Studies of non-Newtonian fluid flows with a stabilized finite element method

The departure from the Newton's postulate in viscosity have been observed in many areas, showing either viscoelastic behavior of solid-like and fluid-like characteristics or non-constant proportionality between shear stress and shear rate. Here we consider the departure occurring in the purely viscous phenomena.; To make the governing equations complete a simplified Reiner-Rivlin fluid model is referred as the constitutive relation for this generalized Newtonian fluid. The viscosity models without a yield stress (Power-law and Carreau-Yasuda) as well as with a yield stress (Bi-viscosity and Casson) have been studied in selected geometries found in polymer processing.; A stabilized finite element formulation has been used in view of the facts that the numerical studies of the generalized Newtonian fluid flow require a robust scheme, which can handle incompressibility in creeping flow as well as advection dominated scalar transport phenomena accurately. The numerical method and the new constitutive models are validated using closed-form solutions in channel flow. The shear regions and viscosities either decrease (shear-thinning) or increase (shear-thickening) depending on the power index, which changes the flow fields substantially. The behavior of the viscosity with respect to the shear rate determines either positive or negative correlation between the viscosity and the driving pressure.; The numerical scheme shows convergence problems with the newly introduced nonlinearity to the viscous flux as the nonlinear effect increases. As flow becomes more shear-thinning dominant, the viscosity varies drastically in the domain and the condition number of the Jacobian matrices increases. Linesearch and higher order polynomial approximation have been investigated and raising polynomial resolution ameliorated the convergence problems.; The study of the flow in a twin cavity mold shows that the Carreau-Yasuda viscosity model predicts the driving pressure more acceptably. The level set front tracking method has been successfully demonstrated to show efficient filling patterns and to predict entrapped air regions in a step mold.