Computational simulations using a low density ratio-based kinetic theory of granular flow in subcritical water fluidized beds

Hydrodynamics of fluid and particles were simulated using a low density ratio-based kinetic theory of granular flow (KTGF) in subcritical water (SbW) fluidized beds (FB). Results indicated that the fluidization state of the SbW-particles mixture changes progressively from particulate to aggregative, indicating that a transitional state exists between aggregative and particulate fluidization. Wavy-like and churn-like flows were found along bed height in SbW FBs, unlike the homogeneous fluidization found in atmospheric water (AW) FBs and wispy-annular-like flow found in supercritical water (SCW) FBs. The predicted axial velocities and RMS fluctuating velocities of particles agreed approximately with measurements reported in the literature. The effect of fluid pressure and temperature, inlet fluid velocity and particle density on distributions of solid volume fractions and velocities were analyzed in SbW FBs.     

Velocity Fluctuations in a Particle-Laden Turbulent Flow over a Backward-Facing Step

Dilute gas-particle turbulent flow over a backward-facing step is numerically simulated. Large Eddy Simulation (LES) is used for the continuous phase and a Lagrangian trajectory method is adopted for the particle phase. Four typical locations in the flow field are chosen to investigate the two-phase velocity fluctuations. Time-series velocities of the gas phase with particles of different sizes are obtained. Velocity of the small particles is found to be similar to that of the gas phase, while high frequency noise exists in the velocity of the large particles. While the mean and rms velocities of the gas phase and small particles are correlated, the rms velocities of large particles have no correlation with the gas phase. The frequency spectrum of the velocity of the gas phase and the small particle phase show the -5/3 decay for higher wave number, as expected in a turbulent flow. However, there is a "rising tail' in the high frequency end of the spectrum for larger particles. It is shown that large particles behave differently in the flow field, while small particles behave similarly and dominated by the local gas phase flow.     

Numerical investigation of gas-particle hydrodynamics in a vortex chamber fluidized bed

Gas-particle hydrodynamic behaviour inside a vortex chamber fluidized bed is studied numerically with respect to different design and operating conditions. A three-dimensional computational fluid dynamics (CFD) model of a cylindrical vortex chamber is developed. Simulations are carried out with particles and without particles. In order to understand the gas-particle flow behavior velocity distribution, particle volume fraction distribution, radial pressure distribution and axial pressure distribution inside the vortex chamber are analyzed in detail. Particles of different diameters are used and its effect on the gas-particle flow behaviour is studied. Design parameters like the number of gas inlet slots and slot width are varied and their impact on the hydrodynamics of the vortex chamber is investigated. The numerical model is validated by comparing the numerical results with experimental results reported in literature.     

Numerical simulation of gas-particle flows behind a backward-facing step using an improved stochastic separated flow model

An improved stochastic separated flow (ISSF) model developed by the present authors is tested in gas-particle flows behind a backward-facing step, in this paper. The gas phase of air and the particle phase of 150 μm glass and 70 μm copper spheres are numerically simulated using the k–ɛ model and the ISSF model, respectively. The predicted mean streamwise velocities as well as streamwise and transverse fluctuating velocities of both phases agree well with experimental data reported by Fessler. The reattachment length of 7.6H matches well with the experimental value of 7.4H. Distributions of particle number density are also given and found to be in good agreement with the experiment. The sensitivity of the predicted results to the number of calculation particles is studied and the improved model is shown to require much less calculation particles and less computing time for obtaining reasonable results as compared with the traditional stochastic separated flow model. It is concluded that the ISSF model can be used successfully in the prediction of backward-facing step gas-particle flows, which is characterised by having recirculating regions and anisotropic fluctuating velocities. Received 20 June 2000     

Numerical simulation of hydrodynamic characteristics in a gas–solid fluidized bed

