Characterization of the continuous-flow mixing of non-Newtonian fluids using the ratio of residence time to batch mixing time

Continuous-flow mixing of pseudoplastic fluids possessing yield stress is a complex phenomenon exhibiting non-ideal flows within the stirred vessels. Electrical resistance tomography (ERT), a non-intrusive technique, was employed to measure the mixing time in the batch mode while dynamic tests were performed to study the mixing system in the continuous mode. This study attempts to explore the effects of the operating conditions and design parameters on the ratio of the residence time (τ) to the mixing time (θ) for the continuous-flow mixing of non-Newtonian fluids. To achieve these objectives, the effects of impeller types (four axial-flow impellers: A310, A315, 3AH, and 3AM; and three radial-flow impellers: RSB, RT, and Scaba), impeller speed (290–754 rpm), fluid rheology (0.5–1.5%, w/v), impeller off-bottom clearance (H/2.7–H/2.1, where H is the fluid height in the vessel), locations of inlet and outlet (configurations: top inlet-bottom outlet and bottom inlet-top outlet), pumping directions of an axial-flow impeller (up-pumping and down-pumping), fluid height in the vessel (T/1.06–T/0.83, where T is the tank diameter), residence time (257–328 s), and jet velocity (0.317–1.66 ms⁻¹) on the ratio of τ to θ were investigated. The results showed that the extent of the non-ideal flows (channeling and dead volume) in the continuous-flow mixing approached zero when the value of τ/θ varied from 8.2 to 24.5 depending on the operating conditions and design parameters. Thus, to design an efficient continuous-flow mixing system for non-Newtonian fluids, the ratio of the residence time to the mixing time should be at least 8.2 or higher.     

Effect of impeller type on continuous‐flow mixing of non‐Newtonian fluids in stirred vessels through dynamic tests

Mixing of non‐Newtonian fluids with axial and radial flow impellers is prone to a significant extent of nonideal flows (e.g., dead zones and channelling) within the stirred reactors. To enhance the performance of the continuous‐flow mixing of pseudoplastic fluids with yield stress, close‐clearance impellers were utilised in this study. We explored the effects of various parameters such as the type of close‐clearance impeller (i.e., the double helical ribbon (DHR) and anchor impellers), impeller speed (25–500 rpm), impeller pumping direction, fluid rheology (0.5–1.5% xanthan gum solution), fluid flow rate (3.20–14.17 L min^?1) and the locations of outlet (configurations: top inlet–top outlet, top inlet–bottom outlet) on the dynamic performance of the mixing vessel. The performance of the DHR impeller was then compared to the performance of various types of impellers such as axial‐flow (Lightnin A320) and radial‐flow (Scaba 6SRGT) impellers. The dynamic tests showed that the DHR impeller was the most efficient impeller for reducing the extent of nonideal flows in the continuous‐flow mixer among the impellers employed in this study. In addition, the mixing quality was further improved by optimising the power input, increasing the mean residence time, decreasing the fluid yield stress, using the up‐pumping impeller mode and using the top inlet–bottom outlet configuration. © 2011 Canadian Society for Chemical Engineering     

最大叶片式桨在假塑性流体中的搅拌流场模拟

为研究最大叶片式桨在高黏假塑性流体中的搅拌流动行为,以黄原胶溶液为研究体系,采用计算流体力学方法重点研究了釜内流体的功耗特性、速率分布、剪切速率、表观黏度分布和总体流动状况。结果表明:最大叶片式桨具有与大多数径流桨相似的"双循环"流型结构,且预测的功耗特性与实验数据一致性良好。最大叶片式桨适用于高黏假塑性流体的混合,而对于高黏牛顿流体的混合则效果不佳。釜内的剪切速率分布较宽泛,且受转速影响较大。转速可作为该桨改善黄原胶体系混合效率的重要参数之一。     

Using Tomography to Characterize the Mixing of Non‐Newtonian Fluids with a Maxblend Impeller

The flow field inside a cylindrical mixing vessel was visualized by electrical resistance tomography (ERT), a non‐intrusive measurement technique. Six tomography planes, each containing 16 sensing electrodes, measured the mixing time in the agitation of pseudoplastic fluid exhibiting yield stress. The effects of various parameters such as impeller types, impeller speed, fluid rheology, power consumption, Reynolds number, and absence of baffles on the mixing time were investigated. The Maxblend impeller was able to improve the mixing performance of non‐Newtonian fluids in a batch reactor. The mixing quality could be further enhanced by decreasing the xanthan gum concentration and using baffles in the mixing vessel.     

