Entrainment of particles and gas induced by draft fan over the particles bed

The draft fan is used to generate a controlled transportation of particles to enhance entrainment of gas and particles from the particles bed. Present investigations show the entrainment behavior of particles induced by an axial 4-blade draft fan hovering over the particles bed. The distributions of velocities and volume fractions of gas and particles are simulated using Euler-Euler two-fluid model (TFM) with kinetic theory of granular flow (KTGF) at different hovering heights and rotational speeds of the draft fan. The dense region with high solids volume fraction and low particles velocity and the dilute region with low solids volume fraction and high particles velocity exist beneath the draft fan along hovering heights. The entrainment of particles increases with the decrease of hovering height and increase of rotational speed of the draft fan. Present numerical simulations confirm that the gas-solid TFM with the kinetic theory of granular flow and multiple reference frame model can be effectively applied to analysis for entrainment of particles induced by draft fan.     

Influence of particle elasticity in shear testers

Two dimensional simulations of non-cohesive granular matter in a biaxial shear tester are discussed. The effect of particle elasticity on the mechanical behavior is investigated using two complementary distinct element methods (DEM): Soft particle molecular dynamics simulations (Particle Flow Code, PFC) for elastic particles and contact dynamics simulations (CD) for the limit of perfectly rigid particles. As soon as the system dilates to form shear bands, it relaxes the elastic strains so that one finds the same stresses for rigid respectively elastic particles in steady state flow. The principal stresses in steady state flow are determined. They are proportional to each other, giving rise to an effective macroscopic friction coefficient which is about 10% smaller than the microscopic friction coefficient between the grains.     

Experimental study and discrete element method simulation of Geldart Group A particles in a small-scale fluidized bed

Geldart Group A particles are of great importance in various chemical processes because of advantages such as ease of fluidization, large surface area, and many other unique properties. It is very challenging to model the fluidization behavior of such particles as widely reported in the literature. In this study, a pseudo-2D experimental column with a width of 5 cm, a height of 45 cm, and a depth of 0.32 cm was developed for detailed measurements of fluidized bed hydrodynamics of fine particles to facilitate the validation of computational fluid dynamic (CFD) modeling. The hydrodynamics of sieved FCC particles (Sauter mean diameter of 148 µm and density of 1300 kg/m³) and NETL-32D sorbents (Sauter mean diameter of 100 µm and density of 480 kg/m³) were investigated mainly through the visualization by a high-speed camera. Numerical simulations were then conducted by using NETL’s open source code MFIX-DEM. Both qualitative and quantitative information including bed expansion, bubble characteristics, and solid movement were compared between the numerical simulations and the experimental measurement. The cohesive van der Waals force was incorporated in the MFIX-DEM simulations and its influences on the flow hydrodynamics were studied.     

Force fluctuations in a pushed granular material

We analyse the time evolution of stresses in a noncohesive granular bed cut by the motion of a tool. Our numerical simulations both in two and three dimensions reveal large fluctuations of the force acting on the tool. These fluctuations have a decreasing exponential distribution. We find that, in spite of fluctuations, the mean force is well fitted by an analytical form obtained from a limit analysis with Coulomb's failure criterion. Received: 7 January 2000     

Simulated pulsed flow of gas and particles in a horizontal oppose-pulsed gas jets of bubbling fluidized bed

Flow behavior of gas and particles with a horizontal oppose-pulsed gas jets are simulated by means of a three dimensional Computational Fluid Dynamics (CFD) model with the kinetic theory of granular flow in a gas-particles bubbling fluidized bed. The effects of amplitudes and frequencies on the hydrodynamics of gas and particles are analyzed. The simulation results are presented in terms of phase velocity vector plot, volume fraction of phases, granular temperature, power spectrum and Reynolds stresses in the bed. Results show that the impingement caused by the oppose-pulsed gas jets oscillates with the variation of pulsed gas velocity. The impingement zone with the high solid volume fraction reciprocates from the left side to the right side through the bed center with the variation of pulsed jet gas velocities. The lateral velocity and gas turbulent kinetic energy, granular temperature and Reynolds stresses of gas and particles are larger near the pulsed gas jets than that at the center of the bed. The large dispersion coefficients of particles using the horizontal oppose-pulsed gas jets enhance the mixing of particles in gas-solid fluidized bed.     

