Rafael Araújo Vidal

Abstract

This work aims to present a computational approach to study two-phase flows using direct numerical simulation. The flows are modeled by the two-dimensional incompressible Navier-Stokes equations, which are approximated using the Finite Element Method. The Galerkin formulation is employed to discretize the NavierStokes equations in the spatial domain, while the semi-Lagrangian method is used to discretize the material derivative in the spatio-temporal domain. A static unstructured triangular mesh is defined in the entire spatial domain. In order to satisfy the Ladyzhenskaya-Babuška-Brezzi condition, the mini and the quadratic elements are used, with pressure and velocity fields being calculated on different sets of the triangular mesh nodes. The interface is modeled using an adaptive moving onedimensional mesh, according to an interface-tracking method, in which connected marker points are moved with the imposed velocity of the static triangular mesh. The interfacial tension is calculated using the interface curvature and a Heaviside function gradient, and then included in the Navier-Stokes equations as a body force. To ensure simulation stability, a smooth transition between fluid properties is defined in the interface region. A coalescence modeling approach is proposed, whereby two bubbles merge into a single one when the distance between them decreases to a minimum threshold based on the mesh refinement level. Several benchmark tests - such as the oscillating droplet, the rising bubble and the Rayleigh-Taylor instability - have been conducted to validate the proposed approach, and the obtained results have demonstrated substantial agreement with analytical solutions and results reported in literature. Based on this strong agreement with theory, experimental data and reference results, the presented approach is validated as an accurate method for describing diverse two-phase flow phenomena. e Sumário

Advising

Advisor: Anjos, G. R.