Modelling of droplet breakage probabilities in an oscillatory baffled reactor

The breakage of droplets dispersed in a continuous aqueous phase determines the performance of many mixing devices and reactors that rely on effective contact between two phases, e.g. emulsion mills, liquid-liquid extraction columns, stirred tank reactors and Oscillatory Baffled Reactors. Quantitative knowledge of the mechanisms involved in the breakage provides parameters for design and prediction. In the work presented here, oil was dispersed in water in a continuous OBR, and a High Speed Camera was used to record the events of breakage of individual oil droplets and probabilities of breakage were estimated. It was confirmed that breakage was more sensitive to changes in the amplitude of oscillation than in the frequency of oscillation. A novel integral model was developed based on an analysis of the total work effected on the deforming droplet in order to interpret the results. The quantitative results from direct observation were compared to the model predictions. The model with fitted parameters was finally extrapolated to smaller diameters, in an attempt to predict the critical drop diameter for breakage.     

FCC内置式四旋分离系统内气固两相流场的数值研究

通过数值模拟的方法,采用RSM湍流模型对FCC内置式四旋分离系统内气固两相流场进行了研究.研究表明,四旋灰斗底部存在错流,不利于排料;储料罐顶部平衡管泄气有利于四旋排料,但同时增加了颗粒逃逸的概率,降低分离系统效率;分离系统内颗粒运动轨迹包括灰斗捕集、排气管逃逸及平衡管逃逸,控制颗粒在平衡管逃逸可通过在储料罐内添加锥形挡板结构实现;四旋环形空间顶部与灰斗底部锥段颗粒浓度较高,易对四旋内壁产生磨损;内置式四旋分离系统优点在于不存在催化剂跑损问题.     

Solution of the droplet breakage equation for interacting liquid-liquid dispersions: a conservative discretization approach

A conservative discretization approach for the population balance equation (PBE) with only droplet breakage describing the hydrodynamics of a continuously interacting liquid-liquid dispersion is presented. The approach is conservative in the sense that it conserves any two integral properties associated with the number droplet distribution and thus it is considered internally consistent. The discrete set of equations is laid down through applying the subdomain method where it is shown that this set of discrete equations is only internally consistent with respect to one integral property. The internal consistency is enforced by introducing a set of two auxiliary functions that are uniquely determined by matching the integral properties obtainable from the discrete set against those from the continuous PBE. However, it is shown that this conservation of integral properties is not exact for all the subdomains and hence it results in what we call the intrinsic discretization error (IDE). This IDE is not only associated with this approach, but also it is found inherently existing in the fixed-pivot (FP) technique of Kumar and Ramkrishna (Chem. Eng. Sci. 51 (1996a) 1333). The derived equations of the IDE for the present discretization approach and the FP technique generalized to continuous flow systems show that the present approach enjoys a small value of the IDE. To validate the discretization approach, two analytical solutions for the continuous PBE are presented, where good agreement is found between the predicted and the analytical solutions. To assess the reliability of the present discretization approach two experimentally validated breakage frequency functions describing droplet breakage in a turbulent continuous phase as well as two daughter droplet distributions are considered. The convergence characteristics show that the present discretization approach has an identical convergence rate as that of the FP technique, and in some cases it is superior to it. This rate of convergence is found approximately proportional to the square of the inverse of the number of subdomains.     

超短接触旋流反应器混合腔内气固混合特性的数值模拟

采用欧拉双流体模型对超短接触旋流反应器内的气固两相流场进行了数值模拟,主要研究了混合腔内固相的体积分数分布情况。计算结果表明：混合腔内的气流在切向进气的作用下得到了一定的混合加速效果,切向的高速射流有效地缩短了气固停留时间,保证短接触反应效果。通过对两种不同混合腔结构反应器的对比计算发现,在相同入口速度条件下结构2（切向进气管位于混合腔顶部）较结构1（切向进气管位于混合腔下部）气固停留时间短,由于切向气流的迅速作用,增加了混合腔内的湍动强度,使催化剂颗粒迅速有效扩散、增强气固接触效果而更有利于催化裂化反应的进行,更易实现短接触操作要求。计算结果与实验测量结果的比较表明模型能有效地描述超短接触旋流反应器内气固两相流动形态。     

