Abstract
SummaryA 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.
Highlights
Multiphase flows, where two or more fluids have interfacial surfaces, are often found in industrial engineering applications, such as oil-and-gas transportation, nuclear reactors, and microfluidics
A novel control volume finite element method with adaptive anisotropic unstructured meshes has been presented for 3D three-phase flows with interfacial tension
The numerical framework consists of a mixed control volume and finite element formulation, a VOF-type method for the interface capturing based on a compressive control volume advection method and second-order finite element methods, and a force-balanced algorithm for the interfacial tension implementation
Summary
Multiphase flows, where two or more fluids have interfacial surfaces, are often found in industrial engineering applications, such as oil-and-gas transportation, nuclear reactors, and microfluidics. Unstructured meshes are very attractive when dealing with complex geometries in engineering applications and there are examples of adaptive unstructured meshes with the interface tracking method,[18] level set method,[19] phase field method,[20] and algebraic VOF method.[21]. The moment-of-fluid method has been developed in dealing with more than two materials.[22,23] A few numerical examples with interfacial tension can be found in the literature for the level set,[24,25] VOF,[26] moment-of-fluid,[27] phase field,[28,29] smooth particle hydrodynamics (SPH),[30,31] and moving mesh[32] methods.
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