Rotation characteristic and granular temperature analysis in a bubbling fluidized bed of binary particles

In this work, a discrete particle model (DPM) was applied to investigate the dynamic characteristics in a gas–solid bubbling fluidized bed of binary solid particles. The solid phase was simulated by the hard-sphere discrete particle model. The large eddy simulation (LES) method was used to simulate the gas phase. To improve the accuracy of the simulation, an improved sub-grid scale (SGS) model in the LES method was also applied. The mutative Smagorinsky constant case was compared with the previously published experimental data. The simulation by the mutative Smagorinsky constant model exhibited better agreement with the experimental data than that by the common invariant Smagorinsky constant model. Various restitution coefficients and different compositions of binary solids were investigated to determine their influences on the rotation characteristics and granular temperatures of the particles. The particle translational and rotational characteristic distributions were related to certain simulation parameters.     

Rotation characteristic and granular temperature analysis in a bubbling fluidized bed of binary particles

In this work,a discrete particle model(DPM) was applied to investigate the dynamic characteristics in a gas-solid bubbling fluidized bed of binary solid particles.The solid phase was simulated by the hardsphere discrete particle model.The large eddy simulation(LES) method was used to simulate the gas phase.To improve the accuracy of the simulation,an improved sub-grid scale(SGS) model in the LES method was also applied.The mutative Smagorinsky constant case was compared with the previously published experimental data.The simulation by the mutative Smagorinsky constant model exhibited better agreement with the experimental data than that by the common invariant Smagorinsky constant model.Various restitution coefficients and different compositions of binary solids were investigated to determine their influences on the rotation characteristics and granular temperatures of the particles.The particle translational and rotational characteristic distributions were related to certain simulation parameters.     

Discrete particle modeling of granular temperature distribution in a bubbling fluidized bed

The discrete hard sphere particle model (DPM) is applied in this work to study numerically the distributions of particle and bubble granular temperatures in a bubbling fluidized bed. The dimensions of the bed and other parameters are set to correspond to those of Müller et al. (2008). Various drag models and operational parameters are investigated to find their influence on particle and bubble granular temperatures. Various inlet superficial gas velocities are used in this work to obtain their effect on flow characteristics. It is found that the superficial gas velocity has the most important effect on granular temperatures including bubble granular temperature, particle translational granular temperature and particle rotational granular temperature. The drag force model affects more seriously the large scale variables such as the bubble granular temperature. Restitution coefficient influences all granular temperatures to some degree. Simulation results are compared with experimental results by Müller et al. (2008) showing reasonable agreement.     

Entropy productions in granular materials

Granular materials display more abundant dissipation phenomena than ordinary materials. In this paper, a brief energy flow path with irreversible processes is illustrated, where the concept of granular temperature T_g, initially proposed for dilute systems, is extended to dense systems in order to quantify disordered force chain configurations. Additionally, we develop the concept of conjugate granular entropy s_g and its production equation. Our analyses find out that the granular entropy significantly undermined the elastic contact between particles, seriously affecting the transport coefficients in granular materials and creating new transport processes.     

关于采用粗粒化提高颗粒材料多尺度模拟守恒特性的研究

连续体-颗粒耦合方法常用来描述连续-非连续颗粒行为或解决颗粒材料与其他可变形构件间相互作用问题。粗粒化coarse-graining (CG)是基于统计力学的均匀化方法,由离散的颗粒运动定义连续的宏观物理场。本文利用粗粒化(CG)推导有限元-离散元(FEM-DEM)表面和体积耦合的一般性表达式。对于表面耦合,CG可以将耦合力分布到颗粒-单元接触点以外的位置,如相邻的积分点;对于体积耦合,CG可以将颗粒尺度的运动均匀化到耦合单元上。由粗粒化推导出的耦合项仅包含一个参数,即粗粒化宽度,为均匀化后的宏观场定义了一个可调整的空间尺度。当粗粒化宽度为零时,表面和体积耦合表达式简化为常规局部耦合。本文通过弹性立方体冲击颗粒床和离散-连续介质间波传播两个数值算例,展示使用粗粒化方法提高耦合系统能量守恒的优势,并结合其他耦合参数(如体积耦合深度)讨论了粗粒化参数对数值稳定性和计算效率的影响。     

