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The paper describes a computational method for two-dimensional vortex sheet motion in incompressible flow. The procedure utilizes a second-order panel method, an adaptive panel scheme and a concept for treating highly rolled-up portions of the vortex sheet. Results are presented for the roll-up of the wake behind an elliptically loaded wing, a ring wing (nacelle), a fuselage/Part-span-flap/wing combination and a delta wing with leading-edge vortex sheets. The examples demonstrate that the method is capable to describe complicated vortex sheet motion in a reliable and stable manner.