Force and moment on a Joukowski profile in the presence of point vortices

OR many purposes, inviscid flow simulation by means of twodimensional potential flow theory and point vortices provides valuable information about unsteady flow over high-aspect-ratio wings.1'2 One way of calculating the flowfield and vortex convection velocities is to represent the foil shape as a conformal mapping of a circle, making use of the powerful theory of functions of a complex variable.3"5 The wake of the profile is discretized into point vortices, and the circle theorem insures that the body boundary condition is satisfied everywhere on the foil. Assuming that the Kutta condition of finite flow velocity at the trailing edge holds,6 new vortices of the appropriate strength are continually released in the wake. An algorithm for time integration is all that is needed to complete the simulation of large-amplitu de foil motion. In cases where the exact profile shape is of secondary importance, a Joukowski mapping can be used, and the resulting expressions for the complex potential become particularly simple.7"11 We show that the force and moment acting on the Joukowski profile throughout the simulation consist of added mass terms as if the flow were free of vortices plus the summed effect of all of the vortices in the flow.