Lattice Boltzmann Research Articles

Three-dimensional solidification modeling of various materials using the lattice Boltzmann method with an explicit enthalpy equation.

Based on the mesoscopic scale, the lattice Boltzmann method (LBM) with an enthalpy-based model represented in the form of distribution functions is widely used in the liquid-solid phase transition process of energy storage materials due to its direct and relatively accurate characterization of the presence of latent heat of solidification. However, since the enthalpy distribution function itself contains the physical properties of the material, these properties are transferred along with the enthalpy distribution function during the streaming process. This leads to deviations between the enthalpy-based model when simulating the phase transition process of different materials mixed and the actual process. To address this issue, in this paper, we construct an enthalpy-based model for different types of materials. For multiple materials, various forms of enthalpy distribution functions are employed. This method still uses the form of enthalpy distribution functions for collisions and streaming processes among the same type of substance, while for heat transfer between different materials, it avoids the direct transfer of enthalpy distribution functions and instead applies a source term to the enthalpy distribution functions, characterizing the heat transfer between different materials through the energy change before and after mixing based on the temperature. To verify the accuracy of the method proposed in this paper, a detailed solidification model for two different materials is constructed using the example of water droplets solidifying in air, and the results are compared with experimental outcomes. The results of the simulation show that the model constructed in this paper is largely in line with the actual process.

Spacing effects on flows around two square cylinders in staggered arrangement via LBM

This study presents a computational analysis of fluid flow characteristics around two staggered arranged square cylinders using the Lattice Boltzmann Method (LBM). With Reynolds number (Re) fixed at 200, numerical simulations explore the influence of varying gap ratios (G) ranging from 0 to 10 times the cylinder size. Emphasis is placed on understanding the impact of cylinders spacing on flow structure mechanisms and induced forces. Investigation of fluid flow parameters includes vorticity behavior, pressure streamlines, and variations in drag and lift coefficients alongside the Strouhal number under different values of G. From the results, four distinct flow patterns emerge: single bluff body flow, flip flopping flow, modulated synchronized flow, and synchronized flow, each exhibiting unique characteristics. This study reveals the strong dependence of fluid forces on G, with low spacing values leading to complex vortex structures and fluctuating forces influenced by jet flow effects. At higher spacing values, proximity effects between cylinders diminish, resulting in a smoother periodic flow. The Strouhal number, average drag force and the rms values of drag and lift force coefficients vary abruptly at narrow gaps and become smooth at higher gap ratios. Unlike the tandem and side-by-side arrangements the staggered cylinders arrangement is found to have significant impact on the pressure variations around both cylinders. Overall, this research could contribute to a comprehensive understanding of staggered cylinder arrangements and their implications for engineering applications.

Numerical simulation for β/α transformation of Ti–6Al–4V alloy using a lattice Boltzmann - Cellular automata method

This paper considers the beta/alpha transformation of Ti–6Al–4V alloy using a lattice Boltzmann method (LBM) – cellular automata (CA) coupled method in terms of microstructural evolution during phase transformation. Particularly, the effects of the cooling rate on microstructures such as beta grain size, alpha colony size, and alpha lath thickness were examined as well as the overall morphologies. The LBM and CA were used to implement the diffusion of alloy components and phase transformation, respectively. Additionally, the thermodynamic and kinetic data for simulating the ternary alloy system were obtained from CALPHAD software to utilize the equilibrium phase diagram calculations. The initial states of the beta grain and its composition fields affect the processing of beta/alpha phase transformation and the final alpha + beta phase morphologies. Validation of the proposed method was conducted to compare the simulation results with experimental trends for microstructures of Ti–6Al–4V from the literature. The error in prediction of microstructural morphologies were 20% in the average alpha thickness with deviation of up to 5 μm.

Lattice Boltzmann approach for acoustic manipulation.

We employ a lattice Boltzmann method to compute the acoustic radiation force produced by standing waves on a compressible object for the density matched case. Instead of simulating the fluid mechanics equationsdirectly, the proposed method uses a lattice Boltzmann model that reproduces the wave equation, together with a kernel interpolation scheme, to compute the first-order perturbations of the pressure and velocity fields on the object's surface and, from them, the acoustic radiation force. The procedure reproduces with excellent accuracy the theoretical expressions by Gor'kov and Wei for the sphere as the 3D case and an infinitely long cylinder as the 2D case, respectively, even with a modest number of lattice Boltzmann cells. The proposed method shows to be a promising tool for simulating phenomena where the acoustic radiation force plays a relevant role, like acoustic tweezers or the acoustic manipulation of microswimmers, with applications in medicine and engineering.

