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 Future 2

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

heig

ht


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

Prob

abili

ty (%

)

0

2

4

6

8

10

12

14sunrise sunrset

Local standard time (h)

0 2 4 6 8 10 12 14 16 18 20 22 24Pr

obab

ility

(%)

0

2

4

6

8OctMay Oct May

NWTC ART TurbineTime-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 18Pr

obab

ility

(%)

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

Prob

abili

ty (%

)

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 1ln ln

dp

Rcp T

p T =

2 2

1 1

dp

Rcp T

p T =


Potential Temperature

/

( )( )

d pR copT z

p zθ

=

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 . . .

*( ) lno

u zU zk 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

Hei

ght (

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

linea

r hei

ght

log

heig

ht

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

uLkgF

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 zRi

u z

θ θ∂ ∂=

∂ ∂

3*

( / )( )/

og wzL 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 wu 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

10-1100101102103104105

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)10-1100101102103104105

z = 25 mz = 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*

kzuε

εϕ = 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, CaliforniaJuly-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 fluxα

1/7


Variation of Heat Flux and Hub-Height (23m) Mean Wind Speed


W/m2

-600

-400

-200

0

200

400

600

800

m/s

12.5

13.0

13.5

14.0

14.5

15.0

Mean vertical heat fluxHub 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

Mean vertical heat fluxHub σUH

Hub TI

HU

hubUσ


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/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

u * m/s

0.64

0.68

0.72

0.76

0.80

0.84

0.88

Heat flux z/L Hub u *


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

Mean vertical heat flux

' 'u w

' 'u v

' 'v w


Diurnal Variation of Vertical Heat Flux and C D 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

C D

0.036

0.040

0.044

0.048

0.052

0.056

Heat flux z/L C D

Variation of Heat Flux, Stability, and Surface Drag Coefficient CD


Variation of Heat Flux and Turbulent Component Std Devs

σu, σv, σw Diurnal 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

σ u

m/s

1.65

1.70

1.75

1.80

1.85

1.90

σ v

m/s

1.2

1.3

1.4

1.5

1.6

1.7

σ w

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

DEL eq (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

Prob

abili

ty (%

)

0

10

20

30

40

50

60

Turbine Layer Vertical Stability, Ri

-0.08 -0.06 -0.04 -0.02 0.00 0.02 0.04Pr

obab

ility

(%)

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

25SERI RotorAeroStar RotorSERI trendAeroStar 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 RotorAeroStar RotorSERI trendAeroStar 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 RotorAeroStar RotorSERI 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


Bla

de r

oot f

lap

DE

L (k

Nm

)

200

210

220

230

240

250

260 P90P95

Diurnal Distribution of Number of Hours in DEL Distribution


Hou

rs o

f rec

ord

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 (kN

m)

200

210

220

230

240

250

260

Uhu

b (m

/s)

8

10

12

14

16

P90 DELP95 DELP50 UhubP90 UhubP95 Uhubrated wind speedmean P50 wind speed


Variation of Root Flap DEL with Ri Observed Diurnal Variation of Turbine Layer RiTL and Corresponding Flapwise Root BM DEL Distributions

Ri T

L

-0.3

-0.2

-0.1

0.0

0.1

0.2

P10P25P50P75P90


kNm

200

210

220

230

240

250

260 P90P95

critical upper limitsignificant 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 0.25B

lade

roo

t fla

p D

EL

(kN

m)

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

Bla

de r

oot f

lap

DE

L (k

Nm

)

50

100

150

200

250

300

Variation of Blade Root Flap DEL with Rotor-Disk Shear Exponent,

Rotor disk shear exponent, a0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40

Bla

de r

oot f

lap

DE

L (k

Nm

)

50

100

150

200

250

300 1/7 shear exponentIEC 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

Bla

de r

oot f

lap

DE

L (k

Nm

)

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

Bla

de r

oot f

lap

DE

L (k

Nm

)

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

Bla

de r

oot f

lap

DE

L (k

Nm

)

50

100

150

200

250

300

58-m37-m15-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 (kN

m)

200

210

220

230

240

250

260

w (

m/s

)

0.3

0.4

0.5

0.6

0.7

DEL P90DEL 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 (σu2 + σv

2 + σw2)

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 (m3/s3)

0 5 10 15 20 25 30 35

Bla

de r

oot f

lap

DE

L (k

Nm

)

50

100

150

200

250

300

58-m37-m15-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

Hub

pea

k C

TKE

(m2 /s

2 )

0

20

40

60

80

100

120

58-m37-m15-m


Vertical Flux of pk CTKE by Height Variation of Blade Flap DEL with Peak Vertical Flux of CTKE

peak w'CTKE(z) (m3/s3)

-600 -400 -200 0 200 400 600

Bla

de r

oot f

lap

DE

L (k

Nm

)

50

100

150

200

250

300

58-m37-m15-m

Indicates strong vertical transport of coherent turbulence is taking place at NWTC


San Gorgonio Diurnal Variations of Flap DEL and Inflow Parameters

Hub

pea

k C

TKE

(m/s

)2

10

20

30

40

50

60

P90


peak

u'w

' (m

/s)2

-100

-80

-60

-40

-20

P90

Uhu

b (m

/s)

4

6

8

10

12

14

16


2 4 6 8 10 12 14 16 18 20 22 24

3-B

lade

Mea

n Fl

apw

ise

BM

DE

L (k

Nm

)

8

10

12

14

16

18

20

22

24

SERI RotorAeroStar 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