粗糙颗粒动理学及稠密气固两相流动的数值模拟

考虑颗粒碰撞过程中摩擦作用,给出了粗糙颗粒碰撞动力学.引入颗粒相拟总温来表征颗粒平动和转动脉动能量的特征.基于气体分子运动论,建立颗粒碰撞中平动和旋转共同作用的粗糙颗粒动理学,给出了颗粒相压力和黏度等输运参数计算模型.运用基于颗粒动理学的欧拉-欧拉气固两相流模型,数值模拟了流化床内气体颗粒两相流动特性,分析了颗粒旋转流动对颗粒碰撞能量交换和耗散的影响.模拟得到的流化床内径向颗粒浓度和提升管内颗粒轴向速度与他人实验结果相吻合.模拟结果表明随着颗粒浓度的增加,颗粒相压力和能量耗散逐渐增加,而颗粒拟总温先增加后下降.随着颗粒粗糙度系数的增加,床内平均颗粒相拟总温和能量耗散增加,表明颗粒旋转产生的摩擦将导致颗粒旋转脉动能量的改变,影响床内气体-颗粒两相宏观流动特性.      

Numerical simulation of gas–solid flow with two fluid model in a spouted-fluid bed

The flow characteristics in a spouted-fluid bed differ from those in spouted or fluidized beds because of the injection of the spouting gas and the introduction of a fluidizing gas. The flow behavior of gas–solid phases was predicted using the Eulerian–Eulerian two-fluid model (TFM) approach with kinetic theory for granular flow to obtain the flow patterns in spouted-fluid beds. The gas flux and gas incident angle have a significant influence on the porosity and particle concentration in gas–solid spouted-fluid beds. The fluidizing gas flux affects the flow behavior of particles in the fountain. In the spouted-fluid bed, the solids volume fraction is low in the spout and high in the annulus. However, the solids volume fraction is reduced near the wall.     

A thermodynamic model of turbulent motions in a granular material

This paper is devoted to a thermodynamic theory of granular materials subjected to slow frictional as well as rapid flows with strong collisional interactions. The microstructure of the material is taken into account by considering the solid volume fraction as a basic field. This variable is of a kinematic nature and enters the formulation via the balance law of the configurational momentum, including corresponding contributions to the energy balance, as originally proposed by Goodman and Cowin [1], but modified here. Complemented by constitutive equations, the emerging field equations are postulated to be adequate for motions, be they laminar or turbulent, if the resolved length scales are sufficiently small. On large length scales the sub-grid motion may be interpreted as fluctuations, which manifest themselves in correspondingly filtered equations as correlation products, like in the turbulence theory. We apply an ergodic (Reynolds) filter to these equations and thus deduce averaged equations for the mean motions. The averaged equations comprise balances of mass, linear and configurational momenta, energy, and turbulent kinetic energy as well as turbulent configurational kinetic energy. They are complemented by balance laws for two internal fields, the dissipation rates of the turbulent kinetic energy and of the turbulent configurational kinetic energy. We formulate closure relations for the averages of the laminar constitutive quantities and for the correlation terms by using the rules of material and turbulent objectivity, including equipresence. Many versions of the second law of thermodynamics are known in the literature. We follow the Müller-Liu theory and extend Müllers entropy principle to allow the satisfaction of the second law of thermodynamics for both laminar and turbulent motions. Its exploitation, performed in the spirit of the Müller-Liu theory, delivers restrictions on the dependent constitutive quantities (through the Liu equations) and a residual inequality, from which thermodynamic equilibrium properties are deduced. Finally, linear relationships are proposed for the nonequilibrium closure relations.Received: 21 March 2003, Accepted: 1 September 2003, Published online: 11 February 2004PACS: 05.70.Ln, 61.25.Hq, 61.30.-vCorrespondence to: I. Luca     

Numerical simulation of gas-solid flow with two fluid model in a spouted-fluid bed

The flow characteristics in a spouted-fluid bed differ from those in spouted or fluidized beds because of the injection of the spouting gas and the introduction of a fluidizing gas. The flow behavior of gas-solid phases was predicted using the Eulerian-Eulerian two-fluid model （TFM） approach with kinetic theory for granular flow to obtain the flow patterns in spouted-fluid beds. The gas flux and gas incident angle have a significant influence on the porosity and particle concentration in gas-solid spouted-fluid beds. The fluidizing gas flux affects the flow behavior of particles in the fountain. In the spouted-fluid bed, the solids volume fraction is low in the spout and high in the annulus. However, the solids volume fraction is reduced near the wall.     

