Inverse Airfoil Design Method for Low-Speed Straight-Bladed Darrieus-Type VAWT Applications

Abstract

The paper demonstrates the application of inverse airfoil design method to improve performance of a low-speed straight-bladed Darrieus-type VAWT. The study shows that an appropriate tailoring of the airfoil surface using the inverse airfoil design technique can help improve performance by eliminating undesirable flow field characteristics at very low Re, such as early transition due to presence of separation bubbles. The increase aerodynamic efficiency then translates into an improved aerodynamic performance of VAWTs specifically at very low chord Reynolds numbers. The study employs an interactive inverse airfoil design method (PROFOIL) that allows specification of velocity and boundary-layer characteristics over different segments of the airfoil subject to constraints on the geometry (closure) and the flow field (far field boundary). Additional constraints to satisfy some desirable features, such as pitching moment coefficient, thickness, camber, etc., along with a merit of performance of the VAWT, such as the required power output for a given tip-speed ratio, are specified as part of the inverse problem. Performance analyses of the airfoil and the VAWT are carried out with the aid of state-of-the-art analyses codes, XFOIL and CARDAAV, respectively. XFOIL is a panel method with a coupled boundary-layer scheme and is used to obtain the aerodynamic characteristics of resulting airfoil shapes. The final airfoil geometry is obtained through a multi-dimensional Newton iteration. A design example is presented to demonstrate the merits of the technique in improving performance of small VAWTs at low speeds. The main findings of the study suggests that the strength of the method lies in the inverse design methodology whereas its weaknesses is in reliably predicting aerodynamic characteristics of airfoils at low Reynolds numbers and high angles of attack. This weakness can, however, be overcome by assessing relative performance of the VAWT with the assumption that the changes in airfoil characteristics be kept small. The results indicate that a 10–15% increase in the relative performance of the VAWT can be achieved with this method.