A stochastic Galerkin lattice Boltzmann method for incompressible fluid flows with uncertainties

Efficient modeling and simulation of uncertainties in computational fluid dynamics (CFD) remains a crucial challenge. In this paper, we present the first stochastic Galerkin (SG) lattice Boltzmann method (LBM) built upon the generalized polynomial chaos (gPC). The proposed method offers an efficient and accurate approach that depicts the propagation of uncertainties in stochastic incompressible flows. Formal analysis shows that the SG LBM preserves the correct Chapman–Enskog asymptotics and recovers the corresponding macroscopic fluid equations. Numerical experiments, including the Taylor–Green vortex flow, lid-driven cavity flow, and isentropic vortex convection, are presented to validate the solution algorithm. The results demonstrate that the SG LBM achieves the expected spectral convergence and the computational cost is significantly reduced compared to the sampling-based non-intrusive approaches, e.g., the routinely used Monte Carlo method. We obtain a speedup factor of 5.72 compared to Monte Carlo sampling in a randomized two-dimensional Taylor–Green vortex flow test case. By leveraging the accuracy and flexibility of LBM and the efficiency of gPC-based SG, the proposed SG LBM provides a powerful framework for uncertainty quantification in CFD practice.

Expression of Concern: Entropy analysis and MHD mixed convection heat transfer of the magnetic nanofluid in an asymmetric T-shaped cavity using the lattice Boltzmann method

Expression of Concern: Entropy analysis and MHD mixed convection heat transfer of the magnetic nanofluid in an asymmetric T-shaped cavity using the lattice Boltzmann method

Effects of hematocrit and non-Newtonian blood rheology on pulsatile wall shear stress distributions in vascular anomalies: A multiple relaxation time lattice Boltzmann approach

In the present study, we investigate the flow dynamics of non-Newtonian blood, focusing on the distribution of wall shear stress (WSS) and hematocrit levels, which is the volume percentage of red blood cells in whole blood. We analyze these factors under pulsatile conditions, in vascular anomalies such as stent channels and intracranial aneurysms. To achieve this, a three-dimensional computational approach based on the lattice Boltzmann method (LBM) with a multiple relaxation time (MRT) collision operator is employed. To represent the blood's shear-thinning properties, we developed a constitutive model inspired by the Carreau–Yasuda model. This model considers the variability in blood viscosity with shear rate correlated with hematocrit levels based on experimental data documented in the literature. The accuracy of the employed MRT-LBM is demonstrated by the consistency of results with analytical solutions for steady state and experimental data for pulsatile WSS distributions in non-Newtonian and Newtonian fluids. Results indicate that, in areas narrowed by stenosis or expanded by aneurysms, hematocrit levels affect flow dynamics. Higher hematocrit levels intensify pulsatile flow through stenotic regions, increasing WSS cyclic variations. We derived a density distribution function to demonstrate how shear rates vary in vascular anomalies, revealing blood viscosity changes and non-Newtonian properties. These properties complicate flow patterns, resulting in non-linear WSS distributions, which are essential for understanding endothelial cell reactions and disease pathways. Pulsatile blood flow and altered rheological properties due to increased hematocrit affect saccular aneurysm fluid dynamics over time and space, causing vorticities to change shape, size, and intensity.

Expression of Concern: Entropy generation of the laminar and mixed flow of alumina/water nanofluid flow in a two-dimensional rectangular enclosure affected by a magnetic field using the lattice Boltzmann method

Expression of Concern: Entropy generation of the laminar and mixed flow of alumina/water nanofluid flow in a two-dimensional rectangular enclosure affected by a magnetic field using the lattice Boltzmann method

Expression of Concern: Hybrid nanofluid mixed convection in a cavity under the impact of the magnetic field by lattice Boltzmann method: Effects of barrier temperature on heat transfer and entropy

Expression of Concern: Hybrid nanofluid mixed convection in a cavity under the impact of the magnetic field by lattice Boltzmann method: Effects of barrier temperature on heat transfer and entropy

