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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 (BLEs) and parabolized stability equations (PSEs), including rotation effects. An important element of the developed BL method 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 model 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 (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 method 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 mean flow without rotation. These results also agree with those from the developed model for cases with low 3D 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 models predict a later transition in the regions where 3D and rotation effects are non-negligible. The developed method, which accounts for these effects, predicted earlier transition onsets in this region (e.g., 19 % earlier than RANS at 26 % of the radius for the constant-airfoil geometry) and shows that transition may occur via highly oblique modes. These modes differ from 2D TS waves 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 and rotation effects are weaker and the adverse pressure gradient is more significant, modes with small wave angles (close to 2D) 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.

Abstract. This work aims at developing a low-order framework to predict the onset of transition over wind-turbine blades without requiring three-dimensional simulations. The effects of three-dimensionality and rotation on the transition location are also analyzed. The framework consists of a model to approximate the base-flow and another to predict the transition location. The former is based on the quasi-three-dimensional Euler and boundary-layer equations and only requires the pressure distribution over an airfoil to provide an approximation for the base-flow over the blade. The latter is based on the envelope of N factors method, where this quantity is computed using the parabolized stability equations (PSE) considering rotational effects. It is shown that rotation accelerates the flow towards the tip of the blade in the fully developed flow region and towards the opposite direction close to the stagnation point. The database method embedded in the EllipSys3D RANS code indicates overly premature transition locations, matching those obtained with a PSE analysis of a two-dimensional base-flow. The consideration of the spanwise velocity, as carried out in the developed model, has a stabilizing effect, delaying transition. Conversely, rotation plays a destabilizing role, hastening the transition onset. Moreover, airfoils with lower pressure gradients are more susceptible to its effects. The increase in the rotation speed makes transition occur through increasingly oblique disturbances from the middle to the tip of the blade, whereas the opposite happens for lower radial positions. Tollmien-Schlichting (TS) waves seem to trigger transition. However, highly oblique critical modes that may be intermediates between TS and crossflow ones occur for low radii. The developed framework allows transition prediction with reasonable accuracy using chordwise cp distributions as input, such as those provided by XFOIL.