THE GROWTH OF CAVERNS FORMED AROUND ROTATING IMPELLERS DURING THE MIXING OF A YIELD STRESS FLUID

The growth of caverns, formed around rotating impellers in a yield stress fluid during mixing in a stirred vessel, has been studied by observing impeller speeds at which fluid motion was first observed at the vessel's wall and base, and at the free liquid surface. The effect of impeller geometry has been studied with a disk turbine (DT), a two bladed paddle (2BP), a pitched blade turbine (PBT) and a marine propeller (MP).

The presence of four baffles (10%) was found to increase the impeller speed at which the cavern reaches the vessel wall by 9% on average over that observed without baffles. After the cavern has reached the vessel walls, impeller type had a small effect upon the vertical expansion of the cavern with increasing impeller speed. Radial flow impellers (DT and 2BP), on average, performed better than an axial flow impeller (MP), with a mixed flow impeller (PBT) in between. Baffles significantly reduce the rate of this vertical expansion of the cavern. Clearance of the impeller from the vessel base had little effect upon the growth of the cavern above the impeller.     

THE GROWTH OF CAVERNS FORMED AROUND ROTATING IMPELLERS DURING THE MIXING OF A YIELD STRESS FLUID

The growth of caverns, formed around rotating impellers in a yield stress fluid during mixing in a stirred vessel, has been studied by observing impeller speeds at which fluid motion was first observed at the vessel's wall and base, and at the free liquid surface. The effect of impeller geometry has been studied with a disk turbine (DT), a two bladed paddle (2BP), a pitched blade turbine (PBT) and a marine propeller (MP).

The presence of four baffles (10%) was found to increase the impeller speed at which the cavern reaches the vessel wall by 9% on average over that observed without baffles. After the cavern has reached the vessel walls, impeller type had a small effect upon the vertical expansion of the cavern with increasing impeller speed. Radial flow impellers (DT and 2BP), on average, performed better than an axial flow impeller (MP), with a mixed flow impeller (PBT) in between. Baffles significantly reduce the rate of this vertical expansion of the cavern. Clearance of the impeller from the vessel base had little effect upon the growth of the cavern above the impeller.     

Effect of Impeller Spacing on the Flow Field of Yield-Pseudoplastic Fluids Generated by a Coaxial Mixing System Composed of Two Central Impellers and an Anchor

The three-dimensional flow field generated by a coaxial mixer composed of double Scaba impellers and an anchor in the mixing of the xanthan gum solution, a non-Newtonian yield-pseudoplastic fluid was investigated using the computational fluid dynamics (CFD) technique. The mixing time measurements were performed by a non-intrusive flow visualization technique called electrical resistance tomography (ERT). To evaluate the influence of the impeller spacing on the hydrodynamics of the double Scaba-anchor coaxial mixer, the upper impeller submergence was set to 0.140?m while the lower impeller clearance and the spacing between two central impellers were changed within a wide range. The experiments and simulations were conducted for both co-rotating and counter-rotating regimes at different impeller spacing. The analysis of the collected data with respect to the power number, flow number, mixing time, and pumping effectiveness proved that the co-rotating mode had superiority over the counter-rotating regime. Furthermore, the impact of the impeller spacing in the co-rotating mode was assessed with respect to the mixing time, power number, and mixing energy. The results demonstrated that a coaxial mixer with the impeller spacing of almost equal to the central impeller diameter (C₂?=?0.175?m) and the impeller clearance of C₃?=?0.185?m was the most efficient configuration compared to the other cases. Additionally, the influence of the impeller spacing on the flow pattern was assessed in terms of the radial velocity, tangential velocity, axial velocity, shear rate, and apparent viscosity profiles. When the impeller spacing (C₂) was varied, the merging flow and parallel flow patterns were observed.     

