Date of Award
Doctor of Philosophy (PhD)
Dr. A.N. Hrymak
Dr. J. Vlachopoulos
Flow phenomena associated with die extrusion and coextrusion have a significant impact on the final product shape and layer uniformity. The present work is concerned with the mathematical modelling and numerical simulation of three dimensional single-component and stratified multi-component extrusion. The objective is to provide an understanding of the flow phenomena involved and investigate their impact on the shape and interface configuration of the extruded article.
A three dimensional non-isothermal study of viscous free-surface flows with exponential dependence of viscosity on temperature is presented. The effects of non-isothermal conditions and/or geometry on the extrudate shape are investigated with a fully three dimensional finite element/Galerkin formulation. Special free surface update schemes (pathline, spine and hybrid spine/pathline methods) are presented and enable the study of the extrudate swelling out of very complicated 3-D geometric shapes. Apart from the well known thermally induced extrudate swelling phenomenon, bending and distortion of the extrudate may occur because of temperature differences and/or geometric asymmetries. A temperature difference across the die can be imposed by heating or cooling the die walls, but can also arise because of asymmetric viscous heat generation due to the die geometry. Temperature differences affect velocity profiles because of the temperature dependence of viscosity and lead to extrudate bending and distortion. It is also shown numerically and confirmed experimentally that the die geometry can induce extrudate bending even in the case of isothermal Newtonian flows.
A powerful finite element algorithm for the 3-D numerical simulation of bicomponent stratified free surface flows is described. The presence of multiple free surfaces (interface, external free surfaces) is tackled with advanced free surface update schemes. The pressure and viscous stress discontinuity at the interface occurring because of the viscosity mismatch is handled with both a double node (u-v-w-P₁-P₂-h₁-h₂) formulation and a penalty function (u-v-w-P-h₁-h₂) formulation.
The interface shape development and extrudate swelling behaviour of stratified flows in a sheath- core configuration is examined. The viscosity mismatch has an effect on both the interface and the external free surface shapes. The flowrate ratio, die geometry and layer configuration are also shown to affect the areas of flow of the individual layers and the extrudate swelling behaviour of the bicomponent system.
The experimentally observed tendency of the less viscous layer to encapsulate the more viscous layer in stratified bicomponent flows of a side-by-side configuration is established with the aid of both a fully 3-D analysis and a 1-D optimization analysis, in agreement with experimental evidence. It is shown that the direction and degree of encapsulation depend directly on the viscosity ratio. For shear thinning fluids exhibiting a viscosity crossover point, interface curvature reversal may occur if the shearing level is such that the crossover point is exceeded. The effects of the length of flow and slip at the wall on the degree of encapsulation are investigated. The effect of initial conditions and design of the layer merging part on the interface shape development downstream is also examined and potential sources of instabilities are identified. The extrudate bending and distortion of the bicomponent system because of the viscosity mismatch is also shown.
Karagiannis, Aristotelis, "Modelling of Single Component and Bicomponent Extrusion Flows" (1989). Open Access Dissertations and Theses. Paper 1942.