Viscous Modelling of Wing-Generated Trailing Vortices

Abstract

Summary The trailing vortex wake system generated by a lifting wing of finite span is modelled with a pair of laminar, viscous vortex models of a new type. The embryonic form of this viscous wake model is matched, at several interior collocation points, to the inviscid Betz model of the wake convolution process that transforms the wing trailing-edge vortex sheet into a pair of axisymmetric trailing vortices. In the near-wake and intermediate-wake regions downstream of the wing, the viscous wake model indicates that the trailing vortex characteristics (particularly the peak swirl velocity and the circulation profile) are strongly influenced by details of the wing span load distribution. Using simple eddy viscosity concepts, the viscous wake model achieves good qualitative agreement with test results from a limited selection of published experimental wake investigations. The present laminar theory appears to offer a useful basis for developing an engineering prediction method of aeroplane wake characteristics.