wake meandering under non-neutral atmospheric stability ... · wake meandering under non-neutral...

Wake meandering under non-neutral atmospheric stability conditions – theory and facts

G.C. Larsen, E. Machefaux and A. Chougule

DTU Wind Energy, Technical University of Denmark

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Outline

• Introduction

• The DWM model

• Atmospheric stability

• DWM atmospheric stability conjecture

• Validation of conjecture

– analysis of full-scale velocity measurements

– analysis of full-scale wake deficit dynamics

• Generalization of DWM to non-neutral conditions

• Conclusions

• Future work

• Acknowledgements

2 26 November

2015




Introduction

• Analyses of full-scale measurements from Danish (offshore) wind farms have shown a significant dependence of wake losses and wake driven loading on atm. stability conditions [e.g. Jensen, EWEC 2007; Hansen, Torque 2012; Hansen, Torque 2014]

• Horns Rev; 8m/s; 90 deg.; un-stable ctr. stable

3 26 November

2015




The DWM model

• DWM is the poor man’s LES

– core of the model is a split of scales

– large turb. scales responsible for meandering

– small turb. scales wake expansion/attenuation

• Computational in-expensive … preserving essential physics of non-stationary wake flows

• Suited for WT design and WF layout optimization 4 26

November 2015


velocity deficit

wake meandering

Wind turbine wake

wake induced

turbulence



Atmospheric stability

• Mechanical friction is dictating turbulence production in the atmospheric boundary layer (ABL) under neutral conditions

• Buoyancy effects adds to friction when it comes to the turbulence production under ABL stability conditions different from neutral

• Buoyancy:

– Increased/decreased turbulence intensity for unstable/stable conditions

– Modify turbulence structure … mainly the large scale regime

5 26 November

2015




DWM atmospheric stability conjecture

• ABL stability impacts “only” the turbulent scales within the meandering regime [Larsen, Euromech 508, 2009]

• Burning questions:

– Does the DWM split in scales match the “split” between turbulence energy producing regime and the inertial subrange regime?

– Can a consistent kinematic model for turbulence modeling under non-neutral ABL be formulated?

6 26 November

2015




Validation setup (1)

• Full-scale sonic measurements (16.5m a.g.l.)

• “Homogeneous” inflow conditions ensured by selecting data from only the (prevailing) wind direction sector (120o- 150o)

• 1122 available 10-minute time series (4-10m/s)

7 26 November

2015




Validation setup (2)

• Pulsed LiDAR mounted on the nacelle of a 500kW Nordtank turbine … facilitating cross sectional scanning in a 7×7 Cartesian grid

• Time series ranging between 3 and 5 hours required for robustness of analysis

8 26

November 2015




Validation approach

• Data binned with respect to mean wind speed and ALB stability

• Focus on lateral turbulence characteristics and lateral wake dynamics (i.e. wake deficit displacements)

• 7 ABL stability classes defined in terms of Monin-Obukhov length (L) [Peña, Royal Met. Soc., 2010]

– Very stable: 10 ≤ L < 50

– Stable: 50 ≤ L < 200

– Near neutral-stable: 200 ≤ L < 500

– Neutral: ׀L500 ≤ ׀

– Near neutral-unstable: -500 < L ≤ -200

– Unstable: -200 < L ≤ -100

– Very unstable: -100 < L ≤ -50

9 26 November

2015




Validation: full-scale velocity recordings (1)

• ABL stability affects turbulence level and turbulence structure

• De-trended lateral turbulence component ... spectral inertial subrange regime hardly affected!

10 26 November

2015





• Lateral turbulence variance normalized with “neutral case” bin wise

• Turbulent energy increase relatively for unstable ABL conditions … and decrease for stable. Most pronounced for low mean wind speeds

11 26 November

2015


0

0,5

1

1,5

2

2,5

3

3,5

4

-3 -2 -1 0 1 2 3

5-6m/s

6-7m/s

7-8m/s

8-9m/s

9-10m/s




• Large scales: frequencies below the DWM frequency split fs = U/(2D)

• Large scale variance normalized with “neutral case”

• Turbulent energy increase relatively for unstable ABL conditions … and decrease for stable

12 26 November

2015


0

0,5

1

1,5

2

2,5

3

3,5

4

-3 -2 -1 0 1 2 3

5-6m/s

6-7m/s

7-8m/s

8-9m/s

9-10m/s




• Small scale variance normalized with “neutral case”

• Small scale turbulence energy level roughly invariant with respect stability conditions

• … thus supporting the DWM stability conjecture 13 26

November 2015


0

0,5

1

1,5

2

2,5

3

3,5

4

-3 -2 -1 0 1 2 3

5-6m/s

6-7m/s

7-8m/s

8-9m/s

9-10m/s



Validation: full-scale wake deficit dynamics (1)

• Three test cases associated with low wind conditions, and therefore pronounced deficits (i.e. high trust), are selected for this part of the analysis

• Focus on lateral wake deficit dynamics

• Wake deficit dynamics is obtained from “instantaneous” LiDAR cross sectional scans … combined with a wake deficit tracking procedure

14 26

November 2015





• Resolved wake deficits expressed in meandering frame of reference almost invariant to the ABL stability conditions ... thus confirming the DWM conjecture

15 26 November

2015





• Normalized variance of the lateral wake center position [6; 7]m/s

• Reasonable agreement between the range of “large” scale variance stability dependence ([6; 7]m/s) and the range of wake centre lateral dynamics variance stability dependence

16 26 November

2015


0

0,5

1

1,5

2

-3 -2 -1 0 1 2 3

3D

4D

5D



Generalization of DWM to non-neutral conditions

• ABL stability impacts only the turbulent scales within the meandering regime

• Buoyancy consistent kinematic model used for turbulence modeling under non-neutral ABL conditions … capturing the spectral “stability cascade”

17 26 November

2015




Conclusions

• DWM split in scales roughly “matches” the split in scales between the turbulence energy-containing range and the turbulence inertial subrange … confirming the DWM stability conjecture

– ABL stability impacts mainly the “large” meandering turbulence scales

– “small” scale turbulence regime can be considered invariant with respect to ABL stability conditions

• Generalized spectral tensor facilitates generalization of DWM to non-neutral stability conditions

18 26 November

2015




Future work

• Improve/refine the fitting procedure for the generalized spectral tensor parameters … on-going

19 26 November

2015




Acknowledgements

The EUDP project “Impact of atmospheric stability conditions on wind farm loading and production”, under contract 64010-0462, is acknowledged for financial support and thus for making this study possible

20 26 November

2015





DWM model

26 November 2015

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