A numerical method for the solution of supersonic streamwise vortex dynamics

In this work a numerical model for the solution of supersonic streamwise vortices is presented. It is known that the canonical solution of the supersonic horseshoe line-vortex collapses to the counterpart subsonic Biot-Savart solution in a region of the domain that is both function of the radial distance from the source as well as the extension of the cone of influence at the specific downstream location. It is proposed in here to separate the flow in two regions: a near field where techniques that have been developed for the treatment of the singularity in subsonic point vortex methods can be employed, and a far field solution of the supersonic vortex source that retains the hyperbolic nature of the problem. The definition of the extent of the respective domains, as well as the conditions for a congruent transition are the subjects of this investigation. A polynomial approximation for the determination of the transition location is derived. A comparison between simulations utilizing the proposed model and measurements from a series of experiments conducted in a Mach 2.5 flow is discussed.