Aplicação do método SUPG na solução numérica do modelo de dois fluidos

Abstract

In the oil industry there are several situations that involve multiphase flow. Although different mathematical approaches are available to model this phenomenon, the two-fluid model is one of the most used. Because the two-fluid model considers conservation equations for each phase, it has greater scope than other models (such as the drift-flux model), which makes it more suitable for describing situations in which the phases are weakly coupled. Due to its complexity, analytical solutions exist only for a few simplified cases involving onedimensional 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. 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. 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: moving discontinuity, water-faucet test, flow in a duct, in a T-junction and in a converging nozzle. The studied cases involved 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.