Lattice Boltzmann Methodology Research Articles

Numerical investigation of fluid flow behavior in steel cord with lattice Boltzmann methodology: The impacts of microstructure and loading force.

Steel cord materials were found to have internal porous microstructures and complex fluid flow properties. However, current studies have rarely reported the transport behavior of steel cord materials from a microscopic viewpoint. The computed tomography (CT) scanning technology and lattice Boltzmann method (LBM) were used in this study to reconstruct and compare the real three-dimensional (3D) pore structures and fluid flow in the original and tensile (by loading 800 N force) steel cord samples. The pore-scale LBM results showed that fluid velocities increased as displacement differential pressure increased in both the original and tensile steel cord samples, but with two different critical values of 3.3273 Pa and 2.6122 Pa, respectively. The original steel cord sample had higher maximal and average seepage velocities at the 1/2 sections of 3D construction images than the tensile steel cord sample. These phenomena should be attributed to the fact that when the original steel cord sample was stretched, its porosity decreased, pore radius increased, flow channel connectivity improved, and thus flow velocity increased. Moreover, when the internal porosity of tensile steel cord sample was increased by 1 time, lead the maximum velocity to increase by 1.52 times, and the average velocity was increased by 1.66 times. Furthermore, when the density range was determined to be 0-38, the pore phase showed the best consistency with the segmentation area. Depending on the Zou-He Boundary and Regularized Boundary, the relative error of simulated average velocities was only 0.2602 percent.

Lattice Boltzmann Simulation of Incompressible Fluid Flow in Two-sided Converging and Diverging Lid-driven Square Cavity

The present study focuses on the predictions of flow behavior, streamlines and some other factors of a two adjacent-sided converging and diverging lid-driven square cavity filled with fluid. In the diverging case, the top wall of the cavity is considered to be in motion from left to right, and the left wall is considered to be in motion from top to bottom simultaneously with identical speeds. It is found that for a low Reynolds number, the flow behavior seems to be symmetric with respect to one of the diagonals of the cavity, and at a critical Reynolds number 1121, the symmetry of the flow behavior blows up, and an asymmetric form is obtained due to the increased inertia and turbulence effects. Any increment in the Reynolds number above the critical Reynolds number develops this asymmetry gradually more and more. In the second phenomenon, the converging phenomenon, the top wall of the cavity is assumed to be in motion from left to right, and the right wall is assumed to be in motion from bottom to top simultaneously with identical speeds so that they converge at the corner of the cavity. This case gives rise to two critical Reynolds numbers Re = 969 and Re = 2053 and the flow behavior for both asymmetric states was found to be opposite. Furthermore, the rate of convergence of the present methodology, lattice Boltzmann methodology, for various Reynolds numbers is found to be very high except for the critical and their nearby Reynolds numbers.

Lattice Boltzmann method with nonreflective boundary conditions for low Mach number combustion

The paper presents a lattice Boltzmann (LB) method for premixed and nonpremixed combustion simulations with nonreflective boundary conditions, in contrast to Navier–Stokes solvers or hybrid schemes. The current approach employs different sets of distribution functions for flow, temperature and species fields, which are fully coupled. The discrete equilibrium density distributions are obtained from the Hermite expansions thus thermal compressibility is included. The coupling among the momentum, energy and species transport enables the model to be applicable for reactive flows with chemical heat release. The characteristic boundary conditions are incorporated into the LB scheme to avoid numerical reflections. The multi-relaxation-time collision schemes are applied to all the LB solution procedures to improve numerical stability. With detailed thermodynamics and chemical mechanisms for hydrogen-air, the LB modelling framework is validated against both premixed flame propagation and nonpremixed counterflow diffusion flame benchmarks. Simulations of circular expanding premixed flames further demonstrate the capability of the new reactive LB method. The developed LB methodology retains the advantages of classic LB methods and extends the LB capability to low Mach number combustion with potential applications in mesoscale and microscale combustors, catalysis, fuel cells, batteries and so on.

Chromo-dynamic multi-component lattice Boltzmann equation scheme for axial symmetry

We validate the chromo-dynamic multi-component lattice Boltzmann equation (MCLBE) simulation for immiscible fluids with a density contrast against analytical results for complex flow geometries, with particular emphasis on the fundamentals of the method, i.e. compliance with inter-facial boundary conditions of continuum hydrodynamics. To achieve the necessary regimes for the chosen validations, we develop, from a three-dimensional, axially-symmetric flow formulation, a novel, two-dimensional, pseudo Cartesian, MCLBE scheme. This requires the inclusion in lattice Boltzmann methodology of a continuously distributed source and a velocity-dependent force density (here, the metric force terms of the cylindrical Navier–Stokes equations). Specifically, we apply our model to the problem of flow past a spherical liquid drop in Re = 0, Ca regime and, also, flow past a lightly deformed drop. The resulting simulation data, once corrected for the simulation’s inter-facial micro-current (using a method we also advance herein, based on freezing the phase field) show good agreement with theory over a small range of density contrasts. In particular, our data extend verified compliance with the kinematic condition from flat (Burgin et al 2019 Phys. Rev. E 100 043310) to the case of curved fluid–fluid interfaces. More generally, our results indicate a route to eliminate the influence of the inter-facial micro-current.

