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Multi-component flow problems are typical of many technological and engineering applications. In this work, we propose an implicit high-order discontinuous Galerkin discretization of the variable density incompressible (VDI) flow model for the simulation of multi-component problems. Indeed, the peculiarity of the VDI model is that the density is treated as an advected property, which can be used to possibly track multiple (more than two) components. The interface between fluids is described by a smooth, but sharp, variation in the density field, thus not requiring any geometrical reconstruction. Godunov numerical fluxes, density positivity, mass conservation, and Gibbs-type phenomena at material interfaces are challenges that are considered during the numerical approach development. To avoid Courant-related time step restrictions, high-order single-step multi-stage implicit schemes are applied for the temporal integration. Several test cases with known analytical solutions are used to assess the current approach in terms of space, time, and mass conservation accuracy. As a challenging application, the simulation of a 2D droplet impinging on a thin liquid film is performed and shows the capabilities of the proposed DG approach when dealing with high-density (water–air) multi-component problems. [ABSTRACT FROM AUTHOR]

The breeding blanket is one of the fundamental components of a nuclear fusion reactor and is responsible for the fuel production, generating tritium through neutronic capture reaction between lithium and neutrons. Lithium is a liquid PbLi alloy and the helium formed as reaction by-product can coalesce into bubbles, generating a two-phase mixture with a high-density ratio ( η ρ ∼ O 5 ). These bubbles can accumulate and stagnate within the blanket channels with potentially harmful consequences. In this work, the interIsoFoam solver of OpenFOAM v2012 is used to simulate bubble motion for a two-phase mixture representative of the He-PbLi system to test its potential for future developments in the field of fusion. In a first phase, several traditional benchmarks were carried out, both 2D and 3D, and considering the two variants of the VOF method implemented in the solver, isoAdvector and plicRDF. Subsequently, He bubbles of different diameters rising in liquid PbLi ( η ρ = 1.2 × 10 5 ) were analysed to investigate different regimes. For a Eötvös number (Eo) greater than 10, it was possible to recreate the axisymmetric, skirted, oscillatory regimes and the peripheral and central breakup regimes. For Eo < 10, non-physical deformations of the interface are observed, probably generated by spurious velocities that have a greater impact on the solution for very small bubbles and rising velocities. [ABSTRACT FROM AUTHOR]

In this paper, an alternative model is presented to simultaneously achieve thermodynamic consistency, leading to high-density ratios, and surface tension adjustment capability based on the pseudo-potential lattice Boltzmann model (LBM). These features are achieved by adding two relatively simple terms, each with an adjustable coefficient, selected from the Taylor expansion of the original interaction force, one for achieving and maintaining thermodynamic consistency, and the other for adjusting the surface tension independent of the density ratio. The model also takes advantage of being independent of using SRT, MRT, 2D or 3D lattice models. The capability of the model is evaluated and verified by performing several static and dynamic benchmark test cases. First, the coexistence densities extracted for a flat interface from the model are compared with those of the Maxwell equal area rule in a wide temperature range. Results show that the thermodynamic consistency is well achieved and the coexistence densities are independent of the surface tension strength as well. Next, the well-known Laplace law for a droplet is evaluated and satisfied with the model. In addition, a wide range of surface tension values is achievable at a fixed temperature by adjusting the surface tension adjustment coefficient. After that, the ellipsoidal droplet oscillation is simulated with a good agreement between the analytical and numerical results for the oscillation period. The spurious velocities around the droplet are then evaluated and shown to be reasonable, and comparatively low even at a relatively high-density ratio around of 2400. It was found that the magnitude of these velocities can be further reduced, especially at high-density ratios, by reducing the liquid to gas dynamic viscosity ratio or equivalently increasing the gas to liquid kinematic viscosity ratio. Next, the stability, and the fascinating phenomenon of symmetric bifurcation of a rotating planar droplet are simulated and formation of two- and four-lobed shapes along with rigid rotation is presented depending on the value of the surface tension. Finally, the droplet impact on a liquid film is simulated at a relatively high-density ratio around of 720, and Reynolds number of 1440. However, the upper limit of physical parameters for simulating this phenomenon is found to be a density ratio of 720 and Re and We numbers of 6600 and 275, respectively. Effects of the surface tension strength are shown as well. The crown spread radius from the model agrees well with the analytical solution reported in the literature. [ABSTRACT FROM AUTHOR]