Lattice Boltzmann Simulation Research Articles

Simplified method for wetting on curved boundaries in conservative phase-field lattice-Boltzmann simulation of two-phase flows with large density ratios

A simplified method is proposed to implement a wetting boundary condition on curved surfaces within the conservative phase-field lattice-Boltzmann (LB) simulation framework. It combines the idea of Huang et al. [“An alternative method to implement contact angle boundary condition and its application in hybrid lattice-Boltzmann finite-difference simulations of two-phase flows with immersed surfaces,” Eur. Phys. J. E 41, 17 (2018)] to find the order parameter on the other side of the wall with the conservative Allen–Cahn equation (CACE) for interface evolution solved by the LB equations. It inherits the advantage of the original method using the Cahn–Hilliard equation to avoid complicated interpolations under different geometries. By using the CACE, the boundary condition for the chemical potential is circumvented (making it more simplified), and the overshooting of the order parameter is also greatly suppressed, enabling it to simulate two-phase flows with solid objects of various shapes and wettabilities at large density and viscosity ratios. Several two-dimensional, axisymmetric, and three-dimensional problems, including some previously studied by experiments, were simulated and the capability of the proposed method is demonstrated through its good agreement with theoretical predictions and/or experimental observations.

A pressure compensation method for lattice Boltzmann simulation of particle-laden flows in periodic geometries

A simple and efficient boundary treatment is proposed for periodic boundary conditions in a lattice Boltzmann method for simulating fully developed, pressure driven particle-laden flows in a complex geometry. The pressure driven effect is implemented by a simple pressure compensation method (PCM) using the pressure difference between the inlet and outlet boundaries. It eliminates the exchange of nonequilibrium distribution functions between inlet and outlet boundary nodes. It also eliminates the nonphysical oscillations of particle trajectory produced by a nonequilibrium extrapolation method when particles cross the periodic boundary. Simulation results show that the present PCM is equivalent to the body force method (BFM) for flow in a periodic straight channel with a uniform cross section. However, the BFM would significantly underestimate the fluid velocity for a flow and, hence, cannot accurately predict the particle trajectory in a periodic complex channel with a nonuniform cross section, especially at high Reynolds numbers.

Numerical Simulation of Particle Deposition in Arterial Bifurcation via Lattice Boltzmann Method

Arterial bifurcation plays a key role in cardiovascular system, so studying the characteristic of the blood flows near bifurcated arteries is of great importance in hemodynamics. The lattice Boltzmann (LB) model is used to observe the behavior of the particle deposition near the bifurcated artery. The mechanical quantity, including particle trajectories, velocities, and angular velocities, is studied numerically by LB simulations. The particle is prone to stasis as it is close to the wall of bifurcated vessel for small flow Reynolds number. Larger branch angle leads to higher possibility of particle stagnation. The numerical results are consistent with the clinical observation. The study provides a basis for understanding the mechanism of hemodynamics near bifurcations and will provide a research basis for clinical diagnosis and treatment of patients with atherosclerosis.

Anisotropic slip boundary condition for three-dimensional lattice Boltzmann simulations of liquid microflows

To explore the anisotropic slip on hydrophobic surfaces, a new anisotropic slip boundary condition is proposed for three-dimensional simulations of liquid microflows using the lattice Boltzmann method with adjustable streamwise/spanwise slip length. The proposed boundary condition is derived based on the moment method, which is no longer limited to the assumption of the unidirectional steady flow. Numerical tests validated the effectiveness of the proposed method. Compared with the bounce-back and specular reflection scheme, the proposed method is more accurate and stable for capturing velocity profiles. The proposed method was applied to explore the effects of anisotropic slip on three-dimensional micro-lid-driven cavity flow. The numerical simulation results showed that the anisotropic slip has a greater influence on the flow than the pure streamwise/spanwise slip, and the streamwise slip plays a more important role in influencing the flow than the spanwise slip. The findings may hold significance for efficient development of microfluidic systems and micro-devices.

