Three-dimensional Lattice Boltzmann Method Research Articles

Lattice Boltzmann modeling of VOC desorption and diffusion in porous materials: VOC desorption and diffusion

This paper presents migration of volatile organic compounds (VOC) in porous building materials which are considered as stochastic porous media for the purpose of theoretical study. Desorption and diffusion processes of VOC in porous materials are simulated by three-dimensional lattice Boltzmann method (LBM) which is derived from binary mixture model. Based on this model, the simulated transient concentration distribution of binary gas diffusion in 3D channel which is obtained from simulation agrees well with analytical solution. The stochastic porous materials are constructed with quartet structure generation set (QSGS) method. This model can predict the effective diffusivity of porous materials successfully through comparing with empirical model and experimental data. A boundary condition of solid–pore interfaces is proposed to simulate desorption process of adsorption phase VOC on solid matrix. The coupling relationship between migration characteristics and key parameters of porous materials, such as partition coefficient, core distribution probability and porosity, is analyzed. The significance of desorption in migration process of VOC is observed.

Study on microchannel flows with a sudden contraction–expansion at a wide range of Knudsen number using lattice Boltzmann method

Numerical simulations have been performed on the pressure-driven rarefied flow through channels with a sudden contraction–expansion of 2:1:2 using isothermal two and three-dimensional lattice Boltzmann method (LBM). In the LBM, a Bosanquet-type effective viscosity and a modified second-order slip boundary condition are used to account for the rarefaction effect on gas viscosity to cover the slip and transition flow regimes, that is, a wider range of Knudsen number. Firstly, the in-house LBM code is verified by comparing the computed pressure distribution and flow pattern with experimental ones measured by others. The verified code is then used to study the effects of the outlet Knudsen number Kn o , driving pressure ratio P i /P o , and Reynolds number Re, respectively, varied in the ranges of 0.001–1.0, 1.15–5.0, and 0.02–120, on the pressure distributions and flow patterns as well as to document the differences between continuum and rarefied flows. Results are discussed in terms of the distributions of local pressure, Knudsen number, centerline velocity, and Mach number. The variations of flow patterns and vortex length with Kn o and Re are also documented. Moreover, a critical Knudsen number is identified to be Kn oc = 0.1 below and above which the behaviors of nonlinear pressure profile and velocity distribution and the variations of vortex length with Re upstream and downstream of constriction are different from those of continuum flows.

Electron Beam Absorption Algorithms for Electron Beam Melting Processes Simulated by a Three-Dimensional Thermal Free Surface Lattice Boltzmann Method in a Distributed and Parallel Environment

This paper introduces two electron beam absorption algorithms for a three–dimensional thermal free surface lattice Boltzmann method simulating electron beam melting processes. The algorithms use a state-of-the-art volume of fluid free surface method of the lattice Boltzmann multi–distribution approach to handle the interaction between the electron beam and the material. Modeling the electron beam gun properties, such as absorption and energy dissipation, is explained in detail. Special emphasis is given to an implementation in a distributed and parallel environment due to the high computational costs of three–dimensional simulations. Finally, a thorough validation for the beam absorption behavior against the analytical solution is proceeded and a concluding example in a powder bed shows the capability of the approach to simulate and support understanding the electron beam melting process.

Microscale Numerical Simulation of the Permeability Reduction due to Trapping of Suspended Fine Particles Within Sand Sediments

The reduction in permeability of sediments due to blockages caused by the trapping of suspended particles is a common concern for the extraction processes of oil or natural gas. In this study, the effect of trapped fine particles in sand sediments is studied numerically using a three-dimensional lattice Boltzmann method. The geometrical properties of larger, immobile, sand grains are digitally extracted by the spherical harmonics series expansions of CT scans of real sand grains. The migrating fine particles are assumed to be spherical in shape with their volumes following a log-normal distribution. These fine particles, together with larger frame sands, are positioned, without overlapping, within a microscopic, cubic, domain with periodic boundaries. The remaining empty volume is filled with water and imposing a pressure gradient simulates the flow of fluid through the sediment. As a result of fine particles becoming trapped by the frame sand, the initial porosity of which is 0.589, the absolute permeability of the system is reduced by approximately 60–90 %, corresponding to fine particle saturations of 0.15–0.29, respectively. The permeability change due to the trapping of fine particles is also modelled theoretically using not only volume saturations but also specific surface areas of both the frame sands and the fine particles with a coefficient of proportionality.

