Scaling factors in granular flow—analysis of experimental and simulations results

The relationship between the design of powder mixers and their performance is of crucial importance for many industrial processes and yet is not well understood. Here the flow patterns generated by an agitator carrying a long flat blade were compared to those generated by a single ploughshare using positron emission particle tracking and DEM. The performances of these agitators were also assessed against those of multi-blade and multi-plough agitators. The powder flows created by the different designs had some qualitative similarities. Indeed, all the agitators were shown to generate a loop of circulation below the free surface of the bed. The radial support of each mixing element was also observed to act as a separatrix for the axial flow, leading to the formation of a loop of circulation on each side of the mixing elements, thus inhibiting axial convection of material. The single-blade agitators, be the flat blade or the plough, were found to induce a pulsing regime, this feature being also observe with the multi-blade agitators but with a lesser amplitude. For moderate agitator frequencies of rotation where inertial effects are negligible, fundamental characteristics of the flow patterns extracted from power spectra of axial displacements could be scaled with the number of blade passes.     

Mixing of viscoelastic fluids with helical-ribbon agitators. I — Mixing time and flow patterns

Batch mixing of viscous fluids with helical-ribbon agitators in 2.4 liter and 13 liter vessels has been studied for agitator speeds up to 200 RPM. Seven different agitators of different dimensions were employed in this work. Mixing times were measured using a decoloration technique and circulation times were determined by the tracer bead method. In addition, velocity profiles were obtained from streak photographs using selective illumination of the vessel and PVC powder as tracer particles. It was found that the mixing times of Newtonian fluids, which agreed with previously published data, were considerably (3 to 7 times) shorter than those of the viscoelastic fluids. The mixing time was strongly affected by the fluids' elasticity; increasing as the fluid elasticity increased. The velocity profiles were qualitatively similar for all the fluids but showed decreased axial circulation and increased circumferential flow as fluid elasticity increased. However, mixing is not only a function of the axial circulation (impeller pumping rate) but also is a function of the perturbations superimposed on the main flow. A simple, first approximation model based on the impeller geometry and flow patterns is proposed to correlate the circulation capacity and mixing time data for the various geometries studied.     

用激光多普勒测速计（LDA）分析粘弹性对Metzner和Otto系数的影响

The Metzner and Otto correlation is the single practical method for incorporating non-Newtonian effects in the mixing process. In this article, the Metzner and Otto' s idea, the role of viscoelasticity on the Metzner and Otto coefficient, ks, effects of flow regime on ks and the determination of ks for Rushton turbine impeller have been studied using the direct method of the laser Doppler anemometry (LDA) velocity measurement for the case of viscoelastic liquids. The normalized mean tangential velocity profiles are independent of Rushton turbine impeller speeds. Contrary to literature findings, it is shown that the variation of local shear rate against the impeller speed is better correlated by the power equation, i.e. γ= ks' · Nb' , in the transition region, i. e. ～ 30 < Re <～ 2000. Also, a correlation between improved coefficient, ks', and the elasticity number of viscoelastic liquids is given which is very helpful in designing of the mixing of both viscoelastic and inelastic non-Newtonian fluids t     

Characterization of helical impellers by circulation times

Measurements of the circulation time during batch mixing of Newtonian and non-Newtonian fluids were used to analyse and compare the performance of six different helical-ribbon impellers and a screw impeller inside a draft coil. The distribution of circulation times obtained from two hundred repeated measurements is shown to depend markedly on the impeller geometry. Mixing time data with the helical-ribbon impellers are correlated with the mean value and the reduced standard deviation of the circulation times. Effective (rapid) mixing corresponds to a large circulation capacity and a wide distribution of the circulation times. The mixing mechanism of Newtonian fluids with the helical-ribbon impellers is qualitatively described by the Voncken model. The helical impellers' circulation capacities are not affected by the shear-thinning properties of non-Newtonian fluids. However, in highly shear-thinning fluids, the presence of important stagnant zones is responsible for much longer mixing times which consequently do not correlate with the circulation parameters. The relative efficiencies of the different impellers in Newtonian fluids are compared using a criterion based on the the total energy required to achieve a certain degree of mixing. The wide blade impeller is the most efficient of the helical-ribbon impellers but is considerably less efficient than the screw impeller in a draft coil.     