Three-dimensional lattice Boltzmann simulation of reactive transport and ion adsorption processes in battery electrodes of cation intercalation desalination cells

Cation intercalation desalination (CID) has gained great popularity in the field of water desalination because of its excellent desalination performance. Due to lack of understanding of the relationship between electrode microstructures and reactive adsorption processes in CIDs, the further development of high-performance CID electrodes has been hindered. To this end, the influences of electrode microstructures on the desalination performance of CID cells were investigated from the pore-scale level in this work. The three-dimensional microstructures of porous electrodes are first reconstructed by an improved random generation method. Based on the reconstructed porous electrodes, the flow, mass transfer and intercalation reaction processes under the constant current are simulated using the lattice Boltzmann method. The effects of applied current density, porosity and size of active particles on the change of liquid-phase sodium concentration and Na-intercalated degree in the solid phase are evaluated. The simulation results show that increasing the current density can accelerate the ion intercalation and desalination rates. During the desalination, the ion concentration is unevenly distributed in the pores of porous electrodes, and the intercalation degrees are different along the electrode thickness direction and in the particle radial direction. The increase of porosity can alleviate the concentration polarization of liquid-phase sodium ion and reduce the difference of particle intercalation degree between the front- and back-sides of the electrode. In addition, the increase of porosity can accelerate the desalination process, but cannot improve the total salt removal. Reducing particle size can shorten the time for particles to reach the sodium-rich state, but it can aggravate the polarization of sodium ion concentration in the liquid phase at both ends of the electrode. This work reveals the ion intercalation behavior in the CID and its relationship with the electrode microstructures, and may provide useful information for the design and research of CID.

Numerical Bifurcation Analysis of PDEs From Lattice Boltzmann Model Simulations: a Parsimonious Machine Learning Approach

We address a three-tier data-driven approach for the numerical solution of the inverse problem in Partial Differential Equations (PDEs) and for their numerical bifurcation analysis from spatio-temporal data produced by Lattice Boltzmann model simulations using machine learning. In the first step, we exploit manifold learning and in particular parsimonious Diffusion Maps using leave-one-out cross-validation (LOOCV) to both identify the intrinsic dimension of the manifold where the emergent dynamics evolve and for feature selection over the parameter space. In the second step, based on the selected features, we learn the right-hand-side of the effective PDEs using two machine learning schemes, namely shallow Feedforward Neural Networks (FNNs) with two hidden layers and single-layer Random Projection Networks (RPNNs), which basis functions are constructed using an appropriate random sampling approach. Finally, based on the learned black-box PDE model, we construct the corresponding bifurcation diagram, thus exploiting the numerical bifurcation analysis toolkit. For our illustrations, we implemented the proposed method to perform numerical bifurcation analysis of the 1D FitzHugh-Nagumo PDEs from data generated by D1Q3 Lattice Boltzmann simulations. The proposed method was quite effective in terms of numerical accuracy regarding the construction of the coarse-scale bifurcation diagram. Furthermore, the proposed RPNN scheme was sim 20 to 30 times less costly regarding the training phase than the traditional shallow FNNs, thus arising as a promising alternative to deep learning for the data-driven numerical solution of the inverse problem for high-dimensional PDEs.

Comparing lattice Boltzmann simulations of periodic fluid flow in repeated micropore structures with longitudinal symmetry and asymmetry

Pumping of a particulate suspension back and forth through a membrane of periodic axisymmetric pores results in no net flow of the fluid; however, the particles are transported along the pores from one side of the membrane to the other. The movement of the particles is dependent on the geometry of the pore walls. Current simulations for this problem utilise standard computational fluid dynamics techniques (e.g. finite element method, boundary element method). However, there are difficulties associated with applying these techniques to this problem, such as the requirement of many spatial periods. The lattice Boltzmann method overcomes these disadvantages by utilising periodic boundary conditions, which are straightforward to implement. Flow simulations in longitudinally symmetric and asymmetric pores with various Reynolds numbers are compared. The importance of pore shape and viscous effects is showcased through streamline plots.

