双区静电除尘模拟设计中的颗粒荷电模型选用

大气污染治理水平的提高对静电除尘器的净化效率提出更高要求。利用数值模拟设计静电除尘器有助于优化结构和提高性能,而模拟过程中选用的颗粒荷电模型很大程度决定了模拟结果的准确性。通过建立双区静电除尘器电场、流场和颗粒运动模型,计算两种荷电模型下双区静电除尘器内部颗粒运动轨迹,分析荷电模型对荷电区和收尘区内颗粒轨迹的影响。通过两种荷电模型下0.4 μm颗粒和7.5 μm颗粒去除率模拟值与实测值的对比,发现荷电模型导致的模拟值差异随颗粒粒径的减小而增大。定电量模型适用于电场荷电为主的大粒径颗粒,对扩散荷电的忽略使得该模型下小粒径颗粒的模拟去除率远小于实测值。综合考虑电场荷电量和扩散荷电量随时间变化的模型可以很好地反映小粒径颗粒的荷电特性,更适用于对小粒径颗粒荷电行为特征的数值模拟。     

Numerical analysis of frictional charging and electrostatic interaction of particles

Triboelectrification due to frictional contacts between particles and surfaces is prevalent in many powder handling processes. Aiming to explore the friction-induced electrostatic charging behavior, a discrete element method (DEM) is developed for the first time in the current article, in which a frictional charging model and electrostatic interaction models are implemented. The charge accumulation on both the particles and the surface in a rotational container is then analyzed numerically and experimentally to evaluate the developed DEM. The numerical results for the frictional electrification between insulant particles and an insulant wall agree well with the experimental measurement. It is also shown that both the net charge on the particles and the degree of the particle dispersion are a function of the charging time. Moreover, it is revealed that the friction-induced particle charge enhances particle dispersion, and increases the granular temperature due to the electrostatic interactions.     

静电除尘器数值模拟

针对静电除尘器建立了其流场、电晕电场、颗粒荷电与运动的三维数值模型,流场采用时均Navier-Stokes方程和雷诺应力标准湍流模型,电晕电场采用非结构有限容积法,颗粒运动采用拉格朗日方法,颗粒荷电采用对荷电率方程进行积分的方法,颗粒湍流扩散采用随机轨道模型,颗粒的粒径分布采用Rosin-Rammler分布描述,模拟计算了实验电除尘器电场分布、流场分布以及颗粒运动,极板上的电流密度分布计算值与实验值符合良好,颗粒向极板运动的速度在距离极板面5 mm处的实验值与计算值也符合良好,在模型验证基础上,进一步分析了电除尘器内部流场的分布、颗粒的荷电特性与运动轨迹以及各个粒径的除尘效率。     

Evaluation of Select Approximations for Calculating Particle Charging Rates in the Continuum Regime

Select approximations for particle charge acquisition in the continuum regime were evaluated by comparison with numerical calculations of continuum field-diffusion theory. Charging rates as calculated by five approximations—White, diffusion, field, Klett, and Wang—were evaluated as a function of dimensionless particle charge, ν, and dimensionless field, ω, over the domains - 20 ≤ ν ≤ 20 and 0.01 ≤ ω ≤ 100. None of the approximations was found to be valid over the full domain of charge and field strength encountered in aerosol charging applications, and the subdomains over which each of the approximations is accurate were determined. Based on these results, various combinations of approximations and polynomial curve fits were evaluated. A combination consisting of the diffusion and field approximations along with a polynomial curve fit was found to yield good estimates of the charging rate over the full domain of charge and field. Sample calculations using this combination to determine charge as a function of time under unipolar conditions compared well with calculations based on field–diffusion theory, and the combination is recommended for continuum regime charging calculations. For estimating steady-state bipolar charge, an empiricism formed by the average of two approximations, one developed by Klett and one consisting of the superposition of the diffusion approximation and the field approximation, is recommended.     

