Viscoelastic flows in complex geometries: An analysis of the filling stage of the injection molding of thermoplastics

Prediction of flow and stress patterns in viscoelastic fluids flowing through channels of complex shape is of theoretical interest in non-Newtonian fluid mechanics but also of large practical interest in the materials processing industry. The first part of this work presents a finite difference computational analysis of the flow of an Upper Convected Maxwell fluid through various geometrically complex channels. The method of Boundary Fitted Curvilinear Coordinates is used to remove the problem of boundary complexity from the finite difference solution of flow problems on arbitrary domains. Several elastic effects, such as vortex growth in contractions and vortex suppression in expanding sections are predicted. The second part of this Thesis is concerned with the modelling of the filling stage of injection molding in a cavity of complex shape with an insert. Non-isothermality, viscoelasticity and the presence of an advancing interface are dealt with in this section. Solution adaptive curvilinear meshes are used for the numerical solution of the model equations on a time-dependent domain. Stress, temperature, pressure, velocity and shear rate profiles within the cavity have been obtained by this analysis. Parametric studies have revealed the effect of key process characteristics on the pressure and thermal gradients during filling. Model predictions are compared to experimental results obtained on an injection molding machine. The model is able to predict with satisfactory accuracy the pressure evolution as well as the pressure gradients developing in the cavity during filling. Finally, a three-dimensional solution of the energy equation revealed the strong spatial and temporal variation of temperature within the mold in both the planar and the thickness directions, and allowed for an evaluation of the crystallinity development in the solidified material during filling.