Measuring Mixing Time in the Agitation of Non‐Newtonian Fluids through Electrical Resistance Tomography

Electrical resistance tomography (ERT), which is a non‐invasive and robust measurement technique, was employed to visualize, in three dimensions, the concentration field inside a cylindrical mixing vessel equipped with a radial‐flow Scaba 6SRGT impeller. The ability of ERT to work in opaque fluids makes this technique very attractive from an industrial perspective. An ERT system with a 4‐plane assembly of peripheral sensing rings, each containing 16 electrodes, was used to measure the mixing time in agitation of xanthan gum solution which is a pseudoplastic fluid with yield stress. An image reconstruction algorithm was used to generate images of the tracer distribution within the sensing zone. In this study, the effect of impeller speed, fluid rheology, power consumption, and Reynolds number on the mixing time was investigated.     

Assessing Blending of Non‐Newtonian Fluids in Static Mixers by Planar Laser‐Induced Fluorescence and Electrical Resistance Tomography

Planar laser‐induced fluorescence (PLIF) and electrical resistance tomography (ERT) were applied simultaneously to monitor the mixing performance of a KM static mixer for the blending of non‐Newtonian fluids of dissimilar rheologies in the laminar regime. The areal distribution method was used to obtain quantitative information from the ERT tomograms and the PLIF images. Comparison of the ERT and PLIF results demonstrates the ability of ERT to detect the mixing performance in cases of poor mixing within the resolution of the measurement, though the accuracy decreases as the condition of perfect mixing is approached. Thus, ERT has the potential to detect poor mixing within the confines of its resolution limit and the required conductivity contrast, providing potential rapid at‐line measurement for industrial practitioners.     

Determination of Mixing Times with Helical Ribbon Impeller for Non‐Newtonian Viscous Fluids Using an Advanced Imaging Method

New results on mixing times for viscous Newtonian and non‐Newtonian fluids being homogenized with a helical ribbon impeller are presented. In particular, a recently developed technique to determine the macromixing kinetics of an impeller in a transparent vessel was applied to investigate the effects of rheological properties on mixing times. Significant differences were observed in the mixing times for viscous Newtonian and non‐Newtonian fluids. Based on the new data obtained in this work, a correlation incorporating the elastic effects is proposed in terms of a Weissenberg number for predicting the mixing time as a function of the Reynolds number and the system geometry.     

Coaxial Mixer Hydrodynamics with Newtonian and non‐Newtonian Fluids

The performance of several combinations of a wall scraping impeller and dispersing impellers in a coaxial mixer operated in counter‐ and co‐rotating mode were assessed with Newtonian and non‐Newtonian fluids. Using the power consumption and the mixing time as the efficiency criteria, impellers in co‐rotating mode were found to be a better choice for Newtonian and non‐Newtonian fluids. The hybrid impeller‐anchor combination was found to be the most efficient for mixing in counter‐rotating or co‐rotating mode regardless of the fluid rheology. For both rotating modes, it was shown that the anchor speed does not have any effect on the power draw of the dispersing turbines. However, the impeller speed was shown to affect the anchor power consumption. The determination of the minimum agitation conditions to achieve the just suspended state of solid particles (N_js) was also determined. It was found that N_js had lower values with the impellers having the best axial pumping capabilities.     

最大叶片式桨流体动力学性能的数值模拟

运用CFD方法研究了最大叶片式桨在层流区域内的流体动力学性能,模拟体系为高粘度牛顿流体和非牛顿流体,主要考察桨叶的功耗特性、Metzner常数、剪切性能和排液性能. 结果表明,功耗计算值与文献实验值基本一致;桨叶的Metzner常数ks=10与流变行为指数n无关;搅拌形成双循环流型,釜中部桨叶所在区剪切速率大、排液量大,产生的漩涡流也大,导致剪切效率低于0.5;随雷诺数增加(Ren=1.4, 5.0, 7.6),全釜平均剪切速率(3.40, 9.91, 15.05 s-1)和全釜平均排液量(0.0014, 0.0033, 0.0052 m3/s)逐渐增加,尤其是桨叶下端两翼区平均剪切速率(4.36, 11.48, 16.35 s-1)和平均排液量(0.0026, 0.0064, 0.0095 m3/s)增加相对较大. 说明Ren增加,搅拌混合作用加强,剪切速率大产生的界面积大,排液量大使高低剪切区内流体快速循环,有利于流体高效混合.     

Using CFD and Ultrasonic velocimetry to Study the Mixing of Pseudoplastic Fluids with a Helical Ribbon Impeller

A commercial CFD package was used to simulate the 3D flow field generated in a cylindrical tank by a helical ribbon impeller. The study was carried out using a pseudoplastic fluid with yield stress in the laminar mixing region. Ultrasonic Doppler velocimetry (UDV), a noninvasive fluid flow measurement technique for opaque systems, was used to measure xanthan gum velocity. From flow field calculations and tracer homogenization simulations, power consumption and mixing time results were obtained. The torque and power characteristics remain the same for upward and downward pumping of the impeller, but the mixing times are considerably longer for the downward pumping mode. Overall, the numerical results showed good agreement with experimental results and correlations developed by other researchers. From the power and mixing time results, two efficiency criteria were utilized to determine the best pumping mode of the impeller.     

