Plunging and heaving airfoils: imposed forward motion or self-propulsion ?

Abstract

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. Even if an increasing body of literature is now available, much research needs to be done to properly simulate the propulsive phenomenon of flapping airfoils. 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, we study a flapping rigid NACA0015 airfoil. In particular, we study the effect of mass ratio and torsion stiffness on the free forward motion of the foil.