Finite element modeling of the laminar and transition flow of the Superblend dual shaft coaxial mixer on parallel computers

The macro-mixing mechanisms of the Superblend coaxial mixer consisting of a Maxblend impeller and a double helical ribbon agitator mounted on two independent coaxial shafts rotating at different speeds are numerically investigated. The simulations are based on the resolution of the Navier-Stokes equations with help of a parallel three-dimensional finite element solver exploiting the capabilities of high performance computers. To model the rotation of agitators a hybrid approach based on a novel finite element sliding mesh and fictitious domain method is used. The power consumption, the flow patterns, the shear rate distribution, the pumping capacity and the mixing time of the Superblend mixer are calculated from the simulated hydrodynamics. The simulations allow observing the flow as it evolves from deep laminar (Re=0.1) to transition (Re=520) regime. As Reynolds number increases, several recirculation zones above and below the middle of the tank are formed. It is found that operating the agitators in co-rotation mode requires less power consumption and exhibits equal or shorter mixing time than counter-rotation mode. The larger power consumption in counter-rotating mode is caused by the presence of high shear vortices generated between the two coaxial agitators. Furthermore it is shown that the shear distribution throughout the Superblend coaxial mixer operating in co-rotation mode is almost homogenous, which is highly desirable for shear sensitive products. In view of the results obtained in this work, the Superblend coaxial mixer is found as a good alternative for tough mixing applications.     

聚合物溶解槽内双搅拌器流场特性的数值模拟

搅拌设备是目前海上油田实施聚合物驱油的配注系统的关键设备之一。利用计算流体力学方法对聚合物溶解过程采用翼型上推式搅拌器KCXU和锚式搅拌器MS的内外3种组合槽内流场进行了数值模拟,获得了搅拌器槽内的流场特性、循环流量及搅拌器的功率消耗。结果表明:在第1种混合状态时,KCXU搅拌器与转动的MS搅拌器组合时的流场变得更为复杂、无序。在第2,3种混合状态时,KCXU搅拌器与正转的MS搅拌器的组合形成的流场速度较大,加强了KCXU搅拌器的流动范围,并,且形成了最大的循环流量,其功率居中。     

Structure of trickle-to-pulse flow regime transition and pulse dynamics at elevated temperature in slow-mode cyclic operation

The effects of temperature and pressure on the structure of the trickle-to-pulse flow regime transition in slow-mode cyclic operation in trickle-bed reactors were reported. The relationship between liquid holdup and liquid velocities at the trickle-to-pulse flow transition in cyclic operation, the shock wave behavior as a function of bed depth, as well as the pulsing flow regime properties were investigated for Newtonian (air-water) and non-Newtonian (air-0.25% carboxymethylcellulose (CMC)) liquids. At a given temperature, the breakthrough, plateau and decay times of the shock wave were found to decrease with bed depth. The pulse velocity and pulse frequency for pulsing flow regime both in cyclic operation and in natural pulsing (constant-throughput operation) were observed to increase with temperature. However, increasing the reactor pressure led to increased pulse frequency and decreased pulse velocity. Analysis of the transition liquid holdups for natural pulse flow and cyclic operation revealed that the liquid holdup decreased with temperature and pressure. The transition liquid holdups and superficial liquid pulse velocities in symmetric peak-base cyclic operation surpassed those in constant-throughput operation for given temperature, pressure and gas velocity, giving rise to wider trickle flow regime area in cyclic operation. The behavior of both Newtonian and power-law non-Newtonian fluids was similar regarding the effect of temperature, pressure and gas velocity.     

Mixing of newtonian and non-newtonian liquids: Screw agitator and draft coil system

Mixing efficiency and power consumption have been investigated for several Newtonian and non-Newtonian liquids in a novel system consisting of a screw agitator rotating in a draft coil. For Reynolds numbers larger than 50, the inertial forces increase the pumping capacity of the screw impeller and hence its mixing efficiency. Shear-thinning effects can be accounted for by taking the effective rate of deformation to be proportional to the impeller rotational speed. Elasticity effects could be satisfactorily correlated with the Weissenberg number. The ratio of the mixing time to the average circulation time is constant. The power number could not be correlated with the Reynolds number; however, the ratio of the power number to the circulation number is inversely proportional to the Reynolds number for Newtonian as well as for shear-thinning inelastic fluids. The power consumption for elastic fluids is much larger.     

