01
0.1
1
λ (m)
10-1
100
101
102
103
104
105
z = 25 m
z = 125 m

Turbulence Spectra Also Scaled by Stability (z/L)
f = cyclic frequency (Hz)
n = non-dimensional or reduced
frequency
S(f) = power spectral density (m/s)2/Hz
3
*
kz
u
ε
ε
ϕ = scales dissipation of TKE

ABL Vertical Structural Characteristics
CBL
SBL
x
z
wind
turbines
wind
turbines
low-level jet height
zi
h
organized
wave motions
convection
cells
Convective
Boundary
Layer
Stable
Boundary
Layer

ABL Diurnal Evolution
Local standard time
wind
turbines
Mixed
Layer
(ML) Residual
Layer
(RL)(SL)
free atmosphere
(geostrophic flow)
transition regions
Real-world
Example

A Real World Example . . .
• Let’s look at the typical diurnal variation in many of
the surface layer parameters we just discussed
• The data was derived from measurements at the
SeaWest Wind Farm in San Gorgonio Pass California
• We start with what drives the whole shmear
The diurnal variation in incoming solar heat
energy . . .

Diurnal Variation of Vertical Heat Flux FH
Mean Diurnal Near-Surface Vertical Heat Flux Over 5-50m Layer
San Gorgonio Pass, California
July-August 1990
0 2 4 6 8 10 12 14 16 18 20 22
W/m2
-400
-200
0
200
400
600
800
sunrise sunset
Measured upwind of the wind farm’s first row of turbines

Variation of Heat Flux and Power Law Wind Shear
Across Rotors, α
0 2 4 6 8 10 12 14 16 18 20 22
W/m2
-600
-400
-200
0
200
400
600
800
α
0.10
0.11
0.12
0.13
0.14
0.15
0.16
Mean vertical heat flux
α
1/7

Variation of Heat Flux and Hub-Height (23m) Mean
Wind Speed
0 2 4 6 8 10 12 14 16 18 20 22
W/m2
-600
-400
-200
0
200
400
600
800
m/s
12.5
13.0
13.5
14.0
14.5
15.0
Hub mean horizontal wind speed

Diurnal Variation of Mean Heat Flux, Hub Wind
Speed, and Turbulence Level
0 2 4 6 8 10 12 14 16 18 20 22
W/m2
-600
-400
-200
0
200
400
600
800
σUH
m/s
2.3
2.4
2.5
2.6
2.7
2.8
2.9
3.0
3.1
0.10
0.11
0.12
0.13
0.14
0.15
0.16
Hub σUH
Hub TI
HU
hubU
σ

Variation of Heat Flux and Stability
Diurnal Variation of Mean Vertical Heat Flux and Stability Over 5-50m Layer
0 2 4 6 8 10 12 14 16 18 20 22
W/m
2
-600
-400
-200
0
200
400
600
800
z/L, Ri
-0.10
-0.05
0.00
0.05
0.10
0.15
0.20
Heat flux
z/L
Ri

Variation of Heat Flux and Mean Shearing Stress, u*
Diurnal Variation of Mean Vertical Heat and Momentum Fluxes and Stability
0 2 4 6 8 10 12 14 16 18 20 22
W/m2
-600
-400
-200
0
200
400
600
800
z/L
-0.10
-0.05
0.00
0.05
0.10
0.15
0.20
u*
m/s
0.64
0.68
0.72
0.76
0.80
0.84
0.88
Heat flux
z/L
Hubu*

Variation of Heat Flux and Mean Reynolds Stresses
0 2 4 6 8 10 12 14 16 18 20 22
W/m2
-600
-400
-200
0
200
400
600
800
m/s
-1.0
-0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4
' 'u w
' 'u v
' 'v w

Diurnal Variation of Vertical Heat Flux andCD
with Stability
0 2 4 6 8 10 12 14 16 18 20 22
W/m
2
-600
-400
-200
0
200
400
600
800
z/L
-0.10
-0.05
0.00
0.05
0.10
0.15
0.20
CD
0.036
0.040
0.044
0.048
0.052
0.056
Heat flux
z/L
CD
Variation of Heat Flux, Stability, and Surface Drag
Coefficient CD

