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.

本文研究二维昆虫翼运动场景，其中流场沿面外方向无变化。在对复杂物理现象进行建模时，既简洁又不过于简化的分析技术便成为必要手段。本文采用基于涡旋（vortex）的分析技术，实现了简洁性与计算精度的平衡。该研究将翼型以翼弦（chord）表征，在二维平面中以直线形式表示。在非定常扑动过程中，翼面上会形成随时间变化的环量模式，该模式通过离散线状涡旋（discrete line vortices）的分布进行建模。翼面上附着涡（bound vortices）的强度由不可穿透条件（non-penetration condition）确定，翼的前缘与后缘各脱落出一个涡旋。流场速度由附着涡与尾迹涡通过二维毕奥-萨伐尔定律（2D Biot–Savart law）计算得到，该定律同时用于尾迹涡的对流输运。随着时间推进，整个计算循环将重复进行。本文在构建适用于扑翼分析的简洁且易于实现的数值方法并展示其优异性能的同时，还通过与纳维-斯托克斯（Navier–Stokes）求解器得到的高精度解进行对比，阐明了该方法的局限性并给出应用建议，以此确保该方法被正确使用，避免其在非定常空气动力学分析中被误用。