The flexible kinematic modeling method and aerodynamic performance of dragonfly wings

Abstract

Dragonflies demonstrate intricate wing motions and structural deformations during flight. To investigate the unsteady aerodynamic mechanisms, this paper establishes a kinematic modeling framework that precisely characterizes the instantaneous flexible deformation of the wings. First, we propose a set of tailored deformation functions to satisfy the geometric constraints of inextensibility and root continuity during wing flapping and twisting. Based on these functions, the model quantitatively describes flexible deformations such as bending, warping, and cambering of the wing. Second, we examined how twist phase, twist amplitude, and camber influence the aerodynamic performance of the wing through numerical simulations. Finally, by analyzing the three-dimensional flow structures under various motion conditions, we reveal the physical mechanisms through which each parameter influences the aerodynamic forces. The results indicate that although rigid and flexible wings exhibit similar mean aerodynamic forces, the rigid wing fails to satisfy the biological geometric constraint of root continuity. In contrast, the flexible wing maintains these geometric constraints while exhibiting smoother aerodynamic force curves and sustaining stronger leading-edge vortices (LEVs). Further analysis shows that advancing the twist phase, increasing twist amplitude, and enhancing camber all help strengthen the aerodynamic force component normal to the stroke plane. Twisting angle not only significantly alters the direction of aerodynamic forces but also promotes a more uniform distribution of LEV strength along the wingspan, thereby maintaining a larger low-pressure region on the wing surface. Meanwhile, camber further stabilizes the outer LEV and enhances suction over the wing. This study provides a theoretical basis for understanding the coupled morphological and kinematic mechanisms of dragonfly wings, and is expected to offer new insights for the design and aerodynamic optimization of bio-inspired flying devices.