Variation of Heat Flux and Turbulent Component
Std Devs
σu, σv, σwDiurnal Variation of Vertical Heat Flux and
0 2 4 6 8 10 12 14 16 18 20 22
W/m
2
-600
-400
-200
0
200
400
600
800
σu
m/s
1.65
1.70
1.75
1.80
1.85
1.90
σv
m/s
1.2
1.3
1.4
1.5
1.6
1.7
σw
m/s
0.80
0.82
0.84
0.86
0.88
0.90
0.92
0.94
Heat flux
σu
σv
σw

Back to the Micon 65 Loads Data …
• Let’s now take a look at the distribution of blade root
damage equivalent blade loads as a function of other
turbulence scaling parameters
• First vertical dynamic stability, Ri

Comparison of Measured Turbine Loads as
Function of Stability, Ri
San Gorgonio Wind Farm Row 37 (7D spacing)
Micon 65/13 Wind Turbines Root Flapwise BM Equivalent Blade Loads
Ri
-0.3 -0.2 -0.1 0.0 0.1 0.2
DELeq
(kNm)
8
10
12
14
16
18
20
22
24
SERI Rotor
AeroStar Rotor

Hmmm . . .
How do these compare with our blade root load
measurements at on the NWTC ART Turbine?

Ri Values Associated with High Blade Root Fatigue Loads for
the San Gorgonio Wind Farm and the NWTC
San Gorgonio Distribution of Turbine Layer Ri Associated
with High Values of Flapwise BM DEL
Turbine Layer Vertical Stability, Ri
-0.06 -0.04 -0.02 0.00 0.02 0.04 0.06 0.08 0.10
Probability(%)
0
10
20
30
40
50
60
Turbine Layer Vertical Stability, Ri
-0.08 -0.06 -0.04 -0.02 0.00 0.02 0.04Probability(%)
0
5
10
15
20
25
NWTC ART Distribution of Turbine Layer Ri Associated
with High Values (P95) of Flapwise BM DEL
Both peaks occur in weakly or slightly stable conditions!

Example of Rotor Encountering a Coherent
Turbulent Structure – Aeroelastic Response
edgewise
root
bending
moment
(kNm)
AeroStar
flapwise
root
bending
moment
(kNm)
SERI blade
AeroStar blade
Blade 1
Blade 2
Blade 3

3-D Coherent Turbulent Structure at Hub Height Responsible for
AeroStar Rotor Response
Instantaneous
local Reynolds
stresses
(m/s)2
Estimated
local vorticity
components
(rad/sec)
ωy
ωz
v’w’
u’v’
u’v’
v’w’
ωx
ωy
ωz

Correlation with Other Turbulence Parameters
• Correlation analysis of root flapwise bending
equivalent loads with a range of turbulence
parameters found strong correlations with the
following:
– The mean hub-height wind speed (as would be expected)
– The hub measurement of –u’w’ or its equivalent, u*hub
– This suggests that large, transient blade loads are often
associated with strong downward bursts of organized
turbulence
– A new fluid dynamics parameter is needed that represents
the intensity of coherent or organized turbulence that can be
correlated with load parameters such as DEL

 Reflects the
larger swept
area of the
SERI rotor
 Underlying
response is
nearly identical
Variation of 3-Blade Mean Flapwise BM with Hub Mean U-component
Uhub (m/s)
4 6 8 10 12 14 16
kNm
5
10
15
20
25
SERI Rotor
AeroStar Rotor
SERI trend
AeroStar trend

Correlation of Flap DEL with Uhub
The fatigue
response of both
rotors is nearly
identical except
at the highest
wind speeds
The slightly lower
fatigue of the
AeroStar rotor is
probably due to
its rated wind
speed is slightly
higher
Variation of Flapwise BM DEL vs Mean U-component
Uhub (m/s)
4 6 8 10 12 14 16
kNm
8
10
12
14
16
18
20
22
24
SERI Rotor
AeroStar Rotor
SERI trend
AeroStar trend

Correlation of Flap DEL with u’w’
Variation of 3-Blade Average Flapwise BM DEL
with Mean Downward Momentum Flux u'w'
u'w'hub (m/s)
-4-3-2-10
kNm
8
10
12
14
16
18
20
22
24
SERI Rotor
AeroStar Rotor
SERI trend
AeroStar trend
Reflects
stall
characteristics
of rotor blades
Both rotors are
responding
similarly to
downward bursts
of organized
turbulence