CFD modelling of oxy-coal combustion in an entrained flow reactor

Oxy-fuel combustion is seen as one of the major options for CO₂ capture for both new and existing coal fired power stations. Coal is burned with a mixture of oxygen and recycled flue gas to obtain a rich CO₂ stream ready for sequestration. Computational fluid dynamics (CFD) tests for coal combustion under different O₂/CO₂ (21-35% vol O₂) atmospheres in an entrained flow reactor (EFR) were carried out using three coals of different volatile matter content. The temperature profiles, burning rates, burnout and concentration of major species, such as O₂, CO₂, CO, were predicted and compared with an air reference case. A decrease in gas temperature and burning rate was observed for 21% O₂/79% CO₂ environment in comparison to the air reference case due to the difference in gas properties between N₂ and CO₂. Experimental coal burnouts obtained in the EFR, were used to test the accuracy of the CFD model. The numerical results showed a decrease in coal burnout when N₂ was replaced by CO₂ for the same oxygen concentration (21%), but an improvement in the O₂/CO₂ atmosphere for an oxygen concentration higher than 30%. The numerical results for oxy-coal combustion were in good agreement with the experimental results.     

多喷嘴射流式分离器内气固流动特性的数值模拟

基于商用软件Fluent 6.3.26,采用雷诺应力模型及DPM离散相模型并结合理论分析,对基于喷嘴造旋的射流式分离器内两相流动特性进行了模拟计算,得到了较为全面的两相流动规律与细节.结果显示,分离器内部切向速度峰值可达160 m·s^-1,自由涡区的切向速度约为130 m·s^-1,旋流强度明显高于传统旋风单管;沿轴向下,下行流流量逐次减少,其中稳流体顶部下行流降低最为明显,下行流减少致使颗粒卷入内旋流概率增加,分离效果下降;分离器内部局部存在顶部贴壁射流、射流区二次流及灰斗口旋涡流等次级流动;分离器压降约为27.43 kPa,喷嘴区内外旋流能耗分别为4.57 kPa(21.8%)、5.76 kPa(27.6%),稳流体区内外旋流能耗分别为5.85 kPa(27.6%)、4.01 kPa(18.9%);分离器对应的切割粒径较小,约为1.6 μm,极限粒径约为10 μm,符合工业应用要求;基于所建颗粒受力模型及模拟条件下,分离空间可分离的临界粒径为1～2 μm,3 μm及以上颗粒的逃逸浓度小于 0.15 g·m^-3,满足下游烟机对气流的净化要求.     

Bubble‐separation dynamics in a planar cyclone: Experiments and CFD simulations

A planar cyclone is designed for visualizing bubbles in the cross‐section of a degassing hydrocyclone. The pressure distribution is studied through a series of experiments and Reynolds stress model simulations. The velocity distribution of the planar cyclone mostly exhibits the quasi‐forced vortex zone and boundary layer zone. The bubble dynamics are simulated using both Euler‐Euler and Euler‐Lagrange approaches, and the output is compared with the imaging results. The Euler‐Euler simulation provides more accurate predictions of the bubble trajectory. The histograms of residence time and traveling distance given by the Euler‐Lagrange approach exhibit a reasonably regular pattern. With higher values of the inlet Reynolds number, stronger forces acting on the bubbles lead to a decreased but more uniform residence time. © 2018 American Institute of Chemical Engineers AIChE J, 64: 2689–2701, 2018     

五级旋风预热器结构合理性的数值模拟

以某项目用洪堡型高分离效率的预热器结构为例,采用数值仿真技术对整套五级旋风预热器进行数值模拟,研究和分析了模拟结果中C1~C5各级旋风筒的压力场、速度场及颗粒分布场,同时定量计算出各级旋风筒的压损、截面速度及物料停留时间,以验证整套预热器结构设计的合理性。     

