| 01 Jul 2025
Computationally efficient aerodynamic modeling of swept wind turbine blades using coupled near wake and vortex cylinder models
Abstract. This study introduces a computationally efficient engineering aerodynamic model specifically designed for load calculations of swept wind turbine blades, overcoming limitations in existing models. The proposed method couples a near wake trailed vortex model with a novel far wake vortex cylinder model. In this coupled model, the near wake, defined as the first quarter revolution of the blade's own trailed wake, is modeled using non-expanding helical vortices. Together with the influence of the curved bound vortex, the sweep effects are effectively captured. This comprehensive approach accounts for the influence of a finite number of blades, eliminating the need for Prandtl's empirical tip-loss correction used in conventional blade element momentum (BEM) methods. The far wake, representing the remaining trailed wake, is modeled using concentric vortex cylinders originating downstream of the rotor plane, replacing the conventional momentum-based approach. The near and far wake contributions are coupled together to obtain the total induction. In this study, a detailed analysis identifies limitations in the original coupling method, leading to two proposed modifications that enhance numerical stability and accuracy. Comparisons with higher-fidelity free-wake lifting line (LL) and Reynolds-averaged Navier-Stokes (RANS) simulations demonstrate the load prediction improvements, particularly for forward swept blades. The model achieves comparable accuracy with significantly reduced computational efforts, making it an ideal tool for design optimization and repetitive aeroelastic simulations of swept wind turbine blades. While developed and validated under steady-state conditions, the formulation readily supports extensions to unsteady aerodynamics using methodologies analogous to unsteady BEM approaches. The model can also be adapted in future work for generalized blade geometries combining sweep and prebend.
Competing interests: DTU Wind and Energy Systems develops and distributes the Navier-Stokes solver EllipSys3D on commercial and academic terms. DTU Wind and Energy Systems also develops, supports and distributes HAWC2 on commercial terms, and HAWC2 is available free of charge for educational and academic research purposes.
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Dear authors,
I had the pleasure to read your study and found it very well organized and complete (both in terms of theory formulation and data analysis). As far as I could check, I did not find any technical issue to be fixed. My only comment is that a little bit more discussion should be added on the switch to the unsteady formulation. Are you expecting it to perform as well as a LLT or an ALM? If it is indeed true that the compuational cost is lower and comparable to BEM, the other two methods are known to perform well in dynamic mode and can be also easily coupled with a structural solver.