Shear viscosity of dilute suspensions of ellipsoidal particles with a lattice Boltzmann method

The intrinsic viscosities for prolate and oblate spheroidal suspensions in a dilute Newtonian fluid are studied using a three-dimensional lattice Boltzmann method. Through directly calculated viscous dissipation, the minimum and maximum intrinsic viscosities and the period of the tumbling state all agree well with the analytical solution for particles with different aspect ratios. This numerical test verifies the analysis on maximum and minimum intrinsic viscosities. Different behavior patterns of transient intrinsic viscosity in a period are analyzed in detail. A phase lag between the transient intrinsic viscosity and the orientation of the particle at finite Reynolds number (Re) is found and attributed to fluid and particle inertia. At lower Re, the phase lag increases with Re. There exists a critical Reynolds number Rea at which the phase lag begins to decrease with Re. The Rea depends on the aspect ratio of the particle. We found that both the intrinsic viscosity and the period change linearly with Re when Re<Rea (low-Re regime) and nonlinearly when Re>Rea (high-Re regime). In the high-Re regime, the dependence of the period on Re is consistent with a scaling law, and the dependence of the intrinsic viscosity on Re is well described by second-degree polynomial fits.

On the Volume Fraction Effects of Inertial Colliding Particles in Homogeneous Isotropic Turbulence

Abstract The main objective of the present study is the investigation of volume fraction effects on the collision statistics of nonsettling inertial particles in a granular medium as well as suspended in an unsteady homogeneous isotropic turbulent flow. For this purpose, different studies with mono-disperse Lagrangian point-particles having different Stokes numbers are considered in which the volume fraction of the dispersed phase is varied between 0.001 and 0.01. The fluid behavior is computed using a three-dimensional Lattice-Boltzmann method. The carrier-fluid turbulence is maintained at Taylor microscale Reynolds number 65.26 by applying a spectral forcing scheme. The Lagrangian particle tracking is based on considering the drag force only and a deterministic model is applied for collision detection. The influence of the particle phase on the fluid flow is neglected at this stage. The particle size is maintained at a constant value for all Stokes numbers so that the ratio of particle diameter to Kolmogorov length scale is fixed at 0.58. The variation of the particle Stokes number was realized by modifying the solids density. The observed particle Reynolds and Stokes numbers are in between [1.07, 2.61] and [0.34, 9.79], respectively. In the present simulations, the fluid flow and the particle motion including particle-particle collisions are based on different temporal discretization. Hence, an adaptive time stepping scheme is introduced. The particle motion as well as the occurrence of inter-particle collisions is characterized among others by Lagrangian correlation functions, the velocity angles between colliding particles and the collision frequencies. Initially, a fluid-free particle system is simulated and compared with the principles of the kinetic theory to validate the implemented deterministic collision model. Moreover, a selection of results obtained for homogeneous isotropic turbulence is compared with in literature available DNS and LES results as well. According to the performed simulations, the collision rate of particles with large Stokes numbers strongly depends on the adopted volume fraction, whereas for particles with small Stokes numbers the influence of particle volume fraction is less pronounced.

Numerical Study of Temperature Distribution in a Spherical Tissue in Magnetic Fluid Hyperthermia Using Lattice Boltzmann Method

This work applies a three-dimensional lattice Boltzmann method (LBM), to solve the Pennes bio-heat equation (BHE), in order to predict the temperature distribution in a spherical tissue, with blood perfusion, metabolism and magnetic nanoparticles (MNPs) heat sources, during magnetic fluid hyperthermia (MFH). So, heat dissipation of MNPs under an alternating magnetic field has been studied and effect of different factors such as induction and frequency of magnetic field and volume fraction of MNPs has been investigated. Then, effect of MNPs dispersion on temperature distribution inside tumor and its surrounding healthy tissue has been shown. Also, effect of blood perfusion, thermal conductivity of tumor, frequency and amplitude of magnetic field on temperature distribution has been explained. Results show that the LBM has a good accuracy to solve the bio-heat transfer problems.

