Aerodynamics of darrieus wind turbines airfoils during start-up

Recent studies have demonstrated that, when rotating around an axis orthogonal to the flow direction, airfoils are virtually transformed into equivalent airfoils with a camber line defined by their arc of rotation. In these conditions, the symmetric airfoils commonly used for Darrieus blades actually behaves like virtually cambered ones or, equivalently, rotors have to be manufactured with counter-cambered blades in order to have the performance of a symmetric airfoil. To complete these analyses, the present study focuses the attention on the airfoils' aerodynamics during the start-up of the rotors. This phase of turbines' functioning is indeed of particular interest since it actually defines the cut-in speed of the rotors and then notably impacts on the annual energy production, especially in case of small-size machines. In the work, unsteady CFD simulations have been carried out in start-up like conditions on three airfoils, i.e. a NACA 0018 and two modified profiles based on the same airfoil. The modified profiles have been conformally transformed to fit their camber lines to the arc of a circle, such that the ratio of the airfoil chord to the circle's radius is 0.114 or 0.25. The study demonstrates that all the conventional theories based on one-dimensional aerodynamic coefficients (e.g. blade element momentum models) are affected by an intrinsic error in evaluating the starting torque profiles. Symmetric airfoils in fact exhibit a counter-intuitive non symmetric starting torque over the revolution. Conversely, airfoils compensated for the virtual camber effect show a substantially different starting torque profile, with a more symmetric distribution between the upwind and the downwind halves. This behavior is due to the effect of the pitching moment, which is usually neglected in lumped parameters models. At very low revolution speeds, its contribution becomes significant due to the very high angles of attack experienced by the blade. In particular, the pitching moment is non symmetric between the upwind and the downwind halves of the revolution. For upwind azimuthal positions the pitching moment reduces the overall torque output, while it changes sign in the downwind section, increasing the torque. The importance of accounting for the pitching moment contribution in low-order models (e.g. a blade element momentum model) is finally discussed by comparing the predicted torque profiles with those obtained by CFD.