Vanella Marcos, Fitzgerald Timothy, Preidikman Sergio, Balaras Elias, Balachandran Balakumar
Department of Mechanical Engineering, University of Maryland, College Park, MD 20742, USA.
J Exp Biol. 2009 Jan;212(Pt 1):95-105. doi: 10.1242/jeb.016428.
In the present study, a computational investigation was carried out to understand the influence of flexibility on the aerodynamic performance of a hovering wing. A flexible, two-dimensional, two-link model moving within a viscous fluid was considered. The Navier-Stokes equations governing the fluid dynamics were solved together with the equations governing the structural dynamics by using a strongly coupled fluid-structure interaction scheme. Harmonic kinematics was used to prescribe the motions of one of the links, thus effectively reducing the wing to a single degree-of-freedom oscillator. The wing's flexibility was characterized by the ratio of the flapping frequency to the natural frequency of the structure. Apart from the rigid case, different values of this frequency ratio (only in the range of 1/2 to 1/6) were considered at the Reynolds numbers of 75, 250 and 1000. It was found that flexibility can enhance aerodynamic performance and that the best performance is realized when the wing is excited by a non-linear resonance at 1/3 of the natural frequency. Specifically, at Reynolds numbers of 75, 250 and 1000, the aerodynamic performance that is characterized by the ratio of lift coefficient to drag coefficient is respectively increased by 28%, 23% and 21% when compared with the corresponding ratios of a rigid wing driven with the same kinematics. For all Reynolds numbers, the lift generated per unit driving power is also enhanced in a similar manner. The wake capture mechanism is enhanced, due to a stronger flow around the wing at stroke reversal, resulting from a stronger end of stroke vortex at the trailing edge. The present study provides some clues about how flexibility affects the aerodynamic performance in low Reynolds number flapping flight. In addition, it points to the importance of considering non-linear resonances for enhancing aerodynamic performance.
在本研究中，进行了一项计算研究，以了解柔性对悬停机翼空气动力学性能的影响。考虑了一个在粘性流体中运动的柔性二维双连杆模型。通过使用强耦合流固相互作用方案，求解了控制流体动力学的纳维-斯托克斯方程以及控制结构动力学的方程。采用谐波运动学来规定其中一个连杆的运动，从而有效地将机翼简化为单自由度振荡器。机翼的柔性通过拍动频率与结构固有频率的比值来表征。除了刚性情况外，在雷诺数为75、250和1000时，考虑了该频率比的不同值（仅在1/2至1/6范围内）。研究发现，柔性可以提高空气动力学性能，并且当机翼在固有频率的1/3处受到非线性共振激励时，可实现最佳性能。具体而言，在雷诺数为75、250和1000时，与以相同运动学驱动的刚性机翼的相应升阻比相比，以升力系数与阻力系数之比表征的空气动力学性能分别提高了28%、23%和21%。对于所有雷诺数，单位驱动功率产生的升力也以类似方式增强。尾流捕获机制得到增强，这是由于在行程反转时机翼周围的流动更强，这是由后缘更强的行程末端涡旋引起的。本研究为柔性如何影响低雷诺数扑翼飞行中的空气动力学性能提供了一些线索。此外，它指出了考虑非线性共振对提高空气动力学性能的重要性。
