Low-Order Modeling of Wingtip Vortices in a Vortex Lattice Method

Abstract

Wingtip-flow effects on the aerodynamic forces and moments of a wing become increasingly significant as the aspect ratio decreases. These effects are dominated by the tip vortex and an associated suction zone, which results in a supplementary “vortex lift” that is not captured by conventional vortex lattice methods (VLMs). Although many augmented VLMs have addressed such free-vortical flows on the leading edges of delta wings and even wingtips, they do not account for the portion of the vorticity that may be supported by the attached flow at the tip. The current work consists of an augmented VLM designed to capture the geometry and strength of the free tip vortex along the wingtip, and it is distinguished from prior models by the capability to allocate vorticity between the bound wingtip flow and the free tip-vortex flow at each chordwise position. This paper presents the model and its predictions of tip-vortex positions, as well as forces and moments on low-aspect-ratio wings. The model demonstrates lift distributions typical of vortex lift, promising agreement with forces and moments from experimental work as well as modulation of the forces and moments by selection of the maximum allowable bound vorticity along the tips.