On the determination of propulsive characteristics of a flapping airfoil with advanced ALE method

摘要

Flapping wings for flying and oscillating fins for swimming stand out as the most complex yet efficient propulsion methods found in nature. Understanding the phenomena involved is a great challenge generating significant interests, especially in the growing field of Micro Air Vehicles. Even if an increasing body of litterature is now available, much research needs to be done to properly simulate the propulsive phenomenon of flapping airfoils. The flexibility of biological foils must be replicated and the airfoil motion induced by the generated thrust must be accounted for. This paper presents an effective computational framework for simulating the propulsive characteristics of a forward-moving flexible flapping airfoil. We use a direct monolithic ALE formulation for the unsteady interaction of a viscous incompressible 2D flow with an elastic structure undergoing large displacements (geometric non-linearities). A point mass approach allows to compute the motion of the airfoil due to the aerodynamic forces induced by airfoil oscillations. The problem is solved in an implicit manner using a Newton-Raphson pseudo-solid finite element approach. High-order implicit Runge-Kutta time integrators are implemented to improve the accuracy and reduce the computational cost. After some verifications of the computational framework with a flapping rigid NACA0015 airfoil, we study the effects of the motion parameters and the flexibility on the propulsion efficiency.