Lattice Boltzmann simulation of laminar forced convection in a parallel-plate duct with evolving porous layers at the walls

The present study conducts lattice Boltzmann simulation of flow in a duct with evolving porous layers (EPL) on the walls. The effects of elapsed time (0 < t < 125 mins), Darcy number (0.0001 < Da < 0.01), Reynolds number (100 < Re < 400), and porosity (0.85 < ε < 0.99) on the problem are studied. The time history of the average Nusselt number ratio is calculated to study thermal performance reduction of the duct. It is seen that the thermal performance is reduced as the EPL grows on the walls. Two stages in the performance reduction over time are identified in the present study, called the initial and evolution stages. At the initial stage, the performance is reduced slightly, and at the evolution stage, that starts at tev, the performance reduction occurs rapidly and approximately at a constant rate. It is shown that at Re = 200 the thermal performance is reduced by 17% and 3.2% for Da = 10−4 and 10−2, respectively, compared to the clear duct. In the present study, correlations for the evolution starting time and average Nusselt number are proposed in terms of Reynolds number, Darcy number, and elapsed time. It is also seen that the porosity has a negligible effect on thermal performance, whereas the effect of Reynolds number is significant.

Lagrangian sensors in a stirred tank reactor: Comparing trajectories from 4D-Particle Tracking Velocimetry and Lattice-Boltzmann simulations

In this study, three-dimensional flow measurements by means of 4D-Particle Tracking Velocimetry (4D-PTV) are carried out in a laboratory-scale 3 L stirred tank reactor in order to investigate the flow-following behavior of two different inertial particle types, Polyethylene (PE) particles and alginate beads, at different impeller frequencies. Applied particles mimic Lagrangian sensor particles, which are intended to determine process parameters such as oxygen concentration at their corresponding position inside a bioreactor. Accompanying Lattice-Boltzmann Large Eddy Simulations (LB LES) provide additional information about the fluid flow and the difference in the trajectories between inertial and non-inertial particles. The data acquired from LB LES is validated with the experimental data by means of a Lagrangian and a Eulerian approach. In their tail, the probability distributions show higher Lagrangian velocities and accelerations for 4D-PTV data compared to LB LES data. Time-averaged Eulerian data is utilized to determine particle Reynolds numbers lower than 200. The Stokes number distributions show 10-fold higher values for the alginate beads than for PE particles, however, both particle types do not sufficiently meet the criterion of a flow-following Stokes number of St≤0.01. Generally, time-averaged results from LB LES are in good accordance to the 4D-PTV data. From the LB LES, a theoretical, maximum particle diameter of approx. 20 μm is determined, which meets the criterion of St≤0.01 throughout the reactor. This result implies that with current sensor particle technology it is not possible to meet the flow-following behavior and depict the lifelines of cells during a cultivation process. Therefore, further research is necessary to understand particle trajectories and to translate them into lifelines of cells.

Lattice Boltzmann study of fluid flow and heat transfer characteristics of a heated porous elliptic cylinder: a two-domain scheme

PurposeThis study aims to investigate lattice Boltzmann (LB) simulation of the fluid flow and heat transfer characteristics of a heated porous elliptic cylinder in uniform flow based on the two-domain scheme. In the present research, the effect of axis ratio (1 ≤ AR ≤ 2), Reynolds number (5 ≤ Re ≤ 40) and Darcy number (10−4 ≤ Da ≤ 10−2) are studied.Design/methodology/approachTo perform the LB simulation based on the two-domain scheme, the nonequilibrium extrapolation method is modified to model the heat transfer interfacial conditions required at the curved interface.FindingsThe results show that the axis ratio as well as Reynolds and Darcy numbers significantly affect the fluid flow and heat transfer characteristics of the porous elliptic cylinder. It is shown that for AR > 1, the phenomenon of detached recirculating zone occurs at much higher Darcy numbers compared with the case of the porous circular cylinder (AR = 1). The results show that the location of maximum temperature within the cylinder moves downstream when the Reynolds number, Darcy number and axis ratio increase. It is also concluded that the average Nusselt number of a porous elliptic cylinder is always lower than that of a porous circular cylinder.Originality/valueThe LB simulation of forced convection from a porous cylinder in uniform flow with a curved interface based on the two-domain scheme has not been studied yet.

Study on the Ways to Improve the CO2-H2O Displacement Efficiency in Heterogeneous Porous Media by Lattice Boltzmann Simulation.