A critical assessment of Navier–Stokes and lattice Boltzmann frameworks applied to high-lift configuration through a multiresolution approach

The present work focuses on a thorough assessment of the influence of two very different numerical approaches, namely, Navier–Stokes (NS) and the lattice Boltzmann method (LBM), to simulate the flow past a three-element airfoil through zonal detached eddy simulation (ZDES). Both computations (ZDES-NS and ZDES-LBM) are compared to the reference results, namely, a wall-resolved large eddy simulation (WRLES) as well as the experimental data. It is shown that despite very different numerical modeling, the two ZDES provide very consistent results, with the first- and second-order statistics obtained with equivalent accuracy in the impingement region. In light of present results, the ZDES mode 2 (2020) turbulence model within an LBM framework appears as a judicious combination for high-lift flow applications owing to its robustness regarding the use of very fine isotropic Cartesian grids. In addition, ZDES-NS exhibits a very good agreement with both references, especially WRLES despite having 40 times less nodes.

Persistence of large-scale coherent structures in a turbulent pipe flow through an improved lattice Boltzmann approach

We simulated a turbulent pipe flow within the lattice Boltzmann method using a multiple-relaxation-time collision operator with Maxwell–Boltzmann equilibrium distribution expanded, for the sake of a more accurate description, up to the sixth order in Hermite polynomials. The moderately turbulent flow (Reτ≈181.3) is able to reproduce up to the fourth statistical moment with great accuracy compared with other numerical schemes and with experimental data. A coherent structure identification was performed based on the most energetic streamwise turbulent mode, which revealed a surprising memory effect related to the large-scale forcing scheme that triggered the pipe's turbulent state. We observe that the existence of large-scale motions that are out of the pipe's stationary regime does not affect the flow's detailed single-point statistical features. Furthermore, the transitions between the coherent structures of different topological modes were analyzed as a stochastic process. We find that for finely resolved data, the transitions are effectively Markovian, but for larger decimation time lags, due to topological mode degeneracy, non-Markovian behavior emerges, in agreement with previous experimental studies.

Lattice Boltzmann simulation on particle suspensions containing porous particles in a narrow channel

The suspension of porous particles in fluids occurs widely in various natural and industrial processes. However, the sedimentation behavior of porous particles is not extensively understood as the solid impermeable counterparts. In this work, the drafting–kissing–tumbling (DKT) phenomenon in a narrow channel containing porous particles is investigated by the multi-relaxation-time (MRT) lattice Boltzmann method (LBM). The initial particle spacing Lp* (1.5∼6) and Darcy number Da (8×10−6∼6×10−2) are examined on the sedimentation process of two particles under three initial arrangements, i.e., the trailing particle is porous (case 1), the leading particle is porous (case 2), and both the particles are porous (case 3). The results show that the presence of porous particles can enhance the interactions between two particles, and increasing the penetrability reduces the particle drag force to accelerate sedimentation. The drafting time is insensitive to Da at small Lp*, and it decreases with Da at large Lp* in cases 1 and 3 while it changes to increase with Da in case 2. A phase diagram with respect to Da and Lp* is further extracted to identify three sedimentation modes of particle pairs. It is found that the transition between the one-off DKT and repeated DKT modes is not affected by Lp* in cases 2 and 3, while the critical condition for the non-DKT and one-off DKT modes depends strongly on Da and Lp* in case 2.

Expression of Concern: Entropy Generation and Mixed Convection in an Enclosure with Five Baffles Exposed to a Uniform Magnetic Field with Volumetric Radiation for the Solar Collectors via Lattice Boltzmann Method

Expression of Concern: Entropy Generation and Mixed Convection in an Enclosure with Five Baffles Exposed to a Uniform Magnetic Field with Volumetric Radiation for the Solar Collectors via Lattice Boltzmann Method

Energy conservation analysis and formation control of multi-tadpoles based on lattice Boltzmann method

Energy conservation analysis and formation control of multi-tadpoles based on lattice Boltzmann method

Three-dimensional lattice Boltzmann flux solver for three-phase/component flow

In this article, an immiscible three-phase/three-component lattice Boltzmann flux solver (TPLBFS) based on diffusion interface method is proposed, which can achieve three-phase flow simulation with high density ratio (1:1000). This model quickly solved (1) the flux at the grid interface using the lattice Boltzmann method (LBM) solution format and (2) the Navier–Stokes (NS) equation and Cahn–Hilliard (CH) equation using a unified format. Compared to LBM, TPLBFS can be applied to unstructured networks. Moreover, TPLBFS can independently add or remove source items and has high secondary development features. Its outstanding computing power has been demonstrated by multiple two-dimensional/three-dimensional (2D/3D) examples, including 2D liquid lens as well as 3D bubble absorption and bubble rising in a three-phase system.

