Effects of Two-Dimensional Steep Hills on the Performance of Wind Turbines and Wind Farms

We use large-eddy simulations with an immersed boundary method to study the performance of wind turbines and wind farms in hilly terrain. First, we analyze the performance of wind turbines in the vicinity of a two-dimensional hill. For turbines that are significantly taller than the hill, the performance improves as the flow speeds up over the hill. For turbines that have approximately the same or a smaller height than the hill, the impact of the hill on the turbine performance depends on the positioning of the turbine in relation to the hill. For these turbines, the performance is better at the hilltop. However, the power production of these turbines is reduced due to blockage effects when they are placed at the base of the hill. The performance of turbines placed on the windward side of the hill is well predicted by superimposing the wind-turbine wake profile for the flat terrain on the hilly-terrain flow field. In contrast, we show that this approach is invalid when the turbine is placed on the leeward side of the hill where flow separation occurs. Subsequently, we consider wind farms with a hill in the middle. The hill wake is very pronounced due to which the performance of turbines located behind and close to the hill is mainly determined by the flow dynamics induced by the hill instead of the wind-turbine wakes. Finally, we study a wind farm located between two hills. We find that, for this particular configuration, there is a unique turbine spacing that maximizes the wind-farm power production in the valley.