Abstract
The current chapter applies the results of the right and skewed vortex cylinder models of rotors, respectively presented in Chaps. 17 and 21. The models are used to determine the velocity field upstream of one or several rotors, a region referred to as the induction zone for a wind turbine or a wind farm. The chapter begins with a small introduction on the topic of induction zone. The chapter briefly recalls the analytical models needed to assess the velocity field upstream of the rotor. A superposition of elementary cylindrical models is used. The superposition is described in Chap. 18 for the right cylinder and Chap. 23 for the skewed cylinder. Results are then compared to CFD actuator disk (AD) simulations in aligned and yawed conditions. Cases with and without wake rotation (swirl) are investigated for moderate and large thrust coefficients. The actuator disk simulation and vortex model results are seen to be in good agreement. The computational time required for the determination of the induction zone with the vortex model is negligible which makes the model a good candidate for the study of induction zones. The application of the model to obtain the induction zone in front of a wind farm is then presented. The effect of turbine spacing, hub-height, operating condition and wind farm layout on the wind farm induction is presented. The results show that the wind speed at 2.5D upstream of a wind farm can easily be reduced up to \(3\%\) compared to the actual free-stream. Most of the results presented in this chapter were published in the article from the author titled “Using a cylindrical vortex model to assess the induction zone in front of aligned and yawed rotors” (Branlard and Meyer Forsting, 2015, [6]). A Matlab source code to evaluate the velocity field in the entire domain induced by the main vorticity component is provided in Sects. 36.2.2 and 38.1.4 for the aligned and yawed case respectively.
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Notes
- 1.
The superposition of cylindrical vortex models is presented in Chap. 18 and [3].
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Branlard, E. (2017). Velocity Field Upstream of Aligned and Yawed Rotors: Wind Turbine and Wind Farm Induction Zone. In: Wind Turbine Aerodynamics and Vorticity-Based Methods. Research Topics in Wind Energy, vol 7. Springer, Cham. https://doi.org/10.1007/978-3-319-55164-7_24
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