Effect of blockage on wind turbine power and wake development

Abstract. Recent work by Lanzilao and Meyers (2024) has shown that wind-farm blockage introduces an unfavourable pressure gradient in front of the farm and a favourable pressure gradient in the farm, which are strongly correlated with the nonlocal efficiency and wake efficiency, respectively. In particular, the favourable pressure gradient in the farm increases the farm wake efficiency, defined as the average farm power normalized by the average front-row power. Here, we investigate the impact of blockage on wake development and the power of wind turbines using an idealized large-eddy simulation setup in which blockage conditions are artificially introduced using a rigid lid, in addition to using neutral stratification and no wind veer. We simulate both infinite and finite single turbine rows, as well as a setup with two staggered rows. Blockage strength is adjusted by varying the boundary layer height (H) and turbine spacing (S). We find that blockage strongly affects near-wake behaviour, altering Froude momentum theory, by introducing a favourable pressure difference (ΔpNW) across the turbine row. The same setup also leads to an unfavourable pressure difference (ΔpFW) in the far wake, which simply follows from the rigid-lid conditions and the change in momentum flux due to wake recovery. A strong positive correlation of −ΔpNW with both the power coefficient (CP) and thrust coefficient (CT) is observed. Specifically, as S and H decrease, −ΔpNW, CP, and CT increase. At the same time, a lower induction is observed at the rotor disc, and a lower wake deficit, in the near wake. The reduction of near-wake velocity deficit as a result of blockage also translates into lower deficits and wake widths in the far wake. When scaling the far-wake development with the initial far-wake deficit and width, we do not see a direct effect of the adverse pressure gradient on the wake recovery. However, we do see a profound effect of H on the wake spreading, with higher boundary layers leading to faster spreading. This relates to the fact that the wake can more freely expand vertically in high-boundary layer cases into a larger region of high-speed flow than for shallow boundary layers. Finally, we introduce a simplified Froude momentum balance to parameterize the relation between blockage, pressure drop, and near-wake properties and compare it to the large-eddy simulation results.