On the influence of virtual camber effect on airfoil polars for use in simulations of Darrieus wind turbines

Darrieus vertical-axis wind turbines are experiencing renewed interest from researchers and manufacturers, though their efficiencies still lag those of horizontal-axis wind turbines. A better understanding of their aerodynamics is required to improve on designs, for example through the development of more accurate low-order (e.g. blade element momentum) models. Many of these models neglect the impact of the curved paths that are followed by blades on their performance. It has been theorized that the curved streamlines of the flow impart a virtual camber and incidence on them, giving a performance analogous to a cambered blade in a rectilinear flow. To test the extent of this effect, wind tunnel experiments have been conducted in a rectilinear flow to obtain lift and drag for three airfoils: a NACA 0018 and two conformal transforms of the profile. The transformed airfoils exhibit the virtual camber that the theory predicts is imparted to a NACA 0018 when used in a Darrieus turbine with blade chord-to-turbine radius ratios, c/R, of 0.114 and 0.25. A parallel computational fluid dynamics campaign has been conducted to study the aerodynamic behavior of the same blades in curvilinear flow in Darrieus-like motion with c/R = 0.114 and 0.25, at tip-speed ratios of 2.1 and 3.1, using novel techniques to obtain blade effective angles of attack. The analysis confirms that the theory holds, with the wind tunnel results for the NACA 0018 being analogous to numerical results for the relevant cambered airfoils. In addition, turbine performance is calculated using computational fluid dynamics and a blade element momentum code, for each of the blades in turn. The computational fluid dynamics results for the NACA 0018 agree closely to blade element momentum results for the equivalent cambered airfoil where c/R = 0.25, for both turbine power and blade tangential forces. Agreement between the two methods using geometrically identical blades is poor at both the blade and turbine level for c/R = 0.25. It is concluded that when modeling a Darrieus rotor using blade element momentum methods, applying experimental data for the profile used in the turbine will yield inaccurate results if the c/R ratio is high, in such cases it is necessary to select a profile based on the virtual shape of the blades.