Unsteady fluid dynamics around a hovering flat plate wing

Insect flight is characterised by complex time-dependent flows in response to the unsteady wing movements. Biological fliers exploit the unsteady flow fields to modulate aerodynamic forces, thereby displaying unmatched flight performance, especially in hover. Naturally, this has inspired the creation of engineering models to replicate the flight behaviour. An in-depth understanding of the flow fields generated during hover and their dependence on the kinematics is paramount to achieve this goal. The two main kinematic components of a hovering wing are the stroke, which refers to the back-and-forth motion, and wing rotation, which refers to the change in angle of attack. The phase relation between stroke and rotation is quantified in terms of phase-shift and is broadly classified into symmetric, advanced, and delayed rotation. The phase-shift and duration of rotation, together referred to as rotational timing, are investigated in this bio-inspired study. The objective is to characterise the effect of rotational timing on the aerodynamic forces and the flow fields generated by a hovering wing. The unsteady flow around a hovering flat plate wing that mimics hoverfly kinematics has been investigated experimentally using particle image velocimetry and direct force measurements. The measurements are conducted at a Reynolds number of Re=220 and a reduced frequency of k=0.32 in order to dynamically match a hoverfly. The Lagrangian finite-time Lyapunov exponent method is used to analyse the unsteady flow fields by identifying dynamically relevant flow features such as the primary leading edge vortex (LEV), secondary vortices, and topological saddles, and their evolution within a flapping cycle. Firstly, the flow and force behaviour was characterised for a typical flapping cycle. The flow evolution in a symmetric, fast rotation is divided into four stages that are characterised by the LEV emergence, growth, lift-off, and breakdown and decay. Tracking saddle points is shown to be helpful in defining the LEV lift-off which occurs at the maximum stroke velocity. The flow fields are correlated with the aerodynamic forces revealing that the maximum lift and drag are observed just before LEV lift-off, which corresponds to the maximum stroke velocity. Secondly, the effect of phase-shift on the formation and evolution of lift-enhancing flow structures are discussed. Two advanced and delayed rotations are compared. The flow development stages and forces are similar for all rotations but the timing of stages varies. The evolution of forces and flow strongly depend on the stroke velocity. Thirdly, the dependence of the flow and force evolution on the stroke velocity was substantiated by doubling the rotational duration in the symmetric rotation. It was found that the timing of the flow stages altered, whereas the flow and forces mostly evolved similarly to that of a fast rotation. The fast rotation, however, produces higher maximum lift and drag compared to the slow