Residence time distribution of a purely viscous non-Newtonian fluid in helically coiled or spatially chaotic flows

This work is dedicated to an experimental study of residence time distributions (RTD) of a pseudoplastic fluid in different configurations of helically coiled or chaotic systems. The experimental system is made up of a succession of bends in which centrifugal force generates a pair of streamwise Dean cells. Fluid particle trajectories become chaotic through a geometrical perturbation obtained by rotating the curvature plane of each bend of ±90° with respect to the neighboring ones (alternated or twisted curved ducts). Different numbers of bends, ranging from 3 to 33, were tested. RTD is experimentally obtained by using a two-measurement-point conductimetric method, the concentration of the injected tracer being determined both at the inlet and at the outlet of the device. The experimental RTD is modeled by a plug flow with axial dispersion volume exchanging mass with a stagnant zone. RTD experiments were conducted for generalized Reynolds numbers varying from 30 to 270. The Péclet number based on the diameter of the pipe is found to increase with the Reynolds number whatever the number of bends in the system. This reduction in axial dispersion is due to both the secondary Dean flow and the chaotic trajectories. Globally, the flowing fraction, which is one of the characteristic parameters of the model, increases with the Reynolds number, whatever the number of bends, to reach a maximum value ranging from 90% to 100%. For Reynolds numbers less than 200, the flowing fraction increases with the number of bends. The stagnant zone models fluid particles located close to the tube wall. The pathlines become progressively chaotic in small zones in the cross section and then spread across the flow as the number of bends is increased, allowing more trapped particles to move towards the tube center. Results have been compared with those previously obtained using Newtonian fluids. The values of the Péclet number are greater for the pseudoplastic fluid, the local change of apparent viscosity affecting the secondary flow. For pseudoplastic fluids, the apparent viscosity is lower near the wall and higher at the center of the cross section. The maximum axial velocity is flattened as the flow behavior index is reduced, inducing a decrease of the secondary flow in the central part of the pipe and an acceleration of it near the wall, which reduces the axial dispersion. These results are encouraging for the use of this system as continuous mixer for complex fluids in laminar regime, particularly for small Reynolds numbers.     

Residence Time and Concentration Distribution in a Kenics Static Mixer

Static mixers, often referred to as motionless mixers, are in-line mixing devices that consist of mixing elements inserted into a length of pipe. Most of the experimental works in this field have concentrated on establishing design guidelines and pressure drop correlations. Due to experimental difficulties, few articles have been published on the investigation of the flow and mixing mechanisms. In this work, a Kenics KMX static mixer was utilized to study concentration and residence time distribution (RTD) and effect of Reynolds number on mixing. The static mixer had six mixing elements arranged in-line along the length of the tube, and the angle between two neighboring elements was 90°. The length of the mixer was 0.98 m with internal and external diameters of 5.0 cm and 6.0 cm, respectively. The main continuous fluid was water, and NaCl solution was used as a tracer. All experiments were conducted with three replications at three Reynolds numbers, Re = 1188.71, 1584.95, and 1981.19. A dispersion model was used to model the RTD data. The experimental results were compared with the model results and reasonable agreement was achieved.     

Pressure drop and mixing behaviour of non‐Newtonian fluids in a static mixing unit

Static or motionless mixers have received wide application in chemical and allied industries due to their low cost and high efficiency. The pressure drop and mixing behaviour of such mixers have been widely studied. However, the available information for non‐Newtonian fluids is scanty. The results of pressure drop and mixing studies conducted with a locally made motionless mixer (MALAVIYA mixer) and four non‐Newtonian fluids—aq. CMC, PVA, and PEG solutions are reported in this article. The new mixer causes less pressure drop compared to some of the commercial mixers. Mixing behaviour of the unit is more closer to plug flow and a two‐parameter model correlates the dispersion data.     

管式振荡流反应器的流动模式研究(Ⅰ)PIV和RTD实验研究

采用粒子成像可视化（PIV）技术研究了管式振荡流反应器（OFR）内的流场形态和混合特点,并采用脉冲进样法测定了OFR在不同振荡条件下的停留时间分布函数。实验结果表明,OFR的混合特性十分复杂,并随振荡强度的变化呈现出不同的特征。振荡强度较低时,振荡使得OFR径向混合加强,减少了滞留区,流体的流动趋于平推流;振荡强度较高时,腔室内布满数目、尺寸和位置不断变化的漩涡,使每个腔室趋向于全混,腔室问的返混增大。实验数据与多级串联全混釜模型的比较结果显示,OFR的混合特性远非简单流动模式模型所能表征。     

