Color-gradient Lattice Boltzmann Model Research Articles

Homogenized color-gradient lattice Boltzmann model for immiscible two-phase flow in multiscale porous media

In this paper, a homogenized multiphase lattice Boltzmann (LB) model is established for parallelly simulating immiscible two-phase flow in both solid-free regions (pore scale) and porous areas (continuum scale). It combines the color-gradient multiphase model with the Darcy–Brinkman–Stokes method by adding a term that includes surface force and drag force of porous matrix to multiple-relaxation-time LB equation in moment space. Moreover, an improved algorithm is proposed to characterize and implement the apparent wettability in the locally homogenized porosity field. Validations and test cases are given to demonstrate the accuracy and robustness of this new model, as well as its applicability for trans-scale fluid simulation of transport and sorption behavior from porous (Darcy flow) area to free (Stokes flow) area. For practicality, the two-phase seepage flow in a composite rock structure with multiscale pores is simulated by this new model, and the effects of viscosity ratio and wettability on the displacement process are discussed.

Generalized equilibria for color-gradient lattice Boltzmann model based on higher-order Hermite polynomials: A simplified implementation with central moments.

We propose generalized equilibria of a three-dimensional color-gradient lattice Boltzmann model for two-component two-phase flows using higher-order Hermite polynomials. Although the resulting equilibrium distribution function, which includes a sixth-order term on the velocity, is computationally cumbersome, its equilibrium central moments (CMs) are velocity-independent and have a simplified form. Numerical experiments show that our approach, as in Wen etal. [Phys. Rev. E 100, 023301 (2019)2470-004510.1103/PhysRevE.100.023301] who consider terms up to third order, improves the Galilean invariance compared to that of the conventional approach. Dynamic problems can be solved with high accuracy at a density ratio of 10; however, the accuracy is still limited to a density ratio of 1000. For lower density ratios, the generalized equilibria benefit from the CM-based multiple-relaxation-time model, especially at very high Reynolds numbers, significantly improving the numerical stability.

Numerical study of droplet behavior passing through a constricted square channel

Snap-off is a crucial mechanism for drop breakup in multiphase flow within porous media. However, the systematic investigation of snap-off dynamics in constricted capillaries with varying pore and throat heights remains limited. In this study, we conducted three-dimensional simulations of drop behavior in a constricted square capillary with non-uniform depth, employing a color-gradient lattice Boltzmann model. Our analysis encompassed a comprehensive range of parameters, including geometrical factors and physical properties, such as capillary number, initial drop size, viscosity ratio, constriction length, and the presence of soluble surfactants. Depending on these parameters, the drop exhibited either breakup or deformation as it traversed the constriction. Upon snap-off occurrence, we quantified two significant aspects: the snap-off time t̂b, which represents the time interval between the drop front passing the constriction center and the snap-off event, and the volume of the first daughter drop V̂d generated by the breakup mechanism. Consistently, we observed a power-law relationship between t̂b and the capillary number Ca. However, the variation of V̂d with Ca exhibited a more complex behavior, influenced by additional factors, such as the viscosity ratio and the presence of surfactants, which break the linear increase in V̂d with Ca. Notably, the inclusion of surfactants is able to homogenize the volume of the first daughter drop. Through our comprehensive numerical study, we provide valuable insight into the snap-off process in constricted capillaries. This research contributes to the understanding of multiphase flow behavior and facilitates the optimization of processes involving snap-off in porous media.

Improved three-dimensional multiple-relaxation-time color-gradient lattice Boltzmann finite-difference model for thermocapillary flows

This study is devoted to developing a color-gradient lattice Boltzmann model capable of simulating thermocapillary flows with variable properties. To achieve the purpose, some modified work is conducted. The equilibrium distribution function for density is modified in the developed model. The scheme of multiple-relaxation-time is applied to deal with the single-phase and perturbation collision operators to enhance the algorithm stability, and a simple correction term is incorporated into the single-phase operator. In addition, the finite-difference method is adopted to solve the temperature field. The developed model is first used to simulate the layered two-phase flow in a horizontal channel to test the density ratio that can be achieved without temperature effect. Then two classical thermocapillary flow problems of thermocapillary-driven flow in a heated microchannel and thermocapillary migration of a deformable droplet or bubble are simulated, and the model is proven to successfully simulate the thermocapillary flows with density ratios up to 10.

