| 12 Feb 2025
Effect of blockage on wind turbine power and wake development
Abstract. Recent work by Lanzilao & Meyers (J. Fluid Mech, 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 power of wind turbines using an idealized large-eddy simulation setup in which blockage conditions are artificially introduced using a rigid-lid, further also 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 (∆pNW) across the turbine row. The same setup also leads to an unfavourable pressure difference (∆pFW) in the far wake, which simply follows from the rigid-lid conditions and the change of momentum flux due to wake recovery. A strong positive correlation was observed of -∆pNW with both power coefficient (CP) and thrust coefficient (CT). Specifically, as S and H decrease, −∆pNW, CP and CT increase. At the same time a lower induction is observed at the rotor disk, 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 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 recovery, with higher boundary layers leading to faster recovery. 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 parametrize the relation between blockage, pressure gradient and near wake properties, and compare it to the LES results.
Competing interests: At least one of the (co-)authors is a member of the editorial board of Wind Energy Science. The authors have no other competing interests to declare.
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