Shannon entropy for local and global description of mixing by Lagrangian particle tracking

If 100 dice cannot be cast simultaneously, one single die can be cast 100 times. On the basis of this simple principle, the experimental technique of positron emission particle tracking has been used to develop and implement a new methodology for quantifying the local and global mixing characteristics within a mechanically agitated fluid batch system. This Lagrangian technique uses a single positron-emitting particle as flow follower. Using a high data acquisition rate, such a tracer is continuously tracked in 3D space and time to accurately determine its trajectory over a considerable period of time. By partitioning its long trajectory, the single particle tracer can be regarded as thousands of simultaneously tracked particles which are instantaneously, locally and non-invasively injected in the mixing system at varying feed positions. A large amount of PEPT data were collected for impeller rotational speeds ranging from 100 to 500 rpm which allowed new statistical tools derived from information theory, such as Shannon entropy and uncertainty, to be implemented in the data analysis. Thus, measurements of entropy mixing indices were obtained as a function of position, time and impeller speed. The method also allowed the determination of characteristic time parameters including the macroscale mixing time which agreed very well with correlations of the dimensionless mixing time available in the mixing literature. Detailed local information is provided on minimum mixing time positions for feed and withdrawal of material, which can be used to optimise the design or operation of stirred batch mixing systems.     

Prediction of turbulent gas‐solid flow in a duct with a 90° bend using an Eulerian‐Lagrangian approach

A dilute, particle‐laden turbulent flow in a square cross‐sectioned duct with a 90° bend is modeled using a three‐dimensional Eulerian‐Lagrangian approach. Predictions are based on a second‐moment turbulence closure, with particles simulated using a Lagrangian particle tracking technique, coupled to a particle‐wall interaction algorithm and a random Fourier series method used to model particle dispersion. The performance of the model is tested for a gas‐solid flow in a horizontal‐to‐vertical duct, with predictions showing good agreement with experimental data. In particular, the consistent use of anisotropic and fully three‐dimensional approaches throughout yields predictions that result in fluctuating particle velocities in acceptable agreement with data. © 2011 American Institute of Chemical Engineers AIChE J, 2012     

Experimental and Numerical Studies of the Flow Field in a Stirred Tank Equipped with Multiple Side‐Entering Agitators

The flow field and the macro‐mixing process in a stirred tank equipped with four side‐entering agitators were investigated experimentally and numerically. Experiments were conducted using two‐dimensional particle image velocimetry (PIV) measurements to characterize the flow field at different positions in the vessel. The computational fluid dynamics (CFD) simulation was performed by the software Fluent 6.3, using the standard k‐ϵ turbulent model and the multiple reference frame together with the sliding mesh technique. The macro‐mixing process was also discussed using CFD and decolorization experiments. The effects of the tracer detection positions and some mounting parameters in the mixing system were discussed. The results show that the mixing process was dominated by the flow field pattern in the stirred tank. According to the mixing times under different conditions using CFD simulation, the mounting parameters including inclination angle, plunging length and mounting height of the shaft were optimized.     

Investigation of Motion in Stirred Media Mills

The objective of this paper is to give a closer insight into the motion of multiphase flows in a stirred media mill by means of simulation and measurement. For the investigation of motion in the stirred media mill, the grinding beads and the fluid were taken into consideration, neglecting the product particles. The turbulent two‐phase flow is modeled with an Eulerian‐Lagrangian approach. Turbulence is modeled with the k‐ϵ‐model. For measurements of the fluid and grinding beads in the grinding chamber particle‐image velocimetry and particle‐tracking velocimetry are used, respectively.     

The Two‐Phase Flow in an Axially Stirred Vessel Investigated Using Phase‐Doppler Anemometry

The phase‐Doppler technique has been used to characterize the two‐phase flow of liquid and particles in a stirred vessel agitated by a pitched blade turbine. The number of measurement locations used is considerably larger than in previous investigations and the behaviour of four different types of particles is studied. The fluid phase and particle phase flow is studied with particular emphasis on the relative velocities of the two phases. The largest slip velocities in the tank were found just beneath the impeller, and large slip velocities generally coincide with large velocity gradients. Generally, particles lag in relation to the fluid when the fluid flow is directed upwards, and vice versa, but exceptions to this are not unusual.     

