Large eddy simulation of a large wind-turbine array in a conventionally neutral atmospheric boundary layer

Abstract

Under conventionally neutral conditions, the boundary layer is frequently capped by an inversion layer, which counteracts vertical entrainment of kinetic energy. Very large wind farms are known to depend on vertical entrainment to transport energy from above the farm towards the turbines. In this study, large eddy simulations of an infinite wind-turbine array in a conventionally neutral atmospheric boundary layer are performed. By carefully selecting the initial potential-temperature profile, the influence of the height and the strength of a capping inversion on the power output of a wind farm is investigated. Results indicate that both the height and the strength have a significant effect on the boundary layer flow, and that the height of the neutral boundary layer is effectively controlled by the capping inversion. In addition, it is shown that the vertical entrainment rate decreases for increasing inversion strength or height. In our infinite wind-farm simulations, varying the inversion characteristics leads to differences in power extraction on the order of 13% ± 0.2% (for increasing the strength from 2.5 to 10 K), and 31% ± 0.4% (for increasing the height from 500 to 1500 m). A detailed analysis of the mean kinetic-energy equation is included, showing that the variation in power extraction originates from the work done by the driving pressure gradient related to the boundary layer height and the geostrophic angle, while entrainment of kinetic energy from the free atmosphere does not play a significant role. Also, the effect of inversion strength on power extraction is energetically not related to different amounts of energy entrained, but explained by a difference in boundary layer growth, leading to higher boundary layers for lower inversion strengths. We further present a simple analytical model that allows to obtain wind-farm power output and driving power for the fully developed regime as function of Rossby number and boundary layer height.