Articles | Volume 8, issue 4
https://doi.org/10.5194/wes-8-503-2023
https://doi.org/10.5194/wes-8-503-2023
Research article
 | 
06 Apr 2023
Research article |  | 06 Apr 2023

A simple vortex model applied to an idealized rotor in sheared inflow

Mac Gaunaa, Niels Troldborg, and Emmanuel Branlard

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Cited articles

Betz, A.: Das Maximum der theoretisch möglichen Ausnützung des Windes durch Windmotoren, Zeitschrift für das gesamte Turbinewesen, 26, 307–309, 1920. a
Boorsma, K., Schepers, G., Aagard Madsen, H., Pirrung, G., Sørensen, N., Bangga, G., Imiela, M., Grinderslev, C., Meyer Forsting, A., Shen, W. Z., Croce, A., Cacciola, S., Schaffarczyk, A. P., Lobo, B., Blondel, F., Gilbert, P., Boisard, R., Höning, L., Greco, L., Testa, C., Branlard, E., Jonkman, J., and Vijayakumar, G.: Progress in the validation of rotor aerodynamic codes using field data, Wind Energ. Sci., 8, 211–230, https://doi.org/10.5194/wes-8-211-2023, 2023. a
Branlard, E.: Wind Turbine Aerodynamics and Vorticity-Based Methods, Springer, https://doi.org/10.1007/978-3-319-55164-7, 2017. a
Branlard, E. and Gaunaa, M.: Cylindrical vortex wake model: right cylinder, Wind Energy, 18, 1973–1987, https://doi.org/10.1002/we.1800, 2015. a, b, c
Branlard, E. and Gaunaa, M.: Superposition of vortex cylinders for steady and unsteady simulation of rotors of finite tip-speed ratio, Wind Energy, 19, 1307–1323, 2016. a, b
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Short summary
We present an analytical vortex model. Despite its simplicity, the model is fully consistent with 1D momentum theory. It shows that the flow through a non-uniformly loaded rotor operating in non-uniform inflow behaves locally as predicted by 1D momentum theory. As a consequence, the local power coefficient (based on local inflow) of an ideal rotor is unaltered by the presence of shear. Finally, the model shows that there is no cross-shear deflection of the wake of a rotor in sheared inflow.
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