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Echanges de masse et de chaleur entre deux phases liquides stratifiées dans un écoulement à bulles

Abstract : During an hypothetical major accident in a pressurized water reactor, the deterioration of the core can produce a stratified pool crossed by a bubbly flow. This latter strongly impacts the heat transfers, whose intensities are crucial in the progression of the accident. In this context, this work is devoted to the diffuse interface modelling for the study of anisotherm incompressible flows, composed of three immiscible components, with no phase change. In the diffuse interface methods, the system evolution is driven by the minimisation of a free energy. The originality of our approach, derived from the Cahn-Hilliard model, is based on the particular form of the energy we proposed, which enables to have an algebraically and dynamically consistent model, in the following sense : on the one hand, the triphasic free energy is equal to the diphasic one when only two phases are present ; on the other, if a phase is not initially present then it will not appear during system evolution, this last property being stable with respect to numerical errors. The existence and the uniqueness of weak and strong solutions are proved in two and three dimensions as well as a stability result for metastable states.

The modelling of an anisotherm three phase flow is further accomplished by coupling the Cahn-Hilliard equations with the energy balance and Navier-Stokes equations where surface tensions are taken into account through volumic capillary forces. These equations are discretized in time and space in order to preserve properties of continuous model (volume conservation, energy estimate). Different numerical results are given, from the validation case of the lens spreading between two phases, to the study of the heat and mass transfers through a liquid/liquid interface crossed by a single bubble or a series of bubbles.
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https://tel.archives-ouvertes.fr/tel-00132564
Contributor : Céline Lapuerta <>
Submitted on : Monday, March 19, 2007 - 3:54:49 PM
Last modification on : Wednesday, October 10, 2018 - 1:26:46 AM
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  • HAL Id : tel-00132564, version 2

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Céline Lapuerta. Echanges de masse et de chaleur entre deux phases liquides stratifiées dans un écoulement à bulles. Mathématiques [math]. Université de Provence - Aix-Marseille I, 2006. Français. ⟨tel-00132564v2⟩

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