Rotational invariance in the three-dimensional lattice Boltzmann method is dependent on the choice of lattice

The lattice Boltzmann method has recently gained popularity as a tool for simulating complex fluid flows. It uses discrete sets of velocity vectors, or lattices, to create a reduced model of the molecular dynamics of a continuum fluid. While several lattices are believed to behave isotropically, there are reports of qualitatively incorrect results. However, thus far, the reason as to why a lack of isotropy occurs is not known. Based on the hypothesis that lower order lattices may not display rotational invariance, this study tests the isotropy of the D3Q15, D3Q19 and D3Q27 lattices by performing simulations at intermediate Reynolds numbers (50–500) and low Knudsen number (<0.0005) in an axisymmetrical geometry with a nozzle leading to a throat followed by a sudden expansion. The symmetry properties of the results were examined. It was found that at Re ⩾ 250 the D3Q15 and D3Q19 lattices produced different results depending on the plane of the lattice with which the flow was aligned. Lattice planes with fewer than six velocity vectors consistently produced results which were qualitatively different from the planes with six or more velocity vectors. These errors were not observed at Re = 50 or when a D3Q27 lattice was used. They appeared to be independent of grid density, collision operator and Ma. This suggests that the lattices which contain these planes are not fully isotropic and therefore do not properly replicate the behavior of a real fluid in this particular situation, notably downstream from the expansion. Predictions made using these models in more complex geometries may therefore be affected by the orientation of the lattice. When using LBM in CFD simulation (including validation) this study highlights the need for caution to ensure that the solution obtained is independent of the lattice orientation throughout the domain.

Evaluation of SOFC anode polarization simulation using three-dimensional microstructures reconstructed by FIB tomography

In order to evaluate the numerical simulation method for solid oxide fuel cell anode polarization, three-dimensional lattice Boltzmann method simulation is carried out using Ni–YSZ microstructures reconstructed by a focused ion beam scanning electron microscope. The effects of reconstructed sample volume size on the three phase boundary length, tortuosity factors and overpotential are first investigated. The YSZ tortuosity factor has remained nearly unchanged when the cross-sectional area exceeds approximately 200 μm 2, while the pore tortuosity factor is almost independent of the sample volume size. On the other hand, the Ni tortuosity shows very large variation regardless of the sample volume size. The overpotential predicted with the largest volume size sample is slightly larger than those of smaller volume samples. Two exchange current models based on patterned electrodes are assessed presently. Both models give weaker dependence on the steam concentration than the experimental data. From the predicted three-dimensional current stream lines, it is found that the mirrored computational structure gives a thinner reactive layer because of the factitious connection of Ni phase. Thus, it is recommended to use larger volume size samples which can cover whole reactive thickness when discussing the local potential and flux distributions.

A Three-Dimensional Semiclassical Lattice Boltzmann Method for Lid-Driven Cubic Cavity Flows

A three-dimensional lattice Boltzmann method based on the Uehling-Uhlenbeck Boltzmann-BGK equation is presented. The method is directly derived by projecting the kinetic governing equation onto the tensor Hermite polynomials and various hydrodynamic approximation orders can be achieved. The intrinsic discrete nodes of the three-dimensional Gauss-Hermite quadrature provide the natural lattice velocities for the semiclassical lattice Boltzmann method. Simulations of the lid-driven cubic cavity flows based on D3Q19 lattice model for several Reynolds numbers and different particle statistics are shown to illustrate the method. The results indicate distinct characteristics of the effects of quantum statistics.

Flow regime transition at high capillary numbers in a microfluidic T-junction: Viscosity contrast and geometry effect

Flow regimes obtained as a consequence of two immiscible fluids interacting at a T-junction are presented for transitional to high capillary numbers and different ratios of the continuous and dispersed phase flow rates and viscosities. Results are presented for the formation of micron-sized droplets using simulations performed based on a three-dimensional lattice Boltzmann method. The influence of viscosity and geometry of the device on the frequency and volume of droplets formed has been examined and the nondimensional drop size correlated with the capillary number and flow rate ratio. This work reveals two important and new physical features: (a) the transition zone separating droplet and jet flows narrows for high capillary numbers and (b) the critical flow rate ratio separating droplet and parallel flows increases as the dispersed to continuous channel width ratio increases, aspects which have been correlated using a simple relation for both transitions from the droplet-at-T-junction to droplet-in-channel and droplet-in-channel to parallel flow. In the droplet-at-T-junction regime, the droplet formation frequency was recorded as a function of the capillary number, flow rate ratio, and the channel width ratio as well. Results show that the transition to stable jets can be delayed and droplets can be formed even at very high flow rate ratios by significantly increasing the viscosity of the continuous phase.