The Use of Positron Emission Particle Tracking in the Study of Multiphase Stirred Tank Reactor Hydrodynamics

This paper describes the use of positron emission particle Tracking (PEPT) in the analysis of local particle and fluid velocities in solid‐liquid stirred tank reactors agitated with a Rushton turbine and an upward‐pumping pitched blade turbine. PEPT captures the full three‐dimensional characteristics of hydrodynamics and mixing in stirred vessels, allowing the analysis of the two‐phase flow fields. Furthermore, by comparing the liquid and particle velocities, the spatial and temporal variation of the relative particle‐liquid velocity can be estimated. Such information reveals considerable heterogeneity in the vessel and facilitates the evaluation of impeller design, particularly with the aim of minimizing mass transfer limitations.     

Effect of baffles on fluid flow field in stirred tank with floating particles by using PIV

PIV technique was applied to elucidate the effect of baffles at different shaft positions and different impeller off‐bottom clearances on the flow field in a stirred tank with floating particles. The investigation was carried out in a cylindrical tank with a flat base, and five different baffle configurations: standard baffles, narrow baffles with a width of 15 mm, narrow baffles with a width of 10 mm, down triangular baffles and up triangular baffles. The measurements show that down triangular baffles offers several advantages over standard baffles at C = T/3: high axial and radial velocities, relatively Low critical agitation speed and power consumption for just drawdown of 1.0 vol.% floating particles. While at C = T/2 this superiority disappears and the fluid flow field is similar to that for standard baffles. The other baffles are similar in performance except for a small difference in the critical agitation speed. An off‐centred shaft helps reduce the critical just drawdown speed and the corresponding power consumption for baffle configurations considered. With down triangular baffles, the critical power consumption to draw down the floating particles for the most eccentric shaft is about 42% of that for a centred shaft. © 2012 Canadian Society for Chemical Engineering     

Mixing dynamics in bubbling fluidized beds

Solids mixing affects thermal and concentration gradients in fluidized bed reactors and is, therefore, critical to their performance. Despite substantial effort over the past decades, understanding of solids mixing continues to be lacking because of technical limitations of diagnostics in large pilot and commercial‐scale reactors. This study is focused on investigating mixing dynamics and their dependence on operating conditions using computational fluid dynamics simulations. Toward this end, fine‐grid 3D simulations are conducted for the bubbling fluidization of three distinct Geldart B particles (1.15 mm LLDPE, 0.50 mm glass, and 0.29 mm alumina) at superficial gas velocities U/Umf = 2–4 in a pilot‐scale 50 cm diameter bed. The Two‐Fluid Model (TFM) is employed to describe the solids motion efficiently while bubbles are detected and tracked using MS3DATA. Detailed statistics of the flow‐field in and around bubbles are computed and used to describe bubble‐induced solids micromixing: solids upflow driven in the nose and wake regions while downflow along the bubble walls. Further, within these regions, the hydrodynamics are dependent only on particle and bubble characteristics, and relatively independent of the global operating conditions. Based on this finding, a predictive mechanistic, analytical model is developed which integrates bubble‐induced micromixing contributions over their size and spatial distributions to describe the gross solids circulation within the fluidized bed. Finally, it is shown that solids mixing is affected adversely in the presence of gas bypass, or throughflow, particularly in the fluidization of heavier particles. This is because of inefficient gas solids contacting as 30–50% of the superficial gas flow escapes with 2–3× shorter residence time through the bed. This is one of the first large‐scale studies where both the gas (bubble) and solids motion, and their interaction, are investigated in detail and the developed framework is useful for predicting solids mixing in large‐scale reactors as well as for analyzing mixing dynamics in complex reactive particulate systems. © 2017 American Institute of Chemical Engineers AIChE J, 63: 4316–4328, 2017     

Experimental study of hydrodynamics and thermal behavior of a pseudo‐2D spout‐fluidized bed with liquid injection

A novel nonintrusive technique is presented to investigate hydrodynamic and thermal behavior of gas–solid spout‐fluidized beds with liquid injection, by simultaneously capturing visual and infrared images. Experiments were performed in a pseudo‐2D bed with draft plates filled with glass or γ‐alumina particles to investigate the effect of liquid injection and particle properties on the flow characteristics. For the glass particles under dry and wet conditions, time‐averaged particle velocities show similar quasi‐steady‐state behavior. However, under wet conditions, lower particle velocities were observed in both spout and annulus as compared with the dry system. Whereas, γ‐alumina particles do not show considerable variation in the particle velocities under dry and wet conditions and fluidize well at higher liquid injection rates. Additionally, for the glass particles, the particle temperature significantly decreases as compared to the γ‐alumina particles. © 2015 American Institute of Chemical Engineers AIChE J, 61: 1146–1159, 2015     

