Flow structure and the effect of macro-instabilities in a pitched-blade stirred tank

Turbulent flow inside a dished bottom baffled stirred tank reactor (STR) with a 45° pitched blade impeller is studied numerically and experimentally. Three different impeller rotational speeds are studied corresponding to impeller Reynolds numbers of 44,000, 88,000 and 132,000, respectively. The numerical study is based on a large-eddy simulation (LES) technique with a fixed body-fitted curvilinear mesh. The moving impeller geometries are modeled using an immersed boundary method (IBM). The experiments consist of particle image velocimeter (PIV) measurements of the flow field. The instantaneous as well as the time-averaged flow field suggests the formation of trailing vortex structures which are associated with higher levels of turbulent kinetic energy relative to the remaining flow field. Instabilities occurring at a frequency lower than the frequency of impeller rotation are identified from the time signal of the velocity components. The role of these lower frequency macro-instabilities (MI) is explored by observing changes in the three-dimensional circulation pattern within the stirred tank. The growth and dissipation of trailing edge vortices are shown to be appreciably influenced by the macro-instability. A significant amount of kinetic energy (velocity fluctuations) is observed to be associated with the low frequency dynamics of the trailing edge vortices during an MI cycle.     

On the Manifestation and nature of macroinstabilities in stirred vessels

The flow variations or macroinstabilities (MIs) occurring in a vessel stirred by a pitched blade turbine (PBT) are studied through particle image velocimetry (PIV) experiments. Proper orthogonal decomposition and fast Fourier transform techniques are applied to the PIV velocity data at one vertical and nine horizontal planes below the impeller, to identify and characterize the flow structures present in the vessel. It is shown that the PBT MI is manifested as a precessional movement around the impeller axis and an oscillation in the direction of the axial mean stream around the shaft axis. The identified flow structures are similar to those previously observed in vessels stirred by Rushton impellers and are characterized by two dominant frequencies, equal to one‐tenth and one‐fifth of the impeller rotational speed. The nature and extent of these structures and their interaction with the trailing vortices emanating from the turbine blades are discussed. © 2011 American Institute of Chemical Engineers AIChE J, 2011     

Liquid flow in impeller region of an unbaffled agitated vessel with an angularly oscillating impeller

The characteristics of a liquid flow were studied in the impeller region of an unbaffled agitated vessel with an angularly oscillating impeller whose unsteady rotation proceeds while periodically reversing its direction at a set angle. The measurement of the velocity of the liquid flow was performed by particle tracking velocimetry (PTV), abreast of that of the torque of the shaft to which the impeller was attached. When a disk turbine impeller with six flat blades was used with variations in operating conditions, such as the frequency and amplitude of impeller angular oscillation, a series of images obtained during one oscillation cycle were analyzed to characterize the internal and discharge streams inside and outside the impeller rotational region. Energy data were inferred on the basis of the circumferential and radial velocities of an internal flow. Results showed that although the total head provided to the liquid by the impeller blades is almost similar, independent of the amplitude of impeller angular oscillation, namely, the acceleration of its movement, the transformation of energy from the pressure head to the velocity head is more efficient at a larger amplitude. In addition, the discharge flow was characterized in terms of volumetric flow rates calculated from the radial and axial velocities. The operation at a smaller amplitude was shown to transform the flow more successfully from the radial direction to the upward and downward axial directions near the vessel wall.     

Liquid flow circulating within an unbaffled vessel agitated with an unsteady forward–reverse rotating impeller

