Numerical solutions for a two-dimensional airfoil undergoing unsteady motion

Abstract

Continuous vorticity panels are used to model general unsteady inviscid, incompressible, and two-dimensional flows. The geometry of the airfoil is approximated by series of short straight segments having endpoints that lie on the actual surface. A piecewise linear, continuous distribution of vorticity over the airfoil surface is used to generate disturbance flow. The no-penetration condition is imposed at the midpoint of each segment and at discrete times. The wake is simulated by a system of point vortices, which move at local fluid velocity. At each time step, a new wake panel with uniform vorticity distribution is attached to the trailing edge, and the condition of constant circulation around the airfoil and wake is imposed. A new expression for Kutta condition is developed to study (i) the effect of thickness on the lift buildup of an impulsively started airfoil, (ii) the effects of reduced frequency and heave amplitude on the thrust production of flapping airfoils, and (iii) the vortex-airfoil interaction. This work presents some hydrodynamic results for tidalstream turbine.

Keywords

unsteady flows / vorticity panels / kutta condition / flapping airfoil / vortex-airfoil interaction