A simplified model for transition prediction applicable to wind-turbine rotors

Abstract

Abstract. This work aims to develop a simple framework for transition prediction over wind-turbine blades, including effects of the blade rotation and spanwise velocity without requiring fully three-dimensional simulations. The framework is based on a set of boundary-layer equations\xa0(BLEs) and parabolized stability equations\xa0(PSEs), including rotation effects. An important element of the developed BL\xa0method is the modeling of the spanwise velocity at the boundary-layer edge. The two analyzed wind-turbine geometries correspond to a constant airfoil and the DTU 10-MW Reference Wind Turbine blades. The BL\xa0model allows an accurate prediction of the chordwise velocity profiles. Further, for regions not too close to the stagnation point and root of the blade, profiles of the spanwise velocity agree with those from Reynolds-averaged Navier–Stokes\xa0(RANS) simulations. The model also allows predicting inflectional velocity profiles for lower radial positions, which may allow crossflow transition. Transition prediction is performed at several radial positions through an “envelope-of-envelopes” methodology. The results are compared with the eN \xa0method of Drela and Giles, implemented in the EllipSys3D RANS code. The RANS transition locations closely agree with those from the PSE analysis of a 2D\xa0mean flow without rotation. These results also agree with those from the developed model for cases with low\xa03D and rotation effects, such as at higher radial positions and geometries with strong adverse pressure gradients where 2D Tollmien–Schlichting (TS) waves are dominant. However, the RANS and PSE 2D\xa0models predict a later transition in the regions where 3D\xa0and rotation effects are non-negligible. The developed method, which accounts for these effects, predicted earlier transition onsets in this region (e.g., 19\u2009% earlier than RANS at 26\u2009% of the radius for the constant-airfoil geometry) and shows that transition may occur via highly oblique modes. These modes differ from 2D\xa0TS\xa0waves and appear in locations with inflectional spanwise velocity. However, except close to the root of the blade, crossflow transition is unlikely since the crossflow velocity is too low. At higher radial positions, where 3D\xa0and rotation effects are weaker and the adverse pressure gradient is more significant, modes with small wave angles (close to\xa02D) are found to be dominant. Finally, it is observed that an increase in the rotation speed modifies the spanwise velocity and increases the Coriolis and centrifugal forces, shifting the transition location closer to the leading edge. This work highlights the importance of considering the blade rotation and the three-dimensional flow generated by that in transition prediction, especially in the inner part of the blade.