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.      

基于离散单元法和人工神经网络的近壁颗粒动力学特征研究

颗粒与壁面的相互作用往往对颗粒流动具有显著影响. 为研究颗粒与壁面作用机理, 对滚筒内颗粒流动过程进行离散单元法(DEM)数值模拟. 基于模拟结果统计分析靠近壁面处颗粒的运动特征, 结果表明, 小摩擦系数时颗粒平动和旋转速度均近似满足正态分布, 但由于壁面影响, 摩擦系数增大时颗粒沿滚筒轴向的旋转速度偏离正态分布, 颗粒动力学理论推导壁面边界条件时应考虑速度正态分布的修正及速度脉动的各向异性. 采用人工神经网络(ANN)构建了颗粒无因次旋转温度、滑移速度和平动温度之间的函数模型, 进而可以在常规双流模型壁面边界条件中考虑颗粒旋转的影响. 基于DEM模拟及结果分析可以为壁面边界条件的理论构造和半经验修正提供基础数据和封闭模型.      

Simulated configurational temperature of particles and a model of constitutive relations of rapid-intermediate-dense granular flow based on generalized granular temperature

In gas–solid flat-base spout bed with a jet, the flow of particles must go through an intermediate regime where both kinetic/collisional and frictional contributions play a role. In this paper, the statistical framework is proposed to define the generalized granular temperature which sums up the configurational temperature and translational granular temperature. The configurational temperature, translational and rotational granular temperatures of particles are simulated by means of CFD-DEM (discrete element method) in a 3D flat-base spout bed with a jet. The configurational temperatures of particles are calculated from instantaneous overlaps of particles. The translational and rotational granular temperatures of particles are calculated from instantaneous translational and angular velocities of particles. Roughly, the simulated translational and rotational granular temperatures increase, reach maximum, and then decrease with the increase of solids volume fractions. However, the configurational temperature increases with the increase of solids volume fractions. At high solid volume fraction, the predicted configurational temperatures are larger than the translational and rotational granular temperatures, indicating that the rate of energy dissipation do contributes by contact deformation of elastic particles. The generalized granular temperature is proposed to show the relation between the variance of the fluctuation velocity of deformation and the variance of the translational fluctuation velocity of particles. The constitutive relations of particle pressure, viscosity, granular conductivity of fluctuating energy and energy dissipation in rapid-intermediate-dense granular flows are correlated to the generalized granular temperature. The variations of particle pressure, shear viscosity, energy dissipation and granular conductivity are analyzed on the basis of generalized granular temperature in a flat-base spout bed with a jet. The axial velocities of particles predicted by a gas–solid two-fluid model of rapid-intermediate-dense granular flows agree with experimental results in a spout bed.     

Numerical simulation of tetrahedral particle mixing and motion in rotating drums

A regular tetrahedron is the simplest three-dimensional structure and has the largest non-sphericity. Mixing of tetrahedral particles in a thin drum mixer was studied by the soft-sphere-imbedded pseudo-hard particle model and compared with that of spherical particles. The two particle types were simulated with different rotation speeds and drum filling levels. The Lacey mixing index and Shannon information entropy were used to explore the effects of sphericity on the mixing and motion of particles. Moreover, the probability density functions and mean values and variances of motion velocities, including translational and rotational, were computed to quantify the differences between the motion features of tetrahedra and spheres. We found that the flow regime depended on the particle shape in addition to the rotation speed and filling level of the drum. The mixing of tetrahedral particles was better than that of spherical particles in the rolling and cascading regimes at a high filling level, whereas it may be poorer when the filling level was low. The Shannon information entropy is better than the Lacey mixing index to evaluate mixing because it can reflect the real change of flow regime from the cataracting to the centrifugal regime, whereas the mixing index cannot.     