The fluidization of quartz particles as bed materials in the fluidized bed has significant influences on the combustion and gasification of refused derived fuels. Three-dimensional (3-D) simulations and analyses are performed for Geldart B particles using the computational fluid dynamics (CFD) method based on the kinetic theory of granular flows (KTGF) to investigate the hydrodynamic behavior. The drag models of Syamlal–O’Brien, Gidaspow, and Wen and Yu are selected to analyze the applicability of the kinetic model. The pressure drop, velocity distribution and solid volume fraction are studied numerically when the gas inlet velocity is changed. The results show that the increase of superficial gas velocity would lead to heterogeneous expansion of solid volume fraction and velocity distributions in both the dense phase zone and free board with a similar distribution pattern. The near wall particles form a dense phase structure with the solid volume fraction being greater than 0.3.     

Motion of Large Particles in a Horizontal Pneumatic Pipe

The horizontal pneumatic transport of large particles with particle to pipe diameter ratio of 0.6 and particle densities of 928 kg/m³ and 2193 kg/m³ was examined experimentally and numerically. The pipe diameter and length were 10 mm and 8.8 m, respectively. The mean air velocity was between 14.2 m/s and 23.0 m/s and the number feed rate of particle was almost constant at seven per second. In this study, the method of characteristics was used for the simulation of gas flow, which considered not only the particle-particle collisions but also the particle-wall collisions. It is found that particle transport is possible even when the mean air velocity is smaller than the terminal settling velocity of particle's and that the arrival time intervals at the downstream section are not always uniform although the particles are fed uniformly. Furthermore, the velocity difference between different density particles becomes small as the mean air velocity decreases, because the particle velocities become uniform due to particle-particle collisions, and the ratio of particle velocity to the mean air velocity is almost independent of air velocity. In addition, it is shown that the particle-wall collision at the pipe joint due to pipeline misalignment can be one of the sources of bouncing motion of particles as shown by simulation results.     

Effect of flow pulsation on fluidization degree of gas-solid fluidized beds by using coupled CFD-DEM

In this paper, the effect of inlet flow type on fluidization of a gas-solid fluidized bed was studied by using numerical simulations. Gas-solid fluidized beds are widely used in processes such as heating, cooling, drying, granulation, mixing, segregating and coating. To simulate the gas-particle flows, the unresolved surface CFD‐DEM was used considering Eulerian–Lagrangian approach. The fluid phase was modeled by computational fluid dynamics (CFD) while the solid phase was solved by discrete element method (DEM), and the coupling between gas and solid phases was considered to be four-way. The uniform and pulsed flows were injected through three nozzles located at the bottom of a rectangular bed. Three types of pulsed flow were considered: sinusoidal, rectangular and relocating. The fluidized bed behavior was discussed in terms of minimum fluidization velocity (MFV), pressure drop, bubble formation, bed expansion, particles velocity and, gas-solid interaction and particle contact forces. The results of different simulations indicated that the minimum fluidization velocity of the beds fluidized by pulsed flows was decreased by up to 33%. The influence of the pulsation amplitude on the minimum fluidization velocity was more significant than that of the pulsation frequency. The bed expansion and particles average velocity were increased by the pulsed flows, while the pressure drop and interaction force were decreased. As the pulsation frequency increased, the pressure drop and gas-solid interaction force increased, although size of the bubbles and bed expansion decreased. It was also observed that in large vibration frequencies, the bubbles became more regular. In the sinusoidal flow, the velocity and contact force between the particles were initially increased by frequency and in larger frequencies they were decreased.     

The effect of particle humidity on separation efficiency for an axial cyclone separator

The objective of this study is to investigate the effects of particle humidity on the inlet particle size distribution, overall efficiency, grade efficiency and cut size diameter for an axial cyclone separator with inner diameter of 150?mm. The collection and grade efficiencies of the cyclone separator were measured by on-line method for inlet velocities, particle concentration and particle humidity in the ranges of 12–18?m/s, 30–500?mg/m³ and 8–30‰, respectively. By employing a set of fixed parameters for inlet velocity and particle concentration, the effect of particle humidity on separation efficiency was investigated. The experimental results show that the volume ratio of larger particle increases with the increasing of particle humidity due to particle agglomeration. When the inlet velocity and particle humidity remain constant, the collection and grade efficiencies improve greatly as the increasing of the particle concentration because of the particle aggregation. However, it was noticed that the grade efficiencies did not always increased with the increasing of particle humidity under the same conditions of inlet velocity and particle concentration. The trends of grade efficiency curves for different particle humidity change at the particle diameter of approximately 10?μm. The grade efficiency improves with the increasing of particle humidity when the particle diameter is larger than 10?μm, while a contrary tendency is observed when the particle diameter is smaller than 10?μm.     

