Unsteady lift on high-amplitude pitching aerofoils with massive flow separation
The ability to accurately predict unsteady lift acting on an aerofoil in real-time when significant flow variations occur is important for a variety of applications such as manoeuvrability and control of small aerial and underwater vehicles. Closed-form analytical solutions to predict unsteady lift, such as Theodorsen’s theory, are only available for small flow fluctuations, which limits their applicability to gentle manoeuvres. This thesis aims to gain new insights on a high amplitude pitching aerofoil characterised by massive flow separation to pave the way for the development of the closed-form analytical formulations for these extreme conditions. High-amplitude, asymmetric pitching motions of a NACA 0018 aerofoil at a Reynolds number of 32000 is investigated using time-resolved force and velocity field measurements. Theodorsen’s theory is employed to predict the unsteady lift on the pitching aerofoil. It is shown that Theodorsen’s theory can be modified to account for high-amplitude and nonsinusoidal pitch oscillations. This theory is compared with unsteady thin-aerofoil theory and it is tested even in conditions when the flow is massively separated. Despite that the underlying assumptions of the model are violated, its accuracy is remarkable, including when large leading-edge vortices (LEVs) are present, but decreases when the leading-edge and trailingedge vortices have a strong interaction. Discrepancies between predicted and measured lift are shown to be due to the vortex lift, which can be estimated by the data-driven approach based on the impulse theory. Based on this result, a new limiting criterion for Theodorsen’s theory for a pitching aerofoil is proposed, that is when a coherent trailing-edge vortex advects downstream at a significantly slower velocity than the freestream velocity. This finding is significant since it extends the conditions where the lift can be confidently predicted by Theodorsen’s theory. A semi-empirical low-order model of the vortex dynamics is developed through the impulse theory, as a first step towards a fully predictive model of the vortex force. The growth of the LEV circulation is estimated from an outer shear-layer velocity, which is empirically computed from the characteristic shear-layer velocity. The detachment mechanism of the LEV is found to be due to the LEV reattachment point reaching the trailing-edge, which limits the size and strength of the LEV. The advection velocity of the trailing-edge vortex is computed from the trailing-edge shear-layer velocity and the velocity induced by the LEV. As a result, the estimated vortex lift is in agreement with results of the data-driven method. Overall, these findings provide insights into the force generation mechanism of massively separated flow and will contribute to the development of fully predictive low-order models.