Two-dimensional Lattice Boltzmann Model Research Articles

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.

Pore-Scale Investigation of Mass Transport in Compressed Cathode Gas Diffusion Layer of Proton Exchange Membrane Fuel Cells

Proton exchange membrane fuel cells (PEMFCs) are considered a promising energy source in the field of transport and distributed power generation. Fundamental research into their key components is needed to improve PEMFC performance and accelerate commercialization. Binder addition and compression induced by assembly pressure can significantly change the microstructure of the gas diffusion layer and affect mass transport. A two-dimensional multicomponent lattice Boltzmann (LB) model considering the cathode electrochemical reaction was developed, and a GDL was reconstructed numerically and considering a binder structure. The effects of the binder and compression on mass transport and electrochemical performance within the GDL were investigated. The results showed that an increase in binder volume fraction led to more chain-like structures and closed pores that were unfavorable for mass transport. Compression increased the mass transfer resistance of the GDL in the region under the rib, leading to a decrease in oxygen concentration and local current density.

TLBfind: a Thermal Lattice Boltzmann code for concentrated emulsions with FINite-size Droplets

In this paper, we present TLBfind, a GPU code for simulating the hydrodynamics of droplets along with a dynamic temperature field. TLBfind hinges on a two-dimensional multi-component lattice Boltzmann (LB) model simulating a concentrated emulsion with finite-size droplets evolving in a thermal convective state, just above the transition from conduction to convection. The droplet concentration of the emulsion system is tunable and at the core of the code lies the possibility to measure a large number of physical observables characterising the flow and droplets. Furthermore, TLBfind includes a parallel implementation on GPU of the Delaunay triangulation useful for the detection of droplets' plastic rearrangements, and several types of boundary conditions, supporting simulations of channels with structured rough walls. Program summaryProgram Title: TLBfindCPC Library link to program files:https://doi.org/10.17632/hbk45696nf.1Developer's repository link:https://github.com/FrancescaPelusi/TLBfindLicensing provisions: MITProgramming language: CUDA-CNature of problem: Hydrodynamics of concentrated emulsions with finite-size droplets in a thermal convective state.Solution method: Single relaxation time Lattice Boltzmann method to solve Navier-Stokes equations for fluids, coupled with the temperature field dynamics. The output describes the dynamics of finite-size droplets of concentrated emulsions in presence of a temperature field. The temperature field obeys the advection-diffusion equation.Additional comments including restrictions and unusual features: Plastic rearrangements of droplets are detected via the parallel implementation of the Delaunay triangulation, and boundary conditions are tunable.

Hybrid quasi-steady thermal lattice boltzmann model for investigating the effects of thermal, surfactants and contact angle on the flow characteristics of oil in water emulsions between two parallel plates

In this work, a two-dimensional hybrid quasi-steady thermal lattice Boltzmann model with temperature-dependent interfacial tension, surfactant and contact angle modules, is used to study the combined multi-physics effects on oil in water (O/W) systems flowing between two-parallel oil-wet plates. The proposed model is used to execute a parametric study for investigating the effects of the droplet radius, source terms, temperature, and surfactants parameters such as concentrations, elasticity, and diffusion coefficients on the flow characteristics of oil in water (O/W) emulsions inside microchannels. Flow conditions such as droplet Reynolds number0.41≤Re≤48, Webber number0.041≤We≤28 dimensionless surfactant surface concentration0.1≤Γ∗≤0.5, and surface Péclet number0.011≤Pes≤31are used in the simulations. The presence of surfactant noticeably enhances the droplets' transportation inside the channel, due to increased droplets' contact angle and deformation. Contaminated droplets with surfactant retain a greater bulk mass center velocity than clean ones to the tune of 2–5 times depending on the simulation conditions. The rise in temperature has a major impact on improving the suspended phase bulk velocity and power number ratio (system's efficiency indicator) for cases with and without surfactant. However, the presence of surfactant at elevated temperatures ameliorates the amount of useful work absorbed by the droplets from the flow significantly. Using specific conditions from the parametric study such as high temperature and surfactants characterized by low diffusion coefficient, results in an effective droplets breakup. The daughter droplets depart from the channel walls by shear lift, which enhances the suspended fluid transportation and increases the power number ratio up to 5.7 times.

