Lattice Boltzmann Model Research Articles

Pore-scale modeling of wettability alteration coupled two-phase flow in carbonate porous media

The Middle East marine carbonate reservoirs are the primary targets for global crude oil exploration and production. In contrast to the clastic rock reservoirs, the marine carbonate reservoirs have undergone more complicated deposition, diagenesis and transformation, and the rock surface tends to be oil-wet or mixed-wet. One of the most effective methods for enhancing oil recovery in marine carbonate reservoirs is the use of an ion matched (IM)-surfactant (S) system to alter the wettability of rock surfaces. In this paper, we propose a microscale mathematical model of wettability alteration-coupled fluid flow by considering oil–water two-phase flow, wettability alteration, solute advection- diffusion and surfactant adsorption. The proposed microscale mathematical model is solved using the multi-component lattice Boltzmann model, and its accuracy is further verified. Finally, the effects of displacing fluid, ion-matched water concentration and surfactant concentration on oil mobilization at pore-scale are studied. Results show that, ion-matched water has a positive effect on wettability alteration, and typically shifts the cross-point of oil–water relative permeability curve to the right. The concentration of ion-matched water primarily affects fluid morphology of the wetting-phase and has little effect on phase permeability. After adding surfactant to the ion-matched water, the Euler coefficient of oil-phase gradually increases as the displacement continues, a large amount of remaining oil is gradually dispersed into scattered oil droplets and the oil-phase relative permeability is further improved.

An Allen-Cahn-based lattice Boltzmann model for two-phase flows with surfactants

An Allen-Cahn-based lattice Boltzmann model for two-phase flows with surfactants

Lattice Boltzmann Model for Rarefied Gaseous Mixture Flows in Three-Dimensional Porous Media Including Knudsen Diffusion

Numerical modeling of gas flows in rarefied regimes is crucial in understanding fluid behavior in microscale applications. Rarefied regimes are characterized by a decrease in molecular collisions, and they lead to unusual phenomena such as gas phase separation, which is not acknowledged in hydrodynamic equations. In this work, numerical investigation of miscible gaseous mixtures in the rarefied regime is performed using a modified lattice Boltzmann model. Slip boundary conditions are adapted to arbitrary geometries. A ray-tracing algorithm-based wall function is implemented to model the non-equilibrium effects in the transition flow regime. The molecular free flow defined by the Knudsen diffusion coefficient is integrated through an effective and asymmetrical binary diffusion coefficient. The numerical model is validated with mass flow measurements through microchannels of different cross-section shapes from the near-continuum to the transition regimes, and gas phase separation is studied within a staggered arrangement of spheres. The influence of porosity and mixture composition on the gas separation effect are analyzed. Numerical results highlight the increase in the degree of gas phase separation with the rarefaction rate and the molecular mass ratio. The various simulations also indicate that geometrical features in porous media have a greater impact on gaseous mixtures’ effective permeability at highly rarefied regimes. Finally, a permeability enhancement factor based on the lightest species of the gaseous mixture is derived.

Enhancement of pool boiling under reduced gravity by the synergistic effect of non-uniform surface structure and electric field: A lattice Boltzmann study

In this paper, a novel non-uniformly structured surface with primary and secondary pillars is conceived to be coupled with the action of an electric field to enhance pool boiling under reduced gravity. On the surface, the secondary pillars are distributed diagonally. A three-dimensional thermal lattice Boltzmann (LB) model combined with an electric field model is employed to investigate the boiling heat transfer performance on the non-uniformly pillar-structured surface and the associated boiling enhancement mechanism. It is found that the synergistic effect of the non-uniform surface structure and the electric field leads to a non-equilibrium electric force that causes the bubbles to be pushed away from the center of the heating surface, which promotes an earlier departure of the bubbles and provides more paths for the fresh liquid replenishment. As a result, the boiling performance under reduced gravity can be significantly enhanced by utilizing such a synergistic effect, with both the critical heat flux (CHF) and the maximum heat transfer coefficient (HTC) on the non-uniformly pillar-structured surface exceeding those on a uniformly pillar-structured surface under normal gravity. Moreover, the influences of the distribution of the secondary pillars on the boiling performance under reduced gravity are also studied. It is shown that the non-uniformly pillar-structured surface whose secondary pillars are distributed diagonally performs much better than those with the secondary pillars being distributed crossly and centrally, and the synergistic effect of the non-uniform surface structure and the electric field results from tuning the distribution of the non-uniform electric force.

