The structure of the turbulence-driven power fluctuations in a wind farm is fundamentally described from basic concepts. A derived tuning-free model, supported with experiments, reveals the underlying spectral content of the power fluctuations of a wind farm. It contains two power-law trends and oscillations in the relatively low- and high-frequency ranges. The former is mostly due to the turbulent interaction between the flow and the turbine properties, whereas the latter is due to the advection between turbine pairs. The spectral wind-farm scale power fluctuations Φ_{P} exhibit a power-law decay proportional to f^{-5/3-2} in the region corresponding to the turbulence inertial subrange and at relatively large scales, Φ_{P}∼f^{-2}. Due to the advection and turbulent diffusion of large-scale structures, a spectral oscillation exists with the product of a sinusoidal behavior and an exponential decay in the frequency domain.
A laboratory experiment examined the effects of energetic coherent motions on the structure of the wake and power fluctuations generated by a model axial-flow hydrokinetic turbine. The model turbine was placed in an open-channel flow and operated under subcritical conditions. The incoming flow was locally perturbed with vertically oriented cylinders of various diameters. An array of three acoustic Doppler velocimeters aligned in the cross-stream direction and a torque transducer were used to collect high-resolution and synchronous measurements of the three-velocity components of the incoming and wake flow as well as the turbine power. A strong scale-to-scale interaction between the large-scale and broadband turbulence shed by the cylinders and the turbine power revealed how the turbulence structure modulates the turbine behavior. In particular, the response of the turbine to the distinctive von Kármán-type vortices shed from the cylinders highlighted this phenomenon. The mean and fluctuating characteristics of the turbine wake are shown to be very sensitive to the energetic motions present in the flow. Tip vortices were substantially dampened and the near-field mean wake recovery accelerated in the presence of energetic motions in the flow. Strong coherent motions are shown to be more effective than turbulence levels for triggering the break-up of the spiral structure of the tip-vortices. C 2015 AIP Publishing LLC. [http://dx.
The flow development above and within homogeneous and heterogeneous canopies was experimentally studied using particle image velocimetry in a refractive-index-matching channel. The experiments were designed to gain insight into the effect of height heterogeneity on the structure and spatial distribution of the turbulence. The homogeneous model (base case) is constituted of elements of height $h$ arranged in a staggered configuration; whereas the heterogeneous canopy resembled a row canopy and consisted of elements of two heights $h_{1}=h+(1/3)h$ and $h_{2}=h-(1/3)h$ alternated every two rows. Both canopies had the same density, element geometry and mean height. The flow was studied under three submergences $H/h=2$, 3 and 4, where $H$ denotes the flow depth. The experiments were performed at Reynolds number $Re_{H}\simeq 6500$, 11 300 and 12 300 and nearly constant Froude number $Fr\simeq 0.1$. Turbulence statistics complemented with quadrant analysis and proper orthogonal decomposition reveal richer flow dynamics induced by height heterogeneity. Topography-induced spatially periodic mean flows are observed for the heterogeneous canopy. Furthermore, and in contrast to the homogeneous case, non-vanishing vertical velocity is maintained across the entire length of the heterogeneous canopy with increased levels at lower submergence depths. Further alternations were induced in the magnitude and distribution of the turbulent kinetic energy, Reynolds shear stress and characteristics of the canopy mixing layer, evidencing enhanced mixing and turbulent transport for the heterogeneous canopy especially at lower submergence depths. Overall, the results indicate that heterogeneous canopies exhibit greater vertical turbulent exchange at the canopy interface, suggesting a potential for greater scalar exchange and a greater impact on channel hydraulic resistance than a homogeneous canopy of similar roughness density.
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