Toward understanding waked flow fields behind a wind turbine using proper orthogonal decomposition
Abstract
This study proposes the use of an approach based on proper orthogonal decomposition (POD) to explore reduced-order wake turbulence fields. Waked turbulence fields are first extracted using large eddy simulation (LES) downwind of a wind turbine in a single plane orthogonal to the streamwise flow field. Based on this extracted turbulence field, statistical summaries in the form of covariance matrices and cross power spectral density (CPSD) matrices are estimated. Using proper orthogonal decomposition, important modes organized by eigenvalues (dominant energy contributions) are evaluated. Based on a subset of these sorted modes, reduced-order turbulence fields can be generated and these are analyzed and compared directly with the original LES-based target wake turbulence field. Statistical descriptions of the turbulence and their effect on wind turbine loads are investigated. To serve as reference, the free-stream turbulence field upwind of the selected wind turbine is also captured using LES. The same decomposition and simulation procedures are performed on the free-stream field. Compared to POD eigenmodes and eigenvalues of the free-stream field, those for the waked wind fields show distinct patterns that describe a systematic increase in turbulence energy around the top of the rotor. CPSD-based POD (spectral proper transformation) is found to be more efficient in capturing dynamic characteristics and spatial patterns in the waked wind fields using a small number of modes. Reduced-order simulation of waked wind fields using varying numbers of POD modes suggests that the top 10% of these most dominant modes—a greater proportion than what is needed for the free-stream field—is required to yield turbine loads comparable to those based directly on the original LES wind fields.
