Simulation of the Brownian coagulation of nanoparticles with initial bimodal size distribution via moment method

The Brownian coagulation of nanoparticles with initial bimodal size distribution, i.e., mode i and j, is numerically studied using the moment method. Evolutions of particle number concentration, geometric average diameter and geometric standard deviation are given in the free molecular regime, the continuum regime, the free molecular regime and transition regime, the free molecular regime and continuum regime, respectively. The results show that, both in the free molecular regime and the continuum regime, the num- ber concentration of mode i and j decreases with increasing time. The evolutions of particle geometric average diameter with different initial size distribution are quite different. Both intra-modal and inter-modal coagulation finally make the polydispersed size distribution become monodispersed. As time goes by, the size distribution with initial bimodal turns to be unimoda/and shifts to a larger particle size range. In the free molecular regime and transition regime, the inter- modal coagulation becomes dominant when the number concentrations of mode i and j are of the same order. The effects of the number concentration of mode i and mode j on the evolution of geometric average diameter of mode j are negligible, while the effects of the number concentration of mode j on the evolution of geometric average diameter of mode j is distinct. In the free molecular regime and continuum regime, the higher the initial number concentration of mode j, the more obvious the variation of the number concentration of mode i.

Nanoparticle Transport and Coagulation in Bends of Circular Cross Section via a New Moment Method

Transport of nanoparticles and coagulation is simulated with the combination of CFD in a circular bend. The Taylor-expansion moment method(TEMOM)is employed to study dynamics of nanoparticles with Brownian motion,based on the flow field from numerical simulation.A fully developed flow pattern in the present simulation is compared with previous numerical results for validating the model and computational code.It is found that for the simulated particulate flow system,the particle mass concentration,number concentration,particle polydispersity, mean particle diameter and geometric standard deviation over cross-section increase with time.The distribution of particle mass concentration at different time is independent of the initial particle size.More particles are concen-trated at outer edge of the bend.Coagulation plays more important role at initial stage than that in the subsequent period.The increase of Reynolds number and initial particle size leads to the increase of particle number concentration.The particle polydispersity,mean particle diameter and geometric standard deviation increase with decreasing Reynolds number and initial particle size.

Nanoparticle coagulation in a planar jet via moment method

Large eddy simulations of nanoparticle coagulation in an incompressible planar jet were performed. The particle is described using a moment method to approximate the particle general dynarnics 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 direction, 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.

Quadrature Method of Moments for Nanoparticle Coagulation and Diffusion in the Planar Impinging Jet Flow

A computational model combining large .eddy simulation with quadrature moment method was em-ployed to study nanoparticle evolution in a confined impinging jet. The investigated particle size is limited in the transient regime, and the particle collision kernel was obtained by using the theory of flux matching. The simulation was validated by comparing it with the experimental results. The numerical results show coherent structure acts to dominate particle number intensity, size and polydispersity distributions, and it also induce particle-laden iet to be diluted by .the ambient.The evolution of particle dynarnics in.the impinging jet flow are strongly related to the Rey-nolds number and nozzle-to-plate distance, and their relationships were analyzed.

NUMERICAL SIMULATION OF NANOPARTICLE COAGULATION IN A POISEUILLE FLOW VIA A MOMENT METHOD

Numerical simulations of coagulating nano-scale aerosols in a two dimensional Poiseuille flow between fixed plates are performed. Evolution of the particle field is obtained by utilizing a moment method to approximate the aerosol general dynamic equation. A moment method is used, which assumes a lognormal function for the particle size distribution and requires knowledge of the first three moments. A Damk？hler number is defined to represent the ratio of the convection time scale to the coagulation time scale. Simulations are performed based on three Reynolds numbers, 100, 500 and 1000, and on three initial particle volume fractions corresponding to Damk？hler numbers 0.1, 0.2 and 1.0. Spatio-temporal evolution of the first three moments along with the geometric mean volume and standard deviation are discussed.

Nanoparticle nucleation and coagulation in a mixing layer

Numerical simulation of nanoparticle nucleation and coagulation in a mixing layer with sulfuric acid vapor binary system is performed using the large eddy simulation and the direct quadrature method of moment. The distributions of number concentration, volume concentration, and average diameter of nanoparticles are obtained. The results show that the coherent structures have an important effect on the distributions of number concentration, volume concentration and average diameter of nanoparticles via continuously transporting and diffusing the nanoparticles to the area of low particle concentration. In the streamwise direction, the number concentration of nanoparticles decreases, while the volume concentration and the average diameter increase. The distributions of number concentration, volume concentration and average diameter of nanoparticles are spatially inhomogeneous. The characteristic time of nucleation is shorter than that of coagulation. The nucleation takes place more easily in the area of low temperature because where the number concentration of nanoparticles is high, while the intensity of coagulation is mainly affected by the number concentration. Both nucleation and coagulation result in the variation of average diameter of nanoparticles.