Incipient motion of gravel and coal beds

An experimental study on incipient motion of gravel and coal beds under unidirectional steady-uniform flow is presented. Experiments were carried out in a flume with various sizes of gravel and coal samples. The critical bed shear stresses for the experimental runs determined using side-wall correction show considerable disagreement with the standard curves. The characteristic parameters affecting the incipient motion of particles in rough-turbulent regime, identified based on physical reasoning and dimensional analysis, are the Shields parameter, particle Froude number, non-dimensional particle diameter and non-dimensional flow depth. Equations of critical bed shear stress for the initial movement of gravel and coal beds were obtained using experimental data. The method of application of critical bed shear stress equations is also mentioned.     

Modeling of a cyclic plane strain compression-extension test in granular bodies within a polar hypoplasticity

In a recent paper, the effect of cyclic shearing on forced shear localization in an infinite granular strip between rough boundaries was numerically investigated. The present paper focuses on the evolution of spontaneous developed shear localization within an granular body under plane strain conditions, constant lateral pressure and cyclic vertical compression-extension. For a simulation of the mechanical behavior of a cohesionless granular material, a micro-polar hypoplastic constitutive is used which takes into account particle rotations, curvatures, non-symmetric stresses, couple stresses and the mean grain diameter as a characteristic length. The proposed model captures the essential mechanical features of granular bodies in a wide range of densities and pressures with a single set of constants. For the calibration of the constitutive constants, the data of a medium quartz sand are used. The attention of numerical simulations is laid on the influence of the number of cycles, the magnitude of the vertical deformation amplitude and the initial density on the evolution of shear zones in an initially prismatic granular specimen.     

Study on a large-scale discrete element model for fine particles in a fluidized bed

The discrete element method (DEM) is widely used to comprehend complicated phenomena such as gas–solid flows. This is because the DEM enables us to investigate the characteristics of the granular flow at the particle level. The DEM is a Lagrangian approach where each individual particle is calculated based on Newton’s second law of motion. However, it is difficult to use the DEM to model industrial powder processes, where over a billion particles are dealt with, because the calculation cost becomes too expensive when the number of particles is huge. To solve this issue, we have developed a coarse grain model to simulate the non-cohesive particle behavior in large-scale powder systems. The coarse grain particle represents a group of original particles. Accordingly, the coarse grain model makes it possible to perform the simulations by using a smaller number of calculated particles than are physically present. As might be expected, handling of fine particles involving cohesive force is often required in industry. In the present study, we evolved the coarse grain model to simulate these fine particles. Numerical simulations were performed to show the adequacy of this model in a fluidized bed, which is a typical gas–solid flow situation. The results obtained from our model and for the original particle systems were compared in terms of the transient change of the bed height and pressure drop. The new model can simulate the original particle behavior accurately.     

Hydrodynamic studies on fluidization of Red mud: CFD simulation

Hydrodynamic studies are carried out for the fluidization process using fine i.e. Geldart-A particles. Effects of superficial velocity on bed pressure drop and bed expansion is studied in the present work. Commercial CFD software package, Fluent 13.0 is used for simulations. Red mud obtained as waste material from Aluminum industry having average particle size of 77 microns is used as the bed material. Eulerian–Eulerian model coupled with kinetic theory of granular flow is used for simulating unsteady gas–solid fluidization process. Momentum exchange coefficients are calculated using the Gidaspow drag functions. Standard k–ε model has been used to describe the turbulent pattern. Bed pressure drop and bed expansion studies are simulated by CFD which are explained with the help of contour and vector plots. CFD simulation results are compared with the experimental findings. The comparison shows that CFD modeling is capable of predicting the hydrodynamic behaviors of gas–solid fluidized bed for fine particles with reasonable accuracy.     

Suitable rolling resistance model for quasi-static shear tests of non-spherical particles via discrete element method

Rolling resistance is a main consideration in quasi-static shear test simulations of particles via the discrete element method. However, not all rolling resistance models can satisfy the required objectivity and rate independence. A suitable model for spherical particles has been selected from five models in our previous works. In the current study, this model is combined with four normal and tangential contact models to confirm its applicability. After confirmation, the model is generalized to simulate direct shear tests on non-spherical particles. The stress–strain and dilatancy curves are rate-independent, and the relative rolling velocity between particles is objective. Furthermore, objectivity and rate independence for arbitrarily shaped particles are unchanged when normal stresses, volume fractions, or normal and tangential contact models are changed. Simulation results are also consistent with other experiment findings. For comparison, results are calculated for two other rolling resistance models; the shear curve at a single speed is consistent with the experiment, which has three stages: elastoplastic increasing, yielding, and keeping. However, the stress–strain curves at different shear rates do not coincide, which means that the models conflict with the rate independence of quasi-static granular systems. The virtues and defects of the five rolling resistance models are discussed from the perspectives of objectivity and rate independence. These two properties provide criteria for determining the appropriateness of a model, which has been rarely discussed in former studies.     

