Contribution of large scale coherence to wind turbine power: A large eddy simulation study in periodic wind farms

Exploring the benefits of vertically staggered wind farms: Understanding the power generation mechanisms of turbines operating at different scales

“…Hence, the energy spectra is defined as the inverse Fourier transform of the horizontally averaged 2‐point correlation of the velocity fluctuations thus owing to the horizontal periodicity of the domain. For more details regarding the definition of spatial energy spectra in periodic wind farms, the reader is referred to Chatterjee and Peet . The spanwise‐averaged 1D premultiplied streamwise and wall‐normal energy spectra ( k x E u u , k x E w w ) in Figure B,C indicate that except for a slight discrepancy at length scales λ x > D L , the u , w energy spectra at and above the hub height z = D L of the large turbines remain the same for the cases L , L S M , L I M .…”

“…Whether these vertical motions can be utilized for power, depends on the organization of structures at the top of the rotor of the smaller turbines and discussed further in the 2D spectra. The experimental studies by Hamilton et al and Chamorro et al as well as our recent numerical studies have revealed the contribution of length scales larger than rotor diameter to the wind turbine power. With these observations in mind, we analyze the 2D premultiplied energy spectra of the multiscale as compared with single‐scale homogeneous wind farm cases with an emphasis on such energetic eddies with the scales in the range D − 10 D in Figures 12 to 15.…”

“…That is, even if we do not capture the largest scales, the smaller scales that we do capture contain the correct information about their scaling laws and spatial coherence. Note that the most energetic eddies that contribute significantly to the energy captured by the wind turbines() (of size D − 10 D and corresponding to 40% to 80% of maximum in Figures 12 to 15) are captured entirely, and the corresponding spectral lines for these scales are closed. Further increasing the domain size to capture the large‐scale motions and their effect on wind turbine power would be an interesting study in the future; however, note that a fourfold to fivefold increase of the horizontal extent of the domain would be required to capture the large and very large scales of motion (LSM's & VLSM's) representative of turbulent boundary layers …”

WInc3D: A novel framework for turbulence‐resolving simulations of wind farm wake interactions

“…This feature is crucial for Direct and Large Eddy Simulations of turbulent flows for which the correct representation of the relevant scales is essential. To the best of our knowledge, only a handful of wind farm simulators use high‐order methods in their implementation, eg, high‐order spectral element methods (SEM) in Chatterjee and Peet . Most other WFSs are based on low‐order numerical schemes for which the required resolution can be substantially more demanding.…”

“…The various models employ different discretisation schemes (eg, finite differences/volumes or pseudo‐spectral) and often use second‐ to fourth‐order accurate schemes. The ability of a WFS to accurately capture complex flow dynamics of utility‐scale wind farms has been demonstrated by Nilsson et al and Churchfield et al for the Lillgrund offshore wind farm and Wu and Porté‐Agel for the Horns Rev wind farm, while a number of other wind farm simulations have been undertaken for theoretical wind farm layouts to, e.g. assess the impact of micrositing.…”