Institute of Engineering, Academic Assembly, Shinshu University, Nagano 380-8553, Japan.
Department of Engineering, Graduate School of Science and Technology, Shinshu University, Nagano 380-8553, Japan.
Phys Rev E. 2019 Jul;100(1-1):013104. doi: 10.1103/PhysRevE.100.013104.
Wing flexibility is one of the important factors not only for lift and thrust generation and enhancement in flapping flight but also for development of micro-air vehicles with flapping wings. In this study, we construct a flexible wing with chordwise flexibility by connecting two rigid plates with a torsion spring, and investigate the effect of chordwise wing flexibility on the flapping flight of a simple butterfly model by using an immersed boundary-lattice Boltzmann method. First, we investigate the effects of the spring stiffness on the aerodynamic performance when the body of the model is fixed. We find that the time-averaged lift and thrust forces and the required power increase with the spring stiffness. In addition, we find an appropriate range of the spring stiffness where the time-averaged lift and thrust forces are larger than those of the rigid wings. The mechanism of the lift and thrust enhancements is as follows: in the downstroke the flexible wings can generate not only the lift force but also the thrust force due to the deformation of wings; in the upstroke the flexible wings can generate not only the thrust force but also the lift force due to the deformation of wings. Second, we simulate free flights when the body of the model can only move translationally. We find that the model with the flexible wings at an appropriate value of the spring stiffness can fly more effectively than the model with the rigid wings, which is consistent with the results when the body of the model is fixed. Finally, we simulate free flights with pitching rotation. We find that the model gets off balance for any value of the spring stiffness. Therefore, the passive control of the pitching motion by the chordwise wing flexibility cannot be expected for the present butterfly model.
翼的灵活性不仅是扑翼飞行中升力和推力产生和增强的重要因素，也是开发具有扑翼的微型飞行器的重要因素。在本研究中，我们通过连接两个带有扭转弹簧的刚性板来构造具有翼弦灵活性的柔性翼，并通过浸入边界-格子玻尔兹曼方法研究翼弦柔性对简单蝴蝶模型扑翼飞行的影响。首先，我们研究了当模型主体固定时，弹簧刚度对空气动力性能的影响。我们发现，平均升力和推力以及所需功率随弹簧刚度的增加而增加。此外，我们发现了一个适当的弹簧刚度范围，在这个范围内，平均升力和推力比刚性翼更大。提高升力和推力的机制如下：在下降冲程中，柔性翼不仅可以由于翼的变形产生升力，还可以产生推力；在上升冲程中，柔性翼不仅可以由于翼的变形产生推力，还可以产生升力。其次，我们模拟了模型主体只能平移运动的自由飞行。我们发现，在适当的弹簧刚度下，具有柔性翼的模型比具有刚性翼的模型飞行更有效，这与模型主体固定时的结果一致。最后，我们模拟了带有俯仰旋转的自由飞行。我们发现，对于任何弹簧刚度值，模型都会失去平衡。因此，对于目前的蝴蝶模型，不能期望通过翼弦的柔性来实现俯仰运动的被动控制。