Numerical simulation of the droplet formation involving fluids with high viscosity ratio by lattice Boltzmann method

A multiple-relaxation-time color gradient lattice Boltzmann model is established for simulating the flow mechanism of viscous fluids or fluids with high viscosity ratios in the microchannel. The regularized method is incorporated in this MRT framework to deal with the high viscosity ratio problems involving practical inlet–outlet boundaries. By taking several static and dynamic cases, we prove that this model could accurately describe interfacial tension, wettability, and flow problems in two-phase flows with a low spurious velocity at the range of viscosity ratio up to O(103). Using this model, we successfully simulate the droplet formation process of fluids with a high viscosity ratio in the common T-junction channel. The results are in good agreement with the experiments in the literature. We further investigate the effect of high viscosity ratios on the dispersion process, revealing that the substantial increase in terms of the viscosity ratio of fluids leads to the enhancement of continuous phase viscous shear and dispersed phase inertia effect, which would bring the deviation of the operating range from mostly reported flow systems.

Lattice Boltzmann simulation of liquid water transport in gas diffusion layers of proton exchange membrane fuel cells: Impact of gas diffusion layer and microporous layer degradation on effective transport properties

Polymer Electrolyte Membrane Fuel Cells (PEMFCs) represent a promising technology for clean drivetrain solutions, in particular for heavy-duty applications. However, lifetime requirements demand high durability of each cell component.In this work, transport of liquid water through pristine and degraded gas diffusion layers (GDL) was simulated with a 3D Color-Gradient Lattice Boltzmann model. The GDL microstructure was reconstructed from high-resolution X-ray micro-computed tomography (μ-CT) of an impregnated Freudenberg H14. The effect of a microporous layer (MPL) was considered by reconstruction of an impregnated and MPL-coated H14. Aged microstructures were generated artificially, assuming loss of polytetrafluoroethylene (PTFE) within the GDL and increase of MPL macroporosity as main degradation mechanisms. Liquid water transport within aged microstructures was simulated by imposing a liquid phase flow rate until breakthrough was reached. Subsequently, the GDL microstructures were analyzed for their breakthrough characteristics by means of saturation and effective gas transport properties. When the MPL was pristine, no distinct GDL degradation effect was observable, this was attributed to the MPL dominating capillary transport. MPL aging, however, led to increased saturations and thus to a deterioration of the effective gas transport. With a partially degraded MPL, aging of the GDL then appeared to affect the breakthrough characteristics.

Color-gradient lattice Boltzmann model for immiscible fluids with density contrast.

We present a color-gradient-based lattice Boltzmann model for immiscible fluids with a large density contrast. The model employs the velocity-based equilibrium distribution function, initially proposed for the phase-field-based model by Zu and He [Phys. Rev. E 87, 043301 (2013)1539-375510.1103/PhysRevE.87.043301], with a modification necessary to satisfy the kinematic condition at the interface. Different from the existing color-gradient models, the present model allows to specify interface mobility that is independent of the fluid density ratio. Further, we provide a unified framework, which uses the recursive representation of the lattice Boltzmann equation, to derive the governing equationsof the system. The emergent color dynamics thus obtained, through an analysis of the segregation operator, is shown to obey the locally conservative Allen-Cahn equation. We use a series of benchmarks, which include a stationary drop, a layered Poiseuille flow, translation of a drop under a forced velocity field, the Rayleigh-Taylor instability, and the capillary intrusion test to demonstrate the model's ability in dealing with complex flow problems.

