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

Navid Borhani, Gustavo Rabello Dos Anjos, John Richard Thome

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. (C) 2014 Elsevier Inc. All rights reserved.

Elsevier2014

Numerical Modelling of Two-Phase Flow with Moving Boundary Fitted Meshes

Erik Gros

In this thesis, a computational approach is used to study two-phase flow including phase change by direct numerical simulation. This approach follows the interface with an adaptive moving mesh. The incompressible Navier-Stokes equations are solved, in two-dimensional and axisymmetric geometries, using the Finite Element Method (FEM). The computational domain is discretized using an unstructured triangular mesh and the mini element is used to satisfy the "inf-sup" compatibility condition. A combination of smoothing mesh velocities and remeshing is used to preserve the mesh quality. Adaptive mesh refinement is used to keep the mesh sufficiently refined where needed. Mesh adaptation strategies, allowing to control the refinement of the computational mesh, are discussed in the context of specific applications. The accurate representation of the interface between the phases is a key issue to model surface tension dominated flows. Here, the interface is represented explicitly by nodes and segments that are a subset of the computational mesh and a sharp transition of the fluid properties can be achieved. The surface tension force is included as a singular volume force, like in the continuum model (CSF). The present discretization is shown to allow for exact equilibrium (up to rounding errors) between the pressure and surface tension terms. This is important in order to suppress spurious currents, which are a common issue in computational two-phase flow. However, an exact computation of the interface curvature is necessary for the spurious currents to be numerically zero. The curvature of the interface, is efficiently and accurately computed by using the Frenet-Serret formulas. A phase change model is implemented via a source term in the continuity equation, which is computed from the jump in conductive heat flux at the interface. The presented approach is shown to provide an accurate description of different two-phase flow phenomena, including phase change, and to handle cases with large material property ratios. Accuracy and robustness of the present method are demonstrated on several benchmark cases, where the results are compared to analytical or semi-analytical solutions and experimental data.

EPFL2018

Numerical Modelling of Two-Phase Flow with Moving Boundary Fitted Meshes

Erik Gros

EPFL2018