Numerical visualization of wind turbine wakes using passive scalar advection–diffusion equation and its application for wake management

Abstract

To visualize and characterize the unsteady properties of the wake trailing behind a wind turbine, we propose a novel numerical methodology in this study. Through a wind-tunnel experiment using a smoke generator, we succeeded in visualizing a compact-type small-scale wind turbine wake using continuous scalar plumes from a single point source. Next, to simulate the above wind-tunnel experiment, we proposed a method using the passive scalar advection–diffusion equation based on a high-fidelity large-eddy simulation (LES). The actuator-line method (ALM) was adopted for the wind turbine model. We succeeded in qualitatively reproducing the wake visualization experiment in the wind tunnel described above and verified the effectiveness of the proposed numerical visualization method. To evaluate the characteristics of wakes generated by wind turbines in more detail, we conducted a quantitative comparison using a disk-shaped volume source with the same size as the swept area, set behind the wind turbine model. The results indicated that the non-dimensional time-averaged passive scalar profile in the near- and far-wake regions qualitatively matched the shape of the stream-wise velocity profile, despite having opposite signs. In other words, it was shown that if a disk-shaped volume source with the same size as the swept area is placed just behind the wind turbine, it is possible to accurately predict the behavior of the wind turbine wake. Finally, to validate the proposed method for wind farm wake management, we performed a visualization of wake flows in a virtual offshore wind farm consisting of 12 wind turbines with short separation distances. Through detailed comparison of two types of numerical results with different wind directions, we showed that the proposed method can effectively demonstrate the range of spatial influence of the wakes formed by the wind turbine with special attention.