An entrainment‐based model for annular wakes, with applications to airborne wind energy

Several novel wind energy systems produce wakes with annular cross‐sections, which are qualitatively different from the wakes with circular cross‐sections commonly generated by conventional horizontal‐axis wind turbines and by compact obstacles. Since wind farms use arrays of hundreds of turbines, g...

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Bibliographic Details
Published in:Wind energy (Chichester, England) England), 2022-03, Vol.25 (3), p.419-431
Main Authors: Kaufman‐Martin, Sam, Naclerio, Nicholas, May, Pedro, Luzzatto‐Fegiz, Paolo
Format: Article
Language:English
Subjects:
airborne wind energy
Arrays
AWE
Barriers
Differential equations
Entrainment
Flow velocity
Large eddy simulation
Mathematical models
Ordinary differential equations
Turbines
wake models
Wind farms
Wind power
Wind turbines
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Summary:Several novel wind energy systems produce wakes with annular cross‐sections, which are qualitatively different from the wakes with circular cross‐sections commonly generated by conventional horizontal‐axis wind turbines and by compact obstacles. Since wind farms use arrays of hundreds of turbines, good analytical wake models are essential for efficient wind farm planning. Several models already exist for circular wakes; however, none have yet been proposed for annular wakes, making it impossible to estimate their array performance. We use the entrainment hypothesis to develop a reduced‐order model for the shape and flow velocity of an annular wake from a generic annular obstacle. Our model consists of a set of three ordinary differential equations, which we solve numerically. In addition, by assuming that the annular wake does not drift radially, we further reduce the problem to a model comprising only two differential equations, which we solve analytically. Both of our models are in good agreement with previously published large eddy simulation results.
ISSN:1095-4244
1099-1824
DOI:10.1002/we.2679