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.     

Experimental investigation and CFD simulation of liquid–solid–solid dispersion in a stirred reactor

For understanding the monosodium aluminate hydrate crystallization from the supersaturated aluminate solution containing red mud as the leaching liquor of bauxite, the liquid–solid–solid dispersion of a simulant system, i.e. glycerite, red mud and sand, in a stirred reactor has been experimentally investigated as well as simulated using computational fluid dynamics model (CFD) for the first time. The computational model is based on the Eulerian multi-fluid model along with RNG k–ε turbulence model, where Syamlal–obrien-symmetric drag force model (Syamlal, 1987) of the inter-phase momentum transfer between two dispersed solid phases is taken into account. A good agreement is obtained between the experimental data of solid distributions and the simulation results in the flow fields of liquid–solid–solid as well as liquid–solid systems. The solid suspension qualities of both liquid–solid and liquid–solid–solid systems in the stirred reactors with and without draft tube were also studied in detail based on mixing time, the standard deviation of solid concentration proposed by Bohnet and Niesmak (1980), the flow pattern and power number. The influence of the interaction between two dispersed solid phases on the suspension of red mud is found significantly greater than that of sand. The holdup of sand below the impeller is considerably larger than that above the impeller and the red mud dispersion approaches homogeneous in the reactor. The mixing time of liquid–solid–solid suspension is longer than that of liquid–solid suspension under the same conditions, and the mixing times of both systems in the stirred reactor with draft tube are longer than that in the reactor without draft tube. Furthermore, the distributions of sand and red mud in the reactor with draft tube were found less homogeneous than those without draft tube in most cases.     

CFD simulations of gas-liquid-solid stirred reactor: Prediction of critical impeller speed for solid suspension

In this work, simulations have been performed for three phase stirred dispersions using computational fluid dynamics model (CFD). The effects of tank diameter, impeller diameter, impeller design, impeller location, impeller speed, particle size, solid loading and superficial gas velocity have been investigated over a wide range. The Eulerian multi-fluid model has been employed along with the standard k-ε turbulence model to simulate the gas-liquid, solid-liquid and gas-liquid-solid flows in a stirred tank. A multiple reference frame (MRF) approach was used to model the impeller rotation and for this purpose a commercial CFD code, FLUENT 6.2. Prior to the simulation of three phase dispersions, simulations were performed for the two extreme cases of gas-liquid and solid-liquid dispersions and the predictions have been compared with the experimental velocity and hold-up profiles. The three phase CFD predictions have been compared with the experimental data of Chapman et al. [1983. Particle-gas-liquid mixing in stirred vessels, part III: three phase mixing. Chemical Engineering Research and Design 60, 167-181], Rewatkar et al. [1991. Critical impeller speed for solid suspension in mechanical agitated three-phase reactors. 1. Experimental part. Industrial and Engineering Chemistry Research 30, 1770-1784] and Zhu and Wu [2002. Critical impeller speed for suspending solids in aerated agitation tanks. The Canadian Journal of Chemical Engineering 80, 1-6] to understand the distribution of solids over a wide range of solid loading (0.34-15 wt%), for different impeller designs (Rushton turbine (RT), pitched blade down and upflow turbines (PBT45)), solid particle sizes (120-) and for various superficial gas velocities (0-10 mm/s). It has been observed that the CFD model could well predict the critical impeller speed over these design and operating conditions.     

Prediction of the Induced Gas Flow Rate from a Self‐Inducing Impeller with CFD

The complex task of describing computationally two‐phase turbulent flows in aerated stirred‐tank reactors was overcome by proposing that the gas flow rate in the hollow impeller can be estimated from single‐phase flow simulations of the liquid phase in the reactor: the pressure at the impeller surface obtained from liquid phase simulations can be related to the gas induction rate. A commercial lab‐scale reactor with a radial six‐bladed hollow impeller was chosen for the study. To validate the presented methodology, the induced gas flow rate was measured experimentally from the tracking of the position of bubbles in a dynamic sequence of flow images. Notwithstanding the simplifications assumed in the presented CFD methodology, good agreement has been obtained between numerical results and experiments.     

Impact of thixotropy on flow patterns induced in a stirred tank: Numerical and experimental studies

Agitation of a thixotropic shear-thinning fluid exhibiting a yield stress is investigated both experimentally and via simulations. Steady-state experiments are conducted at three impeller rotation rates (1, 2 and 8 s⁻¹) for a tank stirred with an axial-impeller and flow-field measurements are made using particle image velocimetry (PIV) measurements. Three-dimensional numerical simulations are also performed using the commercial CFD code ANSYS CFX10.0. The viscosity of the suspension is determined experimentally and is modelled using two shear-dependant laws, one of which takes into account the flow instabilities of such fluids at low shear rates. At the highest impeller speed, the flow exhibits the familiar outward pumping action associated with axial-flow impellers. However, as the impeller speed decreases, a cavern is formed around the impeller, the flow generated in the vicinity of the agitator reorganizes and its pumping capacity vanishes. An unusual flow pattern, where the radial velocity dominates, is observed experimentally at the lowest stirring speed. It is found to result from wall slip effects. Using blades with rough surfaces prevents this peculiar behaviour and mainly resolves the discrepancies between the experimental and computational results.     