Pore-scale study of [formula omitted] desublimation in a contact liquid

Cryogenic carbon capture (CCC) designed to operate in a contact liquid is an innovative technology for capturing CO2 from industrial flue gases, helping mitigate climate change. Understanding CO2 desublimation properties in a contact liquid is crucial to optimizing CCC, but is challenging due to the complex physics involved. In this work, a multiphysics lattice Boltzmann (LB) model is developed to investigate CO2 desublimation in a contact liquid for various operating conditions, with the multiple and fully-coupled physics being incorporated (i.e., two-phase flow, heat transfer across three phases, CO2 transport between the gas and liquid, homogeneous and heterogeneous desublimation of CO2, and solid CO2 generation). The CO2 desublimation process in a contact liquid is well reproduced. Moreover, parametric studies and quantitative analyses are set out to identify optimal conditions for CCC. The decreasing liquid temperature (Tl) and flue gas temperature (T0) are found to accelerate the CO2 desublimation rate and enhance the CO2 capture velocity (vc). However, excessively low Tl and T0 values should be avoided. These conditions increase the energy consumption of cooling while only marginally improving vc, due to the limited CO2 supply. The CCC system performs effectively when purifying flue gases with high CO2 content (Y0). This is because the large Y0 accelerates the CO2 desublimation rate and enhances the overall CO2 capture efficiency. A high gas injection velocity (or Pe) is beneficial for amplifying vc by increasing the gas–liquid interfaces and enhancing the CO2 supply. Nevertheless, too high a Pe should be avoided, as it hinders the transport of CO2 to the liquid or solid CO2 surfaces, ultimately restricting the amount of CO2 available for desublimation and inhibiting the enhancement of vc. This study develops a viable LB model to investigate CO2 desublimation in a contact liquid for varying conditions, which advances the knowledge base of CCC and facilitates its industrial applications.

A lattice Boltzmann model with sharp interface tracking for the motion and growth of dendrites in non-equilibrium solidification of alloys

A lattice Boltzmann model (LBM) with sharp interface tracking is developed to simulate the motion and growth of dendrites in non-equilibrium solidification of alloys. The model is validated through comparative analysis with the drafting-kissing-tumbling (DKT) phenomena of two and three particles and the continuous growth model (CGM), and demonstrates its computational efficiency advantage without compromising accuracy by comparison with the multi-phase field (MPF) model. Subsequently, the model is utilized to investigate the dendrite morphology transition and primary dendritic arm spacing (PDAS). It is found that the velocity dependent solute partition and the resulting changes in constitutional undercooling strongly influence the estimated morphology region and PDAS. Moreover, the segregation and microstructure evolution during the rapid solidification were studied. And the results revealed that free dendrites lead to significant changes in microstructure and segregation under the influence of non-equilibrium effects. This work illustrates the great potential of the proposed model in simulating dendrites and microstructure evolution under a wide range of solidification conditions. Its suitability for extreme conditions and non-equilibrium solidification can contribute to the understanding of microstructure formation patterns and solute segregation in rapid solidification.