Lattice Boltzmann study of bubble dynamics and heat transfer on a hybrid rough surface with a cavity-pillar structure

In this work, a two-dimensional phase-change lattice Boltzmann model is used to investigate the pool boiling from a hybrid rough surface with a single cavity and one or two pillars on the superheated plate for an entire ebullition cycle. The bubble growth and departure dynamics on the hybrid pillared cavity surfaces, namely a single-pillared cavity surface (a surface with one cavity and one neighbouring pillar) and a double-pillared cavity surface (a surface with one cavity and one pillar on its both sides), are also compared with a simple cavity surface (a surface with only one cavity). The results showed that the incorporation of the pillar to the simple cavity surface increases the surface area and distance between the pinning locations of the three-phase contact line (TCL), and thus, enhances the bubble departure diameter and heat flux. It is found that bubble departure diameter and heat flux increase with cavity-pillar spacing up to a certain value, in this case sp∗ = 0.50, beyond which they start to decease and approach the simple cavity surface case at sp∗ = 1.0, while the opposite trend is observed for bubble departure frequency. The bubble departure diameter, frequency and heat flux also increase with pillar width. Compared to uniformly hydrophilic surfaces, the mixed wettability surfaces exhibit large heat flux with relatively small increase in bubble departure diameter.

Modelling flood events with a cumulant CO lattice Boltzmann shallow water model

In this work the development of a semiautomatic procedure based on the coupled use of a GIS subroutine and a two-dimensional hydraulic lattice Boltzmann model solving the shallow water equations is presented. A C code implementing the cumulant collision operator and a limiter velocity strategy to model the wave front on a wet–dry bed is discussed and validated against literature test cases. Finally an application to a real test case, the Malpasset dam break, is shown, highlighting the good performances of the model through a comparison with results from surveys and data from literature.

Numerical study of the antibiotic transport and distribution in the Laizhou Bay, China.

A large number of antibiotic residues are discharged into aquatic environments due to the widespread use of antibiotics in daily life. After a series of processes in the water, the residues will potentially have adverse impacts on water ecosystem and human health. Therefore, it is critical for mediating the pollution to know how the antibiotics transport and distribute in the water. This study utilizes a two-dimensional lattice Boltzmann model to find out the transport and distribution of antibiotics in a highly polluted area, the Laizhou Bay in China. Furthermore, the model was used to simulate two scenarios in the Laizhou Bay, the antibiotics from sewage treatment plants and the contamination of mariculture. The simulated results show that the model as an effective tool can provide a useful basis for the management of antibiotics-related environmental issues in the Laizhou Bay.

Effects of pore characteristics on water-oil two-phase displacement in non-homogeneous pore structures: A pore-scale lattice Boltzmann model considering various fluid density ratios

Understanding immiscible-phase fluid displacement in non-homogeneous pore structures is crucial to enhance resource recovery in the secondary development of old petroleum reservoirs. Reducing residual oil resources requires quantifying the effects of pore characteristics on the development of preferential displacement paths in porous reservoirs, which can be used to predict the preferential path of water displacement during secondary oil recovery, and therefore, to design an effective plugging strategy. The non-homogeneity of pore structures of rocks makes it extremely difficult to directly observe the water-oil displacement in subsurface rock reservoirs and quantify the sensitivity of preferential paths to pore characteristics. As an effective alternative, numerical methods have been applied to explore the fluid displacement process in old petroleum reservoirs. In this study, a two-dimensional (2D) pore-scale multicomponent lattice Boltzmann model (LBM) was developed and used to study water-oil displacement in non-homogeneous pore structures that shared identical topological skeletons and porosities but had different pore size distributions and pore geometries. The effects of pore characteristics on the preferential displacement path of the water-oil imbibition were analyzed. The influence of the density ratios of incompressible fluids on the two-phase displacement was also compared. The comparison between the numerical results of different pore-scale models indicated that the variation of pore size distribution and pore geometry affects the development of water fingering and promotes different local displacement paths. The primary preferential displacement path remains unchanged in different pore structures, which can possibly be attributed to the invariant topological skeleton of the pore structures. The results demonstrate that the fluid density ratio dramatically influences the water-oil displacement behaviors and suggests coupling the real density ratio in an LBM simulation. This study provides a method to quantitatively evaluate the effects of pore characteristics on the water-oil two phase displacement in porous oil reservoirs and to help draft a strategy to enhance the resource recovery of old petroleum reservoirs.