Numerical simulation of wake flow around two square cylinders through passive control method

Two-dimensional numerical simulations are performed to study the effect of height of control plates placed at the downstream location in a vertical direction of a channel for flow past two inline square cylinders. The numerical method used is the lattice Boltzmann method (LBM) and Reynolds number is kept constant at Re = 150 (Re = Uinf d/ν) for fixed gap spacing g = 3.5 (g = s/d). The height of the control plate varies from h = 0.1 to 8. First, the validity of code for the present problem and suitable grid points are checked along the selection of uniform inflow velocity. After that verification, the numerical simulations are performed to obtain the results under the effect of height of control plates using the passive control method. Calculated results are, in terms of vorticity contour, drag and lift coefficients, pressure contour, energy spectrum, and force statistics. Under the discussion of vorticity contour visualization, we obtained six types of flow mode and named them according to flow behavior and their characteristics. In pressure contour, it is visualized that the maximum pressure occurred at near the upstream position of the first cylinder as well as the upper and lower edge of the main cylinder as compared to the downstream cylinder and control plate, but at some position inside the domain, pressure contour contained negative values as well in between the gap of two square cylinders and control plate. In force statistics, we computed the values of Cdmean, Cdrms, Clrms, and St. Mean drag coefficients for both upstream cylinder (C1) and downstream cylinder (C2) are increased as the height of the control plate increased from 0.1 to 1.5, but as the height of the control plate reached its maximum value, the value of Cdmean turned toward the decline. The maximum value of Cdmean obtained at h = 2.25 and the minimum value occurred at h = 8. For cylinder C2, negative values for some selected heights such as h = 0.1–1.25 and h = 4–8 are also observed because of thrust. The value of the Strouhal number for both the cylinders C1 and C2 are similar at h = 0.1–4.5, but at h = 5, the values of the Strouhal number differ for both cylinders, but at the largest values of control plate's height, i.e., h = 6–8, the Strouhal number contains zero values for both cylinders C1 and C2. At these zero values of the Strouhal number, in vorticity contour jet type of flow mode is observed at h = 6–8, as a new flow mode, which is not identified before in the passive control method for flow past two or more square cylinders.

Estimating Residual Oil Saturation in Carbonate Rocks: A Combined Approach of Direct Simulation and Data-Driven Analysis

Summary Estimating residual oil saturation (Sor) post-waterflooding is critical for selecting enhanced oil recovery strategies, further field development, and production prediction. We established a data-driven workflow for evaluating Sor in carbonate samples using microcomputed tomography (μ-CT) images. The two-phase lattice Boltzmann method (LBM) facilitated the flooding simulation on 7,192 μ-CT samples. Petrophysical parameters (features) obtained from pore network modeling (PNM) and feature extraction from μ-CT images were utilized to develop tree-based regression models for predicting Sor. Petrophysical features include porosity, absolute permeability, initial water saturation (Swi), pore size distribution (PSD), throat size distributions (TSD), and surface roughness (Ra) distribution. Our method excludes vugs and macro/nanoporosity, which complicates multiscale simulations—a recognized challenge in modeling carbonate rocks. When subdividing the image into numerous subvolumes, certain subvolumes may contain vugs exceeding the dimensions of the subvolume itself. Hence, these vugs were omitted given the entirety of the image constitutes a vug. Conversely, vugs with dimensions smaller than those of the subvolume were not excluded. Despite scale limitations, our subsampling, supported by substantial data volume, ensures our microscale porosity predictions are statistically reliable, setting a foundation for future studies on vugs and nanoporosity’s impact on simulations. The results show that features obtained from dry-sample images can be used for data-driven Sor prediction. We tested three regression models: gradient boosting (GB), random forest (RF), and extreme gradient boosting (XGBoost). Among these, the optimized GB-based model demonstrated the highest predictive capacity for Sor prediction [R2 = 0.87, mean absolute error (MAE) = 1.87%, mean squared error (MSE) = 0.12%]. Increasing the data set size is anticipated to enhance the models’ ability to capture a broader spectrum of rock properties, thereby improving their prediction accuracy. The proposed predictive modeling framework for estimating Sor in heterogeneous carbonate formations aims to supplement conventional coreflooding tests or serve as a tool for rapid Sor evaluation of the reservoir.

