nwtc turb sim workshop september 22 24, 2008 - turbulence characteristics that influence the dynamic...

National Wind Technology Center Neil Kelley September 22-24, 2008

TurbSim Workshop: Turbulence Characteristics that Influence the Dynamic Response of Wind Turbines

National Renewable Energy Laboratory Innovation for Our Energy Future 2

The Details of Coherent Turbulence Generation in the Stable ABL or SBL

• The weakly stable conditions that we have shown to be present for high rotor loading events indicate the possible presence of Kelvin-Helmholtz Instability or KHI.

• This type of dynamic instability is ubiquitous in the nocturnal boundary layer (NBL) and many believe it is the principal mechanism responsible for turbulent mixing in the NBL.

• Its requirements are strong vertical wind speed shear and a positive temperature gradient (a temperature inversion). A gradient Ri between 0 and +0.25 is necessary.


The Details of Coherent Turbulence Generation in the Stable ABL or SBL – cont’d

• If an air parcel (like the one in the early animated demonstration) is displaced vertically in a stably stratified boundary layer its motion is described by where N is the frequency at which the air parcel will oscillate. The relationship between Ri and buoyancy oscillations can be seen by Typically there are a range of oscillating frequencies active for a given situation. • The National Center for Atmospheric Research (NCAR) developed an LES numerical simulation of the life cycle of a stationary KHI-induced billow flow formation for NREL. We have used this simulation as a mechanism to insert coherent turbulent structures in the TurbSim Code.

( ) iNt iNt gz t Ae Be where Nzθδ

θ− ∂

= + =∂

2 2 2( / )( / ) / ( / ) ( / )Ri g z U z N U zθ θ= ∂ ∂ ∂ ∂ = ∂ ∂


The NCAR KH Billow Simulation


Interaction of KH Billow and a Wind Turbine Rotor

Using Wavelet Analysis to Observe a Time-Frequency Variation of Blade Root Loads Induced by Coherent Turbulence from a Simulated KH Billow Breakdown


Using Wavelet Analysis to Observed Turbulence Rotor Interaction

• Blade root flapwise load time series

• Scalogram showing dynamic stress levels as a function of time and frequency

• Detail band frequency ranges roughly correspond to groups of modal frequencies including . . .

D9 (0.234 – 0.468 Hz) = 1-P, tower 1st bending mode

D5 (3.750 – 7.500 Hz) = blade bending/torsion/tower

D3 (15.00 – 30.00 Hz) = blade bending/torsion/tower

D6 (1.875 – 3.750 Hz) = blade, tower bending modes D7 (0.936 – 1.875 Hz) = blade 1st bending modes

D4 (7.500 – 15.00 Hz) = blade/tower interactions

• Time series of root loads in 7 frequency (detail) bands using the discrete wavelet transform


Coherent structures produce higher frequency loading

Wavelet Continuous Transform Co-Scalograms of CTKE and qc

• Steady, High Shear (α = 1.825)

• Slightly stable (Ri = + 0.05)

• Steady, equilibrium flow conditions

• IEC Kaimal NTM (α = 0.2)

• Neutral stability (Ri = 0)

• Steady, equilibrium flow conditions

• Breaking KH Billow (αo = 1.825)

• Slightly stable (Ri = +0.05)

• Unsteady, non-equilibrium, flow conditions

CTKE Time Series

Dynamic Pressure, qc Time Series

Energy Flux from Coherent Turbulence (CTKE) to Blade Dynamic Pressure at 78% Span Under Three Inflow Conditions


Actual Measurement of Coherent Structure and ART Turbine Interaction

• CTKE measurements from five sonic anemometers on upwind array

• Flapwise root bending measurements

• X-Y-Z velocity measurements from Inertial Measure Unit mounted on low-speed shaft forward billow block immediately behind turbine rotor

