On the roll-up of a trailing vortex sheet in the very near field

Abstract

This paper addresses a discrepancy found between the rate of roll-up of a trailing vortex sheet calculated from point vortex simulations and that from measured data. Measurements of the wake behind a rectangular planform NACA 0012 section wing at 7.5° angle of attack show that some 50 per cent of the circulation in the wake is already present in the vortex core or “rolled-up region” at the trailing edge of the wing, and that there is no increase in the circulation contained within this region within one chord length downstream of the trailing edge. This conflicts with two-dimensional point vortex simulations of sheet roll-up which predict no initial core at the trailing edge and a constantly increasing value of circulation in the vortex in the downstream direction. A modification to include the effect of the tip vortex in the simulation is proposed and is shown to represent the behaviour of the vortex sheet in the very near field accurately.