Three‐dimensional streamlined finite elements: Design of extrusion dies

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Abstract
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 streamsurfaces to form a boundary‐conforming co‐ordinate system. This produces a fixd, computational domain leaving the spatial location of the elements as unknowns to be determined with the standard primary variables (u, v, 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.