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Toward the computational rheometry of filled polymeric fluids
황욱렬,Martien A. Hulsen 한국유변학회 2006 Korea-Australia rheology journal Vol.18 No.4
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.
Direct numerical simulations of hard particle suspensions in planar elongational flow
Hwang, Wook Ryol,Hulsen, Martien A. Elsevier 2006 Journal of non-Newtonian fluid mechanics Vol.136 No.2
<P><B>Abstract</B></P><P>We present a new direct simulation technique of inertialess particle suspensions in planar elongational flow of a Newtonian fluid. The extensional bi-periodic domain concept is introduced such that a single cell problem with a small number of particles may represent a large number of repeated structures of such a cell in planar elongational flow. For implicit treatment of the hydrodynamic interaction between particles and fluid, we employ a finite-element/fictitious-domain method similar to the distributed Lagrangian multipliers (DLM) method together with a rigid-ring description of the particle. The extensional bi-periodic frame is incorporated by constraint equations with Lagrangian multipliers and is implemented by the mortar element method. In our formulation, the bulk stress is evaluated by simple boundary integrals. Concentrating on 2D circular disk particles, we present numerical examples of single-particle, two-particle and 100-particle problems in the extensional bi-periodic frame. We discuss effects of solid fraction and particle configuration on the elongational viscosity of the suspension, in comparison with simple shear flow. We found that, at zero strain, the relative elongational viscosity is almost the same as the relative shear viscosity in simple shear for moderately concentrated suspensions. There is a small increase in elongational viscosity for large strains, which is related to an anisotropic distribution of the particles.</P>
Toward the computational rheometry of filled polymeric fluids
Hwang, Wook-Ryol,Hulsen Martien A. The Korean Society of Rheology 2006 Korea-Australia rheology journal Vol.18 No.4
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.
Simulation of extrudate swell using an extended finite element method
Choi, Young-Joon,Hulsen, Martien A. 한국유변학회 2011 Korea-Australia rheology journal Vol.23 No.3
An extended finite element method (XFEM) is presented for the simulation of extrudate swell. A temporary arbitrary Lagrangian-Eulerian (ALE) scheme is incorporated to cope with the movement of the free surface. The main advantage of the proposed method is that the movement of the free surface can be simulated on a fixed Eulerian mesh without any need of re-meshing. The swell ratio of an upper-convected Maxwell fluid is compared with those of the moving boundary-fitted mesh problems of the conventional ALE technique, and those of Crochet & Keunings (1980). The proposed XFEM combined with the temporary ALE scheme can provide similar accuracy to the boundary-fitted mesh problems for low Deborah numbers. For high Deborah numbers, the method seems to be more stable for the extrusion problem.
Simulation of extrudate swell using an extended finite element method
Young Joon Choi,Martien A. Hulsen 한국유변학회 2011 Korea-Australia rheology journal Vol.23 No.3
An extended finite element method (XFEM) is presented for the simulation of extrudate swell. A temporary arbitrary Lagrangian-Eulerian (ALE) scheme is incorporated to cope with the movement of the free surface. The main advantage of the proposed method is that the movement of the free surface can be simulated on a fixed Eulerian mesh without any need of re-meshing. The swell ratio of an upper-convected Maxwell fluid is compared with those of the moving boundary-fitted mesh problems of the conventional ALE technique, and those of Crochet & Keunings (1980). The proposed XFEM combined with the temporary ALE scheme can provide similar accuracy to the boundary-fitted mesh problems for low Deborah numbers. For high Deborah numbers, the method seems to be more stable for the extrusion problem.