NWTC ART Turbulence-Aeroelastic Response
Correlations
• The ART dataset encompasses a much larger record
of inflow conditions that occurred over an entire wind
season
• There were no large turbines operating upstream so
the response was due to the natural turbulence
experienced at the NWTC and not enhanced by the
presence of multiple rows of upwind turbines
• Five sonic anemometers were employed in an array
upstream of the rotor
• We cross-correlated the root flapwise BM DEL with
several inflow parameters

NWTC 43-m Inflow Array
cup
anemometer
hi-resolution
sonic
anemometer/thermometer
wind
vane
T temperature, DP dewpoint temperature
FT fast-response temperature
∆T Temperature difference
BP Barometric pressure
T
∆T
, DP, BP
NWTC 600 kW
Advanced
Research Turbine No.1
58 m
37 m
15 m
FT
FT

Observed Diurnal Blade Root Flap DEL Tail Distributions
2 4 6 8 10 12 14 16 18 20 22 24
BladerootflapDEL(kNm)
200
210
220
230
240
250
260 P90
P95
Diurnal Distribution of Number of Hours in DEL Distribution
2 4 6 8 10 12 14 16 18 20 22 24
Hoursofrecord
0
4
8
12
16
20
Diurnal Variation of ART High Flap DELs
Data loss due
to frequent
wind speeds
above turbine
cutout

Correlation of ART Hub U-component with Flapwise BM DEL
Variation of ART Flap DEL with Hub Mean U-component
Uhub (m/s)
4 6 8 10 12 14 16 18 20
kNm
50
100
150
200
250
300
350

Diurnal Variation of Flap DEL and Hub Mean Wind Speed
Observed Diurnal Relationship Between Blade Root Flap DEL
and Hub Mean Wind Speed
0 2 4 6 8 10 12 14 16 18 20 22 24
DEL(kNm)
200
210
220
230
240
250
260
Uhub(m/s)
8
10
12
14
16
P90 DEL
P95 DEL
P50 Uhub
P90 Uhub
P95 Uhub
rated wind speed
mean P50 wind speed

Variation of Root Flap DEL with Ri
Observed Diurnal Variation of Turbine Layer RiTL and
Corresponding Flapwise Root BM DEL Distributions
RiTL
-0.3
-0.2
-0.1
0.0
0.1
0.2
P10
P25
P50
P75
P90
2 4 6 8 10 12 14 16 18 20 22 24
kNm
200
210
220
230
240
250
260 P90
P95
critical upper limit
significant turbine response upper limit
Variation of Blade Root Flap DEL with Turbine Layer RiTL
Turbine layer RiTL
-0.25 -0.20 -0.15 -0.10 -0.05 0.00 0.05 0.10 0.15 0.20 0.25
BladerootflapDEL(kNm) 50
100
150
200
250
300

Little or no correlation with the usual suspects
Variation of Blade Root Flap DEL with Hub-Height U
Hub (37-m) U (m/s)
0 1 2 3 4 5
50
100
150
200
250
300
Variation of Blade Root Flap DEL with Rotor-Disk
Shear Exponent, 
Rotor disk shear exponent, a
0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40
50
100
150
200
250
300 1/7 shear exponent
IEC NWP exponent
Variation of Blade Root Flap DEL with Hub Ihub (TI)
Ihub
0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40
50
100
150
200
250
300
Variation of Blade Root Flap DEL with Disk-Averaged u*
Disk averaged u* (m/s)
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6
50
100
150
200
250
300

However with the local value of σw …
Variation of Flapwise DEL with w(z)
w(z) (m/s)
0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0
50
100
150
200
250
300
58-m
37-m
15-m

And Diurnally with the Hub value of σw . . .
Observed Relationship Between Blade Root Flap DEL and Hub (37-m) w
0 2 4 6 8 10 12 14 16 18 20 22 24
DEL(kNm)
200
210
220
230
240
250
260
w(m/s)
0.3
0.4
0.5
0.6
0.7
DEL P90
DEL P95
w P50
w P90
w P95
w P99

Some Hints
• The strong correlation with the flap DEL and σw as a
function of height suggests a strong downward
transport mechanism is a work at the NWTC.
• The question is what is being transported?
• A detailed examination revealed the existence of
intense coherent turbulent structures entering the
rotor disk and its upwind measurement array from
above.
• Clearly we needed to define a turbulence parameter
that reflected the spatial and temporal organization of
these structures and their intensity.

