A free-wake, lifting-surface model using distributed vorticity elements

A higher-order, lifting-surface method is presented that uses elements whose streamwise vorticity is distributed on a vortex sheet that lays between vortex filaments, each having the transverse vorticity concentrated along its length, that form the leading and trailing edges of each element. The vortex filaments have a parabolic circulation distribution in spanwise direction and are of opposite signs. The vortex sheet has a linearly varying vorticity. An analytical solution is used to determine the velocity that is induced by each element at a particular location. One or several spanwise systems of such elements are used to model the lifting surface and the wake. The free wake is developed using a time-stepping method. The elements in the wake stretch and compress in spanwise direction during the roll-up process. The continuous wake and the absence of point or line singularities in the streamwise direction eliminate many of the numerical problems that are encountered with conventional vortex-lattice and panel methods. Thus, the method is a relatively fast tool for determining the location of the free wake and its interaction with complex wing geometries, especially when accurate load predictions are required.