Challenges of Simulating Droplet Coalescence within a Spray

Abstract

This article reports various challenges that have been encountered in the process of developing validated Lagrangian and Eulerian models for simulating particle agglomeration within a spray dryer. These have included the challenges of accurately measuring droplet coalescence rates within a spray, and modeling properly the gas–droplet and droplet-droplet turbulence interactions. We have demonstrated the relative versatility and ease of implementation of the Lagrangian model compared with the Eulerian model, and the accuracy of both models for predicting turbulent dispersion of droplets and the turbulent flow-field within a simple jet system. The Lagrangian and Eulerian droplet coalescence predictions are consistent with each other, which implies that the numerical aspects of each simulation are handled properly, suggesting that either approach can be used with confidence for future spray modeling. However, it is clear that considerable research must be done in the area of particle turbulence modeling and accurate measurement of particle agglomeration rates before any Computational Fluid Dynamics tool can be employed to accurately predict particle agglomeration within a spray dryer.     

Monte Carlo modeling of binder‐Less spray agglomeration in fluidized beds

Fluidized bed spray agglomeration is used in the industry to increase the particle size and to improve several properties, for example, bulk density, flowability, and dissolution behavior of particulate products. Usually, a binder liquid is sprayed on a particle bed. If amorphous materials are used, spraying of pure water may cause agglomeration due to glass transition at wet spots on the particle surface. As no process models covering binder‐less spray agglomeration currently exist, a model based on a Monte Carlo method is presented. In this method, the process is described by events and processes on the single particle scale. Additionally, agglomeration experiments in a lab‐scale fluidized bed using three different maltodextrins are presented. For each experiment, a simulation was performed. The simulation results are compared with the obtained experimental data. © 2018 American Institute of Chemical Engineers AIChE J, 64: 3582–3594, 2018     

Challenges of Simulating Droplet Coalescence within a Spray

This article reports various challenges that have been encountered in the process of developing validated Lagrangian and Eulerian models for simulating particle agglomeration within a spray dryer. These have included the challenges of accurately measuring droplet coalescence rates within a spray, and modeling properly the gas-droplet and droplet-droplet turbulence interactions. We have demonstrated the relative versatility and ease of implementation of the Lagrangian model compared with the Eulerian model, and the accuracy of both models for predicting turbulent dispersion of droplets and the turbulent flow-field within a simple jet system. The Lagrangian and Eulerian droplet coalescence predictions are consistent with each other, which implies that the numerical aspects of each simulation are handled properly, suggesting that either approach can be used with confidence for future spray modeling. However, it is clear that considerable research must be done in the area of particle turbulence modeling and accurate measurement of particle agglomeration rates before any Computational Fluid Dynamics tool can be employed to accurately predict particle agglomeration within a spray dryer.     

双尺度二阶矩两相湍流模型和水平槽道内两相流动的数值模拟

对有颗粒碰撞的两相流动,常常采用将颗粒湍流模型和反映颗粒碰撞作用的动力学模型叠加的方法来构造稠密两相流动的二阶矩湍流模型,在理论上不协调.基于将颗粒脉动分成湍流引起的大尺度脉动和颗粒间碰撞产生的小尺度脉动的概念,建立了两相流动的双尺度二阶矩湍流模型.用该模型对水平槽道内两相流动进行了数值模拟.预报结果和实验结果符合,和单尺度二阶矩湍流模型的结果接近,表明了本模型的可行性.模拟结果还给出了大尺度和小尺度雷诺正应力分布,发现在同一方向上前者比后者大.     

Predictive simulation of nanoparticle precipitation based on the population balance equation

Nanoparticle precipitation is an interesting process to generate particles with tailored properties. In this study we investigate the impact of various process steps such as solid formation, mixing and agglomeration on the resulting particle size distribution (PSD) as representative property using barium sulfate as exemplary material. Besides the experimental investigation, process simulations were carried out by solving the full 1D population balance equation coupled to a model describing the micromixing kinetics based on a finite-element Galerkin h-p-method. This combination of population balance and micromixing model was applied successfully to predict the influence of mixing on mean sizes (good quantitative agreement between experimental data and simulation results are obtained) and gain insights into nanoparticle precipitation: The interfacial energy was identified to be a critical parameter in predicting the particle size, poor mixing results in larger particles and the impact of agglomeration was found to increase with supersaturation due to larger particle numbers. Shear-induced agglomeration was found to be controllable through the residence time in turbulent regions and the intensity of turbulence, necessary for intense mixing but undesired due to agglomeration. By this approach, however, the distribution width is underestimated which is attributed to the large spectrum of mixing histories of fluid elements on their way through the mixer. Therefore, an improved computational fluid dynamics-based approach using direct numerical simulation with a Lagrangian particle tracking strategy is applied in combination with the coupled population balance-micromixing approach. We found that the full DNS-approach, coupled to the population balance and micromixing model is capable of predicting not only the mean sizes but the full PSD in nanoparticle precipitation.     