Liquid‐phase mixing is a common operation, often performed in vessels using mechanically rotating impellers. To enhance axial mixing the vessels are generally equipped with baffles; however, in industries where cleaning the vessel interior is a major concern, i.e. food and pharmaceuticals, and crystallization, where baffles can disturb particle growth, unbaffled vessels are preferred. One method of agitation in unbaffled vessels is an impeller that periodically changes either the direction or rate of rotation: so‐called unsteady rotation. For use in an enhanced agitation vessel, an agitation technology using an unsteady forward–reverse rotating impeller in an unbaffled vessel was investigated. Such unsteady agitation is expected to enhance mixing. However, knowledge of the liquid flows in such an apparatus remains elusive. Thus an aim of this work was to characterize the circulation flow in such a system. Circulation by a disk turbine impeller with six flat blades was studied through examination of tracer particle trajectories. Images showing flow patterns with the forward–reverse rotating impeller resembled those obtained with a unidirectionally rotating impeller in a baffled vessel. The pattern was characterized by a circulation loop whose pathway exits from the impeller rotational region and returns to that region past the wall and bottom of the vessel. Time‐series particle tracking velocimetry (PTV) images obtained during one forward–reverse rotation of the impeller showed that the flow near the vessel wall reduced the periodic fluctuation downstream and that a flow that was almost independent of time was induced near the vessel bottom. For the flow from the bottom to the impeller, unsteadiness was provided by proximity to the impeller. Based on the intensity distribution of the unsteady flow produced by this type of forward–reverse rotating impeller within the vessel, the unsteady flow was shown to have the potential to reach the region near the vessel wall. Copyright © 2010 Society of Chemical Industry     

涡轮桨搅拌槽内流场特性的V3V实验

用体三维速度测量技术（volumetric three-component velocimetry measurements,V3V）实验研究了涡轮桨搅拌槽内桨叶附近流场。通过速度数据得到三维流场特性,确定尾涡三维结构;分析了叶片后方30°截面轴向、径向和环向速度沿径向分布规律;对比了V3V和2D-PIV（particle image velocimetry）径向和轴向速度,发现速度分布吻合较好,特别是尾涡所在的射流区。用2D-PIV方法对尾涡发展规律进行研究,发现受流体自由液面影响,尾涡轨迹向上倾斜,并与水平方向成10°,上、下尾涡运动轨迹不对称,下尾涡运动比上尾涡稍快,衰减亦较快,这与V3V实验结果一致;叶片后方60°尾涡依然清晰可见。用V3V和2D-PIV方法对桨叶附近湍流各向同性假设进行了分析,发现桨叶区和尾涡所在位置湍动能被各向同性假设近似法高估了25%~33%,桨叶区和尾涡所在位置趋向于各向异性。     

LIQUID FLOW IN IMPELLER REGION OF AN UNBAFFLED AGITATED VESSEL WITH UNSTEADILY FORWARD-REVERSE ROTATING IMPELLER

For an unbaffled agitated vessel with an unsteadily forward-reverse rotating impeller whose rotation proceeds with repeated acceleration, deceleration, and stop-reverse processes, the liquid flow in the impeller region was studied based on photographs showing path lines of tracer particles. An image series taken during one cycle of the forward-reverse rotation was analyzed to characterize the internal stream inside the impeller rotational region and the discharge stream outside its region when a disk turbine impeller with six flat blades was rotated unsteadily. Because of the unsteady flow generated inside the impeller rotational region, the velocity vector of outflow from its region fluctuated periodically with the change of the impeller rotation rate. The circumferential velocity was almost in phase with the impeller rotation rate, oscillating periodically. The radial velocity exhibited larger values in the process for the impeller from decelerating to stopping and reversal. The radial flow, whose velocity decreased downstream outside the impeller rotational region, was clarified to be transformed into upward and downward axial flows that are almost uniform in the circumferential direction throughout the region near the vessel wall.     

LIQUID FLOW IN IMPELLER REGION OF AN UNBAFFLED AGITATED VESSEL WITH UNSTEADILY FORWARD-REVERSE ROTATING IMPELLER

For an unbaffled agitated vessel with an unsteadily forward-reverse rotating impeller whose rotation proceeds with repeated acceleration, deceleration, and stop-reverse processes, the liquid flow in the impeller region was studied based on photographs showing path lines of tracer particles. An image series taken during one cycle of the forward-reverse rotation was analyzed to characterize the internal stream inside the impeller rotational region and the discharge stream outside its region when a disk turbine impeller with six flat blades was rotated unsteadily. Because of the unsteady flow generated inside the impeller rotational region, the velocity vector of outflow from its region fluctuated periodically with the change of the impeller rotation rate. The circumferential velocity was almost in phase with the impeller rotation rate, oscillating periodically. The radial velocity exhibited larger values in the process for the impeller from decelerating to stopping and reversal. The radial flow, whose velocity decreased downstream outside the impeller rotational region, was clarified to be transformed into upward and downward axial flows that are almost uniform in the circumferential direction throughout the region near the vessel wall.     

