Wake meandering under non-neutral atmospheric stability conditions theory and facts G.C. Larsen, E. Machefaux and A. Chougule
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 DTU Wind Energy, Technical University of Denmark
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 DTU Wind Energy, Technical University of Denmark
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 velocity deficit wake meandering Wind turbine wake wake induced turbulence Computational in-expensive preserving essential physics of non-stationary wake flows Suited for WT design and WF layout optimization 4 DTU Wind Energy, Technical University of Denmark
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 DTU Wind Energy, Technical University of Denmark
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 DTU Wind Energy, Technical University of Denmark
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 (120 o - 150 o ) 1122 available 10-minute time series (4-10m/s) 7 DTU Wind Energy, Technical University of Denmark
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 DTU Wind Energy, Technical University of Denmark
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 < 500 500 L Neutral: Near neutral-unstable: -500 < L -200 Unstable: -200 < L -100 Very unstable: -100 < L -50 9 DTU Wind Energy, Technical University of Denmark
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 DTU Wind Energy, Technical University of Denmark
Validation: full-scale velocity recordings (2) Lateral turbulence variance normalized with neutral case bin wise 4 3,5 3 2,5 2 1,5 1 5-6m/s 6-7m/s 7-8m/s 8-9m/s 9-10m/s 0,5 0-3 -2-1 0 1 2 3 Turbulent energy increase relatively for unstable ABL conditions and decrease for stable. Most pronounced for low mean wind speeds 11 DTU Wind Energy, Technical University of Denmark
Validation: full-scale velocity recordings (3) Large scales: frequencies below the DWM frequency split f s = U/(2D) Large scale variance normalized with neutral case 4 3,5 3 2,5 2 1,5 1 5-6m/s 6-7m/s 7-8m/s 8-9m/s 9-10m/s 0,5 0-3 -2-1 0 1 2 3 Turbulent energy increase relatively for unstable ABL conditions and decrease for stable 12 DTU Wind Energy, Technical University of Denmark
Validation: full-scale velocity recordings (4) Small scale variance normalized with neutral case 4 3,5 3 2,5 2 1,5 1 5-6m/s 6-7m/s 7-8m/s 8-9m/s 9-10m/s 0,5 0-3 -2-1 0 1 2 3 Small scale turbulence energy level roughly invariant with respect stability conditions thus supporting the DWM stability conjecture 13 DTU Wind Energy, Technical University of Denmark
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 DTU Wind Energy, Technical University of Denmark
Validation: full-scale wake deficit dynamics (2) Resolved wake deficits expressed in meandering frame of reference almost invariant to the ABL stability conditions... thus confirming the DWM conjecture 15 DTU Wind Energy, Technical University of Denmark
Validation: full-scale wake deficit dynamics (3) Normalized variance of the lateral wake center position [6; 7]m/s 2 1,5 1 3D 4D 5D 0,5 0-3 -2-1 0 1 2 3 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 DTU Wind Energy, Technical University of Denmark
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 DTU Wind Energy, Technical University of Denmark
Conclusions DWM split in scales roughly matches the split in scales between the turbulence energycontaining 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 DTU Wind Energy, Technical University of Denmark
Future work Improve/refine the fitting procedure for the generalized spectral tensor parameters ongoing 19 DTU Wind Energy, Technical University of Denmark
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 DTU Wind Energy, Technical University of Denmark
DWM model 21 DTU Wind Energy, Technical University of Denmark 2015