Modeling of polymer processing using the radial function method (RFM)

Meshfree numerical formulations are implemented to model and simulate the flow pattern and the temperature development in two-dimensional and three-dimensional polymer processing flows. The use of meshless techniques avoids the problems associated with the requirements of meshes and uniform grids found in traditional numerical techniques. The solutions are highly nonlinear due to the non-Newtonian behavior of polymers. The energy and the momentum solutions of the systems considered are strongly coupled due to the convective term in the energy equation, the viscous heating during processing and the consideration of temperature dependent viscosities.;The meshfree technique that is used, the radial function method (RFM), is based on the collocation with radial basis functions developed by Kansa; implementing some improvements reported in the literature such as the use of overlapped and non-overlapped subdomains and the use of ghost points in Neumann boundary conditions. Improvements in the numerical technique that have been developed in the present work are used, including the upwind approach of the convective term in the energy equation using finite differences and the introduction of scale factors in the radial definition for geometries with high aspect ratios.;The results delivered by RFM are compared with analytical solutions for a pressure driven slit flow and the isothermal flow during the calender process. The non-Newtonian tube flow is used to validate the method for three-dimensional geometries. FEM results are compared with RFM solutions, to validate the implementation of non-isothermal flows.;Some applications are presented, including the fully developed flow in an unwrapped screw extruder channel, the determination of the viscous heating influence in a pressure slit rheometer, the determination of the impact of viscous heating in a hot runner during the filling of a disk-shaped cavity, the prediction of thermal imbalances in hot runner systems, the description of the thermal interaction between the metal and the polymer in hot runner systems and the prediction of secondary flows in noncircular ducts caused by viscoelastic effects.