Liquid-phase mixing in external-loop airlift bioreactors

Mixing time, circulation time and downcomer linear liquid velocity were measured in two sizes of external-loop airlift bioreactors with Newtonian and non-Newtonian fluids. The mixing time increased as a result of an increase of non-Newtonian characteristics. However, the liquid circulation time was affected only slightly by non-Newtonian flow behaviour. A semi-empirical correlation for circulation time in external-loop airlift bioreactors was proposed. The proposed correlation was compared with the present experimental results and those in the literature. Reasonable agreement was obtained between the predicted and experimental values of circulation times. The downcomer liquid velocity was almost independent of the downcomer-to-rise cross-sectional area ratio. The correlation based on the concept of an eddy diffusivity predicted downcomer liquid velocities in Newtonian and non-Newtonian fluids.     

STUDIES OF MIXING IN A CONCENTRIC TUBE AIR-LIFT REACTOR CONTAINING XANTHAN GUM BY MEANS OF AN IMPROVED FLOW FOLLOWER

The influence of a pseudoplastic non-Newtonian fluid upon the hydrodynamic performance and mixing parameters of a concentric tube air-lift fermenter has been studied using a range of dilute xanthan gum solutions (0-0.5% weight by volume). Liquid circulation times vary in a complex pattern with increasing gum concentration. At low concentrations, circulation was more; rapid due to drag reduction whilst at the highest concentrations circulation times were increased. The column voidage decreased with increasing gum concentration and bubbly flow in the riser was replaced by slug flow. For all gum concentrations the effective dispersion coefficient for a single passage around the loop was increased relative to tap water. An improved radio-pill flow follower system for hydrodynamic studies is described.     

STUDIES OF MIXING IN A CONCENTRIC TUBE AIR-LIFT REACTOR CONTAINING XANTHAN GUM BY MEANS OF AN IMPROVED FLOW FOLLOWER

The influence of a pseudoplastic non-Newtonian fluid upon the hydrodynamic performance and mixing parameters of a concentric tube air-lift fermenter has been studied using a range of dilute xanthan gum solutions (0-0.5% weight by volume). Liquid circulation times vary in a complex pattern with increasing gum concentration. At low concentrations, circulation was more; rapid due to drag reduction whilst at the highest concentrations circulation times were increased. The column voidage decreased with increasing gum concentration and bubbly flow in the riser was replaced by slug flow. For all gum concentrations the effective dispersion coefficient for a single passage around the loop was increased relative to tap water. An improved radio-pill flow follower system for hydrodynamic studies is described.     

BR生产中首釜桨型选择问题的探讨

根据合成高聚物的桨型选择的基本原则,以首釜液体不属于高粘液体为前提,提出了BR生产中首釜聚合工艺对混合的三要素。通过小试用框式桨和螺带桨的混合状态及混合时间的测定,生产装置操作数据与产品性能的分析,指出首釜由框式桨改为螺带桨是有效的。并提出了开发大尺寸轴向流较之螺带式桨相当或稍逊,而微尺寸混合较强的新桨型的建议。     

Rheological phenomena during the polymerization of styrene in a stirred tank

An experimental study of the bulk polymerization of styrene has been carried out. The rate of polymerization, molecular weight, and flow patterns around agitators as a function of conversion have been observed. The rate data are interpreted in terms of free-radical polymerization kinetics. Duerksen and Hamielec's modified termination rate constant and initiator efficiency relations are generally consistent with our data. The flow patterns were interpreted in terms of the mechanics of viscoelastic liquids and observations for nonreacting systems. Specifically, at low conversions for spheres and similar agitators, the flow patterns are dominated by centrifugal forces with fluid drawn in at the poles and expelled at the equator for spherical agitators. At higher conversions, normal stresses interact with the centrifugal forces causing segregated secondary flow regions adjacent to the sphere. At very high concentrations, normal stresses dominate, yielding Weissenberg effects.     

