• Korea-Australia Rheology Journal
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• v.13 no.3
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• pp.131-139
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• 2001

A coupled approach is proposed for the prediction of sheet profile in sheet casting process, which combines one-dimensional analytical method on planar elongational flow region and three-dimensional numerical method on the other region. The strategy is constructed from the observations that the flow domain of sheet casting process can be separated into two parts based old the flow kinematics. The flow field in the central region of sheet, over which the planar elongational flow dominates, is possibly replaced by one-dimensional analytical solution. Then only a partial flow domain near the edge region of sheet, where the flow kinematics cannot be described by the planar elongational flow itself, requires three-dimensional numerical simulation. Good agreement is observed between the coupled approach developed in this study and the full three-dimensional numerical simulation previously developed and reported by the authors. This coupled approach may have provided flexibility with low costs to accommodate a wide range of die sizes in sheet casting process.

• Korea-Australia Rheology Journal
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• v.18 no.4
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• pp.171-181
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• 2006

We present a short review for authors' previous work on direct numerical simulations for inertialess hard particle suspensions formulated either with a Newtonian fluid or with viscoelastic polymeric fluids to understand the microstructural evolution and the bulk material behavior. We employ two well-defined bi-periodic domain concepts such that a single cell problem with a small number of particles may represent a large number of repeated structures: one is the sliding bi-periodic frame for simple shear flow and the other is the extensional bi-periodic frame for planar elongational flow. For implicit treatment of hydrodynamic interaction between particle and fluid, we use the finite-element/fictitious-domain method similar to the distributed Lagrangian multiplier (DLM) method together with the rigid ring description. The bi-periodic boundary conditions can be effectively incorportated as constraint equations and implemented by Lagrangian multipliers. The bulk stress can be evaluated by simple boundary integrals of stresslets on the particle boundary in such formulations. Some 2-D example results are presented to show effects of the solid fraction and the particle configuration on the shear and elongational viscosity along with the micro-structural evolution for both particles and fluid. Effects of the fluid elasticity has been also presented.