Numerical Simulation of Gas‐Liquid Flow in a Stirred Tank with Swirl Modification

Although the standard k‐? model is most frequently used for turbulence modeling, it often leads to poor results for strongly swirling flows involved in stirred tanks and other processing devices. In this work, a swirling number, R_S, is introduced to modify the standard k‐? model. A Eulerian‐Eulerian model is employed to describe the gas‐liquid, two‐phase flow in a baffled stirred tank with a Rushton impeller. The momentum and the continuity equations are discretized using the finite difference method and solved by the SIMPLE algorithm. The inner‐outer iterative algorithm is used to account for the interaction between the rotating impeller and the static baffles. The predictions, both with and without R_S corrections, are compared with the literature data, which illustrates that the swirling modification could improve the numerical simulation of gas‐liquid turbulent flow in stirred tanks.     

Characterization of liquid‐liquid dispersions with variable viscosity by coupled computational fluid dynamics and population balances

Sustaining stable liquid‐liquid dispersion with the desired drop size still relies on experimental correlations, which do not reflect our understanding of the underlying physics and have a limited prediction capability. The complex behavior of liquid‐liquid dispersions inside a stirred tank, which is equipped with a Rushton turbine, was characterized by a combination of computational fluid dynamics and population balance equations (PBE). PBE took into account both the drop coalescence and breakup. With the increasing drop viscosity, the resistance to drop breakage also increases, which was introduced by the local criteria for drop breakup in the form of the local critical Webber number (We_c). The dependency of We_c on the drop viscosity was derived from the experimental data available in the literature. Predictions of Sauter mean diameter agree well with the experimentally measured values allowing prediction of mean drop size as a function of variable viscosity, interfacial tension, and stirring speed. © 2015 American Institute of Chemical Engineers AIChE J, 61: 2403–2414, 2015     

Absorption of Carbon Dioxide into Aqueous Colloidal Silica Solution

Abstract

On the basis of experimental data for carbon dioxide absorption into aqueous nanometer sized colloidal silica solution as a non‐Newtonian fluid, a dimensionless correlation for volumetric liquid‐side mass transfer coefficient (k_La) of CO₂ in the flat‐stirred vessel was proposed. In addition to ordinary liquid properties and operating parameters such as impeller size and speed in the vessel, Deborah number, which is defined as the product of the characteristic material times of the liquid and agitation speed in the flat‐stirred vessel and represents the viscoelastic behavior of non‐Newtonian fluid, was used to present unified expressions for k_La in Newtonian as well as non‐Newtonian liquid. The values of k_La in the aqueous colloidal silica solution were reduced due to elasticity of the solution.     

不溶液-液分散在搅拌槽内的CFD模拟

液滴平均尺寸和液滴尺寸分布是描述不溶液-液分散程度的2个重要参数,决定着两相接触面积的大小,进而决定着相间的传质、传热和化学反应速率。利用CFD方法详细研究了水-油两相在搅拌槽内的分散过程,发现叶轮转速、分散相体积分数和连续相黏度对分散效果有显著影响。当两相组成一定时,增大叶轮转速和连续相黏度均有利于两相的分散。在一定范围内,液滴平均直径与叶轮转速、分散相体积分数均为对数线性关系,相关系数高达0.999。基于个数的液滴尺寸分布在不同转速和连续相黏度条件下出现了双峰分布,而基于体积的液滴尺寸分布则始终为单峰分布。     

Gas hold‐up in stirred tank reactors

Based on a study of the gas hold‐up data for stirred tank reactor generated in the present work and the data available in the literature for large stirred tank reactors (T = 0.57 m to 2.7 m) equipped with disc turbines and pitched blade downflow turbines a correlation is presented which reliably predicts gas hold‐up data over wide range of system configurations and operating parameters. The parameter used, N/N_cd, relates gas hold‐up at impeller speed N with respect to the gas hold‐up at minimum impeller speed for complete dispersion of the gas, N_cd. It is shown that the gas hold‐up data of different workers when compared on the basis of N/N_cd, shows unanimity.     

Hydrodynamic Instabilities of Adhering Droplets Due to a Shear Flow in a Rectangular Channel

This paper reports on the hydrodynamic droplet instabilities of different sizes and viscosities due to shear forces in a rectangular channel. Water‐glycerine droplets of different volumes are investigated. A new and nonambiguous definition for the critical velocity of droplet detachment and a new mathematical correlation between the critical velocity v_crit and the fluid properties are presented. The measurements show that v_crit decreases with the droplet volume but at the same time the contour deformation increases. With increasing viscosity of the liquid droplet, i.e., higher glycerine mass fraction, the contour deformation becomes more prominent and an increase in v_crit can be observed. With respect to the fluid properties and droplet volumes, three different motion patterns are detected.     

