Generalized wake model for dynamic wind turbine thrust and yaw actuation

Simple dynamic wake models are needed to develop improved wind farm designs and for use in operational controllers to regulate wind farm power production and reduce structural loads. We develop an improved wake model for dynamic thrust and yaw actuation. From the Reynolds-averaged Navier-Stokes, we derive a one-dimensional partial differential equation model, where the forcing is specified by an inviscid lifting line approach describing the downstream evolution of the streamwise velocity deficit, transverse velocity, and centerline of the wake. We apply a mixing-length model for the eddy viscosity in the wake that leads to linear downstream wake expansion, with a rate specified using a top-down model for a developing wind turbine array boundary layer (Meneveau 2012, J. Turbulence) where the friction velocity evolves non-monotonically downstream. The streamwise velocity deficits are distributed using a super-Gaussian function that smoothly transitions from a top-hat profile close to the turbine to a Gaussian profile farther downstream. The resulting model reproduces relevant phenomena seen in wind tunnel experiments (Bastankhah & Porte-Agel 2016, JFM) and large-eddy simulations.