Lattice Boltzmann Model Research Articles

An efficient thermal lattice Boltzmann method for simulating three-dimensional liquid–vapor phase change

In this paper, a multiple-relaxation-time lattice Boltzmann (LB) approach is developed for the simulation of three-dimensional (3D) liquid–vapor phase change based on the pseudopotential model. In contrast to some existing 3D thermal LB models for liquid–vapor phase change, the present approach has two advantages: for one thing, some gradient terms, such as the gradient of volumetric heat capacity and the Laplacian term of temperature, that must be computed with finite-difference scheme in previous works is not needed for the present thermal model. For another, the current model is constructed based on the seven discrete velocities in three dimensions (D3Q7), making it more efficient and much easier to be implemented. Also, based on the scheme proposed by Zhou and He (1997), a pressure boundary condition for the D3Q19 lattice is proposed to model the multiphase flow in open systems. This model is then validated by considering the temperature distribution in a 3D saturated liquid–vapor system, the d2 law, the droplet evaporation on a heated surface and the nucleate boiling. It is observed that the numerical results fit well with the analytical solutions, and the results of the finite difference method or the experimental data. Our numerical results indicate that the present approach is reliable and efficient in dealing with the 3D liquid–vapor phase change.

Lattice Boltzmann modeling of buoyant convection in an enclosure with differentially heated porous cylinders

This study employs the Lattice Boltzmann Method, utilizing the Darcy-Brinkmann-Forchheimer model, to investigate buoyancy-driven heat transfer within an enclosure featuring differentially heated porous cylinders. The enclosure comprises two isothermal cylinders (one hot and one cold) separated by a distance within a cooled enclosure. It comprehensively assesses the impact of Darcy numbers ranging from 10-6 to 10-2, Rayleigh numbers spanning from 104 to 106, and various cylinder orientations. Specifically, five distinct configurations are considered, including horizontal alignment of hot and cold cylinders (Case A), vertical alignment of hot and cold cylinders (Cases B & C), and diagonal alignment of hot and cold cylinders (Cases D & E). The key findings highlight that the highest heat dissipation occurs in proximity to the heated cylinder, with certain orientations consistently demonstrating superior heat dissipation. The study explores the heat and flow characteristics at different Rayleigh numbers, examining these through streamlines and isotherms. Also, the impact of cylinder permeability on heat transfer features is comprehensively analyzed and reported. The findings of this research offer valuable insights for optimizing the placement of electronic components within compact electronic cabinets, with potential benefits for electronic cooling and thermal management.

Phase-field lattice Boltzmann model with singular mobility for quasi-incompressible two-phase flows.

In this paper, a lattice Boltzmann for quasi-incompressible two-phase flows is proposed based on the Cahn-Hilliard phase-field theory, which can be viewed as an improved model of a previous one [Yang and Guo, Phys. Rev. E 93, 043303 (2016)2470-004510.1103/PhysRevE.93.043303]. The model is composed of two LBE's, one for the Cahn-Hilliard equation(CHE) with a singular mobility, and the other for the quasi-incompressible Navier-Stokes equations(qINSE). Particularly, the LBE for the CHE uses an equilibrium distribution function containing a free parameter associated with the gradient of chemical potential, such that the variable (and even zero) mobility can be handled. In addition, the LBE for the qINSE uses an equilibrium distribution function containing another free parameter associated with the local shear rate, such that the large viscosity ratio problems can be handled. Several tests are first carried out to test the capability of the proposed LBE for the CHE in capturing phase interface, and the results demonstrate that the proposed model outperforms the original LBE model in terms of accuracy and stability. Furthermore, by coupling the hydrodynamic equations, the tests of double-stationary droplets and droplets falling problems indicate that the proposed model can reduce numerical dissipation and produce physically acceptable results at large time scales. The results of droplets falling and phase separation of binary fluid problems show that the present model can handle two-phase flows with large viscosity ratio up to the magnitude of 10^{4}.

