Three-dimensional Lattice Boltzmann Method Research Articles

Sweeping of the entrapped fluid out of the groove in a three-dimensional channel using lattice Boltzmann method

The entrapment of fluid inside a groove is an important topic of research from past few decades. In many engineering applications, it is seen that the droplet is displaced under the action of gravitational force on one of the wetted grooved wall of a rectangular three-dimensional channel. It is reported in literature that the entrapment of droplet fluid inside groove is undesirable in various applications. Thus, the present study deals with the method of sweeping out the entrapped fluid inside the groove by the displacement of a large size three-dimensional immiscible droplet under gravity. To analyze this problem, a three-dimensional lattice Boltzmann method (LBM) is used and Shan–Chen (S-C) model has been implemented to incorporate multiphase-multicomponent flow. The present problem deals with the single grooved wetted wall of a rectangular three-dimensional channel. The wettability of the groove surface is considered as uniform hydrophobic in two different cases, whereas the wettability of the three-dimensional channel wall outside of the groove is considered as uniform hydrophilic. The analysis shows that the sweeping of entrapped fluid out of the groove largely depends on the capillary number and groove dimensions. It is also observed that sweeping of entrapped fluid takes place only for uniform hydrophobic surface of the groove with contact angle equal to 118°. In case of hydrophobic surface with contact angle equal to 90°, the large size droplet completely trapped inside the groove and does not able to sweep out the previously entrapped fluid.

Implementation of a curved wall- and an absorbing open-boundary condition for the D3Q19 lattice Boltzmann method for simulation of incompressible fluid flows

In this work, a three-dimensional lattice Boltzmann method is developed for numerical simulation of the fluid flows around the arbitrary geometries in the wide range of Reynolds numbers. For efficient simulation of high Reynolds number flow structures in the turbulent regime, a large eddy simulation (LES) approach with the Smagorinsky subgrid turbulence model is employed. An absorbing boundary condition based on the concept of sponge layer is improved and implemented to damp the vorticity fluctuations near the open boundaries and regularize the numerical solution by significantly reducing the spurious reflections from the open boundaries. An off-lattice scheme with a polynomial interpolation is used for implementation of curved boundary conditions for the arbitrary geometries. The efficiency and accuracy of the numerical approach presented are examined by computing the low to high Reynolds number flows around the practical geometries, including the flow past a sphere in a range of Reynolds numbers from 102 to 104 and flow around the NACA0012 wing section in two different flow conditions. The present results are in good agreement with the numerical and experimental data reported in the literature. The study demonstrates the present computational technique is robust and efficient for solving flow problems with practical geometries.

Development of a three-dimensional phase-field lattice Boltzmann method for the study of immiscible fluids at high density ratios

Based on the recent work by Fakhari et al. (2017b), a three-dimensional phase-field lattice Boltzmann method was developed to investigate the rise of a Taylor bubble in a duct. The proposed approach couples the conservative phase-field equation with a velocity-based lattice Boltzmann scheme equipped with a weighted multiple-relaxation-time collision operator to enhance numerical stability. This makes the model ideal for numerical simulation of immiscible fluids at high density ratios and relatively high Reynolds numbers. Several benchmark problems, including the deformation of a droplet in a shear flow, the Rayleigh–Taylor instability, and the rise of a Taylor bubble through a quiescent fluid, were considered to asses the accuracy of the proposed solver. The Rayleigh–Taylor instability simulations were conducted for a configuration mimicking an air-water system, which has received little attention in the literature. After detailed verification and validation, the presented formulation was applied to study the flow field surrounding a Taylor bubble, for which numerical results were compared with the experimental work of Bugg and Saad (2002). The findings highlighted that the experimental bubble rise velocity, instantaneous flow field, and interface profile can be accurately captured by the presented model. In particular, the rise velocity of the present model indicated an improvement in accuracy when compared to the reference numerical solutions. The agreement between various numerical schemes, in some instances, indicated potential experimental difficulties in measuring the local flow field. Future application of the present model will facilitate detailed investigation of the pressure and flow profile surrounding Taylor bubbles evolving in co-current and counter-current flows.