Evaluation of direct quadrature method of moment for the internally circulating fluidized bed simulation with ultrafine particles

In the framework of the Euler-Euler gas–solid two-fluid model, the particle population balance equation is solved by the direct quadrature method of moment. The dynamic process of ultrafine particle movement and aggregation in an internally circulating fluidized bed is simulated. The distribution of the concentration and velocity of the agglomerates in the flow process is given, and the changes of the moments in the bed are shown. The effects of different breakage coefficients and inlet gas rates on the concentration distribution of agglomerates are compared. The results show that the particle size decreases with the increase of breakage coefficient, and the time required to reach steady fluidization state increases; the higher the inlet velocity, the better the effect of circulating particles in the bed. When there is a certain gas velocity difference between the two sides, the effect of circulating particles in the bed is better.     

PIV investigations on particle velocity distribution in uniform swirling regime of fluidization

In this study, hydrodynamics of spherical particles in uniform swirling regime of a fluidized bed were investigated using MATLAB supported particle imaging velocimetry (PIV). A least investigated mesh-type distributor was used to fluidize the bed particles, at different air entry angles, for future applications in coating and granulation industry. A quarter of the bed was photographed using high speed imaging technique and the respective velocity fields of the swirling particles were produced using PIV technique. The Gaussian distribution of the particle velocity profiles was predicted at low superficial air velocity; particles near the border of the bed showed relatively low velocity than that swirled in the middle of the test section. However, at high superficial velocity, the particles near the central cone moved with velocity comparable to the particle velocity in the middle of the test section. Contrarily, the particles in the vicinity of the outer bed-wall maintained their steady state motion at all superficial air velocities. The average particle velocity experienced monotonic increase for more angular air intake. The magnitude of the particle velocity reduced by 6.35% for each \(3^{\circ }\) increment in the air entry angle.     

功能梯度材料制备过程影响因素的数值研究

本文用数值计算的方法对重力浇铸下Al—Si／SiC颗粒系统(合金基质的功能梯度材料)凝固过程进行了研究，分析了凝固条件及各种不同参数对铸件中颗粒和溶质浓度分布的影响。结果表明，凝固件中颗粒体积分数分布都大致可分为三个区域：靠近底部的颗粒堆积区，靠近顶部的颗粒体积分数减小或近似为零区，及中部附近颗粒体积分数近似保持不变区。浇铸的初始温度，颗粒初始体积分数，颗粒直径和冷却速率等参数对颗粒和溶质浓度分布有很大影响。     

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.     

Unsteady flow of a dusty fluid through a circular pipe with impulsive pressure gradient

Summary The unsteady flow of a dusty fluid through a circular pipe induced by a time dependent impulsive pressure gradient, has been studied. The governing equations have been solved using Laplace transform technique. Results have been discussed with the help of graphs. It is observed that the velocity of the fluid phase as well as that of the particle phase decreases with increase of either volume fraction or mass concentration of particle phase. The instantaneous rate of discharge of fluid as well as that of the particle phase decreases with increase of mass concentration of particles. They increase with time and attain a steady state for large time.     