Analysis of instantaneous dynamic states of vibrated granular materials

The behavior of granular materials subjected to continuous vertical vibrations is dependent on a variety of factors, including how energetically the containment vessel is shaken as well as particle properties. Motivation for the investigation reported here is based on phenomenon in which bulk solids attain an increase in density upon relaxation. The results of a detailed, discrete element study designed to examine the dynamic state of a granular material is presented, in which particles are represented as inelastic, frictional spheres. The phase in which the assembly finds itself immediately before vibrations are stopped is quantified by computing depth profiles of the translational energy ratio R in conjunction with profiles of solids fraction ν and granular temperature T. The use of particles that are more frictional tends to hinder or delay thermalization, while particle restitution coefficient plays a role when the flow is collision dominated. The structure before vibrations are applied plays an important role in determining the depth profiles and the phase pattern only at low accelerations. On the other hand, large accelerations can easily dislodge the poured configuration very quickly so that the initial condition is not major factor in the phase pattern.     

DEM simulation of particle mixing in a sheared granular flow

Mixing behaviors of particles are simulated in a sheared granular flow using differently colored but otherwise identical glass spheres, with five different bottom wall velocities. By DEM simulation, the solid fractions, velocities, velocity fluctuations and granular temperatures are measured.The mixing layer thicknesses are compared with the calculations from a simple diffusion equation using the data of apparent self-diffusion coefficients obtained from the current simulation measurements. The calculations and simulation results showed good agreements, demonstrating that the mixing process of granular materials occurred through the diffusion mechanism.     

DEM simulation of particle mixing in a sheared granular flow

Mixing behaviors of particles are simulated in a sheared granular flow using differently colored but otherwise identical glass spheres, with five different bottom wall velocities. By DEM simulation, the solid fractions, velocities, velocity fluctuations and granular temperatures are measured. The mixing layer thicknesses are compared with the calculations from a simple diffusion equation using the data of apparent self-diffusion coefficients obtained from the current simulation measurements. The calculations and simulation results showed good agreements, demonstrating that the mixing process of granular materials occurred through the diffusion mechanism.     

Penetration into a granular bed in the presence of upward gas flows

We present a numerical study on the penetration of spherical projectiles into a granular bed in the presence of upward gas flows. Due to the presence of interstitial fluid, the force chains between particles in the granular bed are weakened significantly, and this distinguishes the penetration behavior from that in the absence of fluid. An interesting phenomenon, namely granular jet, is observed during the penetration, and the mechanism for its formation and growth is attributed to the merging of granular vortices generated by the interaction between the intruder and primary particles. Moreover, both the final penetration depth and the maximum diameter of the crater are found to follow a power-law dependence with the impact velocity, and the maximum height reached by the granular jet tends to increase linearly as the impact velocity increases, agreeing well with the experimental results reported in the literature.     

Description of local dilatancy and local rotation of granular assemblies by microstretch modeling

This study investigates the microstretch continuum modeling of granular assemblies while accounting for both the dilatant and rotational degrees of freedom of a macroelement. By introducing the solid volume fraction and the gyration radius of a granular system, the balance equations of the microstretch continuum are transformed into a new formulation of evolution equations comprising six variables: the solid volume fraction, the gyration radius, the velocity field, the averaged angular velocity, the rate of gyration radius, and the internal energy. The bulk microinertia density, the averaged angular velocity, and the microgyration tensor at a macroscopic point are obtained in terms of discrete physical quantities. The bulk part and the rotational part of the microgyration tensor are proposed as the two indices to measure the local dilatancy and local rotation of granular assemblies. It is demonstrated in the numerical simulation that the two indices can be used to identify the shear band evolution in a granular system under a biaxial compression.     

