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Direct numerical simulations (DNS) of liquid–liquid dispersions in a three-dimensional periodic domain have been performed by means of the lattice–Boltzmann method. The dispersion was agitated by a random force field such as to produce isotropic turbulence. The turbulence levels and its history were based on a fluid parcel in a turbulently stirred tank traversing the impeller swept region. The DNS provide detailed insight in the coalescence and break-up events brought about by the turbulent flow, the evolution of the drop size distribution in time, and the interaction of the small-scale flow and the droplets as witnessed in terms of the spectral characteristics of the turbulence. [ABSTRACT FROM AUTHOR]

A full Newton lattice Boltzmann method is developed for time-steady flows. The general method involves the construction of a residual form for the time-steady, nonlinear Boltzmann equation in terms of the probability distribution. Bounce-back boundary conditions are also incorporated into the residual form. Newton's method is employed to solve the resulting system of non-linear equations. At each Newton iteration, the sparse, banded, Jacobian matrix is formed from the dependencies of the non-linear residuals on the components of the particle distribution. The resulting linear system of equations is solved using a direct solver designed for sparse, banded matrices. For the Stokes flow limit, only one matrix solve is required. Two dimensional flow about a periodic array of disks is simulated as a proof of principle, and the numerical efficiency is carefully assessed. For the case of Stokes flow (Re = 0) with resolution 251×251, the proposed method performs more than 100 times faster than a standard, fully explicit implementation. [ABSTRACT FROM AUTHOR]

In a recent work, a dense fluid flow across a nanoscopic thin plate was simulated by means of Molecular Dynamics (MD) and Lattice Boltzmann (LB) methods. It was found that in order to recover quantitative agreement with MD results, the LB simulation must be pushed down to sub–nanoscopic scales, i.e. fractions of the range of molecular interactions. In this work, we point out that in this sub–nanoscopic regime, the LB method works outside the hydrodynamic limit at the level of a single cell spacing. A quantitative comparison with the Navier–Stokes (NS) solution shows however that LB and NS results are quite similar, thereby indicating that, apart for a small region past the plate, this nanoflow is still well described by hydrodynamic equations. [ABSTRACT FROM AUTHOR]

We propose a numerical model of blood flow and blood clotting whose purpose is to describe thrombus formation in cerebral aneurysms. We identify possible mechanisms that can cause occurrence of spontaneous thrombosis in unruptured giant intracranial aneurysms. Our main claim is that, under normal conditions, there is a low shear rate threshold below which thrombosis starts and growths. This assumption is supported by several evidences from literature. The proposed mechanisms are incorporated into a Lattice Boltzmann (LB) model for blood flow and platelets adhesion and aggregation. Numerical simulations show that the low shear rate threshold assumption together with aneurysm geometry account well for the observations. [ABSTRACT FROM AUTHOR]

The design of industrial crystallizers requires detailed information about the fine structure of turbulence in vessels of complex geometry. The currently available methods (e.g., empirical correlations, experimentation, simple theories, computations based on the Reynolds-averaged Navier–Stokes equations) cannot provide the required information at an adequate level of accuracy for crystallizers of non-standard design. This paper assesses the feasibility of using a computationally efficient large-eddy simulation (LES) technique to quantify the fine scale turbulent structure in an industrial crystallizer. LESs of the single-phase flow in a baffled, industrial crystallizer with a draft tube were performed at three values of the Reynolds number ( Re = 14 000, Re = 82 000 and Re = 350 000). The flow was driven by a standard Rushton turbine. A much weaker secondary flow was generated by a throughput stream that entered through a nozzle at the bottom and exited through the sidewall. The effects of the spatial resolution and the sub-grid scale model were investigated. The mixing performance of the tank was evaluated by means of particle tracking. It was found that the simulations adequately resolved the highly anisotropic fine-scale turbulence generated by the strong interaction between the impeller, the various other internals and the vessel wall at least at the low Reynolds number. The potential significance of the computed flow structures for crystallization performance is briefly noted. [ABSTRACT FROM AUTHOR]

