Aerodynamic forces on an oscillating aerofoil fitted with a spoiler

Abstract

A thin aerofoil performing small harmonic oscillations in an incompressible fluid with flow separation from a prescribed point on the upper surface is the object of a theoretical investigation made in the paper. Two vortex sheets trail downstream, one from the trailing edge and the other from the point of flow separation on the upper surface. The flow separation may be caused by a spoiler or a flap hinge, or by having the aerofoil at incidence. If the incidence is high enough the flow will separate from the leading edge on the upper surface, and the theory includes this limiting case. The separation point is assumed to be fixed during the oscillation, and the pressure on the free streamlines is taken to be constant. Thus the free streamlines enclose a ‘dead-air’ region, which extends downstream as an infinite wake, just as in the Helmholtz model for steady flow. Formulae for the pressure distribution, lift and moment are obtained, and the effect of flow separation on the 'damping’ derivatives is illustrated in a number of graphs. On the whole it is found that a stalled or partially stalled aerofoil has less aerodynamic damping than an unstalled aerofoil.