Agglomeration of alumina powders: A turbidimetric study

Turbidimetry has proved to be an efficient method for the quantitative study of powder agglomeration for particle sizes in the region of 1 μm. This work presents a new application of the technique for the agglomeration of α-alumina in water and in n-heptane. The method of determining the kinetic parameters of agglomeration from the initial time-evolution of turbidity is explained. Turbulent flow in the reactor has also been characterised by laser anemometry. From the turbulence intensity, the number of collisions per unit time is calculated and the agglomeration rate can therefore be determined. Good agreement is found between the values obtained respectively from turbidimetric and hydrodynamic measurements. Addition of KOH modifies the zeta potential of alumina in water and influences the agglomeration kinetics. This can also be quantitatively characterised by turbidimetry. The experimental results obtained for alumina particles of diameter 0.3 μm and 1 μm are interpreted according to the DLVO model of interaction between particles.     

颗粒尾涡增强湍流的大涡模拟以及气固两相流中湍流变动的数值模拟

The turbulence enhancement by particle wake effect is studied by large eddy simulation （LES） of turbulent gas flows passing a single particle. The predicted time-averaged and root-mean-square fluctuation velocities behind the particle are in agreement with the Reynolds-averaged Navier-Stokes modeling results and experimental results. A semi-empirical turbulence enhancement model is proposed by the present-authors based on the LES resuits. This model is incorporated into the second-order moment two-phase turbulence model for simulating vertical gas-particle pipe flows and horizontal gas-particle channel flows. The simulation results show that compared with the model not accounting for the particle wake effect, the present model gives simulation results for the gas turbulence modulation in much better agreement with the experimental results.     

湍流促进器强化微滤过程的实验与CFD模拟研究(英文)

This paper reports experimental and computational fluid dynamics(CFD) studies on the performance of microfiltration enhanced by a helical screw insert.The experimental results show that the use of turbulence pro-moter can improve the permeate flux of membrane in the crossflow microfiltration of calcium carbonate suspension,and flux improvement efficiency is strongly influenced by operation conditions.The energy consumption analysis indicates that the enhanced membrane system is more energy saving at higher feed concentrations.To explore the intrinsic mechanism of flux enhancement by a helical screw insert,three-dimensional CFD simulation of fluid flow was implemented.It reveals that hydrodynamic characteristics of fluid flow inside the channel are entirely changed by the turbulence promoter.The rotational flow pattern increases the scouring effect on the tube wall,reducing the particle deposition on the membrane surface.The absence of stagnant regions and high wall shear stress are respon-sible for the enhanced filtration performance.No secondary flow is generated in the channel,owing to the streamline shape of helical screw insert,so that the enhanced performance is achieved at relatively low energy consumption.     

Computational modeling of microbubble coalescence and breakup using large eddy simulation and Lagrangian tracking

The flow of dispersed microbubbles was studied with an Eulerian–Lagrangian technique using large eddy simulation to predict the continuous liquid flow and Lagrangian tracking to compute bubble trajectories. The model fully accounts for bubble coalescence and breakup and was applied to horizontal and vertical channel flows. With low levels of turbulence, gravity in horizontal, and lift in vertical, channel flows govern the bubble spatial and collision distribution. When turbulence is sufficiently high to, at least partially, oppose bubble preferential concentration, more uniform collision and coalescence distributions are found, although these remain peaked near the wall in both configurations. Almost 100% coalescence efficiency was always found, due to bubbles colliding along similar trajectories, with breakup only recorded in a flow of low surface tension refrigerant R134a. Models like this can provide the required quantitative understanding of the microbubbles complex behavior, as well as supporting the development of more macroscopic modeling closures.     

