Numerical simulations of the reactive mixing in a commercially operated stirred ethoxylation reactor

The computational fluid dynamics (CFD) technique was applied to describe the mixing and the chemical reactions in commercially operated stirred ethoxylation reactors. Two reactor sizes in the existing ethoxylation operations were studied in this work: a laboratory-scale autoclave with a single-Rushton turbine and an industrial-scale reactor with a dual-Rushton turbine. The ethoxylation reactor contents were described as an incompressible, turbulent single-phase liquid mixing regime with chemical species undergoing heat and mass transfer. Since the accurate experimental ethoxylation flow data could not be extracted from the industrial operations, the development of the CFD model for the ethoxylation process was undertaken in two stages. The first stage simulated a single-phase liquid agitation system based on the literature with experimental data on velocities, such as Wu and Patterson [1989. Laser-Doppler measurements of turbulent-flow parameters in a stirred mixer. Chemical Engineering Science 44, 2207–2221], for a Rushton stirred reactor of standard configuration. Once validated, the numerical model was applied to compute the flow field in ethoxylation reactors. The second stage integrated the ethoxylation kinetics into the numerical model and simulated the ethoxylation process. In the simulation of the mean flow field, the qualitative features of the literature data were well reproduced. The computed results of both the ethylene oxide consumption and the temperature calculation compared very well with the measurements in the laboratory-autoclave operations. Reasonably good agreement was also reached between the simulated and experimental data on the time-dependent changes of ethylene oxide mass fraction in the bulk liquid in the industrial ethoxylation operations. These demonstrate that the CFD process model was capable of predicting the reaction behaviour and would be useful for exploration of any opportunity for increasing the ethoxylation capacity in the industrial operations.     

A novel multigrid technique for Lagrangian modeling of fuel mixing in fluidized beds

This paper presents a novel Lagrangian approach to model fuel mixing in gas–solid fluidized beds. In the mixing process, fuel particles are considerably larger than the inert bed material and therefore, the present work proposes three grids to account for the difference in size between the fuel particles and inert solids. The information between the grids is exchanged using an algorithm presented in the paper. A statistical method has been developed to analyze the distribution of the fuel particles in the bed. The results for the preferential positions, velocity vectors and horizontal dispersion coefficients are compared with experimental data in a bed applying simplified scaling relationships for different operating conditions. The effects of initial bed height and inlet gas velocity on the fuel mixing are investigated.It is found that the proposed Lagrangian modeling can capture the complex pattern of the movement of the fuel particles, in spite of the large difference in diameter between inert and fuel particles.     

On the efficiency of turbulent mixing in rotating stirrers

Turbulent mixing is crucial in sterilizing engineering, where it is mandatory to produce the finest and the most homogeneous turbulence all over the fluid domain. This study shows how the turbulence imparted by Rushton impellers, which are typically used in several industrial productions, may be hardly improved by varying the impeller's geometry.An impeller of new design, a perforated paddle that completely removes both limitations of Rushton impellers, is illustrated. The mathematical modeling is based on the RANS equations and the k-? model for turbulence closure; great care was lavished to understand the accuracy of the numerical solution. The results are presented in terms of a global indicator of mixing performance that combines both the Kolmogorov scale and the Gini coefficient.The numerical solution disclosed the formation of a peripheral turbulent spot and a seemingly slow motion zone next to the shaft of the rotating perforated paddle. The imparted turbulence may be usefully fine, but many revolutions are needed to grant the safe target level of spatial homogeneity of the turbulence. This was confirmed by both a dedicated statistics treatment and the conventional statistical analysis.     

Study of the numerical instabilities in Lagrangian tracking of bubbles and particles in two-phase flow

In the context of the Lagrange approach, used in numerical simulations of two-phase flow, the discrete elements that constitute the dispersed phase are tracked through the fluctuating fluid field by solving their equations of motion. It has been shown previously [Laín, S., & Göz, M. F. (2000). Instabilities in numerical simulations of dispersed two-phase flow. Mechanical Research Communication 27, 475; Laín, S., & Göz, M. F. (2001). Numerical instabilities in bubble tracking in two-phase flow simulations. International Journal of Bifurcation and Chaos, 11 (4), 1169] that widely used discretization methods for integrating the particle equation of motion in bubbly flows may lead to artificial instabilities and, eventually, yield spurious oscillations and chaotic behavior via period-doubling bifurcations. The purpose of this paper is the extension of these previous investigations to consider dispersed two-phase flow laden with solid particles, which can be heavier or lighter than the fluid in which they are immersed. As a result, the numerical techniques applied to integrate the particle or bubble equation of motion are quite stable in the case of heavy particles but must be used very carefully when applied to the tracking of bubbles or light solid particles in a fluid. In addition, sound criteria are established for choosing optimal time steps to simultaneously avoid numerical instabilities and guarantee code efficiency, in contrast to the usual but naive trial and error approach.     

