Numerical simulation of single droplet dynamics in three-phase flows using ISPH

In this study, a new surface tension formulation for modeling incompressible, immiscible three-phase fluid flows in the context of incompressible smoothed particle hydrodynamics (ISPH) in two dimensions has been proposed. A continuum surface force model is employed to transform local surface tension force to a volumetric force while physical surface tension coefficients are expressed as the sum of phase specific surface tension coefficients, facilitating the implementation of the proposed method at triple junctions where all three phases are present. Smoothed color functions at fluid interfaces along with artificial particle displacement throughout the computational domain are combined to increase accuracy and robustness of the model. In order to illustrate the effectiveness of the proposed method, several numerical simulations have been carried out and results are compared to analytical data available in literature. Results obtained by simulations are compatible with analytical data, demonstrating that the ISPH scheme proposed here is capable of handling three-phase flows accurately

Numerical simulation of super-square patterns in Faraday waves

We report the first simulations of the Faraday instability using the full three-dimensional Navier-Stokes equations in domains much larger than the characteristic wavelength of the pattern. We use a massively parallel code based on a hybrid Front-Tracking/Level-set algorithm for Lagrangian tracking of arbitrarily deformable phase interfaces. Simulations performed in rectangular and cylindrical domains yield complex patterns. In particular, a superlattice-like pattern similar to those of [Douady & Fauve, Europhys. Lett. 6, 221-226 (1988); Douady, J. Fluid Mech. 221, 383-409 (1990)] is observed. The pattern consists of the superposition of two square superlattices. We conjecture that such patterns are widespread if the square container is large compared to the critical wavelength. In the cylinder, pentagonal cells near the outer wall allow a square-wave pattern to be accommodated in the center

Faraday instability on a sphere: numerical simulation

We consider a spherical variant of the Faraday problem, in which a spherical drop is subjected to a time-periodic body force, as well as surface tension. We use a full three-dimensional parallel front-tracking code to calculate the interface motion of the parametrically forced oscillating viscous drop, as well as the velocity field inside and outside the drop. Forcing frequencies are chosen so as to excite spherical harmonic wavenumbers ranging from 1 to 6. We excite gravity waves for wavenumbers 1 and 2 and observe translational and oblate-prolate oscillation, respectively. For wavenumbers 3 to 6, we excite capillary waves and observe patterns analogous to the Platonic solids. For low viscosity, both subharmonic and harmonic responses are accessible. The patterns arising in each case are interpreted in the context of the theory of pattern formation with spherical symmetry

Coupled DEM-LBM method for the free-surface simulation of heterogeneous suspensions

The complexity of the interactions between the constituent granular and liquid phases of a suspension requires an adequate treatment of the constituents themselves. A promising way for numerical simulations of such systems is given by hybrid computational frameworks. This is naturally done, when the Lagrangian description of particle dynamics of the granular phase finds a correspondence in the fluid description. In this work we employ extensions of the Lattice-Boltzmann Method for non-Newtonian rheology, free surfaces, and moving boundaries. The models allows for a full coupling of the phases, but in a simplified way. An experimental validation is given by an example of gravity driven flow of a particle suspension

Simplex space-time meshes in thermally coupled two-phase flow simulations of mold filling

The quality of plastic parts produced through injection molding depends on many factors. Especially during the filling stage, defects such as weld lines, burrs, or insufficient filling can occur. Numerical methods need to be employed to improve product quality by means of predicting and simulating the injection molding process. In the current work, a highly viscous incompressible non-isothermal two-phase flow is simulated, which takes place during the cavity filling. The injected melt exhibits a shear-thinning behavior, which is described by the Carreau-WLF model. Besides that, a novel discretization method is used in the context of 4D simplex space-time grids [2]. This method allows for local temporal refinement in the vicinity of, e.g., the evolving front of the melt [10]. Utilizing such an adaptive refinement can lead to locally improved numerical accuracy while maintaining the highest possible computational efficiency in the remaining of the domain. For demonstration purposes, a set of 2D and 3D benchmark cases, that involve the filling of various cavities with a distributor, are presented.Comment: 14 pages, 11 Figures, 4 Table