A review of the statistical turbulence theory required extending the population balance closure models to the entire spectrum of turbulence

The models for fluid particle breakage and coalescence due to turbulence are generally limited to the inertial subrange of isotropic turbulence and infinite Reynolds numbers. A rigorous procedure for extending the fluid particle breakage and coalescence closures to the entire spectrum of isotropic turbulence and for a wider range of Reynolds numbers can be established based on statistical turbulence theory. The modeling procedure consists of a three‐dimensional (3‐D) literature model energy spectrum for the dissipation, inertial, and energy containing subranges of isotropic turbulence, and an exact literature integral relation for determining the second‐order longitudinal structure function from the 3‐D energy spectrum. A review of the requisite statistical turbulence theory and the use of the model energy spectrum is provided, because the necessary details are not easily accessible in the chemical engineering literature and misconceptions are found in the publications of the previous modeling attempts. © 2016 American Institute of Chemical Engineers AIChE J, 62: 1795–1820, 2016     

Simulation of Turbulent Emulsification in a Sonolator Mixer: Interpretation of Drop Breakage Time

The simulation of dilute emulsions in a model ACIP2 Sonolator is investigated using computational fluid dynamics and population balance methods. Two breakage frequency models are used that differ in the expression of the drop breakage time. Drop breakage modeling based on homogenous isotropic turbulence (HIT) shows poor agreement of the Sauter mean diameter when compared to the experiments; simulations with the empirical model from Alopaeus et al. yield better agreement. By perturbing the classical HIT spectrum, it is shown that the breakage time in the empirical model corresponds to a non‐isotropic energy spectrum. Such spectra have been observed in the non‐isotropic near field in a model A Sonolator, which provides a plausible explanation of why the empirical model performs better than the HIT‐based model.     

A model for drop and bubble breakup frequency based on turbulence spectra

In this article, a new Eulerian model for breakup frequency of drops induced by inertial stress in homogeneous isotropic turbulence is developed for moderately viscous fluids, accounting for the finite response time of drops to deform. The dynamics of drop shape in a turbulent flow is described by a linear damped oscillator forced by the instantaneous turbulent fluctuations at the drop scale. The criterion for breakup is based on a maximum value of drop deformation, in contrast with the usual critical Weber criterion. The breakup frequency is then modeled as a function of the power spectrum of Weber number (or velocity square), based on the theory of oscillators forced by a random signal, which can be related to classical statistical quantities, such as dissipation rate and velocity variance. Moreover, the effect of viscosities of both phases is included in the breakup frequency model without resorting to any additional parameter. © 2018 American Institute of Chemical Engineers AIChE J, 65: 347–359, 2019     

湍流分散体系中液滴破碎频率模型的黏性修正

在分析研究分散相黏度对液滴变形和破碎影响的基础上,提出了一个改进的液滴破碎频率模型并拓展了液滴破碎判据标准.同时通过Monte Carlo模拟的随机方法,得到了湍流搅拌槽中液-液分散体系的液滴直径分布和Sauter平均直径d₃₂.通过与文献中关于d₃₂的实验结果比较发现,该模型预测的Sauter平均直径更接近实验值,对于黏性分散相改进的液滴破碎频率模型要优于Coulaloglou和Tavlarides提出的模型.计算结果表明对于黏性分散相液滴,其黏度限制了液滴变形,使得液滴破碎频率被大大减少, 液滴直径明显增加,液滴直径分布向右偏移.     

