An approximate method for computing inviscid vortex wake roll-up. Part I: Theory and application

Abstract

In this report an approximate method is described for computing, through the unsteady analogy, the shape of steady vortex wakes downstream of aircraft configurations in steady flight. In the analogy the steady fully three-dimensional problem is reduced to a two-dimensional timedependent problem, corresponding to the evolution of a two-dimensional vortex sheet system in successive cross-flow planes. The geometry of the vortex wake in any cross-flow plane consists of independent segments. Each segment is built up out of a continuous vortex sheet and up to two concentrated vortices which model tightly rolled-up vortex cores. Each of the vortices is connected to one of the edges of the continuous vortex sheet. Both single- and double-branched vortices can be accommodated. The method optionally accounts for symmetry and tunnel-wall influence, as well as for cross-flow plane components of the free stream. A second-order panel method is employed to compute the velocity induced by the vortex sheet and a modified Euler scheme is employed for the integration in time. By employing a curvature dependent panel scheme the accuracy is enhanced and the formation of new rolling-up regions can be predicted quite realistically. In this part. Part I, of the report the theory underlying the computational method is decribed and some examples of application are presented. Part II of the present report provides a detailed description of the computer program V0R2DT developed.