Effect of Shape on Inertial Particle Dynamics in a Channel Flow

Particle dynamics in a channel flow are investigated using large eddy simulation and a Lagrangian particle tracking technique. Following validation of single-phase flow predictions against DNS results, fluid velocities are subsequently used to study the behaviour of particles of differing shape assuming one-way coupling between the fluid and the particles. The influence of shape- and orientation-dependent drag and lift forces on both the translational and rotational motion of the particles is accounted for to ensure accurate representation of the flow dynamics of non-spherical particles. The size of the particles studied was obtained based on an equivalent-volume sphere, and differing shapes were modelled using super-quadratic ellipsoid forms by varying their aspect ratio, with their orientation predicted using the incidence angle between the particle relative velocity and the particle principal axis. Results are presented for spherical, needle- and platelet-like particles at a number of different boundary layer locations along the wall-normal direction within the channel. The time evolution and probability density function of selected particle translational and rotational properties show a clear distinction between the behaviour of the various particles types, and indicate the significance of particle shape when modelling many practically relevant flows.     

垂直旋转流场中单颗粒运动状态判别及受力分析

为研究单颗粒在旋转流场中的运动状态及受力情况,以毫米级球形颗粒为例,利用旋转流场颗粒运动装置,通过使用摄像机记录颗粒在流场中的运动轨迹以获取其运动参数,分析了不同转速和颗粒直径条件下颗粒的运动轨迹,拟合得到了颗粒运动状态判别公式以及颗粒运动轨迹公式,分析了颗粒在旋转流场中的受力情况。结果表明,颗粒在旋转流场平衡状态下运动状态主要分为两类,一类是未离开壁面保持静止,另一类是离开壁面保持稳定周向运动;颗粒进行周向运动的轨迹为椭圆形,并且圆心随着转速的增大靠近旋转中心,而随着粒径的增大靠近壁面;颗粒在旋转流场的运动过程中主要受到离心力和旋转科式力作用。     

Impulsive motion of a suspension: Effect of antisymmetric stresses and particle rotation

A two-phase continuum theory (two-fluid model) for a suspension of rigid spherical particles in a Newtonian fluid is applied to investigate theoretically the flow induced by impulsive motion of an infinite flat plate. Consideration of rotational intertia of the particles gives rise to an antisymmetric part of the volume averaged stress tensor of the continuous phase. The influence of particle rotation and of antisymmetric stresses of the continuous phase, which depend on the relative rotational motion between the particles and the ambient fluid, on the motion of each phase and on the skin friction is examined.Approximate solutions to the equations, corresponding to the physical situation of large and small particle slip, are obtained by power series expansions for small and large times.     

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.     

Multi-level DEM study on silo discharge behaviors of non-spherical particles

The silo discharge of non-spherical particles has been widely practiced in engineering processes, yet the understanding of multi-level mechanisms during solid transportation is still lacking. In this study, a high-fidelity super-ellipsoid Discrete Element Method (DEM) model is established to investigate the discharge behaviors of non-spherical particles with different size distributions. After the comprehensive model validations, we investigated the effects of particle shape (aspect ratio and particle sharpness) on the particle level discharge behaviors. The discharge rates of the ellipsoid particles used in the current work are larger than the spherical particles due to the larger solid fraction. The discharge rates of the cuboid-like particles are determined by the combined effect of the solid fraction and the contact force. Parcel level data show that the translational movements of the ellipsoid particles are more ordered, which is supported by the global level data. Strong correlations exist between the particle level and parcel level data, especially the ellipsoid particles and the large particles in the polydispersed cases.     

