Streamwise development of the wind turbine boundary layer over a model wind turbine array

Abstract

The streamwise development of turbulence statistics and mean kinetic energy in a model wind farm consisting of 3 × 5 wind turbines is studied experimentally in a wind tunnel. The analysis uses planar Particle Image Velocimetry data obtained at the centerline plane of the wind farm, covering the inflow as well as four planes in between five downstream wind turbines. The data analysis is organized by dividing these measurement planes into three regions: the above-rotor, rotor-swept, and below-rotor regions. For each field, flow development is quantified using a properly defined relative difference norm based on an integration over each of the regions. Using this norm, it is found that the mean streamwise velocity approaches a fully developed state most rapidly, whereas the flow development is more gradual for the second-order statistics. The vertical entrainment flux of the mean kinetic energy by the Reynolds shear stress, ⟨U⟩⟨u′v′⟩, is observed to develop at a rate similar to that of the Reynolds shear stress rather than the mean streamwise velocity component. Its development is slowest in the layer nearest to the ground. Analysis of various terms in the mean kinetic energy equation shows that the wind turbine boundary layer has not yet reached fully developed conditions by the fifth turbine but that it is approaching such conditions. By comparing the vertical entrainment flux with the horizontal flux due to the mean flow, it is found that the former increases, whereas the latter decreases, as function of downstream distance, but that the former is already an important contributor in the developing region.