Predicting the diameters of droplets produced in turbulent liquid–liquid dispersion

The droplet size distribution in liquid–liquid dispersions is a complex convolution of impeller speed, impeller type, fluid properties, and flow conditions. In this work, we present three a priori modeling approaches for predicting the droplet diameter distributions as a function of system operating conditions. In the first approach, called the two-fluid approach, we use high-resolution solutions to the Navier–Stokes equations to directly model the flow of each phase and the corresponding droplet breakup/coalescence events. In the second approach, based on an Eulerian–Lagrangian model, we describe the dispersed fluid as individual spheres undergoing ongoing breakup and coalescence events per user-defined interaction kernels. In the third approach, called the Eulerian–Parcel model, we model a sub-set of the droplets in the Eulerian–Lagrangian model to estimate the overall behavior of the entire droplet population. We discuss output from each model within the context of predictions from first principles turbulence theory and measured data.     

Gas recirculation rate and its influences on mass transfer in multiple impeller systems with various impeller combinations

Both the numerical and experimental approaches were used to study the effects of the gas recirculation and non‐uniform gas loading on the mass transfer rate for each impeller in a multiple impeller system. By combining the calculated gas velocity and local gas holdup, the gas recirculation rate around each impeller was estimated. The local mass transfer coefficients for systems equipped with various combinations of the Rushton turbine impeller (R) and pitched blade impeller (P) were determined by using the dynamic gassing out method. It is found that the Rushton turbine impeller has to be served as the lowest impeller in order to have a better gas dispersion and to give a higher overall K_La for a multiple impeller gas‐liquid contactor. The upper pitched blade impeller always enforces the circulating flow around the Rushton turbine impeller just beneath it and gives a higher overall average mass transfer rate. However, the system equipped with only the pitched blade impellers results in a much lower mass transfer rate than the other systems owing to the poor gas dispersion performance of the pitched blade impeller.     

Gas—liquid dispersion and mixing characteristics and heat transfer in a stirred vessel

Properties of gas—liquid dispersion and mixing of seven types of impellers were studied and compared in a stirred vessel with aeration. New correlations for the properties including critical dispersion impeller speed, dispersion regime, power consumption, gas hold-up, discharge flow number and discharge efficiency have been developed. The fluid/wall heat transfer was also studied with several types of dual impeller combinations. There is a critical impeller speed which determines how aeration changes the heat transfer coefficient. Operating conditions influence heat transfer interactively by three factors, which can be expressed by proper dimensionless variables.     

Transient aerodynamic atomization model to predict aerosol droplet size of pressurized metered dose inhalers (pMDI)

Pressurized metered dose inhalers (pMDI) produce large numbers of droplets with smaller sizes than 5 μm to treat asthma and other pulmonary diseases. The mechanism responsible for droplet generation from bulk propellant liquid is poorly understood, mainly because the small length scales and short time scales make it difficult to characterize transient spray formation events. This article describes the development and findings of a numerical atomization model to predict droplet size of pharmaceutical propellants from first principles. In this model, the velocity difference between propellant vapor and liquid phase inside spray orifice leads to formation of wave-like instabilities on the liquid surface. Two variants of the aerodynamic atomization model are presented based on assumed liquid precursor geometry: (1) cylindrical jet-shaped liquid ligaments surrounded by vapor annulus; (2) annular liquid film with vapor flow in the core. The growth of instabilities on the liquid precursor surfaces and the size of the subsequently formed droplets are predicted by numerical solutions of dispersion equations. The droplet size predictions were compared with phase doppler anemometry (PDA) data and the predictions were in good agreement with the number mean diameter D₁₀, which is representative of the respirable droplets. The temporal behavior of droplet size production was captured consistently well during the period of the first 95% of the propellant mass emission. The outcome of our modeling activities also suggests that, in addition to saturated vapor pressure of the propellant, its viscosity and surface tension are also key properties that govern pMDI droplet size.

© 2017 American Association for Aerosol Research     

Experimental Studies on Suspension of Solid Particles in a Low‐Shear Stirred Vessel

A low‐shear stirred vessel was explored. Experimental studies on the suspension of solid particles in solid‐liquid and gas‐solid‐liquid systems were conducted to examine the performance of this new reactor. The method based on the power number curve was modified to determine the critical impeller speeds required for just complete off‐bottom suspension of solids under non‐gassed (N_js) and gassed conditions (N_jsg) in this reactor, and a PC‐6A fiber‐optic probe for the measurement of solid distribution was used to complementarily validate this method. A more homogeneous flow field was gained with a draft tube installed, so that the standard deviations of average shear rate and maximal shear rate are reduced. The modified power consumption method can determine N_js and N_jsg, and the values of N_js with a draft tube are much lower than those without it. N_jsg increases slightly with increasing gas flow rate, and N_jsg with a higher solid weight fraction is larger in this lower‐shear reactor.     