Numerical simulation of multilayer deposition in an obstructed channel flow

Simulation of multilayer deposition of dry aerosol particles in turbulent flows has gained a growing interest in various industrial and research applications. The multilayer deposition of carbonaceous aerosol particles in a turbulent channel flow obstructed by a succession of square ribs is here numerically investigated. The multilayer particle bed growth on the various wall surfaces affects the air flow, which in turn affects the overall deposition rate. An iterative numerical procedure is therefore suggested to simulate the evolution of the graphite layer. The iterative process used to reproduce the layer build-up is decomposed as follows: Reynolds-Avergared Navier Stokes is employed to generate the flow field. The turbulent dispersion of the particles is reproduced through the use of a continuous random walk model. After statistically sufficient deposition of particulate matter, the layer build-up is computed using mechanics of dry granular material. The layer build-up model shows good agreement with data obtained from experimental tests carried out on-site.     

MRI measurement of granular flows and fluid-particle flows

It is difficult to observe directly the particle motion inside a dense granular flow or a fluid-particle flow because of the existence of surrounding particles. MRI (Magnetic Resonance Imaging) is one of the non-invasive and non-destructive measurement techniques for such flows. MRI can measure the velocity distribution (tagging method and phase method), which is an outstanding advantage of the MRI measurement. This paper briefly explains the principle of the MRI measurement. Then MRI is applied to some dense granular flows or fluid-particle flows, such as the rotating drum, vibrated granular bed, hopper flow and spouted bed.     

A semi-analytical model for the effective thermal conductivity of a multi-component polydisperse granular bed

A theoretical model to predict the effective thermal conductivity of a multi-component polydisperse granular bed is presented. A simple energy balance analysis is used to arrive at an approximate analytical expression for the effective thermal conductivity. Simulation of heat transfer in a granular bed is carried out using an open source Discrete Element Method (DEM) package called LIGGGHTS. The derived analytical expressions for the effective thermal conductivity compares well with the results obtained from DEM simulations for granular beds comprising of different components with different sizes.     

STRESSES IN A RAPID FLOW OF SPHERICAL SOLID WITH TWO SIZES

Existing theories that predict the stress-strain rate relationship in a rapidly sheared granular flow can only treat materials that are made of single-size particles. However, granular flows usually involve materials of mixed sizes. It has been observed in many laboratory studies that size distribution has a significant effect on the flow of a granular material. Despite its importance, there has been no quantitative theory that can explain the effect of size distribution. An analytical model is developed here to quantify the stresses in a mixture of spheres with two different sizes and identical material properties. Binary collisions between adjacent particles are considered as the dominating stress-generating mechanism. Comparisons between the theoretical results and the existing laboratory data show good agreement.     

Discrete element analysis for shear band modes of granular materials in triaxial tests

The discrete element method (DEM) is adopted to simulate the triaxial tests of granular materials in this study. In the DEM simulations, two different membrane-forming methods are used to generate triaxial samples. One method is to pack the internal particles first, then to generate the enclosed membrane; the other is to generate the internal particles and the enclosed membrane together. A definition of the effective strain, which combines microscopic numerical results with macroscopic expression in three-dimensional space, is presented to describe the macroscopic deformation process of granular materials. With these two membrane generation methods, the effective strain distributions in longitudinal section and transverse section of the triaxial sample are described to investigate the progressive failure and the evolution of the shear bands in granular materials. Two typical shear band failure modes in triaxial tests are observed in the DEM simulations with different membrane-forming methods. One is a single shear band like a scraper bowl, and the other is an axial symmetric shear band like two hoppers stacking as the shape of rotational “X” in triaxial sample. The characteristics of the shear bands during the failure processes are discussed in detail based on the DEM simulations.     

Rheology of weakly wetted granular materials: a comparison of experimental and numerical data

Shear cell simulations and experiments of weakly wetted particles (a few volume percent liquid binders) are compared, with the goal to understand their flow rheology. Application examples are cores for metal casting by core shooting made of sand and liquid binding materials. The experiments are carried out with a Couette-like rotating viscometer. The weakly wetted granular materials are made of quartz sand and small amounts of Newtonian liquids. For comparison, experiments on dry sand are also performed with a modified configuration of the viscometer. The numerical model involves spherical, monodisperse particles with contact forces and a simple liquid bridge model for individual capillary bridges between two particles. Different liquid content and properties lead to different flow rheology when measuring the shear stress-strain relations. In the experiments of the weakly wetted granular material, the apparent shear viscosity $\eta _g$ η g scales inversely proportional to the inertial number $I$ I , for all shear rates. On the contrary, in the dry case, an intermediate scaling regime inversely quadratic in $I$ I is observed for moderate shear rates. In the simulations, both scaling regimes are found for dry and wet granular material as well.     

