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

The power output of wind farms depends strongly on spatial turbine arrangement, and the resulting turbulent interactions with the atmospheric boundary layer. Wind farm layout optimization to maximize power output has matured for small clusters of turbines, with the help of analytical wake models. On the other hand, for large farms approaching a fully developed regime in which the integral power extraction by turbines is balanced through downward transport of the mean kinetic energy, the influence of turbine layout is much less understood. The main goal of this work is to study the effect of turbine layout on the power output for large wind farms approaching a fully developed regime. For this purpose we employ an experimental setup of a scaled wind farm with 100 porous disk models, of which 60 are instrumented with strain gauges. Our experiments cover a parametric space of 56 different layouts for which the turbine-area density is constant, focusing on different turbine arrangements including nonuniform spacings. The strain-gauge measurements are used to deduce surrogate power and unsteady loading on turbines for each layout. Our results indicate that the power asymptote at the end of the wind farm depends on the layout in different ways. Firstly, for layouts with a relatively uniform spacing we find that the power asymptote in the fully developed regime reaches approximately the same value, similarly to the prediction of available analytical models. Secondly, we show that the power asymptote in the fully developed regime can be lowered by inefficient turbine placement, for instance when a large number of the turbines are located in the near wake of upwind turbines. Thirdly, our experiments indicate that an uneven spacing between turbines can improve the overall power output for both the developing and fully developed part of large wind farms. Specifically, we find a higher power asymptote for a turbine layout with a significant streamwise uneven spacing (i.e., a large streamwise spacing between pairs of closely spaced rows that are slightly staggered). Our results thereby indicate that such a layout may promote beneficial flow interactions in the fully developed regime for conditions with a strongly prevailing wind direction.

Figure 1

A photograph of the NU2-C3 layout with a spanwise shift of $1D$ in the wind tunnel.

Figure 2

Illustration of the wind tunnel test section with the scaled wind farm model at the end, and a fetch region to develop the turbulent boundary layer. Image not to scale.

Figure 3

Porous disk model.

Figure 4

An overview of the studied wind farm layout patterns. Each series consists of a number of layouts, by sliding the indicated (blue) porous disk models in the spanwise direction, over the specified range for $\mathrm{\Delta }y$. The total wind farm layout results from repeating the displayed unit cells five times in the spanwise direction, and until a total of 20 rows is reached in the streamwise direction.

Figure 5

The layout of the wind farm consists of 20 rows with five porous disk models each, and can be altered by sliding rows in the spanwise direction (i.e., $\mathrm{\Delta }yi$ for each row $i)$, or by changing the streamwise spacing between rows (i.e., $S_{xi}$ between row $i$ and $i+1)$. Data were acquired from the three instrumented porous disk models in the middle of each row.

Figure 6

Hot-wire measurements of the mean streamwise velocity and turbulence intensity for an aligned layout [(a),(b)], and for a staggered layout [(c),(d)]. Vertical dotted lines indicate the separate measurement series, and the solid black line shows where the mean velocity reaches $99\%$ of the freestream velocity, as an indication for the boundary layer height. The hot-wire probe was calibrated to measure velocities as low as $3\mathrm{m}/\mathrm{s}$. In the turbulent low-momentum wakes, red contour lines indicate where the measured velocity values were lower than this threshold for a percentage of $1\%,5\%$, or more than $10\%$ of the total measurement points.

Figure 7

Comparison of the hot-wire measurements (HW) of the mean streamwise velocity with the spatially averaged velocity estimated by the porous disk models (PD) for an aligned (a) and staggered (b) layout.

Figure 8

Comparison of the local turbulence intensity, measured by the hot-wire probe (HW), and by the porous disk models (PD) for an aligned (a) and staggered (b) layout.

Figure 9

Wind farm measurements of the mean surrogate power in each row for (a) the U-C1 and (b) the U-C2 layout series. The layouts are indicated with corresponding colors on top of each figure. See Fig. 4 for an overview of all layouts.

Figure 10

Turbulence intensity as measured by the porous disk models in each row for (a) the U-C1 and (b) the U-C2 layout series. The layouts are indicated with corresponding colors on top of each figure. See Fig. 4 for an overview of all layouts.

Figure 11

Wind farm measurements of the mean surrogate power in each row for (a) the NU1-C1 and (b) the NU1-C2 layout series. The layouts are indicated with corresponding colors on top of each figure. See Fig. 4 for an overview of all layouts.

Figure 12

Turbulence intensity as measured by the porous disk models in each row for (a) the NU1-C1 and (b) the NU1-C2 layout series. The layouts are indicated with corresponding colors on top of each figure. See Fig. 4 for an overview of all layouts.

Figure 13

Porous disk measurements of mean surrogate power in each row for (a) the NU2-C1, (b) the NU2-C2, and (c) the NU2-C3 layout series. The layouts are indicated with corresponding colors on top of each figure. See Fig. 4 for an overview of all layouts.

Figure 14

Porous disk measurements of turbulence intensity in each row for (a) the NU2-C1, (b) the NU2-C2, and (c) the NU2-C3 layout series. See Fig. 4 for an overview of the layouts.

Figure 15

The farm-average surrogate power (a) and the average over rows 16–19 (b) as a function of the spanwise shift ${\mathrm{\Delta }}_y$. See Fig. 4 for an overview of the layouts.

Figure 16

The farm-average unsteady loading (a) and the average over rows 16–19 (b) as a function of the spanwise shift ${\mathrm{\Delta }}_y$. See Fig. 4 for an overview of the layouts.