A consistent rescaled momentum transport method for simulating large density ratio incompressible multiphase flows using level set methods

Consistent mass and momentum transport for simulating incompressible interfacial flows with large density ratios using the level set method

A VOSET method combined with IDEAL algorithm for 3D two-phase flows with large density and viscosity ratio

Three-dimensional dynamic gas–liquid flow simulations that accurately track the phase interface are numerically challenging. This article presents a numerical study of the performance of the level-set phase–interface tracking method when combined with extremely high order (7th to 11th) weighted essentially non-oscillatory (WENO) advection schemes for gas–liquid free surface flows. Comparisons between simulation results and prior benchmark results suggest that such a combination of methods can be satisfactorily applied to the level-set and Navier-Stokes equations for free surface flow simulations when volume conservation is enforced at every time step, and minor numerical oscillations are suppressed through use of an artificial viscosity term. In particular, simulations of solid body rotation, the unsteady flow following an ideal dam break, tank sloshing, and the rise of a single bubble all agree with analytical or experimental results to within ± 3.12% when the level-set method is combined with an 11th order WENO scheme. Furthermore, use of an 11th order WENO advection scheme actually has a computational cost advantage because, for the same accuracy, it can be used on a coarser grid when compared with a more-common second-order advection scheme; computational savings of up to 87% are possible.

A simplified method is proposed to implement a wetting boundary condition on curved surfaces within the conservative phase-field lattice-Boltzmann (LB) simulation framework. It combines the idea of Huang et al. [“An alternative method to implement contact angle boundary condition and its application in hybrid lattice-Boltzmann finite-difference simulations of two-phase flows with immersed surfaces,” Eur. Phys. J. E 41, 17 (2018)] to find the order parameter on the other side of the wall with the conservative Allen–Cahn equation (CACE) for interface evolution solved by the LB equations. It inherits the advantage of the original method using the Cahn–Hilliard equation to avoid complicated interpolations under different geometries. By using the CACE, the boundary condition for the chemical potential is circumvented (making it more simplified), and the overshooting of the order parameter is also greatly suppressed, enabling it to simulate two-phase flows with solid objects of various shapes and wettabilities at large density and viscosity ratios. Several two-dimensional, axisymmetric, and three-dimensional problems, including some previously studied by experiments, were simulated and the capability of the proposed method is demonstrated through its good agreement with theoretical predictions and/or experimental observations.

A phase-field lattice Boltzmann model for simulating multiphase flows in porous media: Application and comparison to experiments of CO2 sequestration at pore scale

This study proposes a three-dimensional non-orthogonal multiple-relaxation-time (NMRT) phase-field multiphase lattice Boltzmann (PFLB) model within a recently established unified lattice Boltzmann model (ULBM) framework [Luo et al., Phil. Trans. R. Soc. A 379, 20200397, 2021]. The conservative Allen-Cahn equation and the incompressible Navier-Stokes (NS) equations are solved. In addition, a local gradient calculation scheme for the order parameter of the Allen-Cahn equation is constructed with the non-equilibrium part of the distribution function. A series of benchmark cases are conducted to validate the proposed model, including the two-phase Poiseuille flow, Rayleigh-Taylor instability, binary liquid/metal droplet collision, and a bubble rise in water. The present simulation results are in good agreement with existing simulation and experimental data. In the simulation of the co-current two-phase Poiseuille flow, the present model is proven to resolve the discontinuity at the phase interface and provide accurate results at extremely high density ratios (i.e., up to 106). Finally, the proposed model is adopted to simulate two challenging cases: (1) water droplet splashing during its impacting on a thin liquid film and (2) liquid jet breakup. The simulation results demonstrate an excellent agreement with previous experimental results, both qualitatively and quantitatively. In these simulations, the Weber number and Reynolds number reach 105 and 6000, respectively, and the viscosity can be as low as ∼10−4, in the lattice unit.

An improved lattice Boltzmann model for high gas and liquid density ratio in composite grids

A generic algorithm for three-dimensional multiphase flows on unstructured meshes

Based on the principle of virtual works, a multiphase smoothed particle hydrodynamics (SPH) model is further developed from the foundation of Hu X Y et al. (2006) and Grenier N et al. (2009). In the present model, the surface tension force implementation suitable for the multiphase flows with a large density ratio is applied, and this allows a good continuity at the multiphase interface. Artificial displacement correction is applied to keep the particles distributing uniformly in the whole flow field, and therefore any artificial viscous term is never needed; this is very important in the numerical simulation of viscous flows since the introduction of artificial viscosity changes the Reynolds number. Background pressure and interface sharpness force are added in the equation of state and the equation of momentum respectively to ensure the multiphase interface stability and smoothness; this is essential in the simulation of multiphase flows with large density difference at the multiphase interface. Two types of viscosity expressions suitable for multiphase flows are introduced and analyzed; the conclusion is that the formula proposed by Morris et al. (1997) and its similarly derived forms can give more accurate results. In the numerical validations, an oscillating droplet test is applied first to confirm the accuracy of the surface tension model and good results are achieved. This demonstrates that the artificial displacement and the interface sharp force will make negligible effects to the surface tension implementation. After that, two classic quantitative benchmarks of rising bubbles are simulated and the results of SPH agree well with the reference data. Moreover, in the two numerical benchmarks, the effect of the artificial displacement, the choice of the viscosity expression, and the type of the kernel function are compared and finally an optimal combination of these numerical aspects is recommended. Based on the above numerical investigations, the splitting process of an initially circular bubble is simulated and the numerical results agree well with the experimental data. In the last numerical case, the process of chasing and merging between two rising bubbles in vertical direction is simulated, based on which the mechanisms of these interesting interactions between two rising bubbles are analyzed. It is demonstrated in the present work that further improved multiphase SPH model may provide a potential method for the research of bubble dynamics.