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。     

On the origin, frequency and magnitude of macro-instabilities of the flows in stirred vessels

The mean flow and turbulence fields in a fully baffled vessel stirred by a Rushton impeller at three clearances and a pitched-blade turbine at one clearance have been investigated with laser-Doppler anemometry (LDA) to characterise the macro-instabilities (MIs) present in such flows. Time-resolved velocity measurements were made and the frequency content of the velocity recordings was analysed with FFT techniques. The study aims to throw light into the frequency, magnitude, nature and origin of such flow variations, especially in view of the different findings that have been reported in the published literature.The frequency of the MIs was found to be linearly related to the rotational speed of the impeller and to be essentially independent of impeller design. A single fundamental frequency, around 0.015-0.02N (Hz), where N is the impeller rotational speed, was present for all configurations, together with harmonic frequencies, the prominence of which depended on impeller geometry and/or clearance. The LDA data and direct observations made with laser-sheet flow visualisation indicated clearly that the macro-instability stems from a precessional motion about the vessel axis, similar to the precession encountered in most swirling flows.The results show that MIs, as a mean flow motion superimposed on the flow pattern in the vessel, can result in a broadening of the measured turbulence levels by up to 25%, and a mean velocity variation of up to 0.3V_tip. The findings indicate therefore that it might be necessary and indeed it could be advantageous for improved process prediction to take MI into account in models of the flows in stirred vessels.     

Effect of the shaft eccentricity and rotational direction on the mixing characteristics in cylindrical tank reactors

Strategy of the shaft eccentricity is introduced to enhance the mixing characteristics in a flat bottomed cylindrical vessel without baffles. The mixing is ensured by a six-curved blade impel er. Three solutions which are models of food emulsions are used as working fluids. These solutions have a shear thinning behavior modeled by the power-law. The effects of fluid properties, stirring rates, impeller rotational direction and impeller eccentricity on the 3D flow fields and power consumption are investigated. Three values of impeller eccentricity are consid-ered, namely 0%, 24%and 48%of the vessel diameter. It is found that the opposite clockwise rotational direction reduces the power consumption, compared with the clockwise rotational direction. Also, the obtained results show that an impeller placed at an eccentric position between 24%and 48%of the vessel diameter and at the third of the vessel height may ensure the best mixing characteristics.     

Laser-Doppler measurements of the turbulent flow in stirred vessels to establish scaling rules

A laser-Doppler velocimeter, equipped with a frequency shift so as to eliminate directional ambiguity, has been used to measure the turbulent flow in stirred vessels with diameters of 0.12, 0.29 and 0.90 m of the same geometry. The vessels contained water and measurements were done in the impeller stream region. Scaling rules have been derived for average velocity, the periodic component, turbulent intensities and turbulence power spectra.It appears that close to the impeller the flow is dominated by the periodically fluctuating flow of the trailing vortices behind the impeller blades. The normalized mean velocity in the trailing vortices, and therefore the turbulence intensity close to the impeller, is very sensitive to impeller geometry and shows a slight increase with size of the vessel. In the greater part of the impeller stream region the power spectra have a section with a ?$\text{5}\text{2}$ slope on a log-log scale and consequently the energy of the small eddies decreases with increasing scale. At the vessel wall the vortices have decayed completely to random turbulence and the spectrum shows a ? $\text{5}\text{3}$ slope.     

Turbulent flow field in a stirred vessel agitated by an Impeller with flexible blades

In order to reveal the effect of the blades normal vibration on flow turbulence in the stirred vessel, we designed three kinds of blades: the flexible, flat‐rigid and curved‐rigid blades. The flow fields produced by the impellers with these three kinds of blades were measured by two‐dimensional particle image velocimetry. The results showed that the calculated turbulent kinetic energy (TKE) based on the pseudo‐isotropic assumption is slightly higher than that by the three fluctuating velocities for the flexible and curved‐rigid impellers, and the difference between above two calculations is smaller for the former impeller. For the flexible blades, the trailing vortices slightly move outwards in radial direction than those for the curved‐rigid blades, enhancing TKE transport from the blade to the bulk region of the vessel. For the flexible impeller, the phase‐averaged TKE differs slightly from that for the flat‐rigid impeller, but is higher than that for the curved‐rigid impeller. © 2018 American Institute of Chemical Engineers AIChE J, 64: 4148–4161, 2018     

