The ability to accurately predict the forces on an aerofoil in real-time when large flow variations occur is important for a wide range of applications such as, for example, for improving the manoeuvrability and control of small aerial and underwater vehicles. Closed-form analytical formulations are only available for small flow fluctuations, which limits their applicability to gentle manoeuvres. Here we investigate large-amplitude, asymmetric pitching motions of a NACA 0018 aerofoil at a Reynolds number of $$3.2 \times 10^4$$ 3.2 × 10 4 using time-resolved force and velocity field measurements. We adapt the linear theory of Theodorsen and unsteady thin-aerofoil theory to accurately predict the lift on the aerofoil even when the flow is massively separated and the kinematics is non-sinusoidal. The accuracy of the models is remarkably good, including when large leading-edge vortices are present, but decreases when the leading and trailing edge vortices have a strong interaction. In such scenarios, however, discrepancies between the theoretically predicted and the measured lift are shown to be due to vortex lift that is calculated using the impulse theory. Based on these results, we propose a new limiting criterion for Theodorsen’s theory for a pitching aerofoil: when a coherent trailing-edge vortex is formed and it advects at a significantly slower streamwise velocity than the freestream velocity. This result is important because it extends significantly the conditions where the forces can be confidently predicted with Theodorsen’s formulation, and paves the way to the development of low-order models for high-amplitude manoeuvres characterised by massive separation. Graphic abstract
Vertical axis wind turbines have several attractive features in the context of energy production in urban areas, but the inherent aerodynamic complexity of the flow around them has challenged their development on a larger scale. They generally operate at low tip speed ratios, where dynamic stall occurs on the blades. The vortex shedding associated with dynamic stall causes highly transient and heavy stress cycles that reduce the aerodynamic performance and increase the risk of fatigue and failure. The flow around an airfoil undergoing VAWT blade angle of attack variations was investigated using particle image velocimetry and force measurements. The formation of vortices and the lift force were studied for different tip speed ratios. A special focus was put on the effect of the asymmetry of the motion. The role of dynamic stall vortices on aerodynamic coeffients was evidenced by comparing experimental data to analytical predictions obtained from Theodorsen’s model. For the lowest equivalent tip speed ratio clockwise and counter clockwise rotating dynamic stall vortices formed on the airfoil with increasing and decreasing angle of attack. The asymmetry in motion lead to an asymmetry in size of the clockwise and counter-clockwise vortices. As the asymmetry in motion has a strong effect on the flow behaviour, the local pitch rate was proposed as a governing parameter. The increase of extrema with increasing pitch rate varies for increasing and decreasing angle of attack, indicating an additional influence of the history of the flow development.
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