Wind Farm Wake Effects Estimations by a Mosaic Tile Wake Model.

Wind Farm Wake Effects Estimations by a Mosaic Tile Wake Model.

Ole Steen Rathmann*, Søren Ott*, Mark Kelly*

* Risoe-DTU, Roskilde DENMARK

Wind Farm Wake Effects Estimations by a Mosaic Tile Wake Model2 Risø DTU, Technical University of DenmarkRisø DTU, Technical University of Denmark

In Memory of Sten Frandsen

March 2011

Sten Frandsen achieved in 2007 the Danish Doctoral degree (highest academic degree in Danmark) on turbulence in wind farms.

He was a forerunner in describing wind farm wake effects.He was a key-person in establishing the EU Upwind project and other cooperation projects. He was a great inspiration to colleagues and co-workers in in various international projects.

1951-October 2010

As a IPCC-member:Nobel Peace Price 2007

laureate


OUTLINE

• Introduction• FUGA CFD-modelling of wakes: Basic features• FUGA CFD-modelling: predictions vs. selected wind farm data • FUGA-Light Wake parameterization• Wake-surface and wake-turbine interaction• The new “mosaic tile” concept• Model predictions vs. wind farm data• Downwind recovery and stability impact• Conclusion

March 2011


Introduction• Existing simple parameterized as well as CFD wake models tend to

underestimate the over-all speed- and power deficits in large wind farms.• Existing models also often fail to catch the details in the increase of speed

deficit with downwind distance 1).• Task of this work:

• a fast wake model, able to represent the over-all speed- and power-deficit as well as the variation within a farm with reasonable accuracy;

• to be applicable in engineering wind resource software.

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___________________________________________________________________________________________1) S. Frandsen et al., Analytical Modeling of Wind speed Deficit in Large Offshore Wind Farms, Wind Energy 9, 39-53 (2006).

Risø DTU, Technical University of DenmarkRisø DTU, Technical University of Denmark

Acknowledgments• Work funded by:

• EU-projects TopFarm and Upwind (WP8)• The Offshore Wind Accelerator (OWA) Wake Effects project. OWA is a

Research and Development collaboration which aims to significantly reduce the costs of offshore wind power. The OWA partners are The Carbon Trust, Dong Energy, E-on, Mainstream Renewable Power, RWE Innogy, SSE Renewables, Scottish Power Renewables, Statoil and Statkraft.

• Danish PSO-project WindShadow.

• Thanks are due to Dong Energy and Vattenfall for permission to utilize off-shore wind farm data.

March 2011Wind Farm Wake Effects Estimations by a Mosaic Tile Wake Model5


FUGA2): Linearised CFD modelling for wakes (1)

• Linearised RANS equations (momentum+continuity)• ‘Simple closure’:• BL-domain defined by surface roughness Z0 and inversion layer height Zi.

• Turbine rotor represented by an actuator disk

• Fast, mixed-spectral solver using pre-calculated look-up tables (LUTs)• No computational grid• No numerical diffusion • No spurious mean pressure gradients• No adjustable model parameters• Integration with WAsP: import of wind climate and turbine data.• 105 times faster than conventional CFD!

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____________________________________________________________________________________2) S.Ott: “Linearised CFD Models for Wakes”. Risoe-R-1772(EN). Risoe-DTU (2011).

*t u z


FUGA-Modelling of wakes (2)

• A few rotor-diameters downwind of a wind turbine:o non-linear effects vanish; ando speed deficits of individual wakes scale with Ct and U0.o Effects of different wakes may be superimposed

• Accurate in the far wake even if inaccurate in the near wake• Local reduced wind speed at each turbine used to estimate the individual

turbine thrust coefficient Ct.

• By a downwind marching procedure the entire wind farm is covered

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CFD-model: Comparison to selected WF data• FUGA was used to model selected characteristic flow cases from the

Danish off-shore wind farm Horns Rev• Compares very well with data in view of the somewhat crude assumptions

applied.

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0 2000 4000 6000

D ow nw ind D istance [m ]

0.5

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0.9

1

Rel

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H orns R ev - 8 m /s - 270 o (15 o span)D ata

FU G A

0 2000 4000 6000


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FU G A

Wind farm data: U=8m/s +/- 0.5 m/s


”FUGA-Light” Wake parametrization: (1)• The “near-field” close WT : classical tulip-like stream-line expansion.