Multi-group lattice Boltzmann method for criticality problems

In this paper, Lattice Boltzmann methodology (LBM) has been developed for the criticality search for the nuclear reactor systems. It is noted that the LBM has not been used for criticality calculations in optically thin (mean free path of neutrons close to system dimensions) and highly anisotropic systems. In order to solve such problems the number of angular directions need to be increased. Various criticality benchmarks with one group and multi-group cross-section including both isotropic and anisotropic scattering have been solved. The solution of these 1D benchmark problems not only verifies the solution methodology, but also demonstrates that multiplication factor of the critical systems having dimension close to mean free path of neutron travel can also be accurately predicted using higher angular discretization. Since LBM approach is relatively simple in implementation it can be effectively used and has a potential to provide easy and convenient solution of neutron transport equation.

Water transport and absorption in pharmaceutical tablets \u2013 a numerical study

The quality of a coated pharmaceutical tablet can be strongly affected by the interactions of water droplets with the porous substrate during processes such as coating process. Three different mechanisms co-exist in the coating process: water spreading, absorption and evaporation. Disentangling the fundamental understanding of these phenomena can therefore be crucial for achieving a higher quality of the products (e.g. a longer shelf-life of the tablets) and for controlling the efficiency of the process. This paper aims to investigate the spreading and absorption mechanisms after droplet impingement on a tablet using a Lattice-Boltzmann methodology. Our numerical results (droplet height and spreading, penetration depth and absorbed volume) are in a good agreement with experimental data and numerical simulations available in the literature. In particular, the spreading phase is characterised by the capillary spreading time scale, as confirmed by previous studies. In contrast to previous studies, we find that the absorption process begins at times shorter than the capillary spreading time but with a different power-law in the absorbed volume. We explain this behaviour through a modified Washburn law that takes into account three-dimensional effects. Our data can be used as a benchmark to test novel mathematical models.

Droplet Misalignment Limit for Inkjet Printing into Cavities on Textured Surfaces.

The control of droplets deposited onto textured surfaces is of great importance for both engineering and medical applications. This research investigates the dynamics of a single droplet deposited into a confined space and its final equilibrium morphology, with emphasis given to droplet deposition under print head misalignment, the effect of nonuniform wettability, and deposition of droplets with varying sizes. A multiphase pseudopotential lattice Boltzmann methodology is used to simulate the process of deposition. The print quality is characterized in terms of a parameter referred to as the wetted fraction, which describes the proportion of the cavity that is wetted by the droplet. Our results show how single and multiple axis misalignment affect the final equilibrium morphology, and it was found for comparable configurations that multiaxis misalignment resulted in a higher wetted fraction. Investigations into wettabilities of the substrate and cavity wall revealed how larger ratios of the contact angles between the two enhance the ability for the droplet to self-align within the cavity. Additionally, a range of uniform wettabilities between the substrate and cavity were found, which mitigate against misalignment. Investigations into varying droplet sizes relative to the cavity revealed how misalignment can be compensated for with larger droplets, and limits for filling a cavity with a single drop are defined. Finally, we explore the deposition with misalignment into closely positioned cavities where it is found that the spacing between cavities is a key factor in determining the maximum permissible misalignment.

GPGPU implementation of a lattice Boltzmann methodology for particle transport and deposition in complex flow