Progress in theory and simulations of lattice Boltzmann method for heat transfer enhancement on phase change

As a general phenomenon in science and engineering, phase change has appeared and been applied in many aspects. However, there is a sufficient necessity to enhance the heat transfer in the phase change process due to the low heat transfer efficiency of the phase change material. In order to improve the efficiency of heat transfer during the phase change process, theory and numerical simulations based on computational fluid dynamics, especially the lattice Boltzmann (LB) method, are reviewed. The LB method has become a strong numerical method for heat and mass transfer and fluid dynamics because of its mesoscopic nature and a series of unique merits brought by this nature. In this article, progress in theory and simulations of the LB method for heat transfer enhancement on phase change is reviewed. This review first introduces the basic theories and models of the LB method for flow field and temperature field. Afterward, the development of the LB models for tracing the phase interface is reviewed. The application of the LB method for phase change and investigations of the heat transfer enhancement in the phase change process are also discussed. Finally, future developments in the LB method for phase change problems are prospected.

Evaluating the effectiveness of the modified multi-scale multi-physics coupled model for solid oxide fuel cells: A comparative analysis

A multi-scale multi-physics coupling numerical model serves as an effective tool to study the performance and improve the efficiency of solid oxide fuel cells (SOFCs) and provides the theory and data support for optimizing SOFC structure and operational strategy. To improve the accuracy and reliability of the model, this work established a modified simulation model that considers the effect of operational, structural, and physical parameters of SOFCs. First, the electrochemical kinetics equation, multi-component diffusion lattice Boltzmann (LB) model, and heat transfer LB model are modified by incorporating the reaction gas molar fraction, gas mixture concentration, temperature, and other parameters. Second, a regional hierarchical modeling strategy is proposed, and the multi-scale coupling model is modified by coupling mass and heat transfer. Third, considering the effect of carbon monoxide molar fraction, temperature difference, concentration change and porosity on electrochemical, mass, and heat transfer processes, the effectiveness of modification model is analyzed and validated. Results demonstrate that the modified model considerably improves the numerical simulation to handle the complex operational conditions of SOFCs. The modified model's predictions show better accuracy compared with experimental data, while maintaining consistency with the trends predicted by the original numerical models.

Lattice Boltzmann modeling of individual and collective cell dynamics in the presence of fluid flows

Lattice Boltzmann modeling of individual and collective cell dynamics in the presence of fluid flows

Three-dimensional central-moment pseudopotential lattice Boltzmann model with improved discrete additional term

In this work, a three-dimensional central-moment pseudopotential lattice Boltzmann model is developed to simulate a two-phase flow and wetting phenomena. In this model, an improved discrete additional term is proposed to regulate the thermodynamic consistency and surface tension. Different from the discrete additional terms in previous models where only low-order terms are derived at the macroscopic Navier–Stokes equation level, high-order terms are correctly constructed at the mesoscopic lattice Boltzmann equation level in the present improved discrete additional term so that the high-order central moments can be modified in the collision step. With the improved discrete additional term, the simple relationship between the interaction force and the pseudopotential functions is well preserved. On this basis, a simplified wetting boundary scheme is further proposed, which eliminates the complex process for choosing proper characteristic vectors and interpolation. Numerical simulations demonstrate that the proposed model can achieve better performance in thermodynamic consistency, Galilean invariance, numerical stability and computational efficiency, and have great ability to simulate two-phase flow and wetting phenomena on realistic conditions.

Examining a Conservative Phase-Field Lattice Boltzmann Model for Two-Phase Flows

In this study, a conservative phase-field lattice Boltzmann model is examined for simulating immiscible two-phase flows with large density and viscosity ratios. This model is built upon the Allen–Cahn equation, incorporating a filtered collision operator and high-order corrections in the equilibrium distribution functions. The numerical model is also integrated with the volumetric boundary scheme and the immersed boundary method to achieve various stationary and moving boundary conditions on arbitrary geometries for different application scenarios. A comprehensive evaluation of this phase-field solver is conducted through a range of academic and industrial cases. First, droplet splashing cases at different Reynolds numbers are studied. The phase-field LB model effectively captures the surface wave motion and splashing of the droplet, although some smearing of small structures is observed due to the diffused interface property of the numerical model. Second, a tuned liquid damper is simulated, accurately capturing sloshing forces on solid walls. In the simulation of a dam-breaking case, predicted gauge pressure and free-surface elevation time histories compare well with experimental data. Lastly, a gearbox case under dip lubrication is simulated, with both the gearbox churning loss and oil distribution being well predicted across a range of rotating speeds. The validation studies demonstrate the effectiveness of the present phase-field lattice Boltzmann model in simulating immiscible two-phase flows with large and realistic density and viscosity ratios. The strengths, limitations, and weaknesses of the conservative phase-field LB model are discussed, and suggestions for the development and application of this numerical model are provided.

