(173d) Dimensionalization of Two-Phase Newtonian/Non-Newtonian Flow Problems.

Non-Newtonian fluids are present in a large variety of everyday life applications including paints, foods, adhesives, inks, cements, slurries, polymers and gels. Computational fluid dynamics (CFD) simulations have been widely used to understand, optimize and design products and processes that involve such non-Newtonian fluid flows. Further complicating such challenges are cases wherein flows involve the interactions of multiple phases. Systematically, understanding complex flows is difficult since they generally involve multiple forces including inertial, viscous, gravitational, capillary forces. The present study suggests dimensionless forms for the momentum and continuity equations along with two-phase level-set and phase field equations for non-dimensionalizing two-phase, non-Newtonian fluid flow problems. The Reynolds number, Galilei’s number and Capillary number arise naturally as scaling factors. Fluid dynamic (CFD) simulations using COMSOL Multiphysics^® were used to illustrate comparative numerical analysis between dimensional and dimensionless equation forms for two-phase, non-Newtonian pipe flow and free-surface flow (slump-flow) examples. The effect of non-dimensionlization on computational time was demonstrated for different scale of free-surface flow problem. The importance of not satisfying simultaneously the Reynolds and Galilei’s number similarity for scaling free surface-flow problems is also discussed. Finally, a scaling parameter was quantified and illustrated for both dimensionless and dimensional form of the free-surface flow (slump-flow) problem.