Gustavo Rabello dos Anjos

3D ALE Finite-Element Method for Two-Phase Flows With Phase Change

We seek to study numerically two-phase flow phenomena with phase change through the finite-element method (FEM) and the arbitrary Lagrangian–Eulerian (ALE) framework. This method is based on the so-called “one-fluid” formulation; thus, only one set of equations is used to describe the flow field at the vapor and liquid phases. The equations are discretized on an unstructured tetrahedron mesh and the interface between the phases is defined by a triangular surface, which is a subset of the three-dimensional mesh. The Navier–Stokes equation is used to model the fluid flow with the inclusion of a source term to compute the interfacial forces that arise from two-phase flows. The continuity and energy equations are slightly modified to take into account the heat and mass transport between the different phases. Such a methodology can be employed to study accurately many problems, such as oil extraction and refinement in the petroleum area, design of refrigeration systems, modeling of biological systems, and efficient cooling of electronics for computational purposes, which is the aim of this research. A comparison of the obtained numerical results to the classical literature is performed and presented in this paper, thus proving the capability of the proposed new methodology as a platform for the study of diabatic two-phase flows.

A 3D moving mesh Finite Element Method for two-phase flows

A 3D ALE Finite Element Method is developed to study two-phase flow phenomena using a new discretization method to compute the surface tension forces. The computational method is based on the Arbitrary Lagrangian-Eulerian formulation (ALE) and the Finite Element Method (FEM), creating a two-phase method with an improved model for the liquid-gas interface. An adaptive mesh update procedure is also proposed for effective management of the mesh to remove, add and repair elements, since the computational mesh nodes move according to the flow. The ALE description explicitly defines the two-phase interface position by a set of interconnected nodes which ensures a sharp representation of the boundary, including the role of the surface tension. The proposed methodology for computing the curvature leads to accurate results with moderate programming effort and computational cost. Static and dynamic tests have been carried out to validate the method and the results have compared well to analytical solutions and experimental results found in the literature, demonstrating that the new proposed methodology provides good accuracy to describe the interfacial forces and bubble dynamics. This paper focuses on the description of the proposed methodology, with particular emphasis on the discretization of the surface tension force, the new remeshing technique, and the validation results. Additionally, a microchannel simulation in complex geometry is presented for two elongated bubbles

Moving mesh method for direct numerical simulation of two-phase flow with phase change

Abstract A moving mesh approach is employed to simulate two-phase flow with phase change. The mathematical model is based on the Arbitrary Lagrangian–Eulerian (ALE) description of the axisymmetric Navier–Stokes equations and energy conservation. These equations are discretized by the Finite Element Method (FEM) on a triangular unstructured mesh in which the phase boundary is represented by a set of interconnected nodes and segments that are part of the computational mesh. Here, phase change and surface tension are implemented as source terms, using the one fluid approach. The method is shown to provide an accurate description of the interfacial forces, heat and mass transfer between phases. Several different verifications are presented where the results are compared to analytical and semi-analytical solutions.

ALE-FEM for Two-Phase Flows With Heat and Mass Transfer in Microchannels

A numerical method is described to study two-phase flows for single and multiple bubbles with phase change. The fluid flow equations are based on the Arbitrary Lagrangian-Eulerian formulation (ALE) and the Finite Element Method (FEM), creating a new two-phase method with an improved model for the liquid-gas interface in microchannels. A successful adaptive mesh update procedure is also described for effective management of the mesh at the two-phase interface to remove, add and repair surface elements, since the computational mesh nodes move according to the flow. The Lagrangian description explicitly defines the two-phase interface position by a set of interconnected nodes which ensures a sharp representation of the boundary, including the role of the surface tension. The methodology proposed for computing the curvature leads to accurate results with moderate programming effort and computational cost and it can also be applied to different configurations with an explicit description of the interface. Such a methodology can be employed to study accurately many problems such as oil extraction and refinement in the petroleum area, design of refrigeration systems, modelling of biological systems and efficient cooling of electronics for computational purposes, being the latter the aim of this research. The obtained numerical results will be described, therefore proving the capability of the proposed new methodology.Copyright

Nano-patterning of surfaces by ion sputtering: Numerical study of the damping effect on the anisotropic Kuramoto-Sivashinsky equation

Series Editors: da Costa Mattos, Heraldo, Martins Costa, Maria Laura, Laredo dos Reis, Joao.