MIXING CHARACTERISTICS IN SLURRY STIRRED TANK REACTORS WITH MULTIPLE IMPELLERS

Hydrodynamic parameters such as power consumption, gas holdup, critical impeller speed for solid suspension and mixing time were measured in slurry stirred tank reactors with multiple impellers. The experiments were mainly conducted in a stirred tank of 0.2mi.d. with baffles. It contained two four-pitched blade downflow turbines for gas dispersion and one Pfaudler type impeller for solid suspension. As a part of scaling studies, additional experiments were also carried out in a larger stirred tank reactor (0,8m i.d.) geometrically similar to the smaller one. Glass beads and polymeric particles were used as a solid phase. Solid concentration was in the range of 0-20% (K/K). Tap water and methanol were used as a liquid phase

The power consumption decreased due to an introduction of gas and the presence of solids caused a decrease in the extent of reduction in power consumption. A correlation for power consumption in aerated slurry systems was proposed, It was found that the presence of solids is responsible for a decrease in gas holdup. A new correlation for gas holdup in gas-liquid-solid three-phase stirred tank reactors was developed. It fit the present experimental data reasonably. The critical impeller speed for solid suspensions increased with increasing gas flow rate. However, its increase was rather smaller as compared with the predictions of the correlations available in the literature. We proposed a correlation of the critical impeller speed for solid suspension in the presence of gas. The mixing time complicatedly increased or decreased depending on gas flow rate, impeller speed, solids type and concentration.     

Computational Fluid Dynamics Study of a Styrene Polymerization Reactor

The computational fluid dynamics (CFD) approach was adopted to simulate benzoyl peroxide (BPO)‐initiated styrene polymerization in a laboratory‐scale continuous stirred‐tank reactor (CSTR). The CFD results revealed the effects of non‐homogeneity and the short‐circuiting of the unreacted styrene and initiator on the reactor performance. The study also investigated the effects of the impeller speed and the residence time on the conversion and the flow behavior of the system. The CFD simulation showed that intense mixing remained confined to a small region near the impeller. With increasing impeller speed, it was found that the perfectly mixed region near the impeller expanded, thus reducing non‐homogeneity. Different contours were generated and exhibited the effect of the mixing parameters on the propagation rate and styrene conversion. The monomer and initiator conversions predicted with the CFD model were compared to those obtained with a CSTR model. The CFD model accounts for the non‐ideality behavior of the polymerization reactor, and hence conversion predictions are more realistic.     

乙烯利酯化搅拌反应器的改进与模拟优化

利用计算流体力学（CFD）技术对乙烯利酯化搅拌釜内流场进行了模拟研究,对比了工业酯化釜和新酯化釜的气体分散效果等反应器性能。结果表明,工业酯化釜因桨叶形式不当、桨间距过小等原因,气体分散效果很差;新改进的酯化釜依照工艺要求,调整了桨叶结构,增加了挡板,使气体分散效果得到明显改善,反应器液层空间得到有效利用。模拟研究结果可为工业酯化釜装置的技术改进提供一定的指导。     

CFD analysis of interphase mass transfer and energy dissipation in a milliliter-scale stirred-tank reactor for filamentous microorganisms

A newly developed stirred tank bioreactor for the cultivation of filamentous microorganisms on a milliliter-scale was investigated by means of computational fluid dynamics (CFD). The applied paddle impeller has an asymmetric shape and thus creates a complex liquid vortex in an unbaffled reactor. Size and shape of the formed gas–liquid interface were simulated applying CFD because they cannot be measured experimentally. As expected, higher stirrer speeds correspond to deeper vortices and larger interfacial areas. CFD simulations confirmed stirrer functionality at high liquid viscosities. Volumetric oxygen mass transfer coefficients (k_La) were estimated based on the simulated interfaces. Comparison with experimental data showed good agreement. Simulated maximum energy dissipations were in the same order of magnitude as experimental data at varying stirrer speeds. In contrast to these findings, simulated power characteristics showed significant deviations if compared to measured data. One reason may be the challenging turbulence modeling of two-phase flows with strong streamline curvature and the mostly transitional flow regime. Another reason could be the demanding measurement of very small stirrer torques.     