基于多变量摄动的超临界CO2干气密封动态特性

超临界CO₂压缩机进口端干气密封工况处于临界点附近,强非线性物性及高Reynolds数流动使其密封特性异于常规介质干气密封。在综合考虑四种实际流体效应的稳态膜压求解模型基础上,基于摄动法推导了包括膜压、密度、黏度、Reynolds数、湍流系数和惯性系数在内的多变量摄动干气密封动特性数值模型。对比分析了超临界CO₂和N₂干气密封的动态特性,研究了不同频率比下各实际流体效应和变量摄动形式对超临界CO₂干气密封动特性系数的影响规律,获得了不同条件下动态特性的关键影响因素。结果表明：高频下超临界CO₂干气密封的刚度和阻尼系数较N₂干气密封降幅超过50%,湍流效应和实际气体效应对干气密封动态特性影响显著,低频下采用经典变量摄动和忽略湍流系数摄动会使动特性系数计算偏差很大,而高频下经典变量摄动模型对刚度系数的预测精度可接受。     

Drop break-up in intermittent turbulence: Maximum stable and transient sizes of drops

A multifractal method describing the fine-scale structure of turbulence, including its intermittency, is applied to derive the drop breakage functions for drops whose diameter falls within the inertial subrange of turbulence, including effects of the viscosity of the dispersed phase. The model predicts well the transient drop size distributions of dispersions undergoing breakage at long stirring times. Concepts of quasi-stable and asymptotically stable drop sizes are presented and discussed in relation to the exponent on the Weber number. The functions for drop break-up in the viscous subrange are proposed and discussed.     

气液两相绕流错列管束升力特性的数值模拟

采用混合物模型和RNGk-c紊流模型对气液两相绕流错列圆柱管束升力特性进行了数值模拟。重点研究了节距比、含气率和雷诺数对升力功率谱的影响。结果表明：节距比增大,功率谱峰值增加,节距比为1．5时中间管排出现“双稳态现象”;含气率增加,功率谱峰值减小直至没有峰值,涡街消失;雷诺数增加,功率谱峰值减小;下游圆柱功率谱峰值较中间管排峰值大。模拟结果与实验结果基本吻合,旋涡脱落频率误差为1．03％。     

Comparative efficiency of shear,elongation and turbulent droplet breakup mechanisms: Review and application

The study of phase dispersion of two immiscible fluids in different flows requires identifying the relevant breakup mechanisms. We propose here a detailed investigation of droplet breakup in a multifunctional exchanger-reactor of the vortex generator type in which transfer intensification is due to longitudinal vortical structures. We compare the efficiency of the mean gradients and turbulent mechanisms in droplet breakup in this industrial reactor. This efficiency is essentially characterized by the resulting distribution of droplet diameters. Then, the roles of the mean flow and the turbulent field, intensity, energy spectrum, and turbulence scales are examined in relation to the liquid/liquid dispersion in order to explore the governing mechanisms of drop breakup. In the complex flow considered here – nonhomogeneous and anisotropic turbulence at moderate Reynolds numbers (<15,000) – with weak turbulence intensity (about 10%), it can be demonstrated that turbulent breakup mechanisms largely dominate mean flow effects; elongation and shear effects are shown to have minor effects on the breakup mechanisms. Moreover, the global characteristic scales of the flow are not the relevant parameters in predicting the final size of the emulsion, but instead the Kolmogorov microscale, implying that the residence time in the reactor is not a limiting factor. Hence, the local dissipation rate governs the performance of the actual multifunctional reactor. This study provides some insight in the design and scaling-up of multiphase reactors.     

Pressure drop in pulsed extraction columns with internals of discs and doughnuts

A study on the pressure drop in pulsed extraction columns with internals of immobile discs and rings, usually called Discs and Doughnuts Columns (DDC) is carried out. The local pressure at a desired level of the column is obtained by resolving of turbulent flow model based on Reynolds equations coupled with k–? model of turbulence. Consequently, the pressure drop for a column stage or for a unit of column length is determined. The results are used for development of correlations for determination of pressure drop as a function of plate free area, interplate distance and pulsation parameters – amplitude and frequency. Good correspondence to experimental data is observed. The developed quantitative relations are useful for non-experimental numerical optimization of stage geometry in view of lesser energy consumption.     