Numerical simulation of liquid-solid two-phase flow in a tubular loop polymerization reactor

Understanding hydrodynamics of tubular loop reactors is crucial in proper scale-up and design of these reactors. Computational fluid dynamics (CFD) models have shown promise in gaining this understanding. In this paper, a three-dimensional (3D) CFD model, using a Eulerian-Eulerian two-fluid model incorporating the kinetic theory of granular flow, was developed to describe the steady-state liquid-solid two-phase flow in a tubular loop propylene polymerization reactor composing of loop and axial flow pump. Corresponding simulations were carried out in the commercial CFD code Fluent. The entire flow field in the loop reactor was calculated by the model. The predicted pressure gradient data were found to agree well with the classical calculated data. Furthermore, the model was used to investigate the influences of the circulation flow velocity and the sold particle size on the solid hold-up. The simulation results showed that the solid hold-up has a relatively uniform distribution in the loop reactor at small particles in volume and high-circulation flow velocities.     

管型混合澄清槽内的液-液两相流的数值模拟

管型混合澄清槽在工业生产中具有广阔的应用前景。通过计算流体力学分别对管型混合澄清槽内的混合室和澄清室进行数值模拟,系统地探究了分散相液滴尺寸（d₃₂₌ 100~500 μm）、进料油水比（O∶A = 1∶1~1∶5）、入口挡板及入口位置对混合澄清效果的影响,并将模拟结果与传统方型混合澄清槽进行对比。结果表明,管型混合室内的流场分布更合理,不易形成流动死区。管型混合室内搅拌桨上方和下方形成压力更小的低压区,流体的湍动能更大,搅拌性能更好。在混合室中,降低分散相d₃₂和进料油水比能够提高混合性能。在澄清室中,提高分散相d₃₂和降低进料油水比能够提高澄清性能,入口挡板能够有效提高澄清性能。     

搅拌反应器内气液两相流的CFD研究进展

搅拌式气液反应器因其操作灵活、适用性强等优点,在过程工业中应用广泛.综述了采用计算流体力学CFD技术对搅拌反应器内气液两相流动行为的数值模拟研究.Euler-Euler双流体模型作为主要方法用于描述气液两相流动,在其基础上耦合相对简单的气泡数密度函数模型或复杂的群体平衡模型,可较为准确地预测搅拌反应器内气泡尺寸和局部气含率及其分布规律.CFD模拟结果可用以分析和评价不同搅拌桨叶、搅拌桨组合和气体分布器的气液分散性能,对气液反应器的结构优化和过程强化提供了有效手段.     

Numerical simulation of fixed bed reactor for oxidative coupling of methane over monolithic catalyst

A three-dimensional geometric modelwas set up for the oxidative coupling of methane (OCM) fixed bed reactor loaded with Na₃PO₄-Mn/SiO₂/cordierite monolithic catalyst, and an improved Stansch kinetic model was established to calculate the OCMreactions using the computational fluid dynamicsmethod and Fluent software. The simulation conditions were completely the same with the experimental conditions that the volume velocity of the reactant is 80 ml·min^-1 under standard state, the CH₄/O₂ ratio is 3 and the temperature and pressure is 800 ℃ and 1 atm, respectively. The contour of the characteristic parameters in the catalyst bed was analyzed, such as the species mass fractions, temperature, the heat flux on side wall surface, pressure, fluid density and velocity. The results showed that the calculated valuesmatchedwell with the experimental values on the conversion of CH₄ and the selectivity of products (C₂H₆, C₂H₄, CO,CO₂ and H₂) in the reactor outlet with an error range of ±4%. The mass fractions of CH₄ and O₂ decreased from 0.600 and 0.400 at the catalyst bed inlet to 0.445 and 0.120 at the outlet, where the mass fractions of C₂H₆, C₂H₄, CO and CO₂ were 0.0245, 0.0460, 0.0537 and 0.116, respectively. Due to the existence of laminar boundary layer, the mass fraction contours of each species bent upwards in the vicinity of the boundary layer. The volume of OCM reaction was changing with the proceeding of reaction, and the total moles of products were greater than reactants. The flow field in the catalyst bed maintained constant temperature and pressure. The fluid density decreased gradually from 2.28 kg·m^-3 at the inlet of the catalyst bed to 2.18 kg·m^-3 at the outlet of the catalyst bed, while the average velocity magnitude increased from 0.108 m·s^-1 to 0.120 m·s^-1.     

