Proper Orthogonal Decomposition and Statistical Analysis of 2D Confined Impinging Jets Chaotic Flow

Proper orthogonal decomposition (POD) is shown to be a statistical operation that identifies the main characteristics of chaotic flows and separates them into a few modes. The dynamic chaotic flow is obtained from two‐dimensional (2D) computational fluid dynamics simulations, for different Reynolds numbers, of a confined impinging jets mixer. POD enables reconstruction of the dynamic flow from a few modes that are related to coherent flow structures. The POD flow reconstruction enables a large compression of the flow data set. The decomposition of the flow field into orthogonal modes related to coherent structures provides direct insight into the mixing dynamics and scales which are not accessible from flow dynamics statistic quantities, which were introduced in the context of turbulence and are here applied to chaotic flow.     

A model viscoelastic fluid

Shear stress and first normal stress difference data are presented for materials which exhibit a constant viscosity and yet at the same time exhibit elasticity levels of the same order as polymer melts. Flow pattern observations in circular die entry flows in conjunction with independent shear and normal stress measurement strongly suggest that these fluids would make excellent model fluids for melt studies. Studies in which the influence of elasticity in the absence of shear thinning and fluid inertia can easily be made. Furthermore it is clearly shown that a realistic solution to the die entry flow problem is not obtained using second order flow theory. In the second order region the secondary cell is observed to be almost identical in size to the cell observed for an inelastic Newtonian fluid in creeping flow. Marked growth in the secondary cell as a function of elasticity is not observed until the shear rates exceed the region of second order behavior. This growth in cell size as a result of elasticity is followed at higher shear rates by a spiraling flow instability like that observed for some polymer melts.     

Mixing of Shear‐Thinning Fluids with Dual Off‐Centred Impellers

Mixing times for inelastic shear‐thinning fluids in stirred tanks have been experimentally investigated using a combination of two off‐centred impellers operating in both co‐ and counter‐rotating modes. A colour‐discolouration technique based on fast acid‐base reaction was used for the determination of the mixing times as well as to reveal the possible presence of caverns and dead regions. A statistical plan of experiments allowed determining the effects of the impeller position, the rotational speed, the flow behaviour index, the impeller type and their mutual interactions. A stronger influence of the impeller position on mixing times was observed for both rotating modes with fluids exhibiting pronounced shear‐thinning. It was also found that segregated regions could be readily destroyed by dual off‐centred impellers as compared with the single centred impeller configuration. Mixed flow impellers were shown to be less efficient in terms of mixing times than radial flow impellers. Results obtained under the best operating conditions were compared to steady stirring experiments showing the potential and drawbacks of the proposed scenarios.     

Velocity profiles and frictional pressure drop for shear thinning materials in lid-driven cavities with fully developed axial flow

A finite element numerical study has been carried out on the isothermal flow of power law fluids in lid-driven cavities with axial throughflow. The effects of the tangential flow Reynolds number (Re_U), axial flow Reynolds number (Re_W), cavity aspect ratio and shear thinning property of the fluids on tangential and axial velocity distributions and the frictional pressure drop are studied. Where comparison is possible, very good agreement is found between current numerical results and published asymptotic and numerical results. For shear thinning materials in long thin cavities in the tangential flow dominated flow regime, the numerical results show that the frictional pressure drop lies between two extreme conditions, namely the results for duct flow and analytical results from lubrication theory. For shear thinning materials in a lid-driven cavity, the interaction between the tangential flow and axial flow is very complex because the flow is dependent on the flow Reynolds numbers and the ratio of the average axial velocity and the lid velocity. For both Newtonian and shear thinning fluids, the axial velocity peak is shifted and the frictional pressure drop is increased with increasing tangential flow Reynolds number. The results are highly relevant to industrial devices such as screw extruders and scraped surface heat exchangers.     

