Turbulent Decay of the Yawed Wind Turbine Counter-Rotating Vortex Pair
Carl R. Shapiro1,2, Dennice F. Gayme1, and Charles Meneveau1
1 Department of Mechanical Engineering, Johns Hopkins University, Baltimore, MD 21218
2 AAAS Science & Technology Policy Fellow, US Department of Energy, Washington, DC 20585

Abstract
Yawed wind turbines generate a counter-rotating vortex pair (CVP) that deflects and deforms the turbine’s wake downstream. Informed by large eddy simulations (LES) of yawed wind turbines in the atmospheric boundary layer (ABL) and the airplane trailing vortex literature, we develop a model for the shed vorticity and circulation of the CVP. Analytical integration of a simplified form of the vorticity transport equation yields analytical equations that do not require costly numerical integration. We apply an eddy-viscosity model with the ABL friction velocity and width of the vortex sheets representing the velocity and length scales, respectively. Comparisons of the analytical model to LES measurements of the maximum vorticity and circulation magnitude show considerable agreement. These results indicate that cross-diffusion dominates the CVP decay as the vorticity cancels along the wake’s line of symmetry.

The authors acknowledge funding from the National Science Foundation (grant nos. 1949778 and 1635430) and computational resources from MARCC and Cheyenne (doi:10.5065/D6RX99HX).

Introduction
Yawing has potential to increase or control wind farm power output, and yawed wind turbine wakes have interesting characteristics.

Wind turbine yaw

Counter-rotating vortex pair
Large eddy simulations (LES) of wind turbines in the atmospheric boundary layer (ABL) show that yawed wind turbines shed a counter-rotating vortex pair (CVP) in their wake. The CVP begins as arcs of vorticity that diffuse downstream to become nearly axisymmetric, as shown in the interactive vorticity volume rendering below.

K3D snapshot viewer - Fri, 29 May 2020 19:12:48 GMT