Upwind arrayinflow CTKE

m2 /s

2

0

20

40

60

80

100

120

0

20

40

60

80

100

120rotor top (58m)rotor hub (37m)rotor left (37m)rotor right (37m)rotor bottom (15m)

IMU velocity components

0 2 4 6 8 10 12

mm

/s

-20

-10

0

10

20

-20

-10

0

10

20

Time (s)

492 494 496 498 500 502 504

vertical (Z)side-to-side (Y)fore-aft (X)

zero-meanroot flapbendingmoment

kNm

-400

-300

-200

-100

0

100

200

300

400

-400

-300

-200

-100

0

100

200

300

400

Blade 1Blade 2


Energy Flux from Coherent Structure to ART Drivetrain


TurbSim Coherent Structure Interaction Simulation

Loc

al C

TKE

E

xcita

tion

(m2 /s

2 )2

Lo

cal D

ynam

ic P

ress

ure,

q c

R

espo

nse

(Pa)

2

Lo

cal R

elat

ive

Ene

rgy

Flux

(m

2 /s2 −

Pa)

L

ocal

CTK

E

(m2 /s

2 )

Time (s)

WindPact 1.5 MW Virtual Turbine

Energy flux from turbulence to 78% span blade qc


Measuring and Simulating Coherent Structures

•Coherent structures were determined from the available measurements (San Gorgonio, the NWTC, and the tower in SE Colorado) •The process identifies the intensity (peak CTKE), the total number of structures and their length in a 10-minute record from measured data. •We found that the number of coherent events and the intensity or rate of occurrence in a record could be modeled by a inhomogeneous Poisson Process; i.e., where the rate parameter λ is a function of a combination of the scaling variables in TurbSim including Uhub, Ri, σw, u*, and height.

{ } ( )( )!

nt tP N t n e

nλ λ−= =


San Gorgonio Example for Probability Distribution of the Number of Coherent Structures Contained in a 10-minute Record, Ncoh

SanGor Distribution of Number of Coh Structures with pkCTKE > 5 (m/s)2 Ncoh PDF

Ncoh in a 10-minute record1 10 100

PDF

(1/s

)

0.001

0.010

0.100

1.000

Row 1 (upwind)Row 37 (7D spacing)Row 41 (14D spacing)


San Gorgonio Example for the Probability Distribution of the Total Length of Coherent Structures in a 10-minute Record, Tcoh

SanGor Distribution of Length of Coh Structures with pkCTKE > 5 (m/s)2 Tcoh PDF

Tcoh (s)1 10 100

PDF

(1/s

)

0.001

0.010

0.100

1.000

Row 1 (upwind)Row 37 (7D spacing)Row 41 (14D spacing)


Coherent Structure Properties in San Gorgonio Wind Farm

Length of Coherent Structures

Upwind 7D spacing 14D spacing

(s)

0

50

100

150

200

Coherent Structure Intensity vs Length

Tcoh (s)

0.1 1 10 100Pe

ak C

TKE

(m/s

)20

10

20

30

40

50

60

Upwind7D Spacing14D Spacing

P10 < > P90


Comparing Lamar and NWTC

Lamar U(z) PDFs for Coh Structures Present at All Heights

m/s

0 5 10 15 20 25 30

(m/s)

-1

0.00

0.02

0.04

0.06

0.08

0.10

0.12116mHub (85m)67m54mrated wind speed

NWTC U(z) PDFs for Coh Structures Present at All Heights & Stations

m/s

0 5 10 15 20 25 30

(m/s)

-1

0.00

0.02

0.04

0.06

0.08

0.10

0.12

58mHub (37m)15mrated wind speed

Probability Distributions for Wind Speeds at Which Coherent Structures Are Present at All Heights and Measurement Stations


Spatial Coherence

• The spatial coherence was calculated from the available measurements for the three sites: San Gorgonio, the NWTC, and Lamar.

• The Davenport and the IEC (Thresher-Holley) coherence models were compared with the two parameter IEC model providing the best performance.

