Abstract
The theoretical limit for wind turbine performance, the so-called Betz limit, arises from an inviscid, irrotational analysis of the streamtube around an actuator disk. In a wind farm in the atmospheric boundary layer, the physics are considerably more complex, encompassing shear, turbulent transport, and wakes from other turbines. In this study, the mean flow streamtube around a wind turbine in a wind farm is investigated with large eddy simulations of a periodic array of actuator disks in half-channel flow at a range of turbine thrust coefficients. Momentum and mean kinetic energy budgets are presented, connecting the energy budget for an individual turbine to the wind farm performance as a whole. It is noted that boundary layer turbulence plays a key role in wake recovery and energy conversion when considering the entire wind farm. The wind farm power coefficient is maximized when the work done by Reynolds stress on the periphery of the streamtube is maximized, although some mean kinetic energy is also dissipated into turbulence. This results in an optimal value of thrust coefficient lower than the traditional Betz result. The simulation results are used to evaluate Nishino’s model of infinite wind farms, and design trade-offs described by it are presented.
Highlights
IntroductionEach wind turbine will generally perform worse than an isolated turbine
In a wind farm, each wind turbine will generally perform worse than an isolated turbine
This study has presented mean streamwise momentum and mean kinetic energy budgets for a mean streamtube in a periodic array of actuator disks in a channel flow
Summary
Each wind turbine will generally perform worse than an isolated turbine. The power loss with respect to an isolated turbine can be substantial, with typical losses of 10–20%, but as much as 40% in worst-case scenarios [1]. This degradation in performance occurs because the wakes of other turbines reduce the energy available in the wind. An inviscid and irrotational analysis of a streamtube encountering an idealized actuator disk illuminates a trade-off between turbine force and turbine power. This is the so-called Betz limit, which sets the maximum power coefficient to be 16/27 [3]. The aim of this study is to apply the same streamtube approach to numerical simulation data, which allows the relaxation of certain unrealistic assumptions in the classical analysis, namely that the turbine is isolated, the flow is irrotational, and the inflow is uniform
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
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 call