Three‐Dimensional Numerical Simulation of Dense Pneumatic Conveying of Pulverized Coal in a Vertical Pipe at High Pressure

A two‐fluid model based on the kinetic theory of granular flow was used to study three‐dimensional steady state flow behavior of dense phase pneumatic conveying of pulverized coal in a vertical pipe, where the average solid concentration ranges from 11 % to 30 %, and the transport pressure ranges from 2.6 Mpa to 3.3 Mpa. Since the solid concentration is rather high, a k–?–k_p–?_p model which considers the turbulence interaction between the gas and particle phase, was incorporated into the two‐fluid model. The simulation results including profiles of gas and particle phase axial velocity, profiles of solid concentration, profiles of the turbulence intensity of the particle phase, as well as the value of the pressure gradient were reported. Then, the influences of solid concentration and transport pressure on the flow behaviors were discussed. The experiment was also carried out to validate the accuracy of the simulation results which showed that the predictions of pressure gradient were in good agreement with the experimental data. Simulation results indicate that the location of maximal solid concentration deviates from the pipe center and the deviation becomes more obvious with the solid concentration increasing, which is analogous to the phenomenon in the liquid/solid flow. Besides, pressure gradient declines as the transport pressure decreases, which is validated by experiment described in the paper. Moreover, the analysis indicates that it is necessary to consider the turbulence of particles for the simulation of dense phase pneumatic conveying at high pressure.     

The impacts of standard wall function and drag model on the turbulent modelling of gas–particle flow in a circulating fluidised bed riser

A transient turbulence model was applied to simulate the gas–particle system in a circulating fluidised bed riser. The k–epsilon turbulent equations coupled with the fluctuating energy equation were used to simulate the gas–particle system in a riser. The simulation results were validated by the experimental data of a CFB system. A grid study was implemented to examine the impact of grid discretisation. A comparison between the conventional drag models and the EMMS model was also conducted. Other factors, like the restitution coefficient particle to particle, was also found to have a significant impact on the turbulence model. © 2013 Canadian Society for Chemical Engineering     

A second-order-moment–Monte-Carlo model for simulating swirling gas–particle flows

A second-order moment (SOM) gas-phase turbulence model, combined with a Monte-Carlo (MC) simulation of stochastic particle motion using Langevin equation to simulate the gas velocity seen by particles, is called an SOM–MC two-phase turbulence model. The SOM–MC model was applied to simulate swirling gas–particle flows with a swirl number of 0.47. The prediction results are compared with the PDPA measurement data and those predicted using the Langevin-closed unified second-order moment (LUSM) model. The comparison shows that both models give the predicted time-averaged flow field of particle phase in general agreement with those measured, and there is only slight difference between the prediction results using these two models. In the near-inlet region, the SOM-MC model gives a more reasonable distribution of particle axial velocity with reverse flows due to free of particle numerical diffusion, but it needs much longer computation time. Both models underpredict the gas and particle fluctuation velocities, compared with those measured. This is possibly caused by the particle–wall and particle–particle interaction in the near-wall region, and the effect of particles on dissipation of gas turbulence, which is not taken into account in both models.     

Simulation of structure and mobility of aggregates formed by simultaneous coagulation,sintering and surface growth

In this work, a new model for the simulation of nanostructured aggregates by simultaneous coagulation, sintering and surface growth is presented. Coagulation is treated as cluster–cluster agglomeration along the line connecting the center of mass of both agglomerates and is implemented using a Monte Carlo algorithm. Sintering is modeled as successive overlapping of spheres which cause reduction in the surface area based on a rate law for surface reduction. Surface growth is modeled as an increase in primary particle diameter, e.g. as a result of surface reactions. The evolved aggregates are analyzed by calculating their fractal dimension, radius of gyration, mobility diameter and mobility shape factor. It is found that the aggregates structure tends to be more compact when introducing the surface growth in shorter time comparing to the coagulation-sintering step only. Fractal dimension and the mobility shape factor of the resulting aggregates are correlated to an effective dimensionless time that combines the characteristic times of these three fundamental mechanisms. It is shown that the mobility diameter in the free molecular regime is not proportional to the radius of gyration. A power law relation that correlates the aggregates projected area and the equivalent number of primary particles is found to be in a very good agreement with estimates published in literature.     