Lattice Boltzmann Modeling of Forced Imbibition Dynamics in Dual-Wetted Porous Media

Forced imbibition dynamics are critical for enhancing recovery rates in reservoirs, as efficient fluid displacement directly impacts resource extraction. This study employs the Zou-He velocity boundary condition and a modified convective boundary condition (mCBC) within the multi-component Shan-Chen lattice Boltzmann method (LBM), thus facilitating unobstructed flow of multi-component fluids at the outlet while maintaining constant outlet pressure. The model's validity was established through outflow tests of immiscible droplets in channels. Its accuracy was further confirmed by comparing results from forced imbibition dynamics tests in dual-wetted pores with theoretical predictions. A symmetrical porous medium was constructed using the stacking method, achieving dual wettability by fixing the contact angle in the upper region and varying it in the lower region. We performed 20 simulation sets under unfavorable viscosity ratios and varying capillary numbers, focusing on overall displacement efficiency before and after breakthrough, and employing energy balance equations to evaluate the dominant forces. Results reveal that capillary forces predominantly dictate forced imbibition dynamics in low capillary number scenarios. In strongly wetted regions, the invading fluid fully occupies pore spaces; however, in weakly wetted regions, displacement efficiency significantly declines as wettability approaches neutrality, even nearing zero. As capillary numbers increase, viscous forces become more prominent, controlling dynamics and leading to fingering and trapping of defending fluids. In weakly wetted areas, the increasing influence of viscous forces enhances fluid displacement, resulting in significant improvements in overall displacement efficiency compared to conditions dominated by capillary forces.

Inertial migration of cylindrical micelles formed by comb-like copolymer in Poiseuille flow

By combining the lattice Boltzmann model of fluid flow with the molecular dynamics model of copolymers, we investigate the inertial migration of cylindrical micelles, which is obtained by controlling the length ratios of hydrophilic and hydrophobic segments in a comb-like copolymer. Our results demonstrate that cylindrical micelles gradually deviate from the center of the nanochannel with increasing Reynolds number (Re). For the same Re, the larger the cylindrical micelle is, the closer it is to the center of the nanochannel. Importantly, we find that the change in the equilibrium position is particularly pronounced at Re less than 0.1, while the trend becomes smoother at Re greater than 0.1, which is because of the transition of micelles from cylindrical to disk-like shapes when Re is smaller than 0.1, and does not change as Re further increases. This work provides an understanding of cylindrical micelles' inertial migration, particularly in identifying the effect of morphological changes on the equilibrium position, which could lead to significant advancements in the inertial migration of polymer micelles.

A pore-scale investigation of viscous coupling effect on immiscible two-phase flow in porous media

Viscous coupling effect plays a significant role in immiscible two-phase flow within porous media, while its influence on relative permeability remains uncertain. In this paper, an improved MRT-based viscosity-modified multicomponent multiphase (MCMP) pseudopotential lattice Boltzmann model, capable of handling high viscosity ratio, is employed to simulate two-phase flow with different viscosities in a cross-array circular structure and a real rock structure, respectively. The applicability of this model for two-phase flow with various viscosity ratios has been verified by some typical tests. Systematically, the effects of viscosity ratio, structural configuration, and wetting condition on the relative permeability curves are investigated in conjunction with their component distributions and velocity fields at different two-phase saturations. These results indicate that due to the two-phase flow competition under different structural conditions, the viscous coupling effect has varying degrees of impacts on the mobility of thin phase and viscous phase. Further, the mechanism of two-phase lubricating effect is also discussed under different wetting conditions at Darcy flow regime.

