Toshihiko Umekage

Numerical simulation of air and particle motions in bubbling fluidized bed of small particles

Abstract Air and particle motions in a bubbling fluidized bed of about 100,000 particles of 310 μm in diameter, which are classified as the B particles in the Geldart map, are numerically simulated. Particle–particle interactions were calculated, using the three-dimensional distinct element method (DEM). The Navier–Stokes equation and the Lagrangian type particle equation were simultaneously solved, where the drag and lift forces on particles, the multi-body collisions among particles and the mutual interaction between air and particles were taken into account. The corresponding experiments were also performed. It was found that the calculated results describe well the experimental instantaneous particle positions, and enable us to know the mechanisms of bubble formation, bubble coalescence and bubble disruption in a bubbling fluidized bed.

Numerical simulation of the high Reynolds number slit nozzle gas-particle jet using subgrid-scale coupling large eddy simulation

Large eddy simulation (LES) model in which the effect of the particle existence on subgrid-scale flows have been taken into account is proposed. The kinetic energy of the subgrid-scale flow to obtain a turbulent viscosity coefficient of the subgrid-scale flow in the LES has been calculated in assuming that the interaction terms between the gas and particles, the turbulent production term and the viscous dissipation term were balanced with each other in the kinetic energy equation of the subgrid-scale turbulent flow. Using this model, three-dimensional Navier–Stokes equations and the Lagrangian particle motion equations are simultaneously solved to describe the high Reynolds number (Re=104) gas–particle jet flow and the effect of particle existence on it. The calculated results of air and particle turbulent characteristics which are mean velocity, turbulent intensity and Reynolds stress distributions are in good agreement with experimental data measured by a laser Doppler velocimeter. The existence of particles usually reduces the grid-scale turbulence in the high Reynolds number developed turbulent jet. On the other hand, the particle existence which is some kind of flow disturbance produces grid-scale fluctuations in the initial and the transitional regions of the jet and then it increases the air turbulent intensity. When particle size is much smaller than the grid size, the particle existence reduces the subgrid-scale turbulence. However, when the product of the gas and particle relative velocity and the particle concentration gradient is very large, the particle existence is able to increase the subgrid-scale turbulence.

Numerical simulation of air and particle motions in group-B particle turbulent fluidized bed

Abstract Air and particle motions in a group-B particle turbulent fluidized bed are numerically simulated. The locally averaged three-dimensional Navier–Stokes equations and the Lagrangian particle equations, in which the mutual interactions between air and particles and the two-body collisions between particles were taken into account, were simultaneously solved. Reynolds stress terms and the turbulent mass flux terms caused by the subgrid scale fluctuations have been modeled by the large eddy simulation in which the effect of particle existence on subgrid scale flows has been taken into account. The corresponding experiments were also performed. It is found that calculated results well represent the experimental instantaneous particle positions and flow characteristics of the air and particles, and enable us to know the mechanisms of various phenomena such as the large complex bubbling flow and the particle cluster formation.

Three-dimensional numerical simulation of the motion of particles discharging from a rectangular hopper using distinct element method and comparison with experimental data (effects of time steps and material properties)

The distinct element method (DEM) is a simple numerical model which is capable of describing the motion of granular materials. In this study, the motion of particles discharging from a rectangular hopper has been numerically simulated by the DEM whose time steps are Δt = 10−6, 10−5 and 10−4s, which correspond to stiffness kn = 7.0 × 107, 7.0 × 105 and 7.0 × 103 N/m, respectively. The calculated results have been compared with the experimental data. All of the calculated results not only qualitatively describe the experimental results, but also approximately describe the quantitative characteristics of the measured data, although the stiffness of the calculations is greatly different from the real stiffness of the materials. However, the calculated result of the DEM using the smallest time step (Δt = 10−6s) could not give the best description of the experimental data. This suggests that the calculated results of the DEM could not accurately describe the real granular flow even if the time step is small enough to use the real stiffness of the materials. The most significant approximation of the DEM is that distinct particles do not interact with any other particles and displace independently from one another during one calculation time step. The discrepancy between the model based on this approximation and the real granular flow would not decrease as the time step is decreased.

Flow-field prediction and experimental verification of low Reynolds number gas-particle turbulent jets

Abstract A low Reynolds number (Re = 1700) gas-particle turbulence-free jet has been numerically simulated by a direct numerical simulation (DNS). The averaged Kolmogorov microscale of the flow is nearly equal to the computational cell size in the DNS. A finite difference technique which can easily be applied to turbulent flows having complex geometries was used. The calculated results of air and particle turbulence characteristics (mean velocity distributions, turbulence intensity distributions and Reynolds stress distributions) are in good agreement with experimental data obtained using a laser Doppler anemometer. Comparison of the instantaneous air velocity vector diagrams of two-phase and clean-air jets shows that the additional dissipation by the presence of particles delays the turbulence development of the two-phase jet, shifting it downstream. Particles whose velocity and concentration are uniform at the nozzle outlet become clustered downstream of the jet by interacting with the large-scale vortex motions which originate from the shear at the nozzle exit wall. The air turbulence intensities of the two-phase jet are 20–50% lower than those of the clean-air jet in the jet center-line region where most of the particles are found. This means that fluctuating air motions in the two-phase jet are considerably affected by the presence of particles even if the mass mixture ratio is as small as 0.6.

