Impact of a vortex ring on a conical wall*

In this work we present a numerical and experimental research of a vortex ring impinging a cone. Both the vortex and the conical wall have the same axis of symmetry. For this study we solve the Navier-Stokes and continuity equations in cylindrical coordinates using a finite difference scheme for r, z and time, whereas a Fourier spectral method is used for the angular variable. As initial conditions we assume that velocity is given by the Biot-Savart law for a vorticity distribution of constant magnitude inside a torus. With respect the experiments, measurements of velocity were made with a hot wire anemometer. To have a mapping in space we use a traverse system to place the hot wire probe in points of a grid. Additionally, the measurements of velocity are synchronized with the production of the vortex. Unlike the case of the impact with a flat wall, in this case the diameter of the vortex ring cannot grow. We study the shape of the vortex before the impact, the instabilities and the production of secondary vorticity during the impact. Finally, we made a comparison between experiment and the numerical simulations.