Effects of self-induced gravity waves on finite wind-farm operations using a large-eddy simulation framework

Abstract

In the present study, we use large-eddy simulation (LES) to investigate how a capping inversion in combination with a stable free atmosphere influences the flow development and energy extraction in a large finite wind farm with a staggered and aligned layout. In the conventionally neutral boundary layer (CNBL), we find that gravity waves induce an unfavourable pressure gradient in the induction region of the farm which contributes to the upstream blockage, decreasing the available energy for first-row turbines. However, a favourable pressure gradient establishes through the farm in such conditions, which redistributes the energy and enhances wake recovery. These results are compared with a farm operating in the neutral boundary layer (NBL). Here, we find that only hydrodynamic effects induced by the turbines drag play a role, which cause minor pressure perturbations across the domain. For the selected atmospheric conditions, the power losses generated by the upstream blockage are balanced by the enhanced wake recovery promoted by the favourable pressure gradient throughout the farm. Consequently, the staggered farm efficiency in the CNBL is 8.8% higher than in the NBL. We note that this difference in efficiency is slightly enhanced by the 0.5? difference in wind direction at the location of the first-row turbines between the CNBL and NBL cases, which is caused by the presence of flow blockage. Since both simulations are forced with an equal turbulent velocity profile, the variation in performance is solely caused by the different vertical temperature profiles in the main domain. Finally, the staggered layout leads to a slightly stronger flow blockage than the aligned one when both farms operate in the CNBL.