Dynamics of Large Scale Turbulence in Finite-sized Wind Farm Canopy using Proper Orthogonal Decomposition and a Novel Fourier-POD Framework

Abstract

Large scale coherent structures in atmospheric boundary layer (ABL) are known to contribute to the power generation in wind farms. In the current paper, we perform a detailed analysis of the large scale structures in a finite sized wind turbine canopy using modal analysis from three dimensional proper orthogonal decomposition (POD). While POD analysis sheds light on the large scale coherent modes and scaling laws of the eigenspectra, we also observe a slow convergence of the spectral trends with the available number of snapshots. Since the finite sized array is periodic in the spanwise direction, we propose to adapt a novel approach of performing POD analysis of the spanwise/lateral Fourier transformed velocity snapshots instead of the snapshots themselves. This methodology not only helps in decoupling the length scales in the spanwise and the streamwise direction when studying the energetic coherent modes, but also provides a detailed guidance towards understanding the convergence of the eigenspectra. In particular, the Fourier-POD eigenspectra helps us illustrate if the dominant scaling laws observed in 3D POD are actually contributed by the laterally wider or thinner structures and provide more detailed insight on the structures themselves. We use the database from our previous large eddy simulation (LES) studies on finite-sized wind farms which uses wall-modeled LES for modeling the Atmospheric boundary layer laws, and actuator lines for the turbine blades. Understanding the behaviour of such structures would not only help better assess reduced order models (ROM) for forecasting the flow and power generation but would also play a vital role in improving the decision making abilities in wind farm optimization algorithms in future. Additionally, this study also provides guidance for better understanding the POD analysis in the turbulence and wind farm community.

Wind farm response to mesoscale-driven coastal low level jets: a multiscale large eddy simulation study

“…Figure 6 shows the wake propagation of the wind farm array for the MS and LLJ cases. The most evident effect in the turbine simulations are the presence of deeper farm wakes due to the wake superposition of turbines in the downstream direction as also observed in the author's high-fidelity spectral-element simulations of neutral boundary layer of wind farms [14,15]. As seen in the single turbine case, the wakes are also deeper in the 20-turbine cases with significant amount of dispersion (owing to veering) for the LLJ compared In addition to wake deficits, Figure 7 also indicates that the induction losses are deeper in the LLJ case compared to the MS case.…”

“…Additionally, we observe distortion of wake structures in the LLJ case that can perhaps be attributed to the strong veer. The presence of wake dispersion is unique to LLJ and was also not observed in recent works of similar high fidelity spectral element simulations of neutral boundary layers of wind farm wakes without veer [14,15]. However, further studies using the turbulence kinetic energy (TKE) budget is necessary to validate the hypothesis.…”

Effects of sampling frequency on the proper orthogonal decomposition based reconstruction of a wind turbine wake

“…POD method also been developed to other framework for better use in specific conditions, such as the Extended POD modes (EPOD) [10], Fourier POD modes (FPOD) [13], and Spectral POD modes (SPOD) [23] etc. Hekmati et al [10] focused on the convergence of POD and Extended POD modes, and proposed that any application of POD and EPOD methods requires a preliminary statistical convergence study, furthermore, they pointed out that large scale flow structures can be well captured by the first five modes if the mesh-grid size and the time resolution contains at least 3.5 integral space and time scales, respectively.…”

“…[10] focused on the convergence of POD and Extended POD modes, and proposed that any application of POD and EPOD methods requires a preliminary statistical convergence study, furthermore, they pointed out that large scale flow structures can be well captured by the first five modes if the mesh‐grid size and the time resolution contains at least 3.5 integral space and time scales, respectively. Chatterjee and Yulia [13] observed the slow convergence of the spectral trends of the Fourier‐POD, as well as large scale coherent structures and the corresponding scaling laws. Towne and coworkers [23] introduced the temporal Fourier transform of the correlation function into POD method to deep understand the modal frequency content of the modes.…”

“…POD technique was first introduced to the study of turbulence flow by Lumley [11] and later improved by Sirovich [8] to apply to the analysis of data with fine spatial resolution but poor temporal resolution. In recent years, this method has been popularly adopted to analyse the wind turbine wakes and large scale roll structures of wind farm [12,13], for its computationally cheap and the inherent nature to "rank" the coherent turbulent eddies [14][15][16]. VerHulst and Meneveau [17] conducted a comprehensive three-dimensional POD study on the coherent structures of wind farms with aligned and staggered array of wind turbines, found that the streamwise counter-rotating vortex pairs above the wind turbines are the most energetic coherent structures in the wind farm, and as many as 430 POD modes are needed to capture a kinetic energy of 80%.…”