搅拌槽内固体颗粒对液相速度影响的研究

采用自行研制的双电极电导探针 ,在 0 .75m× 0 .75m× 1m方形搅拌槽中 ,测定了玻璃珠 水体系中固体颗粒对液相速度的影响。实验结果表明 :加入密度大于水的固体颗粒后 ,轴流式向下泵送液体搅拌桨的表观排出流量准数增大 ,但实际排液能力并不增加 ;近壁上流区液相速度衰减 ,衰减幅度随固相浓度不同而不同 ;由于固体颗粒的加入 ,搅拌槽底部液相速度衰减 ,与近壁上流区相比衰减幅度较小。近壁上流区液相速度与搅拌转速成正比 ;不同直径的搅拌桨 ,输送功率相同时 ,近壁上流区液相速度相等。近壁上流区液相速度可作为固液悬浮搅拌槽设计的重要参数     

Non-invasive mixing time estimation in unbaffled stirred tank: An ultrasonic approach

Estimation of mixing time is an essential aspect in characterization of stirred tanks. In this work, we report a novel, non-invasive technique to estimate mixing time in an unbaffled stirred tank using a contact type ultrasonic sensor. Variation in speed of sound in stirred tank is measured by ultrasound and is used to determine the mixing time of solutions. A sensing time of 16.6 ms (~60 Hz) is achieved which leads to an estimation of the mixing process dynamics under forced vortex conditions. The method is validated against colorimetric technique using a dye. The technique is thereafter used to determine mixing time under different operating (impeller speed) and geometrical (impeller design, vessel diameter, and off-bottom clearance) conditions. Though the results presented are specific to unbaffled stirred tank, the method reported is general and can be used in any kind of stirred tank.     

利用声发射技术测量搅拌釜的淤浆悬浮高度

根据颗粒运动碰撞搅拌釜壁面产生声波的机理,结合声信号的频谱分析、小波分解和R/S分析,获得了代表颗粒运动的特征信号频段（d1、d2频段）。同时,基于声波特征信号频段能量沿搅拌釜轴向的规律性变化,提出了声波法测量搅拌釜淤浆悬浮高度的判据,即当声波特征信号频段能量或声波特征信号频段能量比出现阶跃性变化时的高度为淤浆悬浮高度。以水-玻璃珠体系为例,研究发现,无论是盘式涡轮还是桨式叶轮的搅拌桨,基于声信号测定淤浆悬浮高度的判据都能较好地得到验证,与目测法相比,其平均相对误差小于10 %,具有较高的精度。由此,获得了一种简单快捷、灵敏准确、非侵入式的搅拌釜淤浆悬浮高度测量技术,能够实现淤浆悬浮高度的实时监控。     

Numerical simulation of the transient temperature distribution inside moving particles

This work is devoted to the two‐dimensional (2D) numerical simulation of heat and fluid flow by granular mixing in a horizontally rotating kiln. The heat and fluid flow in the gas phase are solved directly using a fixed Eulerian grid. At the same time, the particle dynamics and their collisions are solved on a Lagrangian grid. The no‐slip boundary condition on the particle surface is implemented using the fictitious boundary method. The heat transfer inside the particles is calculated utilising two models: the first is the direct solution of the energy conservation equation in Lagrangian and Eulerian space and the second is the so‐called linear model, which assumes a homogeneous distribution of the temperature inside each particle. Numerical simulations showed that if the thermal diffusivity of the gas phase significantly exceeds the same parameter of the particles, the linear model over‐predicts the heating rate of the particles. The analysis of the time‐averaged flow field inside the kiln showed that in the gas phase a double vortex structure is formed which increases the convective heat transfer in the upper part of the particulate bed. The influence of the particle size, the angular velocity of the drum and the fluid on the heating rates of particles is studied and discussed.     

化工搅拌釜内流动测量技术的应用进展

搅拌釜内的物料混合是一个有限空间中的复杂非定常湍流问题,且常伴有强烈的传质、传热乃至反应过程。搅拌混合过程中影响因素多,理论分析难度大,实验获取搅拌釜内整场流动信息是其机理研究和搅拌混合设备优化设计的重要手段。本文归纳了在搅拌混合研究中传统流动测量技术的应用,分析其各自优缺点,着重探讨了新一代全场光学测速技术——粒子图像速度场仪（PIV）在搅拌混合实验中的应用,指出PIV在搅拌混合研究中具有广泛应用前景。PIV具有很高的空间分辨率和时间解析度,可以得到搅拌釜中混合流体的瞬时2D或3D速度场以及浓度场和温度场等信息,进行非定常湍流特性研究,有助于建立搅拌釜内多相流动模型,验证数值模拟结果,实现搅拌釜的优化设计,从而促进化工搅拌技术的进一步发展。