Numerical and theoretical study of flapping airfoil aerodynamics using a parallelized immersed-boundary method

Abstract

Flight has fascinated humans for centuries. Human inventions such as missiles, aircraft , unmanned aerial vehicles (UAV), and micro air vehicle (MAV) are inspired by natural flying expertise. As natural flyers usually operate in a vortex-dominated environment, interactions between their wings and the vortices have significant influences on force generation and flying efficiency. Some interesting phenomena induced from such vortex-body interactions have gotten a lot of attention in the past few decades. A good example is that birds and insects are credited with extracting energy from ambient vortices. In a simpler form, bio-inspired airfoils with either passive or active flapping motions are found to have the potential to harvest energy from incoming vortices generated from an upstream object, i.e. a cylinder. The current study identified the interaction modes of the leading edge vortex (LEV) and trailing edge vortex (TEV) between the active flapping airfoil and the incoming vortices. The relation between the interaction modes and the energy extraction capacity of an active harvester is investigated guided by a potential theory. The interaction modes induced by a passive energy harvester always benefit the energy extraction efficiency. However, the dynamic response of the passive harvester was found to vary corresponding to the properties of the incoming vortical wake. A profound appreciation of energy extracting mechanisms can provide a solution for the energy consumption issue of MAV and UAV. However, difficulties are encountered in practical applications of energy harvesting on how to detect the locations of generated vortices and what the trajectory of the vortex downstream of the moving body is. Some observations are realized and the fluid dynamics of the phenomena is beyond the fundamentals described in the textbook. One well-known instance is the asymmetric wake formed downstream of a symmetric sinusoidal heaving airfoil. In this study, factors that influence the formation of the asymmetric wakes on both the near wake and far wake regions are demonstrated. Novel vortex models are developed to explore the vortex dynamic mechanisms of the asymmetric wake and its development from the near wake region to the far wake region. In order to analyze the flow fields for the bio-inspired problems, Computational Fluid Dynamics (CFD) provides powerful and convenient tools. The shape of bio-inspired wings/airfoils and their maneuvers are usually very complicated. In CFD, the immersed-boundary (IB) method is an advantageous approach to simulate such problems. In this study, an immersed-boundary method is implemented in a parallel fashion in order to speed up the computational rate.. A variety of numerical schemes have been applied to the IB method, including different spatial schemes and temporal schemes; their performances are investigated. In addition, the IB method has been successfully implemented with the fluid-structure interaction models for studying passive mobile objectives, i.e. the energy harvester. The possibility of coupling other fluid dynamic models, i.e. species transport model and turbulence models, is also demonstrated.