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The discrete element method (DEM) coupled with computational fluid dynamics (CFD) is a powerful tool for exploring the detailed behaviors of dense particle–fluid interaction problems such as fluidized beds. Coarse-graining models have been proposed to decrease the computational cost by increasing the model particle size. In this study, we examine the influence of the model particle size and the spatial resolution on the average size and number of bubbles in coarse-graining DEM-CFD calculations of bubbling fluidized beds. Calculation results indicate that the bubble size is scaled by the model particle size if parameters are following similarity laws defined in a particle scale, as well as the geometric similarity of the whole system is maintained. The usage of coarse spatial resolution increases the bubble size and decreases the number of bubbles. The countervailing influence of the model particle size and the spatial resolution in a practical coarse-graining scenario results in nearly the same bubble size.

In this work, a resolved CFD–DEM coupling model for the simulation of gas-liquid-solid flows is developed: the interface capturing method based on the colour function is employed for fluids (i.e. a gas and liquid) whilst Discrete Element Method (DEM) is used for particles. The Volume Penalisation (VP) method is adopted to consider the hydrodynamic interactions between fluids and particles along with the Immersed Free Surface (IFS) method, which artificially extends the gas-liquid interface into the interior of the particle to account for the wettability. The unique point of the proposed model is that the thickness of the gas-liquid interface can be controlled by using both interface compression and diffuse interface techniques simultaneously. From the simulation results, it is presented that the accurate evaluation of the surface tension force as well as the capillary force can be achieved by appropriately controlling the interface thickness. Moreover, the major two methods in the literature to calculate the capillary force are compared in this work. The validity of the proposed model is presented for both static and dynamic cases. The behaviour of two colliding particles with a dynamic liquid bridge is then simulated to demonstrate the applicability of the proposed model to a complex three-phase system.

A resolved CFD–DEM coupling model for the simulation of particulate flows is proposed in this work. The Volume Penalisation (VP) method, which is a family of the continuous forcing Immersed Boundary (IB) method, is employed to express the particle–fluid interaction. A smooth mask function is used to avoid sharp transition between the solid (particle) and fluid domains that may cause numerical oscillation with moving particles. Optimal permeability is employed to reduce the model error associated with the VP method. It is determined as a function of only the interface thickness and fluid kinematic viscosity. The proposed model is accurate, easy to implement with any discretisation scheme, and only requires small computational overhead for particle–fluid interaction. Several simulations are performed to test the validity of the proposed model in various systems, i.e. from dilute to relatively dense flows, and the results show good agreement with the exact solution or empirical correlation. It is found that the error can be scaled with the ratio between the gap and interface thickness. The proposed model is also applied to predict the relative viscosity of suspensions and the density segregation in fluidised beds.

Simulation based on discrete element method (DEM) coupled with computational fluid dynamics (CFD), coupled DEM-CFD, is a powerful tool for investigating the details of dense particle–fluid interaction problems such as in fluidized beds and pneumatic conveyers. The addition of a mechanical vibration to a system can drastically alter the particle and fluid flows; however, their detailed mechanisms are not well understood. In this study, a DEM-CFD model based on a non-inertial frame of reference is developed to achieve a better understanding of the influence of vibration in a vibrated fluidized bed. Because the high computational cost of DEM-CFD calculations is still a major problem, an upscaled coarse-graining model is also employed. To realize similar behaviors with enlarged model particles, non-dimensional parameters at the particle scale were deduced from the governing equations. The suitability and limitations of the proposed model were examined for a density segregation problem of a binary system. To reduce the computational costs, we show that the ratio between the bed width and model particle size can be reduced to a minimum value of 100; to obtain similar segregation behaviors, the ratio between the bed height and model particle size is considered unchanged.

