Modeling particulate complex flows using XFEM

Abstract

Particulate flows arise in a wide class of research areas and industrial processes, for example, fluidized suspensions, materials separation, rate of mixing enhancement, filled polymers, etc. In many of the applications, the fluid phase displays complex non-Newtonian flow behavior. Adding particles in a complex fluid further complicates the flow behavior. In order to study the particle motion in complex fluids such as viscoelastic fluids, a numerical analysis is an essential requirement due to inherent nonlinear behavior of the fluids. An extended finite element method (XFEM) has been developed for the direct numerical simulation of particulate complex flows. The main advantage of the method is that the movement of particles can be simulated on a fixed Eulerian mesh without any need of remeshing. The proposed method has been applied to various particulate flow problems: • Flow of a viscoelastic fluid around a stationary cylinder The method is verified by comparing the solutions with those of simulations using a boundary-fitted mesh and a fictitious domain method. Our method shows a significant improvement of local accuracy around the rigid body compared to the fictitious domain method, obtaining solutions similar to those of boundary-fitted mesh solutions. • Particle migration in circular Couette flow of a viscoelastic fluid The particle migrates to a stabilized radial position near the outer cylinder regardless of its initial position. As the fluid elasticity increases, the particle migrates more rapidly toward the outer cylinder, and the stabilized radial position of the particle shifts toward the outer cylinder. With increasing the particle size, the particle migrates more rapidly toward the outer cylinder. • Dynamics of particles suspended in two-phase flows A model for the dynamics of particles suspended in two-phase flows is presented by coupling the Cahn-Hilliard theory with the extended finite element method. To demonstrate and validate the technique, the dynamics of a single particle at a fluid-fluid interface is studied. In particular, the effects of interfacial thickness, surface tension, particle size and viscosity ratio of two fluids are investigated. As interfacial thickness increases; surface tension increases; particle size decreases; or viscosity ratio decreases, the particle moves rapidly towards its equilibrium position. The movement of a particle passing through multiple layers of fluids is also presented to demonstrate the wide applicability of the method to problems associated with complex morphology of the fluids.