Comparison of DEM results and Lagrangian experimental data for the flow and mixing of granules in a rotating drum

This work assesses the accuracy of the discrete element method (DEM) for the simulation of solids mixing using non‐intrusive Lagrangian radioactive particle tracking data, and explains why it may provide physically sound results even when non‐real particle properties are used. The simulation results concern the size segregation of polydisperse granules in a rotating drum operated in rolling mode. Given that the DEM is sensitive to simulation parameters, the granule properties were measured experimentally or extracted from the literature. Several flow phenomena are investigated numerically and experimentally, including the particle residence time, the radial segregation, and the radial variation of the axial dispersion coefficient. An analysis of the DEM model is then presented, with an emphasis on the Young's modulus and friction coefficients. Finally, dimensionless motion equations and corresponding dimensionless numbers are derived to investigate the effect of simulation parameters on particle dynamics. © 2013 American Institute of Chemical Engineers AIChE J, 60: 60–75, 2014     

On the mixing properties of spherically symmetric helical coherent structures in turbulence

A paradigmatic family of flow fields for localized, spherically symmetrical flow with maximal helicity—a model for helical coherent structures that are localized—is introduced. The Lagrangian mixing of the lowest order member of the family that is truly 3-D due to spiral arms is analyzed with linear theory, demonstrating that trajectory growth rates for the short, convective time scale are exponential and bounded by the extremal eigenvalues of the Jacobian. However, these rates show strong inhomogeneity and anisotropy associated with anomalous mixing. It was found for nonlinear Lagrangian mixing times that for this paradigm helical coherent structure, 22% of the trajectory pairs were bounded by the initial separation (non-mixing) and 78% mixed in various classifications of convective dispersal. All non-local studies of 10,000 Lagrangian trajectories could be categorized into five classes of growth (decay) patterns which exhibit the effects of localized, finite helicity/momentum associated with this class of velocity field. A scalar dispersion simulation confirms that the “patch” of fluid near the origin is slowly mixing—on the diffusive time scale—and is convected “unmixed” when the influence of molecular diffusion is still not pronounced (short times relative to Pe=100).     

A stochastic Lagrangian approach for simulating the effect of turbulent mixing on algae growth rate in a photobioreactor

It is well known that mixing caused by fluid turbulence can cause significantly increased growth rate of algae in photobioreactor flows under certain conditions. In general, flows in which the light penetrates into only a small fraction of the reactor flow field have the largest growth rate enhancement in the presence of fluid mixing. The current paper seeks to develop a computationally efficient prediction method for algae growth rate in practical photobioreactors using a combination of commercially available RANS turbulence models and a stochastic Lagrangian model for the turbulence fluctuations. The stochastic Lagrangian algae growth rate model is first validated by comparison with simulations of algae growth rate obtained by direct numerical simulation of homogeneous turbulence. We then demonstrate the stochastic Lagrangian model approach for prediction of algae growth rate in turbulent pipe flow, which is representative of the primary photoreaction component in many tubular algae production facilities. The results illustrate how algae growth rate increases as the pipe flow Reynolds number is increased.     

Validation of the Langevin particle dispersion model against experiments on turbulent mixing in a T-junction

The fluctuating fluid velocities seen by particles entrained in a turbulent fluid have recently been modeled using a stochastic model based normalized Langevin Continuous Random Walk (CRW). This model has been quite successful in predicting particle dispersion in mildly complex flows. In the present study, we aim at validating the CRW model further against data collected in a challenging 3D geometry. We consider turbulent fluid mixing downstream of a T-junction using a hybrid Euler-Lagrange approach whereby tracer particle trajectories are computed and mixing of the streams deduced from the relative concentration of particles originating from the two inlet branches of the Tee. In a first simulation, RANS Reynolds Stress Model (RSM) is used to obtain the mean flow field, whereas the fluid fluctuations are specified from a CRW. Simulation results are compared to experimental data on mixing of two isothermal streams consisting of tap and de-ionized water, respectively. It is found that RSM-CRW yields strong under-prediction of the mixing. Closer look at the results shows that the Reynolds stresses, which are required inputs to the CRW, are poorly predicted with RSM. Detached Eddy Simulations (DES) are subsequently performed to provide the mean flow field, and the DES-CRW model predictions are found to compare quite well with the experimental data.     

