Modeling air entrainment in water with the SPH method
Description
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 capturing 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 the 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, a first industrial application case with complex geometry and dynamics is presented. (author)
Abstract (French)
Les ecoulements au sein d'ouvrages hydrauliques - deversement au-dessus d'un barrage, deferlement d'une vague sur une digue, etc. - sont le siege de forts melanges d'eau et d'air qui se traduisent visuellement par la formation d'eaux blanches a la dynamique complexe. Representer fidelement le phenomene d'entrainement/capture des bulles d'air dans l'eau revet donc un aspect strategique important pour le dimensionnement de ces ouvrages. La modelisation tant physique que numerique de tels cas s'avere delicate a cause du fort rapport de densite entre les phases et de la nature multi-echelle de ces ecoulements impliquant des effets de turbulence et de tension de surface. La methode numerique SPH (Smoothed Particle Hydrodynamics), approche totalement lagrangienne qui represente l'ecoulement comme un ensemble de particules en mouvement sans recours a un maillage, est particulierement adaptee a la simulation de tels ecoulements fortement deformes. Neanmoins, les limites actuelles de puissance de calcul empechent encore de simuler finement des cas d'application industriels a large emprise en hydraulique. On se propose donc dans cette these de modeliser ces ecoulements de maniere macroscopique via un modele de melange qui consiste a voir chaque particule SPH comme un volume de melange d'eau et d'air en mouvement. On detaille d'abord la derivation des equations continues de ce modele de melange, puis on presente un etat de l'art des simulations multiphasiques SPH. A partir du modele continu et des outils actuels de discretisation, un modele de melange diphasique SPH est ensuite mis en place en vue de son implementation sur GPU (Graphics Processing Unit). Un accent tout particulier est mis sur les elements originaux de discretisation developpes, notamment la derivation d'un schema aux bonnes proprietes numeriques pour le suivi de l'evolution des volumes par phase et l'ecriture d'un formalisme de frontieres ouvertes pour un melange. La turbulence, centrale dans le phenomene d'entrainement d'air, est modelisee via un modele k-ε incluant un terme de flottabilite. Ce modele de melange est valide sur des cas academiques bidimensionnels de complexite croissante tels que la separation d'un melange eau-huile, un ecoulement de Poiseuille diphasique, l'instabilite de Rayleigh-Taylor et un lache de sediments, illustrant sa polyvalence. La phenomenologie de l'entrainement d'air est ensuite decrite, et le modele applique a des structures communement rencontrees en hydraulique, comme des jets plongeants et des coursiers en marches d'escalier, en introduisant une fermeture specifique de la vitesse relative entre les phases. Enfin, on presente un premier cas d'application industriel a la geometrie et dynamique complexes. (auteur)
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Additional details
Additional titles
- Original title (English)
- Modelisation de l'entrainement d'air dans l'eau avec la methode SPH
Publishing Information
- Imprint Pagination
- 369 p.
- Report number
- FRNC-TH--14161
INIS
- Country of Publication
- France
- Country of Input or Organization
- France
- INIS RN
- 54044079
- Subject category
- S42: ENGINEERING;
- Resource subtype / Literary indicator
- Thesis
- Descriptors DEI
- BINARY MIXTURES; BUBBLES; COMPUTERIZED SIMULATION; ENTRAINMENT; FLOW MODELS; LAGRANGIAN FUNCTION; LAMINAR FLOW; PRESSURE GRADIENTS; RAYLEIGH-TAYLOR INSTABILITY; RIEMANN FUNCTION; SPILLWAYS; SURFACE TENSION; TURBULENCE; TWO-PHASE FLOW; VELOCITY; VISCOSITY
- Descriptors DEC
- DISPERSIONS; FLUID FLOW; FUNCTIONS; INSTABILITY; MATHEMATICAL MODELS; MIXTURES; SIMULATION; SURFACE PROPERTIES
Optional Information
- Notes
- 404 refs.; Available from the INIS Liaison Officer for France, see the INIS website for current contact and E-mail addresses