Applicability of different modal decomposition methods in wind turbine wake meandering analysis

Wind turbines are ever increasing with the rapid advancement of agriculture and industry in recent years. However, wind farms have exhibited a trend toward concentration, due to the limitations of land resources. Particularly, the wake effects of wind turbines in the far wake have led to more complex interactions among turbulent structures. As a result, there are inflow instability and fatigue loads on the downstream turbines. Therefore, the turbulent structures can be optimized to reduce the maintenance costs of the wind equipment for high operational efficiency. The modal decomposition can serve as an effective approach to extracting the structures of the flow field. The key characteristics and dynamics can be identified in the wake. The complex field of wake flow can be dimensionally reduced to extract the mode decomposition. The representative modes can be obtained for the more accurate flow field in the better performance of the wind farm. Nevertheless, the different modal decompositions can vary greatly in the specific application scenarios. This study aims to investigate the applicability of various modal decompositions for the wake-meandering analysis in wind turbines. Firstly, the wake of the NREL 5.0 MW wind turbine was numerically simulated using the large eddy simulation (LES) and the actuator line model (ALM). The flow field data was obtained after the simulation. Subsequently, the flow characteristics of the wake structure were extracted and then compared using the Proper Orthogonal Decomposition (POD), Spectral Proper Orthogonal Decomposition (SPOD), and Dynamic Modal Decomposition (DMD). The results show that the wake structure was effectively extracted to perform the low-dimensional reconstruction. The POD shared the highest convergence speed and the highest efficiency for the reconstruction of the flow field. The low-order datasets of flow fields were also constructed efficiently. The error was 8.43% when reconstructing with the first 85 modes. The errors also dropped to 5.54% with the first 314 modes. The SPOD was used to extract the stable modes with the frequency information and spatial orthogonality in the wake flow field. The energy concentration was the highest at the characteristic frequency of 0.0156 Hz, and the energy proportion of the dominant mode exceeded 50%. As such, the SPOD was suitable for the flow behavior with distinct time-frequency characteristics. The error of SPOD was 8.38% when reconstructing with the first 85 modes. While the error was 8.40% using the first 314 modes. The wake structure was fully extracted by the DMD algorithm. The frequency and growth rate were obtained from the main frequency structure. The reconstruction error of DMD was also comparable to that of POD. The error was 8.44% when reconstructing with the first 85 modes. While the error was 5.57% using the first 314 modes. This finding can also offer theoretical guidance for the wake meandering in the modal analysis of flow structures.