涡轮桨搅拌槽内湍流特性的V3V实验及大涡模拟

分别用体三维速度测量技术（volumetric three-component velocimetry measurements,V3V）和大涡模拟（large eddy simulation,LES）方法对涡轮桨搅拌槽内流场进行研究,发现在完全湍流状态下,涡轮桨搅拌槽内流场的量纲1相平均速度及湍动能分布同Reynolds数无关。用V3V方法实现了Rushton桨叶附近三维流场的重构;探讨尾涡的三维结构及运动规律;分析了叶片后方30°截面轴向、径向和环向速度沿径向分布规律。用V3V实验结果对比了2D-PIV（particle image velocimetry）数据中的尾涡涡对位置和涡量,涡对位置吻合度较好,但2D-PIV中涡量较V3V小37.5%;通过大涡模拟得到完整的尾涡结构,发现在叶片上边缘后侧存在一个和尾涡形成方式相同但不成对出现的涡结构;将大涡模拟结果和2D-PIV及V3V实验结果对比发现,大涡模拟在速度分布及尾涡运动轨迹方面均同实验结果吻合较好,表明大涡模拟能较好地预测涡轮桨搅拌槽内流场。     

最大叶片式桨在假塑性流体中的搅拌流场模拟

为研究最大叶片式桨在高黏假塑性流体中的搅拌流动行为,以黄原胶溶液为研究体系,采用计算流体力学方法重点研究了釜内流体的功耗特性、速率分布、剪切速率、表观黏度分布和总体流动状况。结果表明:最大叶片式桨具有与大多数径流桨相似的"双循环"流型结构,且预测的功耗特性与实验数据一致性良好。最大叶片式桨适用于高黏假塑性流体的混合,而对于高黏牛顿流体的混合则效果不佳。釜内的剪切速率分布较宽泛,且受转速影响较大。转速可作为该桨改善黄原胶体系混合效率的重要参数之一。     

运用粒子图像测速仪研究双层Rushton桨搅拌槽内湍流特性

Particle Image Velocimetry （PIV） has been used to investigate turbulence characteristics in a 0.48 m diameter stirred vessel filled to a liquid height （ H = 1.4T ） of 0.67 m. The agitator had dual Rushton impellers of 0.19 m diameter （ D = 0.4T ）. The developed flow patterns depend on the clearance of the lower impeller above the base of the vessel, the spacing between the two impellers, and the submergence of the upper impeller below the liq- uid surface. Their combinations can generate three basic flow patterns, named, parallel, merging and diverging flows. The results of velocity measurement show that the flow characteristics in the impeller jet flow region changes very little for different positions. Average velocity, trailing vortices and shear strain rate distributions for three flow patterns were measured by using PIV technique. The characteristics of trailing vortex and its trajectory were described in detail for those three flow patterns.
Since the space-resolution of PIV can only reach the sub-grid rather than the Kolmogorov scale, a large-eddy PIV analysis has been used to estimate the distribution of the turbulent kinetic energy dissipation. Comparison of the distributions of turbulent kinetic energy and dissipation rate in merging flow shows that the highest turbulent kinetic energy and dissipation are both located in the vortex regions, but the maxima are at somewhat different lo- cations behind the blade. About 37% of the total energy is dissipated in dual impeller jet flow regions. The obtained distribution of shear strain rate for merging flow is similar to that of turbulence dissipation, with the shear strain rate around the trailing vortices much higher than in other areas.     

Large Eddy Simulation of Turbulent Flow in a Rushton Impeller Stirred Reactor with Sliding‐Deforming Mesh Methodology

The unsteady turbulent flow in a mixing vessel stirred by a Rushton impeller is predicted using the Large Eddy Simulation technique. The interaction between the moving impeller and the static baffles is accounted for explicitly through a sliding‐deforming mesh methodology, thus, eliminating approximations used to account for the effect of the moving impeller. Large‐scale structures associated with the trailing vortices are assessed via the vorticity and the turbulent kinetic energy distributions. The phase‐resolved predictions are compared with measurement data obtained by laser‐Doppler anemometry and favourable agreement is reported both for mean as well as turbulence quantities.     