Magnetic regulating the phase change process of Fe3O4-paraffin wax nanocomposites in a square cavity

The addition of external force provides an alternative way to promote the application of phase change materials in thermal-energy storage, space heating, and cooling systems. However, the experimental investigation using external magnetic force to regulate the phase change process is still limited. Here, magnetic Fe3O4 nanoparticles were added to paraffin wax to form phase change nanocomposites with enhanced thermal properties and controllable magnetism. The thermal properties of nanocomposites were measured and the phase change processes under magnetic controlling were experimentally and numerically investigated. A two-dimensional enthalpy-based lattice Boltzmann model with considering the external magnetic force was proposed and the measured thermal properties were used in the simulation. Good agreement between the experiment and simulation was achieved. The effects of different mass fractions of Fe3O4 nanoparticles (0, 1, 2, 3 and 4 wt%), magnetic directions, magnetic field intensities (0, 20, 40, 60 mT) on the phase change characteristics are discussed. The heat transfer efficiency in a square cavity filled with the nanocomposites developed more quickly when the paraffin wax was doped with a higher Fe3O4 mass fraction. Moreover, the phase change characteristics were controlled by the intensity and direction of the magnetic field. This study presents a method to achieve magnetically regulating phase change heat transfer characteristics that have potential applications in the energy-storage industry.

The rotation of two-dimensional elliptical porous particles in a simple shear flow with fluid inertia

The motion of porous particles in fluid flow is of fundamental importance in both natural and industrial processes. Recent work shows that fluid inertia can essentially alter the rotation of spherical porous particles in a simple shear flow. In this contribution, we examined the influence of fluid inertia on the rotation of elliptical porous particles in shear flow by solving the volume-averaged macroscopic equations with a two-dimensional lattice Boltzmann model. It is confirmed that the Darcy number Da has only a minor effect on the rotation of elliptical porous particles if fluid inertia is neglected. At finite fluid inertia, the elliptical porous particles, however, manifested time-periodic rotation with a non-uniform angular rate. For particles with small to intermediate Da, the period of rotation increases with Reynolds number Re up to a critical Rec above which the particle would stop rotating. It is shown that the maximum and minimum angular rates, as well as the inclination angle at which the particle has a minimum angular rate, are significantly affected by Da. A scaling law for the period of rotation initially proposed for solid impermeable particles can be extended to elliptical porous particles at finite fluid inertia. For a highly permeable ellipse, however, Rec has not been observed, and thus, the scaling law breaks down. We calculated the relative viscosity and intrinsic viscosity for simple shear flow containing elliptical porous particles. A formula developed for suspensions with vanishing Re can also be extended to correlate the intrinsic viscosity to Da at finite Re.

Lattice Boltzmann method for shallow water flow with wave radiation stress

The protection of the marine environment is of growing concern, and the development of hydrodynamic models is required to study ocean processes. In this work, a two-dimensional hydrodynamic lattice Boltzmann model was developed to study wave–current coupling problems that combine wave radiation, bed shear stress and wind shear stress. The model is based on nonlinear shallow water equations and two different forms are developed to model wave radiation stress. The first form uses an additional external force term, including a weight factor in the lattice Boltzmann equation at the streaming step. The second form modifies a local equilibrium distribution function at the collision step. Von Neumann stability method is used to study the two schemes. This model was verified by three classic cases: waves diffracted by a straight vertical wall, waves diffracted by two breakwaters, and waves in a circular channel. The numerical results demonstrate the validity of the proposed model, indicating that it can accurately describe the characteristics of water flow with interactions between waves and currents.

Numerical Study of Sulfonamide Occurrence and Transport at the Near-Shore Area of Laizhou Bay

Antibiotics are extensively applied in aquaculture for the treatment of microbial infections and to improve production. Among various antibiotics, sulfonamides (SA) are popular in fish farming, and SA residues in the aquatic environment have detrimental effects on both ecosystem and human health. Understanding the fate of SA in the aquatic environment is a basic necessity to provide an approach for solving the current problem. In this study, a two-dimensional lattice Boltzmann model was introduced to investigate the transport and occurrence of SA in Laizhou Bay, a prosperous aquaculture area in China. The model is based on the shallow-water equations and advection-diffusion equation with the Bhatnagaar–Gross–Krook scheme. Experimental data are used to verify the model after numerical simulations and the results illustrate the accuracy of the proposed model. This model provides a potential universal method for the simulation of the fate of antibiotics in the aquatic environment.

