Modern large wind turbine rotors can encounter airflow at inflow Mach numbers of around 0.3 and Reynolds numbers of the order of 10 million at the blade tip. Our previous study showed that for these operational conditions, the incompressibility assumption is violated, and supersonic flow can occur locally. The present follow-up study reports on a numerical investigation of the dynamic behavior of the FFA-W3-211 wind turbine tip airfoil in transonic flow using unsteady Reynolds-averaged Navier–Stokes (URANS) simulations. The computations are performed for a highly unsteady aerodynamic regime by imposing a dynamic sinusoidal pitching motion across the transonic threshold determined in our previous study. This way, the airfoil is forced to enter and leave the supersonic flow regime. The simulations are conducted by varying the reduced frequency and the inflow Mach number, while keeping the Reynolds number constant at nine million. The choice of non-negligible inflow Mach numbers combined with high Reynolds numbers results in a realistic combination for full-scale wind turbines, but it is still challenging to achieve experimentally with the test facilities available nowadays. The dynamic pitching motion is found to lead to the formation of a hysteresis loop with an extent, depending on both reduced frequency and inflow Mach number. In particular, it is observed that an increase in one of these two parameters induces an expansion of the hysteresis loop with the consequences of (1) an increase in the magnitude and variability of loads experienced by the airfoil, (2) a delay in the beginning and ending of the transonic flow regime, and (3) the onset of shock waves occurring at inflow Mach numbers lower than those estimated under static conditions. Moreover, since the formation of a hysteresis loop implies a range of conditions in which transonic flow can occur, this needs to be better understood and considered when defining any safety margin in the definition of the transonic threshold for turbine design and operation purposes. In general, this study suggests the need to take into account dynamic effects when predicting aerodynamic loads and performance for next-generation wind turbine rotors.

The interaction between a traveling shock wave and a cylindrical water column was predicted using the open-source CFD toolbox OpenFOAM. The two-dimensional flow in a shock tube device was simulated by using the volume-of-fluid method for tracking the transient interface between the two immiscible fluids. The analysis was based on the Reynolds-averaged Navier-Stokes approach, where an eddy-viscosity model was supplied for the turbulence closure. The acceptably accurate results achieved for this complex fluids engineering problem confirmed the viability of this toolbox for industrial research and development.

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.