To improve the efficiency of CO2 geological sequestration, it is of great significance to in-depth study the physical mechanism of the immiscible CO2–water displacement process, where the influential factors can be divided into fluid–fluid and fluid–solid interactions and porous media characteristics. Based on the previous studies of the interfacial tension (capillary number) and viscosity ratio factors, we conduct a thorough study about the effects of fluid–solid interaction (i.e., wettability) and porous media characteristics (i.e., porosity and non-uniformity of granule size) on the two-phase displacement process by constructing porous media with various structural parameters and using a multiphase lattice Boltzmann method. The displacement efficiency of CO2 is evaluated by the breakthrough time characterizing the displacement speed and the quasi-steady state saturation representing the displacement amount. It is shown that the breakthrough time of CO2 becomes longer, but the quasi-steady state saturation increases markedly with the increase in CO2 wettability with the surface, demonstrating an overall improvement of the displacement efficiency. Furthermore, the breakthrough time of CO2 shortens and the saturation increases significantly with increasing porosity, granule size, and non-uniformity, showing the improvement of the displacement efficiency. Therefore, enhancing the wettability of CO2 with the surface and selecting reservoirs with greater porosity, larger granule size, and non-uniformity can all contribute to the efficiency improvement of CO2 geological sequestration.

Convolutional neural network based prediction of effective diffusivity from microscope images

This study presents a method to predict the effective diffusivity of porous media from a limited set of scanning electron microscope images using deep learning. The electrodeposited nickel oxide film over carbon nanostructure, meant to provide electrochemical capacitance based on diffusion of ions through the film's pore space, was observed under the scanning electron microscope. Gray scale SEM images were converted to binary images, and the effective diffusivity was found using lattice Boltzmann simulations. A convolutional neural network (CNN) model comprising two sets of convolution and pooling layers and a fully connected layer was trained with lattice Boltzmann method data, where the choices of kernel size and stride were made, keeping the homogeneity of the image in perspective. An initial attempt to train a CNN with 900 training instances predicted effective diffusivity with a relative error of 13.33%, 43.49%, and 36.41% for the training, validation, and test set, respectively. However, it was over-predicting the diffusivities for images with very low connectivity. Isolated pores within the images were identified and were eliminated to solve this issue before using the images to train another CNN. This second network worked well for images with low connectivity and brought down the mean relative error from 36.41% to 25.43% for the test set. The error was found to vary across the images due to highly non-even representation of different image types, increasing by complex pore connectivity at lower porosity for which the number of training instances is the least, and overfitting of networks on medium porosity images that are present in greater numbers. The SEM images were further classified based on porosity as well as pore connectivity. The training was performed with one category of images, and the testing was conducted with images of another category at the other end of the spectrum to evaluate CNN efficacy upon encountering a new category of images. The results show the ability of the network to extend the prediction to an unknown electrode morphology, which is critical for the analysis of SEM images.

A theoretical analysis of mass leakage at boundaries within the lattice Boltzmann method

Mass leakage at boundaries can be a critical issue for the reliability of the lattice Boltzmann (LB) method based on Cartesian grids. Despite numerous works based on the LB method, the intrinsic macroscopic mechanisms causing mass leakage are still not fully characterized but are essential to improve the mass conservation of LB simulations. In this paper, an original theoretical investigation of mass leakage at boundaries is proposed within the general LB framework. It is demonstrated that the mass leakage originates from the intrinsic deficiency of the wall-cut LB links at boundary nodes in recovering macroscopic momenta. From a mesoscopic-level definition, i.e., the net loss of distribution functions during the streaming process, the local mass leakage at individual boundary nodes, and its averaged value along smooth boundaries are mathematically expressed using macroscopic variables. The local mass leakage is shown to be dominated by terms proportional to the tangential momentum component. In contrast, the averaged mass leakage is shown to be contributed by various terms, including the boundary curvature, the tangential momentum, and the gradients of density, momentum, and momentum flux. Meanwhile, the amplitude of the averaged mass leakage is theoretically estimated to be proportional to the local grid spacing based on which a first-order accurate correction scheme is proposed. In addition, both the local and averaged mass leakage are demonstrated to be significantly dependent on boundary orientation with respect to the grid. The proposed theoretical analysis is assessed by performing numerical experiments. Two-dimensional weakly compressible flows through straight and curved moving channels are considered to estimate each term appearing in the theoretical analysis. The numerical results are in very good agreement with the proposed analysis, and the proposed mass correction scheme based on the averaged mass leakage effectively cures the mass leakage problems in the considered test cases.