细颗粒物凝并技术机理的研究进展

凝并技术是提高烟气中细颗粒物(PM2.5)去除效率的关键技术之一。凝并机理的研究有利于加深对细颗粒物凝并过程的理解,最大限度地提高PM2.5的凝聚速度,使PM2.5在较短的时间内团聚成大颗粒。本工作对电凝并、化学凝并和声凝并3种凝并效果显著的凝并技术机理进行概述,分别介绍了电凝并机理的核心电凝并系数方程,不同化学添加剂对颗粒的作用机制,同向运动、流体力学和声致湍流作用下的声凝并机理的发展现状。阐述了现有研究的不足,并提出在后续凝并机理的研究中,可利用高速显微摄像技术实时观测颗粒的凝并过程,对已有凝并机理进行验证及修正。同时还需考虑实际烟气成分对颗粒凝并的影响,进一步完善颗粒的凝并机理。     

后台阶气固流动的双流体大涡模拟和二阶矩两相湍流模型的验证

用基于气体Smagorinsky亚网格应力模型和颗粒动理学模型的双流体大涡模拟（LES）和统一二阶矩两相湍流模型的RANS模拟（USM-RANS）,对后台阶气固流动进行了数值模拟。瞬态模拟结果给出各向异性两相湍流结构和颗粒弥散的发展过程。LES经过统计平均得到的颗粒速度及颗粒均方根脉动速度和USM-RANS的模拟结果与实验结果的对照表明,两种模拟结果和实验结果在定量上吻合较好。因此USM模型基本上得到了LES的验证。但是在剪切流区域中,LES得到的颗粒-气体纵向脉动速度关联的峰值大于USM-RANS模拟的结果,这就表明LES和USM-RANS模拟还需要进一步验证和改进。     

导向管液固喷动床的数值模拟研究

本文以液-固两相流理论为基础,用颗粒动力学理论描述颗粒与颗粒间的碰撞,用标准湍流方程模拟液相和颗粒相的湍动,并且考虑液-固两相的相互作用,旨在探索一种工程设计和放大的新方法。对比颗粒循环速率和密相区真实液相流速的模拟结果与实验值,结果吻合较好。     

Coupled CFD–DEM of particle-laden flows in a turning flow with a moving wall

The nature of the particle–solid interactions and particle–fluid interactions in rectangular duct bend geometry with/without a moving wall is studied, taking into account particle collision, colloidal, and hydrodynamic forces, and four way coupling between the fluid flow and particles. The focus is on systems where particles and fluid phase have similar length scales, fluid Reynolds number (Re_f) ∼ 1, and particle's Stokes number (St) ∼ 1. Particles move toward the walls of the channel near the bend, and have long residence times in these regions. Buoyancy force has negligible effect on particle motion, where adhesion and drag forces lead to particle motion and agglomeration patterns. The effect of a free surface on agglomeration sites in the turning flow is elucidated.     

基于液桥效应圆筒制粒机的铁矿粉制粒机理研究

针对圆筒制粒机中存在有不同量级粒径颗粒的制粒问题，本工作对现有的液桥力计算式进行了修正，建立了相对应的离散元模型，通过实验测试与仿真相结合，探讨了修正系数对颗粒运动的影响，得到了修正系数以0.6适宜；以铁矿粉混合料的堆积角为参考，通过仿真和实验测试得到了混合料的物性参数，以此为基础，探讨了铁矿粉混合料颗粒的运动规律与团聚机理及其团聚体的分布，结果表明，团聚体颗粒的自旋速度越大、所受剪切力越小，则越有利于制粒；团聚体粒径沿圆筒的径向呈现先增大后减少的变化，且在靠近混合料表层下存在一个“高效制粒区”，在该区域团聚体的粒径最大、剪切力最小、自旋速度较大，同时建议可采用颗粒碰撞频率或能量损失作为判据来终止颗粒的团聚，以达到节能降耗的目的，所得结论可为铁矿粉圆筒制粒机的研发提供设计依据。     

Direct Numerical Simulation of Kinematics and Thermophoretic Deposition of Inhalable Particles in Turbulent Duct Flows

Three-dimensional, incompressible turbulent air-particle flows in a channel with a temperature gradient are simulated by direct numerical simulations (DNS). The calculations used the fractional projection method to directly solve the Navier-Stokes equations. For obtaining more accurate results, the Oberbeck-Boussinesq model was used for considering the convective heat transfer and applied two-way coupling between the particles and the air phase to accurately simulate flow field state. The particles motions including mutual collisions were calculated with the direct simulation Monte-Carlo method (DSMC). The particles agglomeration and deposition in the turbulent channel flow with a temperature gradient were simulated by the Dahneke model. The research focused on the effects of the Reynolds number, the temperature gradient and particle concentration which simultaneity affect particle kinematics, impacts, agglomerations, and deposition characteristics. The numerical results show that the thermophoresis dominates the particle deposition, which agrees well with the experimental data, the particle concentration determines the particle collision and agglomeration rate, the Reynolds number determines the particle distribution in the duct and the 2.5 μm particles do not obviously affect the air phase motion under comparatively low concentration referred in this research.