Local and overall gas holdup in an aerated coaxial mixing system containing a non-Newtonian fluid

Gas dispersion in non-Newtonian fluids is a challenging task due to the formation of large cavities behind the impeller blades, which leads to the generation of very large bubbles. In this study, the effects of impeller speed, impeller type, pumping direction, and CMC concentration on the local and overall gas holdup inside a coaxial mixing tank comprised of two central impellers and an anchor were investigated through tomography, computational fluid dynamics (CFD), and response surface methodology (RSM). The results showed that an increase in the fluid apparent viscosity resulted in decreasing the gas holdup except for the pitched blade impeller in upward-pumping mode. Although the highest overall gas holdup was accomplished for the downward pumping and co-rotating mode, the local gas holdup data revealed a non-uniform distribution of gas by this configuration. The lowest gas dispersion efficiency was achieved by a system comprised of two Scaba impellers and an anchor.     

On the hydrodynamics characterization of the straight Maxblend impeller with Newtonian fluids

The hydrodynamics generated by the straight version of the Maxblend^® impeller with Newtonian fluids in a baffled stirred vessel under the transitional and turbulent regime has been experimentally characterized by means of the particle image velocimetry technique. The flow fields obtained with the Maxblend were compared with those obtained with a double stage classical pitched blade turbine (PBT) and a double Ekato Intermig^® impellers under the same specific power draw. It is shown that these open impellers induce complex local flows in the radial and axial direction, with an intensity decreasing away from the blades. By contrast, the Maxblend impeller generates a more regular circulation pattern, with efficient top-to-bottom pumping.     

GAS-LIQUID MASS TRANSFER CHARACTERISTICS OF LARGE-SCALE IMPELLERS: EMPIRICAL CORRELATIONS OF GAS HOLDUPS AND VOLUMETRIC MASS TRANSFER COEFFICIENTS IN STIRRED TANKS

Gas dispersion with large-scale impellers consisting of modified large paddle impellers in stirred tanks, with rather large ratios of both impeller diameter and impeller height to tank diameter, was experimentally examined in transition and turbulent mixing ranges. Gas holdups and volumetric gas-liquid mass transfer coefficients with large-scale impellers, i.e., Maxblend and Fullzone impellers, were measured in 0.31 and 0.6 m I.D. stirred tanks, and the gas dispersion performance of large-scale impellers was compared with that of double conventional small-scale high-speed impeller systems, i.e., double four-flat blade disk turbine impellers and double four-flat paddle impellers.

The gas holdups of the large-scale impellers were comparable with those of the small-scale impeller systems at a given rotational speed. The volumetric gas-liquid mass transfer coefficients for large-scale impellers were also similar to those of the small-scale impeller systems. It was found that the large-scale impellers are not more energy efficient than the small-scale impellers in obtaining good gas dispersion.

Empirical correlations for gas holdups and volumetric gas-liquid mass transfer coefficients were developed. They fit the experimental data in transition and turbulent mixing ranges reasonably well, with correlation factors greater than 0.84.     

GAS-LIQUID MASS TRANSFER CHARACTERISTICS OF LARGE-SCALE IMPELLERS: EMPIRICAL CORRELATIONS OF GAS HOLDUPS AND VOLUMETRIC MASS TRANSFER COEFFICIENTS IN STIRRED TANKS

Gas dispersion with large-scale impellers consisting of modified large paddle impellers in stirred tanks, with rather large ratios of both impeller diameter and impeller height to tank diameter, was experimentally examined in transition and turbulent mixing ranges. Gas holdups and volumetric gas-liquid mass transfer coefficients with large-scale impellers, i.e., Maxblend and Fullzone impellers, were measured in 0.31 and 0.6 m I.D. stirred tanks, and the gas dispersion performance of large-scale impellers was compared with that of double conventional small-scale high-speed impeller systems, i.e., double four-flat blade disk turbine impellers and double four-flat paddle impellers.

The gas holdups of the large-scale impellers were comparable with those of the small-scale impeller systems at a given rotational speed. The volumetric gas-liquid mass transfer coefficients for large-scale impellers were also similar to those of the small-scale impeller systems. It was found that the large-scale impellers are not more energy efficient than the small-scale impellers in obtaining good gas dispersion.

Empirical correlations for gas holdups and volumetric gas-liquid mass transfer coefficients were developed. They fit the experimental data in transition and turbulent mixing ranges reasonably well, with correlation factors greater than 0.84.     