Mixing for reaction injection molding. I. Impingement mixing of liquids

The performance of confined impinging jet mixers, commonly used in reaction injection molding, was investigated. A theory is presented which assumes that large scale mixing is always adequate, provided the mixer operates in turbulent flow, and argues that the scale of segregation of the final mixture should depend on the size of the smallest eddies of the turbulent motion. The theory predicts that a length scale describing the quality of the mixture will decrease like the nozzle Reynolds number to the ?3/4 power. Flow visualization experiments were used to find the point of transition to turbulent mixing flow. This transition occurs at a nozzle Reynolds number of 140 for directly opposed nozzles and at higher Reynolds numbers for nozzles angled downstream. Other geometric factors have little influence on the transition point. Quantitative mixing experiments using model fluids support the theory. Momentum ratio is shown to have no effect on mixing quality.     

Residence Time Distribution in Tubular Joule Effect Heaters with and without Geometric Modifications

In the food industry, heat treatment of highly viscous fluids in continuous processes is becoming more and more common, and the process should perform as a homogenous thermal treatment, in order to ensure quality and safety of the final product. To improve treatment homogeneity, geometric modifications can be used even in the laminar regime, to induce flow perturbation and mixing. The objectives of this work include: (i) Investigation of the residence time distribution (RTD) for industrial indirect Joule effect heaters (JEH), with smooth (ST) and modified (MT) tubes, (ii) Demonstration and quantification of the efficiency of the geometrical modifications, and (iii) Proposition of a single semi‐empirical model including the flow regime (10 < Re < 2000) and tube diameters (18 and 23 mm). The results obtained confirm that the simple Dispersed Plug Flow (DPF) model is not adaptable to small Reynolds numbers. Further analysis demonstrates that certain geometrical modifications improve the treatment homogeneity by increasing the plug flow contribution and reducing the value of the reduced variance. These beneficial effects increase when the Reynolds number is increased, the nominal diameter is reduced, and modified tubes are used. The proposed model enables the prediction of the RTD in JEH with an accurate degree of confidence.     

新型同心双轴搅拌器功率与混合特性的数值模拟

基于同心双轴搅拌器的结构与运行特点,建立了兼顾其流动、混合过程的三维数学模型,并以过程工业应用较多的两种不同尺寸双层组合桨作为内桨、框式桨作为外桨构成的同心双轴搅拌器为研究对象,数值模拟了其在中高黏牛顿流体中同向及反向转动模式的功率特性、流场特性及混合特性。模拟结果表明,同向转动模式下,整个系统的搅拌功耗更小、混合效率更高;外桨功耗受内桨影响较大,一般随内桨转速的增大,恒速外桨的功耗同向转动时会减小、反向转动时会增大;对由桨式搅拌器构成的组合式内桨而言,当内桨直径与釜体直径之比为0.35左右时,相同Reynolds数下的单位体积混合能更小;中高黏牛顿流体中,同心双轴搅拌器的内桨采用上层六斜叶桨+下层六直叶桨的组合形式时更高效节能,仅在体系Reynolds数小于36时,上层二斜叶桨+下层二直叶桨的内桨组合形式才具有相对优势。     

Material transport in a continuous rotary drum. Effect of discharge plate geometry

Experimental results on the influence of the discharge plate geometry on the dimensionless residence time distribution (RTD) for material transport in a continuous rotary drum are described. The RTD obtained by a stimulus-response technique for the different discharge plates can be described well by the axial dispersed flow model. Based on the characteristic Peclet number of the flow regime, material flow tended more towards the plug flow condition at an intermediate size discharge opening. Calculation of the axial dispersion coefficient in each case revealed that the open-ended drum behaved more like an ideal mixer. The implication of these results on the design of continuous rotary devices is discussed.     

双层撞击流混合器浓度时间序列的多重分形分析

利用平面激光诱导荧光技术(PLIF)对双层撞击流混合器的浓度场进行了实验测量,获得了不同径向位置处的浓度时间序列,通过多重分形去趋势波动方法(MF-DFA)研究了浓度时间序列中的多重分形特性,得到不同喷嘴间距和射流雷诺数下的多重分形谱,实现了流场特性的定量表征。结果表明,随着喷嘴间距增大,浓度时间序列的奇异性减弱,随着射流雷诺数增大,浓度时间序列的奇异性增强,喷嘴间距对浓度时间序列奇异性的影响比射流雷诺数更为显著。浓度信号的奇异性越强,流体粒子脉动越剧烈,混合效果越强,喷嘴间距对混合的促进作用大于射流雷诺数。通过分析多重分形谱参数(Δα, αmin, α0)随径向位置的变化规律得出了流型的转变区域,并将双层撞击流混合器由撞击中心处向下分为二次撞击区、涡旋区、一次撞击区。浓度信号的奇异性二次撞击区>一次撞击区>涡旋区,对混合的促进作用二次撞击区>一次撞击区>涡旋区。研究结果为更深入地揭示撞击流混合器内部流动模式和撞击流复杂无序的流动机理提供了理论依据。     