CFD study on double-to single-loop flow pattern transition and its influence on macro mixing efficiency in fully baffled tank stirred by a Rushton turbine

For a fully baffled tank stirred by a Rushton turbine(RT), the flow pattern will change from double-to single-loop as the off bottom clearance(C) of the RT decreases from one third of the tank diameter. Such a flow pattern transition as well as its influence on the macro mixing efficiency was investigated via CFD simulation. The transient sliding mesh approach coupled with the standard k-ε turbulence model could correctly and efficiently reproduce the reported critical C range where the flow pattern changes. Simulation results indicated that such a critical C range varied hardly with the impeller rotation speed but decreased significantly with increasing impeller diameter. Small RTs are preferable to generating the single-loop flow pattern. A mechanism of the flow pattern transition was further proposed to explain these phenomena. The discharge stream from the RT deviates downwards from the horizontal direction for small C values; if it meets the tank wall first, the double-loop will form; if it hits the tank bottom first, the single-loop will form. With the flow pattern transition, the mixing time decreased by about 35% at the same power input(P), indicating that the single-loop flow pattern was more efficient than the double-loop to enhance the macro mixing in the tank. A comparison was further made between the single-loop RT and pitched blade turbine(PBT, 45°) from macro mixing perspective. The single-loop RT was found to be less efficient than the PBT and usually required 60% more time to achieve the same level of macro mixing at the same P.     

一种计算搅拌槽混合时间的新方法

基于对混合时间定义的思考,提出了一种新的定义方法,在湍流流场数值计算的基础上通过求解示踪剂的浓度输运方程,研究了单层涡轮桨搅拌槽内的混合过程。结果表明：搅拌转速和搅拌桨安装位置都影响混合时间的大小,而进料位置对混合时间的影响不大。对于不同的搅拌转速而言,随搅拌转速的增大,相同体积分数对应的混合时间逐渐减小。当搅拌桨安装在槽中间位置时所对应的混合时间最小。利用适宜的尺寸和安装位置的导流筒可有效降低混合时间。     

逆流桨强化搅拌槽内流体混沌混合及流场结构失稳研究

在传统三斜叶桨的基础上,结合逆流桨结构,提出三斜叶逆流桨,以破坏或者消除搅拌槽内稳定的对称性流场结构,提高流体传递效率及混沌混合程度。结合实验和模拟两种方法,主要研究了上推式三斜叶桨(PBTU)、外推内压式三斜叶逆流桨(PBTC-U)、外压内推式三斜叶逆流桨(PBTC-D)三种桨叶体系以及不同外层桨叶长度的PBTC-U桨体系内搅拌功耗、混合时间、混沌特性参数、流场结构以及流体速度分布。实验结果表明,N=130 r/min时,PBTC-U桨相对于PBTU桨和PBTC-D桨,体系混合时间分别从22.0、37.5 s缩短到16.5 s,功耗分别降低了5.6%和12.8%,LLE值分别提高了13.69%和37.01%。在确定PBTC-U桨适宜外层桨叶长度的研究中发现当外层桨叶长度D₂=0.375D时,搅拌功耗最低且混合时间最短。PBTC-U型逆流桨通过内外层桨叶的逆流作用,强化体系内流体的随机运动,使得流场的不稳定性得到增强,对称性被破坏,进而流场结构失稳,流体混合效率得到提高。另外,PBTC-U桨可以增强流体轴、径向速度分布的波动性,有利于提高体系的混合效率。     

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.     

Application of Central Composite Rotatable Design for Mixing Time Analysis in Mechanically Agitated Vessels

Central composite rotatable design (CCRD) was applied for analyzing and optimizing the effects of impeller rotational speed, gas flow rate, probe location, and tracer injection point on the gas‐liquid two‐phase mixing time in an agitated vessel with a dual six‐blade Rushton turbine. Knowledge of the effects of independent factors on the mixing time is necessary in order to optimize the mixing process. The mathematical relationship between mixing time and four significant independent variables can be approximated by a nonlinear polynomial model. The obtained results demonstrate that CCRD could efficiently be applied for modeling mixing time. It requires fewer experimental runs and provides sufficient information as compared to a factorial design.     

