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Tailoring wind turbine wake models to incoming free-stream turbulence

Analytical wake models describe the main wake statistics using a reduced number of parameters: for instance, the Gaussian wake model relies on the single parameter k ∗ to predict the mean wake velocity. However, the robustness of these models to different inflows has been seldom tested and the effects of ambient turbulence on these coefficients are reported only in a limited number of studies. With this objective, we measured the wake generated by a model-scale wind turbine operating in a wind tunnel at a ReD ⋍ 105 under different ambient conditions, with turbulence intensities between 3% and 12% and integral time scales between 1/10 and 10 times the convective time-scale. The wake generated by the turbine has been measured by means of planar PIV in a region spanning between 1.25 and 8.75 rotor diameters downstream of the turbine. The results show that a description of the turbine wake with the single parameter k ∗ is not sufficient to obtain accurate predictions, while the quality of the wake estimations can be dramatically improved by introducing a virtual origin x 0. Analysis of the higher-order wake statistics shows how the former can be related to the intensity of the Reynolds shear stress in the wake, and the latter to the erratic motion of the tip-vortices.