翼形桨在气液固三相搅拌反应釜中的混合性能

<正>机械搅拌槽中高速旋转的叶轮产生的排出流中,径向速度主要用于气体的剪切分散,而其轴向速度是固体悬浮和液相轴向混合的主要动力。三相体系的混合不仅要求叶轮具有较强的径向剪切分散能力,而且要有一定的轴向混合能力,以此达到对气体和固体的同时分散。理想的混合水平不仅要求达到二者在宏观上的均匀,而且在微观混合上也要达到一定的均匀度,为此对搅拌桨的设计提出了较高的要求。在气液二相的混合操作中比较多的采用了盘式涡轮桨,而在液固二相的混合操作中比较多的使用螺旋桨,这都是为了利用各自不同的混合优势。涉及到气液固三相混合,由于气体和固体的分散是一个相互制约的问题,完全的径向     

Numerical simulation of micro-mixing in gas–liquid and solid–liquid stirred tanks with the coupled CFD-E-model

The coupled CFD-E-model for multiphase micro-mixing was developed, and used to predict the micro-mixing effects on the parallel competing chemical reactions in semi-batch gas–liquid and solid–liquid stirred tanks. Based on the multiphase macro-flow field, the key parameters of the micro-mixing E-model were obtained with solving the Reynolds-averaged transport equations of mixture fraction and its variance at low computational costs. Compared with experimental data, the multiphase numerical method shows the satisfactory predicting ability. For the gas–liquid system, the segregated reaction zone is mainly near the feed point, and shrinks to the exit of feed-pipe when the feed position is closer to the impeller. Besides, surface feed requires more time to completely exhaust the added H⁺ solution than that of impeller region feed at the same operating condition. For the solid–liquid system, when the solid suspension cloud is formed at high solid holdups, the flow velocity in the clear liquid layer above the cloud is notably reduced and the reactions proceed slowly in this almost stagnant zone. Therefore, the segregation index in this case is larger than that in the dilute solid–liquid system.     

搅拌槽内液-固两相体系的数值研究(Ⅱ)临界搅拌转速的预测

The critical impeller speed, NJS, for complete suspension of solid particles in the agitated solid-liquid two-phase system in baffled stirred tanks with a standard Rushton impeller is predicted using the computational procedure proposed in Part Ⅰ. Three different numerical criteria are tested for determining the critical solid suspension. The predicted NJS is compared with those obtained from several empirical correlations. It is suggested the most reasonable criterion for determining the complete suspension of solid particles is the positive sign of simulated axial velocity of solid phase at the location where the solid particles are most difficult to be suspended.     

Agitation and mobilization of thixotropic liquids

Direct numerical simulations of transitional and turbulent flows of purely viscous thixotropic liquids in stirred tanks have been performed. The simple thixotropy model used is based on the notion of a network in the liquid with an integrity that builds up with finite rate under quiescent conditions, and breaks down under liquid deformation. We solve a transport equation for the network integrity which is two‐way coupled to the lattice‐Boltzmann‐based flow solver. The liquid's time scale characterized by the dimensionless Deborah number shows a profound impact on the level of mobilization and the flow patterns in the mixing tanks, especially if the time scale of the liquid is of the same order as the circulation time in the tank. It is also demonstrated to what extent increasing the impeller speed improves mobilization and mixing. © 2010 American Institute of Chemical Engineers AIChE J, 2010     

Drag models, solids concentration and velocity distribution in a stirred tank

Drag force influences both the particle suspension and solids concentration distribution in a stirred tank. The influence of drag models on the prediction of solids suspension in a tank stirred by a hydrofoil impeller was studied in the present work using computational fluid dynamics (CFD) and experimental techniques. A comparison was made between the drag models based on Reynolds number only and those that take solid volume fraction into account or those that account for the effect of the free stream turbulence. One of the drag models investigated was a function of the energy dissipation rate, and therefore, the influence of the methods of determining the energy dissipation rate on the prediction of solids suspension was investigated. It was shown that a better agreement between the CFD simulation and experimental results can be obtained using drag models based on solids volume fraction than those that are based on Reynolds number only.     

CFD simulation of mixing in tall gas-liquid stirred vessel: Role of local flow patterns

In this work, we have used the computational fluid dynamics (CFD)-based models to investigate the gas-liquid flows generated by three down-pumping pitched blade turbines. A two-fluid model along with the standard k-ε turbulence model was used to simulate the dispersed gas-liquid flow in a stirred vessel. Appropriate drag corrections to account for bulk turbulence [Khopkar and Ranade, 2005. CFD simulation of gas-liquid flow in a stirred vessel: VC, S33 and L33 flow regimes. A.I.Ch.E. Journal, accepted for publication] were developed to correctly simulate different flow regimes. The computational snapshot approach was used to simulate impeller rotation and was implemented in the commercial CFD code, FLUENT4.5 (of Fluent. Inc., USA). The computational model has successfully captured the flow regimes as observed during experiments. The particle trajectory simulations were then carried out to examine the influence of the different flow regimes on the circulation time distribution. The model predictions were verified by comparing the predicted results with the experimental data of [Shewale and Pandit, 2006. Studies in multiple impeller agitated gas-liquid contactors. Chemical Engineering Science 61, 489-504]. The computational model and results discussed in this study would be useful for explaining the implications local flow patterns on the mixing process and extending the applications of CFD models for simulating large multiphase stirred reactors.     

