Three-dimensional streamlined finite elements: design of extrusion dies

A method to determine three-dimensional die shapes from extrudate swell and vice versa is presented using a three-dimensional Galerkin finite element method based on a streamlined formulation with the fluid velocities and pressures represented by triquadratic and trilinear basis functions respectively. The three-dimensional streamlined method, an extension of the two-dimensional formulation, uses successive stream-surfaces to form a boundary-conforming co-ordinate system. This produces a fixed computational domain leaving the spatial location of the elements as unknowns to be determined with the standard primary variables (u, u, w, p). The extrudate produced by a die of a given shape is considered for moderate Reynolds numbers. Finally, the method is extended to address the problem of die design, where a die profile is sought to produce a target extrudate shape. KEY WORDS Streamlined finite elements Extrusion Free surface flows Die design Three-dimensional flows Three-dimensional finite element