A lattice Boltzmann method for simulating transport and agglomeration of resolved particles

The main purpose of this contribution is to present a lattice Boltzmann method for modelling the transport, collision and agglomeration of freely moving spherical particles and agglomerates. In order to take the hydrodynamic interaction between fluid and particles into account, the particle surface is fully resolved by the numerical grid using a curved no-slip boundary condition. In addition to various test cases with sedimenting single particles and particle pairs, a comparison with a finite element simulation is performed to evaluate the LBM-based treatment of flow-induced particle forces for gap widths smaller than the resolution limit of the fluid. Furthermore, the influence of viscous forces on the motion of approaching particles is analysed. As a final step, first results on the transient agglomeration inside a poly-sized particle cluster settling under gravity are presented for demonstrating the applicability of the code to more complex problems such as agglomeration in turbulent two-phase flows. The obtained agglomerate morphologies are characterised by various structural parameters such as a convex hull-based porosity and the radius of gyration. In the simulations, the observed particle Reynolds numbers are in the range [0.2, 84.8].     

A many-component lattice Boltzmann equation simulation for transport of deformable particles

We review the analysis of single and N-component lattice Boltzmann methods for fluid flow simulation. Results are presented for the emergent pressure field of a single phase incompressible liquid flowing over a backward-facing step, at moderate Reynolds Number, which is compared with the experimental data of Denham & Patrick (1974 Trans. IChE 52, 361-367). We then access the potential of the N-component method for transport of high volume fraction suspensions of deformable particles in pressure-driven flow. The latter are modelled as incompressible, closely packed liquid drops. We demonstrate the technique by investigating the particles' transverse migration in a uniform shear ('lift'), and profile blunting and chaining.     

格子-Boltzmann方法模拟霜结晶生长

为了研究冷壁面上霜结晶的生长过程以及各参数的变化规律,利用格子-Boltzmann方法(LBM)方法,建立一个二维介观模型,实验验证了模型的可靠性,分析了霜层温度变化和密度增长规律,并直观模拟出霜结晶凝聚变化过程.结果表明:霜层表面温度在早期阶段迅速增加,但增加率随着结霜时间增加而减小;霜层内部温度随霜层厚度的增加呈线性增长;霜层平均密度随结霜时间增加呈现出先慢后快的规律;随着结霜过程的进行,由于越往上,霜晶体积分数越小,导致霜层内部密度随霜层厚度的上升而减小.     

Dynamics of bi-dispersed settling suspension of non-colloidal particles in rotating cylinder

Non-neutrally buoyant suspension of bi-dispersed non-colloidal particles in viscous fluid rotating in a horizontal cylinder displays in-homogeneities in particle distribution with alternate bands of high and low particle concentrations along the symmetric axis of the cylinder. Experiments were carried out to characterize the axial segregation in bi-dispersed suspension at various filling fraction and rotation speed of cylinder. The mixture of same particles in absence of any suspending fluid did not show any segregation. However, in case of particles suspended in water it was observed that the rate of segregation increases with increase in filling fraction. Once the particles get segregated along the full length of the cylinder, these bands start to migrate along the tube axis finally merging to give wider bands. For a given filling fraction the rate of segregation increases with the angular speed of the rotating cylinder. When the tube is partially filled the particle segregation is observed at higher angular speed, whereas in fully filled case the segregation starts at much lower rotation speed for the same concentration of particles. The segregation pattern changes as the rotation speed is increased. At higher speed the centrifugal force dominates over gravitational and viscous drag forces and this result into completely different segregation patterns. We have also analyzed the evolution of concentration profile from the image analysis of the particles.     

