The Actuator Farm Model for LES of Wind Farm-Induced Atmospheric Gravity Waves and Farm-Farm Interaction

Abstract. This study introduces the actuator farm model (AFM), a novel parameterization for simulating wind turbines within large eddy simulations (LESs) of wind farms. Unlike conventional models like the actuator disk (AD) or actuator line (AL), the AFM utilizes a single actuator point at the rotor center and only requires 2–3 mesh cells across the rotor diameter. Turbine force is distributed to the surrounding cells using a new projection function characterized by an axisymmetric spatial support in the rotor plane and Gaussian decay in the streamwise direction. The spatial support's size is controlled by three parameters: the half-decay radius r_1/2, smoothness s, and streamwise standard deviation σ. Numerical experiments on an isolated NREL 5MW wind turbine demonstrate that selecting r_1/2=R (where R is the turbine radius), s between 6 and 10, and σ ≈ Δx/1.6 (where Δx is the grid size in the streamwise direction) yields wake deficit profiles, turbine thrust, and power predictions similar to those obtained using the ADM, irrespective of horizontal grid spacing down to the order of the rotor radius.

Using these parameters, LESs of a small cluster of 25 turbines in both staggered and aligned layouts are conducted at different horizontal grid resolutions using the AFM. Results are compared against ADM simulations employing a spatial resolution that places at least 10 grid points across the rotor diameter. The wind farm is placed in a neutral atmospheric boundary layer (ABL) with turbulent inflow conditions interpolated from a previous simulation without turbines, referred to as a precursor. The implications of coarsening the grid are discussed for both the precursor and the wind farm simulation, and a new wall modelling approach is introduced that ensures a correct shear stress profile throughout the boundary layer, even when the grid resolution is too coarse to strictly guarantee law of the wall scaling. At horizontal resolutions finer than or equal to R/2, the AFM yields similar velocity, shear stress, turbine thrust and power as the ADM. Coarser resolutions reveal the AFM's ability to accurately capture power at the non-waked wind farm rows, although underestimating the power of waked turbines. However, the far wake of the cluster can be predicted well even when the cell size is of the order of the turbine radius. 

Finally, combining AFM with a domain nesting method allows us to conduct simulations of two aligned wind farms in a fully-neutral ABL and of wind farm-induced atmospheric gravity waves under conventionally neutral ABL, obtaining excellent agreement with ADM simulations but with much lower computational cost.  The simulations highlight the AFM's ability to investigate the mutual interactions between large turbine arrays and the thermally stratified atmosphere.