The reaction kinetics of laser-induced particle formation in an aqueous/EtOH solution of PdCl42– without a photoactivator was investigated by transmission electron microscopy (TEM) and dispersive X-ray absorption fine structure (DXAFS) measurements. Pd particles were generated by the irradiation of a nanosecond pulsed 266 nm laser with a fluence of 19.9–59.7 mJ/cm2. The TEM observation showed the dependence of the particle size on the laser fluence and the promotion of particle growth by the irradiation of a high-fluence laser. The DXAFS data were analyzed by three methods: deconvolution of the X-ray absorption near-edge structure (XANES) spectrum by a linear combination fitting, model fitting of the extended XAFS (EXAFS) oscillation of the PdCl42– ion, and fitting of the spectrum edge of XANES using an error function. These methods give the ratio of Pd2+, the coordination number of Pd–Cl bond, and the edge width of XANES, which are related to the Pd2+ concentration. Temporal changes of the Pd2+ concentra...

The interactions of bubbles and particles with fixed cylindrical tubes in two-dimensional fluidized beds were investigated by experiments and by simulations, based on results for single bubbles impinging on a tube. The experimental results based on PIV analysis support our previous force origin model and indicate that the model is able to successfully model bubble behavior and particle motion around fixed objects. The simulation results give useful predictions, dynamic force induced on a tube consists of the force from pressure gradient, fluid viscous force and particle contact force. The predominant force component is from the pressure gradient. As bubbles directly interact with a tube, the particle contact force contribution briefly becomes predominant. Bubble behavior and particle motion are greatly affected by the state of the emulsion phase as the medium of the fluidized bed into which gas is injected. Hence the dynamic forces on immersed objects are directly affected by the state of the emulsion phase.

Snapshots of particle concentration and velocity fields in bubbling gas–solid fluidized beds were acquired using magnetic resonance imaging. Using a recently developed multichannel radiofrequency receiver coil in combination with fast readout techniques, adapted from medical MRI protocols, the temporal resolution was 7 and 18 ms for two-dimensional images of particle concentration and velocity fields, respectively. A cylindrical bed with 190 mm diameter and 300 mm height was filled to heights of 100, 150, and 200 mm with spherical 1 and 3 mm diameter particles and fluidized at ratios of superficial gas velocity to minimum fluidization velocity (U/Umf) of 1.2, 1.5, 2.0, 3.0, and 4.0. The effects of these varying parameters on the number of bubbles, bubble diameter, bed height, and particle speed are investigated. It is hoped that these data sets will become important benchmarks against which computational, analytical, and empirical models can be validated.

The validity of the lubrication force model on particles in the normal direction due to a pendular liquid bridge of power-law fluid based on the Reynolds lubrication theory is investigated by comparing it with Direct Numerical Simulation (DNS) results. It is found that the model can predict the force with less than 10% error when the dimensionless separation distance is smaller than 0.05. In the DNS results, a spike of the pressure at the edge of the bridge as well as a drop in pressure around the axis connecting the centres of the particles are observed on the particle surface. It is revealed that these phenomena are caused by the component of the viscous stress tensor which is neglected in the lubrication theory. A new closed-form solution of the lubrication force model is also proposed in this study which can be easily incorporated into the Discrete Element Method (DEM) framework.

Direct numerical simulation is used to study the dynamics of particle settling for Reynolds number from 0.1 to 50 and solid volume fraction from single particle to 0.4. The principle investigations are the effects of Reynolds number and solid volume fraction on average settling velocity, velocity fluctuations and particles structuring during settling. It is observed that average settling velocity deviates from the well-known power law for dilute suspension and moderate range of Reynolds number. Moreover, the increase of velocity fluctuations with domain size saturates and becomes about constant for moderate range of Reynolds numbers in contrast to low Reynolds number in which the fluctuations keep increasing. These behaviors are due to the separated particle pairs which are formed due to inter-particle wake interactions. As the solid volume fraction increases, the smaller inter-particle distances diminish the wake effects and corresponding particle structures.

