New expression for collision efficiency of spherical nanoparticles in Brownian coagulation

The collision efficiency of dioctyl phthalate nanoparticles in Brownian coag- ulation has been studied. A set of collision equations is solved numerically to find the relationship between the collision efficiency and the particle radius varying in the range of 50 nm to 500 nm in the presence of Stokes resistance, lubrication force, van der Waals force, and elastic deformation force. The calculated results are in agreement with the experimental data qualitatively. The results show that the collision efficiency decreases with the increase of the particle radii from 50 nm to 500 nm. Based on the numerical data, a new expression for collision efficiency is presented.     

RESEARCH ON THE COLLISION EFFICIENCY OF NANO-PARTICLE-TO-WALL WITH EXTERNAL ELECTRIC FIELD

着重考虑了电场作用下,壁面排斥力对颗粒-壁面碰撞效率的影响. 采用Matlab 中的龙格库塔方法,对颗粒-壁面碰撞的压缩阶段及回弹阶段的动力学方程组进行求解,并对Maxwell 速度分布进行积分获得不同速度方向下的碰撞效率. 研究表明,颗粒的碰撞效率随着碰撞角度的增加而增大,并最终达到一个临界值,即完全凝并时的碰撞效率;且颗粒的碰撞效率将因壁面排斥力的影响而减小,即壁面排斥力在一定程度上阻碍了颗粒的凝并.     

Nanoparticle coagulation in a planar jet via moment method

Large eddy simulations of nanoparticle coagulation in an incompressible pla- nar jet were performed.The particle is described using a moment method to approximate the particle general dynamics equations.The time-averaged results based on 3000 time steps for every case were obtained to explore the influence of the Schmidt number and the Damkohler number on the nanoparticle dynamics.The results show that the changes of Schmidt number have the influence on the number concentration of nanoparticles only when the particle diameter is less than 1 nm for the fixed gas parameters.The number concentration of particles for small particles decreases more rapidly along the flow di- rection,and the nanoparticles with larger Schmidt number have a narrower distribution along the transverse direction.The smaller nanoparticles coagulate and disperse easily, grow rapidly hence show a stronger polydispersity.The smaller coagulation time scale can enhance the particle collision and coagulation.Frequented collision and coagulation bring a great increase in particle size.The larger the Damkohler number is,the higher the particle polydispersity is.     

DEM simulation of polydisperse systems of particles in a fluidized bed

Numerical simulations based on three-dimensional discrete element model (DEM) are conducted for mono-disperse, binary and ternary systems of particles in a fluidized bed. Fluid drag force acting on each particle depending on its size and relative velocity is assigned. The drag coefficient corresponding to Ergun’s correlation is applied to the system of fluidized bed with particle size ratios of 1:1 for the mono-disperse system, 1:1.2, 1:1.4 and 1:2 for the binary system and 1:1.33:2 for the ternary system b...     

Nanoparticle dispersion and coagulation in a turbulent round jet

Nanoparticle dispersion and coagulation behaviors in a turbulent round jet were studied in this article. An experimental system was designed to generate a uniformly distributed air–nanoparticle two-phase flow in a turbulent round jet. The particle size distribution (PSD) was measured by a scanning mobility particle sizer (SMPS) in the near field of the jet. The particle diameters were nearly constant in the potential core due to the high carrying velocity and laminar characteristic of the flow but grew larger in the region of high turbulence intensities because the vortex structures in the mixing layer promoted coagulation. Furthermore, the migration property of small-sized nanoparticles forced them to be preserved in the potential core also leading to the diameter increase. The comparison of the particle concentration distributions at different sections indicated that the shear layer is the major region for the mixing of particle-laden stream and ambient air. The particle diameters in the axial direction experienced three stages including a slightly changed stage, an increasing stage and a constant stage. The diameter increase should be attributed to turbulence coagulation.     

电场作用下纳米颗粒与竖直壁面的碰撞效率

着重考虑了电场作用下,壁面排斥力对颗粒-壁面碰撞效率的影响. 采用Matlab 中的龙格库塔方法,对颗粒-壁面碰撞的压缩阶段及回弹阶段的动力学方程组进行求解,并对Maxwell 速度分布进行积分获得不同速度方向下的碰撞效率. 研究表明,颗粒的碰撞效率随着碰撞角度的增加而增大,并最终达到一个临界值,即完全凝并时的碰撞效率;且颗粒的碰撞效率将因壁面排斥力的影响而减小,即壁面排斥力在一定程度上阻碍了颗粒的凝并.      