Abstract: A two-dimensional single component two-phase lattice Boltzmann model was used to simulate the Rayleigh–Taylor instability in a closed system. Spatiotemporally variable densities were generated by gravity acting on the fluid density. The density fluctuations were triggered by rapid changes in the fluid velocity induced by changes in the interface geometry and impact of the dense fluid on the rigid lower boundary of the computational domain. The ratio of the maximum density fluctuations to the maximum fluid velocity increased more rapidly at low velocities than at high velocities. The ratio of the maximum density fluctuations in the dense phase to its maximum velocity was on the order of the inverse of the sound speed. The solution became unstable when the density-based maximum local Knudsen number exceeded 0.13. [Copyright &y& Elsevier]

Abstract: We hypothesize that anisotropy in soil properties arises from pore-scale heterogeneity caused by the alignment of aspherical soil particles. We developed a method to predict the permeability tensor from particle shape and packing structure. Digital geometry maps were created for the pore space in regular cubic and random packs of particles with various aspect ratios using a numerical packing algorithm. The lattice-Boltzmann method was used to simulate saturated flow through these packs, and the effect of particle shape and degree of alignment on the permeability tensor was characterized. Results show that the degree of anisotropy in permeability depends not only upon particle shape and alignment, but also on the three-dimensional structure of the pack. In random packs, more oblate particles and higher degrees of particle alignment lead to reduced permeability perpendicular to the direction of particle alignment compared to the direction parallel to particle alignment. [Copyright &y& Elsevier]

Abstract: For micro-machined membranes, it is possible to choose pore size, pore geometry and membrane porosity, within certain limits. Different pore geometries (circular, square, slit shaped and triangular pores), particle size to pore size ratios, pore edges and membrane porosities were evaluated with lattice-Boltzmann computer simulations and torque balance considerations for various modes of operation. We focused on hydrodynamic interactions and assumed uncharged neutral surfaces of the particle and the pore. However, the model can easily be extended with additional relations for such interactions in practical systems with defined properties. It was concluded that pore geometry can have a large effect on the flux (up to 60%). Further, the effect of shielding could be quantified. Above a surface coverage of 0.05, the particles effectively shield each other from the flow field, therewith necessitating either a higher cross flow velocity or a lower transmembrane pressure for particle removal. Based on the simulations, an extended criterion for the critical flux was developed, which includes the effects of pore geometry, particle to pore size ratio and membrane porosity. Different optimal membrane choices follow for processes aimed at retention of all particles, and for processes aimed at fractionation of particles into different fractions. [Copyright &y& Elsevier]

Computations of flows in explicitly resolved porous media reported in the literature so far are based on binarized porous media data mapped to uniform Cartesian grids. The voxel set is directly being used as the computational grid and thus the geometrical representation is usually only first-order accurate due to stair-case patterns. In this work, we pursue a more elaborate approach: starting from a highly resolved tomographic grey value data set we utilize a Marching Cube algorithm to reconstruct the surface of the porous medium as a set of planar triangles. The numerical resolution of the Cartesian grid for the simulation can then be chosen independently from the voxel set. As we take into account the subgrid distances between the nodes of the Cartesian grid and the planar triangle surfaces, one can utilize a second-order accurate lattice Boltzmann flow solver to efficiently compute, e.g. permeabilities. As these interpolation-based no-slip boundary conditions are not mass preserving, we also present a local modification of the no-slip boundary condition restoring mass conservation. Our numerical results demonstrate that for saturated flow simulations this coupled approach allows a substantial acceleration of saturated flow computations in porous media. [ABSTRACT FROM AUTHOR]

Abstract: We compare two-dimensional and three dimensional lattice-Boltzmann (LB) simulations of fluid flow in a pseudo-2D micromodel used in experimental work. We show that 2D LB simulations can be used to compute the average velocity field in 3D systems in which the third dimension is small compared with the other two dimensions, and where the velocity component along the third dimension is zero. Correct results are obtained provided a viscous drag force, representing the effect of the third dimension, is used in the 2D model. The use of 2D simulations allows to significantly reduce the computational cost of the calculations, and hence to increase the size and resolution of the systems that can be studied using the LB method. [Copyright &y& Elsevier]

