One- and two-step semi-Lagrangian integrators for arbitrary Lagrangian-Eulerian-finite element two-phase flow simulations

Semi-Lagrangian (SL) schemes are of utmost relevance to simulate two-phase flows where advection dominates. The combination of SL schemes with the finite element (FE) method and arbitrary Lagrangian-Eulerian (ALE) dynamic meshes yields a strong ingredient to deal with applications in Earth sciences, environmental engineering, and oil and gas industry whose numerical background is incipient. This article is intended to propose a second-order time multistep SL/ALE/FE scheme to track particle trajectories traveling amidst single- or two-phase incompressible flows both in fixed and moving mesh situations. The novel scheme is a BDF2-like implementation that considers the mesh velocity as part of its backward-in-time integration. Trajectory departure points are searched through extrapolation and followed by a multistep interpolation corrector that works both for constant and varying time steps. A series of two-phase benchmark flow simulations are carried out by using the cubic element to compare the performance of the new integrator against single-step approximations as well as to analyze enhancements in representing the two-phase flow dynamics. We use the 2D axisymmetric Navier-Stokes equations as underlying model. Error analyses, convergence tests, quantitative, and qualitative comparisons are presented and discussed to highlight the superior conservative feature of the novel scheme.

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

Gustavo Rabello Dos Anjos

A new numerical method is proposed to study two-phase flow and heat transfer for interlayer cooling of the new generation of multi-stacked computer chips. The fluid flow equations are developed in 3-dimensions 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. A new adaptive mesh update procedure is also proposed 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 new 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 so far all the obtained results have compared well to analytical solutions and experimental results found in the literature, demonstrating that the new proposed methodology to simulate two-phase flows provides good accuracy to describe the interfacial forces and bubble dynamics. The new code was then used to simulate elengated bubble flows in square microchannels, being considered for two-phase interlayer cooling in future 3D-IC compute chips.

EPFL2012

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

Navid Borhani, Gustavo Rabello Dos Anjos, John Richard Thome

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.

Taylor & Francis2014

Interface-fitted moving mesh method for axisymmetric two-phase flow in microchannels

Erik Gros, Gustavo Rabello Dos Anjos, John Richard Thome

A boundary-fitted moving mesh scheme is presented for the simulation of two-phase flow in two-dimensional and axisymmetric geometries. The incompressible Navier-Stokes equations are solved using the finite element method, and the mini element is used to satisfy the inf-sup condition. The interface between the phases is represented explicitly by an interface adapted mesh, thus allowing a sharp transition of the fluid properties. Surface tension is modelled as a volume force and is discretized in a consistent manner, thus allowing to obtain exact equilibrium (up to rounding errors) with the pressure gradient. This is demonstrated for a spherical droplet moving in a constant flow field. The curvature of the interface, required for the surface tension term, is efficiently computed with simple but very accurate geometric formulas. An adaptive moving mesh technique, where smoothing mesh velocities and remeshing are used to preserve the mesh quality, is developed and presented. Mesh refinement strategies, allowing tailoring of the refinement of the computational mesh, are also discussed. Accuracy and robustness of the present method are demonstrated on several validation test cases. The method is developed with the prospect of being applied to microfluidic flows and the simulation of microchannel evaporators used for electronics cooling. Therefore, the simulation results for the flow of a bubble in a microchannel are presented and compared to experimental data.

Wiley2018