Three-dimensional color-gradient lattice Boltzmann model for simulating droplet ringlike migration under an omnidirectional thermal gradient

Thermocapillary migration is a typical flow problem in Marangoni flows, and it is driven by a temperature gradient, which is widely encountered in many engineering and scientific applications. The temperature distribution is heterogeneous on the substrates in many practical applications, which causes that the temperature gradient is directionally unstable and the droplet migration direction is uncertain or omnidirectional. To investigate the migration behavior of a droplet under an omnidirectional thermal gradient, a three-dimensional color-gradient lattice Boltzmann model is applied in the present study. The capability of this model to simulate the interactions of the fluid and solid for a small contact angle is first verified. Then the migration behavior of droplet initially in the center of the substrate (highest temperature region) is studied, and the droplet ringlike migration is observed and analyzed. Next a systematic study of the droplet volume and wetting properties is conducted. Finally, the migration behavior of droplet initially away from the center of the substrate is investigated and compared with that in the center, and the influence of the offset distance is explored.

Lattice Boltzmann simulation of liquid water transport in gas diffusion layers of proton exchange membrane fuel cells: Parametric studies on capillary hysteresis

Water management is crucial for reliable operation of Polymer Electrolyte Membrane Fuel Cells (PEMFC). Here, the gas diffusion layer (GDL) plays an essential role as it has to ensure efficient water removal from and oxygen transport to the catalyst layer.In this study water transport through porous carbon felt GDLs was simulated using a 3D Color-Gradient Lattice Boltzmann model. Simulations were carried out on microstructures of plain and impregnated fiber substrates of a Freudenberg H14. The GDL microstructures were reconstructed from high-resolution X-ray micro-computed tomography (μ-CT). For the distinction of carbon fibers and polytetrafluoroethylene (PTFE) in the binarized microstructures an in-house algorithm was developed. The additive was specified heterogeneously in the GDL through-plane direction employing a PTFE loading profile as derived based on μ-CT image data. In the in-plane direction the additive was furthermore defined in a realistic fashion near carbon fiber intersections. Prior to parametric studies on capillary behavior a sophisticated modeling approach for semipermeable membranes had to be developed to account for experimental boundary conditions. Capillary hysteresis was then investigated by simulation of intrusion and drainage curves and subsequent comparison to testbench data.

Effects of grain shape and packing pattern on spontaneous imbibition under different boundary conditions: Pore-scale simulation

Core-scale spontaneous imbibition experiments and numerical simulations have demonstrated that the macroscopic imbibition performance is significantly different under different boundary conditions. However, the detailed pore-scale flow mechanisms behind these phenomena and the influence of porous media's geometric features on the imbibition behavior under different boundaries have not been addressed in depth. In this work, an optimized color-gradient lattice Boltzmann model is applied to simulate spontaneous imbibition in granular media under four boundary conditions. The influence of grain shape and packing pattern on the two-phase interface evolution and the recovery factor during spontaneous imbibition is investigated while fixing different models' porosity, grain number, and size distribution. It is found that the grain shape has little influence on the drainage interface evolution at the initial stage but it has a more significant influence on the imbibition interface during counter-current spontaneous imbibition. The grain packing pattern influences the evolution of drainage and imbibition interfaces and the recovery factor. Spontaneous imbibition with different boundary conditions has different imbibition rates and ultimate recovery factors. The fastest imbibition rate and highest ultimate recovery are obtained under all faces open and two faces open (free) boundary conditions, respectively. This research provides pore-scale insights into the complex dynamic fluid displacement mechanism between the fracture and matrix of fractured oil and gas reservoirs.

Numerical study of droplet thermocapillary migration behavior on wettability-confined tracks using a three-dimensional color-gradient lattice Boltzmann model

