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An ALE Finite Element method for the simulation of 3D multiphase flows


Multiphase bubbly flows are important in many industrial applications. One important application is the simulation of hydrate formation in oil and gas industry. In fact, hydrate formation is considered one of the most important problems in the oil industry. As off-shore production migrates to deeper zones, hydrate formation in lines and production equipment becomes a more severe restriction. The study of the first stages of hydrate formation requires the knowledge of lift and drag forces over bubbles and drops. Hence, detailed modeling of bubble flows and interface phenomena is required for the understanding of hydrate formation dynamics.
This work presents a novel method to solve 3D bubble flows. The method is based on a ALE approach on an unstructured Finite Element discretization using the Taylor-Hood Mini element. The surface tension effects are included in a consistent way, avoiding spurious oscillations and parasitic currents.
The convective terms are discretized using a semi-Lagrangian technique, which is unconditionally stable for arbitrary integration time steps and Reynolds numbers. The pressure and velocity computations are decoupled employing a projection method based on an approximate block LU factorization, producing a very efficient methodology.
Interface is represented by faces, edges and vertices of the tetrahedralization. The interfacial vertices are moved in a Lagrangian fashion, while the other vertices are moved in order to keep the good quality of the mesh, thus avoiding remeshing procedures.
The method is an extension of the method described in [Sousa et al.] for the simulation of 3d flows.
The method was validated against analytical solutions in simple cases, as well as experimental results with bubbles,
showing excellent mass conservation properties, stability, and computational performance.

Gustavo Rabello
Luis M. Portela
Fabricio Simeoni Souza
Norberto Mangiavacchi
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