Purpose This study aims to modify the standard probabilistic lattice Boltzmann methodology (LBM) cellular automata (CA) algorithm to enable a more realistic and accurate computation of the ensemble rather than individual particle trajectories that need to be updated from one time step to the next (allowing, as such, a fraction of the collection of particles in any lattice grid cell to be updated in a time step, rather than the entire collection of particles as in the standard LBM-CA algorithm leading to a better representation of the dynamic interaction between the particles and the background flow). Exploitation of the inherent parallelism of the modified LBM-CA algorithm to provide a computationally efficient scheme for computation of particle-laden flows on readily available commodity general-purpose graphics processing units (GPGPUs). Design/methodology/approach This paper presents a framework for the implementation of a LBM for the simulation of particle transport and deposition in complex flows on a GPGPU. Towards this objective, the authors have shown how to map the data structure of the LBM with a multiple-relaxation-time (MRT) collision operator and the Smagorinsky subgrid-scale turbulence model (for turbulent fluid flow simulations) coupled with a CA probabilistic method (for particle transport and deposition simulations) to a GPGPU to give a high-performance computing tool for the calculation of particle-laden flows. Findings A fluid-particle simulation using our LBM-MRT-CA algorithm run on a single GPGPU was 160 times as computationally efficient as the same algorithm run on a single CPU. Research limitations/implications The method is limited by the available computational resources (e.g. GPU memory size). Originality/value A new 3D LBM-MRT-CA model was developed to simulate the particle transport and deposition in complex laminar and turbulent flows with different hydrodynamic characteristics (e.g. vortex shedding, impingement, free shear layer, turbulent boundary layer). The solid particle information is encapsulated locally at the lattice grid nodes, allowing for straightforward mapping of the datastructure onto a GPGPU enabling a massive parallel execution of the LBM-MRT-CA algorithm. The new particle transport algorithm was based on the local (bulk) particle density and velocity and provides more realistic results for the particle transport and deposition than the standard LBM-CA algorithm.

Lattice Boltzmann simulations of nonequilibrium fluctuations in a nonideal binary mixture.

In recent years the lattice Boltzmann (LB) methodology has been fruitfully extended to include the effects of thermal fluctuations. So far, all studied cases pertain to equilibrium fluctuations, i.e., fluctuations with respect to an equilibrium background state. In this paper we take a step further and present results of fluctuating LB simulations of a binary mixture confined between two parallel walls in the presence of a constant concentration gradient in the wall-to-wall direction. This is a paradigmatic setup for the study of nonequilibrium (NE) fluctuations, i.e., fluctuations with respect to a nonequilibrium state. We analyze the dependence of the structure factors for the hydrodynamical fields on the wave vector q in both the directions parallel and perpendicular to the walls, highlighting the long-range (∼|q|^{-4}) nature of correlations in the NE framework. Results at the small scales (high wave numbers) quantitatively agree with the predictions of fluctuating hydrodynamics without fitting parameters. At larger scales (low wave numbers), however, results show finite-size effects induced by confinement and call for further studies aimed at controlling boundary conditions in the fluctuating LB framework as well as compressibility effects. Moreover, in the presence of a nonideal equation of state of the mixture, we also observe that the (spatially homogeneous) average pressure changes, due to a genuinely new contribution triggered by NE fluctuations. These NE pressure effects are studied at changing the system size and the concentration gradient. Taken all together, we argue that the results of this article are useful and instrumental to boost the applicability of the fluctuating LB methodology in the framework of NE fluctuations, possibly in conjunction with experiments.

Non-symmetric branching of fluid flows in 3D vessels

Nonsymmetric branching flow through a three-dimensional (3D) vessel is considered at medium-to-high flow rates. The branching is from one mother vessel to two or more daughter vessels downstream, with laminar steady or unsteady conditions assumed. The inherent 3D nonsymmetry is due to the branching shapes themselves, or the differences in the end pressures in the daughter vessels, or the incident velocity profiles in the mother. Computations based on lattice-Boltzmann methodology are described first. A subsequent analysis focuses on small 3D disturbances and increased Reynolds numbers. This reduces the 3D problem to a two-dimensional one at the outer wall in all pressure-driven cases. As well as having broader implications for feeding into a network of vessels, the findings enable predictions of how much swirling motion in the cross-plane is generated in a daughter vessel downstream of a 3D branch junction, and the significant alterations provoked locally in the shear stresses and pressures at the walls. Nonuniform incident wall-shear and unsteady effects are examined. A universal asymptotic form is found for the flux change into each daughter vessel in a 3D branching of arbitrary cross-section with a thin divider.

NONSYMMETRIC BRANCHING OF FLUID FLOWS IN 3D VESSELS

Nonsymmetric branching flow through a three-dimensional (3D) vessel is considered at medium-to-high flow rates. The branching is from one mother vessel to two or more daughter vessels downstream, with laminar steady or unsteady conditions assumed. The inherent 3D nonsymmetry is due to the branching shapes themselves, or the differences in the end pressures in the daughter vessels, or the incident velocity profiles in the mother. Computations based on lattice-Boltzmann methodology are described first. A subsequent analysis focuses on small 3D disturbances and increased Reynolds numbers. This reduces the 3D problem to a two-dimensional one at the outer wall in all pressure-driven cases. As well as having broader implications for feeding into a network of vessels, the findings enable predictions of how much swirling motion in the cross-plane is generated in a daughter vessel downstream of a 3D branch junction, and the significant alterations provoked locally in the shear stresses and pressures at the walls. Nonuniform incident wall-shear and unsteady effects are examined. A universal asymptotic form is found for the flux change into each daughter vessel in a 3D branching of arbitrary cross-section with a thin divider.