Thermocapillary migration describes the phenomenon whereby liquid droplets move from warm to cold regions on a nonuniformly heated hydrophilic surface. Surface modifications can be applied to manipulate this migration process. In the present study, a three-dimensional color-gradient lattice Boltzmann model is used to investigate the droplet migration behavior on a series of wettability-confined tracks subject to a uniform temperature gradient. The model is validated by simulating the thermocapillary-driven flow with two superimposed planar fluids in a heated microchannel and the capillary penetration of a wetting fluid in a capillary tube. An in-depth study of the wettability-confined tracks confirms the capacity to manipulate the droplet migration process, that is, the wettability-confined tracks can accelerate thermocapillary migration compared with a smooth surface. The effects of changes in the viscosity ratio and interfacial tension are investigated, and it is found that a lower viscosity ratio and larger interfacial tension cause the droplet to migrate faster. Moreover, a systematic study of the track vertex angle is conducted, and the mechanism through which this parameter influences the droplet migration is analyzed. Then the effect of the track wettability on droplet migration is explored and analyzed. Finally, a serial wettability-confined track is designed to realize long-distance droplet migration, and the narrow side width of the connection region is found to play a key role in determining whether the droplets can migrate over long distances. The results provide some guidance for designing tracks that enable precise droplet migration control.

Modeling of three-phase displacement in three-dimensional irregular geometries using a lattice Boltzmann method

Three-phase displacement process in a porous media is significantly influenced by wettability of the solid surfaces. It remains a research challenge to model and simulate three-phase flows with moving contact lines, especially on arbitrary complex three-dimensional surfaces. We propose a color-gradient lattice Boltzmann model to simulate immiscible three-phase flows with contact-line dynamics. Unlike the previous models in dealing with wettability through assigning virtual mass fractions to the solid surfaces, the present model realizes the prescribed contact angles by correcting the orientation of the color-gradient parameter at the solid surfaces. We first validate this model against analytical solutions by simulating several typical cases, including a Janus droplet deposited on a flat surface and on a spherical surface, and the spontaneous imbibition of ternary fluids in a cylindrical tube. We then use it to study the displacement of residual oil during tertiary gas injection process. To mimic this process, gas is injected into a simple pore-throat connecting structure after water flooding. Results show that in displacement process, an oil spreading layer forms, which changes the oil flow state from adhering to the bottom wall to spreading over the entire interface between gas and water. Therefore, residual oil can be easily recovered in the form of gas-to-oil-to-water double displacement chain, leading to a high oil recovery regardless of the wetting properties of the solid surface. In the cases without the presence of oil spreading layer, increasing capillary number favors the oil recovery under certain wetting conditions only.

Lattice Boltzmann Simulation of Water Transport through Gas Diffusion Layers with Homogeneous and Heterogeneous PTFE Distributions

In recent years Polymer Electrolyte Fuel Cells have gained increasing attention in the e-mobility sector being a compelling powertrain solution and alternative to battery-driven electrical vehicles. Short refueling periods, long range capacity and reliability at high loads amongst others render the fuel cell technology advantageous, especially for heavy duty applications such as public transport and commercial vehicles [1]. These use cases however come along with challenging demands for stable operation due to their dynamic load profiles. In fuel cell operation such requirements can only be fulfilled when reactant gases are steadily provided while at the same time product water is efficiently removed. This multiphase counterflow is typically realized using carbon-based gas diffusion layers (GDLs) coated with a hydrophobic additive easing water removal. However, multiphase flow in GDLs is very complex and underlying transport phenomena not yet sufficiently understood. In addition, material design and experimental testing is expensive and long-lasting. A simulation approach offers therefore a large potential to deepen understanding of occurring transport phenomena while promoting material development.In our work we simulate the flow of liquid water through porous gas diffusion media using a 3D color-gradient Lattice Boltzmann model [2]. The simulations are carried out on complex geometries as derived by binarization of µCT images for a real microstructure of a Freudenberg GDL. To investigate the influence of mixed wettability on multiphase flows a hydrophobic additive (PTFE) is furthermore included using an in-house distribution algorithm. With this routine different homogeneous and heterogeneous spatial distributions of PTFE are realized within the GDL. Imposing variable capillary pressures we then derive material dependent effective transport parameters such as capillary pressure-saturation curves for different additive contents and distributions. By simulating the consecutive intrusion and drainage of water we recover a characteristic hysteresis behavior for the liquid saturation depending on the PTFE distribution. These investigations contribute on the one hand to a better comprehension of transport mechanisms within GDLs. On the other hand can these effective transport parameters be used in cell-level simulation suites offering a more realistic description for multiphase flow in porous GDL material as compared to commonly used relations such as the standard Leverett approach [3].The research leading to these results has received funding from the European Union's Horizon 2020 research and innovation program within the project ID Fast: Investigations on degradation mechanisms and Definition of protocols for PEM Fuel cells Accelerated Stress Testing, under grant agreement n°779565. Literature [1] Cullen, D.A., Neyerlin, K.C., Ahluwalia, R.K. et al., "New roads and challenges for fuel cells in heavy-duty transportation", Nat Energy, (2021), doi: 10.1038/s41560-021-00775-z[2] Rothman, D.H., Keller, J.M., "Immiscible cellular-automaton fluids", J. Stat. Phys. 52, 1119–1127 (1988), doi: 10.1007/BF01019743[3] Leverett, M.C., "Capillary Behavior in Porous Solids", Trans. 142, 152–169 (1941), doi: 10.2118/941152-G Figure 1: Workflow as developed for this research. Top left: GDL microstructures are reconstructed by binarization of µCT images. Top right: PTFE is distributed as a hydrophobic agent onto the binarized fiber structure using an in-house algorithm. Bottom: Effective transport parameters such as capillary pressure-saturation relations are derived by simulating liquid water transport through GDL microstructures using the Lattice Boltzmann Method (LBM). Figure 1

