A hybridized snapshot proper orthogonal decomposition-discrete wavelet transform technique for the analysis of flow structures and their time evolution

A novel hybrid technique has been proposed in order to reveal in a greater detail the turbulent flow structures and their time evolution, and to address the issues and limitations related to the application of snapshot proper orthogonal decomposition (POD) and wavelet transform technique. The proposed hybrid technique combines the inherent abilities of the snapshot proper orthogonal decomposition and the two-dimensional discrete wavelet transform technique. The POD gives us the overall view of the most energetic flow pattern in an ensemble by decomposing the flow field into spatial and temporal modes, while two-dimensional wavelet transform gives us the localized spatial information through scale wise decomposition of the flow field. In this work, we apply the wavelet transform on the POD spatial modes. This enables us to understand the space scale structure of the flow events captured by the spatial POD modes, and the scale wise selectivity of these spatial POD modes. Thus, we are able to relate the most energetic flow events over a period of time (as obtained in spatial modes of snapshot POD) with the localized dominant scales that are contributing to it. Further, this information is utilized in the selection of those pod spatial modes that can effectively reconstruct a flow structure and its time evolution. The proposed technique has also been able to address the issues in the literature concerning the application of POD when the flow is less deterministic, as then a single POD mode may not reveal the flow structure and combination of modes is required to reconstruct it. In the present work, this hybrid methodology has been used to reveal the near wall intermittent events in channel flow: the ascending streaks and the bursts and their time evolution, the vortex tube and leading edge vortices in jet and the Taylor-Couette and irregular small chaotic vortices in Taylor-Couette flow. The planar dataset used for such an analysis has been obtained from particle image velocimetry and large eddy simulation studies.     

Study of trailing vortices and impeller jet instabilities of a flat blade impeller in small-scale reactors

The design of economically feasible and profitable production processes has driven companies toward integrated continuous manufacturing by reducing working volumes and increasing operating frequencies. Thus, the development of robust small-scale devices capable of multivariate process optimization is essential. The aim of this work is to characterize the flow developed in a ml-scale stirred tank operating at intermediate 𝑅𝑒 ~3732, and assess trailing vortex stability with respect to baffle presence and size. Velocity characteristics are computed via computational fluid dynamics (CFD) and validated experimentally for an unbaffled (UB) and two baffled configurations. Proper orthogonal decomposition (POD) is used to extract dominant spatial–temporal flow features affecting the underlying flow patterns. Results show very good agreement between simulations and experiments, while POD analysis revealed the existence of highly energetic and periodic modes, linked to interactions between impeller jet and reactor walls. These modes are responsible for an impeller jet instability, which is amplified by the presence and size of baffles.     

Time-dependent flow structures and Lagrangian mixing in Rushton-impeller baffled-tank reactor

The object of this work is to investigate the role of large-scale convective structures in promoting mixing in a stirred tank. We focus on a standard geometry (flat bottom, four-baffle reactor stirred by a six-blade Rusthon impeller) and we use an Eulerian-Lagrangian approach to investigate numerically the dispersion of fluid particles. The three-dimensional, time-dependent, fully developed flow field is calculated with a computationally efficient procedure using a RANS solver with k-ε turbulence modeling and the flow field is assessed precisely against experimental data. Then, fluid parcels are tracked in the calculated flow field. Analyzing the trajectory of fluid parcels, the segregated regions within the flow are identified and mixing indicators are calculated (mixing time, circulation length and sojour time distribution). A physical explanation is thus proposed to establish a link between large-scale mixing and complex fluid dynamics generated by the interactions of radial-discharge jet, ring vortices, and upper counter rotating vortex.     

Scale-up of continuous flow stirred tank reactors

A model of a continuous flow stirred tank reactor based on laboratory experiments successfully describes the behavior of a pilot plant reactor. This model simulates the pilot plant performance over the full range of operating conditions: at high impeller speeds where performance approaches that of a perfectly mixed reactor and at low impeller speeds where performance significantly differs from perfect mixing. The micro-mixed feed model divides the continuous flow stirred tank reactor into a small micro-mixed impeller zone and a large macro-mixer.     

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.     

