Assessing the Blockage Effect of Wind Turbines and Wind Farms Using an Analytical Vortex Model

Emmanuel Branlard, Alexander R. Meyer Forsting

Research output: Contribution to journalArticlepeer-review

42 Scopus Citations


Wind farm blockage effects are currently neglected in the prediction of wind farm energy yield, typically leading to an overestimation of the production. This work presents a novel method to assess wind farm production, while accounting for blockage effects. We apply a vortex model, based on a cylindrical wake, to assess induction effects. We present variations of the model to account for finite wake length, finite tip-speed ratios, and the proximity to the ground. The results are applied to single rotors in aligned and yawed conditions and to different wind farm layouts. We provide far-field approximations for faster estimates of the velocity field. Further, this article includes a new methodology to couple the induction model to engineering wake models, such as the ones present in the FLOw Redirection and Induction in Steady State (FLORIS). We compare the results to actuator disk simulations for various operating conditions of a single turbine and different wind farm layouts. We found that the mean relative error of the model in the induction zone is typically around 0.2% compared with actuator disk simulations. The computational time of the velocity field using the analytical vortex model is three orders of magnitude less than the one obtained with the actuator disk simulation.

Original languageAmerican English
Pages (from-to)2068-2086
Number of pages19
JournalWind Energy
Issue number11
StatePublished - 2020

Bibliographical note

Publisher Copyright:
© 2020 The Authors. Wind Energy published by John Wiley & Sons Ltd

NREL Publication Number

  • NREL/JA-5000-76525


  • actuator disk
  • induction zone
  • vortex models
  • wind farm blockage


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