Mass and heat exchange between two stratified liquid phases in a bubble flow
Céline LAPUERTA, doctorate of University Aix-Marseille I, 216 p, defended on the 5th october 2006
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 anisothenn 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 weIl as a stability result for metastable states.
The modelling of an anisothenn three phase fiow 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 arder 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.