On the Evolution of the Integral Time Scale within Wind Farms

A wind-tunnel investigation was carried out to characterize the spatial distribution of the integral time scale (Tu) within, and in the vicinity of, two model wind farms. The turbine arrays were placed over a rough wall and operated under high turbulence. The two layouts consisted of aligned units distinguished only by the streamwise spacing (∆xT ) between the devices, set at five and ten rotor diameters dT (or Sx = ∆xT /dT = 5 and 10). They shared the same spanwise spacing between turbines of 2.5dT ; this resulted in arrays of 8 × 3 and 5 × 3 horizontal-axis turbines. Hotwire anemometry was used to characterize the instantaneous velocity at various vertical and transverse locations along the central column of the wind farms. Results show that Tu was modulated by the wind farm layout. It was significantly reduced within the wind farms and right above them, where the internal boundary layer develops. The undisturbed levels above the wind farms were recovered only at ≈dT/2 above the top tip. This quantity appeared to reach adjusted values starting the fifth row of turbines in the Sx = 5 wind farm, and earlier in the Sx = 10 counterpart. Within the adjusted zone, the distribution of Tu at hub height exhibited a negligible growth in the Sx = 5 case; whereas it underwent a mild growth in the Sx = 10 wind farm. In addition, the flow impinging the inner turbines exhibited Tu/Tu inc < 1, where T u inc is the integral time scale of the overall incoming flow. Specifically, Tu → βTu inc at z = zhub, where β < 1 within standard layouts of wind farms, in particular β ≈ 0.5 and 0.7 for Sx = 5 and 10.