CFD simulation of high-temperature effect on EHD characteristics in a wire-plate electrostatic precipitator☆

A computational fluid dynamics (CFD) model is carried out to describe the wire-plate electrostatic precipitator (ESP) in high temperature conditions, alming to study the effects of high temperature on the electro-hydrodynamic (EHD) characteristics. In the model, the complex interactions at high temperatures between the electric field, fluid dynamics and the particulate flow are taken into account. We apply different numerical methods for different fields, including an electric field model, Euler–Lagrange particle-laden flows model, and particle charging model. The effects of high temperature on ionic wind, EHD characteristics and collection effi-ciency are investigated. The numerical results show high temperature causes more significant effects of the ionic wind on the gas secondary flow. High viscosity of gas at high temperature makes particles follow the gas flow pattern more closely. High temperature reduces the surface electric strength, so that the mean electric strength weakens the space charging. On the contrary, there is an increase in the diffusion charging at high tem-perature compared with at low temperature. High temperature increases the ratio of mean drag force over mean electrostatic force acting on the particles which may contribute to a decline of collection efficiency.     

Experimental validation of CFD models for fluidized beds: Influence of particle stress models, gas phase compressibility and air inflow models

This work compares numerical simulations of fluid dynamics in fluidized beds using different closure models and air feed system models. The numerical results are compared to experiments by means of power spectral density distributions of fluctuating pressure signals and bubble statistics obtained from capacitance probe measurements. Two different particle rheology models are tested in combination with two different values of the maximum particle volume fraction. The first particle model predicts the particle pressure by an exponential power law and assumes a constant particle viscosity (CPV), and the second model predicts the stresses using the kinetic theory of granular flow (KTGF). Furthermore, two model approaches for the air inflow are evaluated. The first inflow model includes the coupling between the air-feed system and the fluidized bed in the simulation, and the second model assumes a constant mass flow of gas into the fluidized bed. Finally, the influence of the compressibility of the gas phase on the numerical predictions is investigated. The numerical simulations are made using the CFX-4.4 commercial flow solver.The simulations show that the KTGF model gives a more evenly distributed bubble flow profile over the bed cross-section, while the CPV model gives a more parabolic bubble flow profile, with a higher bubble flow in the central part of the bed. This work shows that the KTGF model results are in significantly better agreement with the experiments. It is furthermore shown that the modelling of the air-feed system is crucial to for predicting the overall bed dynamic behaviour.     

Hydrodynamic modelling of dense gas-fluidised beds: comparison and validation of 3D discrete particle and continuum models

A critical comparison of a hard-sphere discrete particle model, a two-fluid model with kinetic theory closure equations and experiments performed in a pseudo-two-dimensional gas-fluidised bed is made. Bubble patterns, time-averaged particle distributions and bed expansion dynamics measured with a nonintrusive digital image analysis technique are compared to simulation results obtained at three different fluidisation velocities. For both CFD models, the simulated flow fields and granular temperature profiles are compared. The effects of grid refinement, particle-wall interaction, long-term particle contacts, particle rotation and gas-particle drag are studied. The mechanical energy balance for the suspended particles is introduced, and the energy household for both CFD models is compared. The most critical comparison between experiments and model results is given by analysis of the bed expansion dynamics. Though both models predict the right fluidisation regime and trends in bubble sizes and bed expansion, the predicted bed expansion dynamics differ significantly from the experimental results. Alternative gas-particle drag models result in significantly different bed dynamics, but the gap between model and experimental results cannot be closed. In comparison with the experimental results, the discrete particle model gives superior resemblance. The main difference between both CFD models is caused by the neglect of particle rotation in the kinetic theory closure equations embedded in the two-fluid model. Energy balance analysis demonstrates that over 80% of the total energy is dissipated by sliding friction. Introduction of an effective restitution coefficient that incorporates the additional dissipation due to frictional interactions significantly improves the agreement between both models.     