Numerical study of the effect of tortuosity and mixed wettability on spontaneous imbibition in heterogeneous porous media

Spontaneous imbibition in porous media plays an important role in numerous industrial processes, but its underlying mechanisms are still poorly understood due to the complicated structure and multiple surface properties of natural porous media. In order to fill this gap, a quasi-three-dimensional color-gradient lattice Boltzmann model is applied to simulate the spontaneous imbibition in heterogeneous porous media micromodels, where the influence of viscosity ratio, tortuosity and mixed wettability is systematically investigated. Results show that the tortuosity has less influence on imbibition than the viscosity ratio, which leads to unstable displacement for viscosity ratios smaller than unity and to stable displacement for viscosity ratios greater than unity. By establishing the power-law relationship between wetting fluid saturation and time, it is found that the scaling exponent is not only affected by tortuosity, but also related to pore throat structure of the micromodel. In addition, the mixed wettability is found to significantly influence the stability of displacement, especially when the contact angle difference of two constituents is large. Specifically, the greater the mixing degree of two wettabilities, the more unstable the displacement will become, which results in an enhanced interface roughening. Accordingly, the scaling exponent deviates more from the prediction from the Lucas-Washburn equation. Due to the reduced connectivity of flow paths, the wetting fluid imbibition rate in mixed wettability condition is lower than that in uniform wettability condition, no matter whether the latter theoretically corresponds to a slow displacement or not. Cited as: Diao, Z., Li, S., Liu, W., Liu, H., Xia, Q. Numerical study of the effect of tortuosity and mixed wettability on spontaneous imbibition in heterogeneous porous media. Capillarity, 2021, 4(3): 50-62, doi: 10.46690/capi.2021.03.02

Numerical study of thermocapillary migration behaviors of droplets on a grooved surface with a three-dimensional color-gradient lattice Boltzmann model

Thermocapillary actuation is used extensively in droplet-based microfluidic devices to manipulate the dynamic behaviors of droplets. In this study, a three-dimensional color-gradient lattice Boltzmann model is used to investigate the migration behaviors of droplets in the Wenzel state on a grooved surface that is subject to a uniform temperature gradient. On the solid surface, the wetting boundary condition is used to improve the accuracy of the simulations and to suppress spurious velocities at the contact line. The model is used to simulate the thermocapillary migration of a three-dimensional deformable droplet and the thermocapillary migration of a two-dimensional droplet on a solid substrate, and its accuracy is verified against theoretical predictions. The migration behavior of droplets on a smooth surface is investigated, and the flow field and corresponding temperature field around the droplets are analyzed. The experimental findings numerically confirm that a surface with micro-grooves parallel to the temperature gradient can accelerate thermocapillary migration to a greater extent than a smooth surface, indicating the influence of the grooves. The influence of the viscosity ratio is investigated, and it is found that the use of high-viscosity fluids is an effective means of obstructing migration. To determine the influence of surface roughness, a systematic and parametric study of groove depth and width is conducted. Finally, the influence of the orientation of the surface topography is investigated, and it is demonstrated that a surface with micro-grooves perpendicular to the temperature gradient can obstruct migration.

