Numerical simulations of transition and long-term response of a wind turbine airfoil

Abstract

Numerical simulations are performed for an FFA-W3 wind-turbine airfoil corresponding to a section of the DTU 10-MW Reference Wind Turbine. Wall-resolved large-eddy simulations (LES) are carried out with Nek5000 and EllipSys at chord Reynolds number $Re_c=1\times10^5$ and effective angle of attack $AoA=3.1^\circ-3.3^\circ$. A spanwise domain width of 10 percent of the chord is sufficient to reproduce the time-averaged flow and the evolution of the main disturbances. EllipSys is validated against Nek5000 for LES, showing close agreement for the mean flow and most amplified perturbations. EllipSys underpredicts the amplitude of Tollmien-Schlichting waves in the attached boundary layer, owing to higher numerical dissipation, but closely predicts the evolution of the Kelvin-Helmholtz (KH) mode in the laminar separation bubble, in agreement with parabolized stability equation (PSE) results. The mode shape is extracted using spectral proper orthogonal decomposition (SPOD), revealing the KH wavepacket forming in the separation bubble. Long-time EllipSys simulations show a slow modulation of the normal-force coefficient, with amplitude 10.5 percent and period 48 flow-through times, corresponding to $f=f^*c/U_\infty=0.021$ and $St=f\sin(AoA)=0.0012$. This frequency is associated with low-frequency oscillations reported in airfoil studies, although the Strouhal number is lower than previously observed and occurs at smaller angle of attack. For the DTU 10-MW turbine, the oscillation period corresponds to 7.7 blade rotations. Periodic stalling and reattachment may trigger the oscillation, while sufficiently high reverse flow on both sides of the airfoil may permit absolute instability and periodic bubble bursting.