The velocity field within a vortex ring with a large elliptical cross-section

Abstract

The velocity field within a steady toroidal vortex is found for arbitrary mean core radius and section ellipticity. The problem is solved by transforming to coordinates that define invariant sets. The method allows the properties of the coordinate system metric tensor to be exploited in the continuity equation in order to obtain the solution. The vorticity is found to decrease monotonically with distance from the symmetry axis. For a given outer radius and outer perimeter velocity, the circulation of the vortex ring can be either smaller or larger than that of Hill's spherical vortex.

Reynolds-number effect on vortex ring evolution in a viscous fluid

“…To the best of the author's knowledge, there have been very few attempts to investigate elliptical cored vortex ring analytically. 20,21 However, many of these studies were limited to the ideal fluid. Fukumoto and Moffatt 22, 23 derived the high-Reynolds-number asymptotics for a viscous vortex ring with elliptical deformation of the core taken into account.…”

Estimating the mean flow field in combustion chambers

“…While not all of the above complexities neglected by the usual solid-body treatment will be addressed herein, the purpose of the present work is to provide a means of estimating, with a minimal set of velocity measurements through the vortex, complete steady-flow fields in gas turbine combustors, as well as instantaneous flow fields in port-injected piston engines during intake. The work extends a method given previously for finding the velocity field in a torus with an elliptical cross section 22,23 to one for which an irrotational toroidal velocity (irrotational swirl) component is present. Depending upon how the swirl is generated, this irrotationality assumption may not be out of place in studies of engine swirl.…”

“…Rather, an experimental velocity profile along some path to the vortex center is incorporated, and the continuity equation and an irrotationality condition are used to determine the instantaneous flow throughout the remainder of the domain. The steady continuity equation for general coordinate systems 22,23…”

Problems related to the beam propagation in the tubulent atmosphere

“…The proposed method can be applied for further investigation of the effect of heat flux on vortical structures. We considered the evolution of a vortex ring with a large elliptical cross-section [4]. The initial value problem is as follows.…”