振荡流反应器的物料停留时间分布模型研究

提出了一个基于马尔柯夫链（Markov chains）的考虑腔室间返混的振荡流反应器物料停留时间分布模型。通过对在内径50mm,长1．95m的振荡流反应器进行的理想脉冲示踪试验数据的统计分析,给出了模型的唯一参数回流比R的经验计算公式。发现在试验条件下,存在一个与最小回流比R相对应的振荡条件。这振荡条件可表示为振荡流雷诺数（Reo）与净流雷诺数（Ren）的比值ζ,其范围为1．6〈ζ〈2．5。     

Characterization of mixing and residence time distributions in nozzle-type reactors

Studies of flow characteristics and residence time distribution, (RTD), have been undertaken in a range of geometrically similar, laboratory nozzle-type reactors. High-speed cine-photography was employed to record the complex phenomena of liquid mixing in the reactor and also to record on film the colour of an injected tracer solution leaving in the effluent. A novel atomic absorption spectrophotometric (AAS) technique was applied to transform the results of the latter film into response curves. This technique provide detailed quantitative data on the residence time distributions (RTD) for different feed rates. A multiparameter model, comprising a network of CSTR's and plug flows, was developed to simulate the experimental response data. Good agreement was obtained between model predictions and experimental results. The experimental technique and theoretical approach are recommended for analyzing the flow patterns and mixing mechanisms in such reactors.     

多孔错流喷射混合器内液体射流轨迹线

利用平面激光诱导荧光测试技术对多孔错流喷射混合器内液体混合过程进行了研究,考察了操作条件（射流速度比r、混合流股Reynolds数Re_M）和混合器的结构参数（射流小孔直径d、孔径管径比d/D、射流小孔个数n）对射流轨迹线的影响。结果表明,混合流股Reynolds数对射流轨迹线影响较小,射流速度比和混合器的结构参数是影响射流轨迹线的主要因素。建立了射流轨迹线的数学模型,并利用实验结果回归了模型参数。模型预测的液体混合过程射流轨迹线与实验结果基本吻合。     

Dimensional analysis for planetary mixer: Mixing time and Reynolds numbers

Mixing time number is a convenient parameter to characterize mixing performance of stirred tanks. This dimensionless number is now well established for agitated vessels equipped with vertically and centrally mounted impeller for Newtonian as well as for non-Newtonian fluids. To our knowledge, there is more ambiguity concerning its definition for planetary mixers especially when they have dual motion (around two perpendicular axes) to achieve homogenization. In this study, dimensional analysis of mixing time and reliability of the modified Reynolds and mixing time numbers are proposed for such a planetary mixer particularly named as TRIAXE^® system. These two numbers are based on the maximum tip speed of mixer as the characteristic velocity. Modified dimensionless numbers are consistent with the definition of conventional Reynolds and mixing numbers (when only one revolving motion around the vertical axis of the mixing device occurs in the vessel).Mixing time experiments with TRIAXE^® mixer for highly viscous Newtonian fluids showed that the proposed modified Reynolds and mixing time numbers succeeded to obtain a unique mixing curve irrespective of the different speed ratio chosens. This agreement proves that the proposed modified dimensionless numbers can be well adapted for engineering purposes and they can be used to compare the mixing performance of planetary mixers.     

Markov chain model of residence time distribution in a new type entrained-flow gasifier

A continuous-time Markov chain has been used to establish the residence time distribution (RTD) model in a new type entrained-flow gasifier, which is called entrained-flow gasifier with opposed multi-burner. According to the measurement results of the flow fields in the gasifier, the state transfer diagram of Markov chain formed in the case of the flow fields are simplified. The results show that this method is feasible in modeling the flow system which consists of ideal mixing cells and plug flow regions. The flow pattern of the gasifier is closed to continuous stirred tank reactor (CSTR). The simulation results are in good agreement with the experimental data. The established model has been applied to forecast the RTD in the industrial gasifier.     

