Assessing spacing impact on coherent features in a wind turbine array boundary layer

Abstract. As wind farms become larger, the spacing between turbines becomes a significant design consideration that can impose serious economic constraints. To investigate the turbulent flow structures in a 4 × 3 Cartesian wind turbine array boundary layer (WTABL), a wind tunnel experiment was carried out parameterizing the streamwise and spanwise wind turbine spacing. Four cases are chosen spacing turbines by 6 or 3D in the streamwise direction, and 3 or 1.5D in the spanwise direction, where D = 12 cm is the rotor diameter. Data are obtained experimentally using stereo particle image velocimetry. Mean streamwise velocity showed maximum values upstream of the turbine with the spacing of 6 and 3D in the streamwise and spanwise direction, respectively. Fixing the spanwise turbine spacing to 3D, variations in the streamwise spacing influence the turbulent flow structure and the power available to following wind turbines. Quantitative comparisons are made through spatial averaging, shifting measurement data and interpolating to account for the full range between devices to obtain data independent of array spacing. The largest averaged Reynolds stress is seen in cases with spacing of 3D × 3D. Snapshot proper orthogonal decomposition (POD) was employed to identify the flow structures based on the turbulence kinetic energy content. The maximum turbulence kinetic energy content in the first POD mode is seen for turbine spacing of 6D × 1.5D. The flow upstream of each wind turbine converges faster than the flow downstream according to accumulation of turbulence kinetic energy by POD modes, regardless of spacing. The streamwise-averaged profile of the Reynolds stress is reconstructed using a specific number of modes for each case; the case of 6D × 1.5D spacing shows the fastest reconstruction to compare the rate of reconstruction of statistical profiles. Intermediate modes are also used to reconstruct the averaged profile and show that the intermediate scales are responsible for features seen in the original profile. The variation in streamwise and spanwise spacing leads to changes in the background structure of the turbulence, where the color map based on barycentric map and Reynolds stress anisotropy tensor provides an alternate perspective on the nature of the perturbations within the wind turbine array. The impact of the streamwise and spanwise spacings on power produced is quantified, where the maximum production corresponds with the case of greatest turbine spacing.