The dynamics of particles settling at moderate Reynolds number is studied with periodic boundary conditions. The particle Reynolds number ranges from 0.1 to 50, and the solid volume fraction ranges from single sphere to 0.4. Particle-fluid interactions are solved by immersed boundary method and particle-particle interactions are solved by discrete element method. The principal results are the average settling velocity and the structure formation of particles. The average sedimentation velocities of particles for moderate Reynolds number showed deviation from the well-known power law, and the difference keeps on increasing with decrease in solid volume fractions. This deviation is removed by proposing the division of the power law into three regions of Reynolds number for dilute and non-dilute regimes. By analyzing the particle structures, this difference is due to the particle arrangements by the wake interactions at moderate Reynolds number.

Finite sized particles settling under the action of gravity are investigated by immersed boundary method for dilute suspensions and low to high range of Reynolds number. The Reynolds number based on the terminal velocity of a single particle is varied from 1 to 300 and the solid volume fraction ( φ ) is varied from 0.005 to 0.05. The studied range of Reynolds number corresponds from streamlined flow to downstream vortex shedding flow for single particle. For φ = 0.005, 0.01 and high Reynolds number ( Re ≧ 175), settling particles clusters due to the entrapment in high fluid shear regions. However for Re = 50 and 100, particles form separated pairs due to relatively weak strength of wakes that promote to drafting–kissing and tumbling scenario. These particle structures at high Reynolds number changes the settling behaviors of particles e.g. increase in the settling velocity and fluid velocity fluctuations. For φ = 0.03, 0.05, hindered settling effects dominate and reduce the effects of particles clustering due to Reynolds number.

The behavior of dense gas–solid flows in engineering applications such as fluidized beds and pneumatic conveyers is highly complex and a reliable numerical model is required. Such flows are usually within solid walls that considerably affect the flow fields, and it is important to correctly include this effect in numerical models to improve their prediction capability. The observation of microscopic flows near walls can enhance our understanding of the flow behavior and assist in improving models. In this study, direct simulations are performed to investigate the effect of a wall on flow fields at a microscopic level. The effects of the bulk void fraction, particle Reynolds number, and particle diameter are investigated. The prediction performances of existing correlation equations usually used in mesoscopic model calculations are also investigated. It is found that the Ergun and Beetstra equations produce large discrepancies in the region within a distance equal to the particle diameter from the wall.

A DEM-MPS coupled model for solid-liquid two phase flows is developed. Fluid motion is calculated for locally phase-averaged variables. The present model is applied to a collapse behavior of the assembly of aluminum particles in a rectangular container with and without liquid. The corresponding experiment is performed to validate the present model. The trajectory of each particle is traced by using the PTV (Particle Tracking Velocimetry) measurement. Calculated collapse behaviors agree well with the observed behaviors in the corresponding experiment. The calculated horizontal position of leading particle and particle velocity also agree well with the experimental results.

The behavior of flows in engineering applications such as a fluidized bed and a pneumatic conveyer is highly complex and a reliable numerical model has been desired. The flows are usually with solid walls that give considerable effects on flow field. To enhance the prediction capability of a model, it is important to include its effect properly. Observation of microscopic flow near walls shall enhance our understandings on flow behavior and model improvements. In the present study, direct simulations were performed to investigate the effect of walls on a flow field in the microscopic level. The effects of void fraction, particle Reynolds number and particle diameter were discussed. A prediction performance of existing correlation equations usually used in model calculations was also investigated. It is found that, by using Ergun and Beetstra equations, there is a large discrepancy in the region within 1 particle diameter from a wall.

It is important to develop a numerical simulation method to predict the behavior of droplets in granular media, which concerns wide range of natural phenomena and industrial particulate processes. Mainly empirical methods have been applied to complex granular problems including liquid transport by granular motion such as liquid transport by granular convection, liquid bridge formation between particles, breakup of a liquid bridge and so on. Effective numerical simulation method will enable us to design products more effectively. In this study we examined the applicability of MPS (Moving Particle Semi-implicit) method to the wetting behavior of droplet on a solid plane and between particles. We performed the numerical simulations of a droplet motion on an inclined plane and between a couple of particles by using the MPS method contains surface tension and wetting model, and made validation using the corresponding experiments.