• Coherence models were determined for all three wind components and at all available measurement stations at each location.


Spatial Coherence – cont’d

• The IEC Coherence Model is where the decrement a and b/Lc term are the two free variables fitted to the data. The IEC values for Ed.3 are 12 and 0.12 respectively.

• Both parameters were found to be functions of wind speed and stability (Ri) and, in some cases, height as well.

• Only the U and V components are available for San Gorgonio

( )( )0 52 2.

( , ) exp / ( ( / )hub cCoh r f a f r V r b L = − ⋅ +


San Gorgonio Spatial Coherence

V-component

U (m/s)

0 5 10 15 20 25 30

"a"

cohe

rent

dec

rem

ent

1.5

2

3

45678

15

20

30

4050607080

1

10

100

b/L term

0.001

0.01

0.1

Upwind "a" parameterDownwind "a" parameter Upwind b/L parameterDownwind b/L parameter

b/L

term

U-component

U (m/s)

0 5 10 15 20 25 30

"a" coherent decrement

2

4

6

8

10

12

14

16

0.0001

0.001

0.01

0.1

IEC NTM (Ed.3) " b/L "

IEC NTM (Ed.3) " a "


NWTC Spatial Coherence

U-component

U (m/s)

0 5 10 15 20 25 30

"a"

cohe

renc

e de

crem

ent

0

10

20

30

40

50

60STC1 ( RiTL < -1)STC2 (-1 <= RiTL < 0)STC3 (0 <= RiTL < +0.1)STC4 (0.1 <= RiTL < 0.25)STC5 (RiTL >= 0.25)

STC1

STC2

STC3

STC4

STC5

IEC Ed 3

IEC Ed 2

NWTC

U (m./s)0 5 10 15 20 25 30

b/L

u ter

m

0.0001

0.001

0.01

0.1

IEC

V-component

U (m/s)

0 5 10 15 20 25 30

"a"

cohe

renc

e de

crem

ent

0

10

20

30

40

50

60

STC1STC2STC3STC4STC5

STC3

STC2

STC1

STC4

STC5

NWTC

U (m./s)

0 5 10 15 20 25 30

b/L v t

erm

0.0001

0.001

0.01

0.1

W-component

U (m/s)

0 5 10 15 20 25 30

"a"

cohe

renc

e de

crem

ent

0

10

20

30

40

50

60

STC1STC2STC3STC4STC5

STC3

STC2

STC1STC4

STC5

NWTC

U (m./s)

0 5 10 15 20 25 30

b/L w

term

0.0001

0.001

0.01

0.1

1


Lamar Spatial Coherence

IEC

U-component

U (m/s)

0 5 10 15 20 25 30

"a"

cohe

renc

e de

crem

ent

0

5

10

15

20

25

30

STC2

STC3

STC4

STC5

IEC Ed 3

IEC Ed 2

Lamar

U (m./s)

0 5 10 15 20 25 30

b/L u

term

0.0001

0.001

0.01

0.1

1

STC1 ( RiTL < -1)STC2 (-1 <= RiTL < 0)STC3 (0 <= RiTL < +0.1)STC4 (0.1 <= RiTL < 0.25)STC5 (RiTL >= 0.25)

IEC

V-component

U (m/s)

0 5 10 15 20 25 30

"a"

cohe

renc

e de

crem

ent

0

5

10

15

20

25

30

STC2STC3STC4STC5

STC3

STC2

STC4

STC5

Lamar

U (m./s)

0 5 10 15 20 25 30

b/L v

term

0.0001

0.001

0.01

0.1

1

W-component

U (m/s)

0 5 10 15 20 25 30

"a"

cohe

renc

e de

crem

ent

0

5

10

15

20

25

30

STC2STC3STC4STC5

STC3

STC2STC4STC5

Lamar

U (m./s)0 5 10 15 20 25 30

b/L w

term

0.0001

0.001

0.01

0.1

1