Low-order modeling for transition prediction applicable to wind-turbine rotors

Abstract

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.