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.
Highlights
Analytical models of various fluid mechanical phenomena in wind energy play an important role for basic understanding and for design and control of wind farms
Achieving increased power output through wake steering involves turbines, often in the front rows of wind farms, being intentionally operated in yawed conditions to redirect their wakes away from downwind turbines. This reduces the power produced by the yawed turbines, research has shown that the total wind farm efficiency can improve as a result of more power generated by downwind turbines (Park & Law 2016; Bastankhah & Porté-Agel 2019; Fleming et al 2019; Howland, Lele & Dabiri 2019; King et al 2021)
In this study we develop an analytical model to describe the wake shape and its downstream evolution for both uniform ideal inflow and turbulent boundary layer background flow
Summary
Analytical models of various fluid mechanical phenomena in wind energy play an important role for basic understanding and for design and control of wind farms. In order to exploit the basic understanding of induced velocity and circulation of CVPs generated by finite-span wings, Shapiro, Gayme & Meneveau (2018) proposed to regard a yawed turbine as a lifting surface with an elliptical planform. Based on this approach, the lateral component of the thrust force can be regarded as the transverse lift force.
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