Drop breakage and coalescence in the toluene/water dispersions with dissolved surface active polymers PVA 88% and 98%

The influence of two PVAs of the same molecular weight (13,000–23,000) and different degree of hydrolysis equal to 88% and 98% on breakage and coalescence of toluene droplets in the liquid/liquid dispersion were considered for PVA concentration range 0.001–0.01%. Analysis of experimental results shows that drop coalescence is significant only in the system containing 0.001% PVA. Drop coalescence for polymer concentration range 0.002–0.01% is strongly limited. Therefore, population balance was solved using breakage and coalescence expressions with assumed partially mobile drop interfaces for the lowest PVA concentration. For c ≥ 0.002% drop size distributions were properly predicted using only breakage model. Multifractal formalism was used to take into account intermittent character of turbulence and explain drop behavior. Larger drop size reduction by PVA of lower degree of hydrolysis observed experimentally was confirmed by the model.     

AlCl3-异丙醇络合催化1-十二碳烯烃与环己烯共聚反应的研究

聚烯烃润滑油是重要的合成润滑油之一。采用AlCl3作催化剂对环己烯与1-十二烯烃的共聚反应进行了研究。考察了催化剂AlCl3的用量、n(异丙醇)∶n(AlCl3)、反应温度和反应时间对产品收率的影响。确定了最佳工艺条件,即x(AlCl3)=4%,n(异丙醇)∶n(AlCl3)=0.5,反应温度50～60℃,反应时间6h。在最佳工艺条件下,调节环己烯与1-十二碳烯的混合比例进行了实验,研究了产品的物化性能。实验结果表明:采用n(1-十二烯烃)∶n(环已烯)=2∶1时,可以合成100℃粘度为6.10mm2/s,粘度指数为157,凝点为-35℃的聚烯烃合成油,收率为86%。具有粘度低、凝点低、粘度指数高的显著特点,是高质量的聚烯烃合成油。     

Effect of Sub-Grid Scales on Large Eddy Simulation of Particle Deposition in a Turbulent Channel Flow

Large-eddy simulations (LES) of particle transport and deposition in turbulent channel flow were presented. Particular attention was given to the effect of subgrid scales on particle dispersion and deposition processes. A computational scheme for simulating the effect of subgrid scales (SGS) turbulence fluctuation on particle motion was developed and tested. Large-eddy simulation of Navier-Stokes equations using a finite volume method was used for finding instantaneous filtered fluid velocity fields of the continuous phase in the channel. Selective structure function model was used to account for the subgrid-scale Reynolds stresses. It was shown that the LES was capable of capturing the turbulence near wall coherent eddy structures.

The Lagrangian particle tracking approach was used and the transport and deposition of particles in the channel were analyzed. The drag, lift, Brownian, and gravity forces were included in the particle equation of motion. The Brownian force was simulated using a white noise stochastic process model. Effects of SGS of turbulence fluctuations on deposition rate of different size particles were studied. It was shown that the inclusion of the SGS turbulence fluctuations improves the model predictions for particle deposition rate especially for small particles. Effect of gravity on particle deposition was also investigated and it was shown that the gravity force in the stream wise direction increases the deposition rate of large particles.     

UTILIZATION OF POPULATION BALANCES IN SIMULATION OF LIQUID-LIQUID SYSTEMS IN MIXED TANKS

A simulation model has been developed to model drop populations in a mixed tank. A multiblock mixed tank model has been used with the drop population balance equations developed in the literature. The drop breakage and coalescence functions used in the population balance model take into account the local turbulent energy dissipation values. The drop breakage and coalescence function parameters are fitted against drop size measurements from dense liquid-liquid dispersions, which were assumed fully turbulent. Since the local turbulence and flow values of a mixed tank are used in the present model, the fundamental breakage and coalescence phenomena can be taken into closer examination. Furthermore, the present model is capable of predicting inhomogeneities occurring in a mixed tank. It is also considered as an improved tool for process scale-up, compared to the simple vessel-averaged population balance approach, or use of correlations of dimensionless numbers only. The present model can use two sources of data for fitting parameters in the drop rate functions. One is the transient data of the measured drop size distribution as the impeller speed is changed. The other is the time-averaged data measured at different locations of the mixed tank. Different flow regions can be chosen from direct measurements or from the CFD simulations in a straightforward manner. CFD flow simulation results can be used when no experimentally obtained flow conditions are available. This is especially useful for nonstandard vessels, such as reactors containing cooling coils.     