Constitutive Relations and Computer Simulation of Granular Material

The main research subject in the continuum approach of dense granular materials is the derivation of constitutive relations needed for closure. These relations have been derived using many kinds of model. The brief outlines of these models, simulation results for mechanical fields using these relations and the experimental verifications are presented. There are not so many as these studies explain correctly the detailed behaviors of granular materials. It would be necessary to verify the simulation results based on these models by direct comparison with the experimental data performed under the same conditions as the calculation. The reason for the lack of simulation results to describe behaviors of dense granular materials is the difficulty in calculating the mechanical fields in which statics and dynamics are simultaneously involved under real-life boundary values using these constitutive relations. We describe briefly our constitutive equations based on the mechanical data of dense granular materials obtained by distinct element method calculation and show the simulation results of real flow fields (granular collapse and heap) using our constitutive equations by the smoothed particle hydrodynamics (SPH) method and the verification by the direct comparison with experimental data presented in a previous paper. It seems that a Lagrangian approach, e.g. the SPH method, is a simple and reliable method for the calculation of dense granular materials using these complicated constitutive relations under real-life boundary conditions.

Numerical simulation for blockage of cohesive particles in a hopper using the distinct element method and its correlation with experimental results of real cohesive granular materials

We numerically simulated the blockage phenomena in the three-dimensional rectangular hopper using the distinct element method (DEM) in which the effects of cohesion forces between particles were taken into account. We also measured the critical blockage states using four different cohesive granular materials, i.e. talc, calcium carbonate, flyash and corn starch. The calculated results describe well the blockage, which is greatly affected by the cohesion force. The mass discharge rate decreases and its relative fluctuation increases with an increase of the cohesion force. The normal and shear stresses on the wall increase with an increase of the cohesion force. We found the critical blockage states by calculation and experiment under the various conditions, and calculated the blockage state diagram using the dimensionless numbers based on the properties which affect the blockage phenomena. The calculated and experimental critical blockage states are described by the same straight line (the critical blockage state line). The results of this study make it possible to predict the critical conditions under which the blockage occurs.

Simulation of Granular Flows and Pile Formation in a Flat-Bottomed Hopper and Bin, and Experimental Verification

Granular flows of 200 μm particles and the pile formation in a flat-bottomed hopper and bin in the presence of air and in a vacuum were predicted based on three-dimensional numerically empirical constitutive relations using Smoothed Particle Hydrodynamics and Computational Fluid Dynamics methods. The constitutive relations for the strain rate independent stress have been obtained as the functions of the Almansi strain including the large deformation by the same method as Yuu et al. [1]. The constitutive relations cover the elastic and the plastic regions including the flow state and represent the friction mechanism of granular material. We considered the effect of air on the granular flow and pile by the two-way coupling method. The granular flow patterns, the shapes of piles and the granular flow rates in the evolution are compared with experimental data measured under the same conditions. There was good agreement between these results, which suggests that the constitutive relations and the simulation method would be applicable for predicting granular flows and pile formation with complex geometry including free surface geometry. We describe the mechanisms by which the air decreases the granular flow rate and forms the convergence granular flow below the hopper outlet.

Numerical simulation of the velocity and stress fields for a flowing powder using the smoothed particle method and experimental verification

Abstract Numerical simulation of the velocity and stress fields for a flowing powder which consists of uncountablly numerous particles is one of the most difficult problems in powder technology. We have numerically simulated these fields of flowing powder using the smoothed particle (SP) method based on the relationships of the stress-strain rates obtained by the Distinct Element Method. In the SP method, the partial differential equations, which are the governing equations of the flow fields, are transformed to ordinary differential equations, which are Lagrangian-type equations of particle motions. The numerical analysis of ordinary differential equations is much easier than that of partial differential equations. Moreover, Lagrangian analysis is suitable for the description of the characteristics of discrete particles. The calculated results of the velocity and stress fields in a two-dimensional rectangular hopper are compared with the measured values obtained under nearly the same conditions, and a fairly good agreement among them is obtained. These results show that the SP method is an effective tool to simulate the various flow fields of powders which consist of uncountablly numerous particles.

Numerical simulation for the friction mechanism of a powder bed using two-dimensional distinct element method

Abstract The motion of particles under shear stress has been numerically simulated using two-dimensional distinct element method. The calculated results well describe the stick-slip phenomena caused by the friction in the particle bed. The results also show that the motions that govern these phenomena are particle rotations which give rise to the slip motion from the static stick state of the particle bed. These motions of particle rotations are transmitted fairly deep inside the particle bed due to particle-particle interaction. Based on these calculated results, we have also obtained the friction loop which is qualitatively in good agreement with the data measured by Nasuno et al. However, the calculated friction coefficient of the particle bed is about 30% of that measured by Nasuno et al. The main cause seems to be the difference in the clearance between the cover plate particles and the bed particles from the experimental state in the powder bed.