Generation and decay of counter-rotating vortices downstream of yawed wind turbines in the atmospheric boundary layer

Abstract

Abstract

Quantification of wake shape modulation and deflection for tilt and yaw misaligned wind turbines

“…The change in wake shape can result in more wake deflection in the centre, thereby improving the benefits for a downstream turbine. The improved understanding of this wake-deflection mechanism has helped to develop better physics-based models for wake deflection of yawed wind turbines (Shapiro et al 2018(Shapiro et al , 2020Zong & Porté-Agel 2019;Martínez-Tossas et al 2019). Yet, a thorough understanding of tilt-wake deflection, and detailed experimental studies of a tilted wake are missing.…”

“…The circulation is smaller than the measured circulation, which indicates that the correction factor k WT in the model is too small for the used wind turbine model. The LES results of Shapiro et al (2020) show an evolution of circulation which remains more or less constant up to x/D ≈ 3, before decaying. In this experiment, and according to the point-vortex model, circulation is found to decay from the earliest measurement location, x/D = 2 for tilt.…”

“…with Γ p the circulation of the point vortex, y 0 and z 0 the point location and η(x) the viscous length scale of the vortex. Shapiro et al (2020) show that in the wake of a wind turbine, operating in a turbulent boundary layer, the viscous length scale η(x) of the vortices can be expressed in terms of the wake expansion coefficient, and the downstream distance by…”

“…U H , CT, λ), a wake coefficient of k = u * /U H = 0.068, using 36 point vortices along the rotor circumference and one in the rotor centre. The virtual origin is found from x 0 = −24 1/4 Δ/k (Shapiro et al 2020), with Δ = 0.004 m based on the blade-tip chord length. Equation (3.3) is used to calculate the net circulation of the tip-vortices with k WT = 0.45.…”

“…This finding provides further support that gains of tilt-misalignment may exceed those of yaw. More recently, Shapiro, Gayme & Meneveau (2020) developed an analytical expression for the decay of circulation for each of the counter-rotating vortex cores in a yawed wake, based on the growth rate of the vorticity length scale (taken as the width of the vorticity distribution) and the boundary layer friction velocity. This new model shows good agreement with LES results for a yawed porous disk.…”