Streamline and Vortex Line Analysis of the Vortex Breakdown in a Confined Cylinder Flow

Abstract

The vortex breakdown phenomenon occurring in a rotating flow within a closed cylinder is still a challenging research field. In particular the goal to describe all significant order parameters of vortex breakdown is not reached. For further insight the viscous and laminar Newtonian flow inside a cylinder with a rotating lid has been calculated by solving the full Navier Stokes equations. During the sim ulation the rotational speed of the lid has been increased, which causes a gradual transition of the internal flow field topology. Starting from a flow field without any reversed flow at the vortex axis the vortex breakdown phenomenon develops indi cated by one or more vortex breakdown bubbles. A phenomenological description of the vortex breakdown process is given by applying a topological analysis to the flow field, which illustrates the main flow structures, their behaviour and changes. By visualization of critical points, at which the velocity magnitude vanishes, the topological flow structure change of the velocity field becomes obvious. Additionally their associated separatrices are integrated into the field, which allows to illustrate the shape of the vortex breakdown bubbles. In particular the spherical shape of the first appearing breakdown bubble leads to the idea to introduce a streamfunction, which describes the spherical breakdown bubble approximately. Applying a Taylor expansion of the velocity field leads to an analytical description of the local stream line topology nearby one critical point of a breakdown bubble. The interpretation of the appendant differential equations allows a deeper insight into the dynamical behaviour of the breakdown phenomenon and its main enforcing parameters. The paper presents the results of a local streamline and vortex line topology analysis, especially the dynamical relation between the velocity and vorticity field in regard to the topological structure of the vortex breakdown phenomenon in the lid driven cylinder.