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

Author

Peter August Liver

Date of Award

12-1987

Degree Type

Dissertation

Degree Name

Doctor of Philosophy

Major

Aerospace Engineering

Major Professor

J. M. Wu

Committee Members

F. G Collins, K. C. Reddy, T. H. Moulden, R. L. Young

Abstract

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 trebling 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.

Recommended Citation

Liver, Peter August, "Roll-up of a vortex sheet trailing from a vortex generator. " PhD diss., University of Tennessee, 1987.
https://trace.tennessee.edu/utk_graddiss/12104