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 引用本文: 何皓翔, 付嘉钧, 白宏磊. 极小昆虫翅膀拍动模式的气动特性实验研究. 力学学报, 待出版.
He Haoxiang, Fu Jiajun, Bai Honglei. A study on the aerodynamic characteristics of very small insects wing flapping pattern. Chinese Journal of Theoretical and Applied Mechanics, in press.
 Citation: He Haoxiang, Fu Jiajun, Bai Honglei. A study on the aerodynamic characteristics of very small insects wing flapping pattern. Chinese Journal of Theoretical and Applied Mechanics, in press.

## A STUDY ON THE AERODYNAMIC CHARACTERISTICS OF VERY SMALL INSECTS WING FLAPPING PATTERN

• 摘要: 不同于较大的昆虫 (如熊蜂, 果蝇和鹰蛾等, 飞行雷诺数Re > 100), 极小昆虫 (如丽蚜小蜂、西花蓟马和瘿蚊等, Re < 100) 的翅膀采用更复杂的三自由度拍动形式, 对应特殊的非定常高升力机制——“划桨”机制; 同时, 微小型飞行器 (MAV) 的飞行雷诺数较高 (Re = 103 ~ 105), 其任务环境复杂多变, 当MAV面对超载荷或高机动任务时, 利用极小昆虫翅膀拍动模式飞行或许可以作为一种新的解决方案. 为了深入理解MAV雷诺数下极小昆虫翅膀拍动模式的气动特性, 本文基于三自由度拍动翅膀模型实验(包括直接测力和染色液流动显示, Re = 3.9 × 103 ~ 1 × 104)对三种典型极小昆虫(丽蚜小蜂、西花蓟马和瘿蚊)悬停飞行状态下、翅膀拍动模式的气动力特性进行研究. 我们发现, 在上挥(Upstroke)阶段初期, 即“划桨(Rowing)”阶段, 翅膀受到的铅垂升力急剧增大; 在所考虑的雷诺数范围内, 翅膀在整个上挥阶段的平均铅垂升力系数(大于3.1, 丽蚜小蜂)明显大于较大昆虫翅膀拍动模式下获得的铅垂升力系数(1.5 ~ 2.0). 同时, 我们观察到在“划桨”阶段初期, 翅膀的前缘和后缘产生一对旋转方向相反的旋涡; 进入“划桨”阶段中末期, 后缘旋涡脱落, 但是前缘旋涡始终附着. 这表明在MAV雷诺数下, 翅膀上挥过程中的高升力产生机制为“延迟失速机制”, 而不是极低雷诺数下的“划桨机制”. 此外, 我们发现在翅膀上挥下拍冲程交替即“打开(Fling)”阶段, 其高升力机制仍然是“打开机制”; 然而, 我们也注意到雷诺数效应和双翅效应对“打开”阶段的气动力影响很大.

Abstract: Unlike larger insects (such as bumblebees, fruit flies and hawkmoth, Reynolds number Re > 100), very-small insects (such as Encarsia Formosa EF, Frankliniella occidenalis FO and Anbremia sp AS, Re < 100 etc.) have much complex patterns of wing flapping, with three degrees-of-freedom (DOF) being involved and corresponding to different under-lying mechanisms of high-lift generation. Meanwhile, micro aerial vehicles (MAV) are associated with relatively high Re, i.e., Re = 103 ~ 105, and their mission environment is complex and changing. When MAVs are faced with overload or high maneuverability mission, flying with very small insect wings flapping patterns may be a new method. To better understand the aerodynamic characteristics of wing flapping pattern of very small insects at high Re, flapping wing model-based experiments are conducted at a range of Reynolds number from 3.9 × 103 to 1 × 104, taking into account wing planforms and flapping kinematics of three typical very-small insects (i.e., EF, FO and AS). It is found that the vertical lift on the wing increases dramatically at the beginning ‘Rowing’ phase of the upstroke. It is further noticed, however, the time-mean vertical lift coefficient ( \bar \boldsymbol C_V^\text Upstroke ) on the wing of very small insects is significantly increased during the upstroke in the Re range considered in this work, e.g., \bar \boldsymbol C_V^\text Upstroke > 3.1 for EF, which is noticeably greater than those (1.5 ~ 2.0) of their larger counterparts. Moreover, it is observed that a pair of counter-rotating vortices are produced at the leading and trailing edges of the wing at the starting of the ‘Rowing’ phase. With the ‘Rowing’ advancing, the trailing-edge vortex sheds while the leading-edge vortex keeps attached, indicating that the high-lift generation during the upstroke is attributed to the delayed stall at the MAV Re range, instead of the ‘rowing’ mechanism identified at the very-low Re range. In addition, it is noticed that the ‘fling’ mechanism still plays a key role in generating the high lift during the ‘Fling’ phase, although Re effects and wing-wing interactions may strongly influence the force behavior.

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