The effects of non-uniform density and stagnation pressure on the breakdown characteristics of a vortex

Abstract

This paper is concerned with the extension of the theory of vortex breakdown, that was presented in previous publications by the present author and others, to cases of non-uniform density and non-uniform stagnation pressure outside the vortex core. The effects of radial density and velocity variations play an essential role for the layout of modern low-emission burners for premixed combustion. Furthermore, these effects turn out to be important with respect to an improved understanding of the formation of zones of flow recirculation in tornado-like vortices. With the help of the extension of a variational principle for axisymmetric flow to the case of non-uniform density it is possible to discuss inviscid flows of non-uniform density and stagnation pressure in great generality. A numerical solution method is given for general axisymmetric vortex flows, including flows that undergo vortex breakdown. The influences of density and stagnation pressure variations on vortex breakdown are analyzed in detail, for the special case of a generalized Rankine vortex. It is found that a radially increasing density leads to a reduction of the swirl number at which vortex breakdown occurs, whereas a radially decreasing axial velocity component in the approach flow of a vortex breakdown bubble leads to a substantially enlarged bubble. Finally, a Richardson number criterion is proposed for the scaling of a vortex breakdown bubble in a tornado.