Reproducing kernel particle methods for structural dynamics

This paper explores a Reproducing Kernel Particle Method (RKPM) which incorporates several attractive features. The emphasis is away from classical mesh generated elements in favour of a mesh free system which only requires a set of nodes or particles in space. Using a Gaussian function or a cubic spline function, flexible window functions are implemented to provide refinement in the solution process. It also creates the ability to analyse a specific frequency range in dynamic problems reducing the computer time required. This advantage is achieved through an increase in the critical time step when the frequency range is low and a large window is used. The stability of the window function as well as the critical time step formula are investigated to provide insight into RKPMs. The predictions of the theories are confirmed through numerical experiments by performing reconstructions of given functions and solving elastic and elastic–plastic one-dimensional (1-D) bar problems for both small and large deformation as well as three 2-D large deformation non-linear elastic problems. Numerical and theoretical results show the proposed reproducing kernel interpolation functions satisfy the consistency conditions and the critical time step prediction; furthermore, the RKPM provides better stability than Smooth Particle Hydrodynamics (SPH) methods. In contrast with what has been reported in SPH literature, we do not find any tensile instability with RKPMs.     

Hygroscopic behavior of substrate-deposited particles studied by micro-FT-IR spectroscopy and complementary methods of particle analysis

The application of microscopic Fourier transform infrared (micro-FT-IR) spectroscopy combined with complementary methods of particle analysis is demonstrated here for investigations of phase transitions and hygroscopic growth of micron-sized particles. The approach utilizes the exposure of substrate-deposited, isolated particles to humidified nitrogen inside a sample cell followed by micro-FT-IR spectroscopy over a selected sample area. Phase transitions of NaCl, sea salt, NaNO3, and (NH4)2SO4 particles are monitored with this technique to evaluate its utility and applicability for particle hydration studies. The results are found in excellent agreement with literature data in terms of (a) reliable and reproducible detection of deliquescence and efflorescence phase transitions, (b) quantitative measurements of water-to-solute ratios in particles as a function of relative humidity, and (c) changes in the IR spectra resulting from phase transitions and changing relative humidity. Additional methods of particle analysis are employed to complement and assist in the interpretation of particle hygroscopicity data obtained from micro-FT-IR measurements. The analytical approach and the experimental setup presented here are relatively simple, inexpensive, readily available and therefore may be practical for hydration studies of environmental particles collected in both laboratory and field studies.     

Coupled lattice Boltzmann method and discrete element modelling of particle transport in turbulent fluid flows: Computational issues

This paper presents essential numerical procedures in the context of the coupled lattice Boltzmann (LB) and discrete element (DE) solution strategy for the simulation of particle transport in turbulent fluid flows. Key computational issues involved are (1) the standard LB formulation for the solution of incompressible fluid flows, (2) the incorporation of large eddy simulation (LES)‐based turbulence models in the LB equations for turbulent flows, (3) the computation of hydrodynamic interaction forces of the fluid and moving particles; and (4) the DE modelling of the interaction between solid particles. A complete list is provided for the conversion of relevant physical variables to lattice units to facilitate the understanding and implementation of the coupled methodology. Additional contributions made in this work include the application of the Smagorinsky turbulence model to moving particles and the proposal of a subcycling time integration scheme for the DE modelling to ensure an overall stable solution. A particle transport problem comprising 70 large particles and high Reynolds number (around 56 000) is provided to demonstrate the capability of the presented coupling strategy. Copyright © 2007 John Wiley & Sons, Ltd.     

A lattice Boltzmann model of flow blunting

We review our recent multi-component lattice Boltzmann equation method for the simulation of a large number of mutually immiscible liquid species and then apply it to the simulation of dense volume fraction suspensions of deformable particles in internal geometry. In particular, we illustrate the scope of our method by applying it to the simulation of pipe flows containing a high volume fraction of monodisperse suspended, deformable particles. The particles are modelled as immiscible, relatively viscous liquid drops. We modify the 'solidity' of the particles by modifying their viscosity and surface tension and demonstrate the effect of the solidity upon the blunting of the velocity profile.     

Influence of walls on the migration of non-Brownian spherical particles in creeping flow: a lattice Boltzmann study

The influence of walls on binary encounters of spherical particles under creeping flow is studied by means of the lattice Boltzmann method. Depending on the initial particle displacement different behaviours can be observed, including the 'swapping' trajectories. The domain of the swapping trajectories is identified for interacting spheres with the same diameter; some preliminary results are given for the case of two spheres with different diameters. Finally, the influence of particle swapping on the dynamics of monodisperse suspensions is also described.     

