Starting vortex, separation bubbles and stall: a numerical study of laminar unsteady flow around an airfoil

Abstract

The stalling characteristics of an airfoil in laminar viscous incompressible fluid are investigated. The governing equations in terms of the vorticity and stream function are solved using an implicit finite-difference scheme and point successive relaxation procedure. The development of the impulsively started flow, the initial generation of circulation, and the behaviour of the forces at large times are studied.Following the impulsive start, the lift is at first very large and then it rapidly drops. The subsequent growth of circulation and lift is associated with the starting vortex. After incipient separation, the lift increases owing to enlargement of the separation bubble and intensification of the flow rotation in it. The extension of this bubble beyond the trailing edge causes it to rupture and brings about the stalling characteristics of the airfoil. Subsequently, new bubbles are formed near the upper surface of the airfoil and are swept away. The behaviour of the lift acting on the airfoil is explained in terms of the strength and sense of these bubbles. The lift increases when attached clockwise bubbles grow and when counterclockwise bubbles are swept away and vice versa.