基于Fluent软件数值分析新型旋风筒气固两相流场

采用Fluent软件模拟一具有倾斜顶板、过渡性蜗壳、偏心内筒和倾斜出口的旋风筒的气相流场及颗粒运行轨迹。模拟过程中气体的湍流流动采用RNG k-ε数学模型,生料的颗粒运动采用颗粒随机轨道模型。结果表明：该旋风筒有强涡旋流动,中心区域明显有一气芯柱,近似为入口处速度的2倍;切向速度分布为不对称的驼峰型;蜗壳部位有径向速度分布;该结构更有利于颗粒的气固分离。     

催化裂化用短接触旋流反应器内气固滑移特性

利用欧拉-欧拉双流体模型对短接触旋流反应器分离腔内气固滑移特性进行了数值模拟,主要研究了切向气固滑移速度的分布规律,并考察了操作参数和物性参数对分离腔内切向滑移速度的影响。计算结果表明,分离腔内切向气固滑移速度沿径向呈“驼峰”分布;当气相入口速度增大或者剂气比减小时,切向气固滑移速度变小,颗粒切向速度增大,离心力增大,有利于提高气固分离效率;颗粒密度对切向滑移速度分布影响不大;颗粒粒径较大时,在排尘口易出现堵塞,不利于长周期运行;建立了截面平均切向气固滑移速度计算模型,计算值与模拟结果误差在±7.0%以内。     

CFD–DEM simulation of the gas–solid flow in a cyclone separator

In this work, a numerical study of the gas–solid flow in a gas cyclone is carried out by use of the combined discrete element method (DEM) and computational fluid dynamics (CFD) model where the motion of discrete particles phase is obtained by DEM which applies Newton’s equations of motion to every individual particle and the flow of continuum fluid by the traditional CFD which solves the Navier–Stokes equations at a computational cell scale. The model successfully captures the key flow features in a gas cyclone, such as the strands flow pattern of particles, and the decrease of pressure drop and tangential velocity after loading solids. The effect of solid loading ratio is studied and analysed in terms of gas and solid flow structures, and the particle–gas, particle–particle and particle–wall interaction forces. It is found that the gas pressure drop increases first and then decreases when solids are loaded. The reaction force of particles on gas flow is mainly in the tangential direction and directs mainly upward in the axial direction. The reaction force in the tangential direction will decelerate gas phase and the upward axial force will prevent gas phase from flowing downward in the near wall region. The intensive particle–wall collision regions mainly locate in the wall opposite to the cyclone inlet and the cone wall. Moreover, as the solid loading ratio increases, number of turns travelled by solids in a cyclone decreases especially in the apex region of the cyclone while the width of solid strands increases, the pressure drop and tangential velocity decrease, the high axial velocity region moves upwards, and the radial flow of gas phase is significantly dampened.     