Identification and characterization of flow structures in chemical process equipment using multiresolution techniques

Planar information of velocity from 2D particle image velocimetry (PIV) and large eddy simulation (LES) data have been studied using multiresolution wavelet transform (WT) formalisms, i.e., discrete and continuous WT. Identification of dominant energy containing structures with their characterization in terms of fractal spectra have been carried out for industrially important equipment exhibiting turbulent behavior. These include annular centrifugal contactor, jet loop reactor, ultrasound reactor, channel flow, stirred tank and bubble column reactor. The characterization of their dynamics based on denoising the data and studying the local energy along the WT scales show sensitive variation and this helps in identifying the size and shape of structures. A dependency is seen between mixing time and the higher order moments of length scale distribution, viz., skewness and kurtosis and a generalized correlation has been built up for important types of equipment and associated flow parameters. The correlation is not only based on the knowledge of reactor geometry and operating conditions but also on the flow structures via their statistical parameters. Wavelet transform modulus maxima (WTMM) methodology has been used to study the evolution of structures and their interaction in a reduced dimensionality by evaluating the fractal spectra. Classification studies have been carried out using principal component analysis (PCA) of the fractal spectra. The results obtained show clear classes for the six types of equipments and delineate regimes to obtain benchmark patterns of flow hydrodynamics based on PCA co-ordinates. This methodology offers a generalized way for the optimal design and operation of different types of reactors.     

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.     

Reynolds number scaling of flow in a Rushton turbine stirred tank. Part I—Mean flow, circular jet and tip vortex scaling

We consider scaling of flow within a stirred tank with increasing Reynolds number. Experimental results obtained from two different tanks of diameter 152.5 and 292.1 mm, with a Rushton turbine operating at a wide range of rotational speeds stirring the fluid, are considered. The Reynolds number ranges from 4000 to about 78,000. Phase-locked stereoscopic PIV measurements on three different vertical planes close to the impeller give phase-averaged mean flow on a cylindrical surface around the impeller. The scaling of θ- and plane-averaged radial, circumferential and axial mean velocity components is first explored. A theoretical model for the impeller-induced flow is used to extract the strength and size of the three dominant elements of the mean flow, namely the circumferential flow, the jet flow and the pairs of tip vortices. The scaling of these parameters with Reynolds number for the two different tanks is then obtained. The plane-averaged mean velocity scales with the blade tip velocity above a Reynolds number of about 15,000. However, parameters associated with the jet and tip vortices do not become Reynolds number independence until Re exceeds about 10⁵. The results for the two tanks exhibit similar Reynolds number dependence, however, a perfect collapse is not observed, suggesting a sensitive dependence of the mean flow to the finer details of the impeller.     

泰勒流反应器的流动及反应特性

利用由静态混合器、喷嘴和分气盒组成的新型布气装置在搅拌釜式反应器中诱导生成泰勒流,对反应器流动特性及反应特性进行了实验研究。结果表明,与常规搅拌釜式反应器相比,泰勒流反应器内物料流动更加接近于平推流流型,泰勒流的生成在反应器内构建出局部平推流区域,降低了物料返混程度。反应器反应性能因流动特性改变而得以增强,相同实验条件下,在泰勒流反应器中进行的蔗糖水解反应转化率比在常规搅拌釜式反应器中高出26.7%。在一定操作范围内,局部平推流区域和反应转化率均随搅拌转速或进气量的增加而增大。泰勒流反应器可简化为平推流区和全混流区并联的流动模型,推导出了反应转化率与平推流区域占反应器总体积比率之间的关联关系。     

几种框式桨搅拌槽内流动特性的比较研究

用粒子成像测速（PIV）技术对传统框式桨、传统框式组合桨和新型框式组合桨的流动特性进行研究,对比了三种框式桨在相同工况下搅拌槽内的速度、流型和湍动能。结果表明：传统框式桨搅拌槽内流体流动以水平环流为主,在框式桨上方和框式桨中间区域流体流动不充分;传统框式组合桨搅拌槽内框式桨上方由于二折叶桨的作用使得框式桨上部流体流速变大,槽内流体上下部的流动得到加强,但在框式桨中心区域依旧存在流动死区;新型框式组合桨搅拌槽内两层桨叶间的连接流得到了加强,框式桨底部和中间区域物质和能量的交换更加充分。在考察的三种框式桨中,新型框式组合桨的混合效果更好。研究结果可为新型框式组合桨应用于化工合成工业中提供参考。     

