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.     

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.     

同心双轴复合式搅拌釜用于牛顿流体时的功耗及混合特性

在直径0.48 m的椭圆底搅拌槽内,液位与槽径比(H/T)为0.6,采用不同粘度的牛顿流体糖浆溶液,研究了分别以CBY, 45o四斜叶桨及Rushton涡轮桨作为快速分散桨、锚式桨作为慢速桨构成的同心双轴搅拌系统,在快、慢速轴同向和异向2种旋转方式操作时的功率特性和混合性能. 结果表明,分散桨对锚式桨的功率消耗影响较大. 两轴同向旋转时,分散桨会使锚式桨的功耗降低,转速比RN增加,降低幅度也增大,RN=14时,锚式桨功率可降至单独旋转时的约10%;异向旋转时锚式桨的功率随RN增加而增加,RN=14时,锚式桨功率可增至单独旋转时的2倍左右. 但锚式桨对分散桨的功率消耗影响很小,在±5%以内. 计算同心双轴复合搅拌系统的复合功率准数和复合雷诺数关系时考虑了RN的影响,使在实验条件下不同转向及RN的功率曲线较好吻合. 混合效果同向旋转优于异向旋转,在牛顿流体中,达到相同混合效果时,CBY桨的能量消耗仅为其他2个分散桨的20%~30%.     

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.     

牛顿流体单螺杆挤出中速度场的坐标系依赖性

利用简化同心无限长圆筒地牛顿流体单螺杆挤出中不同坐标系选取,即机筒转、螺杆静止和直转、机筒静止两种情形,讨论了所产生的速度场差异问题。结果表明,速度场对坐标系存在着依赖性。螺杆、机筒间间隙相对机筒直径值（Ｈ／Ｄ）越大,引起的差异就越大,深螺槽时效应尤为明显。还给出了定量评价此作用的一个修正系数。     

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.     

Flow of a Newtonian fluid and a yield stress fluid around a plate inclined at 45° in interaction with a wall

This experimental and numerical study focuses on the determination of drag and lifts forces acting on inclined plate at 45° placed near a wall in a uniform flow of Newtonian and yield stress fluid. The inertia of the fluid is considered negligible. The influences of yield stress, shear thinning, and the distance between the plate and the wall were examined precisely. It is shown that the drag and lift coefficients decrease as the Oldroyd number increases and increase as the gap decreases. The unyielded zones around the plate were also determined. Their surfaces increase with the Oldroyd number. When the yield stress is low, the decrease of the shear thinning index n tends to decrease these unyielded zones. For the experimental part, a Carbopol gel was used as a fluid model. Experimental measurements were compared with numerical and published results, particularly in the plasticity context developed for soil mechanics. Differences are discussed in terms of the influence of elasticity and plasticity.     

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.     

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.     

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.     

Hybrid rheological model for non‐Newtonian turbulent pipe flow

Many slurry rheograms do not follow the Bingham model, but are curved (convex upwards) at low‐strain rates. Alternate models such as the yield‐power law (YPL), provide a good fit to the low‐strain rate data, but they tend to underestimate apparent viscosities at high‐strain rates. The current paper considers a hybrid rheological model consisting of a cubic‐spline fit to the low‐strain rate data merging into a Bingham linear model above a limiting strain rate. This model predicts turbulent flow well, depending only on the area difference between the Bingham rheogram and the cubic spline.     

Experimental investigations of non‐Newtonian/Newtonian liquid‐liquid flows in microchannels

The plug flow of a non‐Newtonian and a Newtonian liquid was experimentally investigated in a quartz microchannel (200‐µm internal diameter). Two aqueous glycerol solutions containing xanthan gum at 1000 and 2000 ppm were the non‐Newtonian fluids and 0.0046 Pa s silicone oil was the Newtonian phase forming the dispersed plugs. Two‐color particle image velocimetry was used to obtain the hydrodynamic characteristics and the velocity profiles in both phases under different fluid flow rates. The experimental results revealed that the increase in xanthan gum concentration produced longer, bullet‐shaped plugs, and increased the thickness of the film surrounding them. From the shear rate and viscosity profiles, it was found that the polymer solution was in the shear‐thinning region while the viscosity was higher in the middle of the channel compared to the region close to the wall. Circulation times in the aqueous phase increased with the concentration of xanthan gum. © 2017 The Authors AIChE Journal published by Wiley Periodicals, Inc. on behalf of American Institute of Chemical Engineers AIChE J, 63: 3599–3609, 2017     