Experimental and numerical studies of rotational relaxation behind a strong shock wave in air

This paper describes the experimental and numerical investigations of unknown characteristics of the rotational nonequilibrium phenomena behind a strong shock wave in air. Experiments were carried out using a piston-driven shock tube with helium as driving gas and air as driven (test) gas, operated as a two-stage shock tube. In the experiments, emission spectra of NO were measured to evaluate the rotational temperature behind a strong shock wave. The numerical calculations use the computational code for the thermal and chemical nonequilibrium flow behind a strong shock wave developed by the present author's group, where 11 chemical species (N, O, NO, N, O, N, O, NO, N, O, e) and 48 chemical reactions of high-temperature air are considered. The thermal nonequilibrium is expressed by introducing an 8 temperature model composed of translational temperature, rotational and vibrational temperatures for N, O, NO, and electron temperature. The coupling of a rotation, vibration and dissociation (CRVD) model was incorporated to take sufficiently into account the rotational nonequilibrium. The calculations were conducted for the same conditions as the experimental ones. From the calculated flow properties, emission spectra were re-constructed using the code for computing spectra of high temperature air “SPRADIAN”. Furthermore, rotational and vibrational temperatures of NO (0,1) were determined from a curve fitting method and compared with the computed results. Received 12 September 2001 / Accepted 18 February 2002     

Interception of two spheroidal particles in shear flow

A numerical method is developed for simulating the motion of particles with arbitrary shape in an effectively infinite or bounded viscous flow. The particle translational and angular velocities are computed directly by solving an integral equation of the second kind arising from the double-layer representation for Stokes flow, subject to a specified force and torque. The deflated integral equation is solved by the method successive substitutions using a spectral boundary-element method. In the case of force- and torque-free particles, the contribution of the particles to the effective viscosity of the suspension is expressed in terms of the distribution density of the double-layer potential over the particle surfaces. The method is applied to investigate the interception of two spheroidal particles in simple shear flow, with emphasis on the net particle displacement and shift in the phase of rotation after separation, and on the transient signature of the interception on the effective viscosity of the suspension. The net particle displacement normal to the streamlines of the shear flow is found to have both positive and negative values depending on the relative particle configuration before interception. For moderate particle separations, the phase of rotation is shifted only slightly with respect to the Jeffery orbit executed by a particle in isolation.     

The motion of rigid rod-like particles suspended in non-homogeneous flow fields

Equations are written for the velocities of rotation and translation of rigid rod-like particles suspended in arbitrary Stokes flows. These make use of the first approximation from slender body theory for the evaluation of drag forces parallel and transverse to the particle axis, and neglect couples induced by shear stress at the particle surface. They are therefore asymptotically valid as the particle axis ratio becomes large. Simple forms of the equations, applying in constant viscosity flows, are solved, where possible analytically and otherwise numerically, and results obtained for particle motion in planar Poiseuille and sink flows. These are discussed and displayed in terms of appropriate dimensionless groups in a comprehensive set of plots, that can conveniently be used to provide information on translational and rotational velocities, and orientation and displacement as a function of time, including particle slip along and across streamlines, for a wide range of cases. In this way the effects of non-homogeneity in the flow fields are quantified.     

极高超声速稀薄气体原子辐射效应的p-DSMC方法

极高超声速流动激波层内的高温导致内能模态的激发并伴随热辐射发生, 过高的温度使得空气分子完全解离, 原子组分对辐射热的贡献将达到80%以上. 本文基于优化的原子辐射模型, 提出追踪光子?直接模拟蒙特卡罗(p-DSMC)方法, 研究了稀薄流区不同马赫数下的高超声速二维圆柱绕流的壁面辐射加热, 获得了有无激发辐射效应的壁面压力和热流以及沿驻点线变化的平动、振动和转动温度. 在不考虑激发辐射效应的情况下, 得到的壁面压力和热流与已有的模拟结果符合的非常好, 误差均在5%以内, 尤其是在驻点位置, 误差在1%以内; 获得的平动、振动以及转动温度均与文献结果符合的很好. 在相同的来流条件下, 考虑辐射效应后发现, 来流速度低于10 km/s时, 辐射加热不明显, 在驻点区域, 辐射加热占对流加热比重在7%左右; 来流速度大于10 km/s时, 在驻点区域, 辐射加热占对流加热比重将超过30%. 考虑辐射效应后, 对非平衡区的平动、转动和振动温度的最大值影响不大. 此外, 另一个重要结论是, 流场中原子的浓度是影响壁面辐射热流大小的一个重要因素.      