Influence of fractal surface roughness on multiphase flow behavior: Lattice Boltzmann simulation

Accurate characterization of surface roughness and understanding its influence on multiphase flow behavior are important for industrial and environmental applications such as enhanced oil recovery, CO2 geological sequestration, and remediation of contaminated aquifers. Although some experimental and simulation studies have been conducted for investigating surface roughness in regular geometry structures, a more realistic description of roughness and its quantitative influence on multiphase flow need to be further explored. In this study, an optimized color-gradient lattice Boltzmann model is applied to simulate the steady-state two-phase flow in two-dimensional porous media modeled by a fourth-order Sierpinski carpet. The model is validated by comparing with the analytical solution and literature results, indicating reliability of our method. Then, rough surfaces with different roughness height and surface fractal dimension are characterized by a modified Weierstrass-Mandelbrot function and these effects on two-phase flow are investigated systematically by our model. The results show that the surface roughness has a negative effect on single-phase and two-phase fluid flow, which implies that the absolute and relative permeabilities for both wetting phase and nonwetting phase decreases with the increase of roughness height or surface fractal dimension. In addition, the surface roughness has influence on the two-phase distribution, velocity distribution and fluid-fluid/fluid-solid interface area, especially under the neutral wetting condition. Our study provides a pore-scale insight into the effect of surface roughness on two-phase flow, which is important for a fundamental understanding on macroscopic multiphase flow behaviors.

Simulation of quasi-static drainage displacement in porous media on pore-scale: Coupling lattice Boltzmann method and pore network model

Lattice Boltzmann method (LBM) and pore network model (PNM) are two types of simulation methods for modelling the fluid flow in porous media at the pore scale. LBM is accurate in representing the pore structures but is computationally expensive, while PNM is very efficient but cannot capture the details of pore structures. In this work, we propose to couple these two methods to simulate two-phase drainage flow in porous media. To describe the throat geometry more accurately, an improved pore network extraction method is proposed based on watershed method, where throat bonds with real throat cross sections are extracted. A multi-relaxation-time color-gradient lattice Boltzmann model is adopted to simulate the flow properties for each throat bond, namely critical entry capillary pressure, capillary pressure – saturation relationship, single-phase conductance and relative conductance – saturation relationship for both phases, which are the input parameters for PNM simulations. To further improve the computational efficiency, five artificial neural network models are developed which relate the five flow properties to the actual shape of throat cross sections, where the shape is characterized by 9 parameters. The database consists of LBM simulations of the flow properties of 1421 throat cross sections extracted from 5 sandstone digital rocks. The trained artificial neural network models show much better performance than the conventional PNM when predicting the flow properties for each throat bond. Finally, the accuracy of the improved PNM coupled with LBM is validated by both the single-phase flow and two-phase drainage flow in a Berea sandstone.

Multiphase lattice Boltzmann method and its applications in phase-change heat transfer