Lattice Boltzmann morphodynamic model

Morphological change due to sediment transport is a common natural phenomenon in real flows. It involves complex processes of erosion and deposition such as those along beaches and in river beds, imposing a strong strain on human beings. Studying and understanding morphodynamic evolution are essential to protect living environment. Although there are conventional numerical methods like finite difference method and finite volume method for forecast of morphological change by solving flow and morphodynamic equations, the methods are too complex/inefficient to be applied to a real large scale problem. To overcome this, a lattice Boltzmann method is developed to simulate morphological evolution under flows. It provides an alternative way of studying morphodynamics at the full advantages of the lattice Boltzmann methodology. The model is verified by applications to the evolution of one and two dimensional sand dunes under shallow water flows.

On the lattice Boltzmann method for phonon transport

The lattice Boltzmann method is a discrete representation of the Boltzmann transport equation that has been employed for modeling transport of particles of different nature. In the present work, we describe the lattice Boltzmann methodology and implementation techniques for the phonon transport modeling in crystalline materials. We show that some phonon physical properties, e.g., mean free path and group velocity, should be corrected to their effective values for one- and two-dimensional simulations, if one uses the isotropic approximation. We find that use of the D2Q9 lattice for phonon transport leads to erroneous results in transient ballistic simulations, and the D2Q7 lattice should be employed for two-dimensional simulations. Furthermore, we show that at the ballistic regime, the effect of direction discretization becomes apparent in two dimensions, regardless of the lattice used. Numerical methodology, lattice structure, and implementation of initial and different boundary conditions for the D2Q7 lattice are discussed in detail.

Alternative approach to the solution of the dispersion relation for a generalized lattice Boltzmann equation

The simplest and most efficient lattice Boltzmann model that is able to recover the Navier-Stokes equations is based on a single-parameter scattering matrix, where the parameter is the first nonzero eigenvalue of the collision matrix. This simple model, based on a single relaxation time, has many shortcomings. Among these is the lack of freedom to extend the model to complex fluids whose stress tensors are characterized by more complicated constitutive relations. The lattice Boltzmann methodology may be generalized by considering the full collision matrix and tuning the matrix elements to obtain the desired macroscopic properties. The generalized hydrodynamics of a generalized lattice Boltzmann equation (LBE) was studied by Lallemand and Luo [Phys. Rev. E 61, 6546 (2000)] by solving the dispersion equation of the linearized LBE. In this paper, an alternative approach to solving the dispersion equation based on a formal perturbation analysis is described. The methodology outlined is systematic, can be readily applied to other lattices, and does not require the reciprocals of the relaxation times to be small.

A hybrid lattice Boltzmann model for solid–liquid phase transition in presence of fluid flow

In the present Letter, a hybrid lattice Boltzmann methodology is developed for simulating convection–diffusion transport processes pertinent to melting/solidification problems. The model is derived by coupling a modified thermal lattice Boltzmann model with an adapted enthalpy-porosity technique. The hydrodynamic variables are simulated using a single particle density distribution function, whereas the thermodynamic variables are obtained from an enthalpy density distribution function. An exhaustive comparison with other standard methods reveals that the proposed technique is computationally more convenient to be implemented for solving topologically-complicated phase boundary evolution problems during solidification of pure materials, such as the growth of an equiaxed dendrite in an undercooled melt.

Methods for microscopic characterization of oral biofilms: analysis of colonization, microstructure, and molecular transport phenomena.

Assessment of the role of biofilm microstructure in biofilm-specific activities requires non-destructive measurement techniques for parameterization of structural characteristics in parallel with relevant biochemical and physiological data. This paper briefly reviews some current methods for biofilm structural analysis, with emphasis on new developments in optical imaging and mathematical modeling methods. Fluorescence imaging studies of bacterial colonization events occurring on exposed model tooth surfaces indicated that bacterial adhesion to sessile organisms was of central importance to the early colonization process and that this occurred in a non-random manner. Structural studies of mature biofilms by confocal microscopy demonstrated the spatial distribution of individual species using fluorescent antibodies. Biofilms grown under different physiological conditions exhibited differences in structure, and methods were developed for parameterizing the spatial orientations of the bacteria. Diffusive processes within biofilm microstructures were studied using a random walk model in both 2-D and 3-D. Modeling of convective flow within biofilm microstructures was achieved by application of lattice Boltzmann methodology.