Regular and stochastic dynamics of particles during vortex generation in a rotating stream with shear

The results of an experimental study of the initial stage of development of a concentrated vortex are given.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 53, No. 1, pp. 37–42, July, 1987.     

低温回热制冷机内交变流动与换热的格子-Boltzmann方法模拟

采用格子-Boltzmann方法(LBM)分别通过对二维通道及多孔介质内交变流动与换热进行了数值模拟,以研究低温回热制冷机中脉冲管内及回热器内交变流动与换热规律.结果表明:二维通道交变流动结果与解析解吻合得很好.当交变流动数较大时,出现速度环形效应,温度表现为周期波动变化.多孔介质内各点速度总体均呈现交替波动变化,但振...     

Micromixing with linked chains of paramagnetic particles

Paramagnetic colloidal particles aggregate into linear chains under an applied external magnetic field. These particles can be chemically linked to create chains that can be magnetically actuated to manipulate microscopic fluid flow. The flexibility of the chain can be adjusted by varying the length of the linker molecule. In this paper, we describe the use of a suspension of linked paramagnetic chains in a rotating magnetic field to perform microscale mixing. The effect of chain rotation and flexibility on the diffusion of molecules is studied by observing the mixing of an acid and base in a microchannel. We show that, as the chain rotation frequency increases, there is marked increase in the effective mixing between fluid streams; however, a maximum frequency exists and above this frequency the chains are no longer effective in mixing. More flexible chains are more effective at mixing over a larger range of frequencies.     

Parallelization of lattice Boltzmann method for incompressible flow computations

Parallel computation of the two and three-dimensional decaying homogeneous isotropic turbulence using the lattice Boltzmann method are presented. BGK type approximation for collision term in 9 velocity square lattice model is used. It is found that the lattice Boltzmann method is able to reproduce the dynamics of decaying turbulence and could be an alternative for solving the Navier-Stokes equations. The lattice Boltzmann method is parallelized by using domain decomposition and implemented on a distributed memory computer, Hitachi SR2201. It is found that vertical decomposition gives the highest speedup. In the case of horizontal decomposition the longer the number of lattice units in horizontal direction of each subdomain, the shorter the CPU time. Extension to three-dimension is carried out using 15 velocity cubic lattice model. Compared with the result of two-dimensional case, a higher speedup is obtained than in the three-dimensional simulation. Further investigation is needed on the accuracy and efficiency of cubic lattice BGK model.     

Projection methods in flexible multibody dynamics. Part II: Dynamics and recursive projection methods

In Part I of this paper the kinematic relationships between the absolute, elastic and joint accelerations are developed. In this paper, these kinematic equations are used with the generalized Newton-Euler equations and the relationship between the actual and generalized reaction forces to develop a recursive projection algorithm for the dynamic analysis of open-loop mechanical systems consisting of a set of interconnected rigid and deformable bodies. Optimal matrix permutation, partitioning and projection methods are used to eliminate the elastic accelerations while maintaining the inertia coupling between the rigid body motion and the elastic deformation. Recursive projection methods are then applied in order to project the inertia of the leaf bodies onto their parent bodies. This leads to an optimal symbolic factorization which recursively yields the absolute and joint accelerations, and the joint reaction forces. The method presented in this paper avoids the use of Newton-Raphson algorithms in the numerical solution of the constrained dynamic equations of open-loop kinematic chains since the joint accelerations are readily available from the solution of the resulting reduced system of equations. Furthermore, the method requires only the inversion or decomposition of relatively small matrices and the numerical integration of a minimum number of co-ordinates. Open-loop multibody robotic manipulator systems are used to compare the results and efficiency of the recursive methods with that of the augmented formulations that employ Newton-Raphson algorithms.     