硬球加强模型在CFD-DEM耦合计算中的验证与分析

针对CFD-DEM耦合计算中,颗粒计算时间步的选取影响颗粒碰撞计算精度和效率的问题。本文引入插值算法,将动量定理求解颗粒碰撞前后速度进行加权平均;根据弹性理论计算得到颗粒碰撞力,进行动力学方程求解;通过速度收敛准则修正初值速度并自动调整迭代求解次数,提出一种计算精度不受计算时间步长影响,无需对碰撞过程进行精细描述的高效率和高精度的加强硬球模型。对两个颗粒匀和变速碰撞算例进行数值模拟,碰撞后速度、碰撞力和碰撞时间与理论计算误差小于4%,与采用软球碰撞模型的DEM方法相比,颗粒碰撞计算精度不受计算时间步长影响,计算效率提高36.3%和36.8%。对单个颗粒在静水中沉降进行数值模拟,计算步长取10 s～5 s,颗粒与壁面即可得到精确解,计算效率提高33.5%。通过压力损失实验验证了该模型能够准确计算颗粒体积分数小于12%条件下两相流的压力损失。     

颗粒物质在竖直管中下行蠕动流动的实验测量

颗粒流蠕动行为是颗粒物质在竖直管中流动时常见的一种流动现象,其产生机理较复杂。为此,本文在在内径为150mm、高为5000mm的竖直管实验装置上,以FCC催化剂为固体颗粒物料,采用PV6型颗粒速度测量仪,测量不同颗粒流率下竖直管中的颗粒下行蠕动流动速度以及颗粒固含率,系统地考察了颗粒物质在竖直管中下行流动时的蠕动流动特性及产生机理。实验结果表明,颗粒物质在竖直管中下行流动时的流动行为可划分为两种形式。在颗粒流率较小时,颗粒物质下行速度呈现脉冲式变化,有速度停滞,可称之为蠕动I型流动。随着颗粒流率的增加,颗粒下行速度停顿消失,但仍是起伏变化,为蠕动II型流动。当颗粒流率增大到一定值后,颗粒物质下行蠕动行为消失,转变为流化流动。颗粒物质下行的蠕动行为是出口区颗粒成拱与崩塌、颗粒与器壁滑动摩擦和颗粒力链作用的综合反映。     

水击谐波流场中乳化油液滴粒径的PIV测量

为了掌握乳化油液滴在水击谐波流场中的碰撞、破裂、聚集和变形等微观形态的变化规律,采用粒子图像测速(PIV)技术对水平方管中乳化油液滴的水击谐波流场进行了测量,分析了在水击谐波流场中,不同激振力作用下乳化油液滴的粒径变化。测量结果表明,在水击谐波流场作用下,乳化油液滴平均粒径的增长率随着激振力的减小而减小,随着作用时间的增大呈增加趋势,直至粒径处于一种动态平衡;乳化液滴随着激振力增大到达波节聚集位置的时间减少,可见增大水击谐波激振力有利于乳化液滴的聚集并合并为大尺度的液滴,从而有效地提高了水击谐波流场作用下的油水分离效果。     

A Modelling Study of Evolving Particle-laden Turbulent Pipe-flow

An Eulerian turbulent two phase flow model using kinetic theory of granular flows for the particle phase was developed in order to study evolving upward turbulent gas particle flows in a pipe. The model takes the feedback of the particles into account and its results agree well with experiments. Simulations show that the pipe length required for particle laden turbulent flow to become fully developed is up to five times longer than an unladen flow. To increase the understanding of the dependence of the development length on particle diameter a simple model for the expected development length was derived. It shows that the development length becomes shorter for increasing particle diameters, which agrees with simulations up to a particle diameter of 100 ??m. Thereafter the development length becomes longer again for increasing particle diameters because larger particles need a longer time to adjust to the velocity of the carrier phase.     

Basset力研究进展与应用分析

Basset力为两相流中颗粒与流体存在相对加速度时所产生的一种非恒定气动力 ,以往对其进行了大量的实验研究、理论分析和数值模拟。本文通过对Basset力研究文献的综述 ,分析并归纳了各种不同两相流动问题中该力的影响情况 ,得到的结论是 :对于气泡在液体内的流动问题 ,当气泡运动的脉动频率很大或很小时可以忽略Basset力对其运动的影响 ;对于固体或液体颗粒在气体中的运动问题可以忽略Basset力的影响 ;而其它两相流动问题则需要根据具体问题的特点来决定是否考虑Basset力的影响 ,其中需要考察 :流体与颗粒密度差别 ,颗粒尺寸 ,流动特征时间和颗粒运动弛豫时间 ,相对加速度 (或减速度 )等因素。本文还探讨了Basset力研究的发展方向。     