A new expression of the Ks factor for helical ribbon agitators

The purpose of this note is to present a new model that is able to predict an effective shear rate in a vessel equipped with helical ribbon agitators, when mixing shear‐thinning fluids. This model is based on well established results obtained for non‐Newtonian flow in cylindrical ducts.     

Numerical investigation of the mixing efficiency of the Ekato Paravisc impeller

The viscous mixing characteristics of the Ekato Paravisc are compared with those of an anchor and a double helical ribbon. The methodology is based on 3D CFD finite element-based simulations. The predictions are first validated by comparing the Newtonian and non-Newtonian power consumptions and mixing times against literature experimental data. Then, the computed 3D laminar flow patterns and several mixing performance criteria (power consumption, pumping capability, intensity of segregation, mixing time, mixing efficiency and specific energy) of the impellers are investigated. It is shown that the Paravisc mixer characteristics lie between that of the other impellers at low Reynolds number.     

Mixing time in stirred vessels:A review of experimental techniques

Mixing time is defined as the time required for achieving a certain degree of homogeneity of injected tracer in a unit operation vessel. It has been used as a key parameter for assessing the performance of a mixing system. From an experimental standpoint, several techniques have been developed for measuring the mixing time. Based on the disturbances to flow, they can be classified into two groups:non-intrusive and intrusive. However, depending on the type of data generated, they can be also classified into direct measurements and indirect measurements (Eulerian and Lagrangian). Since the techniques available for measuring mixing times in an agitated tank do not provide the same information, its choice depends on several factors, namely:accuracy, reproducibility, suitability, cost, sampling speed, type of data, and processing time. A review of the experimental techniques reported in the literature in the last 50 years for the measurement of mixing time in stirred vessels under single and gas–liquid flow conditions with Newtonian and non-Newtonian fluids in the laminar and turbulent regime is made, and a comparison between these techniques is also presented.     

Prediction of flow pattern for the co-current flow of gas and non-newtonian liquid in horizontal pipes

Previous work on delineating flow patterns for the horizontal two-phase flow of gas and Newtonian liquid is briefly described. One of the flow pattern maps has been slightly adjusted to take account of the evidence from more recent studies. It is shown that physical properties of the system have relatively little influence on flow regime. It is then established that this map is also applicable when the liquid shows shear-thinning non-Newtonian properties.     

行星轮式搅拌器及其性能分析

介绍了行星轮式搅拌器的结构特征和工作原理,并且应用fluent软件模拟其流场。对锚式、推进式及行星轮式3种搅拌器的功率准数和相对混合效率数进行了对比分析。结果表明,在相同的工作条件下,行星轮式搅拌器的功率准数与锚式、推进式搅拌器的基本相等,而行星轮式搅拌器的相对搅拌混合效率远大于锚式和推进式搅拌器的。     

Flow Compartments in Viscoelastic Fluids Using Radial Impellers in Stirred Tanks

The influence of viscoelastic flow properties on fluid dynamics using radial impellers is investigated. The use of transparent model fluids allows for the optical measurement of general flow behavior with a fluorescence dying technique. By varying viscoelastic flow properties, size of agitators and rotational frequency, the impact of these parameters on fluid dynamics is analyzed. Toroidally shaped, cavern‐like flow compartments form around the agitators in all fluids in specific rotational frequency ranges, preventing an efficient mixing. By balancing elastic with centrifugal forces, a simple model is developed with which compartment sizes can be predicted with good accuracy. The results indicate a good suitability of the elasticity number as a scale‐up criterion.     

Onset of pulsing in trickle beds: Evaluation of current tools and state-of-the-art correlation

The transition between trickle flow and pulse flow regimes in cocurrent trickle-bed reactors is not properly predicted by existing phenomenological, semi-theoretical and empirical tools. Based on the most complete flow regime transition data base (700 measurements, 30 gas–liquid systems, 18 columns diameters, 38 packing materials, high pressure conditions, coalescing, non-coalescing and pseudoplastic non-Newtonian aqueous and organic liquids), a state-of-the-art explicit correlation of trickle-to-pulse flow changeover was derived relying on neural network modeling. Robustness of the proposed correlation was verified, and the limitations of the literature correlations and models were demonstrated through systematic statistical testing over the constructed data base. The overall result was a net improvement in predicting the trickle-to-pulse flow regime transition.