• A parameterization is picked from the FUGA CFD-model

• Characteristic length scale derived from most important part of FUGA momentum equation controlling the momentum diffusion:

• =>

• All spatial dimensions scaled by Lν :

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-2 -1 0 1 2

-0.75

-0.5

-0 .25

0

0.25

0.5

0.75

A R A w 0

U 0 U w 0

T

212 0TT C U

0 0(1 )wU a U 1 1 Ta C

0w RA A1

21

1

a

a

T RA A a

* 0 * 0; ; ( ) / ln( / )eddy tsymmu z U h u h Z U U U 0/ ln( / )L H H Z

# # # # #/ , / , / , / , /x x L y y L L H H L D D L


”FUGA-Light” Wake parametrization (2)• Presently limited to off-shore: Z0=0.2mm

• Cross-wind reduced-speed profile at Z=H:• Ecellent Gaussian representation:

• Downwind evolution: wake expands horizontally appr. as ½-power-law, including a shift in x#:

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6

6.5

7

7.5

8

8.5

9

9.5

10

10.5

-150 -100 -50 0 50 100 150

Spee

d [m

/s]

Cross wind distance Y [m]

DR=50, Zh=50; Ct=0.8; X=5DR

Red. U

Gaussian

2 2 20 exp ( ) ( ) / 2TU U A y y z H

0

5

10

15

20

25

0 500 1000 1500

σ #

x'#

Wake expansion (dimensionless units)

H=50, Dr=25

H=50, Dr=50

H=100, Dr=50

H=100, Dr=100

2

# # #,0 #,0 #' ;x x x x D

Applied x#-shift in wake expansion rule:


”FUGA-Light” Wake parametrization (3)Surface Interactions

• FUGA-Light uses the approximation that vertical wake profile is equal to the horizontal one – thereby omitting a direct description of wake interaction with sea/ground surface.

• Indirectly, the surface interaction and the effect of the height-depending diffusivity are described by the Q# dependence on downwind distance: Q#(x#).

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0.05

0.055

0.06

0.065

0.07

1 10 100 1000 10000

Q#

Scaled doown wind distance X#

Wake Strength - dimensionless units

H=50, Dr=25H=50, Dr=50H=100, Dr=50"H=100, Dr=100""Fit"

2# 0 #

2# # #

/( );tA A U C D

Q A


Influence of Near-Turbine flow• Effect on wake of “tulip-flow” expansion

at originating turbine described by additional x#-offset to achieve:

• Interaction of a wake with the “tulip-flow” at a downwind turbine “j” described by a discrete x#-shift, causing an “sudden” wake expansion:

(Foverlap : the fraction of turbine rotor “j” covered by the wake in question.)

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( )wake R RA x D A

,( ) ( ) ( )wake j wake j R j j j overlapA x A x A a F -2 -1 0 1 2

-1.25

-1

-0 .75

-0.5

-0 .25

0

0.25

0.5

0.75

1

1.25

A R At2

w 0

U t1

Ut2

w0

At1

w

At1

w+ A T,1


New “Mosaic tile concept”• The mosaic-tile model: Redefinition of the original concept 3) • Rotor area divided in a “tiles-mosaic”, each with a sampling point• Mean reduced wind speed over the rotor area calculated as a weighted

mean of reduced wind speeds in each tile

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3) S.Frandsen, H.E.Jørgensen, R.Barthelmie, O.Rathmann et al.: ”The Making of a second-generation wind farm efficiency model-complex ”., EWEC 2008. paper 49.

Vertical plane cut, perpendicular to wind direction, indicating the turbine rotor divided in a number of ’tiles’.


Wind farm data: Horns Rev• Turbines: 2MW, DR = 80m, Hhub = 70m

• Layout: sr = sf = 7

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WT01

WT02

WT03

WT04

WT05

WT06

WT07

WT08

WT11

WT12

WT13

WT14

WT15

WT16

WT17

WT18

WT21

WT22

WT23

WT24

WT25

WT26

WT27

WT28

WT31

WT32

WT33

WT34

WT35

WT36

WT37

WT38

WT41

WT42

WT43

WT44

WT45

WT46

WT47

WT48

WT51

WT52

WT53

WT54

WT55

WT56

WT57

WT58

WT61

WT62

WT63

WT64

WT65

WT66

WT67

WT68

WT71

WT72

WT73

WT74

WT75

WT76

WT77

WT78

WT81

WT82

WT83

WT84

WT85

WT86

WT87

WT88

WT91

WT92

WT93

WT94

WT95

WT96

WT97

WT98

423 424 425 426 427 428 429 430

Easting (km) UTM Zone32

6147

6148

6149

6150

6151

6152

Nor

thin

g (k

m)

222 deg.