双层组合桨搅拌槽内气液微观分散特性

采用双电导电极探针法对双层组合桨搅拌槽内气液相界面积特性进行了实验研究,考察了通气量、搅拌转速和桨组合对槽内相界面积的影响。结果表明:对于上层桨为上翻斜叶桨和下层桨为凹叶桨的组合,随着通气量的增加,搅拌槽内大部分区域的相界面积增大,但在槽底区域减小。随着搅拌转速的增加,在叶轮区域的相界面积增加明显,而在槽底和液面区域基本不变化。上下层桨的分散能力和气体分布器结构和操作条件密切相关。对于近壁管式气体分布器搅拌槽,在较低通气量下,上层桨对气液分散起着主要作用,而在高通气量下,下层桨的作用增强,起主要作用。带圆盘的搅拌桨对气体具有良好的阻缓作用,不同气速下均具有优异的气液分散能力。     

锚式搅拌槽中高粘弹性流体的流速分布及其功率消耗

用照相法测定了锚式搅拌槽中高粘弹性流体的流型和流速分布,另测定了搅拌功率消耗,结果发现:1.与牛顿流体相比,在低Re数下,粘弹性流体的切向速度较大,而径向速度则较小.2.转速相同时,在高剪切率区域,粘弹性流体的剪切率大于牛顿流体.由CEF方程导出功率计算式N_pRe_af_s~(1-n)=k_pf_vf_s~2[1+F_1avf_s~(m-n-3)Wi/K_s~2]用实验数据确定f_(?)和F_(1av),得到可适用于牛顿流体、假塑性流体和粘弹性流体的普适功率计算式,计算结果与实验值比较接近.     

Effect of Particle Image Velocimetry Setting Parameters on Local Velocity Measurements in an Agitated Vessel

Although they are obtained under the same conditions, results on the flow field in an agitated vessel achieved using particle image velocimetry (PIV) may vary due to differences in the PIV conditions. The influence on turbulence characteristics of the main PIV setting parameters, i.e., PIV spatial resolution, sampling frequency, and recording time, was investigated. Tests were performed with three different liquids in a developed turbulent field for a Rushton turbine impeller using two‐dimensional time‐resolved PIV. To obtain the relevant velocity gradients, a minimum recording time is needed. No effect of sampling frequency was observed if the sampling frequency was higher than approximately 17 times the impeller frequency, which is about three times the impeller blade frequency.     

Direct numerical simulation of turbulent particle dispersion in an unbaffled stirred-tank reactor

Turbulent dispersion of inertial particles in a flat-bottom stirred-tank reactor equipped with an eight-blade Rushton impeller is investigated using accurate numerical techniques (Verzicco et al., 2004, Flow in an impeller-stirred tank using an immersed-boundary method. A.I.Ch.E. Journal, 50(6), 1109-1118.). Direct Numerical Simulation of the turbulent flow field in the vessel is obtained using a second-order finite-difference scheme coded in a cylindrical reference frame, and an immersed-boundary approach is used to simulate the motion of the impeller. The flow scales are resolved explicitly down to the Kolmogorov scale. To give a comprehensive picture of the turbulence structure in the vessel, angle-resolved averages of turbulent kinetic energy, turbulent energy dissipation rate and Kolmogorov time-scales are evaluated in vertical planes aligned with the blade and mid-way between two blades. The dispersion of heavy particles of different diameter is then investigated by Lagrangian tracking. The particle-to-fluid mass loading ratio is low enough to assume one-way coupling momentum transfer between continuous and dispersed phase. Three sets of particles, characterized by different response time, are investigated and, for each set, two equal, randomly distributed swarms are initially released above and below the impeller, which is placed mid-way between top and bottom of the tank. Statistics calculated after 3 impeller revolutions are used to evaluate the evolution of particle dispersion in the flow and to quantify their preferential accumulation into specific regions of the tank.