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Modélisation de l’entraînement d’air dans l'eau avec la méthode SPH

Abstract : Flows over hydraulic works – a nappe falling over a spillway, a wave breaking on a dike, etc. – undergo strong mixtures of air and water that lead to the appearance of white waters with complex dynamics. Faithfully capture the phenomenon of air bubbles entrainment/entrapment in the flowing water is therefore pivotal for the design of those works. Both experimental and numerical modeling prove to be complex due to high density ratio between phases and the multiscale nature of those flows involving turbulence and surface tension effects. The SPH (Smoothed Particle Hydrodynamics) method, a fully Lagrangian approach that models the flow as a set of moving particles without any mesh, is particularly well-suited to simulate such highly-distorted flows. Nevertheless, the current computational limits still prevent one from finely simulating industrial application cases with large domains in hydraulics. In this work, we aim at simulating macroscopically those flows with a mixture model in which each SPH particle stands for a moving volume of air and water. The derivation of the continuous equations of this mixture model is first detailed, then a state of the art of multiphase simulations in SPH is presented. Equipped with this continuous model and the existing discretization tools, a two-phase SPH mixture model is then derived and implemented on GPU (Graphics Processing Unit). A focus is made on original elements developed in the discretization, especially the derivation of a scheme with good numerical properties to follow the phase volume variations and the writing of an open boundary framework for mixtures. Turbulence, prominent for the air entrainment phenomenon, is modeled with a k-ϵ model including a buoyancy term. This model is validated against bidimensional academic test cases of increasing complexity, namely an oil-water separation, a two-phase Poiseuille flow, the Rayleigh-Taylor instability and a sand dumping case, proving its versatility. The air entrainment phenomenology is then described and the model is applied to common structures in hydraulics such as plunging jets and stepped spillways by introducing a specific closure for the relative velocity between phases. Finally, first industrial application cases with complex geometries and dynamics are presented
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Thomas Fonty. Modélisation de l’entraînement d’air dans l'eau avec la méthode SPH. Hydrologie. Université Paris-Est, 2019. Français. ⟨NNT : 2019PESC1013⟩. ⟨tel-02869795⟩

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