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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]

Flow boiling is a common phenomenon in modern technology and industries. A finite difference Front Tracking method is used to study film boiling on a flat plate subject to a constant heat flux. Large density ratios are examined (1000, 2000). The flow structure including the circulation zones, the vortex developing areas, and vortex pair generation are studied in detail. The numerical method is validated by comparing the result with the analytic solution for a simple problem. Large bubbles comparable to the computational domain are formed at large density ratios. The bubble either breaks up and departs from the rest of the gas, or a jet is formed depending on the heat flux imposed. It is found that the Nusselt number depends on the heat flux on the wall. Specifically, the Nusselt number decreases as the heat flux is raised. The Morton number also affects the Nusselt number in agreement with experimental correlations. The Nusselt number increases when the Morton number is raised. The results obtained agree with experimental correlations at relatively low heat fluxes. Agreement gets worse at large heat fluxes. Experimental correlations estimate larger Nusselt numbers compared to the present study. The flow enhances along the direction of the gravitational acceleration at large density ratios (2000). A wide neck is formed that stabilizes at a specific position inside the flow. The microstructure of the flow shows a vortex pair that develops beneath the root of the bubble at a large density ratio (2000). [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]

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.

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 (ηρ∼O5). 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 (ηρ=1.2×105) 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.

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]

An improved Moving-Particle Semi-Implicit (MPS) method is proposed for multiphase flows with high-density ratios and violent deformation of the interface. First, a particle number density compensation (PNDC) model is developed to remove the ghost particles out of the boundary thoroughly. The model is verified via static pressure simulations. Then, based on previous works (Shakibaeinia et al., 2012; Khayyer et al., 2013; Duan et al., 2017 [1] ; Duan et al., 2017 [2] ; Sun et al., 2015), the MPS method is extended to a multiphase flow solver. Finally, the improved MPS method is applied to model static pressure, Rayleigh–Taylor instability, sloshing flow, and two-phase dam-break. The comparative analysis with the available experimental datum and other published numerical results proved the applicability and accuracy of the proposed MPS method for simulating multiphase flows with high-density ratios and violent deformation of interface. • A PNDC model is proposed for multiphase flows with high-density ratios in MPS method. • The PNDC model guarantees particle number density accuracy near the boundary. • The method accurately simulates multiphase flows with violent interface deformation. [ABSTRACT FROM AUTHOR]

Abstract: A numerical scheme for fully resolved simulation of particle–fluid systems with freely moving rigid particles is developed. The approach is based on a fictitious domain method wherein the entire particle–fluid domain is assumed to be an incompressible fluid but with variable density. The flow inside the particle domain is constrained to be a rigid body motion using an additional rigidity constraint in a fractional step scheme. The rigidity constraint force is obtained based on the fast computation technique proposed by Sharma and Patankar (2005) [1]. The particle is assumed to be made up of material points moving on a fixed background mesh where the fluid flow equations are solved. The basic finite-volume solver is based on a co-located grid incompressible but variable density flow. The incompressibility constraint is imposed by solving a variable-coefficient pressure equation. Use of density-weighted reconstruction of the pressure gradients was found to give a stable scheme for high density ratio particle–fluid systems. Various verification and validation test cases on fixed and freely moving particles are performed to show that the numerical approach is accurate and stable for a wide range ( – ) of particle–fluid density ratios. [Copyright &y& Elsevier]

This work examines the ability of the improved pseudo-potential model in simulating the two-phase flows on the curved surface with the angular velocity. Owing to this purpose, the movement of a two-dimensional droplet on a cylinder is investigated using the lattice Boltzmann method. To calculate the cohesion forces the model of Kupershtokh is used. Also, the distribution functions near the surface are approximated using the bounce-back method with the ability to calculate the surface velocity. After validation, results are presented for two droplets with and without initial velocity. Accordingly, the effects of the capillary number and Galilei number in the static droplet and the effect of Reynolds number and Weber number for a thrown droplet are investigated considering effects of contact angle and angular velocity. Results show that increasing the Galilei number leads to droplet dripping from the cylinder, while the reduction of the capillary number causes the droplet to oscillate before reaching the equilibrium state. Also, at low angular velocities, the dripping of the droplet is accelerated but with a further increase of the angular velocity the droplet completely covers the surface of the cylinder without detaching it. On the other hand, the inertia of the droplet causes more surface wetting, while further increase in the inertia causes the droplet to be fragmented and it removes the surface before complete surface wetting. • Ability of improved pseudo-potential model is examined in rotating curved boundary. • The Kupershtokh method is extended adding adhesion forces on the curved boundary. • Numerical density ratios follow the values of the equation of state. • For a stationary droplet effects of Galilei and capillary numbers are investigated. • For a thrown droplet effects of Reynolds and Weber numbers are investigated. [ABSTRACT FROM AUTHOR]