Mixing Time Studies in Multiple Impeller Agitated Reactors

Mixing time studies have been carried in a 0.3m diameter and 0.9m tall vessel equipped with three impellers. Conductivity measurement technique has been used for the measurements of mixing time. Effect of the various parameters i.e. tracer density, tracer volume, speed of rotation and impeller combination on mixing time has been studied for two impeller combinations used viz. PTD‐PTD‐PTD and PTD‐PTD‐DT. A compartment model (with one fitted parameter, the exchange flow rate Q_E) with single compartment per agitation stage has been used to predict the conductivity response and the exchange coefficients are calculated from the model parameter. An attempt has been made to explain the experimental results on the basis of the liquid phase axial dispersion coefficient and cell residence time, calculated from the model parameter Q_E     

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.     

Investigations of fluid dynamics in mechanically stirred aerated slurry reactors

The fluid dynamics of stirred aerated slurry reactors with A-310® propeller, 4-blade 45° pitch turbine and 6-blade Rushton disc turbine were studied over a wide range of gas flow rates. With respect to power consumption, gas hold-up, and fluid dynamically limiting cases, viz., suspension and flooding, the Rushton disc turbine was found to be the best in stirred aerated slurry reactors. The influence of particle density, shape and mass fraction and of liquid properties on gassed critical stirrer speed, N_jsg, and of gassed power input per unit volume, P_jsg, on particle suspension and gas dispersion, were investigated. Empircal correlations in combination with that of Zwietering were established for scale-up design in three-phase slurry reactors.     

Gas-Liquid Mixing in a Grid-Disc Impeller Stirred Tank

To enhance the gas-liquid mixing performance in stirred tanks, the grid-disc impeller was designed by replacing the solid disc of the standard Rushton impeller with a grid disc. Gas-liquid hydrodynamics of the new impeller was studied by employing the Eulerian-Eulerian two-phase model coupled with the dispersed k-ε turbulence model. Rotation of the impeller was simulated with the multiple reference frame method. Flow field, gas holdup, and power consumption were investigated and compared with the standard Rushton impeller. The numerical method was validated by comparing the gas holdup with literature. The grid-disc impeller performed better than the Rushton impeller in terms of gas dispersion performance, axial pumping capacity, and energy requirement, indicating its potential for gas-liquid mixing applications.     

Particle‐resolved PIV experiments of solid‐liquid mixing in a turbulent stirred tank

Particle Image Velocimetry (PIV) experiments on turbulent solid‐liquid stirred tank flow with careful refractive index matching of the two phases have been performed. The spatial resolution of the PIV data is finer than the size of the spherical, uniformly sized solid particles, thereby providing insight in the flow around individual particles. The impeller is a down‐pumping pitch‐blade turbine. The impeller‐based Reynolds number has been fixed to Re = 10⁴. Overall solids volume fractions up to 8% have been investigated. The PIV experiments are impeller‐angle resolved, that is, conditioned on the angular position of the impeller. The two‐phase systems are in partially suspended states with an inhomogeneous distribution of solids: high solids loadings near the bottom and near the outer walls of the tank, much less solids in the bulk of the tank. The liquid velocity fields show very strong phase coupling effects with the particles increasingly attenuating the overall circulation patterns as well as the liquid velocity fluctuation levels when the solids volume fraction is increased. © 2017 American Institute of Chemical Engineers AIChE J, 63: 389–402, 2018     

The effects of impeller speed and holdup on mean drop size in a mixer settler with spiral‐type impeller

An experimental investigation has been carried out in order to analyse the drop size distributions of liquid–liquid dispersion in a single stage mixer settler extractor. In this paper, the effects of the impeller speed and the holdup on mean drops size, D₃₂, have been investigated. D₃₂ was decreased with an increase in the impeller speed. Furthermore, D₃₂ was increased with an increase in the holdup. In addition, a new and modified correlation was established based on these results. The average absolute relative deviation is 3.36%.     

Modeling of cavern formation in yield stress fluids in stirred tanks

Prediction of cavern formation in yield stress fluids in stirred tanks is of great importance for optimization. A new torus model is developed and then validated by experimental data and computational fluid dynamics simulation. Unlike existing mathematical models, the new torus model assumes that the circular center of the torus should not be outside the impeller swept region as the Reynolds number (Re) increases. Hence the cavern boundary is shaped like an apple torus rather than a horn torus. The new model also considers the cavern‐vessel interactions. At relatively high Re, the new model predicts cavern shape and size better than other models. It correctly captures the cavern outline at various Re, which verified the assumption about torus center. The new model is then used to identify the influence of rheological parameters on cavern formation, and further extended to the cavern prediction of the dual‐impeller system. © 2014 American Institute of Chemical Engineers AIChE J, 60: 3057–3070, 2014