A lifting line theory for yawed wind turbine actuator disks

Deflecting wind turbine wakes by yawing, which can increase wind farm power production, is receiving increased interest. Achieving this benefit requires improved predictions of the transverse velocity induced by the transverse component of the thrust force and the circulation of the counter-rotating vortex pair shed from the rotor. We focus on the inviscid region directly behind the turbine, which we treat as a porous lifting surface (airfoil). Prandtl's lifting line theory is applied by distributing the total transverse force along a lifting line through the center of the rotor. The resulting circulation distribution is elliptic and the theory is used to predict the induced constant transverse velocity in the wake and the counter-rotating vortex pair's circulation. The average velocity through the rotor and streamwise velocity in the wake are then found using mass and momentum conservation. The lifting line model is compared to numerical simulations of an actuator disk under uniform inflow and found to more accurately predict the transverse velocity (wake skewness) angle than other models. Using it to generate an initial condition also improves the accuracy of wake models for yawed turbines.