动态旋风分离器数值模拟及实验研究

旋风分离器具有结构简单性能稳定等优点,但对于粒径10μm以下颗粒,分离效率较低。本文对普通旋风分离器进行改进,设计了带有旋转叶片的动态旋风分离装置,并进行了实验和数值模拟研究。数值模拟气相采用RNG k-ε模型与RSM模型相结合的算法,颗粒相与气相之间采用以欧拉-拉格朗日气固两相流耦合思想为基础的DPM模型进行模拟,主要研究了装置内部流场和颗粒分离效率与进口气速和转子转速之间的关系,并与实验中通过静电低压悬浮颗粒取样器（ELPI）获得的装置分离效率进行了对比。模拟和实验结果表明,装置切向速度场中转子部分的切向速度主要由叶片转速决定,转子外部区域的切向速度则主要由进口气速决定,且在一定的转速和进口气速下,动态旋风分离器对粒径在5μm以上的颗粒有良好的脱除效果。     

Analysis of particle trajectories in a quick-contact cyclone reactor using a discrete phase model

The Eulerian–Lagrangian approach with a discrete phase model (DPM) is used to investigate the motion trajectories of the particles at the range of 1–50 μm in the quick-contact cyclone reactor, in which the cracking reactions and the separations of catalysts and products can occur respectively and simultaneously. The results show that the typical motion trajectories of the particles in the quick-contact cyclone reactor can be described as three types: trapping, escaping and dust ring. The first typical motion of particles corresponds to the particles successfully separated from the gas flow, while the other two types can lead to more coking and erosion in the reactor. Moreover, a pre-vortex flow is observed in the mixing-reaction chamber. Additionally, the grade separation efficiency of each particle size is also obtained by counting the numbers of escaping and capturing particles. The particles with diameter larger than 10 μm are separated completely from the gas. The reactor also has a strong capability to trap the particles of small diameters (5 μm <d_p<10 μm). Both results indicate that the separation efficiency of the reactor has met the requirement as a primary separator. Compared with the experimental results, the separation efficiency in the simulated method is higher than 98% with errors of no more than 1.31%. It is illustrated that separation efficiency of the reactor can be predicted by CFD simulation.     

不同入口形式的固液分离旋流器壁面磨损研究

基于计算流体力学(CFD)软件Fluent中的颗粒随机轨道模型(DPM),对两种入口形式的固液分离旋流器的壁面磨损进行数值模拟的比较,结果表明:单入口式固液分离旋流器顶板的最大磨损位于方位角140°~210°,环形空间壁面最大磨损位于方位角120°和190°,底流口附近壁面最大磨损在周向方向180°的底流口上方1~2mm位置;双入口式旋流器的壁面磨损呈对称分布,最大磨损在底流口位置,顶板壁面最大磨损在两个入口区域,顶板外层最大磨损位于方位角80°~110°和260°~290°,环形空间壁面最大磨损位于方位角120°和300°;相同条件下,双入口式旋流器顶板和环形空间的壁面磨损小于单入口式旋流器顶板和环形空间的壁面磨损;而对于底流口附近的壁面磨损,双入口式固液分离旋流器底流口附近的壁面磨损略大。     

An investigation of the droplet size distributions in a cyclone reactor for liquid-liquid heterogeneous reactions using FBRM and PVM

A multi-element process coupled cyclone reactor for the liquid-liquid heterogeneous reaction was proposed. This paper presents the investigation of dispersed phase droplet size distributions near the wall surface using FBRM and PVM. To translate a chord length distribution (CLD) measured by the FBRM instrument into its droplet size distribution (DSD), a CLD-DSD transformation model was proposed. Moreover, the effects of operational parameters on the droplet size distributions were studied. The results show that the total inlet flow plays a decisive role on the dispersed phase droplet size distributions, while the influence of feed ratio is mainly reflected in inhibiting the probability of droplet coalescence. In comparison, the influence of overflow ratio on the droplet size distributions can be neglected.     

气升式内环流反应器流场及传质特性数值模拟

采用双流体模型和气液二相流体动力学理论建立了气升式环流反应器流体流动的数学模型,在此模型的基础上利用溶质渗透理论和各向同性湍流理论建立了局部液相体积传质系数数学模型。采用计算流体软件F luent对气升式环流反应器内气液二相流动状况进行模拟,模拟结果较好地解释了气升式环流反应器内的流动行为及传质特性。模拟计算值与文献实验值的吻合说明了模型的可行性。