搅拌槽中酯化反应热失控的CFD模拟

热失控是化工过程中常见的安全风险之一。在间歇釜式反应器中,桨叶的机械转动可以增强流体的循环流动、湍流强度、混合程度以及传热,进而有效防范热失控。防控效果与反应器结构和搅拌桨型密切相关。针对丙酸异丙酯酯化反应,采用计算流体力学模拟研究了桨型(Rushton桨、30o PBT桨及60o PBT桨)、转动方向和挡板对釜式反应器内温度演化的影响,从流动结构方面分析了原因。基于散度的失控判据比较了三种搅拌桨抑制热失控的能力,抑制能力为Rushton桨＞30° PBTD桨＞60° PBTD桨。本研究可为搅拌反应器热失控的优化设计提供一定的理论依据。     

叶片形状对涡轮桨搅拌槽内尾涡特性的影响

Particle image velocimetry technique was used to analyze the trailing vortices and elucidate their rela-tionship with turbulence properties in a stirred tank of 0.48 m diameter,agitated by four different disc turbines,in-cluding Rushton turbine,concaved blade disk turbine,half elliptical blade disk turbine,and parabolic blade disk turbine.Phase-averaged and phase-resolved flow fields near the impeller blades were measured and the structure of trailing vortices was studied in detail.The location,size and strength of vortices were determined by the simplified λ2-criterion and the results showed that the blade shape had great effect on the trailing vortex characteristics.The larger curvature resulted in longer residence time of the vortex at the impeller tip,bigger distance between the upper and lower vortices and longer vortex life,also leads to smaller and stronger vortices.In addition,the turbulent ki-netic energy and turbulent energy dissipation in the discharge flow were determined and discussed.High turbulent kinetic energy and turbulent energy dissipation regions were located between the upper and lower vortices and moved along with them.Although restricted to single phase flow,the presented results are essential for reliable de-sign and scale-up of stirred tank with disc turbines.     

Rushton涡轮搅拌槽内流场特性及颗粒运动行为数值模拟

基于计算流体动力学（CFD）方法,采用大涡模拟（LES）和拉格朗日颗粒追踪技术计算了Rushton涡轮搅拌槽内流场特性及三种St颗粒的运动行为。平均流场（切向速度、轴向速度和径向速度）、颗粒速度及浓度分布方面与实验值的吻合度较好,验证了数值模拟的可靠性。结果表明,搅拌流场及颗粒运动均呈现循环流特性,当转速N=313r/min不变时,St=0.24的小颗粒几乎实现了均匀分布;而St=37.3的大颗粒与流体的跟随性较差,底部沉积率较高,容器顶部会出现一定的颗粒空白区。叶轮附近产生一系列的湍流涡结构,并且由于剧烈的颗粒-壁面碰撞,该位置颗粒拟温度最高;小颗粒（St=0.24）的运移主要受叶片后方尾涡的控制,均匀分布在低涡量区;而大颗粒（St=37.3）由于具有较大的惯性,运动不再由涡主导,很快被叶轮甩向边壁,穿过了尾涡所形成的高涡量区,故而叶轮对附近大颗粒的搅拌效果较差。     

改进型框式组合桨搅拌釜内流场特性

对5m³树脂反应釜及釜内改进型框式-二斜叶双层组合桨等比例缩小建立模型,基于计算流体力学（CFD）中的多重参考系法对该双层组合桨搅拌釜流场进行了模拟研究,并利用粒子图像测速（PIV）实验对模拟结果进行了验证。分析了桨叶离底间距、桨间距及组合桨安装角度的变化对流场产生的影响。随着离底间距的增大,搅拌釜下层框式桨横梁处产生往槽底的轴向流强度会逐渐减弱,不利于底部物料的混合;桨间距的增加导致两桨间对流减弱,不利于两桨间流体的混合,当桨间距与釜内径的比值为0.77时,搅拌釜内的整体流动情况较好。对上下层桨叶安装角度分别为0°、45°和90°这3种工况下的釜内流场特性研究表明,安装角度为90°时,斜叶桨产生的轴向流强度最大,此时搅拌釜内流体的混合效果最好。研究结果为改进型框式桨与二斜叶桨双层组合桨应用于树脂聚合反应实际工程提供参考。     