Numerical Study of Single Bubble Growth on and Departure from a Horizontal Superheated Wall by Three-dimensional Lattice Boltzmann Method

A three-dimensional hybrid lattice Boltzmann method was used to simulate the progress of a single bubble’s growth and departure from a horizontal superheated wall. The evolutionary process of the bubble shapes and also the temperature fields during pool nucleate boiling were obtained and the influence of the gravitational acceleration on the bubble departure diameter (BDD), the bubble release frequency (BRF) and the heat flux on the superheated wall was analyzed. The simulation results obtained by the present three-dimensional numerical studies demonstrate that the BDD is proportional to $g^{\mathrm {-0.301}}$ , the BRF is proportional to $g^{\mathrm {-0.58}}$ , and the averaged wall heat flux is proportional to $g^{\mathrm {0.201}}$ , where g is the gravitational acceleration. These results are in good agreement with the common-used experimental correlations, indicating the rationality of the present numerical model and results.

A three-dimensional lattice Boltzmann method based reactive transport model to simulate changes in cement paste microstructure due to calcium leaching

In this paper, a newly developed lattice Boltzmann method based reactive transport model to simulate changes in microstructure of ordinary Portland cement paste due to calcium leaching is presented. The model takes three-dimensional digitized cement paste microstructure as input and is capable to capture an evolution of microstructure due to leaching, accounting for the dissolution of portlandite and corresponding increase in capillary porosity and the decalcification of C-S-H resulting in increase in gel porosity. The developed model has been applied to microstructures generated using two cement hydration models, CEMHYD3D and HYMSOTRUC, for three water-to-cement ratios. It was observed that the rate of leaching is directly proportional to ability of microstructure to transport calcium ions and higher fraction of percolated capillary pores result in higher rate of leaching. The model qualitatively reproduces experimentally observed changes in cement paste porosity and pore size distribution due to leaching. The quantitative validation of model at this scale is not possible by comparison of leaching obtained experiments and simulations which can be attributed to several factors including the differences in the scales of experiment and modelling study presented in this paper.

Implementation of D3Q19 Lattice Boltzmann Method with a Curved Wall Boundary Condition for Simulation of Practical Flow Problems

In this paper, implementation of an extended form of a no-slip wall boundary condition is presented for the three-dimensional (3-D) lattice Boltzmann method (LBM) for solving the incompressible fluid flows with complex geometries. The boundary condition is based on the off-lattice scheme with a polynomial interpolation which is used to reconstruct the curved or irregular wall boundary on the neighboring lattice nodes. This treatment improves the computational efficiency of the solution algorithm to handle complex geometries and provides much better accuracy comparing with the staircase approximation of bounce-back method. The efficiency and accuracy of the numerical approach presented are examined by computing the fluid flows around the geometries with curved or irregular walls. Three test cases considered herein for validating the present computations are the flow calculation around the NACA0012 wing section and through the two different porous media in various flow conditions. The study shows the present computational technique based on the implementation of the three-dimensional Lattice Boltzmann method with the employed curved wall boundary condition is robust and efficient for solving laminar flows with practical geometries and also accurate enough to predict the flow properties used for engineering designs.

Effects of Flow Fluctuation on Dilution and Spreading in a Self-Affine Fracture.

In this work, the spreading and dilution (mixing) processes of the miscible compound were analyzed numerically by three-dimensional Lattice Boltzmann Method (LBM) at a pore scale in a non-uniform flow field. The authors proposed an aperture-related dilution index to quantify the local dilution process in the different aperture regions. The results showed that the fluctuation of the compound spreading caused by the flow fluctuation depended on both the aqueous diffusivity and the frequency of the flow fluctuation. The flow fluctuation increased remarkably the original dilution index when the aqueous diffusivity of the miscible compound was relatively low. However, the analysis of the aperture-related dilution index showed that the degree of the dilution in smaller aperture regions was less than that in larger aperture regions, indicating that there was more incomplete dilution (mixing) in the smaller aperture region.

Three-dimensional lattice Boltzmann method benchmarks between color-gradient and pseudo-potential immiscible multi-component models

In this paper, a lattice Boltzmann color-gradient method is compared with a multi-component pseudo-potential lattice Boltzmann model for two test problems: a droplet deformation in a shear flow and a rising bubble subject to buoyancy forces. With the help of these two problems, the behavior of the two models is compared in situations of competing viscous, capillary and gravity forces. It is found that both models are able to generate relevant scientific results. However, while the color-gradient model is more complex than the pseudo-potential approach, numerical experiments show that it is also more powerful and suffers fewer limitations.

