Compressible inviscid flow solutions for isolated leading-edge vortex cores

Abstract

To model the flow inside a leading-edge vor- tex core the steady, compressible and axisymmetric form of the Euler equations is used. Two different isen- tropic conical similarity flow solutions satisfying iden- tical boundary conditions are obtained. One solution being a jet-like swirling flow solution and the second a wake-like swirling flow solution. Analysis reveals that the azimuthal component of the vorticity has changed sign between both solutions. A switch in direction of the azimuthal vorticity is considered to be a key factor for the vortex breakdown phenomenon. These results suggest that the breakdown phenomenon might be a bifurcation event of the governing equations. To investigate the behaviour of the leading-edge vor- tex a finite-volume method has been developed. An isolated and unconfined vortex core is considered. The influence of the external flow onto the vortex core is modeled through boundary conditions. To ensure that the flow inside the leading-edge vortex core is prop- erly simulated a quasi 1-dimensional characteristic ap- proach is adopted at the boundaries of the computa- tional domain. It is demonstrated that the final flow solution strongly depends on the swirl number. Fur- thermore, results indicate that the method might be capable of simulating vortex breakdown.