CFD‐Modellierung von Nasselektroabscheidern mit koaxial angeordneten Draht‐und Rohrelektroden

The design of electrostatic precipitators is very complex, especially if the intended operational conditions are characterized by the presence of a very high load of particles or droplets. In this case the high amount of particle bounded charge leads to a significant disturbance of the corona development causing a deterioration of precipitation efficiency. This effect is known as corona quenching. The objective of this work is the development of a numerical model based on computational fluid dynamics and capable to cover this working range.     

Arbitrary shaped ice particle melting under the influence of natural convection

This work is devoted to numerical simulations of an arbitrary shaped ice particle melting inside water under the influence of natural convection. Specifically, four different shapes of the ice particle have been studied: sphere, cylinder, cross shaped cylinder, and irregular sphere with radial bumps on its surface. A 2D axisymmetric particle‐resolved numerical model has been employed on a fixed grid to study the detailed melting dynamics of an ice particle. The solid‐liquid interface is treated as a porous medium characterized by the permeability coefficient which is used to damp the velocity values inside the interface. The model results have been compared with an existing experimental results produced by A. Shukla et al. (Metal Mater Trans B. 2011; 42(1):224–235). Very good agreement between our predictions and experimental data have been achieved. Based on the analysis of numerical simulation results, melting process is found to advance through two distinct regimes, namely, establishment of the natural convection and active melting of ice particle exhibiting substantial amount of fluid‐particle interactions. A set of dimensionless parameters have been identified to distinguish between regimes. Finally, we developed a semi‐empirical to predict the melting of any arbitrary shaped ice particle and validated it against the particle‐resolved numerical simulation and experimental results. The comparison showed good agreement. Finally, the presented semi‐empirical model can be used as sub‐grid model in Euler‐Lagrange based numerical models to study the phase change phenomena in particulate flow systems. © 2017 American Institute of Chemical Engineers AIChE J, 63: 3158–3176, 2017     

Influence of flame-generated ions on the simultaneous charging and coagulation of nanoparticles during combustion

Flames generate a large amount of chemically and thermally ionized species, which are involved in the growth dynamics of particles formed in flames. However, existing models predicting particle formation and growth do not consider particle charging, which may lead to bias in the calculated size distribution of particles. In this study, Fuchs' charging theory was coupled with a monodisperse particle growth model to study the simultaneous charging and coagulation of nanoparticles during combustion. In order to quantify the charging characteristics of nanoparticles, a high-resolution DMA was used to measure the mobilities of ions generated from a premixed flat flame operated at various conditions. The effect of temperature on ion–particle and particle–particle combination coefficients was further examined. The proposed model showed that the influence of charging on particle growth dynamics was more prominent when the ion concentration was comparable to or higher than the particle concentrations, a condition that may be encountered in flame synthesis and solid fuel-burning. Simulated results also showed that unipolar ion environments strongly suppressed the coagulation of particles. In the end, a simplified analysis of the relative importance of particle charging and coagulation was proposed by comparing the characteristic time scales of these two mechanisms.

© 2017 American Association for Aerosol Research     

Application of a modified Eulerian model to study the particle deposition on a vertical surface in turbulent flow

In this study the v2-f model was used with the two-phase Eulerian approach to predict the particle deposition rate on a vertical surface in a turbulent flow. The standard Eulerian particle model was adopted from the literature and modified, considering the majority of particle transport mechanisms in the particle deposition rate. The performance of the modified model was examined by comparing the rate of particle deposition on a vertical surface with the experimental and numerical data in a turbulent channel flow available in the literature. The model took into account the effects of drag force, lift force, turbophoretic force, electrostatic force, inertia force and Brownian/turbulent diffusion on the particle deposition rate. Electrostatic forces due to mirror charging and charged particles under the influence of an electric field were considered. The predictions of the modified particle model were in good agreement with the experimental data. It was observed that when both electrostatic forces are present they are the dominant factor in the deposition rate in a wider range of particle sizes.     

