Outline

2. Outline • Motivation and scope • Lagrangian particle model • Simulation results • Comparison with measurements • Outlook • Conclusions

3. Dynamic behavior of the far wake

4. Main assumption Wind turbine wake meanders similar to passive tracers

5. Wake modelling as emitted passive disks Stationary wake Without effect of large scale atmospheric turbulence Meandering wake Wake meandering driven by large scale turbulence in the atmosphere

6. Simplified approach Constant passive disk advection Low-pass filtered wind direction

7. t2 t1 Particle Puff-Particle Model Puff trajectories estimated with a single particle Lagrangian model Single particle trajectory Low-pass filter Puff centroid trajectory

8. Disk-Particle Model Disk trajectories estimated with a Puff-Particle model Single particle trajectory Low-pass filter Disk centroid trajectory Meandering is estimated with a Puff-Particle approach (filtered particle trajectories) Superposition of two independent problems Internal wake flow is calculated without meandering (e.g. modified Ainslie)

9. Particle movement in turbulent atmosphere Functions a and b are dependent on turbulence characteristics in the atmospheric boundary layer Particle source

10. Disk trajectory estimation Particle speed filtered with a low pass filter Characteristic filter window is two turbine diameters Meandering contribution Filtered out Filtering High frequency components in turbulent wind speed are filtered out

11. Model implementation • Finite differences and • Initial conditions ( , ) • Inflow conditions at wind turbine hub height • Model variables a and b • Three dimensional • Unstable boundary layer • Boundary layer • Mean and turbulence scaling • Meandering • Low pass filter on particle wind speeds

12. Lateral movement – small scale turbine Stability Near unstable Particles 100 Initial conditions zo = 30m uo ~5m/s vo : random with sv wo : random with sw • Disks preserve their initial direction • Disks hitting at half-rotor diameter

13. Vertical movement – small scale turbine Stability Near unstable Particles 100 Initial conditions zo = 30m uo ~5m/s vo : random with sv wo : random with sw • Trajectories not as straight as in cross-wind • Disks covering whole rotor

14. Vertical movement – large scale turbine Trajectories for higher source present higher spread

15. Wake meandering in stable atmosphere at 4D (4x19) Modelled transversal meandering based on metmast in wake and assuming wake as non-stochastic advecting disks. Tracked transversal meandering from lidar measurements Cross-wind movement [m]

16. Outlook • Extension to generate stochastic time series of wake meandering • Planned measurements in the wake of a 5MW wind turbine (Diam 116m) with two pulsed LiDARs (begin middle of April 2009) Multibrid M5000 Photo: Rettenmeier

17. Conclusions • A Disk-Particle-Model has been implemented for wake meandering statistics estimation under unstable atmosphere • The model shows enhancement of vertical meandering with respect to lateral meandering in convective boundary layer • The validity and applicability of the main assumption of the wake behaving as a passive tracer is going to be further validated with full field measurements

18. Acknowledgements This work is done in the framework of the project LIDAR - „Development of lidar technologies for the German offshore test field“ funded by The German Federal Ministry for the Environment