A study on melting characteristics of micron aluminum particles by lattice Boltzmann method

In this article, a two-dimensional lattice Boltzmann model, utilizing enthalpy as a basis, has been constructed to explore the melting behavior of aluminum particles in the micron size range. The study investigates the impacts of several key factors such as particle size, Rayleigh number, Stefan number, and porosity on temperature distribution, liquid fraction, solid-liquid interface, and melting end time. The findings demonstrate that an increase in particle size stimulates the melting process, with a weakened effect observed as particle size continues to increase. Rayleigh number has a significant effect on natural convection and heat transfer, promoting the development of these processes. Additionally, Stefan number presents a noticeable impact on the melting process, with a more apparent effect in the range of low Stefan numbers. Finally, the increase of porosity proves to be a compelling factor in the promotion of the melting process.

GPU parallel computing based on PF-LBM method for simulating dendrites growth under natural convection conditions

This study introduces a GPU-based parallel computing approach that combines the phase-field model (PF) and the lattice Boltzmann model (LBM). By establishing a coupled multiphase field model incorporating physical external fields such as flow field, temperature field, and solute field, the research simulates the growth of single grains and multiple grains under the influence of natural convection. The variations in dendritic morphology, flow field, and solute field during dendritic solidification processes are observed. Initially, the study analyzes the morphology of equiaxed dendrites and the growth patterns of primary dendrites arms under natural convection conditions. The evolution of equiaxed dendrites in single grains and multiple grains under various conditions is investigated. Furthermore, the study explores the impact of different anisotropy strengths on the growth of single grains and multiple grains under natural convection. Notably, a distinct “necking” phenomenon is observed when the anisotropy strength of a single grain is 0.05. In the case of multiple grains, where competition between dendrites is present in addition to the influence of natural convection, a pronounced “necking” phenomenon is evident at an anisotropy strength of 0.03. Moreover, OpenCL parallel technology is designed on the GPU platform to accelerate the solution of the model. The parallelization of the phase-field model coupled with the LBM model on the GPU demonstrates a clear advantage. The parallel computation based on GPU not only exhibits absolute superiority but also shows more significant acceleration effects as the computational domain increases.

Enhancing flow boiling using a microchannel with pillar–cavity mixed structures: A lattice Boltzmann study

Enhancement of flow boiling in microchannels through adjusting surface structures has attracted much attention in recent years. However, most of the existing studies focus on homogeneous surface structures. In the present study, a novel vertical microchannel with pillar–cavity mixed structures is conceived to enhance flow boiling heat transfer. In the mixed microchannel, cavities and pillars are distributed on the vertical sidewalls of the upstream and downstream flow channel, respectively. A multicomponent phase-change lattice Boltzmann model is employed to investigate the flow boiling performance of the mixed microchannel. Numerical results show that the cavities in the mixed microchannel can supply effective nucleation sites for timely departure of bubbles, while the pillars in the mixed microchannel can suppress the expansion of the vapor film from the outlet toward the inlet. Moreover, the bubbles from the upstream cavities can entrain the cold liquid to disrupt the vapor film covering the downstream pillars for the rewetting of the heated surface. As a result, the flow boiling performance can be significantly enhanced by the synergistic effect of the pillar and cavity structures, and the best flow boiling performance can be achieved by controlling the ratio of the number of cavities to the total number of structures in the mixed microchannel to optimize the synergistic effect. The influences of the structural parameters of pillars and cavities on the flow boiling performance have also been studied. It is found that the height of the pillars and the depth of the cavities have important influences on the flow boiling performance, while the boiling performance is not sensitive to the width of the pillars.

Three-dimensional modelling of cavitation bubble collapse using non-orthogonal multiple-relaxation-time lattice Boltzmann method