Computational Investigation of an Industrial Cyclone Separator with Helical‐Roof Inlet

An industrial cyclone separator with helical‐roof inlet TsN‐11 has been numerically investigated as to pressure and flow field, pressure drop, fractional efficiency, and particle trajectories inside the cyclone. The turbulence was modeled with Reynolds stresses and large eddy simulations (LES) based on three different subgrid‐scales (SGS). The results with the different setups were compared to experimental data from previous studies. For a proper calculation of the flow field, LES combined with a dynamic SGS model was used for predicting cyclone performance. Individual particles were tracked through the unsteady flow field using the Lagrangian approach. The results of the numerical calculations of the tangential and axial velocity, pressure drop, and cut size are in good agreement with experimental measurements.     

液体横掠热圆柱体时旋涡脱落的频谱分析

引言 流体(液体)横掠柱体时的工况是许多工业设备特别是换热器工作的主要工况.在这种工况下,流体横掠柱体的旋涡脱落特性、流动参数的分布、柱体受力及流动阻力等均是设备运行和设计的关键问题.而这些问题均源自流体横掠柱体时旋涡的脱落,因此,对流体横掠柱体旋涡脱落特性特别是其频谱特性的研究,对设备的高效节能、安全和稳定运行有重要意义.     

液-液水力旋流器中的液滴破碎

在总结前人研究成果的基础上,分析了液-液水力旋流嚣中液滴破碎产生的原因,指出流场的湍流特性是产生液滴破碎的主要原因。对水力旋流器中的湍流度、雷诺切应力及颗粒的湍动能进行了分析,给出了水力旋流器中液滴破碎可能性较大的几个部位,并对旋流器边壁液滴破碎的可能性进行了讨论。分析了水力旋流器中液滴破碎的机理,阐明了液滴破碎判据——临界Weber数的表达式,并对理想球形液滴的破碎进行了分析。     

Development of a multi-scale simulation method for design of novel multiphase reactors

In this paper a multi-scale simulation method for modelling dispersions in a novel multiphase reactor is presented. This novel reactor is a continuous reactor which consists of repeated identical small mixing elements. The reactor is excellent for studying the effect of turbulence on drop size distributions since turbulence is continuously produced and dissipated along the reactor. Furthermore the energy dissipation within each element is very homogeneous. In addition it allows optical access at all positions along the reactor.Simulations were performed for a wide range of turbulence intensities for different dispersed phase hold-up. Each simulation was validated with measurements of the size distribution along the reactor. Good quantitative agreement was obtained at low hold-up in terms of prediction of the breakage rates and prediction of the size distributions. At higher hold-up the model gave reasonable predictions at low turbulence intensity however too large drops were predicted at high turbulence intensity. This can be a result of turbulence modulation and shows that reliable turbulence models for multiphase flows are necessary in this simulation method. The results show that physical models describing breakup and coalescence combined with CFD provide a good tool for efficient development and optimisation of novel multiphase reactors.     

Kenics型静态混合器内分散相液滴破碎和聚结过程的CFD-PBM数值模拟

采用CFD-PBM耦合方法对Kenics型静态混合器内分散相油滴破碎及聚并行为进行数值模拟研究,分析了雷诺数、混合元件数、元件长径比等参数对分散相液滴粒径的影响,揭示了分散相在Kenics静态混合器内流动过程中液滴粒径的演化规律。结果表明,随雷诺数增大,分散相液滴出口粒径不断减小,并出现临界趋势;静态混合器的前几个元件段粒径下降较快,雷诺数越高,油滴破碎达到稳定粒径所需的流动距离越短,而元件数仅在较低雷诺数下对粒径有明显影响;相同雷诺数下元件的长径比越小,其出口粒径越小,且达到稳定所需流动距离越短。