Since great emphasis is being placed on the material processing research in the department of defense, other government research agencies, and industries; currently, extensive research needs to be conducted in this field. Design and analysis programs for metal processing are well developed and easily available. However, the design and analysis of flows in extrusion dies for polymer processing has not been fully explored. One of the reason is lack of good three dimensional analysis programs for flows of such fluids and the die design methodology for it.
The objective of this research was to develop a finite element methodology, formulate and program the finite element equations to model three dimensional flows of non-Newtonian fluids inside an extrusion die. The weighted residual technique with Galerkin criterion was used as the means of formulating the finite element equations. The weighted residuals method is a technique for obtaining approximate solutions to linear and non-linear differential equations. The power law constitutive model was used to update the non-linear viscosity.
Extrusion is a complicated process, and polymeric fluids, because of their non-linear characteristics, compounds its effects. The extrusion die is the heart of the process. Die design is very critical for obtaining a better product. The die design package was modified to design streamlined dies for fiber spinning, co- extrusion, and thin film extrusion.
A finite element program was developed to calculate the velocities and pressure for flows in three dimensional geometries using the power law model. The power law equation for viscosity calculation is one of the most well known and widely used empiricism in the polymer processing industry. The power law model provides a good estimate of the effects of the non-Newtonian viscosity in polymeric flows. It can describe the viscosity for a wide range of shear rates but cannot predict memory effects which exist in some polymer flows. Three test cases were analyzed and the results were compared to analytical or experimental data and were found to be in good agreement. The mesh density was also varied to determine the effect of finer mesh on the accuracy of the results.