A control volume finite element method for three‐dimensional three‐phase flows

Abstract

Summary A novel control volume finite element method with adaptive anisotropic unstructured meshes is presented for three‐dimensional three‐phase flows with interfacial tension. The numerical framework consists of a mixed control volume and finite element formulation with a new P1DG‐P2 elements (linear discontinuous velocity between elements and quadratic continuous pressure between elements). A “volume of fluid” type method is used for the interface capturing, which is based on compressive control volume advection and second‐order finite element methods. A force‐balanced continuum surface force model is employed for the interfacial tension on unstructured meshes. The interfacial tension coefficient decomposition method is also used to deal with interfacial tension pairings between different phases. Numerical examples of benchmark tests and the dynamics of three‐dimensional three‐phase rising bubble, and droplet impact are presented. The results are compared with the analytical solutions and previously published experimental data, demonstrating the capability of the present method.

Open-source finite volume solvers for multiphase (n-phase) flows involving either Newtonian or non-Newtonian complex fluids

“…A1, A2 and A3) as predicted by our new multiFluidInterFoam solver for various combinations of the interface compression parameter C a i and the Laplacian filter parameter n lf i . Our solutions are compared with previous numerical results of Xie et al [6] and Kim and Lowengrub [47] The initially circular droplet spreads and its final shape, depicted in Fig. 3, depends on the values of the surface tension coefficients of each system.…”

“…( 12) in order to account for the surface tension. In the present work, the interfacial tension coefficient decomposition method is employed to deal with tension pairings between different phases using a compositional approach [3,6,7,10]. The physical interfacial tension coefficients σ * ij between phase i and phase j are decomposed into phase-specific interfacial tension coefficients as σ * ij = Σ * i + Σ * j .…”

“…The spreading of a liquid lens is a very classic benchmark problem and it has been widely used previously to assess the numerical methods for three-phase flows [3,6,8,9,10,40]. Here, we examine this benchmark problem in detail and consider the cases of partial and full spreading of the droplet in order to investigate whether the newly developed numerical solver is capable of accurately predicting the dynamics of spreading and also producing the correct equilibrium contact angles with triple junction points.…”

“…With the rapid development of computer technology, numerical modeling provides reliable and accurate tools and it has a considerable role in the detailed investigation of multiphase flows. In the past, many efforts have been made to develop numerical approaches for the simulation of three-phase flows based on the numerical solution of Navier-Stokes equations together with various approaches devoted to the capturing or tracking of the interfaces between fluids, such as the level-set [2,3], front-tracking [4], volume-of-fluid [5,6], smoothed particle hydrodynamics [7], and phase field [8,9,10]…”

A finite volume coupled level set and volume of fluid method with a mass conservation step for simulating two-phase flows

“…In particular, the accurate numerical simulation of two-phase flows of two immiscible fluids faces the problem of resolving moving interfaces that deform under the influence of various forces such as surface tension and gravitational forces. Two of the most popular implicit methods for capturing the interface in interfacial flows that involve large topological changes are the volume of fluid (VOF) method 1,2,3,4,5,6,7,8,9,10,11 and the level set (LS) method 12,13,14,15,16,17,18,19,20 . One of the most attractive features of both methods is their ability to naturally adapt to any topological changes and the calculation of curvature can be implemented through simple formulations.…”