Enhancement of air purification by unique W-plate structure in two-stage electrostatic precipitator: A novel design for efficient capture of fine particles

In this paper, a novel W-plate two-stage ESP was developed and investigated systematically through the experimental and simulated process. Numerical models and available calculation procedure of solving coupling electrostatic field, fluid field, and particle dynamics were established, whose accuracy was validated by experiments. The relationship among collection efficiency, gas velocity, and particle diameter was studied, and the distribution of electrostatic field, the evolution of EHD flow and fluid field, and particle dynamics, including particle charging, particle trajectory, transverse velocity, and particle concentration, were also investigated thoroughly. Results showed that W-plate two-stage ESP exhibited excellent number-based collection efficiency for fine particles which benefited from the reasonable structure design and the exceeding weak influence of EHD flow. Besides, the particle charging process suggested that the diameter decided the dominant charging mechanism, and the trajectory also played an important role in controlling the charging action. Compared with the behavior of each particle injected at different inlet positions, fine particles injected near the discharge wire got more charging number and quicker capture. Importantly, W-plate structure could exert its crucial role in capturing particles with the help of fluid field and inertial effect when inlet gas velocity increased rapidly. W-plate two-stage ESP had more than 90% number-based collection efficiency for >3 μm diameter particles and more than 75% number-based collection efficiency for 0.3–1 μm diameter submicron particles at 2 m/s gas velocity in both experimental and simulated investigations.     

Jamming in granular shear flows of frictional,polydisperse cylindrical particles

In this work, frictional, cylindrical particle shear flows with different size distributions (monodisperse, binary, Gaussian, uniform) are simulated using the Discrete Element Method (DEM). The influences of particle size distribution and interparticle friction coefficient on the solid phase stresses, bulk friction coefficient, and jamming transition are investigated. In frictional dense flows, shear stresses rise rapidly with the increasing solid volume fraction when jamming occurs. The results suggest that at the jamming volume fraction, stress fluctuation and granular temperature achieve the maximum values, and the rate of the stress increase with increasing solid volume fraction approaches the peak value. Meanwhile, the degree of cylindrical particle alignment approaches a valley value. In the polydisperse flows, the jamming volume fraction exhibits significant dependences on the fraction of the longer particles and the particle size distribution. Two models considering the effect of particle size distribution are discussed for predicting the jamming volume fractions of polydisperse flows with frictional, cylindrical particles.     

Numerical Model for Heat Transfer in Dilute Turbulent Gas-Particle Flows

The heat transfer between a vertical pipe wall and turbulent gas-particle flow is numerically investigated according to the Eulerian-Lagrangian approach and the k-ε turbulence model. The particles are introduced homogeneously into the simulation volume by a unique technique referred to as an artificial feeding volume. The numerical code using additional computer programs is validated with available experimental results for the constant heat flux boundary condition. An average deviation of about 4% and a maximum deviation of about 7% were attained from the numerical predictions for various particle and pipe diameters. The effect of the geometrical parameters and the flow parameters on the gas/particle temperature, the convection heat transfer coefficient between the wall and the gas-particle mixture, and the thermal entry length were studied. An increase in particle diameter (loading ratio ≈ 0.5) extended the thermal entry length and decreased the bulk mixed temperature, particle temperature, and convection heat transfer coefficient. Increasing the pipe diameter led to a significant reduction in bulk mixed temperature and thermal entry length, in addition to a decrease in particle temperature and Nusselt number. Increasing the loading ratio up to 2.36 led to a reduction in wall temperature and bulk mixed temperature, in addition to an increase in the convective heat transfer coefficient and thermal entry length.     

Numerical Model for Heat Transfer in Dilute Turbulent Gas-Particle Flows

The heat transfer between a vertical pipe wall and turbulent gas-particle flow is numerically investigated according to the Eulerian-Lagrangian approach and the k-ε turbulence model. The particles are introduced homogeneously into the simulation volume by a unique technique referred to as an artificial feeding volume. The numerical code using additional computer programs is validated with available experimental results for the constant heat flux boundary condition. An average deviation of about 4% and a maximum deviation of about 7% were attained from the numerical predictions for various particle and pipe diameters. The effect of the geometrical parameters and the flow parameters on the gas/particle temperature, the convection heat transfer coefficient between the wall and the gas-particle mixture, and the thermal entry length were studied. An increase in particle diameter (loading ratio ≈ 0.5) extended the thermal entry length and decreased the bulk mixed temperature, particle temperature, and convection heat transfer coefficient. Increasing the pipe diameter led to a significant reduction in bulk mixed temperature and thermal entry length, in addition to a decrease in particle temperature and Nusselt number. Increasing the loading ratio up to 2.36 led to a reduction in wall temperature and bulk mixed temperature, in addition to an increase in the convective heat transfer coefficient and thermal entry length.     