Lattice Boltzmann method/computational fluid dynamics-discrete element method applications for transport and packing of non-spherical particles during geo-energy explorations: A review

Understanding the behavior of dispersed particles in subsurface porous media is essential for studying many transport phenomena in geo-energy exploration. Relevant phenomena include fluid transport through rock matrices, undesirable production of formation sands, colloid migration, circulation of drilling cuttings, and displacement of proppants in hydraulic fractures. The discrete element method (DEM), when coupled with the lattice Boltzmann method (LBM) and computational fluid dynamics (CFD), represents a useful numerical approach to studying these microscopic processes. This integrated approach allows for detailed modeling of particle–fluid and particle–particle interactions, which is particularly useful in dealing with particles with non-spherical shapes. This review focuses on recent advancements in DEM implementations for such particles and their coupling schemes with LBM and CFD numerical tools. It aims to assist scholars and practitioners in selecting the most effective LBM/CFD-DEM strategy for studying particle transport and packing in geo-energy scenarios. Although tailored for geophysical flows, the methodologies and analytical frameworks presented here also apply to fundamental investigations of particle-laden flows.

Lattice Boltzmann study of droplet dynamic behaviors impinging on textured surfaces under an external electric field

Textured surfaces contribute to enhancing the cooling effectiveness of electrostatic spray, while the droplet impacting dynamics on such substrates under the influence of electric field are crucial for cooling efficiency. This study utilized a multiphase lattice Boltzmann method combined with the leaky dielectric model to systematically examine the dynamics of droplet impingement on textured surfaces when exposed to electric field. The impact of Weber number, microstructural surface parameters, and electric field strength on droplet impact behavior was discussed in detail. Simulation outcomes reveal that, without the presence of an electric field, the impingement of droplets on textured surfaces results in three distinct deposition states: the Cassie state, partial penetration state, and Wenzel state, primarily contingent upon the surface solid fraction and the droplet impingement velocity. In the Cassie impact regime influenced by an applied electric field, the droplet spreading behaviors exhibit minimal sensitivity to the electric field, with surface tension and inertia primarily governing the spreading dynamics. Throughout the retraction stage, the droplet elongated the direction of the electric field as a result of electric field forces, and eventually, as the electric field strength grows, it bounces off the surface. In the Wenzel impact regime, as the strength of the electric field escalates, the droplet undergoes upward stretching and splits into satellite droplets during the retraction phase, attributed to the dynamic pressure and electrostatic pressure at the apex exceeding the capillary pressure and gravity. These findings could aid in advancing electrostatic spray cooling technology.

Lattice Boltzmann simulation of counter-current imbibition of oil and water in porous media at the equivalent capillarity

The characterization of oil and water displacement in porous media often relies on the capillary number (Ca = μv/σ cos θ). However, limited investigations have been conducted to explore the relative significance of interfacial tension and wettability in determining oil recovery, particularly under the imbibition mode. To address this research gap, the modified color gradient lattice Boltzmann method has been employed. This study aims to systematically investigate the transient imbibition characteristics, pore-scale events, and morphological features of the two-phase distribution in the matrix, all under the same capillarity but varying capillary numbers. The obtained results indicate that, for a given capillary number, a more water–wet condition generally leads to a higher imbibition recovery. Conversely, the influence of capillary number on oil recovery is complex and contingent upon the capillarity value, i.e., the interfacial tension between oil and water. Additionally, the oil recovery data from all cases have been effectively fitted using the Minkowski functionals, demonstrating a linear correlation. Moreover, an attempt has been made to elucidate the mechanism behind the varying oil recovery observed in different capillarity combinations. This analysis considers factors such as energy conversion, the transient change of the ratio of viscous force over capillarity, and the capillary valve effect. The findings of this study contribute to our understanding of the use of chemical agents to enhance oil recovery and provide valuable insights for determining key two-phase parameters in reservoir simulations.