Cellular Automata Coupled with Two‐Phase Lattice Boltzmann Model for Modeling of Kinetics of Formation and Structure of Silica‐Based Sol–Gel Materials

A numerical model describing the sol–gel process on a mesoscopic scale is presented. The model is implemented as a cellular automaton‐based system, specifically reaction‐limited aggregation merged with two‐phase lattice Boltzmann method, which allows to describe the sol–gel process together with microscopic phase separation occurring during this process. The influence of model parameters on the structural properties of the resulting gel porosity, mesoporosity, and specific surface area, as well as on the kinetics of the gelation process: the shape of the kinetics curve and the structure formation time, is examined. It is proposed to combine the model parameters with the composition of the reaction mixture (the content of individual reagents and catalysts) and the process conditions.

Modified lattice Boltzmann model based on the system performance optimization life cycle for decaying isotropic turbulence simulations

A new optimization strategy based on system performance optimization life cycle (SPOLC) is introduced for high-performance lattice Boltzmann simulations of three-dimensional decaying isotropic turbulence. This strategy improves the performance of turbulent flow simulations in periodic boxes at different resolutions using the lattice Boltzmann method (LBM). The strategy improves the performance by modifying the lattice Boltzmann model, mathematical representation, computational algorithm, software implementation, and computing hardware utilization. The modifications include: (1) Establishing the slice concept as a logical grouping layer added to the LBM, applying an aggregation–disaggregation mechanism, enabling two-dimensional (2D) operation on the three-dimensional (3D) model, (2) improving lattice data access pattern by using an alternative one-dimensional (1D) array for numerical representation instead of the 3D cubic representation, (3) major reduction in memory access iterations by switching from function-wise iteration method to lattice-wise iteration method by applying code fusion to the streaming, velocity and collision model functions and iterations, (4) applying process parallelization and data vectorization, (5) achieving a much more efficient utilization of modern compute units by increasing the adaption of stream processing model. Furthermore, a correctness validation process has been applied by conducting lattice-wise value comparisons between the proposed solution output and the original implementation output. Simulations of decaying isotropic turbulence at resolutions ranging from [Formula: see text] to [Formula: see text] using the LBM are carried out for these purposes. Calculations are performed on two systems with distinct specifications, to validate the effectiveness and portability of the SPOLC strategy. The calculation times are significantly reduced after applying the SPOLC strategy on S1 with the lattice Boltzmann relaxation time [Formula: see text] by over [Formula: see text] compared to S2’s original time, increasing to [Formula: see text] at higher resolutions. Different features of the flow fields are depicted and their characteristics are discussed. Thin tubes are visualized, and the energy spectra are studied. All fields are initialized by a forced turbulent field simulated in a previous study using the LBM.

An automatic approach for the stability analysis of multi-relaxation-time lattice Boltzmann models

This paper is concerned with the weighted L2-stability of the lattice Boltzmann method (LBM) for the incompressible Navier-Stokes equations. Such stability is formulated for the linearized LBM and can lead to convergence proof of the nonlinear problem. A key step in this stability analysis is to find an appropriate decomposition for the Jacobian matrix of the collision term. For multi-relaxation-time (MRT) models, it is very difficult to analytically obtain such a decomposition and how to overcome this difficulty for MRT models is still a challenge. In this paper, we propose an automatic approach to prove the weighted L2-stability of the LBM with general collision models. Instead of exploring the decomposition for each specific model, we partially fix the decomposition and turn to show the symmetry and semi-negative definiteness of the other part of the decomposition, which can be automatically examined by a simple computer code. We apply our automatic approach to ten MRT models and stability conditions are generated by the code immediately. In particular, for the popular D2Q9 orthogonal MRT model, the stability condition we obtained has one less constraint than that given in previous work. As verifications, we also provide some analytical proofs for the stability of orthogonal and weighted-orthogonal MRT models. The proofs are much more complicated than the automatic approach, not to mention that those for nonorthogonal models are unavailable. These demonstrate the efficiency and superiority of the proposed automatic approach. With this approach, proving the weighted L2-stability and thereby the convergence of general MRT models becomes straightforward.