Experimental and Numerical Analysis of the Viscous Fingering Instability of Shear‐Thinning Fluids

Miscible flow displacements in a rectilinear Hele‐Shaw cell of Newtonian as well as rheologically well‐characterized shear‐thinning fluids are examined through experimental measurements and numerical modelling. Water is used as a displacing fluid while the displaced fluid consists of either a reference Newtonian glycerol solution or shear‐thinning solutions of Alcoflood? polymers of different molecular weights. The experimental measurements revealed that the shear‐thinning behaviour of the non‐Newtonian solutions resulted in more complex instability patterns and new finger structures not previously observed in the case of Newtonian displacements are identified and characterized. An analysis of the effects of the rheological behaviour of the shear‐thinning fluids on instability characteristics such as the finger width and finger tip velocity is presented. Numerical simulations using a pseudo‐spectral method are conducted and allowed to compare the predictions of the mathematical model based on an effective Darcy's law with the experimental measurements.     

黏弹性表面活性剂溶液中颗粒沉降特性研究

黏弹性表面活性剂溶液悬浮颗粒流广泛存在于自然界和工业生产中,黏弹性表面活性剂溶液的非线性流变性质及应力松弛效应对其中颗粒沉降有着显著影响。采用FENE-P和Giesekus黏弹性本构模型对表面活性剂溶液中颗粒沉降特性进行研究,发现两种本构模型不仅表现出剪切稀化,而且出现拉伸硬化。颗粒在沉降初期的不稳定性主要是由溶液自身的弹性效应引起,弹性效应越强,颗粒沉降速度不稳定性越强,而剪切稀化效应会减弱颗粒沉降速度的不稳定。颗粒沉降过程中在其尾部形成一个“负尾迹”,随着剪切稀化和拉伸硬化效应增强,负尾迹区增大,弹性效应增加,负尾迹增强,负尾迹区流体内部反向速度分布导致的表面活性剂溶液中微观胶束的拉伸断裂和重构可能是引起颗粒沉降速度持续波动的原因。     

Numerical simulation of viscous fingering of shear‐thinning fluids

The viscous fingering instability of miscible shear‐thinning fluids has been examined using a pseudo‐spectral numerical technique based on the Hartley transform. The instability was studied for a flow in a rectilinear Hele‐Shaw cell, and the shear‐thinning character of the fluids has been modelied using the Carreau equation. New mechanisms of viscous fingering not previously observed in the case of similar Newtonian flow displacements have been identified. These mechanisms, which are reminiscent of the fractal patterns observed in experimental studies, were interpreted in terms of the velocity‐dependent mobility of the flow.     

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.     

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.     

Influence of carrier fluid on the electrokinetic and rheological properties of shear thickening fluids

This paper presents a study on the influence of hydroxyl groups and oxygen atoms together with chain length and branching of carrier fluid on the rheological and electrokinetic properties of shear thickening fluid (STF). An STF is non-Newtonian fluid behaviour in which the increase of viscosity increases with the applied shear rate. Ethylene glycol, triethylene glycol, 1,3-propanediol, glycerin, poly(propylene glycol) of different molecular weight and poly(propylene glycol) triol were used as the carrier fluids (dispersants). Silica powder with an average particle size of 100 nm was used as the solid phase. Zeta potential, particle size distribution (by DLS technique), steady-state and dynamic rheological measurements were conducted. Experimental results indicate that a different amount of hydroxyl groups and oxygen atoms together with chain length and branching of carrier fluids have a significant influence on the intermolecular interactions thereby and on the rheological properties of suspensions. Depending on the composition, it is possible to control rheological properties. The use of a suitable carrier fluid allows the required pattern flow to be obtained, from Newtonian through shear thinning to shear thickening, given specific shear conditions.     

非牛顿流体中气泡群传质的研究

CO2气泡群在液相中的传质在化工过程中广泛存在.对CO2气泡群在3种不同流体(牛顿流体、非弹性剪切变稀流体和黏弹性剪切变稀流体)中的气液传质过程进行了研究.利用CO2探针测定了不同操作条件下CO2的体积传质系数,考察了液相浓度,气体流量以及流变性质对体积传质系数的影响.结果表明:在3种流体中,体积传质系数均随气体流量的...     

THE FLOW OF MICROEMULSIONS THROUGH PACKED BEDS AND CAPILLARY TUBES

The flow behavior of water-in-oil microemulsions through beds packed with glass spheres was studied experimentally. The microemulsions used in this study exhibited a shear thinning viscosity described by a simple power law model. The flow of the microemulsions was accompanied by significant apparent slip effects, quantified by an effective slip velocity. The effective slip velocity increased with increasing surfactant concentration, but it differed in magnitude for the packed bed and the capillary tube flows.

