Shinichi Yuu

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.

The reduction of pressure drop due to dust loading in a conventional cyclone

Abstract Experiments have been conducted to examine the effect of dust loading on pressure drop in a conventional cyclone. The presence of dust in the air stream reduced the cyclone pressure drop by as much as 30%, even at extremely low concentrations, such as 0.2 g/m 3 . In the range of 1.5–50 g/m 3 , the pressure drop ratio (the ratio of the pressure drop of dusty air to that of pure air with the same inlet velocity) was independent of dust concentration, and kept nearly constant; but it decreased as the concentration increased above 50g/m 3 . It was observed that the presence of dust reduced the tangential velocity. However the radii of a cross section of the cyclone, where the pressures are equal to those of the entrance and the exit, did not change noticeably. Calculating the pressure drop by integrating the term due to centrifugal force is also examined.

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. n nThe 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.

Collection of submicron particles in electro-flotation

Abstract A theoretical analysis is presented to describe the deposition of Brownian particles onto hydrogen bubbles under surface interactions. Single collection efficiency has been numerically calculated for zeta potentials, having assumed that the effective Hamaker constant is equal to 3.0 × 10−14erg though our choice of Hamaker constant is rather arbitrary. From a mass balance, total collection efficiency or the rate of flotation has been determined. In this way, electro-flotation process is quantitatively described. Experimentally, the electro-flotation of polystyrene latices of mean diameter 0.6 μm has been studied to examine the effect of the charge on both particles and bubbles on the total collection efficiency. The bubbles were of mean diameter 20 μm. The electrolyte was AlCl3. To measure the charge on the bubbles, we directly sampled solution including very small bubbles with a glass tube from a flotation vessel and poured into a micro-electrophoresis cell. The horizontal velocity measured when the bubbles rose up a “stationary level” in the cell under the known potential gradient gave the electromobility. The charge on the latex particles were found to change its sign from negative to positive as flotation time went on. The theoretical total collection efficiency has been in close agreement with the experimentally determined one.

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.

Numerical analysis of fine powder flow using smoothed particle method and experimental verification

Abstract Numerical simulation of velocity and stress fields for flowing powder composed of an infinite number of particles presents a most difficult problem in powder technology. The distinct element method (DEM) is useful for determining each particle trajectory which involves multi-body interactions. However, total particle cannot be computed using DEM. The particle number which can be calculated for a three-dimensional spherical system would be in hundreds of thousands. A description of flow characteristics for a small amount of powder would not be practical. Simulation within a tank would thus be virtually impossible. The authors have conducted numerical simulation of flowing powder using the smoothed particle (SP) method through application of continuum dynamics. The authors’ group is the first to contrive to apply this method to powder flows. In the SP method, partial differential equations that govern flow fields are transformed to ordinary differential equations of the Lagrangian-type for particle motion. Numerical analysis of ordinary differential equations is much simpler compared to partial differential equations. Lagrangian analysis is suitable for determining the characteristics of discrete particles. The equation of powder pressure exerted on tank bed due to differences in density and constitutive equations that consider yield stress have been used as basic equations and the latter were obtained by the authors’ group using DEM. These equations provide clarification of the rheological characteristics of powder flow. Glass beads (particle diameter: 100 μm ) were used in the present study as test powder stored in a tank and discharged by gravitational force. Calculated velocity distribution, free surface in the tank and the rate of discharge were compared with experimental data and a good agreement was noted. Based on the results of this study, the SP method in conjunction with the model equation for yield stress appears quite useful for simulating the flow of fine powder.

The calculation of particle deposition efficiency due to inertia, diffusion and interception in a plane stagnation flow

Abstract The particle deposition mechanism in a plane stagnation flow is investigated analytically and numerically. Particle deposition efficiency η TID is obtained theoretically by taking into account particle inertia, diffusion and interception. It is compared with various calculated deposition efficiencies, i.e. η T (due to inertia) + η I (due to interception) + η D (due to diffusion), η TI , (due to inertia and interception) + η D , etc. In the region where all of the three deposition mechanisms, i.e. inertia, interception and diffusion, act at the same time, real deposition efficiency η TID is not accurately expressed by η T + η I + η D . However, η TID is nearly equal to η TI + η D unless the interception parameter is zero. The calculated results of particle concentration indicate that a high concentration region is formed near the deposition plate, and that the concentration becomes higher as particle inertia increases.

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.