A 6M digital twin for modeling and simulation in subsurface reservoirs

Heat transfer and phase change in multiphase media involve complex behavior such as multi-physics coupling, unsteady interfaces, and boundary generation/disappearance. The smoothed particle hydrodynamics (SPH) method is used to simulate multicomponent problems (initially solid material surrounded by a fluid) characterized by heat transfer, solid–liquid phase change, and multiphase flow. First, the interface behavior of the melted liquids and ambient fluids are simulated by a multiphase SPH model, where corrected algorithms and techniques are adopted to provide a stable simulation for the interface with a large density ratio. The wetting effect of the solid surface by melted liquids is considered by extending the continuum surface force model to three phases including solid, melted liquid and ambient fluid. Second, a thermal dynamics model is incorporated with the multiphase SPH model. The solid–liquid phase change occurs in a small temperature interval in which the latent heat is incorporated using the equivalent heat capacity. Third, the numerical model is validated using several benchmark examples. Five specially configured cases are simulated to demonstrate the robustness, adaptability, and stability of the model. The intriguing phenomena of evolution of the fluid interface of melted liquids, accumulation of thin-layer liquids, and melted droplet formation are reproduced.

Today there is a great interest in micro-scale multiphase fluid flow. In the paper, the numerical simulation of two-phase flow inside 3 mm minichannel was carried out. The liquid- gas interface was captured using the level-set method. During the calculation, the stabilization and reinitialization of level set function was performed in order to obtain the proper accuracy of the simulation. Incompressible Navier-Stokes equations were solved using the COMSOL Multiphysics® on a two-dimensional mesh. The process of formation of different two-phase flow patterns in the minichannel has been investigated. During the simulation it has been analysed three flow patterns: the bubbly flow and two kinds of slug flow with short and long slugs. It has been shown that unsteady flow at the inlet of the minichannel is responsible for the chaotic character of changes of the slug and bubble sizes. Such unsteady flow modifies the distance between the bubbles and slugs. It has been shown that for the low water inlet velocity the two-phase flow pattern becomes more stable.

Thermodynamic consistency is a key factor in heat and mass transfer simulation. A modified lattice Boltzmann pseudopotential model with the ability to simulate multiphase and multicomponent flow with a large density and viscosity ratio is proposed. Relative to a model using the exact difference method, a better thermodynamic consistency is obtained through introducing an improved external force term, a multi-relaxation-time collision operator, and a scaling coefficient k of the equation of state. The coefficient of scale k = 0.1 is preferred due to its better thermodynamic consistency, lower spurious current and a smaller surface tension. The inter-particle interaction strength has little influence over the thermodynamic consistency due to its limited contributions to the surface tension. With the model, the bubble dissolution under pressure is investigated and Henry’s law is validated.

In the subsurface, fluids play a critical role by transporting dissolved minerals, colloids, and contaminants (sometimes over long distances); by mediating dissolution and precipitation processes; and by enabling chemical transformations in solution and at mineral surfaces. Although the complex geometries of fracture apertures, fracture networks, and pore spaces may make it difficult to accurately predict fluid flow in saturated (single‐phase) subsurface systems, well‐developed methods are available. The simulation of multiphase fluid flow in the subsurface is much more challenging because of the large density and/or viscosity ratios found in important applications (water/air in the vadose zone; water/oil, water/gas, gas/oil, and water/oil/gas in hydrocarbon reservoirs; water/air/nonaqueous phase liquids (nonaqueous phase liquids/dense nonaqueous phase liquids) in contaminated vadose zone systems; and gas/molten rock in volcanic systems, for example). In addition, the complex behavior of fluid‐fluid‐solid contact lines and their impact on dynamic contact angles must also be taken into account and coupled with the fluid flow. Here we review the methods that are currently being used to simulate pore‐scale multiphase fluid flow and reactive transport in fractured and porous media. After the introduction, the review begins with an overview of the fundamental physics of multiphase fluids flow followed by a more detailed discussion of the complex dynamic behavior of contact lines and contact angles, an important barrier to accurate pore‐scale modeling and simulation. The main part of the review focuses on five different approaches: pore network models, lattice gas and lattice Boltzmann methods, Monte Carlo methods, particle methods (molecular dynamics, dissipative particle dynamics, and smoothed particle hydrodynamics), and traditional grid‐based computational fluid dynamics coupled with interface tracking and a contact angle model. Finally, the review closes with a discussion of future trends and challenges.

Simulation of incompressible two-phase flows with large density differences employing lattice Boltzmann and level set methods