Flow Adjustment Inside and Around Large Finite-Size Wind Farms

Abstract

Abstract:In this study, large-eddy simulations are performed to investigate the flow inside and around large finite-size wind farms in conventionally-neutral atmospheric boundary layers. Special emphasis is placed on characterizing the different farm-induced flow regions, including the induction, entrance and development, fully-developed, exit and farm wake regions. The wind farms extend 20 km in the streamwise direction and comprise 36 wind turbine rows arranged in aligned and staggered configurations. Results show that, under weak free-atmosphere stratification (Γ = 1 K/km), the flow inside and above both wind farms, and thus the turbine power, do not reach the fully-developed regime even though the farm length is two orders of magnitude larger than the boundary layer height. In that case, the wind farm induction region, affected by flow blockage, extends upwind about 0.8 km and leads to a power reduction of 1.3% and 3% at the first row of turbines for the aligned and staggered layouts, respectively. The wind farm wake leads to velocity deficits at hub height of around 3.5% at a downwind distance of 10 km for both farm layouts. Under stronger stratification (Γ = 5 K/km), the vertical deflection of the subcritical flow induced by the wind farm at its entrance and exit regions triggers standing gravity waves whose effects propagate upwind. They, in turn, induce a large decelerating induction region upwind of the farm leading edge, and an accelerating exit region upwind of the trailing edge, both extending about 7 km. As a result, the turbine power output in the entrance region decreases more than 35% with respect to the weakly stratified case. It increases downwind as the flow adjusts, reaching the fully-developed regime only for the staggered layout at a distance of about 8.5 km from the farm edge. The flow acceleration in the exit region leads to an increase of the turbine power with downwind distance in that region, and a relatively fast (compared with the weakly stratified case) recovery of the farm wake, which attains its inflow hub height speed at a downwind distance of 5 km.

Wind Farm Blockage and the Consequences of Neglecting Its Impact on Energy Production

“…The hub-to-hub distances in the wind tunnel were generally tight compared to modern wind farms (2.66 D laterally and 4 D streamwise, with D = rotor diameters), and there is also risk that the wind tunnel walls could influence the observed blockage. That said, large-eddy simulation results from two recent studies, [13,14], both showed significant wind speed decreases upstream of infinitely wide, full-scale wind farms. Allaerts [13] attributed the upstream flow decelerations to adverse pressure gradients induced by gravity waves.…”

“…Allaerts [13] attributed the upstream flow decelerations to adverse pressure gradients induced by gravity waves. Wu [14] also attributed upstream deficits to gravity waves, but also to cumulative turbine induction, with the balance between the two influences strongly dependent on atmospheric conditions.…”

Effect of layout on asymptotic boundary layer regime in deep wind farms

“…In their study, the staggered layout was found to produce the highest power output, showing good agreement with wind tunnel experiments of aligned and staggered wind farms [13-15]. Stevens et al [16] investigated the effect of changing the alignment angle with the wind direction of originally streamwise oriented turbine columns.It was found that an alignment angle smaller than fully staggered can result in an overall higher power output, indicating that a staggered layout is not necessarily the most optimal.While the layout clearly influences the power of the first few rows of the farm, LES results [16][17][18] and wind tunnel measurements [14,15] show that after approximately ten rows, the average row-power becomes independent of row number, thus indicating the approach of a fully-developed regime.…”

“…While the layout clearly influences the power of the first few rows of the farm, LES results [16][17][18] and wind tunnel measurements [14,15] show that after approximately ten rows, the average row-power becomes independent of row number, thus indicating the approach of a fully-developed regime.…”

Two-scale momentum theory for time-dependent modelling of large wind farms

“…The theory presented above is based on the assumption that the flow over the turbine array is in a fully developed state, i.e., the same local flow pattern around each turbine is repeated over the entire farm (except for the farm edge region). In reality, however, the flow over the array may not be fully developed and the flow pattern around each turbine may vary over the entire farm, depending on, for example, the atmospheric stability conditions (Wu and Porté-Agel, 2017). This assumption may also be violated simply due to an irregular turbine arrangement, variation of turbine operating conditions and/or inhomogeneity of the natural atmospheric flow over the farm area.…”