Modelling of single component and bicomponent extrusion flows

The present work is concerned with the mathematical modelling and numerical simulation of three dimensional (3-D) single component and bicomponent extrusion flows.; A 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 3-D finite element/Galerkin formulation. Special free surface update schemes (pathline, spine and hybrid spine/pathline methods) are employed. 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 asymmetry. A temperature difference across the die can be imposed by heating or cooling the die walls, but can also occur because of asymmetric viscous heat generation due to the die geometry. Temperature differences affect velocity profiles and lead to extrudate bending and distortion. It is also shown numerically and confirmed experimentally that the die geometry induces extrudate bending even in the case of isothermal Newtonian flows.; A finite element algorithm for the 3-D numerical simulation of bicomponent stratified free surface flows is described.; The interface shape development and extrudate swelling behavior of stratified flows in sheath-core configuration is examined. It is found that the viscosity mismatch has an effect on both the interface and the external free surface shapes.; The experimentally observed tendency of the less viscous layer to encapsulate the more viscous layer in stratified bicomponent flows of 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, it is demonstrated that 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. Extrudate bending and distortion of the bicomponent system because of the viscosity mismatch is also displayed.