LOCAL ANALYSIS OF THE SINGULARITY AT A CORNER FOR A FREE-SURFACE FLOW

The swelling of polymer jets at the exit of a cylindrical tube or an orifice corresponds, from a kinematical point of view, to the separation of a fluid from a wall. The junction point P//s between the free surface (of nonzero velocity) and the wall (where the fluid adheres) appears to be a singular point. Numerical simulations which are performed in order to compute the swelling ratio of the maximal jet radius to the interior tube radius are not concerned by a specific treatment of the neighborhood of the singular point P//s. In the present paper, the authors use a theoretical framework based on the stream function concept in relation to the incompressibility of the fluid and the geometry of the duct. This enables them to describe the singularity zone close to P//s and propose analytical expressions for the velocity in this zone. These equations can be involved in a numerical simulation technique related to the swelling of a Newtonian jet (12%) at the exit of the cylindrical tube.