A new approach for the detection of particle interactions for large-inertia and colloidal particles in a turbulent flow

The purpose of the paper is to present a new principle and a new algorithm for the direct numerical simulation of particle interactions within a turbulent flow. This approach has been developed in order to be able to compute agglomeration kernels with a numerical method which can still be applied at reasonable costs for very small colloidal particles. In this paper, classical algorithms are first tested and analyzed. They are shown to yield correct results but to require the use of time steps that are so small that they become intractable for colloidal particles. Their direct applications using large steps with respect to the relaxation time scale of the smallest particles reveal drastic errors that increase with the time step and with decreasing particle diameters. The new principle introduces the notion of continuous relative trajectories between possible collision partners and evaluates the exact probability for this trajectory to reach the minimum distance where two particles actually collide. Based on this new physical point of view and on the use of a probabilistic approach, a novel algorithm has been devised and numerical outcomes confirm that accurate predictions for the collision kernel are obtained independently of the particle diameter and for very large time steps. It is believed that the present ideas open interesting possibilities for the simulation of particle interactions over a whole range of particle behavior, from a ballistic to a diffusive regime, and can be extended to take into account new phenomena. Although present developments arise in the context of a numerical study, the new ideas that are introduced in this paper rely on the use of continuous stochastic bridges and, in that respect, propose a new approach to address physical issues of two-phase flow modeling.     

EFFECT OF MAGNETIC NANOPARTICLES ON THE MECHANICAL PROPERTIES OF TYPE-II SUPERCONDUCTORS

In this paper, the effect of magnetic nanoparticles on the mechanical properties of a type-II superconductor is investigated both theoretically and numerically. Magnetic part of the pinning force associated with the interaction between a finite-size spheroidal magnetic inclusion and an Abrikosov vortex is calculated in the London approximation. It is found that the size and shape of magnetic nanoparticles result in different enhancements of vortex pinning in large-κtype-II superconductors. Meanwhile, the screening current induced by a magnetic spheroid suffer the action of Lorentz force, which will lead to prestress in the superconductor, so further numerical calculations are needed to explore the interaction between the spheroidal magnetic particle and superconductor. The distribution of displacement, stress and strain in the superconductor are finally obtained. It is shown that different sizes and shapes of nanoparticles also can change the distributions of these quantities.     

Dynamics of the flow around colliding spheres

An investigation of the flow resulting from the collision of two spheres at low Reynolds numbers is presented. Each sphere starts from rest and traverses a distance of 5 sphere diameters to the point of contact. Experimental and numerical results are compared for a symmetric collision; that is, a collision between two spheres of the same diameter and travelling with the same velocity. The flow consists of two axisymmetric recirculation zones which become a pair of colliding vortex rings, expanding radially from the collision point. Several examples of unbalanced collisions are also presented numerically, with one or both of the velocity and diameter of the spheres altered. These collisions break the symmetry, altering the post-collision expansion of the vortex rings.     

INTEGRAL COLLISION KERNEL FOR THE GROWTH OF AEROSOL PARTICLES

Integral collision kernel is elucidated using experimental results for titania, silica and alumina nanoparticles synthesized by FCVD process, and titania submicron particles synthesized in a tube furnace reactor. The integral collision kernel was obtained from a particle number balance equation by the integration of collision rates from the kinetic theory of dilute gases for the free-molecule regime, from the Smoluchowski theory for the continuum regime, and by a semi-empirical interpolation for the transition regime between the two limiting regimes. Comparisons have been made on particle size and the integral collision kernel, showing that the predicted integral collision kernel agreed well with the experimental results in Knudsen number range from about 1.5 to 20.     

