Self-similarity and turbulence characteristics of wind turbine wakes via large-eddy simulation (Invited)

In this study, a new large-eddy simulation code, the Wind Turbine and Turbulence Simulator (WiTTS), is developed to study the wake generated from a single wind turbine in the neutral ABL. The WiTTS formulation is based on a scale-dependent Lagrangian dynamical model of the sub-grid shear stress and uses actuator lines to simulate the effects of the rotating blades. WiTTS is first tested against wind tunnel experiments and then used to study the commonly-used assumptions of self-similarity and axis-symmetry of the wake under neutral conditions for a variety of wind speeds and turbine properties. The mean velocity deficit shows good self-similarity properties following a normal distribution in the horizontal plane at the hub-height level. Self-similarity is a less valid approximation in the vertical near the ground, due to strong wind shear and ground effects. The mean velocity deficit is strongly dependent on the thrust coefficient or induction factor. A new relationship is proposed to model the mean velocity deficit along the centerline at the hub-height level to fit the LES results piecewise throughout the wake. A logarithmic function is used in the near and intermediate wake regions whereas a power function is used in the far-wake. These two functions provide a better fit to both simulated and observed wind velocity deficits than other functions previously used in wake models such as WAsP. The wind shear and impact with the ground cause an anisotropy in the expansion of the wake such that the wake grows faster horizontally than vertically. The wake deforms upon impact with the ground and spreads laterally. WiTTS is also used to study the turbulence characteristics in the wake. Aligning with the mean wind direction, the streamwise component of turbulence intensity is the dominant among the three components and thus it is further studied. The highest turbulence intensity occurs near the top-tip level. The added turbulence intensity increases fast in the near-wake and reaches its maximum at about x/D ~ 5, then it gradually decreases further downstream. In the far-wake, the added turbulence intensity is primarily dependent on the induction factor and the ambient turbulence: it increases with the induction factor and ambient turbulence and it decays exponentially downstream. An analysis of the added TKE budget shows that production by shear and advection by the mean flow dominate throughout the wake, whereas dissipation and turbulent transport are less important. In the near-wake, TKE is entrained from the upper regions of the annular shear layer into the center of the wake. The nacelle causes a significant increase of production, advection, and dissipation in the near-wake. Wind shear and momentum fluxes are reduced in the lower part of the wake, thus TKE production is reduced at the bottom-tip level. In summary, we find that the WiTTS model, although applied to a simplified case of neutral stability with a single wind turbine, was able to offer new insights into wake properties, including non-symmetric wake growth and reduced vertical mixing near the ground.