In this study, we employ a three-dimensional (3D) non-orthogonal multiple relaxation time (MRT) pseudo-potential lattice Boltzmann (LB) model to simulate the dynamics of cavitation bubble evolution. We benchmark the model against the Laplace law and the Rayleigh–Plesset (R–P) equation, confirming its efficacy in accurately capturing cavitation phenomena. We then apply the model to examine the collapse dynamics of a singular bubble located near a plane wall boundary and right-angled wall corner. Additionally, the dynamic interactions among five cross-shaped bubbles revealed the dimensionless jet volume Vj*, which is the ratio of the jet volume to the maximum bubble volume, exhibits a power relationship with the bubble distance δ. The simulation results demonstrate the accuracy of the model in discerning the effect of the wall boundary and the protective mechanisms inherent to multi-bubble interactions. These results further validate the aptness of the model for cavitation bubble dynamics simulations. Moreover, the tested case studies provide a foundational basis for future research into more complex cavitation behaviours. In summary, the developed 3D non-orthogonal MRT pseudo-potential LB model is capable of reproducing fluid flows, capturing pressure waves, and measuring wall pressures. Our work provides a deep insight into cavitation bubble dynamics and a solid basis for both applied and fundamental research.

Magnetic field induced acceleration or deceleration of bubble rising inside ferrofluids: A fractional step lattice Boltzmann investigation

Bubble rising process inside a ferrofluid commonly occurs in industrial applications, but the interface deformation, the bubble motion, and their underlying mechanisms are not fully understood. In the present study, a magnetic field coupling fractional step lattice Boltzmann model is employed to simulate the complex interface behaviors and the magnetic flux density distribution during the bubble rising process. The magnetic field is solved by a self-correcting Poisson equation solver, and the flow properties and the interface are first predicted by the equilibrium distribution functions and then corrected by the nonequilibrium distribution functions and source terms. The acceleration and deceleration of the rising bubble under the combination effects of the hydrodynamic force, the surface tension force, and the magnetic force are investigated. This study aims to reveal the mechanisms of the magnetic effects, especially the magnetic field induced bubble interface deformation, and the acceleration and deceleration effects on the bubble rising process. Applying a vertical uniform magnetic field, the bubble rising velocity accelerates with the magnetic field strength, and various shape types are observed. However, when a horizontal uniform magnetic field is applied, the bubble rising velocity decelerates with an increase in the magnetic field strength. Meanwhile, the initial shape remains elongated only along the magnetic field direction. The numerical results from both the conditions show that the external magnetic field indirectly impacts on the bubble rising process through the squeezing effect generated by the surrounding magnetized ferrofluid. A shape regime map is presented for different bubble shapes during the rising process over wide range of the parameter space. Besides, by employing an appropriate combination of the surface tension and the magnetic field strength and direction, it is possible to either accelerate or decelerate the rising bubble. These findings not only provide valuable insights into the underlying mechanisms of the bubble deformation and the rising velocity, but also offer potential technical support for industrial applications.

Study of experimental and numerical simulation on the influence of gravel on the interflow of slope land.

The formation of interflow is of great significance for the stability of mountain slopes and soil erosion. Hillsides are often covered with a certain amount of gravel, and research on interflow of slope land with different gravel ratios needs to be carried out. This article is based on indoor experiments and numerical models to study the formation law of interflow in hillside soil under different gravel coverage ratios. It was found that the interflow in the soil rapidly increased in the early stage and began to decrease after briefly reaching equilibrium. The formation of interflow is a complex process that is related to slope, soil characteristics, and rainfall intensity, but the correlation is not high when viewed separately. The lattice Boltzmann model can effectively simulate such problems and achieve high simulation accuracy. The [Formula: see text] of the simulated data and measured data ranged from 0.5217 to 0.7403, and [Formula: see text] of the simulated data and measured data ranged from 0.4051 to 0.5711.

Comparative Study of 2D Lattice Boltzmann Models for Simulating Seismic Waves

The simulation of seismic wavefields holds paramount significance in understanding subsurface structures and seismic events. The lattice Boltzmann method (LBM) provides a computational framework adept at capturing detailed wave interactions, offering a new approach to improve seismic wavefield simulations. Our study involves a novel comparative analysis of wavefields using different lattice Boltzmann models, focusing on how relaxation times, discrete velocity models, and collision operators affect simulation accuracy and efficiency. We explore the impacts of distinct relaxation times and evaluate their effects on wave propagation speed and fidelity. By incorporating four discrete velocity models of LBM, we innovatively investigate the trade-off between spatial resolution and computational complexity. Additionally, we delve into the implications of employing three collision operators—single relaxation time (SRT), two relaxation times (TRT), and multiple relaxation times (MRT). By comparing their accuracy and stability, we provide insights into selecting the most suitable collision operator for capturing complex wave interactions. Our research provides a comprehensive framework to optimize the LBM parameters, enhancing both accuracy and efficiency in seismic wave simulations, and offers valuable insights to benefit wave simulation across diverse disciplines.

