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.

中文翻译：

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二维陡坡对风力涡轮机和风电场性能的影响

我们使用大涡模拟和浸入边界方法来研究风力涡轮机和风电场在丘陵地带的性能。首先，我们分析了二维山丘附近风力涡轮机的性能。对于明显高于山丘的涡轮机，性能会随着流过山丘的速度加快而提高。对于高度与山丘大致相同或小于山丘的涡轮机，山丘对涡轮机性能的影响取决于涡轮机相对于山丘的位置。对于这些涡轮机，在山顶的性能更好。然而，当这些涡轮机放置在山脚下时，它们的发电量会由于堵塞效应而减少。通过在丘陵地形流场上叠加平坦地形的风力涡轮机尾流剖面，可以很好地预测放置在山丘迎风侧的涡轮机的性能。相比之下，我们表明，当涡轮机放置在发生流动分离的山的背风侧时，这种方法是无效的。随后，我们考虑中间有一座小山的风电场。山丘尾流非常明显，因为位于山丘后面和附近的涡轮机的性能主要取决于山丘引起的流动动力学，而不是风力涡轮机尾流。最后，我们研究了位于两座山之间的风电场。我们发现，对于这种特殊配置，有一个独特的涡轮机间距，可以最大限度地提高山谷中的风电场发电量。