Three-dimensional lattice Boltzmann method for magnetic fluids in the presence of weak magnetic field

A lattice Boltzmann method for two-phase flows with large density ratios proposed by T. Inamuro, et al. (2004) is extended in order to simulate behavior of magnetic fluids in the presence of steady weak magnetic field. A new additional term corresponding to the Maxwell stress tensor is introduced into the distribution function. The additional term is determined by using the Chapman-Enskog expansion. Surface deformation of a magnetic fluid drop in the presence of magnetic field is simulated by using this method, and the results are qualitatively agree well with the experimental results.

Wetting dynamics and particle deposition for an evaporating colloidal drop: A lattice Boltzmann study

A three-dimensional lattice Boltzmann method (LBM) has been developed for multiphase (liquid and vapor) flows with solid particles suspended within the liquid phases. The method generalizes our recent two-dimensional model [A. Joshi and Y. Sun, Phys. Rev. E 79, 066703 (2009)] to three dimensions, extends the implicit scheme presented therein to include interparticle forces and introduces an evaporation model to simulate drying of the colloidal drop. The LBM is used to examine the dynamical wetting behavior of drops containing suspended solid particles on homogeneous and patterned substrates. The influence of the particle volume fraction and particle size on the drop spreading dynamics is studied as is the final deposition of suspended particles on the substrate after the carrier liquid evaporates. The final particle deposition can be controlled by substrate patterning, adjusting the substrate surface energies and by the rate of evaporation. Some of the envisioned applications of the model are to develop a fundamental understanding of colloidal drop dynamics, predict particle deposition during inkjet printing of functional materials and to simulate the drying of liquids in porous media.

Droplet impingement and breakup on a dry surface

In this work, new results of droplet impingement and breakup have been obtained using three-dimensional lattice Boltzmann method. All four phases after impingement, the kinematic, spreading, relaxation and equilibrium phases, leading to breakup have been obtained for a range of Weber number, Reynolds number and density ratio. Conditions have been chosen such that Re ≪ We for comparison with available data in the literature. The maximum spread factor compares well with experiments as well as the theoretical value of 0.5 Re 0.25. At Oh < 0.15 and Capillary number, Ca < 1.0, the relaxation phase is marked by the presence of strong oscillations in the spreading diameter. An analytical solution for breakup based on the conservation of energy is provided. Criteria for three-dimensional droplet breakup have been developed as functions of Re and We.

Velocity slip and temperature jump simulations by the three-dimensional thermal finite-difference lattice Boltzmann method

Two problems exist in the current studies on the application of the lattice Boltzmann method (LBM) to rarefied gas dynamics. First, most studies so far are applications of two-dimensional models. The numbers of velocity particles are small. Consequently, the boundary-condition methods of these studies are not directly applicable to a multispeed finite-difference lattice Boltzmann method (FDLBM) that has many velocity particles. Second, the LBM and FDLBM share their origins with the Boltzmann equation. Therefore, the results of LBM and FDLBM studies should be verified by the results of the continuous Boltzmann equation. In my review to date on the LBM studies, it appears that such verifications were seldom done. In this study, velocity slip and temperature jump simulations in the slip-flow regime were conducted using a three-dimensional FDLBM model. The results were compared with preceding theoretical studies based on the continuous Boltzmann equation. The results agreed with the theory with errors of a few percent. To further improve the accuracy of the FDLBM, it seems necessary to increase the number of velocity particles.