Kinematics and dynamics of suspended gasifying particle

The effect of gasification on the dynamics and kinematics of immersed spherical and non-spherical solid particles have been investigated using the three-dimensional lattice Boltzmann method. The gasification was performed by applying mass injection on particle surface for three cases: flow passing by a fixed sphere, rotating ellipsoid in simple shear flow, and a settling single sphere in a rectangular domain. In addition, we have compared the accuracy of employing two different fluid–solid interaction methods for the particle boundary. The validity of the gasification model was studied by comparing computed the mass flux from the simulation and the calculated value on the surface of the particle. The result was used to select a suitable boundary method in the simulations combined with gasification. Moreover, the reduction effect of the ejected mass flux on the drag coefficient of the fixed sphere have been validated against previous studies. In the case of rotating ellipsoid in simple shear flow with mass injection, a decrease on the rate of rotation was observed. The terminal (maximum) velocity of the settling sphere was increased by increasing the ratio of radial flux from the particle boundary.

Permeability in multi-sized structures of random packed porous media using three-dimensional lattice Boltzmann method

The permeability of random porous media composed of multi-sized particles is calculated by using the lattice Boltzmann method. This paper studies the randomness of porous structure, particle size level and particle shape on flow characteristics. Results show that randomness has significant effects on permeability when the number and size of spheres or cubes are fixed, especially for the cubes. As the particle size level increases, the normalized permeability increases. When the size level increases to five, the permeability does not continue to increase. Furthermore, this paper studies the effect of particle shape on flow characteristics. The results show that the normalized permeability of sphere particle is larger than cube particle. In addition, our research results extend studies to a case where the cube length is smaller than the cube height.

Lattice Boltzmann simulation of the trapping of a microdroplet in a well of surface energy

In this paper, a three-dimensional phase-field lattice Boltzmann method is used to simulate the dynamical behavior of a droplet, subject to an outer viscous flow, in a microchannel that contains a cylindrical hole etched into its top surface. The influence of the capillary number and the hole diameter (expressed as the ratio of hole diameter to channel height, b) is investigated. We demonstrate numerically that the surface energy gradient induced by the hole can create an anchoring force to resist the hydrodynamic drag from the outer flow, resulting in the droplet anchored to the hole when the capillary number is below a critical value. As b increases, the droplet can be anchored more easily. For b < 2, the droplet partially enters into the hole and forms a spherical cap; whereas for b > 2, the spherical cap of droplet reaches the top wall of the hole, making the hole depth into an additional important parameter. These observations are consistent with the previously reported experiments. However, the droplet does not fully fill the hole for b > 2, departing from the expectation of Dangla et al. [R. Dangla, S. Lee, C. N. Baroud, Trapping microfluidic drops in wells of surface energy, Phys. Rev. Lett. 107 (2011) 124501]. Also, it is observed in the anchored state that the rear of the droplet rests at a small distance away from the junction. Finally, the droplet undergoes a slow-down process only when its rear passes through the hole, regardless of b.

Motion of a spherical capsule in branched tube flow with finite inertia

We computationally study the transient motion of an initially spherical capsule flowing through a right-angled tube bifurcation, composed of tubes having the same diameter. The capsule motion and deformation is simulated using a three-dimensional immersed-boundary lattice Boltzmann method. The capsule is modelled as a liquid droplet enclosed by a hyperelastic membrane following the Skalak’s law (Skalak et al., Biophys. J., vol. 13(3), 1973, pp. 245–264). The fluids inside and outside the capsule are assumed to have identical viscosity and density. We mainly focus on path selection of the capsule at the bifurcation as a function of the parameters of the problem: the flow split ratio, the background flow Reynolds number $Re$, the capsule-to-tube size ratio $a/R$ and the capillary number $Ca$, which compares the viscous fluid force acting on the capsule to the membrane elastic force. For fixed physical properties of the capsule and of the tube flow, the ratio $Ca/Re$ is constant. Two size ratios are considered: $a/R=0.2$ and 0.4. At low $Re$, the capsule favours the branch which receives most flow. Inertia significantly affects the background flow in the branched tube. As a consequence, at equal flow split, a capsule tends to flow straight into the main branch as $Re$ is increased. Under significant inertial effects, the capsule can flow into the downstream main tube even when it receives much less flow than the side branch. Increasing $Ca$ promotes cross-stream migration of the capsule towards the side branch. The results are summarized in a phase diagram, showing the critical flow split ratio for which the capsule flows into the side branch as a function of size ratio, $Re$ and $Ca/Re$. We also provide a simplified model of the path selection of a slightly deformed capsule and explore its limits of validity. We finally discuss the experimental feasibility of the flow system and its applicability to capsule sorting.