Self-consistent force scheme in the spectral multiple-relaxation-time lattice Boltzmann model.

In the present work, the force term is first derived in the spectral multiple-relaxation-time high-order lattice Boltzmann model. The force term in the Boltzmann equationis expanded in the Hermite temperature rescaled central moment space (RCM), instead of the Hermite raw moment space (RM). The contribution of nonequilibrium RCM moments beyond second order are neglected. For the collision operator in the RCM space, each order of the force term can be incorporated directly. Through the transformation between the RCM space and the RM space, the force term for practical numerical implementation in the RM space can be derived. It can be demonstrated that the present force scheme is self-consistent for the isothermal flow and compressible thermal flow with adjustable Prandtl number via the numerical experiments.

Two-phase flow dynamics study in the trapezoidal gas channel of PEM fuel cell based on lattice Boltzmann model

ABSTRACT Water management is a critical challenge in ensuring the performance and durability of low-temperature proton exchange membrane fuel cells (PEMFCs). This study utilizes the phase-field lattice Boltzmann method to conduct three-dimensional numerical simulations, investigating the dynamics of two-phase flow in the cathode gas channel (GC) of PEMFC with a trapezoidal cross-section. The effects of the water inlet location, the surface wettability of GC, the open angle of GC, and the air velocity on liquid water distribution and discharge are analyzed. The results indicate that positioning the water inlet in the middle of the GC significantly enhances PEMFC performance while having minimal impact on average pressure drop. A wall contact angle of 70° or 110°Can optimize fuel cell performance from different directions. Setting a wall contact angle at 70° optimizes gas flow stability and maintains a low-pressure drop value for the GC. A wall contact angle of 110° focuses on optimizing gas reactant diffusion ability into porous electrodes and GC drainage rate. An opening angle of 55° for the trapezoidal gas channel improves overall fuel cell performance. Increasing air velocity facilitates the film flow formation of liquid water on top wall surfaces within the GC.

Numerical study on the impact of carbon deposition on methane/steam mass transport in solid oxide fuel cell porous anode using lattice Boltzmann modeling

Solid Oxide Fuel Cell (SOFC) is an energy conversion device with high efficiency and cleanliness. However, anode carbon deposition severely affects SOFC performance during reforming with hydrocarbon fuels. In this paper, numerical simulations based on the Lattice Boltzmann (LB) method are used to construct the porous anode structure after carbon deposition by means of the binary dilation method, and the effects of different carbon deposition behaviors on the methane/steam flow behaviors and mass transport in the porous medium of SOFC anode are investigated. The results show that anode carbon deposition decreases the methane/steam mass transfer efficiency, and as the degree of carbon deposition increases, dead pores are formed and gas passage is impeded. This paper investigates the effect of different degrees of carbon deposition behavior on anode gas transport, which can further understand the importance of carbon removal in SOFC anode during the methane reforming reaction.

Exploration of the coupled lattice Boltzmann model based on a multiphase field model: A study of the solid–liquid–gas interaction mechanism in the solidification process

