A vortex sheet based analytical model of the curled wake behind yawed wind turbines

TL;DR

This paper introduces an analytical vortex sheet model to predict the shape and deflection of curled wakes behind yawed wind turbines, aiding in wake steering strategies for wind farm optimization.

Contribution

The study develops a novel vortex sheet-based analytical model for curled wake shapes, incorporating turbulence effects and ground influence, validated against simulations and experiments.

Findings

Universal wake shape solution using dimensionless variables

Model accurately predicts wake deflection and shape

Enhanced Gaussian wake model with curled wake features

Abstract

Motivated by the need for compact descriptions of the evolution of non-classical wakes behind yawed wind turbines, we develop an analytical model to predict the shape of curled wakes. Interest in such modelling arises due to the potential of wake steering as a strategy for mitigating power reduction and unsteady loading of downstream turbines in wind farms. We first estimate the distribution of the shed vorticity at the wake edge due to both yaw offset and rotating blades. By considering the wake edge as an ideally thin vortex sheet, we describe its evolution in time moving with the flow. Vortex sheet equations are solved using a power series expansion method, and an approximate solution for the wake shape is obtained. The vortex sheet time evolution is then mapped into a spatial evolution by using a convection velocity. Apart from the wake shape, the lateral deflection of the wake including ground effects is modelled. Our results show that there exists a universal solution for the shape of curled wakes if suitable dimensionless variables are employed. For the case of turbulent boundary layer inflow, the decay of vortex sheet circulation due to turbulent diffusion is included. Finally, we modify the Gaussian wake model by incorporating the predicted shape and deflection of the curled wake, so that we can calculate the wake profiles behind yawed turbines. Model predictions are validated against large-eddy simulations and laboratory experiments for turbines with various operating conditions.