A SEMI-EMPIRICAL APPROACH TO PREDICT THE TOTAL COLLECTION EFFICIENCY OF ELECTROSTATIC PRECIPITATORS

Using empirical data for the effective migration velocity, the Deutsch-Anderson equation has been widely used for calculation of the total collection efficiency and design of electrostatic precipitators (ESPs). Based on a normal particle size distribution, the present paper develops a semi-empirical equation for the total collection efficiency of ESPs. The equation is then simplified and extended to other particle size distributions. The simplified equation shows that the total collection efficiency increases with increasing mass median diameter of particles and with increasing electrical field strengths. The effective migration velocity is found to be directly proportional to the mass median diameter and to the electrical field strengths for particle charging and collection. Moreover, an example is given to illustrate how to use the present simplified model in the design of ESPs.     

A SEMI-EMPIRICAL APPROACH TO PREDICT THE TOTAL COLLECTION EFFICIENCY OF ELECTROSTATIC PRECIPITATORS

Using empirical data for the effective migration velocity, the Deutsch-Anderson equation has been widely used for calculation of the total collection efficiency and design of electrostatic precipitators (ESPs). Based on a normal particle size distribution, the present paper develops a semi-empirical equation for the total collection efficiency of ESPs. The equation is then simplified and extended to other particle size distributions. The simplified equation shows that the total collection efficiency increases with increasing mass median diameter of particles and with increasing electrical field strengths. The effective migration velocity is found to be directly proportional to the mass median diameter and to the electrical field strengths for particle charging and collection. Moreover, an example is given to illustrate how to use the present simplified model in the design of ESPs.     

Evolution of particle metrics in a buoyant aerosol cloud from explosive releases

Abstract

The detonation of high explosive (HE) material generates a cloud containing a high concentration of detonation products in the form of aerosol particles and gases. Modeling and simulation of aerosol metrics in an explosive cloud is a complex problem as it involves various processes such as chemical reaction, nucleation, volume expansion, and coagulation. Several models have been developed to study the atmospheric dispersion of these detonation products, but very few or no model is available to study the evolution of aerosol metrics at the early stage. In this work, we present a numerical model to simulate the temporal evolution of aerosol metrics in an expanding cloud by coupling transient thermodynamic properties with important microphysical processes. To illustrate the application, the numerical model is applied to a typical HE, and the aerosol particle properties such as size distribution, number concentration, and average size are estimated from the numerical results. These results will provide the essential input conditions for atmospheric dispersion models to estimate the atmospheric concentration and deposition of aerosol particles.

Copyright © 2020 American Association for Aerosol Research     

Estimating aerosol particle charging parameters using a Bayesian inversion technique

A Bayesian inversion routine is described in which data from tandem differential mobility analysis (TDMA) can be used to determine fundamental parameters for charging models as a function of particle size. The measurement and inversion techniques were verified using simulated data for particles in the 50–500 nm range undergoing unipolar diffusion charging as described by Fuchs’ limiting sphere theory, for which the fundamental charging parameter is the product of the unipolar ion concentration and residence time within the charger, the so-called nt product. Under conditions where the average particle charge is greater than one unit charge, the inversion routine is precisely and accurately able to determine the nt value. The inversion routine breaks down, however, when the average number of charges per particle is well below unity, i.e. for low nt values or for small particle sizes. Incorporation of charging efficiency data in addition to TDMA data can allow for use of the inversion routine when the average number of charges per particle is low. With its limitations known, the inversion routine was applied to determine the nt value for the unipolar charger used in the TSI electrical aerosol detector (EAD), model 3070A, for particles in the 50–200 nm size range. The effective nt value within the EAD charger decreased with decreasing particle size, implying that charged particle losses occur within the EAD charger. The described inversion routine is unique in its ability to determine size dependent charge model parameters, and can be utilized with any given charging model. It is expected that this technique will be of use in advancing the understanding of aerosol particle charging models and in future design of unipolar chargers.     