A multiphase field model coupled with a lattice Boltzmann (PF-LBM) model is proposed to simulate the distribution mechanism of bubbles and solutes at the solid-liquid interface, the interaction between dendrites and bubbles, and the effects of different temperatures, anisotropic strengths and tilting angles on the solidified organization of the SCN-0.24wt.% butanedinitrile alloy during the solidification process. The model adopts a multiphase field model to simulate the growth of dendrites, calculates the growth motions of dendrites based on the interfacial solute equilibrium; and adopts a lattice Boltzmann model (LBM) based on the Shan–Chen multiphase flow to simulate the growth and motions of bubbles in the liquid phase, which includes the interaction between solid–liquid–gas phases. The simulation results show that during the directional growth of columnar dendrites, bubbles first precipitate out slowly at the very bottom of the dendrites, and then rise up due to the different solid–liquid densities and pressure differences. The bubbles will interact with the dendrite in the process of flow migration, such as extrusion, overflow, fusion and disappearance. In the case of wide gaps in the dendrite channels, bubbles will fuse to form larger irregular bubbles, and in the case of dense channels, bubbles will deform due to the extrusion of dendrites. In the simulated region, as the dendrites converge and diverge, the bubbles precipitate out of the dendrites by compression and diffusion, which also causes physical phenomena such as fusion and spillage of the bubbles. These results reveal the physical mechanisms of bubble nucleation, growth and kinematic evolution during solidification and interaction with dendrite growth.

Heat transfer investigation on the thermal energy storage using phase change material in low-carbon building

The use of high-conductivity porous medium is an effective method to enhance the heat transfer rate of phase change material (PCM) in thermal energy storage (TES), reducing the energy consumption of low-carbon buildings. This paper establishes a solid-liquid phase change lattice Boltzmann model of a TES unit and investigates the effects of Rayleigh number, inclination angle, porous array, and porosity. The findings indicate that inserting the porous medium enhances conductive heat transfer and weakens convective heat transfer. When the Rayleigh number is increased from 103 to 104, the liquid fraction increases by 3.0%, while an increase from 104 to 105 only results in a 1.6% increase, suggesting a diminishing effect of increasing the Rayleigh number. Results also show that the inclination angle can be disregarded in this study. Furthermore, increasing the specific surface area enhances conductive heat transfer. However, when the array n is changed to 7, the fastest variation of liquid fraction is obtained among the range from 5 to 9. Increasing the porosity will delay the moment that temperature standard deviation reaches to the maximum, getting the temperature distribution more nonuniform. The findings from this paper are valuable for the design of TES systems in low-carbon buildings. Practical application The porous medium can enhance heat transfer in the phase change process. In the field of low-carbon buildings, porous medium is applied to strengthen the energy storage rate. By investigating the parameters of the Rayleigh numbers, inclination angles, porosities and arrangement of porous medium arrays of the composed energy storage unit, the regularity of the effects on the energy characteristics are obtained, which would provide some valuable practice references for designing these parameters of the energy storage units in the future energy-efficient building sector.

A new lattice Boltzmann model for liquid–solid phase transition and its application in the simulation of sessile droplet solidification – focusing on volume change

This paper introduces a new modification to the convective Cahn–Hilliard equation and a lattice Boltzmann framework to simulate liquid–solid phase transitions in multicomponent systems. The model takes into account changes in properties, such as density, caused by solidification, which leads to volume expansion or contraction. After validating the proposed model against classical problems and experimental data, the solidification of a sessile droplet was investigated in detail. Results of numerical simulations suggest that the environmental conditions are as important as the surface condition in deciding the freezing time and the final shape of the droplet. The environmental properties can also affect the freezing time indirectly through interaction with surface wettability. It has been demonstrated that hydrophobic surfaces may lose their advantages over hydrophilic surfaces in terms of anti-icing performance when primary solidification is initiated from the interface between the droplet and the environment fluid. The deformations of droplets, either with contraction or expansion, were confirmed and compared in different environments. This study offers a new perspective on droplet solidification by exposing the strong influence of environmental conditions and meanwhile provides a useful numerical method to predict the phase change process.

Lattice Boltzmann modelling of multicomponent and multiphase flow with high density ratio

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.