Granular materials: Bridging damaged solids and turbulent fluids

Granular materials exhibit abundant dissipations due to fluctuations in both granular motions and configurations (i.e., granular skeleton) evolutions. Twin granular temperatures T_k and T_e are introduced accounting for two types of fluctuations, and the so-called twin granular temperatures theory is established as an extension of granular solid hydrodynamics. By using simulations, the nonaffine deformations in a 2D assembly are simulated by using discrete element methods. By analogizing with microdamages in deformed solids, double scalar damage variables, D_P and D_q, are proposed to describe the deformed granular solid under triaxial compressions. Granular flows are found intrinsically turbulent due to the presence of T_k and the Naiver–Stokes equation is obtained for granular flows.     

基于颗粒物质流体动力学的三轴力学分析

构建了颗粒体系热力学特征函数, 确定了宏观尺度不可逆过程的迁移系数, 将颗粒物质流体动力学理论应用于密砂的三轴加载力学性质分析, 得到了应力-应变关系和体积应变-应变关系, 还得到了颗粒温度演化过程.      

基于介观力学信息的颗粒材料损伤——愈合与塑性宏观表征

本文在二阶计算均匀化框架下提出了颗粒材料损伤--愈合与塑性的多尺度表征方法. 颗粒材料结构在宏观尺度模型化为梯度Cosserat连续体,在其有限元网格的每个积分点处定义具有离散颗粒介观结构的表征元. 建立了表征元离散颗粒系统的非线性增量本构关系. 表征元周边介质作用于表征元边界颗粒的增量力与增量力偶矩以表征元边界颗粒的增量线位移与增量转动角位移、当前变形状态下表征元离散介观结构弹性刚度、以及凝聚到表征元边界颗粒的增量耗散摩擦力表示. 基于平均场理论与Hill定理,导出了基于介观力学信息的梯度Cosserat连续体增量非线性本构关系. 在等温热动力学框架下定义了表征颗粒材料各向异性损伤--愈合和塑性的损伤、愈合张量因子与综合损伤、愈合效应的净损伤张量因子和塑性应变. 此外,定义了损伤和塑性耗散能密度与愈合能密度,以定量比较材料损伤、愈合、塑性对材料失效的效应. 应变局部化数值例题结果显示了所建议的颗粒材料损伤--愈合--塑性表征方法的有效性.      

Discrete simulation and micromechanical analysis of two-dimensional saturated granular media

In this study, a novel approach to incorporate the pore water pressure in the discrete element method （DEM） to comprehensively model saturated granular media was developed. A numerical model was constructed based on the DEM by implanting additional routines in the basic DEM code; pore water pressure calculations were used with a two-dimensional （2D） model to simulate the undrained behavior of satu- rated granular media. This model coupled the interaction of solid particles and the pore fluid in saturated granular media. Finally, several 2D undrained shear tests were simulated. The test results showed that the model could predict the response of the saturated granular soil to shear loading. The effect of initial compaction was investigated. Biaxial tests on dense and loose specimens were conducted, and the effect of the initial density on the change in shear strength and the volume change of the system was inves- tigated. The overall behavior of loose and dense specimens was phenomenologically similar to the real granular material. Constant volume tests were simulated, and the results were compared to those from the coupled model. Induced anisotropy was micromechanically investigated by studying the contact force orientation. The change in anisotropy depended on the modeling scheme. However, the overall responses of the media obtained usinz the couoled and constant volume methods were similar.     

Two-fluid smoothed particle hydrodynamics simulation of submerged granular column collapse

In this paper, a two-fluid smoothed particle hydrodynamics (SPH) model, based on the mixture theory, is employed to investigate the complex interactions between the solid particles and the ambient water during the process of submerged granular column collapse. From the simulation, two regimes of the collapse, one being quick and the other being slow, are identified and the reasons of formation are analyzed. It is found that, a large internal friction angle of the granular phase, representing large drag force between solid particles, helps form the slow regime. Small hydraulic conductivity, representing large inter-phase drag force, also retards the collapse dramatically. Good agreements between our numerical results and other researchers’ numerical and experimental results are observed, which demonstrates the capability of the proposed two-fluid SPH approach in dealing with saturated water–soil mixture flows.