Abstract
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.
Highlights
Allowing insufficient space between wind turbines in an array leads to decreased performance through wake interaction, decreased bulk flow velocity, and an increase in the accumulated fatigue loads and intermittency events on downstream turbines (Viggiano et al, 2016; Ali et al, 2016a)
The proper orthogonal decomposition (POD) eigenvectors illustrate the spatial structure of the turbulent flow and the eigenvalues measure the energy associated with corresponding eigenvectors
Characterization of the wind turbine wake flow is presented by the streamwise mean velocity and Reynolds shear stress, with the aim to understand the influence of turbine-to-turbine spacing
Summary
Allowing insufficient space between wind turbines in an array leads to decreased performance through wake interaction, decreased bulk flow velocity, and an increase in the accumulated fatigue loads and intermittency events on downstream turbines (Viggiano et al, 2016; Ali et al, 2016a). The actual spacing of wind turbines can vary greatly from one array to another and depending on the direction of the bulk flow. Yang et al (2012) used LES to study the influence of the streamwise and spanwise spacing on the power output in aligned wind farms under a fully developed regime. Wu and PortéAgel (2013) investigated turbulent flow within and above aligned and staggered wind farms under neutral conditions. Stevens et al (2016) investigated the power output and wake effects in aligned and staggered wind farms with different streamwise and spanwise turbine spacings. Investigation of wind farms with limited spacing is important in order to quantify the effects of wind turbine wake interaction on the power production. The Reynolds stress anisotropy tensor is employed to differentiate the balance of energy in the turbulence field for the test cases
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