The influence of mixing on lysozyme renaturation during refolding in an oscillatory flow and a stirred-tank reactor

Protein refolding is a key unit operation in many processes that produce recombinant biopharmaceuticals using Escherichia coli. Yield in this step generally controls overall process yield, and at industrially relevant protein concentrations is limited by aggregation. While most refolding operations are optimised with respect to chemical environment, the physical processes affecting yield have been neglected. In this study, we demonstrate that refolding yield for the model protein lysozyme is dependent on mixing intensity during dilution refolding. This is shown for two different reactor configurations: a standard stirred-tank reactor and a novel oscillatory flow reactor. We further show that the effect of mixing is dependent on the type of chaotrope employed for denaturation. Yield falls significantly when mixing intensity is decreased following urea denaturation, while the effect of mixing is not apparent when guanidine hydrochloride is employed as the denaturant. In batch tests we further confirm that, for urea, the “path” of dilution affects yield, and hence the observed sensitivity to mixing is not unexpected. We conclude that mixing is a critical parameter that must be optimised in industrial reactors, along with the usual chemical and protein-specific parameters.     

Lagrangian marker particle trajectory and microconductivity measurements in a mixing tank

Large regions of inhomogeneous mixing have been observed in industrial, bottom-sweeping impeller crystallizers. To investigate this phenomenon, we conducted experiments on a one-tenth volume model of this kind of mixing tank. Results are reported of Lagrangian marker particle (LMP) and microconductivity measurements using the model mixing tank with impeller tip Reynolds numbers of 25,000. Surprising structure is found in this high Reynolds number flow. Using the LMP trajectory data, we show the flow consists of a narrow region of rapidly moving, upward spiralling flow at the tank perimeter. This flow returns slowly through a vertical stack of tori and through a quiescent region centered on the impeller. These tori are concentric with the impeller and exist at loci of regions of shear found adjacent to the quiescent central region and the tank perimeter.Conditional analysis of the microconductivity signals reveals that large concentration fluctuations occur in the perimeter flow. In contrast, only small diffusive-like concentration fluctuations occur in the center of the tank. This segregation of regions of rapid transport in the perimeter flow from regions of micromixing in the quiescent region results in inhomogeneous mixing in the tank. The complexity of the flow is reflected in the large dynamical dimension (≈24) of the flow obtained from the calculation of the Kolmogorov entropy production rate. The return-time distribution was found to be composed of a superposition of two log-normal distributions. Period doubling phenomenon was also found in these distributions.     

Fluid dynamics and mixing of single-phase flow in a stirred vessel with a grid disc impeller: Experimental and numerical investigations

We report experimental and numerical investigations of a novel grid disc impeller for mixing of single-phase flow in stirred vessels. We performed detailed mean velocity measurements using LDA to understand the flow generated by the grid disc impeller and we also measured the mixing time and power consumption of the grid disc impeller. Measurements showed that the performance of the grid disc impeller, which has radial flow characteristics, is equivalent to a standard propeller in terms of the degree of mixing achieved per unit power consumption. We also performed numerical simulations to predict the flow generated by the grid disc impeller and its mixing performance. It was shown that the present computational model predicts the mean velocities, power consumption and mixing time in good agreement with the measurements. The experimentally validated computational model was further used to understand the effects of impeller rotational speed and grid disc configuration on the fluid dynamics and mixing performance of the grid disc impeller.     

CFD simulation of liquid-phase mixing in solid-liquid stirred reactor

A comprehensive CFD model was developed to gain an insight into solid suspension and its implications on the liquid-phase mixing process in a solid-liquid stirred reactor. The turbulent solid-liquid flow in a stirred reactor was simulated using a two-fluid model with the standard k-ε turbulence model with mixture properties. The multiple reference frames (MRFs) approach was used to simulate impeller rotation in a fully baffled reactor. The computational model with necessary sub-models was mapped on to a commercial solver FLUENT 6.2 (of Fluent Inc., USA). The predicted solid concentration distribution was compared with the experimental data of Yamazaki et al. [1986. Concentration profiles of solids suspended in a stirred tank. Powder Technology 48, 205-216]. The computational model was then further extended to simulate and understand the implications of the suspension quality on liquid-phase mixing process. The computational model and the predicted results discussed here will be useful for understanding the liquid-phase mixing process in stirred slurry reactors in various stages of solid suspension.     

Effect of the rotor shape on the mixing characteristics of a continuous flow Taylor-vortex reactor

Macro- and micromixing in a continuous flow Taylor-vortex reactor with novel ribbed rotors were investigated and compared to the features of a classical cylindrical rotor. The characterisation was performed in a wide hydrodynamic range (40<Ta<2500 and 0.03<Re<0.51) through tracer experiments and the analysis of the rotor power consumption. Additionally, the flow patterns were visualised by using a rheoscopic fluid. The results show that the novel rotors equipped with ribs immobilise and stabilise the vortices. As compared to cylindrical rotors, micromixing is clearly enhanced while axial dispersion can be simultaneously reduced. Through the use of ribbed rotors, the operational window can be broadened considerably, in which the reactor runs at very low or moderate extent of macromixing.