270 deg.

222° +/-7.5° (15°)

8, 10 m/s +/- 0.5 m/s

270° +/-7.5° (15°)

8, 10 m/s +/- 0.5 m/s


Model predictions vs. Horns Rev data

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0 2000 4000 6000


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FU G A

FU G A-L ight

0 2000 4000 6000


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Pow

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FU G A

FU G A-L ight

0 2000 4000 6000


0.5

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FU G A

FU G A-L ight

0 2000 4000 6000


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FU G A

FU G A-L ight

FUGA and Fuga-Light prelimin. results8 m/s 10 m/s

270°

222°


Wind farm data: Nysted• Turbines: 2.33 MW, DR = 82.4m, Hhub = 68.8m

• Layout: sr = 10.6, sf = 5.9

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WT11WT21

WT31WT41

WT51WT61

WT71WT81

WT12WT22

WT32WT42

WT52WT62

WT72WT82

WT13WT23

WT33WT43

WT53WT63

WT73WT83

WT14WT24

WT34WT44

WT54WT64

WT74WT84

WT15WT25

WT35WT45

WT55WT65

WT75WT85

WT16WT26

WT36WT46

WT56WT66

WT76WT86

WT17WT27

WT37WT47

WT57WT67

WT77WT87

WT18WT28

WT38WT48

WT58WT68

WT78WT88

WT19WT29

WT39WT49

WT59WT69

WT79WT89

673 674 675 676 677 678

Easting (km) UTM Zone 32

6046

6047

6048

6049

6050

Nor

thin

g (k

m)

Nysted

263

277

263° +/-7.5° (15°)

8, 10 m/s +/- 0.5 m/s

277° +/-7.5° (15°)

8, 10 m/s +/- 0.5 m/s


FUGA model predictions vs. Nysted data

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FUGA and Fuga-Light prelimin. results8 m/s 10 m/s

278°

263°

0 2000 4000 6000


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ower

N ysted - 8 m /s - 278 o (15 o span)D ata

FU G A

FU G A-L ight

0 2000 4000 6000


0.5

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FU G A

FU G A-L ight

0 2000 4000 6000


0.5

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ower


FU G A

FU G A-L ight

0 2000 4000 6000


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FU G A-L ight


Downwind Speed Recovery• FUGA – and thus also Fuga-light - predicts a much ”slower” speed

recovery than standard wake models. • For HR rec.distance is about 16 km; somewhat slower than observed 4)

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Normalized wind speed through the wind farm and behind the wind farm compared to measurements at Horns rev. Full curves are canopy-CFD-model predictions.

_______________________________________________________________________________________4) R.J.Barthelmie et al., ” Flow and wakes in large wind farms: Final report for UpWind WP8”. Risø-R1765(EN) (2011).


Stability impact on wake effects• From wind farm data5) it is clear the

stability has an effect:

• In FUGA – and in Fuga-Light – stability may be included via the diffusivity:

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Horns Rev row 4,5-8 m/s, 270 °+/-10°

*

1 ( / )tMO

u z

z L

_______________________________________________________________________________________5) Alfredo Peña, private communication, Risoe-DTU (2011).


Conclusions and Future Development

• FUGA model predictions compare encouragingly well with wind farm data• Deviations in downwind speed- and power deficits should be analyzed –

and possible model improvements implemented • Downwind speed recovery distance seems realistic, but may have to be

improved• Inclusion of stability impact possible

• FUGA-Light, in a future version:• parameterization to be improved to match FUGA better• the non-Gaussian vertical profile should be taken into account• should be verified also for on-shore roughnesses by analyzing single-

wake profiles from FUGA for such conditions

• FUGA-Light seems suitable for inclusion in engineering wind resource estimation software.

March 2011

Wind Farm Wake Effects Estimations by a Mosaic Tile Wake Model.

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