Computational Investigation of Vortex Dynamics and Aerodynamic Performance in Flapping Propulsion

Flapping motion is widely utilized in many biological propulsion systems, including insect/bird wings and fish pectoral fins. To survive through millions of years of evolution, these natural flyers/swimmers have developed superior and complex propulsive mechanisms to avoid predators and hunt for prey. However, achieving biological levels of aero/hydro-performance in bio-inspired robots design has proven elusive. This is due to our lack of understanding of the fundamental physics of deformable wings/fins and the technical difficulties in studying their complex locomotion.

The current dissertation focuses on two aspects of flapping wings. Firstly, we investigate the dominant flow control parameters that govern vortex development and aerodynamic performance using simplified canonical models. A Cartesian grid based immersed boundary incompressible Navier-Stokes solver is used to simulate the corresponding unsteady flows. The parametric study of 2-D flapping plates reveals that the rotational phase difference between the leading-edge and trailing-edge is the dominant parameter to achieve force enhancement. A moderate phase difference is able to feed extra circulation into the trailing-edge vortex which induces a stronger counterpart leading-edge vortex. As a result of local flow modulation, the vortex on the suction side is pulled down closer to the plate, which leads to the improvement of force production up to 26%. Our 3-D flapping plates demonstrate that the phase difference between pitching and rolling motion is a critical parameter to achieve the optimal aerodynamic performance. This is because the phase difference directly alters the interaction between leading-edge vortices and trailing-edge vortices, and thus minimizes the wake deflection in the downstream direction. The simulation results show that an optimal phase difference can improve the cycle-averaged force and efficiency of up to 23% and 15%, respectively. In addition, a unique vortex structure (named “double-C”-shaped vortex rings) produced by low-aspect-ratio flapping plates is first reported here. This vortex structure is found to be quite robust over a range of Strouhal numbers and Reynolds numbers.

Secondly, the wake topology and propulsive performance of real insect wings are examined via a combined experimental and computational approach. High-speed photogrammetry and accurate 3-D reconstruction are used to measure the deformable wing kinematics of freely flying dragonflies with precise detail. Then, flow simulations are conducted to evaluate the unsteady flow characteristics and the associated aerodynamic performance. The quantitative measurements of wing kinematics and surface deformation show that the phase difference between leading-edge and trailing-edge rotation observed in nature is in line with the optimal value we found in the aforementioned canonical model studies. Our flow simulations further reveal that the enhancement of aerodynamic functions can be achieved in two ways: 1) improving the power economy by preventing the tip vortex from bursting, and 2) improving the leading-edge vortex attachment by suppressing the generation of the secondary vortex. These findings have the potential to help us connect specific features in complex flapping locomotion with observed vortex dynamics and aerodynamic force production, so as to bring new insights into the design of high-efficient bio-inspired robotic systems.