Numerical Study of Solid-Liquid Two-Phase Flow in StirredTanks with Rushton Impeller(Ⅱ) Prediction of Critical Impeller Speed

The critical impeller speed, NJS, for complete suspension of solid particles in the agitated solid-liquid two-phase system in baffled stirred tanks with a standard Rushton impeller is predicted using the computational procedure proposed in Part I. Three different numerical criteria are tested for determining the critical solid suspension. The predicted NJS is compared with those obtained from several empirical correlations. It is suggested the most reasonable criterion for determining the complete suspension of solid particles is the positive sign of simulated axial velocity of solid phase at the location where the solid particles are most difficult to be suspended.     

Study on the solid–liquid suspension behavior in a tank stirred by the long-short blades impeller

We investigated the solid–liquid suspension characteristics in the tank with a liquid height/tank diameter ratio of 1.5 stirred by a novel long-short blades(LSB) impeller by the Euler granular flow model coupled with the standard k–ε turbulence model. After validation of the local solid holdup by experiments,numerical predictions have been successfully used to explain the influences of impeller rotating speed,particle density, particle size, liquid viscosity and initial solid loading on the soli...     

CFD Prediction of the Critical Agitation Speed for Complete Dispersion in Liquid‐Liquid Stirred Reactors

A computational fluid dynamics (CFD) model is adopted to simulate the turbulent immiscible liquid‐liquid flow in a stirred vessel based on a two‐fluid model with a k‐ϵ‐A_P turbulence model. An improved inner‐outer iterative procedure is adopted to deal with the impeller rotation in a fully baffled stirred tank. Different drag formulations are examined, and the effect of the droplet size on both the dispersed phase holdup distribution and the velocity field is analyzed. Two different numerical criteria are tested for determining the critical impeller speed for complete dispersion. The simulated critical impeller speeds are generally in good agreement with the correlations in the literature when the fixed droplet size is properly selected. This demonstrates that the modeling approach and the numerical criteria proposed in this work are promising for predicting the dispersion characteristics in liquid‐liquid stirred tanks.     

Numerical simulation of micro-mixing in gas-liquid and solid-liquid stirred tanks with the coupled CFD-E-model

The coupled CFD-E-model for multiphase micro-mixing was developed, and used to predict the micro-mixing effects on the parallel competing chemical reactions in semi-batch gas-liquid and solid-liquid stirred tanks. Based on the multiphase macro-flow field, the key parameters of the micro-mixing E-model were obtained with solving the Reynolds-averaged transport equations of mixture fraction and its variance at low computational costs. Compared with experimental data, the multiphase numerical method shows the satisfactory predicting ability. For the gas-liquid system, the segregated reaction zone is mainly near the feed point, and shrinks to the exit of feed-pipe when the feed position is closer to the impeller. Besides, surface feed requires more time to completely exhaust the added H⁺ solution than that of impeller region feed at the same operating condition. For the solid- liquid system, when the solid suspension cloud is formed at high solid holdups, the flow velocity in the clear liquid layer above the cloud is notably reduced and the reactions proceed slowly in this almost stagnant zone. Therefore, the segregation index in this case is larger than that in the dilute solid-liquid system.     

Critical impeller speed for solid suspension in multi-impeller three phase agitated contactors

The critical impeller speed for solid suspension in gas-liquid-solid systems has been measured in multi-impeller agitated contractors of 0.15 and 0.30 m and ID and 1.0 m height. Three types of impellers, i.e. disk turbine (DT), pitched turbine downflow (PTD) and pitched turbine upflow (PTU) were used. Air, deionised water and sand particles were used as the gas, liquid and solid phases, respectively. The superficial gas velocity and solid loading were varied in the ranges 0–15 mm/s and 0.5 to 10% w/w, respectively. The effects of impeller type and its diameter, particle size and loading and gas flow rate were studied. Some measurements of gas hold-up and mixing time were also made in order to get some insight of the hydrodynamic behaviour of the reactor. The critical impeller speed for solid suspension in the presence of gas (n_isg) was found to be more than that in the absence of the gas and the increase of critical speed correlated well with the gas flow rate. The influence of particle—liquid parameters on solid suspension speed in the gassed system was similar to but relatively weaker than that in the ungassed condition.