Simulation of flows in stirred vessels agitated by dual rushton impellers using computational snapshot approach

Flow in baffled stirred vessels involves interactions between flow around rotating impeller blades and stationary baffles. When more than one impeller is used (which is quite common in practice), the flow complexity is greatly increased, especially when there is an interaction between two impellers. The extent of interaction depends on relative distances between the two impellers and clearance from the vessel bottom. In this paper we have simulated flow generated by two Rushton (disc) impellers. A computational snapshot approach was used to simulate single-phase flow experiments carried out by Rutherford et al. (1996). The computational model was mapped on the commercial CFD code FLUENT (Fluent Inc., USA). The simulated results were analyzed in detail to understand flow around impellers and interaction between impellers. The model predictions were verified using the data of Rutherford et al. (1996). The results presented in this paper have significant implications for applications of computational fluid mixing tools for designing multiple impeller stirred reactors.     

SIMULATION OF FLOWS IN STIRRED VESSELS AGITATED BY DUAL RUSHTON IMPELLERS USING COMPUTATIONAL SNAPSHOT APPROACH

Flow in baffled stirred vessels involves interactions between flow around rotating impeller blades and stationary baffles. When more than one impeller is used (which is quite common in practice), the flow complexity is greatly increased, especially when there is an interaction between two impellers. The extent of interaction depends on relative distances between the two impellers and clearance from the vessel bottom. In this paper we have simulated flow generated by two Rushton (disc) impellers. A computational snapshot approach was used to simulate single-phase flow experiments carried out by Rutherford et al. (1996). The computational model was mapped on the commercial CFD code FLUENT (Fluent Inc., USA). The simulated results were analyzed in detail to understand flow around impellers and interaction between impellers. The model predictions were verified using the data of Rutherford et al. (1996). The results presented in this paper have significant implications for applications of computational fluid mixing tools for designing multiple impeller stirred reactors.     

Gas‐Liquid Floating Particle Mixing in an Agitated Vessel

The influence of impellers and baffles on the mixing of gas‐liquid floating particles in agitated vessels was investigated. Fifty‐two kinds of impeller combinations and twelve types of baffle arrangements were used. The associated power, gas holdup and solids concentration at the vessel bottom were measured. It is concluded that the mixing characteristics of three‐stage impellers were superior to those of two‐stage impellers for aspect ratios larger than 1.6. The optimal combination of impellers and baffles was proposed. The correlations of the relative power and the gas holdup for the optimal combination of impellers under all types of baffles were obtained.     

CFD Investigation of the Mixing of Yield‐Pseudoplastic Fluids with Anchor Impellers

The study was carried out to simulate the 3D flow domain in the mixing of pseudoplastic fluids possessing yield stress with anchor impellers, using a computational fluid dynamics (CFD) package. The multiple reference frames (MRF) technique was employed to model the rotation of the impellers. The rheology of the fluid was approximated using the Herschel–Bulkley model. To validate the model, the CFD results for the power consumption were compared to the experimental data. After the flow fields were calculated, the simulations for tracer homogenization were performed to simulate the mixing time. The effects of impeller speed, fluid rheology, and impeller geometry on power consumption, mixing time, and flow pattern were explored. The optimum values of c/D (impeller clearance to tank diameter) and w/D (impeller blade width to tank diameter) ratios were determined on the basis of minimum mixing time.     

CFD simulation of impeller shape effect on quality of mixing in two-phase gas–liquid agitated vessel

Mixing efficiency in two-phase gas-liquid agitated vessel is one of the important challenges in the industrial processes. Computational fluid dynamics technique (CFD) was used to investigate the effect of four different pitched blade impellers, including 15°, 30°, 45° and 60°, on the mixing quality of gas-liquid agitated vessel. The multiphase flow behavior was modeled by Eulerian-Eulerian multiphase approach, and RNG k-ε was used to model the turbulence. The CFD results showed that a strong global vortex plays the main role on the mixing quality of the gas phase in the vessel. Based on the standard deviation criterion, it was observed that the axial distribution of the gas phase in the 30° impeller is about 55% better than the others. In addition, the results showed that the 30° impeller has a uniform radial distribution over the other impellers and the maximum gas phase holdup in the vessel. Investigation of the power consumption of the impellers showed that the 30° impeller has the highest power consumption among the other pitched blade impellers. Also, examine the effect of same power condition for pitched blade impellers showed that the 30° impeller has the best mixing quality in this condition.     