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.     

Non‐Newtonian Heat Transfer on a Plate Heat Exchanger with Generalized Configurations

For the configuration optimization of plate heat exchangers (PHEs), the mathematical models for heat transfer and pressure drop must be valid for a wide range of operational conditions of all configurations of the exchanger or the design results may be compromised. In this investigation, the thermal model of a PHE is adjusted to fit experimental data obtained from non‐Newtonian heat transfer for eight different configurations, using carboxymethylcellulose solutions (CMC) as test fluid. Although it is possible to successfully adjust the model parameters, Newtonian and non‐Newtonian heat transfer cannot be represented by a single generalized correlation. In addition, the specific heat, thermal conductivity and power‐law rheological parameters of CMC solutions were correlated with temperature, over a range compatible with a continuous pasteurization process.     

Tomography images to analyze the deformation of the cavern in the continuous‐flow mixing of non‐Newtonian fluids

Tomography, an efficient nonintrusive technique, was employed to visualize the flow in continuous‐flow mixing and to measure the cavern volume (V_c) in batch mixing. This study has demonstrated an efficient method for flow visualization in the continuous‐flow mixing of opaque fluids using two‐dimensional (2‐D) and 3‐D tomograms. The main objective of this study was to explore the effects of four inlet‐outlet configurations, fluid rheology (0.5–1.5% xanthan gum concentration), high‐velocity jet (0.317–1.660 m s^?1), and feed flow rate (5.3 × 10^?5?2.36 × 10^?4 m³ s^?1) on the deformation of the cavern. Dynamic tests were also performed to estimate the fully mixed volume (V_{fully mixed}) for the RT, A310, and 3AM impellers in a continuous‐flow mixing system, and it was found that V_{fully mixed} was greater than V_c. Incorporating the findings of this study into the design criteria will minimize the extent of nonideal flows in the continuous‐flow mixing of complex fluids and eventually improve the quality of end‐products. © 2013 American Institute of Chemical Engineers AIChE J, 60: 315–331, 2014     

LDA Velocity Measurements of High‐Viscosity Fluids in Mixing Vessel with Vane Geometry Impeller

The object of this work was to measure the velocity field in non‐Newtonian fluids inside mixing vessel. The six‐bladed vane rotor used for mixing was designed from rotating vane geometry of a sensor system, commonly used for rheometrical measurements of complex fluids (Barnes and Nguyen, J. Non‐Newtonian Fluid Mech. 98 , 1‐14 (2001); Schramm, 1994). During mixing, the viscosity was determined by measuring the torque at different impeller speeds, and compared to rheologically obtained shear dependent viscosity. The velocity field was determined by LDA measurements at twelve places inside mixing vessel. It was observed that axial and radial component of the velocity were insignificant at all measurement points. On the other hand, the results showed the periodic nature of tangential component of the velocity, which was confirmed with computer‐aided visualization method.     

Energy Dissipation Rates of Newtonian and Non‐Newtonian Fluids in a Stirred Vessel

Energy dissipation rates of water and glycerol as Newtonian fluids and carboxyl methyl carbonate solution as non‐Newtonian fluid in a stirred vessel are investigated by 2D particle image velocimetry and compared. Mean velocity profiles reflect the Reynolds (Re) number similarity of two flow fields with different rheological properties, but the root mean square velocity profiles differ in rheology at the same Re‐number. Energy dissipation rates are estimated by direct calculation of fluctuating velocity gradients. The varying energy dissipation rates of Newtonian and non‐Newtonian fluids result from the difference in fluid rheology and apparent viscosity distribution which decides largely the flow pattern, circulation intensity, and rate of turbulence generation.     

Computational Fluid Dynamics Simulation of Generation and Coalescence of Bubbles in Non‐Newtonian Fluids

The successive generation and coalescence behaviors of bubbles from two parallel nozzles in non‐Newtonian fluids were numerically simulated by using the volume of fluid (VOF) method. Three flow patterns for bubbles and the related flow regime transition lines were obtained. Two critical nozzle intervals exist: one for the bubble coalescence before pinch‐off, and another for alternating bubble formation then in‐line coalescence under different conditions. Two correlations were proposed to predict the dimensionless critical nozzle intervals for the transition of bubble‐flow patterns. The influences of nozzle diameter, gas flow rate, nozzle interval, and rheological properties of fluid on bubble‐flow patterns were investigated systematically.     

Bubble Volume and Aspect Ratio Generated in Non‐Newtonian Fluids

Bubble formation from an orifice submerged in quiescent polyacrylamide aqueous solution was investigated numerically with a sharp‐interface coupled level‐set/volume‐of‐fluid method based on the rheological characteristics of the fluid. In both non‐Newtonian fluids and Newtonian fluids, the numerical approach was able to capture accurately the deformation of the bubble surface, validated by comparison with experimental results. The effects of orifice diameter, solution mass concentration, and gas flow rate on bubble volume and aspect ratio were evaluated. Both the instantaneous and detached volume decrease with the orifice diameter but increase with mass concentration and gas flow rate. The aspect ratio at the departing point tends to rise with the orifice diameter and mass concentration and falls with the gas flow rate.     