A numerical study on the elastic modulus of volume and area dilation for a deformable cell in a microchannel.

A red blood cell (RBC) in a microfluidic channel is highly interesting for scientists in various fields of research on biological systems. This system has been studied extensively by empirical, analytical, and numerical methods. Nonetheless, research of predicting the behavior of an RBC in a microchannel is still an interesting area. The complications arise from deformation of an RBC and interactions among the surrounding fluid, wall, and RBCs. In this study, a pressure-driven RBC in a microchannel was simulated with a three-dimensional lattice Boltzmann method of an immersed boundary. First, the effect of boundary thickness on the interaction between the wall and cell was analyzed by measuring the time of passage through the narrow channel. Second, the effect of volume conservation stiffness was studied. Finally, the effect of global area stiffness was analyzed.

Simulation of dendritic growth of Al-4 wt.% Cu alloy from an undercooled melt

Abstract Three-dimensional dendritic growth of an Al-4 wt.% Cu alloy during solidification in the presence of forced flow was simulated by using a three-dimensional cellular automaton model. The three-dimensional Lattice–Boltzmann method was used in computing the flow dynamics. The effects of forced flow on the growth Péclet number, dendrite tip selection parameter, and secondary arm spacing were investigated. The simulated relationships of growth Péclet number and dendrite tip selection parameter with the forced flow are in good agreement with the Oseen–Ivantsov solution. The results indicate that with the increase in forced flow velocity, the secondary arm spacing first increases and then decreases.

Underfill flow simulation based on lattice Boltzmann method

Underfill process is carried out mainly to prevent interconnection failures caused by the mismatch of CTE between the die and the substrate in flip chip encapsulation. Owing to troubles in calculating the capillary force, i.e., result-based and interface reconstruction, the underfill flow cannot be well characterized by current simulation methods. In this paper, we present a mesoscale underfill simulation method based on three-dimensional LBM (lattice Boltzmann method) with D3Q19 velocity set and LBGK (lattice-Bhatnagar–Gross–Krook) evolution model. In this method, the GIPM (generalized interparticle-potential model) is first proposed to model the capillary flow, which can solve the fluid–fluid interaction and the solid–fluid interaction in a unified manner. A geometric model for underfill simulation is then developed. The solid wall is divided into three parts, i.e., the substrate, the die and the solder bump, and each part is allowed to have a different wettability by assigning a mesoscale interaction parameter. For verification purpose, three underfill cases, which are different in wall wettability, are examined. In each case, besides the experimental results, we also present numerical results predicted by a VOF multiphase method with CSF capillary model. The results show that the proposed method has a good performance in the underfill simulation.

Numerical and experimental study on the motion characteristics of single bubble in a complex channel

This paper is an extended study from previous work. In this study, the focus is paid to the dynamics of bubble rising and deformation in a complex channel, while the previous work is in straight channel. For this purpose, a three-dimensional lattice Boltzmann method (LBM) is employed to simulate the dynamics behaviour of a bubble rising in a complex channel consisting of three half-round throats. To validate the numerical method, a visual experiment was carried out by means of a high-speed digital camera and computer image processing technology. The behaviour of the rising bubble through glycerine solution in a complex channel was recorded. Some physical parameters such as rising velocities, trajectory and shapes of the bubble were calculated and processed based on the experimental data. In the same conditions, the trajectory, shapes and rising velocities of the bubble were simulated during its rising process by the proposed LBM. The numerical results are in good agreement with the experimental results. It demonstrates that LBM used in this work is feasible for simulating two-phase flow in such a complex channel.

