Effects of a three-dimensional hill on the wake characteristics of a model wind turbine

The spatial evolution of a turbine wake downwind of a three-dimensional sinusoidal hill is studied using large-eddy simulations and wind tunnel measurements. The computed flow fields behind the hill show good agreement with wind tunnel measurements. Three different heights of the hill, i.e., hhill = zh-0.5D, ≈ zh and =zh + 0.5D (where zh is the turbine hub height and D is the diameter of the turbine rotor), were considered. The effect of the hill turbine spacing was investigated through a comparative analysis with the turbine wake results in the undisturbed turbulent boundary layer. It is observed that the turbine wakes downwind of the hill with hhill ≈ zh and hhill = zh + 0.5D recover faster because of the increased entrainment of ambient flow into the turbine wake, which is due to the enhanced turbulent transport in both spanwise and vertical directions. In comparison with the turbine only case, significant increases in the turbulence kinetic energy (TKE) in the turbine wake are observed for the hill-turbine cases with hhill ≈ zh and hhill = zh + 0.5D. A velocity scale UT, defined in terms of the thrust force acting on the turbine, is introduced for the turbine-added velocity deficit and TKE. For the turbine-added velocity deficit, UT is shown to be an appropriate scale at wake locations sufficiently far downwind of the turbine (i.e., greater than or equal to 8D). The vertical profiles of the turbine-added TKE normalized by U T 2 are shown to nearly collapse in the wake both for the turbine only and hill-turbine cases at all locations greater than 4D downwind of the turbine. A simple model for the turbine-added TKE in complex terrain is also proposed based on the new physical insights obtained from our simulations.