Lattice Boltzmann simulations of gas bubble transport in proton exchange membrane water electrolysis cells

Gas/liquid two-phase transport is the key fundamental scientific issue in the proton exchange membrane (PEM) water electrolysis cell, which has important effects on the overall performance of water electrolysis and microstructure optimization. In this study, a combination of the lattice Boltzmann two-phase model and the QSGS numerical method was used to numerically model the porous diffusion layer and the micro-channel structure, and investigate the effects of porosity and wettability properties on the gas/liquid two-phase transport process. Simulation results show that the value of porosity will obviously affect the association and distribution pattern of solid particles inside the porous diffusion layer, and the reduction of porosity will cause the association part of solid particles to be narrower and longer, resulting in complex and variable pore channels. Some closed pore channels will appear inside the diffusion layer, which is not conducive to the smooth transmission of gas bubbles. In addition, the increase of contact angle will enhance the interaction force between the bubble and the solid wall, making it difficult for the bubble to fall off from the solid surface. Moreover, the increased interaction force will slow down the sliding speed of gas bubbles, which will result in the fusion of more gas bubbles and increase the risk of blocking the flow micro-channel. This study has initially grasped the mechanisms of micro/meso scale gas bubble transport in the PEM water electrolysis cell, which will provide theoretical basis for the optimized development of high-performance water electrolysis system for hydrogen production.

Lattice Boltzmann simulation of particles inertial migration with slippery surface and moderate concentration in circular tube flow

Hydrodynamic migration of spherical slippery particles suspended in a cylindrical channel flow is numerically studied in this paper. The effects of the particle concentration of particle ([Formula: see text], tube-to-particle diameter ratio ([Formula: see text] and Knudsen number (Kn), respectively, with ranges of [Formula: see text] and [Formula: see text] with the channel Reynolds number of [Formula: see text], are concerned in the simulations. The objective of this work is to explore the pipeline transportation of relatively large and moderately dense particles with slippery surface, for which the characteristics have not been comprehensively exhibited in the literature. Such particle-resolved suspension flow is solved by a three-dimensional lattice Boltzmann method, where a curved kinetic boundary condition is adopted to resolve the velocity slip phenomenon at the fluid-particle interface, and the particle-particle collision is performed by a repulsive force model. The results elucidate that the effect of particle focusing is less marked at intermediate concentrations. At larger [Formula: see text], some particles may migrate to the center of channel due to the aggravation of the mutual collision. The increase of Re contributes to the particle focusing at low [Formula: see text], but not for the case of higher [Formula: see text]. On the other hand, the [Formula: see text] generally has a negative effect on the inertial focusing. Furthermore, the migration velocity of particles reduces and the behavior of inertial focusing is enhanced simultaneously, with the increase of Kn.

Simple lattice Boltzmann method algorithm with low memory usage

As lattice Boltzmann simulation codes require updating several million floating point values thousands of times, optimized implementation and efficient data structure are crucial to minimize memory consumption and use all the available computational power. In this paper, a new lattice Boltzmann algorithm is proposed, suitable for the simulation of large-scale systems by avoiding storing the data of solid nodes. As a structure-of-array memory layout is used, the streaming step is performed by a simple shift operation. The advantages of this algorithm are the simplicity of the memory layout and streaming function implementation. Because the algorithm utilizes an indirect addressing scheme, particularly for low void fraction geometries the memory resources are used efficiently. As no computation is carried out for solid nodes, a good performance for irregular geometries with low void fractions is also achieved. To verify the implementation of the proposed algorithm several academic benchmarks are studied, including Poiseuille flow, Cavity flow, and Cylinder flow. A theoretical estimation of the memory consumption is carried out for different void fractions. Then the performance of the implemented code is investigated by simulating flow around two complex geometries and the memory usage and computational performance compared to the Palabos code.

