Computation of vortex formation over ELAC-1 configuration using vorticity confinement

Abstract

A new “Vorticity Confinement” method is described which involves adding a term to the discretized momentum conservation equations of fluid dynamics. This term depends only on local variables and is zero outside vortical regions and viscous boundary regions. The partial differential equations with this extra term admit solutions which consist of Lagragian-like confined vortical regions in the shape of vortex filaments in 3-D, which convcct with a fixed internal structure, without spreading, cven if the equations contain diffusive terms. Solutions of the discretized equations on a fixed Eulerim grid show the same behavior, in spite of numerical diffusion. This modification appears to be useful in the numerical solution of flow problems involving thin vortical regions. The discretized Navier--Stokes equations with the extra term can be solved on fairly coarse, Eulerian coniputational grids with simple low-order (first or second) accurate numerical methods, but will still yield concentrated vortices which convect without spreading due to numerical diffusion. Since only a fixed grid is used with local variables, the Vorticity Confinement method is quite general and can automatically accommodate general vortical configurations and changes in vortex topology, such as merging. The “Vorticity Confinement” method was used to calculate the vortex formation over the flight configuration ELAC-1. The fore-body of this configuration is essentially a delta wing with rounded leading edges. The leading edge vortices caused by the delta wing and a set of tip vortices generated by two vertical fins in the rear part of the confignration combine to form a complex vortical system. Copyright @ 1994 by John S. Steinhoff, Published by the American Institute of Aeronautics and Astronautics, Inc. with permission. In this paper the results of the 3-D incompressible Navier-Stokes calculation over ELAC-1 are presented and compared to experimental data.