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Published November 2014 | Published
Journal Article Open

Low-order modeling of wind farm aerodynamics using leaky Rankine bodies


We develop and characterize a low-order model of the mean flow through an array of vertical-axis wind turbines (VAWTs), consisting of a uniform flow and pairs of potential sources and sinks to represent each VAWT. The source and sink in each pair are of unequal strength, thereby forming a "leaky Rankine body" (LRB). In contrast to a classical Rankine body, which forms closed streamlines around a bluff body in potential flow, the LRB streamlines have a qualitatively similar appearance to a separated bluff body wake; hence, the LRB concept is used presently to model the VAWT wake. The relative strengths of the source and sink are determined from first principles analysis of an actuator disk model of the VAWTs. The LRB model is compared with field measurements of various VAWT array configurations measured over a 3-yr campaign. It is found that the LRB model correctly predicts the ranking of array performances to within statistical certainty. Furthermore, by using the LRB model to predict the flow around two-turbine and three-turbine arrays, we show that there are two competing fluid dynamic mechanisms that contribute to the overall array performance: turbine blockage, which locally accelerates the flow; and turbine wake formation, which locally decelerates the flow as energy is extracted. A key advantage of the LRB model is that optimal turbine array configurations can be found with significantly less computational expense than higher fidelity numerical simulations of the flow and much more rapidly than in experiments.

Additional Information

© 2014 AIP Publishing LLC. Received 3 December 2014; accepted 12 December 2014; published online 31 December 2014. This work was funded by an NSF Graduate Research Fellowship to D.B.A. and the Carol Carmichael Research Fellowship to A.E.C. Funding to J.O.D. from ONR N000141211047 and the Gordon and Betty Moore Foundation through Grant No. GBMF2645 is also gratefully acknowledged.

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August 20, 2023
October 20, 2023