A numerical study of wind turbine wakes under various atmospheric stability conditions

Archer, Cristina L.The goal of this research is to investigate the properties of wind turbine wakes and their interactions with the atmospheric boundary layer (ABL) via large-eddy simulations (LES) with special emphasis on the effects of atmospheric stability. The ABL is considered stable when the ground surface is cooler than the air, unstable when the opposite happens, and neutral when the temperature effect is negligible. In the literature, neutral conditions have been studied extensively, whereas the effects of stability have not. A new LES code, named Wind Turbine and Turbulence Simulator (WiTTS), was developed based on finite-difference (FD) schemes. First, the code's sensitivity to numerous aspects of the FD LES, such as the subgrid-scale (SGS) model, resolution, numerical treatment of the convective term, and filter types, was analyzed by simulating a neutral ABL. It was found that the Lagrangian-averaged scale-dependent (LASD) SGS model performs better than other scale-invariant Smagorinsky-type models. Second, the WiTTS was used to study the wakes from a miniature wind turbine inside a wind tunnel, following the setup of past experimental and numerical studies. It was found that those wakes are spatially anisotropic, with lateral growth faster than the vertical. Based on this, a new wake model is proposed and the Gaussian-type self-similarity is obtained for this simplified scenario. Third, to study a more realistic ABL, the stability conditions have been considered by the Boussinesq approximation and by varying thermal conditions on the ground surface, together with a constant Coriolis force. The LES results indicate that the properties of utility-scale wind turbine wakes are strongly correlated to the stability conditions. The wake recovery is enhanced by the increased turbulence due to buoyant convection in the unstable ABL, while in the stable ABL the spreading of the wake is significantly larger in the lateral direction than in the vertical direction. The stability-related wind veering from the Coriolis force causes noticeable distortion and skewness of the wakes, especially in the stable ABL, which leads to enhanced lateral mixing but deviations from the Gaussian-type self-similarity. The influence of wind veering is reduced in wind farm wakes compared to single-turbine case. Spatial variations of temperature are introduced mainly by the advection of wake rotation, which is more discernible in the stable ABL. Atmospheric stability also influences the power extraction of the wind farm via two factors: upstream wind speed and wake recovery rate. For the same upper-level (geostrophic) wind and surface roughness, the power is highest in the stable ABL due to strongest upstream wind, but the wake loss is minimized in the unstable ABL due to fastest wake recovery. In conclusion, our LES results suggest that the properties of wind turbine wakes are strongly correlated to the atmospheric stability and the Coriolis force, which therefore should be taken into consideration when assessing wind power generation in a wind farm and environmental impacts of wind turbine wakes.University of Delaware, School of Marine Science & PolicyPh.D