Quasi-steady aerodynamic modelling of hovering miniature insects

Characterized by Reynolds numbers of the order of ten and wing lengths of approximately 1mm, the aerodynamics associated with miniature insects are distinguishable with respect to the rest of the general insect domain. The uniqueness of their aerodynamic environment is reflected in some atypical physical attributes, such as bristled wing morphologies and swimming-like flapping profiles. Owing to those distinctive attributes, our aerodynamic understanding of the miniature insect domain is, comparatively, in its infancy. In this study, a semi-empirical quasi-steady framework is proposed and assessed for its suitability in representing miniature-scale aerodynamics. The present analysis includes considerations towards the absence of stall and the clap and fling aerodynamic mechanisms, which have been implemented into a suitable kinematic framework. Most significantly, the prescribed quasi-steady treatment allows for translational effects to be adequately captured for angles of attack across the first quadrant via the normal force model. Furthermore, we demonstrate good agreement between the outputs from our clap and fling model, obtained via simple deployment of four additional clap and fling coefficients, and those from previous experimental investigations in the literature. The analysis provides preliminary insights into the utility of quasi-steady modelling in the miniature domain, whilst highlighting areas where further work is required in order to build a more robust representation of miniature insect aerodynamics.