A finite element analysis of generalized Newtonian fluids through spiral mandrel dies

A method is described which calculates the fluid flow pattern for any generalized Newtonian fluid forced through the narrow annular space between two concentric cylindrical surfaces. The inner surface is engraved with a number of identical equally spaced spiral channels of small constant pitch angle but of varying cross-sectional area. For equal flow into the spiral passages, the pressure distribution along them is described by a quasi-linear ordinary difference-differential equation. A finite element approximation is employed to solve this equation for the pressure and resultant flow field. The method is illustrated by calculating and comparing flow patterns through two different spiral geometries.