Exploring the Role of Initial Droplet Position in Coalescence-Induced Droplet Jumping: Lattice Boltzmann Simulations

Coalescence-induced droplet jumping on superhydrophobic surfaces with different initial positions was numerically simulated using the 2D multi-relaxation-time (MRT) Lattice Boltzmann method (LBM). Simulation results show that for coalesced droplets with radii close to the structure length scale, the change of initial droplet positions leads to a significant deviation of jumping velocity and direction. By finely tuning the initial droplet positions on a flat-pillared surface, perpendicular jumping, oblique jumping, and non-jumping are successively observed on the same structured surface. Droplet morphologies and vector diagrams at different moments are considered. It is revealed that the asymmetric droplet detachment from the structured surface leads to the directional transport of liquid mass in the droplet and further results in the oblique jumping of the coalesced droplet. In order to eliminate the influence of initial droplet position on droplet jumping probability, a surface with pointed micropillars is designed. It is demonstrated that compared to flat-topped micropillars, a surface with pointed micropillars can suppress the initial droplet position effects and enhance droplet jumping probability. Furthermore, the effect of droplet/structure scale on droplet jumping is investigated. The influence of initial positions on coalescence-induced droplet jumping from the refined surface can be ignored when the droplet scale is larger than three times the structure scale. This study illustrates the role of initial droplet position in coalescence-induced droplet jumping and provides guidelines for the rational design of structured surfaces with enhanced droplet self-shedding for energy and heat transfer applications.

Parallel GPU-accelerated adaptive mesh refinement on two-dimensional phase-field lattice Boltzmann simulation of dendrite growth

Simulations of dendritic solidification involving melt convection and solid motion usually require a considerably higher computational domain than the dendrite size, whose computational efficiency with a uniform mesh is extremely low. In this study, to accelerate those two-dimensional simulations using the phase-field and lattice Boltzmann (PF-LB) methods, we developed a parallel computing method with multiple graphics processing units (GPUs) for the adaptive mesh refinement (AMR) method with dynamic load balancing (parallel-GPU AMR). It was confirmed that parallel-GPU AMR simulations were faster than those with the uniform mesh when the number of grid points in the adaptive mesh was around 40% or less than those in the uniform mesh. We also demonstrate that the developed parallel-GPU AMR can greatly accelerate the PF-LB simulations of dendrite growth with melt convection and solid motion.

Lattice Boltzmann simulation of liquid water transport in gas diffusion layers of proton exchange membrane fuel cells: Parametric studies on capillary hysteresis

Water management is crucial for reliable operation of Polymer Electrolyte Membrane Fuel Cells (PEMFC). Here, the gas diffusion layer (GDL) plays an essential role as it has to ensure efficient water removal from and oxygen transport to the catalyst layer.In this study water transport through porous carbon felt GDLs was simulated using a 3D Color-Gradient Lattice Boltzmann model. Simulations were carried out on microstructures of plain and impregnated fiber substrates of a Freudenberg H14. The GDL microstructures were reconstructed from high-resolution X-ray micro-computed tomography (μ-CT). For the distinction of carbon fibers and polytetrafluoroethylene (PTFE) in the binarized microstructures an in-house algorithm was developed. The additive was specified heterogeneously in the GDL through-plane direction employing a PTFE loading profile as derived based on μ-CT image data. In the in-plane direction the additive was furthermore defined in a realistic fashion near carbon fiber intersections. Prior to parametric studies on capillary behavior a sophisticated modeling approach for semipermeable membranes had to be developed to account for experimental boundary conditions. Capillary hysteresis was then investigated by simulation of intrusion and drainage curves and subsequent comparison to testbench data.

Numerical study on melting performance improvement with fractal tree-shaped fins

In this paper, the melting performance improvement of phase change material (PCM) in latent heat thermal energy storage (LHTES) systems with fractal tree-shaped fins has been discussed via lattice Boltzmann simulation. The abundant melting phenomena are comprehensive results of the heat conduction and convection. Based on the numerical results, it is found that the existence of tree-shaped fins significantly improves the melting performance, compared with the radical-fin LHTES unit. More specifically, the stretched tree-shaped fins uniform the temperature field and make great contributions for heat transfer enhancement at the early stage of melting process and thereby accelerating the generation of convection with the increase in the liquid phase. Moreover, it is observed that the melting efficiency improves with the increase in branch level (k) of tree-shaped fins, and this tendency reverses when k exceeds a critical value. The results also indicate both the length ratio and width ratio of tree-shaped fin have a significant influence on melting performance, and the optimal values for the ratios of length and width are 1.0 and 4/9, respectively. Additionally, different arrangements of tree-shaped fins are also considered to reveal the relationships between heat conduction and convection for melting performance improvement.