三叶后掠-HEDT组合桨搅拌釜内流场的模拟及实验

对应用于聚乙烯聚合反应中的三叶后掠-HEDT组合桨的搅拌釜内流场进行了模拟研究,分析组合桨的离底距C ₁、桨间距C ₂以及转速N的变化对搅拌釜内流场的影响,利用PIV实验对模拟结果进行了验证;将该组合桨与三叶后掠-六直叶圆盘涡轮组合桨进行了模拟对比研究。结果表明：当桨间距与釜内径的比为0.35时,釜内桨叶间的流体流动效果最好,该条件下能够改善搅拌釜上层流体的速度分布;当离底距与釜内径的比值为0.29时,组合桨下方出现了整体的环流,有利于釜底流体的混合;桨叶转速N=90 r/min时釜内流体速度分布均匀,同时上层HEDT桨叶产生的射流方向趋于水平。两种组合桨的对比研究表明：二者流型相近,但前者搅拌功率能够得到明显降低。研究结果可为三叶后掠-HEDT组合桨在聚乙烯聚合反应釜中的工程应用提供参考。     

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     

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。     

Numerical simulation of fluid dynamics in the stirred tank by the SSG Reynolds Stress Model

The Speziale, Sarkar and Gatski Reynolds Stress Model (SSG RSM) is utilized to simulate the fluid dynamics in a full baffled stirred tank with a Rushton turbine impeller. Four levels of grid resolutions are chosen to determine an optimised number of grids for further simulations. CFD model data in terms of the flow field, trailing vortex, and the power number are compared with published experimental results. The comparison shows that the global fluid dynamics throughout the stirred tank and the local characteristics of trailing vortices near the blade tips can be captured by the SSG RSM. The predicted mean velocity components in axial, radial and tangential direction are also in good agreement with experiment data. The power number predicted is quite close to the designed value, which demonstrates that this model can accurately calculate the power number in the stirred tank. Therefore, the simulation by using a combination of SSG RSM and MRF impeller rotational model can accurately model turbulent fluid flow in the stirred tank, and it offers an alternative method for design and optimisation of stirred tanks.     

轴流桨搅拌槽内轴向流动速度的研究

为研究轴流桨搅拌槽内轴向速度的分布,在直径为300 mm的平底圆筒搅拌槽内,采用相位多普勒粒子分析仪(PDPA)对轴流式搅拌器主流区的流场进行测量。在不同转速和离底间隙条件下,对挡板前轴向时均速度在径向和轴向的分布进行分析和研究,采用壁面射流理论,建立搅拌槽内壁面射流流动模型,揭示轴向流动特性。结果表明:轴向速度沿径向的分布具有相似性;轴向最大速度沿轴向衰减;轴向流边界沿轴向线性扩展。研究结果有助于进一步了解搅拌槽内部流动特性,为固-液悬浮操作、过程放大和搅拌设备的优化设计提供理论依据。     

Non-ideal flow in an annular photocatalytic reactor

This study deals with the modelling of non-ideal flow in a tubular photocatalytic reactor with thin layer of TiO₂ photocatalyst. The objective was to analyse different level of mixing in the photoreactor applying basic principles of chemical reaction engineering. For this purpose photocatalytic oxidation of toluene was used as the model reaction. Photocatalytic reactor was operated in two different flow modes: classic type of an annular reactor with basically ideal (plug) flow with some extent of dispersion and annular flow reactor acted as stirred tank reactor with mixing of reaction mixture accomplished by recirculation. A series of experiments with step input disturbance at the entrance of the reactor with different air flow was performed in order to achieve better understanding of the reactor hydrodynamics. Several reactor models are applied, such as one dimensional model of tubular reactor at the steady state conditions, axial dispersion model at non-stationary conditions and the model of the continuous non-stationary stirred tank reactor. Numerical methods necessary for solving model equations and parameter estimation were described.