Statistics of Wind Farm Wakes for Different Layouts and Ground Roughness

In this work, wakes of wind farms are investigated using large-eddy simulation with an actuator disk model for the wind turbine. The effects of streamwise turbine spacings, number of wind turbine rows and roughness lengths of ground surface on the characteristics of wind farm wakes are examined. The simulation results showed that the effects of S-x (streamwise turbine spacings) are mainly located in the near wake of wind farm (less than 20 rotor diameters downstream from the last row of the wind farm), where the turbulence intensity is higher for smaller values of S-x. In the far wake of wind farms (more than 90 rotor diameters downstream from the last row of the wind farm), the streamwise velocity deficit as well as the Reynolds stresses from cases with different streamwise turbine spacings are close to each other. For cases with more wind turbine rows (N-row) and larger roughness length of ground surface (k0), faster velocity recovery and higher turbulence intensity are observed. Terms in the budget equation for mean kinetic energy (MKE) are examined. The analyses showed that the vertical MKE transport via mean convection and turbulence convection plays a dominant role in the velocity recovery in wind farm wakes, being different from the wind farm region where streamwise MKE flux due to mean convection also plays a role. Lastly, an analytical model for the velocity deficit in wind farm wake is proposed based on the Emeis model. Improvements on the model predictions are observed for all the simulated cases. The velocity deficit at one downstream location of the wind farm needs to be given is one major limitation of the analytical model of this type.