Three-dimensional pore-scale study of methane hydrate dissociation mechanisms based on micro-CT images

<p>Methane hydrate is a promising source of alternative energy. An in-depth understanding of the hydrate dissociation mechanism is crucial for the efficient extraction. In the present work, a comprehensive set of pore-scale numerical studies of hydrate dissociation mechanisms is presented. Pore-scale lattice Boltzmann (LB) models are proposed to simulate the multiphysics process during methane hydrate dissociation. The numerical simulations employ the actual hydrate sediment pore structure obtained by the micro-CT imaging. Experimental results of xenon hydrate dissociation are compared with the numerical simulations, indicating that the observed hydrate pore habits evolution is accurately captured by the proposed LB models. Furthermore, simulations of methane hydrate dissociation under different sediment water saturations, fluid flow rates and thermal conditions are conducted. Heat and mass transfer limitations both have significant effects on the methane hydrate dissociation rate. The bubble movement can further influence the dissociation process. Dissociation patterns can be divided into three categories, uniform, non-uniform and wormholing. The fluid flow impacts hydrate dissociation rates differently in three-dimensional real structures compared to two-dimensional idealized ones, influenced by variations in hydrate pore habits and flow properties. Finally, upscaling investigations are conducted to provide the permeability and kinetic models for the representative elementary volume (REV)-scale production forecast. Due to the difference in the hydrate pore habits and dissociation mechanisms, the three-dimensional upscaling results contrast with prior findings from two-dimensional studies. The present work provides a paradigm for pore-scale numerical simulation studies on the hydrate dissociation, which can offer theoretical guidance on efficient hydrate extraction.</p>

A computational study of cell membrane damage and intracellular delivery in a cross-slot microchannel.

We propose a three-dimensional computational framework to simulate the flow-induced cell membrane damage and the resulting enhanced intracellular mass transport in a cross-slot microchannel. We model the cell as a liquid droplet enclosed by a viscoelastic membrane and solve the cell deformation using a well-tested immersed-boundary lattice-Boltzmann method. The cell membrane damage, which is directly related to the membrane permeability, is considered using continuum damage mechanics. The transport of the diffusive solute into the cell is solved by a lattice-Boltzmann model. After validating the computational framework against several benchmark cases, we consider a cell flowing through a cross-slot microchannel, focusing on the effects of the flow strength, channel fluid viscosity and cell membrane viscosity on the membrane damage and enhanced intracellular transport. Interestingly, we find that under a comparable pressure drop across the device, for cells with low membrane viscosity, the inertial flow regime, which can be achieved by driving a low-viscosity liquid at a high speed, often leads to much larger membrane damage, compared with the high-viscosity low-speed viscous flow regime. However, the enhancement can be significantly reduced or even reversed by an increase of the cell membrane viscosity, which limits cell deformation, particularly in the inertial flow regime. Our computational framework and simulation results may guide the design and optimisation of microfluidic devices, which use cross-slot geometry to disrupt cell membranes to enhance intracellular delivery of solutes.

A mesoscopic numerical method for enhanced pool boiling heat transfer on conical surfaces under action of electric field

The saturated pool boiling heat transfer on a conical structure surface under the action of an electric field is numerically investigated by using the lattice Boltzmann (LB) model coupled with an electric field model. A comparison study of boiling heat transfer phenomenon smooth surface and conical surface without the action of an electric field is first conducted in order to quantitatively analyze the mechanism of the electric field effect on boiling heat transfer on the conical structure surface. It is discovered that the conical structure has more active nucleation sites during the nucleate boiling regime, improving the boiling heat transfer efficiency and enhancing the critical heat flux (CHF). However, in the transition boiling stage and film boiling stage, the conical structure increases the flow resistance of the fluid on the fin surface, hindering heat transfer between the vapor and liquid and producing lower heat transfer performance than smooth surface. Based on the aforementioned findings, the boiling heat transmission on the conical structure surface is enhanced by applying an electric field. Numerical results indicate that the effect of the electric field on the boiling heat transfer performance on the conical structure surface is related to the boiling regime. In the earlier stage of the nucleation boiling regime, when an electric field is present, the onset time of bubble nucleation is slightly delayed, bubble size decreases a little, and boiling is slightly suppressed. However, the combination effect of electric field and conical structure, especially the tip effect, prevents the spread and diffusion of dry areas on the heating surface, thereby enhancing boiling heat transfer in the fully developed nucleate boiling stage. The tip effect grows more evidently in the transition boiling regime and film boiling regime, and increasing electric field intensity causes boiling to continue in the nucleate boiling regime at a higher superheat level. As a result, boiling heat transfer performance is greatly improved, and CHF steadily rises.