Numerical investigation on bubble dynamics during pool nucleate boiling in presence of a non-uniform electric field by LBM

Previous experimental studies proved that an external electric field could accelerate the detachment of vapor bubble. However, it was difficult to investigate the influencing mechanism of an electric field on bubble dynamics because of the limit of experimental technical methods. To solve this problem, a two-dimensional lattice Boltzmann model was developed in this paper to simulate the pool boiling in presence of an external electric field by coupling the pseudopotential model with phase-change model and electric field model. The growth and detachment of a single bubble on a horizontal wall during pool nucleate boiling with a non-uniform electric field was simulated. The influence of gravitational acceleration and electric field intensity on bubble dynamics was investigated in detail, and the influencing mechanism of an external electric field on bubble dynamics during pool nucleate boiling was analyzed. The numerical results showed that increasing electric filed intensity could decrease both bubble departure diameter and bubble release period. Decreasing gravitational acceleration could strengthen the influence of electric field intensity on bubble departure diameter and bubble release frequency. In other words, the non-uniform electric field established at present study could effectively reduce the possibility of heat transfer deterioration under microgravity.

Numerical study on saturated pool boiling heat transfer in presence of a uniform electric field using lattice Boltzmann method

For the industrial equipment with boiling, critical heat flux (CHF) is an important parameter that determines its upper limit of heat load for safe operation. Therefore, increasing CHF is of great importance in engineering field. Previous studies proved that it’s an effective way to enhance boiling heat transfer and CHF by electrohydrodynamics (EHD). However, it is difficult to investigate the influence mechanism of the electric field on the bubble dynamics and boiling heat transfer because of the limit of experimental technical methods. Thus, in this paper, a two-dimensional lattice Boltzmann model was established by coupling the pseudopotential model with phase-change model and electric field model to meet the lack of studies on simulating the pool boiling in presence of an electric field. After validating the rationality of the two-dimensional lattice Boltzmann model established at present study, the heat transfer during nucleate boiling and film boiling under a uniform electric field were studied in detail. In addition, the influence of electric field intensity on boiling curves and CHF was investigated quantitatively. In the partial nucleate boiling regime, a uniform electric field had limited influence on bubble dynamics and boiling heat transfer. In the fully developed nucleate boiling regime, increasing electric field intensity could enhance boiling heat transfer obviously. In the film boiling regime, increasing electric field intensity could slightly enhance averaged heat flux at first. After the electric field intensity reached a certain value, averaged heat flux increased rapidly. Increasing electric field intensity could expand the nucleate boiling regime, and enhance CHF and the wall temperature at CHF point.

Two-dimensional off-lattice Boltzmann model for van der Waals fluids with variable temperature

We develop a two-dimensional Lattice Boltzmann model for liquid–vapour systems with variable temperature. Our model is based on a single particle distribution function expanded with respect to the full-range Hermite polynomials. This model relies on a set of 25 off-lattice momentum vectors, whose Cartesian projections are the roots of the Hermite polynomial of order Q=5. The time evolution, spatial advection and gradient computations are performed using finite difference techniques. Our implementation is extensively benchmarked in the following contexts: the planar interface, the Laplace pressure test, the damping of shear and longitudinal waves, as well as the Galilean invariance test. We then investigate the liquid–vapour phase separation between two parallel walls kept at a constant temperature Tw, which is smaller than the critical temperature Tc, and discuss the main features of this process.

Axisymmetric lattice Boltzmann simulation of the heat-exchanger method-based sapphire crystal growth

The crystal-growth process in a heat-exchanger method (HEM)-based system was simulated using the lattice Boltzmann technique. The two-dimensional enthalpy-based lattice Boltzmann model was extended to treat the axisymmetric solid-liquid phase change problems. The proposed model demonstrates high accuracy over a large range of Biot and Stefan numbers and exhibits superiority over the first-order perturbation method, especially, in cases involving large Stefan numbers. Macroscopic crystal-growth simulations primarily focus on flow patterns in the melt and heat-transfer processes inside the crucible. Effects of dimensionless convective boundaries and Rayleigh numbers (Ra) on transport phenomena and the crystal/melt interface have also been discussed. It was observed that a decrease in the superheating temperature causes an increase in crystal fraction and decline in convection intensity. The area of the cooling zone mainly influences crystal growth rate during the initial stages of the process. In the later stages, however, the Biot number corresponding to the heating boundary assumes a more significant role. At low Rayleigh numbers, heat transfer via conduction is dominant in the melt. With increase in Ra values, melt convection tends to strengthen, thereby tending to deform the isothermal lines and phase interface.