<p indent=0mm>In the past three decades, the lattice Boltzmann (LB) method has been developed into an efficient numerical method for simulating fluid flow and heat transfer. It is a mesoscopic numerical approach, sitting in the middle between the molecular dynamic method and conventional numerical methods based on the continuum assumption. Unlike conventional numerical methods, the LB method is built on the mesoscopic kinetic equation. It tracks the evolution of a particle distribution function and then accumulates the particle distribution function to obtain the macroscopic properties. Owing to its kinetic nature, the LB method has exhibited many advantages over conventional numerical methods. For example, in the LB equation the convective operator is linear, whereas the convective terms of the Navier-Stokes equations are nonlinear. Moreover, in the LB simulations the complex boundary conditions can be formulated with the elementary mechanical rules such as the bounce-back rule according to the interaction of the “LB particles” with the solid walls. Furthermore, the LB method is ideal for parallel computing because of its explicit scheme and local interactions. Particularly, the intermolecular interactions of fluids can be easily incorporated into the LB method. As a result, the interface between different phases can arise, deform, and migrate naturally in the LB modeling without using any techniques to track or capture the interface, which is often required in the VOF or Level Set method. The existing multiphase LB models can be generally classified into four categories, i.e., the color-gradient model, the pseudopotential model, the free-energy model, and the phase-field model. In the color-gradient LB model, two distribution functions are introduced to represent two different fluids and a color-gradient-based perturbation operator is employed to generate surface tension. Moreover, a recoloring step is used in the color-gradient model so as to separate different phases. The pseudopotential LB model is the simplest and the most popular multiphase LB model. In this model, the fluid interactions are mimicked by an interparticle potential, through which the separation of different phases or components can be achieved naturally. Accordingly, the interface between different phases can arise, deform and migrate naturally. The free-energy LB model was developed based on thermodynamics considerations, which modifies the second-order moment of the particle equilibrium distribution function so as to include a non-ideal thermodynamic pressure tensor. The phase-field LB model is based on the phase-field theory, in which the interface dynamics is described by an order parameter that obeys the Cahn-Hilliard equation or a Cahn-Hilliard-like equation. In this paper we briefly review some recent advances in these multiphase LB models. Particularly, recent progress in the pseudopotential LB model is highlighted. It is shown that the thermodynamic consistency of the pseudopotential model can be achieved by adjusting the mechanical stability condition via an improved forcing scheme. Furthermore, an alternative approach is presented to tune the surface tension of the pseudopotential model and an improved contact angle scheme is introduced, which retains the advantages of the original virtual-density scheme but does not suffer from an unphysical thick mass-transfer layer near the solid boundary. Moreover, the applications of the pseudopotential LB model to boiling and condensation heat transfer are outlined.

Study on corium jet breakup and fragmentation in sodium with a GPU-accelerated color-gradient lattice Boltzmann solver

In this paper, the color-gradient lattice Boltzmann model (Saito et al., Phys. Re. E 98, 013,305, 2018) is used to study 3D hydrodynamic corium jet breakup and fragmentation in sodium. Firstly, an in-house GPU-accelerated color-gradient lattice Boltzmann solver is introduced in detail. Then, the solver is validated by comparing the simulation results with two demo Wood's metal jet experiments. Finally, the solver is used to study the characteristics and mechanisms of molten corium jet breakup and fragmentation in sodium under severe accident scenarios in a sodium-cooled fast reactor. The corium jet morphologies, breakup and fragmentation mechanisms, penetration depth, breakup length and fragment size distribution are extensively studied.

Improved three-dimensional color-gradient lattice Boltzmann model for immiscible two-phase flows.

In this paper, an improved three-dimensional color-gradient lattice Boltzmann (LB) model is proposed for simulating immiscible two-phase flows. Compared with the previous three-dimensional color-gradient LB models, which suffer from the lack of Galilean invariance and considerable numerical errors in many cases owing to the error terms in the recovered macroscopic equations, the present model eliminates the error terms and therefore improves the numerical accuracy and enhances the Galilean invariance. To validate the proposed model, numerical simulations are performed. First, the test of a moving droplet in a uniform flow field is employed to verify the Galilean invariance of the improved model. Subsequently, numerical simulations are carried out for the layered two-phase flow and three-dimensional Rayleigh-Taylor instability. It is shown that, using the improved model, the numerical accuracy can be significantly improved in comparison with the color-gradient LB model without the improvements. Finally, the capability of the improved color-gradient LB model for simulating dynamic two-phase flows at a relatively large density ratio is demonstrated via the simulation of droplet impact on a solid surface.