Coherent Turbulence Kinetic Energy (CTKE)
• Turbulent kinetic energy is defined as
TKE = ½ (σu
2 + σv
2 + σw
2)
it says nothing about the correlations between u, v,& w
• However the off-axis Reynolds stress components
represent the covariance and cross-correlation
between these three orthogonal components – u’w’,
u’v’, and v’w’
• Extending the TKE concept, we define a coherent
kinetic energy parameter as
CTKE = ½ [(u’w’)2 + (u’v’)2 + (v’w’)2)]1/2
where CTKE is always ≤ TKE and is 0 in isotropic flow

NWTC ART Flap DEL vs pk CTKE
Max Flap BM RF cycle
1 10 100
kNm
0
100
200
300
400
500
600
700
Flap BM DEL
kNm
0
50
100
150
200
250
300
350
Flap BM DEL
kNm
0
50
100
150
200
250
300
350
Max Flap BM RF cycle
Hub Peak CTKE (m2
/s2
)
1 10 100
kNm
0
100
200
300
400
500
600
700
Entire Population Below-Rated Sub-population

High Blade Fatigue Loads are Induced by Intense,
Fluctuating Vertical Transport of CTKE
Variation of Flapwise DEL with Standard Deviation of Vertical Flux of CTKE
w'CTKE(z) standard deviation (m
3
/s
3
)
0 5 10 15 20 25 30 35
50
100
150
200
250
300
58-m
37-m
15-m

Variation of Hub Peak CTKE with w(z)
w(z) (m/s)
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0
HubpeakCTKE(m2
/s2
)
0
20
40
60
80
100
120
58-m
37-m
15-m

Vertical Flux of pk CTKE by Height
Variation of Blade Flap DEL with Peak Vertical Flux of CTKE
peak w'CTKE(z) (m
3
/s
3
)
-600 -400 -200 0 200 400 600
50
100
150
200
250
300
58-m
37-m
15-m
Indicates strong vertical transport of coherent turbulence is taking place at NWTC

San Gorgonio Diurnal Variations of Flap DEL and
Inflow Parameters
HubpeakCTKE(m/s)2
10
20
30
40
50
60
P90
2 4 6 8 10 12 14 16 18 20 22 24
peaku'w'(m/s)2
-100
-80
-60
-40
-20
P90
Uhub(m/s)
4
6
8
10
12
14
16
2 4 6 8 10 12 14 16 18 20 22 24
3-BladeMeanFlapwiseBMDEL(kNm)
8
10
12
14
16
18
20
22
24
SERI Rotor
AeroStar Rotor
P90
rated
P90
Uhub Hub pk CTKE
Flap DEL Pk u’w’

CTKE – cont’d
• CTKE is easy to measure with the three-axis sonic
anemometers we have used to measure the turbulent
properties of the inflows to the San Gorgonio Micon
65 turbines and the NWTC ART.
• On the average, the ratio of CTKE/TKE is about 0.4
but it can range from 0.2 to 0.9.
• CTKE represents the intensity of turbulent coherent
elements in the flow as they pass through the
measurement volume of a sonic anemometer.

Our Conclusions Are …
• The largest turbine fatigue loads are primarily associated with
slightly stable conditions within a narrow range of the turbine-
layer gradient Ri stability parameter
• They are often not associated with the high values of σU or
turbulence intensity (σU/U)
• The vertical transport of coherent turbulence energy from above
and within the wind farm rotor disk layer is a major contributor to
high fatigue loads.
• It is important when simulating turbine inflow turbulence to
include the ability to (1) model a range of stability conditions and
(2) develop a method to include organized, turbulent structures.

Problem:
• Modern multi-megawatt turbines often operate their
rotors simultaneously in both the surface and mixed
layers
• No consensus on the best way to scale turbulence in
this layer. Some form of a combination of SL and
local scaling is generally used
• We have found that the average height of the SL is
the order of 50-60 m and higher during the day and
lower at night
• We have scaled it in our TurbSim code from actual
measurements taken at two locations: the NWTC
Test Site and Lamar, Colorado

Defining Additional Flow Variables for Coherent
Turbulence
• We would like a single variable that reflects the
intensity of highly correlated turbulent structures seen
in the three cross-axis Reynolds stresses

Nwtc turb sim workshop september 22 24, 2008- boundary layer dynamics and wind turbines

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