In the absence of apparent slip effects, the capillary-power law (CPL) model predicted the superficial velocities in the packed beds with an average error of less than 6%. This provides a direct verification of the applicability of the capillary-power law model to inelastic shear thinning fluids in the absence of “anomalous” wall effects.     

Analysis of gas holdup in bubble columns with non-Newtonian fluid using electrical resistance tomography and dynamic gas disengagement technique

This paper presents an experimental analysis of the influence of the liquid rheology on the gas flow pattern in a bubble column reactor. Aqueous solutions of xanthan are selected as an example of non-Newtonian shear thinning fluid. Averaged gas holdup is determined by two experimental techniques: parietal pressure probes and electrical resistance tomography (ERT). ERT is also used to provide 2D images of the gas phase distribution in a column cross-section. Bubble size distributions are evaluated by a gas disengagement technique using the parietal pressure probes. All these techniques clearly show the gas flow pattern is different in Newtonian and non-Newtonian fluids. Gas holdup values decrease when increasing the liquid viscosity and reach a minimum or a plateau. Homogeneous flow regime, observed in water at low gas velocities, tends to disappear when viscosity increases. This evolution is visualized by a much less isotropic distribution of the gas phase within cross-section of the column and by the appearance of much larger bubbles due to an increased coalescence phenomenon.     

基于实验数据的湍流扩散POD模态分析

采用粒子成像测速（PIV）和激光诱导荧光（LIF）技术同时测量了水平通道中湍流扩散过程的流速和荧光剂浓度的瞬时分布,并利用实验数据,通过本征正交分解（POD）模态分析方法,实现了湍流条件下荧光剂扩散过程中浓度分布的数值重构。该方法应用于瞬时浓度分布的特征分析中,得到了瞬时分布的各阶模态,并分析各阶模态空间分布特征及其所含能量。结果表明,浓度分布在距离荧光剂入口较近的区域具有较强的周期性,且低阶POD模态能量占主导地位。应用POD分析得到的模态可以较准确地重构距离荧光剂入口较近区域的浓度分布的基本特征,相对误差主要集中于距离荧光剂入口较远的区域,表明本文提出的基于POD模态分析的湍流条件下浓度场的数值重构更适用于周期性较强的系统,为预测未知时刻的湍流扩散浓度分布提供了基础。     

CFD investigation of the pipe transport of coarse solids in laminar power law fluids

A numerical parametric study of the laminar pipe transport of coarse particles in non-Newtonian carrier fluids of the power law type has been conducted using an Eulerian-Eulerian computational fluid dynamics (CFD) model. The predicted flow fields have been successfully validated by experimental measurements of particle velocity profiles obtained using a positron emission particle tracking technique, whilst solid-liquid pressure drop has been validated using relevant correlations gleaned from the literature. The study is concerned with nearly-neutrally buoyant particles flowing in a horizontal or vertical pipe. The effects of various parameters on the flow properties of such mixtures have been investigated over a wide range of conditions. The variables studied are: particle diameter (2-9 mm), mean solids concentration (5-40% v/v), mean mixture velocity (25-125 mm s⁻¹), and rheological properties of the carrier fluid (k=0.15-20 Pa sⁿ; n=0.6-0.9). A few additional runs have been conducted for shear thickening fluids, i.e. n>1. Whilst the effects of varying the power law parameters and the mixture flowrate for shear thinning fluids are relatively small over the range of values considered, particle size and solids concentration have a significant bearing on the flow regime, the uniformity of the normalised particle radial distribution and of the normalised velocity profiles of both phases, and the magnitude of the solid-liquid pressure drop. The maximum particle velocity is always significantly less than twice the mean flow velocity for shear thinning fluids, but it can exceed this value in shear thickening fluids. In vertical down-flow, particles are uniformly distributed over the pipe cross-section, and particle diameter and concentration have little effect on the normalised velocity and concentration profiles. Pressure drop, however, is greatly influenced by particle concentration.     