Numerical simulation of the flow and the collection mechanism inside a scale hybrid particulate collector

Numerical technology has been widely used for the study of the electrostatic precipitators (ESP) and the bag filters. This paper presents a numerical model for a scale hybrid particulate collector (HPC), which combines the ESP technology and the filtration technology together. The collection process of the HPC is unsteady as the pressure drop across the bag filter increases with the deposition of the particles. The physical processes of the model include the corona discharge, the fluid flow, the particle charging and the filtration. The corona discharge field is solved by using a finite volume method. For the fluid field, the unsteady and incompressible Navier–Stokes equations with the RNG κ–ε turbulence equations are solved. The effect of the electric field on the fluid field named electro-hydrodynamic is also considered. For the particle charging, the filed-diffusing combined model of Lawless (1996) [37] is adopted. For the filtration, an unsteady cake formation model is proposed. The pressure drop across the cake is calculated according to the mass density of the cake. The coefficient between the pressure drop and the mass density of the cake comes from the experimental data. Applying the numerical model to the HPC, the influence of the hole diameter of the perforated-plate on the collection efficiency of the electrostatic zone is analyzed. Numerical results show that the collection efficiency of the electrostatic zone of the HPC has no certain relation with the hole diameter of the perforated plate. The effect of the hole diameter of the perforated-plate on the collection efficiency of the electrostatic zone becomes weaker with increasing the applied voltage.     

Individual electrostatic particle interaction in pneumatic transport

Electrostatic charging and discharging of particles in pneumatic transport has been experimentally investigated under a variety of conditions. The basic system consisted of flowing glass beads 75 μm and 150 μm in diameter at dilute loadings up to 1.0 with varying relative humidities from 25 to 65%. A series of five nickel electrodes 228 μm in diameter measured particle interactions with the wall along the flow path. The charge and currents transferred were measured by an electrometer-based recording system. Different types of particle—wall interaction were noted and contact frequencies were measured. Analogy of the particle hit was made with the penetration theory. At constant loadings, greater electrostatic effects were seen for small particles over large particles due to the high particle number density and thus increased interactions for the smaller particles. Higher loadings at low relative humidities also produced increased electrostatic effects.     

Modeling of particle deposition in a vertical turbulent pipe flow at a reduced probability of particle sticking to the wall

Particle deposition on the wall in a dilute turbulent vertical pipe flow is modeled. The different mechanisms of particle transport to the wall are considered, i.e., Brownian motion, turbulent diffusion and turbophoresis. The Saffman lift force, the electrostatic force, the virtual mass effect and wall surface roughness are taken into account in the model developed. A boundary condition that accounts for the probability of particle sticking to the wall is suggested. An analytical solution for deposition of small Brownian particles is obtained. A particle relaxation time range, where the model developed is reliably applicable, is evaluated. Computational results obtained at different particle-wall sticking probabilities in the wide particle relaxation time range are presented and discussed.     

Triboelectric charging of powders: A review

Particles are often electrostatically charged by frictional contact during powder-handling operations. This phenomenon is called ‘triboelectric charging’ or ‘contact electrification’. The charged particles cause problems such as particle deposition and adhesion. In addition, if particles are excessively charged, an electrostatic discharge may occur, which can pose a risk of fire and explosion hazards; thus, to mitigate the adverse effects, it is important to elucidate the underlying triboelectric charging mechanisms. The electrostatics is, on the other hand, very useful in a number of applications that have been developed using the principles. In this review, the basic concepts and theories of charge transfer between solid surfaces are summarized, and chemical factors depending on materials and environmental effects are described. To theoretically analyze the process of particle charging, relevant models are discussed. Using the models, particle charging by repeated impacts on a wall is formulated. To experimentally evaluate particle charging, measurement and characterization methods are outlined. Furthermore, important applications and computer simulations are described.