Droplet spindown in a high-temperature gas environment

The spindown and heating of a spherical droplet in an initially undisturbed infinite fluid is investigated by means of a numerical model based on finite-difference discretization techniques. The nonevaporating droplet enters the hot gas while rotating about a diameter and has no translational motion with respect to the suspending medium. Special attention is given to the transient secondary (nonrotational) motion developed as a result of shear interaction between the two phases. The results indicate that for droplet sizes and rotation frequencies representative of droplet combustion applications; i.e., Reynolds ∼ O(0.1), the secondary motion in both phases remains weak and heat transport is conduction-dominated. On the other hand, the secondary motion is strengthened with increased values of the rotational Reynolds number. The characteristic time for droplet spindown is found to be proportional to the square of the droplet radius. The results also show that the rotational deceleration time is of the same order of magnitude with the translational response time of the droplet. Finally, the thermocapillary stress effects on fluid dynamics and heat transfer are investigated in this flow configuration.     

Formation, evolution, and decay of a vortex street in the wake of a streamlined body

The decay of a Kármán vortex street and the formation of a secondary vortex structure in the far wake of a streamlined cylinder are studied. The dynamics of spatially evolving vortex structures is examined in the free flow and in the following ways of external influence on this flow: rotation with a constant velocity and translational and rotational oscillations of the cylinder. The results are obtained by numerically solving the Navier-Stokes equations with two different methods. The corresponding boundary value problems are formulated in the domains extended up to 500 radii of the cylinder.     

A method for characterising solids translational and rotational motions using Multiple-Positron Emission Particle Tracking (Multiple-PEPT)

Solid motion can be classified into translational motion and rotational motion; both play an important role in a wide range of engineering processes. While translational motion has been extensively studied in various systems, there is a lack of information on rotational motion, possibly due to a lack of appropriate experimental techniques. For a number of mixing processes involving heat transfer for solid–liquid mixtures, the heat transfer coefficient between solid and liquid is critical in determining process times and overall product characteristics, and is greatly dependent on both rotational and translational behaviours of the solids, which ideally need to be studied simultaneously. This paper presents a new technique, Multiple-Positron Emission Particle Tracking (Multiple-PEPT), which can follow multiple particles simultaneously through a considerable thickness of surrounding material. Both translational and rotational motions of the solid can be reconstructed. The accuracy of the method for the translational velocity was better than 10% while for the angular velocity 23% for speeds up to 0.25 m/s. Multiple-PEPT will therefore offer the possibility to study translational and rotational motions for a range of engineering systems. The potential applications of tracking solid translational and rotational motions are illustrated by an example of tracking a cubed potato in a rotating can.     

On translational and rotational relative velocities of fibers and fluid in a turbulent channel flow with a backward-facing step

A dilute fiber suspension in a turbulent channel with a backward-facing step is investigated by means of Feature Tracking. Its combination with a phase-discrimination methodology, which is described in detail, allows simultaneous and separate measurement of carrier and dispersed phases velocity fields, the orientation and rotation rate of fibers as well as the fiber–fluid translational and rotational slip velocities. The patterns of fibers concentration, angular velocity and the probability distribution of fibers velocity appear to be dominated by the mechanical interactions with the wall and the local high shear rather than by near-wall turbulent structures. The translational slip velocity obtained from instantaneous data shows that fibers move faster than the surrounding fluid inside the buffer layer, the velocity gap reducing gradually when approaching the channel centerline. On the other hand, the rotational slip profile suggests a gradual decoupling of the translational and rotational dynamics. Downstream of the step, the excess of streamwise velocity displayed by fibers is still observed and extends in the free-shear region, whereas the rotation rate slip decreases at a relatively short distance from the step, as the effect of the wall presence fades away.