Naseem Ali

Evaluation of Higher Order Moments and Isotropy in the Wake of a Wind Turbine Array

Hot-wire measured signals are analyzed using the third and fourth order statistical moments as well as the energy spectra and structure functions in the wake of a model wind turbine array. The skewness experiences sharp excursions, away from a Gaussian behavior, due to the presence of the turbine rotor. Kurtosis is maximized at the top tip, hub, and bottom tip of the turbine. A below Gaussian kurtosis level in the probability density function (pdf) results for the streamwise direction moving away from the wall, while the hub and top tip of the pdf converge to a Gaussian behavior. At one diameter downstream of the turbine, the wall-normal kurtosis at the top tip, hub region, and slightly above the wall positions shows an increase in comparison to the other wall-normal locations. Similar peaks in wall-normal kurtosis are found five diameters and one diameter downstream of the turbine in near-wall region. These peaks converge to Gaussian behavior moving away from the wall. Energy spectra and structure functions indicate that the inertial subrange extends near the top tip in the near-wake and away from the wall in the far-wake. Utilizing the cross-spectra and mixed structure function, anisotropic behavior is held for all near- and far-wake region with exception at some small scales. Based on the structure function ratios of wall-normal and streamwise velocities, the wake is highly anisotropic for all locations except at top tip and the majority of scales in the near-wake. Contrary to this result, the ratio between the wall-normal and streamwise spectrum displays a defined range of scales behaving isotropically at most locations, the only exception being at hub height. In far-wake, the structure function ratio and spectral ratio show a significant reduction in anisotropic behavior at larger scales.

Structure functions, scaling exponents and intermittency in the wake of a wind turbine array

Hot-wire measurements obtained in a 3 × 3 wind turbine array boundary layer are utilized to analyze high order structure functions, intermittency effects as well as the probability density functions of velocity increments at different scales within the energy cascade. The intermittency exponent is found to be greater in the far-wake region in comparison with the near-wake. At hub height, the intermittency exponent is found to be null. Extended self-similarity scaling exponents of the second, fourth, and fifth order structure functions remain relatively constant as a function of height in the far-wake; whereas in the near-wake, these are highly affected by the passage of the rotor where tip vortices reside, thus showing a dependence on physical location. When comparing with proposed models, these generally overpredict the structure functions in the far-wake region. The probability density function distributions in the far-wake region display wider tails compared to the near-wake region, and the constant sk...

Inverse Structure Functions in the Canonical Wind Turbine Array Boundary Layer

Wind tunnel measurements for a 3 × 3 canonical wind turbine array boundary layer are obtained using hot-wire anemometer velocity signals. Two downstream locations are considered, referring to the near- and far-wake, and 21 vertical points are acquired per profile. Velocity increments and exit distances are used to quantify inverse structure functions at both downstream locations. Inverse structure functions in the near-wake show a similar profile for the main vertical locations, but diverge as the moment is increased. In the far-wake, inverse structure functions converge toward a single function for all vertical location and moments. The scaling exponents for inverse structure functions are calculated directly and relatively, using extended self similarity. Scaling exponents show strong dependence on vertical position along the wind turbine profile in the near-wake and remain relatively constant in the far-wake. Intermittency in the near-wake is indicated by the nonlinear behavior of the direct and relati...

Focused-based multifractal analysis of the wake in a wind turbine array utilizing proper orthogonal decomposition

Hot-wire anemometry measurements have been performed in a 3 × 3 wind turbine array to study the multifractality of the turbulent kinetic energy dissipation. A multifractal spectrum and Hurst exponents are determined at nine locations downstream of the hub height, bottom and top tips. Higher multifractality is found at 0.5D and 1D downstream of the bottom tip and hub height. The second order of the Hurst exponent and combination factor shows the ability to predict the flow state in terms of its development. Snapshot proper orthogonal decomposition (POD) is used to identify the coherent and incoherent structures and to reconstruct the stochastic velocity signal using a specific number of the POD eigenfunctions. The accumulation of the turbulence kinetic energy in the top tip location exhibits fast convergence compared with the bottom tip and hub height. The dissipation of the large and small scales is determined using the reconstructed stochastic velocities. The higher multifractality is shown in the dissip...

Anisotropy stress invariants of thermally stratified wind turbine array boundary layers using large eddy simulations

In the interest of understanding the dynamics and energy transfer between the atmospheric boundary layer and large wind turbine arrays, a description of the turbulence anisotropy in the wake region of wind turbines is necessary. Flux of high momentum flow into the wind turbine array by anisotropic turbulence is a dominant factor of mean kinetic energy resupply for the wind farm. Under thermal stratification, the behavior of the turbulence field, and the energy flux, is significantly altered. Here, a thermally stratified wind turbine array boundary layer is studied in detail using a combination of Lumley and barycentric maps together with the recently introduced spheroid and color maps. The atmospheric flow is modelled using a large eddy simulation driven by a constant geostrophic wind and a time-varying ground surface temperature, obtained from a selected period of the Cooperative Atmosphere-Surface Exchange Study-99 field experiment. The wind farm is modelled using the traditional actuator-disk with rota...