Numerical investigation of the effects of porosity and tortuosity on soil permeability using coupled three-dimensional discrete-element method and lattice Boltzmann method.

Permeability of porous materials is an important characteristic which is extensively used in various engineering disciplines. There are a number of issues that influence the permeability coefficient among which the porosity, size of particles, pore shape, tortuosity, and particle size distribution are of great importance. In this paper a C++ GPU code based on three-dimensional lattice Boltzmann method (LBM) has been developed and used for investigating the effects of the above mentioned factors on the permeability coefficient of granular materials. Multirelaxation time collision scheme of the LBM equations is used in the simulator, which is capable of modeling the exact position of the fluid-solid interface leading to viscosity-independent permeabilities and better computational stability due to separation of the relaxations of various kinetic models. GPU-CPU parallel processing has been employed to reduce the computational time associated with three-dimensional simulations. Soil samples have been prepared using the discrete element method. The obtained results have demonstrated the importance of employing the concept of effective porosity instead of total porosity in permeability relationships. The results also show that a threshold porosity exists below which the connectivity of the pores vanishes and the permeability of the soils reduces drastically.

Numerical investigations on hatching process strategies for powder-bed-based additive manufacturing using an electron beam

This paper investigates in hatching process strategies for additive manufacturing using an electron beam by numerical simulations. The underlying physical model and the corresponding three-dimensional thermal free-surface lattice Boltzmann method of the simulation software are briefly presented. The simulation software has already been validated on the basis of experiments up to 1.2kW beam power by hatching a cuboid with a basic process strategy, whereby the results are classified into porous, good, and uneven, depending on their relative density and top surface smoothness. In this paper, we study the limitations of this basic process strategy in terms of higher beam powers and scan velocities to exploit the future potential of high power electron beam guns up to 10kW. Subsequently, we introduce modified process strategies, which circumvent these restrictions, to build the part as fast as possible under the restriction of a fully dense part with a smooth top surface. These process strategies are suitable to reduce the build time and costs, maximize the beam power usage, and therefore use the potential of high power electron beam guns.

Domain and droplet sizes in emulsions stabilized by colloidal particles.

Particle-stabilized emulsions are commonly used in various industrial applications. These emulsions can present in different forms, such as Pickering emulsions or bijels, which can be distinguished by their different topologies and rheology. We numerically investigate the effect of the volume fraction and the uniform wettability of the stabilizing spherical particles in mixtures of two fluids. For this, we use the well-established three-dimensional lattice Boltzmann method, extended to allow for the added colloidal particles with non-neutral wetting properties. We obtain data on the domain sizes in the emulsions by using both structure functions and the Hoshen-Kopelman (HK) algorithm, and we demonstrate that both methods have their own (dis)advantages. We confirm an inverse dependence between the concentration of particles and the average radius of the stabilized droplets. Furthermore, we demonstrate the effect of particles detaching from interfaces on the emulsion properties and domain-size measurements.

Three dimensional thermal Lattice Boltzmann simulation of heating/cooling spheres falling in a Newtonian liquid

This paper presents a numerical study of heat transfer from spheres settling under gravity in a box filled with liquid. Three-dimensional Lattice Boltzmann Method is applied to simulate fluid-particle interaction. Firstly the developed numerical model is validated in comparison with experimental and numerical data for a falling sphere in a box filled with liquid. Then the effects of Reynolds, Prandtl and Grashof numbers (Re, Pr, Gr) are investigated for a settling particle at fixed/varied temperature. The time variations of velocity, height and Nusselt number of the settling particle are also investigated. The results depict that the maximum settling velocity of the particle at varied surface temperature is higher at lower Reynolds numbers. As the Reynolds number increases, the settling velocity of the particle for both cases of constant and varied temperature is the same. However, the Nusselt number of the particle at varied temperature is lower compared with that for the particle at constant surface temperature. Increasing the Grashof number leads to slower settling and larger average Nusselt number. Finally sedimentation of 30 hot spherical particles in an enclosure and their hydraulic and heat transfer interactions with the surrounding fluid are studied. The results depict how the presence of heat transfer phenomena can significantly alter the behavior of settling particles.