Abstract
Large scale coherent structures in the atmospheric boundary layer (ABL) are known to contribute to the power generation in wind farms. In order to understand the dynamics of large scale structures, we perform proper orthogonal decomposition (POD) analysis of a finite sized wind turbine array canopy in the current paper. The POD analysis sheds light on the dynamics of large scale coherent modes as well as on the scaling of the eigenspectra in the heterogeneous wind farm. We also propose adapting a novel Fourier-POD (FPOD) modal decomposition which performs POD analysis of spanwise Fourier-transformed velocity. The FPOD methodology helps us in decoupling the length scales in the spanwise and streamwise direction when studying the 3D energetic coherent modes. Additionally, the FPOD eigenspectra also provide deeper insights for understanding the scaling trends of the three-dimensional POD eigenspectra and its convergence, which is inherently tied to turbulent dynamics. Understanding the behaviour of large scale structures in wind farm flows 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 of the POD analysis in the turbulence and wind farm community.
Highlights
Wind farms in the atmospheric boundary layer (ABL) pose a complex dynamical system with turbulent phenomenology occurring at multiple length scales, mainly due to the interaction of atmospheric boundary layer turbulent eddies [1] and the turbulence generated by the wind turbine wakes [2,3,4]
We present the results obtained from the proper orthogonal decomposition (POD) analysis of a finite-sized wind turbine array
The snapshots for the layout were each Te /5 (Te is the flow through time) snapshots apart, which were much frequent than the snapshots “3Te apart” as reported in Ref. [15]. This essentially means that the current POD analysis were carried out in the framework of “smaller time scales”
Summary
Wind farms in the atmospheric boundary layer (ABL) pose a complex dynamical system with turbulent phenomenology occurring at multiple length scales, mainly due to the interaction of atmospheric boundary layer turbulent eddies [1] and the turbulence generated by the wind turbine wakes [2,3,4]. These interactions are manifested in the small scale structures (of the order or smaller than the turbine rotor diameter) and in the large scale structures (one or two orders of magnitude larger than the turbine rotor diameter) [5]. Ref. [11] illustrated the similarity of neutrally-stratified atmospheric surface layer flows and canonical wall-bounded turbulence and Energies 2020, 13, 1660; doi:10.3390/en13071660 www.mdpi.com/journal/energies
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