A numerical investigation into the effects of flapping modes on the aerodynamic performance of insect hovering flight is carried out through the solution of the two-dimensional unsteady Navier-Stokes equations. Four types of idealized flapping modes with the identical quasi-steady lift force are compared, and the influences of the Reynolds number (Re), the translational duration and the rotational duration on the aerodynamic characteristics of the hovering are systematically analyzed flight. It is found that the instantaneous aerodynamic forces of the wing differ significantly in each flapping mode. The mode with harmonic translation and harmonic rotation leading the highest lifting efficiency is suitable for long-time flight while the mode with harmonic translation and trapezoid rotation giving the largest instantaneous forces is suitable for maneuvering flight. When Re increases from 100 to 1000, the lift force and lifting efficiency of the wing are increased significantly with the increasing Re first, and then slow down with the further increase in Re. In addition, the fast-translational mode with short translational duration will reduce the time-averaged lift force and the efficiency, whereas the fastrotational mode with short rotational duration can enhance the time-averaged lift force with the sustained efficiency.

通过二维非定常Navier-Stokes方程的求解，对扑动模式对昆虫盘旋飞行的空气动力性能的影响进行了数值研究。比较了具有相同准稳态升力的四种理想化拍击模式，并比较了雷诺数（Re），系统地分析了悬停的空气动力学特性的平移持续时间和旋转持续时间。结果发现，机翼的瞬时空气动力在每种拍动模式下均存在显着差异。谐波平移和谐波旋转导致最高提升效率的模式适用于长时间飞行，而谐波平移和梯形旋转产生最大瞬时力的模式适用于机动飞行。当再增加从100到1000，机翼的升力和提升效率显著具有增加的增加重新第一，然后用在进一步增加减慢再。另外，具有短平移持续时间的快速平移模式将减小时均提升力和效率，而具有短持续时间的快速旋转模式可提高时均提升力并具有持续的效率。