A lattice Boltzmann study of frost growth on a cold surface

A two-dimensional Lattice Boltzmann model was established to study the dynamic physical process of frost growth on a cold flat surface. It is verified that the theoretical results are in good agreement with the experiment data with better accuracy. The frost morphology is explored by showing two-dimension density distribution with different cold surface temperatures. The results also include dynamic characteristics of frost properties such as thickness, deposition weight, volume fraction, density, temperature. According to the results, it is found that the nearer it is from the cold flat plate, the larger of frost crystal volume fraction and density are. The frost surface temperature increases rapidly at the early period of frosting and then increases gradually towards the triple point temperature of the water. The frost internal temperatures rise in a linear tendency with the frost thickness and decrease at the same frost layer location with frost growth. Super-saturation degree of moist air has non-negligible effect on frost growth parameters such as frost thickness, frost crystal deposition mass, frost deposition rate and frost crystal volume fraction.

Cell-resolved blood flow simulations of saccular aneurysms: effects of pulsatility and aspect ratio.

We study the effect of pulsatile flow on the transport of red blood cells (RBCs) and platelets into aneurysm geometries with varying dome-to-neck aspect ratios (AR). We use a validated two-dimensional lattice Boltzmann model for blood plasma with a discrete element method for both RBCs and platelets coupled by the immersed boundary method. Flow velocities and vessel diameters were matched with measurements of cerebral perforating arteries and flow was driven by a synthetic heartbeat curve typical for such vessel sizes. We observe a flow regime change as the aspect ratio increases from a momentum-driven regime in the small aspect ratio to a shear-driven regime in the larger aspect ratios. In the small aspect ratio case, we see the development of a re-circulation zone that exhibits a layering of high (greater than or equal to 7 s) and low (less than 7 s) residence cells. In the shear-driven regime, we see high and low residence cells well mixed, with an increasing population of cells that are trapped inside the aneurysm as the aspect ratio increases. In all cases, we observe aneurysms that are platelet-rich and red blood cell-poor when compared with their respective parental vessel populations. Pulsatility also plays a role in the small aspect ratio as we observe a smaller population of older trapped cells along the aneurysm wall in the pulsatile case when compared with a steady flow case. Pulsatility does not have a significant effect in shear-driven regime aspect ratios.

A novel two-dimensional coupled lattice Boltzmann model for thermal incompressible flows

A novel two-dimensional coupled lattice Boltzmann model is developed for thermal incompressible fluid flows. A modified equilibrium distribution function is proposed in the present model. A mesoscopic discrete force is coupled into the modified equilibrium distribution function based on the Boussinesq approximation. The outstanding advantages of the standard lattice Boltzmann method are retained in present model besides better numerical stability. The present model is validated by the numerical simulation of the natural and Rayleigh–Benard convection at a wide range of Rayleigh numbers. Excellent agreement between the present results and previous lattice Boltzmann method or theoretical prediction demonstrates that present model is an efficient numerical method for natural and Rayleigh–Bénard convection. Further, present model is also successfully assessed considering Rayleigh–Taylor instability. It is also easier and convenient to be implemented as compared with the previous thermal models.

A Numerical Investigation of Frost Growth on Cold Surfaces Based on the Lattice Boltzmann Method

A numerical investigation of frost growth on a cold flat surface was presented based on two-dimensional Lattice Boltzmann model. This model has been validated to have less prediction error by past experiments. According to the results, it is shown that average frost density appears different at an increasing rate at different frosting stages. In addition, cold surface temperature has great influence on frost growth parameters such as frost crystal deposition mass, frost deposition rate, and frost crystal volume fraction. It was found that the frost crystal deposition mass, frost crystal volume, and the deposition rate first increase rapidly, then gradually slow down, finally remaining unchanged while the cold surface temperature decreases. The further away from the cold surface, the more sparser the frost layer structure becomes due to the smaller frost crystal volume fraction.