Abstract: The drag force term appearing in two-fluid models for fluid–particle flows is commonly closed by expressing it as a function of the local quantities, such as the local particle volume fraction, the local slip velocity between the particle and fluid phases, and the local mean-squared fluctuating velocity of the particles. The adequacy of such closures for inhomogeneous suspensions has been debated in the literature and some researchers have suggested the need for additional terms involving spatial gradients in these quantities. To test this proposition, simulations of flow in inhomogeneous steady beds of particles have been performed using the lattice-Boltzmann method. The particle beds consisted of disordered assemblies with a density profile on a scale much larger than the particle radius. Inhomogeneous beds with a controlled density profile were generated in three different ways, (i) by inhomogeneous stretching of the particle bed in one direction, (ii) by applying an inhomogeneous force to the particle phase during random motion of the particles, and (iii) by taking snapshots of a direct simulation of a traveling wave in a fluidization simulation. The global structure of the three beds was comparable, while assessment of the radial distribution functions showed that the three beds exhibited clearly different microscopic structures. The force profiles along the inhomogeneous direction of the particle bed were obtained from the flow simulations. These were analyzed by applying spatial averaging in a manner identical to the averaging procedure that is used to derive the two-fluid model equations. The force profiles were compared to predictions based on flow simulations of homogeneous disordered particle beds over a range of volume fractions. To assess the role of the microstructure of the particle bed also simulations were executed where the homogeneous disordered bed was modified by either applying homogeneous stretching or by applying a lubrication force during generation of the particle bed. This study demonstrated that the microscopic structure of the particle bed has a severe impact on the closure of the drag force. Our computations did not reveal any evidence supporting the need for terms involving gradients in particle volume fraction in the drag force closure. [Copyright &y& Elsevier]

A method of coupling grids of different mesh size is developed for classical Lattice-Boltzmann (LB) algorithms on uniform grids. The approach is based on an asymptotic analysis revealing suitable quantities equalized along the grid interfaces for exchanging information between the subgrids. In contrast to other couplings the method works without overlap zones. Moreover the grid velocity (Mach number) is not kept constant, as the time step depends not linearly but quadratically on the grid spacing. To illustrate the basic idea we use a simple LB algorithm solving the advection-diffusion equation. The proposed grid coupling is validated by numerical convergence studies indicating, that the coupling does not affect the second-order convergence behavior of the LB algorithm which is observed on uniform grids. In order to demonstrate its principal applicability to other LB models, the coupling is generalized to the standard D2P9 model for (Navier-)Stokes flow and tested numerically. As we use analytic tools different from the Chapman-Enskog expansion, the theoretical background material is given in two appendices. In particular, the results of numerical experiments are confirmed with a consistency analysis. [ABSTRACT FROM AUTHOR]

We demonstrate a “coarse time-stepper” based approach for the extraction of continuum-level stability and bifurcation information from kinetic theory based, LB simulations. Acting directly on the LB simulator, we sidestep the necessity of deriving macroscopic, explicitly closed continuum conservation equations. The approach is used to analyze the dynamics and the oscillatory instability of two-dimensional periodic arrays of gas bubbles rising in a liquid. [Copyright &y& Elsevier]

We simulate two-fluid-phase flow at the pore scale using a lattice Boltzmann (LB) approach. Using a parallel processing version of the Shan-Chen model that we developed, we simulate a set of ideal two-fluid systems and a model two-fluid-phase porous medium system comprised of a synthetic packing with a relatively uniform distribution of spheres. We use the set of ideal two-phase systems to validate the approach and provide parameter information, which we then use to simulate a sphere-pack system. The sphere-pack system is designed to mimic laboratory experiments conducted to evaluate the hysteretic capillary pressure saturation relation for a system consisting of water, tetrachloroethylene, and a glass bead porous medium. Good agreement is achieved between the measured hysteretic capillary pressure saturation relations and the LB simulations when comparing entry pressure, displacement slopes, irreducible saturation, and residual entrapment. Our results further show that while qualitatively similar results are obtained when comparing systems consisting of 1200 spheres and 150 spheres, there is a significant difference between these two levels, suggesting a lower bound on the size of a representative elementary volume. [ABSTRACT FROM AUTHOR]

The Lattice-Boltzmann method is an effective tool for solving fluid mechanics problems, but there isn’t still a good scheme to determinate some parameters in Boltzmann equations. In this paper, a technique using evolutionary algorithm to automatically model Boltzmann equations is introduced. Numerical simulation shows that the designed scheme is fast and efficient. [ABSTRACT FROM AUTHOR]

