A vortex approach for unsteady insect flight analysis in 2D

This paper considers 2D insect wing motion in which the flow field does not change in the out-of-plane direction. When modelling complex phenomena, simpler, but not overly simple, analysis techniques become imperative. We achieve the balance of simplicity and accuracy by a technique based on the vortex. The wing is represented by its chord, described by a line in 2D. During the unsteady flapping, a time-dependent circulation pattern is developed over the wing, modelled by the distribution of discrete line vortices. The magnitudes of the bound vortices on the wing are determined by the non-penetration condition. Two vortices at the wing’s leading and trailing edges are shed. The velocity is determined by the bound and wake vortices using 2D Biot–Savart law, which is also used to convect wake vortices. The entire cycle is repeated as the time progresses. While establishing a simple affordable numerical method for flapping wing analysis and highlighting its remarkable performance, the limitation of the method is delineated and recommendations made in comparison with more accurate solutions obtained by a Navier–Stokes solver. This will ensure the proper use of the method and avoid its misuse in the unsteady aerodynamics analysis.