Richard J.A.M. Stevens

Physics of Fluids

University of Twente

Publication 65 · Wind-farm flow

Why vertical staggering helps at the entrance but not deep in the farm

M. Zhang, M.G. Arendshorst, and R.J.A.M. Stevens, Wind Energy 22(2), 189–204 (2019).

The article and figure are open access under a Creative Commons Attribution License.

Main finding

Vertical staggering increased cumulative power in the first two rows by up to 20% in the strongest tested case, but produced little or negative benefit over the last four rows in most cases. The diagnostics are consistent with local wake avoidance improving the entrance without increasing the downward turbulent energy supply to the deep farm.

Normalized cumulative power through successive turbine rows for vertically staggered small and large wind farms at three streamwise spacings
How to read the figure. Each panel tracks cumulative power through successive turbine rows relative to the corresponding aligned reference. The left column uses 100 m rotors and the right column 150 m rotors; streamwise spacing increases from top to bottom. Larger vertical offsets produce the strongest entrance gains at tight spacing, but the cumulative ratios approach one farther downstream. The insets enlarge the downstream portions of the tight-spacing cases. Open the full-resolution figure. Figure 4, cropped. M. Zhang, M.G. Arendshorst, and R.J.A.M. Stevens (2019), Creative Commons Attribution License.

Why this matters

Wake avoidance and atmospheric energy supply are different layout problems. Raising alternate rows can expose entrance-region turbines to stronger flow, but a gain is not sustained automatically as the farm modifies the atmospheric boundary layer. In these simulations, the downstream diagnostics are consistent with slowly recovering wakes behind the lower rows offsetting the taller-row gains when vertical staggering does not strengthen downward turbulent transport.

Research context

The study uses neutral, flat-terrain large-eddy simulations of finite farms with two alternating hub heights, fixed inflow direction, constant region-II thrust, and one surface roughness. It evaluates aerodynamic energy extraction rather than electrical power or annual energy production, and includes no Coriolis force, stability variation, yaw, control, loads, or wind-rose averaging. The last-four-row average is an operational downstream measure rather than an infinite-farm limit, especially for the shorter farms. Similar vertical-flux profiles support the proposed energy-supply explanation but do not uniquely establish causality.

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