Flow structures induced by bubbles formed in three-dimensional shallow rectangular gas-fluidized beds are investigated by the DEM–CFD coupling simulation. A numerical code is parallelized and more than 4.5million particles are tracked in the maximum by using 16 CPUs. To investigate the domain-size dependency, the cross-sectional area of beds is enlarged by the factors up to 82 and the results are compared. Under the ideal uniform inflow condition, multiple bubbles are spontaneously formed in large cross-section cases. The dependency of bubble size on the cross-section size is not so clear under the same bed height condition. Clear circulation patterns are observed in the time-averaged data. Down-flows of particles exist in low void fraction portions selectively with particle up-flows dominating in the high void fraction regions. Three-dimensional visualization of bubble shape is also conducted. Bubbles that have complex structures such as worm-like one exist in addition to the conventional spherical cap.

Unsteady three-dimensional simulation of interactions between uniform flow and fixed identical two particles is performed for particle Reynolds number 30, 100, 200 and 250. The drag force of interactive particles depends on Reynolds number as well as the inter-particle distance. They are attenuated when particles are aligned streamwise, augmented when they are held side by side against the mean flow. These are compared with available experimental data. Existence of periodical double-sided vortex shedding at relatively low Reynolds number is observed when particles are almost touching. The method adopted in this paper is not only simple and easy, but also accurate with a proper resolution.

To improve the energy efficiency of construction and mining machineries such as hydraulic excavator and bulldozer, it is important to optimize the shape of tools, which are used to handle ground materials directly such as buckets and blades, and earthmoving processes. It is impossible without a deep understanding of interactions between mechanical tools and ground materials. In the present study, a DEM model based on multi-sphere approach is developed for the gravel excavation process using a hydraulic excavator bucket. Granular materials in nature include several geometrical factors over different scales and it is computationally expensive to model real particle shapes as they are, especially for practical engineering design problems. It is mandatory to develop a simplified model which only includes essential geometrical factors that are important for gravel-tool interactions. In the present study, the role of particle roundness on digging process is investigated. We find that smaller roundness prevents the rotational motion of particles and strengthens the shear resistance of the layer. In addition, particles with higher angular velocity are localized in a narrow zone where the formation of shear band is expected during digging processes.

Spatial scale characteristics of particle clusters are investigated by directly performing Fourier transform of spatial particle concentration distributions. Flow field data are obtained by large-scale Eulerian / Lagrangian simulations. All calculations are performed in three-dimensions and more than sixteen million particles are tracked in the maximum case. The inter-particle collision plays an important role for the development of particle clusters. In this study, results obtained by using the stochastic model based on direct simulation Monte Carlo (DSMC) are compared with that by the deterministic model. The results obtained by DSMC method agree quantitatively with deterministic model. Particle clusters consist of multiple-spatial scale components and the low wave-number, hence large-scale structure, is dominant. Dependency on the domain size and resolution is also investigated in detail.Copyright © 2007 by ASME

Spatial scale characteristics of particle clusters are investigated by using the flow field data obtained from time-dependent three-dimensional numerical simulations. Eulerian/Lagrangian approach with two-way coupling is adopted and individual particle–particle collisions are taken into account by using the hard-sphere deterministic model. More than sixteen million particles are tracked in the maximum case. The results show that the particle cluster consists of multiple-spatial scale components and a low wave number, hence the large-scale structure, is dominant. Three-dimensional structure reconstructed from the low-pass filtered data enables us to investigate the essential dynamics of particle clusters in detail. From the domain size-dependency study, it is found that the structure of particle cluster is sensitive to the horizontal domain size when the periodic boundary condition is used.