Lattice Boltzmann Simulation of Spatial Fractional Convection-Diffusion Equation.

The space fractional advection-diffusion equation is a crucial type of fractional partial differential equation, widely used for its ability to more accurately describe natural phenomena. Due to the complexity of analytical approaches, this paper focuses on its numerical investigation. A lattice Boltzmann model for the spatial fractional convection-diffusion equation is developed, and an error analysis is carried out. The spatial fractional convection-diffusion equation is solved for several examples. The validity of the model is confirmed by comparing its numerical solutions with those obtained from other methods The results demonstrate that the lattice Boltzmann method is an effective tool for solving the space fractional convection-diffusion equation.

Study on the evolution of heterogeneous double-cavity induced by near-wall and the fluctuation characteristics of load field

It is well known that the collapse of heterogeneous multi-cavity near the wall will induce the fluctuation of the load field. To address this problem, the Lattice Boltzmann Method (LBM) is applied to model the three-phase coupling between gas-liquid-solid. The objective is to investigate the evolution of heterogeneous double bubbles and the spatial-temporal distribution characteristics of wall loads induced near the wall. In this study, the pseudopotential Multi-Relaxation-Time Lattice Boltzmann Model (MRT-LBM) and the Carnahan-Starling Equation of State (C-S-EOS) with an extended format for the external force term are used. The effects of the distance of the bubble to the wall, the pressure differences between the inside and outside of the bubble, and the relative size of the bubble on the dynamic evolution and the load distribution characteristics of heterogeneous multi-bubbles near the wall are investigated in order to determine the influence of these factors. Under a two-dimensional pressure field, the collapse process of double cavitation bubbles is visualized. Through the flow field, the morphological changes of the cavitation bubble collapse near the wall are also described. Various parameters are found to have an influence on the evolution of double cavitation bubbles near the wall and the resulting load field. The study employs the Lattice Boltzmann Method and the Potential Model for the analysis of the heterogeneous bubble collapses in the near wall region.

A novel framework of the lattice Boltzmann model for multilayer shallow water systems

This study proposes a novel framework of the lattice Boltzmann model for multilayer shallow water equations, considering the mass and momentum exchanges between layers (LABMSWE+). Compared with the original LABMSWE model consisting of N two-dimensional lattice Boltzmann method for shallow water equation (LABSWE) models, the new model includes 1+N LABSWE models. The singular LABSWE model with unit relaxation time is introduced to update the total water depth, and thus, the layer water depths can be obtained explicitly through the fixed layer ratios. The N-layer LABSWE models with the multiple-relaxation-time operator evolve the layer velocities. These two modules are coupled by the total water depth and depth-averaged velocities. The constructed model avoids the freely variable layer thicknesses, which is considered as the main source of the instability. In addition, the mass exchanges enable this model to simulate vertical circulation flows, which are beyond the application of the LABMSWE model. Several numerical tests are then conducted to validate the proposed model. The results show that it exactly satisfies the C-property. In addition, the central difference scheme is more stable and accurate than the upwind and nonequilibrium schemes in the computing of the mass exchanges. The numerical results have an excellent agreement with analytical solutions and reference data, while some unstable and nonphysical results are obtained by the original LABMSWE model. Moreover, the computational time is about 40%–60% of that for the MIKE3, a finite volume solver for the three-dimensional shallow water equations by the Danish Hydraulic Institute.