Development and application of moment method on nanoparticles evolution due to coagulation and deposition

In this study,the Taylor-series expansion method of moments is developed to describe the dynamic behaviour of nanoparticles considering both the effects of coagulation and deposition in closed environments,where the two effects have always been studied separately before.Compared with traditional methods of moments,the new method could give more accurate results for solving the general dynamics equation.In addition,moment equations with respect to coagulation and deposition considering the fractal dimension(Df)of particles are acquired,and the results are compared with experimental data and are more accurate than the simulation results under the assumption of spherical mode.The new dynamic model could be applied in more real conditions with different microstructures of nanoparticles.With decreasing Dt,the particle number concentration decreases more rapidly,additionally,Df has a relatively greater effect on the agglomeration of smaller particles under the same initial concentration.Moreover,the effect of the initial number concentration on coagulation is also studied.The results show that a higher initial number concentration or a smaller particle size could have a greater effect of coagulation on the evolution of particles.

A modified TEMOM model for Brownian coagulation of nanoparticles based on the asymptotic solution of the sectional method

The Taylor-series expansion method of moments(TEMOM)is modified to match the behavior of real self-preserved aerosols by taking advantage of the numerical results obtained by the sectional method for Brownian coagulation in both continuum and free molecular regimes.The newly proposed model is able to predict the evolution of the zeroth and second moments more accurately than the original TEMOM when the aerosol size distribution approaches self-preserving or the coagulation time is sufficiently long.A special kind of coordinate diagram,which describes the relationship between the moment equations and one non-dimensional moment is first used to investigate different methods of moments that only involve the first three moments.The errors produced by different methods of moments can be qualitatively explained by these diagrams.By polynomial fitting,a new set of moment equations for Brownian coagulation in the free molecular regime is proposed in the framework of the log-normal preserving theory.

平面射流中纳米粒子积聚的矩方法

应用大涡模拟方法求解平面湍射流场,矩方法求解纳米粒子的一般动力学方程.通过对每种情况3000个时间步的平均,得到了Schmidt数和Damkohler数对纳米粒子动力学特性的影响.结果发现,当气体参数不变时,Schmidt数的变化只对直径小于1 nm的颗粒数密度的分布产生影响.直径小的颗粒其颗粒数密度沿流动方向下降迅速,而具有大Schmidt数的颗粒,沿横向的分布较窄.较小的颗粒容易发生积聚和扩散,并且体积增长较快,因而颗粒多分散性较为明显.小的颗粒积聚时间尺度能增强颗粒的碰撞和积聚频率,导致颗粒尺寸迅速增大.Damkohler数越大,颗粒的多分散也越明显.

纳米颗粒多相流体动力学研究及应用

纳米颗粒多相流研究是目前多相流研究中新的研究方向及重点发展领域.为探索纳米尺度多相流相间作用机理及内部存在机制,采用理论分析及数值计算手段,对一般动力学方程的封闭处理、颗粒碰撞率宏观模型的有效构建、颗粒凝并系统动力学演变特性的机理分析、非稀相问题碰撞率的求取、双变量问题求解方法的建立以及一些实际应用进行了系统研究,提出了新的针对纳米尺度颗粒动力学演变的一般动力学方程求解方法,并将其应用于实际工业过程问题的研究.该文对上述研究工作进行了综述.

水基铜纳米流体管内颗粒凝并的数值模拟研究

采用大涡模型和泰勒展开矩方法对三维水平圆管中水基铜纳米流体的运动和颗粒扩散及凝并过程进行了数值模拟,主要研究了纳米流体中纳米颗粒在管内的演化过程.结果显示,随着颗粒凝并的进行,颗粒粒径增加,数密度减小;小颗粒的混合和颗粒凝并同时改变颗粒粒径,最终使粒径在径向呈现抛物线分布;流场雷诺数越大对凝并的抑制作用越强.

微通道中压力驱动Poiseuille流数值分析

采用26阶矩方程方法对稀薄气体在平板微通道与微圆通道中压力驱动的Poiseuille流动进行数值分析,获得稀薄气体在微通道内的速度分布、压力分布规律。数值分析结果表明:气体压力在微通道中沿主流方向呈非线性分布,且非线性程度随Kn数的增大而减小,分布趋势随Kn数的改变产生微小的变化;随Kn数的增大,微圆通道中气体沿径向速度分布出现双峰现象。研究结果与DSMC方法及格子-Boltzmann方法对比符合较好。