Modern wind turbines are the largest rotating machines ever built, with blade lengths exceeding 100 m. Previous studies demonstrated how the flow around the tip airfoils of such large machines reaches local flow Mach numbers (Ma), at which the incompressibility assumption might be violated, and, even in normal operating conditions, local supersonic flow could appear. In the present study, a numerical analysis of the FFAW3- 211 wind turbine tip airfoil is performed. The results are obtained by means of the application of numerical tools: (1) XFOIL with the Prandtl–Glauert compressible correction and (2) computational fluid dynamic (CFD) simulations, where an unsteady Reynolds-averaged Navier–Stokes (URANS) model is used. A preliminary validation of the latter CFD model is performed to demonstrate that the URANS approach is a viable method for predicting the aerodynamic performances in compressible and transonic flow that provides additional and more reliable information compared to the classical compressibility corrections. From this study, three key findings can be highlighted. Primarily, the main transonic features of the FFA-W3-211 wind turbine tip airfoil have been assessed, selecting specific test cases of particular industrial interest. Then, the threshold between subsonic and supersonic flow is provided, considering also an increase of the Reynolds number (Re) from a characteristic value used in the wind tunnel experiments to the one realistic for large rotors. A strong dependence on this quantity is observed, revealing that, for the same Mach number, also the Reynolds number plays a crucial role in promoting the occurrence of transonic flow. Finally, the possible presence or absence of shock waves was investigated. The results indicate that the appearance of transonic flow is a necessary but not a sufficient condition to lead to shock formation. @en

This study performed an aerodynamic characterization of the FFA-W3-211 wind turbine tip airfoil in transonic flow using Unsteady Reynolds-Averaged Navier-Stokes (URANS) simulations, for both steady and dynamic operational conditions. First, the boundary between subsonic and supersonic flow in static conditions was identified, depending on the angle of attack, the approach flow Mach number, and the Reynolds number. The analysis points out that higher Reynolds numbers promote the occurrence of local supersonic flow. Thereafter, to investigate the dynamic behavior in the transonic flow regime, a sinusoidal pitching motion with representative values was imposed. A hysteresis, similar to but distinct from dynamic stall, was observed for entering and leaving the supersonic and subsonic regions. Elevated reduced frequencies widened the hysteresis loop, resulting in increased normal forces on the airfoil. The study indicated that an increase in reduced frequency leads to an earlier onset of transonic flow. In conclusion, the risk of transonic flow occurring during normal operation of the next generation wind turbines predicted in earlier studies could be corroborated. Moreover, dynamic effects and Reynolds number dependencies can be significant.

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