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Interaction d'une fibre et d'un écoulement en géométrie confinée

Benoît Semin 1, 2 
2 POEMS - Propagation des Ondes : Étude Mathématique et Simulation
Inria Saclay - Ile de France, UMA - Unité de Mathématiques Appliquées, CNRS - Centre National de la Recherche Scientifique : UMR7231
Abstract : The motion of elongated objects in a fluid is encountered in many scientific fields, ranging from oil recovery and paper production to microorganism swimming. In the present thesis we study the behavior of a long cylindrical fiber in a confined flow (fracture, microfluidic channel). We first determine both experimentally and numerically the drag on this object as a function of its orientation and position in the aperture. A fiber parallel to the flow only slightly perturbs the flow, and the force on it can be estimated using 2D models. On the contrary, if it is perpendicular to the flow, the latter becomes 3D if blockage is partial. In this configuration, the lift is sufficient to keep the cylinder in the middle of the flow. For Reynolds numbers higher than 20, this position becomes unstable and the cylinder oscillates between the walls. The threshold of this instability is lower than that of Bénard-Von Kármán vortex shedding. The position of the cylinder satisfies a Van der Pol equation, which allows for a quantitative prediction of the Hopf bifurcation of the system. A hydrodynamic interpretation of the coefficients of this equation is given. We also develop and validate a new image processing method, which give the shape of the fiber with a sub-pixel precision. Moreover, the tangent vector angle and the curvature, of interest because it is related to the bending moment, are accurately measured.
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Submitted on : Sunday, November 28, 2010 - 8:00:00 AM
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Benoît Semin. Interaction d'une fibre et d'un écoulement en géométrie confinée. Mécanique des fluides [physics.class-ph]. Ecole Polytechnique X, 2010. Français. ⟨pastel-00006340⟩

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