The lattice Boltzmann model is a simplified kinetic method based on the particle distribution function. We use this method to simulate problems in MEMS, in which the velocity slip near the wall plays an important role. It is demonstrated that the lattice Boltzmann method can capture the fundamental behaviors in micro-channel flow, including velocity slip, nonlinear pressure drop along the channel and mass flow rate variation with Knudsen number. The Knudsen number dependence of the position of the vortex center and the pressure contour in micro-cavity flows is also demonstrated. [ABSTRACT FROM AUTHOR]

We report results of extensive two-phase lattice-Boltzmann simulations of capillary rise dynamics. We demonstrate that the method can be used to model the hydrodynamic behaviour inside a capillary tube provided that the diameter of the tube is large enough, typically at least 30 lattice units. We also present results for the dependence of the cosine of the dynamic contact angle on the capillary number Ca. Its deviation from the static advancing contact angle has a power-law form, with the value of the exponent very close to 3/2 for capillary rise at zero gravity, while behaviour is more complex in the presence of gravity. [ABSTRACT FROM AUTHOR]

The mechanisms of momentum transfer and shear stress of liquid-particle suspensions in two-dimensional Couette flow are studied using direct numerical simulation by lattice-Boltzmann techniques. The results obtained display complex flow phenomena that arise from the two-phase nature of the fluid including a nonlinear velocity profile, layering of particles, and apparent slip near the solid walls. The general rheological behaviour of the suspension is dilatant. A detailed study of the various momentum transfer mechanisms that contribute to the total shear stress indicates that the observed shear thickening is related to enhanced relative solid phase stress for increasing shear rates. [ABSTRACT FROM AUTHOR]

This paper reviews applications of the lattice-Boltzmann method to simulations of particle-fluid suspensions. We first summarize the available simulation methods for colloidal suspensions together with some of the important applications of these methods, and then describe results from lattice-gas and lattice-Boltzmann simulations in more detail. The remainder of the paper is an update of previously published work,(69, 70) taking into account recent research by ourselves and other groups. We describe a lattice-Boltzmann model that can take proper account of density fluctuations in the fluid, which may be important in describing the short-time dynamics of colloidal particles. We then derive macro-dynamical equations for a collision operator with separate shear and bulk viscosities, via the usual multi-time-scale expansion. A careful examination of the second-order equations shows that inclusion of an external force, such as a pressure gradient, requires terms that depend on the eigenvalues of the collision operator. Alternatively, the momentum density must be redefined to include a contribution from the external force. Next, we summarize recent innovations and give a few numerical examples to illustrate critical issues. Finally, we derive the equations for a lattice-Boltzmann model that includes transverse and longitudinal fluctuations in momentum. The model leads to a discrete version of the Green–Kubo relations for the shear and bulk viscosity, which agree with the viscosities obtained from the macro-dynamical analysis. We believe that inclusion of longitudinal fluctuations will improve the equipartition of energy in lattice-Boltzmann simulations of colloidal suspensions. [ABSTRACT FROM AUTHOR]

This paper describes scale-resolving unsteady flow simulations performed using a Lattice-Boltzmann based solver, applied, for the first time, to a full-scale helicopter main rotor in forward flight. The simulation setup is obtained through a fully automated in-house developed workflow. Validation is performed by comparing thrust and power coefficients with reference wind tunnel data; with and without trimming based on an in-house developed Newton-Raphson trim algorithm. Results for different rotor advance ratios yield insight in both aerodynamic and acoustic quantities for the rotor, highlighting both mean as well as unsteady behavior. Finally, digital helicopter noise certification is performed by calculating the ground noise map for a helicopter in landing condition. [ABSTRACT FROM AUTHOR]

