Banca de QUALIFICAÇÃO: LEONARDO ASFORA DE OLIVEIRA

Uma banca de QUALIFICAÇÃO de DOUTORADO foi cadastrada pelo programa.
STUDENT : LEONARDO ASFORA DE OLIVEIRA
DATE: 22/07/2022
TIME: 15:00
LOCAL: Remota (Google Meet)
TITLE:

Application of the SUPG method in the numerical solution of the two-fluid model

KEY WORDS:

Multiphase flow, two-fluid model, finite element, SUPG

PAGES: 100
BIG AREA: Engenharias
AREA: Engenharia Civil
SUMMARY:

In the oil industry there are several situations that involve multiphase flow, such as gas-liquid flow in pipelines and in differential pressure flow meters. Of the different mathematical approaches commonly used to model this phenomenon, the two-fluid model is one of the most used. This is because in its most general form, it does not assume any simplifying assumptions about flow, having greater scope than other types of mathematical formulations (such as the drift-flux model). Among its main characteristics, the fact that it considers different conservation equations for each phase stands out, allowing the analysis of situations in which the phases are weakly coupled. Due to its complexity, analytical solutions exist only for a few simplified cases involving one-dimensional flow. In this context, numerical methodologies are essential in the analysis of more complex problems, with the Finite Element Method (FEM) being one of the options. As main attributes of the FEM, its ability to deal with irregular geometries and complex boundary conditions stands out. In this thesis, the stabilized formulation based on Streamline-Upwind/Petrov-Galerkin (SUPG) finite elements will be used to solve the two-dimensional, transient and isothermal equations of the two-fluid model. This choice of stabilized formulation allows the development of a semi-discrete formulation, allowing the use of the same framework used for Galerkin's conventional method. In order to exert better control over the gradients of the solutions, discontinuity capture terms were used. The spatial domain was discretized through conventional bilinear elements, while the time discretization was obtained through a semi-implicit scheme. The resulting system of algebraic equations was linearized using the Newton-Raphson method, being solved in a fully-coupled manner. Some case studies were used to validate the developed formulation, namely: water-faucet test, flow in a duct, in a T-junction and in a converging nozzle. These tests made it possible to cover scenarios involving incompressible and compressible fluids, laminar and turbulent flow, and plane and axisymmetric flows. Numerical solutions were compared with reference solutions obtained from the literature and from the CFX software, and in general satisfactory results were obtained in all cases.

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