A finite element method for the solution of potencial flow in two dimensions

Abstract

This report presents a method for the solution of two dimensional, potential flow around an aerofoil base on a Finite Element Method for the solution of Laplace’s equation. Solutions to approximate the “real” flow are constructed from the observation that potential flow solutions are linear and thus, many potential flows may be superimposed to yield the desired flow. Indeed, in this way, one of the effects of viscosity, that of fixing the rear stagnation point to the trailing edge for up to moderate angle of attack cases, is modelled by the imposition of a potential flow due to a point vortex (located at the ¼ chord point) sufficient to fix the rear stagnation point at the trailing edge (Kutta condition).

It must be remembered however, that potential flow solutions are inviscid and as such do not model correctly the flow separation point and further, the absence of viscosity falsely causes the model to predict zero drag caused by the aerofoil. However, the predictions made for the lift (derived from the calculated circulation to fix the Kutta condition via the Kutta-Joukowski theorem) are shown to be good for low Mach number cases at moderate angles of attack.