Improved Wind Turbine Parameterizations in LES of Large Wind Farms Using Vorticity Dynamics

Representing the effect of small scale features of the atmospheric boundary layer (ABL) flow over large wind farms in large eddy simulations (LES) remains a challenge. The scales present in large wind farms span many orders of magnitude, from the tens of kilometer scale of the farm to the millimeter scale viscous sublayer on the turbine blades. Typical LES of wind farms parameterize the net effect of the subgrid forces along the blades using actuator methods, which accurately represent the total force exerted by the turbines and their effects on the ABL. However, these methods yield poor predictions for local velocities and power generation because the forces are effectively filtered by the simulation grid and thus fail to capture the small-scale vorticity shed from the rotor plane. Analytic representations of the vorticity shed from the modeled rotor as a result of the filtered force provide analytic corrections to these simulation errors. They also expand our knowledge of the flow past yawed and tilted turbines, approaches of current interest for optimizing wind farm designs and operations.