Aerodynamic Modelling of Insect Wings Using Joukowski Transformation

A leading-edge vortex (LEV) is known to form on the upper surface of flapping/revolving wings leading to noticeably higher lift coefficient values. Whilst there have been many experimental and numerical studies to investigate the LEV aerodynamics within insect flight, there remains a need to develop simple theoretical models to improve our understanding of the underlying physics of this high-lift mechanism. For this purpose, we employed a low-order quasi-steady theoretical model based on the well-known Joukowski transformation simulation of a flat plate with a free vortex, and extended it to take into account other essential aerodynamic features of insect-like wings including downwash flow and non-linearity of the lift curve at high angles of attack. The model was used to assess the lift production of eight different insect species. On average, the lift force when excluding the LEV contribution was found to be only 4% lower than the force required to balance the weight of these eight insects, suggesting that the LEV may not be primarily contributing to lift production through providing additional circulatory lift. Instead, this result supports a recent perspective that LEVs forming on insect wings mainly provide a means for flow reattachment at high angles of attack, hence enhancing lift production through prevention of stall.