Predicting Power for a Scaled‐up Non‐Newtonian Biomass Slurry

High‐solids biomass slurries exhibit non‐Newtonian behavior with a yield stress and require high power input for mixing. The goals were to determine the effect of scale and geometry on power number P₀, and estimate the power for mixing a pretreated biomass slurry in a 3.8 million L hydrolysis reactor of conventional design. A lab‐scale computational fluid dynamics model was validated against experimental data and then scaled up. A pitched‐blade turbine and A310 hydrofoil were tested for various geometric arrangements. Flow was transitional; laminar and turbulence models resulted in equivalent P₀ which increased with scale. The ratio of impeller diameter to tank diameter affected P₀ for both impellers, but impeller clearance to tank diameter affected P₀ only for the A310. At least 2 MW is required to operate at this scale.     

Characterization of Bubble Shapes in Non‐Newtonian Fluids by Parametric Equations

Based on experiments with single air bubbles rising in stagnant non‐Newtonian fluids, an innovative model containing the aspect ratio (E) and two parameters (α, β) was proposed and proved to be capable of characterizing the bubble shape from spherical/ellipsoidal to prolate/oblate‐tear with good accuracy. Several impacts on bubble deformation were investigated, involving the rheological properties of the fluids and different forces exerted on the bubble, which were quantified by multiple dimensionless numbers (e.g., Reynolds, Eötvös, and Deborah number). Within a wide range, the empirical correlations were obtained for parameter β, and between α and β. Together with the shape model, a complete system was set up for bubble shape characterization and prediction that will provide new ideas for future studies on bubble hydrodynamics.     

Volumetric Mass Transfer Coefficient in non‐Newtonian Fluids in Spout Fluid Beds

The volumetric liquid‐phase mass transfer coefficient, k_La, was determined by absorption of oxygen in air using six different carboxy‐methyl cellulose (CMC) solutions with different rheological values in three phase spout‐fluid beds operated continuously with respect to both gas and liquid. Three cylindrical columns of 7.4 cm, 11.4 cm, and 14.4 cm diameters were used. Gas velocity was varied between 0.00154–0.00563 m/s, liquid velocity between 0.0116–0.0387 m/s, surface tension between 0.00416–0.0189 N/m, static bed height between 6.0–10.8 cm, and spherical glass particles of 1.75 mm diameter were used as packing material. A single nozzle sparger of 1.0 cm diameter was used in the spouting line. The volumetric mass transfer coefficient was found to increase with gas velocity, liquid velocity, and static bed height and to decrease with the increase of the effective liquid viscosity of the CMC solution. A dimensionless correlation was developed and compared with those listed in the literature.     

Pressure Drop Models for Gas/Non‐Newtonian Power‐Law Fluids Flow in Horizontal Pipes

Models commonly used in literature are evaluated versus 696 data points to predict the pressure drop of gas/non‐Newtonian power‐law fluids flow in horizontal pipes. Suitable models are recommended. A new correlation is developed by ignoring the pressure drop across the gas slug and adopting the liquid slug holdup of gas/non‐Newtonian fluid flow into the homogeneous model. The theoretical curves can capture the test data trends and the overall agreement of predicted values with experimental data is sufficient to be practically applied in industry.     

Improving the dynamic performance of continuous-flow mixing of pseudoplastic fluids possessing yield stress using Maxblend impeller

The strategic approach of this article is to characterize the continuous-flow mixing of pseudoplastic fluids possessing yield stress in a stirred reactor with the Maxblend impeller. Dynamic experiments were carried out through the frequency-modulated random binary input of a brine solution to determine the extent of non-ideal flows. Mixing quality was determined on the basis of the extent of channeling and fully mixed volume. The effects of important parameters such as impeller speed (25–500 rpm), absence of baffles, fluid rheology (0.5–1.5%), fluid flow rate (3.20–14.17 L min⁻¹), and the locations of inlet/outlet on the dynamic performance of the continuous-flow mixing vessel were explored. The performance of the Maxblend impeller was then compared to the performances of various types of impellers such as close-clearance (an anchor), axial-flow (a Lightnin A320), and radial-flow (a Scaba 6SRGT) impellers. It was found when the channeling approached zero and the fully mixed volume approached the total fluid volume in the vessel, the power drawn by the A320 impeller and the Scaba impeller were about 2.9 and 4.3 times greater than that of the Maxblend impeller. Thus, the Maxblend impeller was able to drastically improve the performance of continuous-flow mixing with huge power savings. The mixing quality was further improved by optimizing the impeller speed, decreasing the fluid flow rate, decreasing the fluid concentration, and using bottom inlet- top outlet configuration. The flow non-ideality of the mixing system increased in the absence of the baffles. Thus, better mixing quality and more energy savings can be achieved by employing the findings of this study.