Influence of Rheological Behavior of Purely Viscous Fluids on Analytical Residence Time Distribution in Straight Tubes

In an effort to better understand the homogeneity of heat treatment of foodstuffs in holding tubes, the cumulative residence time distribution function is derived for a Herschel‐Bulkley fluid from fully developed laminar flow in a straight circular tube under isothermal conditions when diffusional effects are negligible. The proposed analytical solution can be reduced to solutions for Newtonian, shear‐thinning, dilatant, Bingham fluids by setting particular rheological parameters, and consequently, it is possible to successfully explain the dependence of residence time distribution on fluid properties for almost all of the rheological models used for time‐independent purely viscous fluids.     

Experimental determination of the shear rate in a stirred tank with a non‐newtonian fluid: Carbopol

The local shear rate generated in a cylindrical tank equipped with a Rushton turbine was investigated using particle image velocimetry in a shear‐thinning fluid (Carbopol). This non‐Newtonian fluid was used in an attempt to mimic fermentation broths. Three Reynolds numbers corresponding to the transition regime were investigated. The hydrodynamics is analyzed, and the velocity field is decomposed by proper orthogonal decomposition into mean flow, organized motion, and turbulence. Then, the contributions of each flow structure to the total dissipation of kinetic energy are presented. The spatial heterogeneity of shear rate is discussed and a new expression is proposed for shear rate. This work shows that the local shear rate is highly heterogeneous in a tank. Future works will need to focus on other types of stirrer and investigate the effect of scaling up reactors on the shear rate heterogeneity. © 2012 American Institute of Chemical Engineers AIChE J, 59: 2251–2266, 2013     

Heat transfer in lid driven channels with power law fluids in a hydrodynamic fully developed flow field

We present a finite element numerical study of heat transfer in lid driven channels with fully developed axial flow for non-Newtonian power law fluids. The effect of channel aspect ratio and material properties on temperature distribution and wall heat transfer are studied. The results show that in comparison with Newtonian fluids the shear thinning property of the fluids acts to reduce the local viscous dissipative heating and as a result the axial local fluid temperature is reduced. Applications of the results to scraped-surface heat exchanger design and operation are recommended.     

Particle image velocimetry (PIV) experimental investigation of flow structures and dynamics produced by a centripetal turbine

Turbines are capable of producing powerful radial discharge flow, which is why they are widely applied in such fields as chemical, petroleum, pharmaceutical, and so on. The centripetal turbine (CT) represents a new type of optimized turbine structure based on the Rushton turbine (RT). In order to reveal the characteristics of turbulence, centripetal and Rushton turbines were designed. The flow fields of impellers were measured by two-dimensional particle image velocimetry (PIV), in combination with the time-averaged method, phase-resolved method, and proper orthogonal decomposition (POD) method for comparative analysis. Within the measured area, the time-averaged velocity and phase-resolved velocity of the CT is smaller compared to the RT. The numeric range of fluctuation velocity for the two types of impeller is basically the same, but the high-value area of CT is more widely distributed. The swirling strength of the CT is significantly smaller than that of the RT. Besides, the wake structure is significantly weakened, which is conducive to reducing power consumption. The POD triple decomposition method proves effective in decoupling the instantaneous flow field into mean part, coherent part, and turbulence part. In each phase of blade passage, the turbulence part energy of the CT is considerably higher. For different blade passages, the cyclic variation of the CT is more significant. The flow field generated by the CT exhibits stronger eddy diffusion, which is conducive to mixing or reaction. It provides a basis for understanding the turbulent flow characteristics of CTs and impeller optimization.     

Effects of shear thinning on forward roll coating

This paper described the forward mode roll coating process of generalised non-Newtonian fluids characterised by the Ellis model. The fluid in the coating bead and the free surface formation are described by the lubrication approximation and the stability is also considered using a perturbation analysis of the downstream meniscus. Results highlight the complex behaviour of this coating process and volume flow rate and film thickness results are obtained for a range of operating conditions. The stability of the downstream meniscus is observed to improve with increasing level of shear thinning when τ_1/2 (the shear stress at which the viscosity is half that of the zero shear stress viscosity) is small, however as τ_1/2 increases the meniscus stability decreases with increasing levels of shear thinning.