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Large-eddy simulation of wind-turbine wakes over two-dimensional hills

Wind-turbine wakes over two-dimensional (2D) hills with different slope gradients are systematically investigated using large-eddy simulation (LES) with wind turbine parameterized as actuator disk model (ADM) and hilly terrain modeled by immersed boundary method (IBM). The chosen hill models represent typical hilly terrains with and without flow recirculation in the wake of the hills. The flow characteristics of wind-turbine wakes and the power performance are analyzed and the related flow mechanisms are elucidated in our study. It is found that the velocity deficit in turbine wakes can not be acceptably represented by the Gaussian model in the wake of the steep hill until at a further distance. It is also found that the assumption that the wake-centre trajectory maintains a nearly constant elevation downwind of the hilltop proposed by Shamsoddin and Porté-Agel may not be applicable in particular for the steep hill cases. Furthermore, the hilltop is the optimal location for turbine placement because the turbine harvests more wind energy due to the speed-up effect and suffers less fatigue loading due to the lower turbulence levels. Both the turbulence levels and the magnitude of vertical turbulent flux are found to drop below those of the flat ground case on the windward side of the hills and they also decrease within the hill wake region compared with the no-turbine cases. A detailed analysis of MKE budgets reveals that the budgets of pressure transport (PT) and mean convection (MC) are mainly responsible for balancing the MKE in turbine wakes over hilly terrain.