An Analytical Model for Wind Turbine Wakes under Pressure Gradient

Arslan Salim Dar and Fernando Porté-Agel
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Arslan Salim Dar: Wind Engineering and Renewable Energy Laboratory (WIRE), École Polytechnique Fédérale de Lausanne (EPFL), 1015 Lausanne, Switzerland
Fernando Porté-Agel: Wind Engineering and Renewable Energy Laboratory (WIRE), École Polytechnique Fédérale de Lausanne (EPFL), 1015 Lausanne, Switzerland

Energies, 2022, vol. 15, issue 15, 1-13

Abstract: In this study, we present an analytical modeling framework for wind turbine wakes under an arbitrary pressure gradient imposed by the base flow. The model is based on the conservation of the streamwise momentum and self-similarity of the wake velocity deficit. It builds on the model proposed by Shamsoddin and Porté-Agel, which only accounted for the imposed pressure gradient in the far wake. The effect of the imposed pressure gradient on the near wake velocity is estimated by using Bernoulli’s equation. Using the estimated near wake velocity as the starting point, the model then solves an ordinary differential equation to compute the streamwise evolution of the maximum velocity deficit in the turbine far wake. The model is validated against experimental data of wind turbine wakes on escarpments of varying geometries. In addition, a comparison is performed with a pressure gradient model which only accounts for the imposed pressure gradient in the far wake, and with a model that does not account for any imposed pressure gradient. The new model is observed to agree well with the experimental data, and it outperforms the other two models tested in the study for all escarpment cases.

Keywords: wakes; wind turbines; pressure gradient; analytical modeling (search for similar items in EconPapers)
JEL-codes: Q Q0 Q4 Q40 Q41 Q42 Q43 Q47 Q48 Q49 (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (5)

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