Modified gas‐perturbed liquid model (GPLM) for minimum fluidization velocity in a two‐phase inverse fluidized bed reactor with Newtonian and non‐Newtonian systems

In the present investigation minimum fluidization velocity, U_mf, in a two‐phase inverse fluidized bed reactor is determined using low‐density polyethylene and polypropylene particles of different diameters (4,6 and 8 mm) by measuring pressure drop. In a glycerol system U_mf decreased gradually with increase in viscosity up to a value of 6.11 mPa s (60%) and on further increase there was a slight increase in U_mf. In the case of the glycerol system the U_mf was found to be higher when compared to water. In the non‐Newtonian system (carboxymethylcellulose), U_mf decreased with increase in concentration in the range of the present study. The U_mf was found to be lower when compared to water as liquid phase. The modified gas‐perturbed liquid model was used to predict the minimum fluidization liquid velocity (U_lmf) for Newtonian and non‐Newtonian systems. Copyright © 2006 Society of Chemical Industry     

非牛顿流体在周期性突扩突缩通道中的流动阻力特性

以聚丙烯酰胺水溶液（２００ｗｐｐｍ，５００ｗｐｐｍ，１４００ｗｐｐｍ）为介质，实验研究了此粘弹性流体在直管充分发展段和周期性突扩突缩充分发展段的流动阻力特性。雷诺数变化范围为５×１０３～７×１０４。实验结果表明此浓度范围内的聚丙烯酰胺溶液在直管中的阻力系数可比纯水中的降低４０％，而在周期性突扩突缩通道中无明显的减阻现象     

CFD Modeling of Active Volume Creation in a Non‐Newtonian Fluid Agitated by Submerged Recirculating Jets

Computational fluid dynamics (CFD) models were employed to investigate flow conditions inside a model reactor in which yield stress non‐Newtonian liquid is mobilized using submerged recirculating jets. The simulation results agree well with the experimental results of active volume in the reactor obtained using flow visualization by the authors in a previous study. The models developed are capable of predicting a critical jet velocity (v_c) that determines the extent of active volume obtained due to jet mixing. The v_c values are influenced both by the rheological properties of the liquid and the nozzle orientation. The liquid with higher effective viscosity leads to higher v_c for a downward facing injection nozzle. However, an upward facing injection nozzle along with a downward facing suction nozzle generates enhanced complementary flow fields which overcome the rheological constraints of the liquid and lead to lower v_c.     

Drag on two co-axial rigid spheres moving normal to a plane: Newtonian and Carreau fluids

The boundary effect and the presence of a nearby entity on the drag of a rigid entity is investigated by considering the movement of two identical, rigid, coaxial spheres normal to a plane in both a Newtonian and a Carreau fluid at a low to medium large Reynolds number. The parameters key to the phenomenon under consideration, including the nature of the fluid, the separation distance between two spheres, the distance between the near sphere and the plane, and the Reynolds number, on the drag coefficient are discussed. We show that the influence of a boundary on the drag coefficient is more important than that of the nature of a fluid and that of the separation distance between two spheres. The variation of the drag coefficient as a function of Reynolds number for a Carreau fluid is similar to that for a Newtonian fluid. Due to the shear-thinning nature of the former the drag coefficient in the former is smaller than that in the latter. The influence of the index parameter of a Carreau fluid becomes appreciable only if the Carreau number is sufficiently large. Correlations between the drag coefficient and the key parameters of a system are developed for the case when the Reynolds number is smaller than l.     

牛顿及非牛顿流体中的气泡生成与对比

采用激光成像结合CCD摄像技术分别对牛顿及非牛顿流体(甘油和羧甲基纤维素钠水溶液)中的气泡生成行为进行了研究,对2种流体气泡生成过程中气泡形状和体积变化进行了比较。分析了非牛顿流体的弹性效应对气泡生成过程气泡形状的影响。实验结果表明,在实验条件范围内,甘油中,气泡生长初期,气泡体积增加较快,到了后期,增加幅度减缓,气速对气泡生长过程气泡体积影响很小;羧甲基纤维素钠(CMC)水溶液中,气泡生长初期,气泡缓慢生长,气速对气泡体积影响很小,到了后期,气泡体积增加幅度变大,气泡体积随着气速的增大而增大。