Characterization of magnetic forces by means of suspended particles in paramagnetic solutions

A new technique, whereby the so-called "iso-directional-force lines" may be illustrated directly, is proposed. The method is based on the levitation forces acting on a particle immersed in paramagnetic fluid in nonhomogeneous magnetic field. An ordered set of capillaries, each containing a small particle suspended in the fluid, may be used to depict the iso-directional-force lines by the equilibrium positions of the particles. Once the field is mapped (by a selected standard system), its characteristics are known, with respect to any other fluid particle combinations. The latter is of significance for research and technology.     

The smooth piecewise polynomial particle shape functions corresponding to patch-wise non-uniformly spaced particles for meshfree particle methods

In the previous papers (Kim et al. Submitted for publication, Oh et al. in press), for uniformly or locally non-uniformly distributed particles, we constructed highly regular piecewise polynomial particle shape functions that have the polynomial reproducing property of order k for any given integer k ≥ 0 and satisfy the Kronecker Delta Property. In this paper, in order to make these particle shape functions more useful in dealing with problems on complex geometries, we introduce smooth-piecewise-polynomial Reproducing Polynomial Particle shape functions, corresponding to the particles that are patch-wise non-uniformly distributed in a polygonal domain. In order to make these shape functions with compact supports, smooth flat-top partition of unity shape functions are constructed and multiplied to the shape functions. An error estimate of the interpolation associated with such flexible piecewise polynomial particle shape functions is proven. The one-dimensional and the two-dimensional numerical results that support the theory are resented. June G. Kim is Visiting Professor of the University of North Carolina at Charlotte.     

Strength and crack properties of nanoscale materials by ab initio molecular dynamics and temperature lattice Green’s function methods

The crack nucleation and propagation processes in nanoscale materials are studied using the ab initio constraint molecular dynamics method and the lattice Green’s function method. We investigate the strength and fracture behaviors of carbon related nanoscale materials, especially the graphen sheets in comparison with those of carbon nanotubes. The linear elastic parameters, non-linear elastic instabilities, thermal lattice expansion and fracture behaviors are studied in detail. We will show that the thermodynamic and strength properties of the nanoscale materials exhibit characteristic features and they are different from those of the corresponding bulk materials.     

Combined three‐dimensional lattice Boltzmann method and discrete element method for modelling fluid–particle interactions with experimental assessment

A general algorithmic framework is established in this paper for numerical simulations of three‐dimensional fluid–particle interaction problems with a large number of moving particles in turbulent flows using a combined lattice Boltzmann method (LBM) and discrete element method (DEM). In this approach, the fluid field is solved by the extended three‐dimensional LBM with the incorporation of the Smagorinsky turbulence model, while particle interactions are modelled by the DEM. The hydrodynamic interactions between fluid and particles are realized through the extension of an existing two‐dimensional fluid–particle hydrodynamic interaction scheme. The main computational aspects comprise the lattice Boltzmann formulation for the solution of fluid flows, the incorporation of a large eddy simulation‐based turbulence model within the framework of the three‐dimensional LBM for turbulent flows, the moving boundary condition for hydrodynamic interactions between fluid and moving particles, and the discrete element modelling of particle‐particle interactions. To assess the solution accuracy of the proposed approach, a much simplified laboratory model of vacuum dredging systems for mineral recovery is employed. The numerical results are compared with the experimental data available. It shows that the overall correspondence between numerical results and experimental measurements is good and thus indicates, to a certain extent, the solution accuracy of the proposed methodology. Copyright © 2009 John Wiley & Sons, Ltd.     

Magnetostatic energy of paramagnetic particles in magnetic separators

A general form for the magnetostatic interaction energy of an infinitely long cylinder of arbitrary cross-section, uniformly magnetized in a direction perpendicular to its long axis, and a spherical paramagnetic particle is obtained. For cylindrical and rectangular cross-sections, expressions for this energy are given which involve simple functions only.     

Magnetostatic energy of paramagnetic particles in magnetic separators

A series expansion is obtained for the magnetostatic interaction energy of an infinitely long cylinder of arbitrary cross section, uniformly magnetized in a direction perpendicular to its long axis, and a spherical paramagnetic particle, in powers of the radius of the paramagnetic particle. For a cylinder of elliptic cross section magnetized in an arbitrary direction, the first three terms in this series are evaluated explicitly.