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Modélisation et simulation numérique de l'écoulement d'un fluide complexe

Abstract : This work is dedicated to numerical simulation of flow of solid-liquid mixtures. The fluid flow obeys a Newtonian behavior and suspended particles are modeled by rigid spheres or sticks. This suspension is appropriate for composites injection molding. Our goal is to better understand the rheological behavior of such a mixture under a shear flow. So we consider the evolution of this mixture in a cubic cell, under a shear flow, with pseudo-periodic boundary conditions. We extend the velocity-pressure equations to solid domain by adding a rigid constraint. Thus we obtain a system of velocity-pressure equations defined on the whole fictitious domain that we solve by a Finite Element method. In this multidomain approach, we have to follow the evolution of the positions of solid particles. The solid domain is represented by a characteristic function. A lagrangian transport is used to update the positions of particles, and the corresponding characteristic function is deduced at any time thanks to a Level-Set method. A collision algorithm is used after this transport to correct positions and prevent particles from interpenetrating. Homogenization calculus have been done in order to estimate equivalent viscosity for suspensions of spheres, and behavior laws and models for evolution of orientation tensors in suspensions of fibers. Boundary effects are reduced thanks to pseudo-periodic boundary conditions. Moreover the interface description is improved by a h-adaptation technique. Our results are in rather good agreement with theoretical models, and a first simulation of a 3D mixture flow is presented.
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Submitted on : Monday, September 14, 2009 - 11:10:37 AM
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  • HAL Id : tel-00416435, version 1

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Grégory Beaume. Modélisation et simulation numérique de l'écoulement d'un fluide complexe. Mécanique [physics.med-ph]. École Nationale Supérieure des Mines de Paris, 2008. Français. ⟨NNT : 2008ENMP1642⟩. ⟨tel-00416435⟩

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