Effects of specularity and particle-particle restitution coefficients on the hydrodynamic behavior of dispersed gas-particle flows through horizontal channels

Specularity coefficient ($?$) and particle–particle restitution coefficient (e) are two important parameters governing the flow physics of dispersed gas-particle flows. In this work, a detailed numerical analysis is carried out to get an insight into the effects of these two parameters in the flow hydrodynamics of dispersed gas-particle flows through horizontal channels. Investigations have also been carried out to find the $?$-e pair for which the phase velocities become an extremum. It has been found that at a particular value of e, both gas and particle velocities at the centerline of the channel increase with increase in the value of $?$, whereas near the wall, they tend to decrease. At a fixed non-zero value of $?$, both gas and particle velocities tend to increase with increase in the value of e. For $?$ equal to zero, which corresponds to free-slip boundary condition for particle velocity, there is no significant variations in gas and particle velocities with changes in e. Out of all combinations of values of $?$ and e investigated herein, it is found that both gas and particle velocities attain a maximum value when both the values of $?$ and e are maximum.     

风雪流滞空颗粒受力及运动行为的数值模拟

为研究稀疏风雪流系统下滞空颗粒在介质中的变加速运动行为及非线性气动特性,以运动学微分方程为基础,建立了微观层面下不同粒径、密度颗粒的三维动网格计算模型。采用时间-空间离散的数值积分方法,求解了小时空尺度下,单个雪颗粒在静止空气及梯度风场中的自由沉降与强迫运动问题。通过对比不同颗粒参数及流场环境的模拟结果发现:颗粒自由沉降所能达到的终端线速度及对应稳定时间均随平均粒径及密度的增大而增大,粒径确定的情况下,相同时间内大密度颗粒沉降距离相对更远,自由沉降初期的非线性变速运动行为可近似考虑为小时空尺度问题;剪切流条件下,较小的风速梯度可能引起颗粒在来流及自重方向运动速度的波动,所受气动外力的改变总是滞后于运动速度的变化,强风环境下颗粒将具有更好的流场跟随性,其非线性变速阶段仍可视为小时空尺度问题。滞空雪颗粒在流场中的运动行为基本满足多相流理论的局部短时空尺度均衡假定。     

Effects of momentum transfer on particle dispersions of dense gas–particle two-phase turbulent flows

A modified momentum transfer coefficient of dense gas–particle two-phase turbulent flows is developed and its effect on particle dispersion characteristics in high particle concentration turbulent downer flows has been numerically simulated incorporating into a second-order moment (USM) two-phase turbulent model and the kinetic theory of granular flow (KTGF) to consider particle–particle collisions. The particle fractions, the time-averaged axial particle velocity, the particle velocities fluctuation, and their correlations between gas and particle phases based on the anisotropic behaviors and the particle collision frequency are obtained and compared using traditional momentum transfer coefficients proposed by Wen (1966), Difelice (1985), Lu (2003) and Beetstra (2007). Predicted results of presented model are in good agreement with experimental measurement by Wang et al. (1992). The particle fluctuation velocity and its fluctuation velocity correlations along axial–axial and radial–radial directions have stronger anisotropic behaviors. Furthermore, the presented model is in a better accordance with Lu’s model in light of particle axial velocity fluctuation, particle temperature, particle kinetic energy and correlations of particle–gas axial–axial velocity fluctuation. Also, they are larger than those of other models. Beetstra’s model is not suitable for this downer simulation due to the relative lower particle volume fraction, particle collision and particle kinetic energy.