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

Abstract

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.