颗粒群碰撞搜索及CFD-DEM耦合分域 求解的推进算法研究

在采用计算流体力学-离散元耦合方法(computational fluiddynamics-discrete element method, CFD-DEM)进行固液两相耦合分析时, 颗粒计算时间步的选取直接影响到耦合计算精度和计算效率. 为此, 本文选取每个目标颗粒为研究对象, 引入插值函数计算时间步的运动位移, 构建可变空间搜索网格; 通过筛选可能碰撞颗粒建立搜索列表, 采用逆向搜索方式判断碰撞颗粒, 从而提出一种改进的DEM方法(modified discreteelement method, MDEM). 该算法在颗粒群与流体耦合计算中, 颗粒计算初始时间步选取不受颗粒碰撞时间限制, 通过自动调整和修正实现大步长, 由颗粒和流体耦合条件实时更新流体计算时间步, 使颗粒计算时间步选取过小导致计算效率低、选取过大导致颗粒碰撞漏判的问题得以解决, 为颗粒与流体耦合的数值模拟提供了行之有效的计算方法. 通过两个颗粒和多个颗粒的数值模拟, 得到的颗粒间碰撞力、碰撞位置及次数, 与理论计算结果的相对误差均低于2%, 与传统的DEM碰撞搜索算法相比, 在选取的3种计算时间步均不会影响计算精度, 且有较高的计算效率. 通过多个颗粒与流体的耦合数值模拟, 采用传统的CFD-DEM方法, 只有颗粒计算时间步选取10$^{-6}$ s或更小才能得到精确解, 而采用本文方法取10$^{-4}$ s也能够得到精确解, 避免了颗粒碰撞随时间步增大而出现的漏判问题, 且计算耗时降低了16.7%.      

Measurements of the dynamic lift force acting on a circular cylinder in cross-flow and exposed to acoustic resonance

A piezoelectric transducer is developed to perform direct measurements of the dynamic lift force acting on a circular cylinder in cross-flow, in the presence and absence of acoustic resonance. Details of the force transducer design are presented in the paper. The dynamic lift force is measured for a single cylinder with two different diameters, D=12.7 and 15.8 mm. During the tests, the first transverse acoustic mode of the duct housing the cylinder is self-excited. The fluctuating pressure on the top wall of the duct is measured simultaneously with the dynamic lift force. In the absence of acoustic resonance, the measured dynamic lift coefficients agree favorably with those reported in the literature. However, when the acoustic resonance is initiated, the dynamic lift experiences a drastic increase in amplitude associated with abrupt changes in the phase between the lift force and the acoustic pressure. A methodology to extract the hydrodynamic lift component from the total lift measured during acoustic resonance is also proposed. The hydrodynamic lift force is then decomposed into in-phase and out-of-phase components, with respect to the resonant sound pressure. This decomposition procedure provides new insights into the nature of the aeroacoustic sources in the cylinder wake. The proposed methodology, together with the test results provide a general design approach to assess the increase in the dynamic fluid loading on bluff bodies in cross-flow due to the excitation of acoustic resonance.     

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。     

Role of particle stiffness and inter-particle sliding friction in milling of particles

Discrete element method （DEM） has been used to investigate the effects of particle elastic modulus and coefficient of inter-particle sliding friction on milling of mineral particles. An autogeneous mill of 600 mm diameter and 320 mm length with 14,500 particles has been selected for the simulation. Various mill performance parameters, for example, particle trajectories, collision frequency, collision energy and mill power have been evaluated to understand the effects of particle elastic modulus and inter-particle sliding friction during milling of particles. For the given model, it has been concluded that at high energy range, as the elastic modulus and particle sliding friction increase the energy dissipated among the particles increases. The collision frequency increases with the increase in elastic modulus, however, this trend is not clearly observed with increasing inter-particle sliding friction. The power draw of the mill increases with the increase in fraction of mill critical speed.     

各向同性湍流内颗粒碰撞率的直接模拟研究

对 Re_{\lambda } 约为51均匀各向同性湍流内 St_{k}(=\tau_{p}/\tau_{k}) 为 0 ~10.0 的 有限惯性颗粒的碰撞行为进行了直接数值模拟，以研究湍流对有限惯性 颗粒碰撞的影响. 结果表明，具有一定惯性颗粒的湍流碰撞率完全不同于零惯性的轻颗粒 (St_{k}=0) 和可忽略湍流作用的重颗粒 (St{k} \to \infty) , 其变化趋势极其复杂： 在Stk为 0~1.0 之间，颗粒的碰撞率随 St 的增加而近乎线性地剧烈增长，在 Stk≈1.0 3.0(对应的StE=τp/Te≈0.5)附近，颗粒碰撞率出现两个峰值，在Stk>3.0以后，颗粒的碰撞率随惯性增 大而逐渐趋向于重颗粒极限；在峰值处，有限惯性颗粒的平均碰撞率的峰值较轻颗粒增强了 30倍左右. 为进一步分析湍流作用下颗粒碰撞率的影响因素，分别使用可能发生碰撞 的颗粒对的径向分布函数和径向相对速度来量化颗粒的局部富集效应和湍流掺混效应，表明 St_{k} \approx 1.0 时局部富集效应最为强烈，使得颗粒的碰撞率出现第1个峰值； 湍流掺混效应则随着颗粒Stk的增大而渐近增大；局部富集和湍流掺混联合作用的结果， 使得颗粒碰撞率在 St_{k} \approx 3.0 附近出现另一个峰值.