Lattice Boltzmann simulations to determine drag, lift and torque acting on non-spherical particles

The drag, lift and moment coefficients of differently shaped single particles have been determined as a function of the angle of incidence at particle Reynolds numbers between Re = 0.3 and 240 under different conditions. For this purpose simulations of the flow around these particles have been performed using the three-dimensional Lattice Boltzmann method. In the first case studied a particle is fixed in a uniform flow, in the second case the particle is rotating in a uniform flow to determine, among others, the Magnus lift force and in the third case the particle is fixed in a linear shear flow. In the first case six particle shapes are considered, i.e. a sphere, a spheroid, a cube, a cuboid and two cylinders with an axis ratio of 1 and 1.5, respectively. In the second and third case the sphere and the spheroid are considered. At the higher Re considered, the drag depends strongly on particle shape, the angle of incidence and particle rotation. The lift and the torque of both the sphere and the spheroid are strongly affected by particle rotation and fluid shear. For approximately Re ⩽ 1, the shear induced lift for unbounded flow could not be simulated as the top and bottom wall have a significant influence in the current flow configuration. The shear induced lift of the sphere changes direction at approximately Re = 50 and the mean (over the orientation) shear induced lift of the spheroid changes direction at approximately Re = 90.

Three-dimensional lattice Boltzmann method for simulating blood flow in aortic arch

The three-dimensional (3D) lattice Boltzmann models, 3DQ15, 3DQ19 and 3DQ27, under different wall boundary conditions and lattice resolutions have been investigated by simulating Poiseuille flow in a circular cylinder for a wide range of Reynolds numbers. The 3DQ19 model with improved Fillippova and Hanel (FH) curved boundary condition represents a good compromise between computational efficiency and reliability. Blood flow in an aortic arch is then simulated as a typical haemodynamic application. Axial and secondary fluid velocity and effective wall shear stress profiles in a 180° bend are obtained, and the results also demonstrate that the lattice Boltzmann method is suitable for simulating the flow in 3D large-curved vessels.

Three-dimensional simulation of gaseous slip flow in different aspect ratio microducts

Three-dimensional lattice Boltzmann method based simulations of a microduct have been undertaken in this paper. The objectives are to understand the different physical phenomena occurring at these small scales and to investigate when the flow can be treated as two dimensional. Toward this end, the Knudsen number and aspect ratio (depth to width ratio) are varied for a fixed pressure ratio. The pressure in the microduct is nonlinear with the nonlinearity in pressure reducing with an increase in the Knudsen number. The pressure behaves somewhat similar to two-dimensional microchannels, even when the aspect ratio is unity. The slip velocity at the impenetrable wall has two components: along and perpendicular to the primary flow direction. Our results show that the streamwise velocity near the centerline is relatively invariant along the depth for an aspect ratio of more than three, suggesting that the microduct can be modeled as a two-dimensional microchannel. On the other hand, the velocity component along the depth is never identically zero, implying that the flow is not truly two dimensional, although for practical purposes a two-dimensional treatment might suffice. A curious change in the vector direction in a plane normal to the flow direction is observed around an aspect ratio of four. These three-dimensional results are significant because they will help in theoretical development and flow modeling at microscales.

Shear viscosity of bulk suspensions at low Reynolds number with the three-dimensional lattice Boltzmann method

We report three-dimensional parallel Lagrangian particle simulations using the lattice Boltzmann method, conducted at a low Reynolds number. Using modified Lees-Edwards boundary conditions and directly calculated viscous dissipation, we show that it is possible to recover excellent agreement with the Einstein viscosity formula in the low concentration limit and to predict viscosity corrections for larger concentrations.

Numerical investigation of flows in Czochralski crystal growth by an axisymmetric lattice Boltzmann method

An alternative new method called lattice Boltzmann method (LBM) is applied in this work to simulate the flows in Czochralski crystal growth, which is one of the widely used prototypical systems for melt-crystal growth. The standard LBM can only be used in Cartesian coordinate system and we extend it to be applicable to this axisymmetric thermal flow problem, avoiding the use of three-dimensional LBM on Cartesian coordinate system. The extension is based on the following idea. By inserting position and time dependent source terms into the evolution equation of standard LBM, the continuity and NS equations on the cylindrical coordinate system [1] can be recovered. Our extension is validated by its application to the benchmark problem suggested by Wheeler [2].