Relaxed-Wake Vortex-Lattice Method Using Distributed Vorticity Elements

TLDR: In this article, a lifting surface method is presented that uses elements having distributed vorticity to model lifting surfaces and their shed wakes, allowing the representation of a force-free continuous wake-vortex sheet that is free of numerical singularities and is thus robust in its numerical rollup behavior.

Abstract: A lifting-surface method is presented that uses elements having distributed vorticity to model lifting surfaces and their shed wakes. Using such distributed vorticity elements allows the representation of a force-free continuous wake-vortex sheet that is free of numerical singularities and is thus robust in its numerical rollup behavior. Unlike other potential-flow methods that use discrete vortex filaments having solid-core models at their centers to avoid problems with the singularities, the numerical robustness of the new method is achieved without the subsequent solution being dependent on the choice of a cutoff distance or core size. The computed loads compare well with results of classical theory and other potential-flow methods. Its numerical robustness, computational speed, and ability to predict loads accurately make the new method ideal for the investigation of applications in which the loadings on a lifting surface depend strongly on the influence of the wake and its shape, as is the case for the two application examples presented: formation flight and rotating-wing systems.