Micromechanic modeling and analysis of unsteady-state granular flow in a cylindrical hopper

This paper presents a numerical study of the micro- and macro-dynamic behavior of the unsteady-state granular flow in a cylindrical hopper with flat bottom by means of a modified discrete-element method (DEM) and an averaging method. The results show that the trends of the distributions of the microscopic properties such as the velocity and forces, and the macroscopic properties such as the velocity, mass density, stress and couple stress of the unsteady-state hopper flow are similar to those of steady-state hopper flow, and do not change much with the discharge of particles. However, the magnitudes of the macroscopic properties in different regions have different rates of variation. In particular, the magnitudes of the two normal stresses vary little with time in the orifice region, but decrease in other regions. The magnitude of the shear stress decreases with time when far from the bottom wall and central axis of the hopper. The results also indicate that DEM can capture the key features of the granular flow, and facilitated with a proper averaging method, can also generate information helpful to the test and development of an appropriate continuum model for granular flow.     

Thermal stress numerical study in granular packed bed storage tank

Thermal energy storage (TES) systems are central elements of various types of power plants operated using renewable energy sources. Packed bed TES can be considered as a cost-effective solution in concentrated solar power plants. Such a device is made up of a tank filled with a granular bed through which a heat-transfer fluid circulates. However, in such devices, the tank might be subjected to an accumulation of thermal stresses during cycles of loading and unloading due to the differential dilatation between the filler and the tank walls. The evolution of tank wall stresses over thermal cycles, taking into account both thermal and mechanical loads, is studied here using a numerical model based on the discrete element method. Simulations were performed for two different thermal configurations: (i) the tank is heated homogeneously along its height or (ii) with a vertical gradient of temperature. Then, the stresses resulting from the two different loadings applied on the tank are compared as well the kinematic response of the internal granular material. The kinematics of the granular material are analyzed at the particles scale (i.e. discrete elements), with a focus on the effect of particle/particle and wall/particle friction. Results show that a faster rearrangement of the packing occur when a thermal gradient is moving along the tank, leading to higher values of stresses applied on the tank walls. In addition to this, the behavior of the packed bed is dependent on the friction levels in the tank, whether the friction between particles themselves or the friction at the contact of particles with the shell. The influence of the slenderness ratio of the tank is investigated as well. Moreover, a reduction of 20% of thermal applied stresses can be obtained when inclined wall boundaries are used. The combination of an homogeneous configuration with low levels of friction (using lubricants) in thermocline storage tanks with inclined fixed boundaries can decrease significantly the induced stresses applied on the wall.     

Application of a new method for experimental validation of polydispersed DEM simulation of silo discharge

There are numerous experimentally validated simulations for mono-dispersed systems in the literature based on discrete element method (DEM). In practice, however, most of granular systems consist of polydispersed assemblies of particles. Few studies have considered the effect of polydispersity, and yet fewer have experimentally validated the results. In this study, application of a new experimental method for granular flow analysis is presented, capable of validating the results of an in-house developed GPU-based DEM solver in both monodispersed and polydispersed assemblies. Silo discharge is chosen as the case study in which discharge time, flow pattern and more importantly, the outlet composition variation with time (for polydispersed configurations) have been experimentally evaluated and validated with numerical results. The outlet composition, which is the ratio of fine to coarse particles in the outlet stream, is an essential measure of segregation in polydispersed silos, and its numerical prediction can be correct only if the interactions between fine and coarse particles within the silo are modelled precisely. Measuring this parameter is not possible using conventional experimental methods established in silo discharge studies such as high speed photographing or high-frequency weight measurement of the bed. A new apparatus has been developed which can measure this parameter. The device is a compartmented wheel rotating with a motor which gathers the outlet stream of the silo into different compartments. Due to practical limitations, design and function of the apparatus are not ideal. Forward mixing, distribution of particles with the same resident time in different compartments, is the most critical problem. Non-idealities must be compensated by means of post-processing codes so that comparable results are obtained from experiment and simulation.