Aeroacoustic feedback mechanisms in rectangular cavities are strongly dependent on length-to-depth ratio and free stream velocity. The capability to predict the effects of these parameters using a scale-resolving transonic lattice-Boltzmann flow simulations is assessed, for the first time, by considering the M219 benchmark configuration for two different length-to-depth ratios (10:1 and 5:1) and two free-stream Mach numbers (0.85 and 1.35). Numerical results are compared and validated using unsteady wall pressure measured in wind tunnel tests. Tonal and broadband components of the pressure fluctuations are properly captured. For the shallow cavity configuration, an increase in Mach number is found to enhance the development of Rossiter modes inside the cavity. A more detailed analysis of these Rossiter modes is carried out for the shallow cavity at supersonic speed, for which physical insight is gained through the usage of spectral proper-orthogonal decomposition and wavelet/Fourier analyses. [ABSTRACT FROM AUTHOR]

Capsules are liquid droplets enclosed by a thin membrane which can resist shear deformation. They are widely found in nature (e.g. red blood cells) and in numerous applications (e.g. food, cosmetic, biomedical and pharmaceutical industries [1]), where they often flow through a complicated network of tubes or channels: this is the case for RBCs in the human circulation or for artificial capsules flowing through microfluidic devices. Central to these flows is the dynamic motion of capsules at bifurcations, in particular the question of path selection. A good understanding of this problem is indeed needed to elucidate some intriguing phenomena in human circulation and to design multibranched microfluidic devices to sort and enrich suspensions of artificial microcapsules or biological cells depending on their properties. Thanks to the extensive in vivo and in vitro experiments conducted on blood flows in branched capillaries and microchannels [2], it has been well established that the daughter branch with a higher flow rate receives a larger number of RBCs than the other branch: this is classically referred to as the Zweifach-Fung effect [3,4]. Similar phenomena have also been observed in experiments on suspensions, where the RBCs are modelled as flexible disks and the white blood cells as solid spheres [5], and in dilute suspensions of solid spheres [6]. This is a consequence of the plasma skimming effect due to the particle- free layer near the wall of the vessel [7] and of the particle screening effect due to the deviation of the particle trajectories from the background flow fluid streamlines as a result of the hydrodynamic interaction between the particles and vessel geometry at the bifurcation [8, 6]. In the dilute limit, the problem has, however, not been thoroughly studied experimentally, possibly due to the difficulty of manipulating individual cells. The problem has mostly been studied in recent years using two-dimensional numerical models [9, 10]. The results showed that, at equal flow rate between the two downstream channels, the capsule tends to flow into the side branch in particular when the capsule is highly deformable. But to what extent the results obtained from previous two-dimensional simulations can be applied to three-dimensional flows remains unclear. The objective of the present study is to conduct a systematic and in-depth three-dimensional numerical study of a deformable capsule in a branched tube and to determine the influence of inertia. Contrary to many biological systems, for which neglecting inertia is a good assumption, capsules are not necessarily small in size and the flow speed can be fast in some applications [11]. In the present work, we computationally study the motion of an initially spherical capsule flowing through a straight channel with an orthogonal lateral branch, using a three-dimensional immersed- boundary lattice Boltzmann method [12, 13]. Our primary focus is to study the influence of the geometry of the side branch on the capsule path selection. The capsule is enclosed by a strain-hardening membrane and contains an internal fluid of the same viscosity as the fluid in which it is suspended. It is initially centered on the axis of the feed channel. We impose the flow rate split ratio between the two downstream branches of the bifurcation. We analyze the reference cases wherein the side channel has the same cross- section as the main branch, and then compare the results to other geometries, in which the side branch has a half cross-sectional area as compared to the main branch. We consider different capsule-to-channel size ratio, flow Reynolds number (Re) and ratio of capillary to Reynolds numbers, and summarize the results in phase diagrams indicating the critical flow split ratio above which the capsule flows into the side branch. The capsule trajectory does not always obey the classical Fung's bifurcation law. For Re = 5 and equal flow rate split between the two downstream branches, the capsule will enter a branch which is narrow in the spanwise direction, but will not enter a branch which is narrow in the flow direction. We show that this novel phenomenon results primarily from the background flow which is strongly influenced by the side branch cross-section geometry. For higher values of Re, the capsule relative size and deformability also play a specific role in the path selection: increasing the capillary number generally promotes cross-stream migration of the capsule towards the side branch. The present results obtained for dilute systems open new perspectives on the design of microfluidic systems with optimal channel geometries and flow conditions to enrich cell and particle suspensions. [ABSTRACT FROM AUTHOR]