Mixing efficiency of a multilamination micromixer with consecutive recirculation zones

Adding recirculation zones to a mixer for a microplant is proposed for enhanced mixing efficiency. A multilamination interdigital micromixer has been widely used in microchemical plants for precision or small scale chemical process. The mixing efficiency of this micromixer is relatively low as the mixing of two fluids is executed by the laminar diffusion process. To assist the mixing by fluid action, a series of recirculation zones were added to the mixing chamber. The effectiveness of the recirculation zones on mixing was estimated through a numerical simulation which indicated the dependence on Reynolds number. Mixing efficiency increased at Reynolds number that is relevant to the condition that is prevalent in a microchemical plant. The proposed micromixer was fabricated by the lithography process on the photosensitive glass wafers. The mixing qualities of the fabricated micromixer were measured by two methods; the flow visualization of dilution type experiments and the reactivity measurement. The measurement of color intensity of the mixed fluid followed the predictions by the simulation. For a Reynolds number greater than 400 that was relevant in mixers for microchemical plant, a mixing efficiency higher than 90% was obtained by adding the recirculation zones.     

Laminar mixing of shear thinning fluids in a SMX static mixer

Flow and mixing of power-law fluids in a standard SMX static mixer were simulated using computational fluid dynamics (CFD). Results showed that shear thinning reduces the ratio of pressure drop in the static mixer to pressure drop in empty tube as compared to Newtonian fluids. The correlations for pressure drop and friction factor were obtained at Re_MR?100. The friction factor is a function of both Reynolds number and power-law index. A proper apparent strain rate, area-weighted average strain rate on the solid surface in mixing section, was proposed to calculate pressure drop for a non-Newtonian fluid. Particle tracking showed that shear thinning fluids exhibit better mixing quality, lower pressure drop and higher mixing efficiency as compared to a Newtonian fluid in the SMX static mixer.     

Heat transfer to newtonian and non-newtonian liquids in a screw agitator and draft coil system

Heat transfer has been investigated for several Newtonian and non-Newtonian liquids mixed in a flat bottomed vessel equipped with a screw agitator and a coil acting simultaneously as draft tube and heat exchanger. Heat transfer rates from coil to liquid were determined for different coil designs, rheological properties and operating conditions in the heating and cooling modes. A circulation Reynolds number is defined, the characteristic length being the effective height of the heat exchanger (the coil) and the characteristic velocity being the circulation velocity of the fluid which was determined experimentally. Using this Reynolds number, it was possible to establish a single correlation for the Nusselt number as a function of Reynolds and Prandtl numbers. Geometric ratios do not appear in this correlation which could adequately represent more than 200 experimental data. A similar single correlation could not be obtained when using the conventional mixing Reynolds number. This novel system is shown to be very efficient for handling rheologically complex fluids.     

Reynolds number effects in a simple planetary mixer

Planetary mixers are widely used in a diverse range of industrial applications. This paper presents an experimental investigation of mixing in a planetary mixer, and a comparison with numerical simulations based on a simple mathematical model of the flow. The model allows an exact expression for the velocity field in the Stokes flow regime, apparently the first for a mixer with genuinely moving parts, which permits accurate numerical tracking of material interfaces. Experiments performed at low Reynolds number (Re?1) show good agreement with corresponding numerical simulations, but as the Reynolds number is increased, the agreement between experiments and Stokes-flow numerics worsens, in a manner that reflects improving experimental mixing quality. Specifically, we find that islands of poor mixing shrink as Re increases. Our results suggest that, while numerical simulations in the Stokes flow regime may be used as a ‘sieve’ to select good mixing protocols at small Re, experiments or computational fluid dynamics simulations are required properly to evaluate mixing protocols operated at finite Reynolds numbers.     

Influence of the meandering channel geometry on the thermo-hydraulic performances of an intensified heat exchanger/reactor

In the global context of process intensification, heat exchanger/reactors are promising apparatuses to implement exothermic chemical syntheses. However, unlike heat exchange processes, the implementation of chemical syntheses requires to control the residence time to complete the chemistry. A way to combine the laminar regime (i.e. enough residence time) with a plug flow and the intensification of both heat and mass transfers is the corrugation of the reaction path.In this work, the experimental set-up is based on plate heat exchanger/reactor technology. 7 milli-channel corrugated geometries varying the corrugation angle, the curvature radius, the developed length, the hydraulic diameter and the aspect ratio have been designed and experimentally characterized (heat transfer, mixing times, pressure drops, RTD). The objectives were to assess their respective performances to derive some correlations depending on the channel design.The results confirmed the benefits of the reaction channel corrugation. Heat and mass transfers have been intensified while maintaining a plug flow behaviour in the usually laminar flow regime. Moreover, whatever the meandering channel's curvature radius, the results highlighted the relevance of considering the Dean number as the scale-up parameter. This dimensionless number, more than the Reynolds number, seems to govern the flow in the wavy channels.