Eventos Anais de eventos
ENCIT 2022
19th Brazilian Congress of Thermal Sciences and Engineering
Axisymmetric Two-phase Finite Element Simulation Using a Front Tracking Method on an Unstructured Mesh
Submission Author:
Daniel Barbedo Vasconcelos Santos , RJ
Co-Authors:
Daniel Barbedo Vasconcelos Santos, Gustavo Rabello dos Anjos
Presenter: Daniel Barbedo Vasconcelos Santos
doi://10.26678/ABCM.ENCIT2022.CIT22-0402
Abstract
The goal of this research is to accurately depict two-phase dynamics, using axisymmetric finite element numerical simulation. To achieve this goal, the incompressible Navier-Stokes equations for two-phase flows, with variable fluid properties, are solved through the Finite Element Method (FEM), using a two-phase separation strategy where there are two distinct meshes, one for the two-phase fluid and one for the interface. The mini element is utilized in order to respect the LBB condition, and avoid artificial stabilization terms in the fluid motion equations. The non-linear convective term on the Navier-Stokes equation is solved by applying a first order semi-Lagrangian scheme. Of the two meshes used, the fluid mesh has a vast quantity of finite element nodes and is fixed, not requiring any remeshing or interference during the simulation. The interface mesh moves and requires remeshing, but has quite fewer points relative to the fluid mesh, and so the movement and remeshing computational costs are negligible. The fluid and interface meshes are decoupled; the only link between them is the interface mesh position update, based on the velocity fields obtained from the fluid mesh, through the finite element solution. Fluid properties are smoothed over a fictional thickness of the fluid interfaces, to avoid numerical instability. Surface tension is implemented using the well-known continuum surface tension model, using the Laplace-Beltrami operator for curvature computation. The surface tension force is added explicitly to the Navier-Stokes equations as a volume force through the gradient of a Heaviside function, and thus the momentum equation is solved using a one-fluid approach. As validation for the discussed approach, three test cases will be presented. The static droplet, where a droplet stays still while surface tension is balanced by pressure; the oscillating droplet, where a droplet starts in elliptical shape, and oscillates, converging to an spherical shape; and the gravity driven bubble, where a bubble rises inside a quiescent fluid, dominated by gravity force, changing shape as it rises. The test cases will be run for high Reynolds numbers, and the results compared to analytical data and available works. In addition to the test cases, in an effort to improve stability, a relationship between the spurious current intensity and interface mesh node quantity will be presented.
Keywords
Front Tracking, Finite Element Method, Two-phase Flow, Axisymmetric flows