Critical Rotational Speed for a Floating Particle Suspension in an Aerated Vessel

The critical suspension speeds of floating particles in a gas‐liquid‐floating particle three‐phase system were measured in a multiple‐impeller agitated vessel. Three types of impellers, i.e., simple axial‐flow impeller upflow (SPU) and downflow (SPD), disk turbine (DT) and wing turbine (WT), twelve types of baffles and three kinds of gas spargers were used. The influences of impeller types, baffle configurations, gas spargers, gas superfacial velocity and particle loading on the critical suspension speeds of floating particles were systematically investigated. The optimum regressions of critical suspension speeds were respectively obtained for some better combinations of impellers, bafffles and spargers, such as (a) the 45SPU+45SPD+DT triple impellers, two high‐level baffles and two low‐level baffles (symmetric allocation), gas spargers, (b) the 45SPU+45SPD+DT three‐impeller, standard baffle and small gas sparger. Their errors were smaller than 11 %.     

Using electrical resistance tomography and computational fluid dynamics modeling to study the formation of cavern in the mixing of pseudoplastic fluids possessing yield stress

Electrical resistance tomography (ERT) provides a non-intrusive technique to examine, in three dimensions, the homogeneity and flow pattern inside the mixing tank. In this study, a 4-plane 16-sensor ring ERT system was employed to study the shape and the size of cavern generated around a radial-flow Scaba 6SRGT impeller in the mixing of xanthan gum solution, which is a pseudoplastic fluid possessing yield stress. The size of cavern measured using ERT was in good agreement with that calculated using Elson's model (cylindrical model). The 3D flow field generated by the impeller in the agitation of xanthan gum was also simulated using the commercial computational fluid dynamics (CFD) package (Fluent). The CFD model provided useful information regarding the impeller pumping capacity, flow pattern, and the formation of cavern around the impeller. CFD results showed good agreement with the experimental data and theory.     

CFD simulation of impeller shape effect on quality of mixing in two-phase gas–liquid agitated vessel

Mixing efficiency in two-phase gas–liquid agitated vessel is one of the important challenges in the industrial processes. Computational fluid dynamics technique (CFD) was used to investigate the effect of four different pitched blade impellers, including 15°, 30°, 45° and 60°, on the mixing quality of gas–liquid agitated vessel. The multiphase flow behavior was modeled by Eulerian–Eulerian multiphase approach, and RNG k − ε was used to model the turbulence. The CFD results showed that a strong global vortex plays the main role on the mixing quality of the gas phase in the vessel. Based on the standard deviation criterion, it was observed that the axial distribution of the gas phase in the 30° impeller is about 55% better than the others. In addition, the results showed that the 30° impeller has a uniform radial distribution over the other impellers and the maximum gas phase holdup in the vessel. Investigation of the power consumption of the impellers showed that the 30° impeller has the highest power consumption among the other pitched blade impellers. Also, examine the effect of same power condition for pitched blade impellers showed that the 30° impeller has the best mixing quality in this condition.     

Characterisation of fluid mixing in novel designs of mesoscale oscillatory baffled reactors operating at low flow rates (0.3-0.6 ml/min)

For the first time two mesoscale oscillatory baffled designs (central and integral baffles with their volumes of 5.2 ml and 4.4 ml, respectively) were experimentally characterised at net flow rates as low as 0.3 ml/min (Re_n ∼ 1.25), giving a residence time of around 15-17 min over a wide range of oscillation conditions. The purpose was to identify the lower limits of operability, thereby determining the maximum residence time per unit reactor volume for these mesoscale units. The characteristics of fluid flow were found to be strongly affected by Strouhal number at these low net flows. For the integral baffles, the oscillation conditions exhibited little influence on the fluid mixing. For the central baffles, there were three distinct flow regimes, depending on Strouhal numbers which affect the fluid characteristics differently. At two regimes of Sts, St ≥ 0.8 and 0.13 ≤ St ≤ 0.2, an increase in frequency did not alter the axial dispersion. At St ≥ 0.8, the fluid experienced less uniform mixing, representing by right-skewed residence time distribution (RTD) curves. At 0.20 ≤ St ≤ 0.13, the fluid mixing was significantly improved, indicated by narrow and symmetrical RTD curves with Re_o up to 700. At 0.4 ≤ St ≤ 0.27 and St ≤ 0.1, the degree of plug flow was a function of Re_o. The maximum number of tanks achieved at these low flow rates was in the range 30-35, occurring at a velocity ratio (Re_o/Re_n) of 39-40.