Computational modeling of unsteady low Reynolds number flapping wing aerodynamics

Abstract

The unsteady low Reynolds number aerodynamics of biomimetic airfoils and wings stands out as one of the most challenging areas of research to the scientific community. As opposed to steady flow where substantial amount of research has been accomplished in understanding the concepts of separation and transition, apart from turbulence, unsteady low Reynolds number flows have not gained much attention except for the past few years owing to difficulties in modeling and simulating such complex flows on arbitrary domains of interest like insect and bird flight, flutter prediction etc. The basic underlying mechanisms of lift and thrust production by birds and insects are well known and have been established by early researchers through extensive experiments and lower order numerical computations, supported by classical theories of unsteady aerodynamics. Nevertheless, to date, experiments and numerical computations of this problem have been focused on predicting aerodynamic forces and moments with specified wing kinematics. The airfoil or wing under study is usually constrained to move along a particular direction with a fixed freestream velocity. The rigid body dynamics of plunging/pitching/flapping bodies have however, received less attention. In the present work, numerical computations have been carried out to simulate the dynamics of plunging airfoils and wings in incompressible flow by coupling rigid body dynamics to the governing equations of fluid motion. In this case, the body accelerates from the state of rest to the state of motion due to the aerodynamic forces and traces a particular trajectory. During the course of the study, the effect of prescribed wing flexibility on forward flight has also been analyzed. A fluid-structure coupling algorithm has been formulated to allow for airfoil and wing deformation, and critical numerical issues relating to the coupling are dealt with in detail. It is shown that, when the deformation of an airfoil is prescribed, under certain conditions, the airfoil with the highest deformation amplitude travels the fastest. However when the deformation is passive, or is obtained from the forces, the airfoil with a moderate flexibility travels the fastest.