Roll-up of a vortex sheet trailing from a vortex generator

The roll-up of a vortex sheet trailing from an airfoil type vortex generator has been investigated through various analytical models. The generator represents one element in an infinite row of counter-rotating vortex generators mounted on a flat plate. The effects of a finite size vortex sheet and the effects of viscosity on the vortex trajectory are included as important factors. The problem is treated as two-dimensional with the streamwise direction being replaced by the time coordinate assuming that streamwise gradients are small compared to the development in the crossflow plane.;The strength and the distribution of vorticity in the wake sheet trailing from the vortex generator are determined using a modified vortex lattice approach. The influence of the airfoil represented by its camber distribution and the effects of the velocity profile of the oncoming boundary layer are investigated.;The effects of finite size of the initial vortex sheet and the associated finite formation rate of the trailing vortex are isolated by employing an inviscid vortex sheet roll-up calculation. A discrete vortex representation with an amalgamation of vorticity in the spiral core is used for this task.;Viscous effects on the vortex strength and on the trajectory are included by the application of the vorticity-streamfunction form of the Navier-Stokes equations. A small time asymptotic expansion provides initial conditions for the sheet originating as a singular line from the trailing edge. The influence of the wall is investigated by comparing calculations with a slip wall and a no-slip wall boundary condition. The results are compared with simple line vortex calculations.